diff --git a/.claude/agents/clean-code-reviewer.md b/.claude/agents/clean-code-reviewer.md index bcdb99c3..38d2699c 100644 --- a/.claude/agents/clean-code-reviewer.md +++ b/.claude/agents/clean-code-reviewer.md @@ -93,6 +93,6 @@ For each issue, provide: - Follow the commit message format: `MODULE - TAG - Detailed message` - Be aware of 0-based to 1-based indexing conversions from Fortran - Ensure compatibility with the existing test structure in `test/` -- Consider whether changes affect diagnostic outputs (jpec.h5, and legacy files gsec.h5, gse.h5, gsei.h5) +- Consider whether changes affect diagnostic outputs or user-facing APIs Your goal is to help create code that a fusion physicist with moderate Julia experience can read, understand, and maintain confidently. diff --git a/.github/copilot-instructions.md b/.github/copilot-instructions.md index 0c691768..7769f08a 100644 --- a/.github/copilot-instructions.md +++ b/.github/copilot-instructions.md @@ -5,7 +5,7 @@ - Data flow: equilibrium setup → vacuum response → stability analysis (documented in [CLAUDE.md](CLAUDE.md)). ## Architecture and entry points -- Main entry point: `JPEC.main()` in [src/JPEC.jl](src/JPEC.jl). +- Main entry point: `GeneralizedPerturbedEquilibrium.main()` in [src/GeneralizedPerturbedEquilibrium.jl](src/GeneralizedPerturbedEquilibrium.jl). - Equilibrium: `setup_equilibrium(path|config)`; types in [src/Equilibrium](src/Equilibrium). - Vacuum: `compute_vacuum_response()`; code in [src/Vacuum](src/Vacuum). - ForceFreeStates (ideal MHD stability): types and functions in [src/ForceFreeStates](src/ForceFreeStates). @@ -39,7 +39,7 @@ - Many routines use 0-based indexing for historical consistency with the original GPEC Fortran code before converting to 1-based Julia indexing (see [CLAUDE.md](CLAUDE.md)). ## Configuration examples -- Unified configuration: `jpec.toml` uses `[Equilibrium]`, `[Wall]`, `[ForceFreeStates]`, `[PerturbedEquilibrium]`, and `[ForcingTerms]` sections. +- Unified configuration: `gpec.toml` uses `[Equilibrium]`, `[Wall]`, `[ForceFreeStates]`, `[PerturbedEquilibrium]`, and `[ForcingTerms]` sections. - Legacy configs (`equil.toml`, `dcon.toml`, `vac.in`) are deprecated. - Example configs in [examples/DIIID-like_ideal_example](examples/DIIID-like_ideal_example) and [examples/Solovev_ideal_example](examples/Solovev_ideal_example). diff --git a/Project.toml b/Project.toml index 19b241e4..7d74e308 100644 --- a/Project.toml +++ b/Project.toml @@ -17,6 +17,7 @@ JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" +PlotlyJS = "f0f68f2c-4968-5e81-91da-67840de0976a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" @@ -41,6 +42,7 @@ JLD2 = "0.6.3" LinearAlgebra = "1" OrdinaryDiffEq = "6.102.0" Pkg = "1" +PlotlyJS = "0.18.17" Plots = "1.40.15" Printf = "1" SparseArrays = "1" diff --git a/docs/make.jl b/docs/make.jl index 3b742f65..58c076f6 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -29,7 +29,8 @@ makedocs(; "Equilibrium" => "equilibrium.md", "Utilities" => "utilities.md", "Forcing Terms" => "forcing_terms.md", - "Perturbed Equilibrium" => "perturbed_equilibrium.md" + "Perturbed Equilibrium" => "perturbed_equilibrium.md", + "Analysis" => "analysis.md" ], "Citations" => "citations.md", ], diff --git a/docs/src/analysis.md b/docs/src/analysis.md new file mode 100644 index 00000000..8940a3e4 --- /dev/null +++ b/docs/src/analysis.md @@ -0,0 +1,24 @@ +# Analysis Module + +The Analysis module provides post-processing and visualization utilities for GPEC simulation outputs. + +## Submodules + +- `ForceFreeStates`: Plotting functions for DCON-style ideal MHD stability results +- `Equilibrium`: Plotting functions for equilibrium objects + +```@docs +GeneralizedPerturbedEquilibrium.Analysis +``` + +## ForceFreeStates + +```@autodocs +Modules = [GeneralizedPerturbedEquilibrium.Analysis.ForceFreeStates] +``` + +## Equilibrium + +```@autodocs +Modules = [GeneralizedPerturbedEquilibrium.Analysis.Equilibrium] +``` diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl new file mode 100644 index 00000000..19253758 --- /dev/null +++ b/examples/DIIID-like_ideal_example/analyze_example.jl @@ -0,0 +1,10 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium, Plots, PlotlyJS +using GeneralizedPerturbedEquilibrium: Analysis +plotlyjs() + +h5path = joinpath(@__DIR__, "gpec.h5") +p_modes = Analysis.ForceFreeStates.plot_mode_displacement(h5path; modes=1:5) +p_eigen = Analysis.ForceFreeStates.plot_eigenmode_summary(h5path) +p_stab = Analysis.ForceFreeStates.plot_stability_criterion(h5path) diff --git a/examples/DIIID-like_ideal_example/run_and_analyze.ipynb b/examples/DIIID-like_ideal_example/run_and_analyze.ipynb deleted file mode 100644 index 88c3bdb3..00000000 --- a/examples/DIIID-like_ideal_example/run_and_analyze.ipynb +++ /dev/null @@ -1,215 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "## Overview\n", - "In this notebook, we will run GPEC on a Solovev ideal example equilibrium and plot the results" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "# Load in necessary packages\n", - "using Pkg\n", - "using LinearAlgebra\n", - "using HDF5\n", - "using Plots\n", - "using LaTeXStrings" - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "## Run the code\n", - "We will run GPEC using the inputs specified in `gpec.toml`. We output the `gpec.h5` file." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# Run\n", - "Pkg.activate(\"../..\")\n", - "using Revise, GeneralizedPerturbedEquilibrium\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "results = GeneralizedPerturbedEquilibrium.main([\"./\"]) # \"./\" tells us to obtain inputs and direct outputs to our current folder" - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "## Analyze Outputs\n", - "We will now analyze the outputs of the run, the most important of which are located in the `gpec.h5` output file" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "# Read in the gpec.h5 data\n", - "eh5 = h5open(\"gpec.h5\", \"r\")\n", - "mlow = read(eh5[\"info/mlow\"])\n", - "xi_psi = read(eh5[\"integration/xi_psi\"])\n", - "psifac = read(eh5[\"integration/psi\"])\n", - "wt = read(eh5[\"vacuum/wt\"])\n", - "crit = read(eh5[\"integration/crit\"])\n", - "psio = read(eh5[\"equil/psio\"])\n", - "et = read(eh5[\"vacuum/et\"])\n", - "close(eh5)\n", - "\n", - "# scale energy eigenvector matrices\n", - "chi1 = 2π*psio\n", - "wt = wt*(chi1*1e-3)\n", - "println(\"Done reading gpec.h5\")" - ] - }, - { - "cell_type": "markdown", - "id": "7", - "metadata": {}, - "source": [ - "### Plot comparison of xi_psi for a few poloidal mode numbers" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "p = plot()\n", - "for m in 1:5\n", - " plot!(psifac, imag.(xi_psi[m - mlow + 1, 1, :]), label=\"m=$m\")\n", - "end\n", - "xlabel!(L\"\\psi_N\")\n", - "ylabel!(L\"\\mathrm{Im}(\\xi_\\psi)\")\n", - "title!(\"Least Stable Eigenmode \" * L\"\\xi_\\psi\" * \" for \" * \"m=1-5\")" - ] - }, - { - "cell_type": "markdown", - "id": "9", - "metadata": {}, - "source": [ - "### Compare the eigenvectors and eigenvalues of each DCON energy matrix eigenmode\n", - "This is analagous to the DCON summary plot creating by OMFIT GPEC" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "10", - "metadata": {}, - "outputs": [], - "source": [ - "# I got tired of trying to get the Plots version of this to work, so here's a PyPlot version\n", - "using PyPlot\n", - "\n", - "# Axes labels\n", - "xlabel = \"m\"\n", - "ylabel = \"mode (least to most stable)\"\n", - "\n", - "yvals = 1:size(wt, 2)\n", - "xvals = (1:size(wt, 1)) .+ (mlow + 1)\n", - "\n", - "# Create figure and grid layout\n", - "fig = figure(figsize=(9, 7))\n", - "gs = fig.add_gridspec(2, 3, height_ratios=[0.25, 0.75], width_ratios=[0.75, 0.21, 0.04])\n", - "\n", - "# Top-left: Eigenvector amplitude\n", - "ax0 = fig.add_subplot(gs[1, 1])\n", - "ax0.plot(xvals, abs.(wt[:, 1]), color=\"blue\", marker=\"o\", markersize=3)\n", - "ax0.set_ylabel(\"|Eigenvector|\")\n", - "ax0.set_xlabel(\"\")\n", - "ax0.set_title(\"Mode 1, eigenvalue = $(round(abs(et[1]), digits=3))\")\n", - "\n", - "# Bottom-left: Heatmap\n", - "ax1 = fig.add_subplot(gs[2, 1])\n", - "im = ax1.imshow(abs.(wt') , aspect=\"auto\", origin=\"lower\",\n", - " cmap=\"viridis\", extent=[xvals[1], xvals[end], yvals[1], yvals[end]])\n", - "ax1.set_xlabel(xlabel)\n", - "ax1.set_ylabel(ylabel)\n", - "\n", - "# Right middle: Eigenvalue amplitude\n", - "ax2 = fig.add_subplot(gs[2, 2])\n", - "ax2.plot(abs.(et), yvals, color=\"red\", marker=\"o\", markersize=3)\n", - "ax2.set_xlabel(\"Eigenvalue\")\n", - "ax2.set_xscale(\"log\")\n", - "ax2.set_xlim(0.1 * minimum(abs.(et)), 10 * maximum(abs.(et)))\n", - "ax2.set_yticks([])\n", - "\n", - "# Colorbar (bottom right)\n", - "cax = fig.add_subplot(gs[2, 3])\n", - "cb = fig.colorbar(im, cax=cax)\n", - "cb.set_label(\"|W_t_eigenvector|\")\n", - "\n", - "# Display and save figure\n", - "display(fig)" - ] - }, - { - "cell_type": "markdown", - "id": "11", - "metadata": {}, - "source": [ - "### Plot crit (the smallest eigenvalue of $W^{-1}$) versus $\\Psi$\n", - "If crit changes signs during integration, we know we are unstable to an ideal fixed-boundary instability." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "12", - "metadata": {}, - "outputs": [], - "source": [ - "# Plot crit vs psi\n", - "p = plot(psifac, crit, legend=false)\n", - "xlabel!(L\"\\psi_N\")\n", - "ylabel!(L\"crit\")\n", - "title!(\"Smallest eigenvalue of \" * L\"W^{-1}\" * \"(crit) versus \" * L\"\\psi_N\")" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.11.6", - "language": "julia", - "name": "julia-1.11" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.11.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/DIIID-like_ideal_example/run_example.jl b/examples/DIIID-like_ideal_example/run_example.jl new file mode 100644 index 00000000..fa0a9e53 --- /dev/null +++ b/examples/DIIID-like_ideal_example/run_example.jl @@ -0,0 +1,4 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium +GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)]) diff --git a/examples/Solovev_ideal_example/analyze_example.jl b/examples/Solovev_ideal_example/analyze_example.jl new file mode 100644 index 00000000..19253758 --- /dev/null +++ b/examples/Solovev_ideal_example/analyze_example.jl @@ -0,0 +1,10 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium, Plots, PlotlyJS +using GeneralizedPerturbedEquilibrium: Analysis +plotlyjs() + +h5path = joinpath(@__DIR__, "gpec.h5") +p_modes = Analysis.ForceFreeStates.plot_mode_displacement(h5path; modes=1:5) +p_eigen = Analysis.ForceFreeStates.plot_eigenmode_summary(h5path) +p_stab = Analysis.ForceFreeStates.plot_stability_criterion(h5path) diff --git a/examples/Solovev_ideal_example/run_and_analyze.ipynb b/examples/Solovev_ideal_example/run_and_analyze.ipynb deleted file mode 100644 index f748bf49..00000000 --- a/examples/Solovev_ideal_example/run_and_analyze.ipynb +++ /dev/null @@ -1,200 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "## Overview\n", - "In this notebook, we will run GPEC on a Solovev ideal example equilibrium and plot the results" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "# Load in necessary packages\n", - "using Pkg\n", - "using LinearAlgebra\n", - "using HDF5\n", - "using Plots\n", - "using LaTeXStrings" - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "## Run the code\n", - "We will run the GPEC code using the inputs specified in `gpec.toml`. We output the `gpec.h5` file." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# Run\n", - "Pkg.activate(\"../..\")\n", - "using GeneralizedPerturbedEquilibrium\n", - "GeneralizedPerturbedEquilibrium.main([\"./\"]) # \"./\" tells us to obtain inputs and direct outputs to our current folder" - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "## Analyze Outputs\n", - "We will now analyze the outputs of the run, the most important of which are located in the `gpec.h5` output file" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "# Read in the gpec.h5 data\n", - "eh5 = h5open(\"gpec.h5\", \"r\")\n", - "mlow = read(eh5[\"info/mlow\"])\n", - "xi_psi = read(eh5[\"integration/xi_psi\"])\n", - "psifac = read(eh5[\"integration/psi\"])\n", - "wt = read(eh5[\"vacuum/wt\"])\n", - "crit = read(eh5[\"integration/crit\"])\n", - "psio = read(eh5[\"equil/psio\"])\n", - "et = read(eh5[\"vacuum/et\"])\n", - "close(eh5)\n", - "\n", - "# scale energy eigenvector matrices\n", - "chi1 = 2π*psio\n", - "wt = wt*(chi1*1e-3)\n", - "println(\"Done reading gpec.h5\")" - ] - }, - { - "cell_type": "markdown", - "id": "6", - "metadata": {}, - "source": [ - "### Plot comparison of xi_psi for a few poloidal mode numbers" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "p = plot()\n", - "for m in 1:5\n", - " plot!(psifac, imag.(xi_psi[m - mlow + 1, 1, :]), label=\"m=$m\")\n", - "end\n", - "xlabel!(L\"\\psi_N\")\n", - "ylabel!(L\"\\mathrm{Im}(\\xi_\\psi)\")\n", - "title!(\"Least Stable Eigenmode \" * L\"\\xi_\\psi\" * \" for \" * \"m=1-5\")" - ] - }, - { - "cell_type": "markdown", - "id": "8", - "metadata": {}, - "source": [ - "### Compare the eigenvectors and eigenvalues of each DCON energy matrix eigenmode\n", - "This is analagous to the DCON summary plot creating by OMFIT GPEC" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "9", - "metadata": {}, - "outputs": [], - "source": [ - "# I got tired of trying to get the Plots version of this to work, so here's a PyPlot version\n", - "using PyPlot\n", - "\n", - "# Axes labels\n", - "xlabel = \"m\"\n", - "ylabel = \"mode (least to most stable)\"\n", - "\n", - "yvals = 1:size(wt, 2)\n", - "xvals = (1:size(wt, 1)) .+ (mlow + 1)\n", - "\n", - "# Create figure and grid layout\n", - "fig = figure(figsize=(9, 7))\n", - "gs = fig.add_gridspec(2, 3, height_ratios=[0.25, 0.75], width_ratios=[0.75, 0.21, 0.04])\n", - "\n", - "# Top-left: Eigenvector amplitude\n", - "ax0 = fig.add_subplot(gs[1, 1])\n", - "ax0.plot(xvals, abs.(wt[:, 1]), color=\"blue\", marker=\"o\", markersize=3)\n", - "ax0.set_ylabel(\"|Eigenvector|\")\n", - "ax0.set_xlabel(\"\")\n", - "ax0.set_title(\"Mode 1, eigenvalue = $(round(abs(et[1]), digits=3))\")\n", - "\n", - "# Bottom-left: Heatmap\n", - "ax1 = fig.add_subplot(gs[2, 1])\n", - "im = ax1.imshow(abs.(wt') , aspect=\"auto\", origin=\"lower\",\n", - " cmap=\"viridis\", extent=[xvals[1], xvals[end], yvals[1], yvals[end]])\n", - "ax1.set_xlabel(xlabel)\n", - "ax1.set_ylabel(ylabel)\n", - "\n", - "# Right middle: Eigenvalue amplitude\n", - "ax2 = fig.add_subplot(gs[2, 2])\n", - "ax2.plot(abs.(et), yvals, color=\"red\", marker=\"o\", markersize=3)\n", - "ax2.set_xlabel(\"Eigenvalue\")\n", - "ax2.set_xscale(\"log\")\n", - "ax2.set_xlim(0.1 * minimum(abs.(et)), 10 * maximum(abs.(et)))\n", - "ax2.set_yticks([])\n", - "\n", - "# Colorbar (bottom right)\n", - "cax = fig.add_subplot(gs[2, 3])\n", - "cb = fig.colorbar(im, cax=cax)\n", - "cb.set_label(\"|W_t_eigenvector|\")\n", - "\n", - "# Display and save figure\n", - "display(fig)" - ] - }, - { - "cell_type": "markdown", - "id": "10", - "metadata": {}, - "source": [ - "### Plot crit (the smallest eigenvalue of $W^{-1}$) versus $\\Psi$\n", - "If crit changes signs during integration, we know we are unstable to an ideal fixed-boundary instability." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "11", - "metadata": {}, - "outputs": [], - "source": [ - "# Plot crit vs psi\n", - "p = plot(psifac, crit, legend=false)\n", - "xlabel!(L\"\\psi_N\")\n", - "ylabel!(L\"crit\")\n", - "title!(\"Smallest eigenvalue of \" * L\"W^{-1}\" * \"(crit) versus \" * L\"\\psi_N\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/Solovev_ideal_example/run_example.jl b/examples/Solovev_ideal_example/run_example.jl new file mode 100644 index 00000000..fa0a9e53 --- /dev/null +++ b/examples/Solovev_ideal_example/run_example.jl @@ -0,0 +1,4 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium +GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)]) diff --git a/examples/Solovev_ideal_example_multi_n/analyze_example.jl b/examples/Solovev_ideal_example_multi_n/analyze_example.jl new file mode 100644 index 00000000..724ab4d3 --- /dev/null +++ b/examples/Solovev_ideal_example_multi_n/analyze_example.jl @@ -0,0 +1,17 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium, Plots, PlotlyJS +using GeneralizedPerturbedEquilibrium: Analysis +plotlyjs() + +# Analyze the multi-n run +h5path = joinpath(@__DIR__, "gpec.h5") +p_modes = Analysis.ForceFreeStates.plot_mode_displacement(h5path; modes=1:5) +p_eigen = Analysis.ForceFreeStates.plot_eigenmode_summary(h5path) +p_stab = Analysis.ForceFreeStates.plot_stability_criterion(h5path) + +# Analyze the single-n runs +h5path_n1 = joinpath(@__DIR__, "single_n_1", "euler_n1.h5") +h5path_n2 = joinpath(@__DIR__, "single_n_2", "euler_n2.h5") +p_modes_n1 = Analysis.ForceFreeStates.plot_mode_displacement(h5path_n1; modes=1:5) +p_modes_n2 = Analysis.ForceFreeStates.plot_mode_displacement(h5path_n2; modes=1:5) diff --git a/examples/Solovev_ideal_example_multi_n/run_and_analyze.ipynb b/examples/Solovev_ideal_example_multi_n/run_and_analyze.ipynb deleted file mode 100644 index c15cc1dd..00000000 --- a/examples/Solovev_ideal_example_multi_n/run_and_analyze.ipynb +++ /dev/null @@ -1,291 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "## Overview\n", - "In this notebook, we will run DCON on a Solovev ideal example equilibrium and plot the results" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "# Load in necessary packages\n", - "using Pkg\n", - "using HDF5\n", - "using Plots\n", - "using LaTeXStrings" - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "## Run the code\n", - "We will run GPEC using the inputs specified in `gpec.toml`. We run the code 3 times: once with both n=1 and n=2 at the same time using the files in this folder, and then for a single-n to compare the outputs with in their respective subfolders. Each run will output a `gpec.h5` file (but we set the default file naming in the `dcon.toml` to contain an \"_n1\" and \"_n2\" for the single-n cases), which is a Julia version of the `euler.bin` file." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# Run\n", - "Pkg.activate(\"../..\")\n", - "using GeneralizedPerturbedEquilibrium\n", - "GeneralizedPerturbedEquilibrium.main([\"./\"]) # \"./\" tells us to obtain inputs and direct outputs to our current folder\n", - "GeneralizedPerturbedEquilibrium.main([\"./single_n_1\"])\n", - "GeneralizedPerturbedEquilibrium.main([\"./single_n_2\"])" - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "## Analyze Outputs\n", - "We will now analyze the outputs of the run, the most important of which are located in the `gpec.h5` output file. We load in the data from both single-n runs and the multi-n run here." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "# Read in the multi-n run gpec.h5 data\n", - "eh5 = h5open(\"gpec.h5\", \"r\")\n", - "mlow = read(eh5[\"info/mlow\"])\n", - "mhigh = read(eh5[\"info/mhigh\"])\n", - "nlow = read(eh5[\"info/nlow\"])\n", - "psio = read(eh5[\"equil/psio\"])\n", - "xi_psi = read(eh5[\"integration/xi_psi\"])\n", - "psifac = read(eh5[\"integration/psi\"])\n", - "wt = read(eh5[\"vacuum/wt\"])\n", - "et = read(eh5[\"vacuum/et\"])\n", - "mn_index = read(eh5[\"info/mn_index\"])\n", - "close(eh5)\n", - "\n", - "# scale energy eigenvector matrices\n", - "chi1 = 2π*psio\n", - "wt .*= (chi1*1e-3)\n", - "println(\"Done reading gpec.h5\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "# Read in the single-n run with n=1 gpec.h5 data\n", - "eh5 = h5open(\"single_n_1/euler_n1.h5\", \"r\")\n", - "mlow = read(eh5[\"info/mlow\"])\n", - "psio = read(eh5[\"equil/psio\"])\n", - "xi_psi_n1 = read(eh5[\"integration/xi_psi\"])\n", - "psifac_n1 = read(eh5[\"integration/psi\"])\n", - "wt_n1 = read(eh5[\"vacuum/wt\"])\n", - "mn_index_n1 = read(eh5[\"info/mn_index\"])\n", - "close(eh5)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "# Read in the single-n run with n=2 gpec.h5 data\n", - "eh5 = h5open(\"single_n_2/euler_n2.h5\", \"r\")\n", - "mlow = read(eh5[\"info/mlow\"])\n", - "psio = read(eh5[\"equil/psio\"])\n", - "xi_psi_n2 = read(eh5[\"integration/xi_psi\"])\n", - "psifac_n2 = read(eh5[\"integration/psi\"])\n", - "mn_index_n2 = read(eh5[\"info/mn_index\"])\n", - "close(eh5)" - ] - }, - { - "cell_type": "markdown", - "id": "8", - "metadata": {}, - "source": [ - "### Plot comparison of $\\xi_{\\psi}$ for a few poloidal mode numbers\n", - "For clarity, we dump the `mn_index` in the output HDF5 file to make it clear which component in the first dimension of $\\xi_{\\psi}$ is being extracted. We show here how to use it to extract a desired $(m,n)$ mode. Note that in the multi-n case, the least stable mode corresponds to an n=1 perturbation and the second least stable mode to an n=2 perturbation. Therefore, when comparing the n=1 components we look at the first column (the least stable mode) of both runs; however, when comparing n=2 we must look at the second column of the multi-n run which is identical to the least stable mode computed in the n=2 only run." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "9", - "metadata": {}, - "outputs": [], - "source": [ - "p = plot()\n", - "n = 1\n", - "for m in 1:2\n", - " plot!(psifac, imag.(xi_psi[findfirst(x -> x[1] == m && x[2] == n, eachrow(mn_index)), 1, :]), linewidth = 3, label=\"m=$m, n=$n, multi-n\")\n", - " plot!(psifac_n1, imag.(xi_psi_n1[findfirst(x -> x[1] == m && x[2] == n, eachrow(mn_index_n1)), 1, :]), linestyle = :dash, linewidth = 3, label=\"m=$m, n=$n single-n\")\n", - "end\n", - "n = 2\n", - "for m in 1:2\n", - " plot!(psifac, imag.(xi_psi[findfirst(x -> x[1] == m && x[2] == n, eachrow(mn_index)), 2, :]), linewidth = 3, label=\"m=$m, n=$n, multi-n\")\n", - " plot!(psifac_n2, imag.(xi_psi_n2[findfirst(x -> x[1] == m && x[2] == n, eachrow(mn_index_n2)), 1, :]), linestyle = :dash, linewidth = 3, label=\"m=$m, n=$n single-n\")\n", - "end\n", - "xlabel!(L\"\\psi_N\")\n", - "ylabel!(L\"\\mathrm{Im}(\\xi_\\psi)\")\n", - "title!(\"Least Stable Eigenmode \" * L\"\\xi_\\psi\")\n", - "display(p)" - ] - }, - { - "cell_type": "markdown", - "id": "10", - "metadata": {}, - "source": [ - "### Compare the eigenvectors and eigenvalues of each DCON energy matrix eigenmode\n", - "This is analagous to the DCON summary plot creating by OMFIT GPEC" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "11", - "metadata": {}, - "outputs": [], - "source": [ - "# I got tired of trying to get the Plots version of this to work, so here's a PyPlot version\n", - "using PyPlot\n", - "\n", - "# Axes labels\n", - "xlabel = \"m\"\n", - "ylabel = \"mode (least to most stable)\"\n", - "\n", - "yvals = 1:size(wt, 2)\n", - "xvals = 1:size(wt, 1)\n", - "\n", - "# Compute corresponding m and n\n", - "mpert = mhigh - mlow + 1\n", - "m_vals = [(i - 1) % mpert + mlow for i in xvals]\n", - "n_vals = [(i - 1) ÷ mpert + nlow for i in xvals]\n", - "\n", - "# Create figure and grid layout\n", - "fig = figure(figsize=(9, 7))\n", - "gs = fig.add_gridspec(2, 3, height_ratios=[0.25, 0.75], width_ratios=[0.75, 0.21, 0.04])\n", - "\n", - "# Top-left: Eigenvector amplitude\n", - "ax0 = fig.add_subplot(gs[1, 1])\n", - "ax0.plot(xvals, abs.(wt[:, 1]), color=\"blue\", marker=\"o\", markersize=3)\n", - "ax0.set_ylabel(\"|Eigenvector|\")\n", - "ax0.set_xlabel(\"\")\n", - "ax0.set_xticks([])\n", - "ax0.set_title(\"Mode 1, eigenvalue = $(round(abs(et[1]), digits=3))\")\n", - "\n", - "# Bottom-left: Heatmap\n", - "ax1 = fig.add_subplot(gs[2, 1])\n", - "im = ax1.imshow(abs.(wt') , aspect=\"auto\", origin=\"lower\",\n", - " cmap=\"viridis\", extent=[xvals[1], xvals[end], yvals[1], yvals[end]])\n", - "ax1.set_xlabel(xlabel)\n", - "ax1.set_ylabel(ylabel)\n", - "\n", - "# ===== UPPER X-AXIS: m =====\n", - "step_m = max(1, Int(length(xvals) ÷ 10))\n", - "xticks_m = xvals[1:step_m:end]\n", - "ax1.set_xticks(xticks_m)\n", - "ax1.set_xticklabels([\"$(m_vals[i])\" for i in 1:step_m:length(xvals)])\n", - "ax1.set_xlabel(\"m\")\n", - "\n", - "# ===== LOWER X-AXIS: n =====\n", - "# Create secondary axis *below* the first one\n", - "ax_n = ax1.secondary_xaxis(\"bottom\", functions=(x->x, x->x))\n", - "ax_n.xaxis.set_label_position(\"bottom\")\n", - "ax_n.xaxis.set_ticks_position(\"bottom\")\n", - "\n", - "# Position slightly below the original\n", - "ax_n.spines[\"bottom\"].set_position((\"outward\", 40))\n", - "\n", - "# Show only one n per mpert group\n", - "n_indices = [i for i in mpert÷2:mpert:length(xvals)]\n", - "xticks_n = xvals[n_indices]\n", - "xticklabels_n = [\"$(n_vals[i])\" for i in n_indices]\n", - "\n", - "ax_n.set_xticks(xticks_n)\n", - "ax_n.set_xticklabels(xticklabels_n)\n", - "ax_n.set_xlabel(\"n\")\n", - "\n", - "# Right middle: Eigenvalue amplitude\n", - "ax2 = fig.add_subplot(gs[2, 2])\n", - "ax2.scatter(abs.(et), yvals, c=\"red\", s=30)\n", - "ax2.set_xlabel(\"Eigenvalue\")\n", - "ax2.set_xscale(\"log\")\n", - "ax2.set_xlim(0.1 * minimum(abs.(et)), 10 * maximum(abs.(et)))\n", - "ax2.set_yticks([])\n", - "\n", - "# Colorbar (bottom right)\n", - "cax = fig.add_subplot(gs[2, 3])\n", - "cb = fig.colorbar(im, cax=cax)\n", - "cb.set_label(\"|Wₜ|\")\n", - "\n", - "display(fig)" - ] - }, - { - "cell_type": "markdown", - "id": "12", - "metadata": {}, - "source": [ - "### Plot crit (the smallest eigenvalue of $W^{-1}$) versus $\\Psi$\n", - "If crit changes signs during integration, we know we are unstable to an ideal fixed-boundary instability. It has the same interpretation when running with multiple toroidal modes, since the number of eigenvalues double but we still only need to monitor the smallest in magnitude. This data is saved in the `crit.h5` file." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "13", - "metadata": {}, - "outputs": [], - "source": [ - "# Read in the crit.h5 data\n", - "crit_h5 = h5open(\"crit.h5\", \"r\")\n", - "psi = read(crit_h5[\"psi\"])\n", - "crit = read(crit_h5[\"crit\"])\n", - "close(crit_h5)\n", - "\n", - "# Plot crit vs psi\n", - "p = plot(psi, crit, legend=false)\n", - "xlabel!(L\"\\psi_N\")\n", - "ylabel!(L\"crit\")\n", - "title!(\"Smallest eigenvalue of \" * L\"W^{-1}\" * \"(crit) versus \" * L\"\\psi_N\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "14", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/Solovev_ideal_example_multi_n/run_example.jl b/examples/Solovev_ideal_example_multi_n/run_example.jl new file mode 100644 index 00000000..29645cc4 --- /dev/null +++ b/examples/Solovev_ideal_example_multi_n/run_example.jl @@ -0,0 +1,6 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium +GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)]) +GeneralizedPerturbedEquilibrium.main([joinpath(@__DIR__, "single_n_1")]) +GeneralizedPerturbedEquilibrium.main([joinpath(@__DIR__, "single_n_2")]) diff --git a/notebooks/CHEASE_INP1/equil.toml b/notebooks/CHEASE_INP1/equil.toml deleted file mode 100644 index 049efb6c..00000000 --- a/notebooks/CHEASE_INP1/equil.toml +++ /dev/null @@ -1,30 +0,0 @@ -[EQUIL_CONTROL] -eq_type = "efit" # Type of the input 2D equilibrium file -eq_filename = "INP1" # path to equilibrium file - -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r -power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r -power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r - -grid_type = "ldp" # Radial grid packing -psilow = 1e-4 # Min psi (normalized) -psihigh = 0.993 # Max psi (normalized) -mpsi = 128 # Radial grid intervals -mtheta = 256 # Poloidal grid intervals - -newq0 = 0 # Override q(0) -etol = 1e-7 # Reconstruction tolerance -use_classic_splines = false # Use classical spline (vs. tri-diagonal) - -input_only = false # Quit after input read - -[EQUIL_OUTPUT] -gse_flag = false # Output G-S equation accuracy diagnostics -out_eq_1d = false # ASCII output of 1D eq data -bin_eq_1d = false # Binary output of 1D eq data -out_eq_2d = false # ASCII output of 2D eq data -bin_eq_2d = true # Binary output of 2D eq data (used by GPEC) -out_2d = false # ASCII output of processed 2D data -bin_2d = false # Binary output of processed 2D data -dump_flag = false # Binary dump of equilibrium data diff --git a/notebooks/Chease_Binary_example/INP1 b/notebooks/Chease_Binary_example/INP1 deleted file mode 100644 index 7a39ceea..00000000 Binary files a/notebooks/Chease_Binary_example/INP1 and /dev/null differ diff --git a/notebooks/beta_1.00 b/notebooks/beta_1.00 deleted file mode 100644 index 4cd103c8..00000000 --- a/notebooks/beta_1.00 +++ /dev/null @@ -1,3596 +0,0 @@ - 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3.843336059E-02 6.351602462E-02 8.912230337E-02 1.152236726E-01 1.417947312E-01 - 1.688122570E-01 1.962541894E-01 2.240994216E-01 2.523278801E-01 2.809205195E-01 - 3.098593131E-01 3.391272243E-01 3.687079588E-01 3.985857436E-01 4.287454786E-01 - 4.591728569E-01 4.898543392E-01 5.207770769E-01 5.519288850E-01 5.832982738E-01 - 6.148744331E-01 6.466471733E-01 6.786068680E-01 7.107444589E-01 7.430514674E-01 - 7.755199631E-01 8.081424982E-01 8.409120662E-01 8.738221095E-01 9.068665214E-01 - 9.400396239E-01 9.733361185E-01 1.006751031E+00 1.040279589E+00 1.073917791E+00 - 1.107664852E+00 1.141503570E+00 1.675591531E-01 1.494382862E-01 1.316636290E-01 - 1.143008639E-01 9.735287372E-02 8.083347504E-02 6.475812689E-02 4.914167497E-02 - 3.399831051E-02 1.934635463E-02 5.212139136E-03-8.511315813E-03-2.226343914E-02 --3.618846566E-02-5.026314994E-02-6.446278709E-02-7.876831597E-02-9.315992030E-02 --1.076169563E-01-1.221181725E-01-1.366413702E-01-1.511631799E-01-1.656590270E-01 --1.801041507E-01-1.944749909E-01-2.087486750E-01-2.229018431E-01-2.369106661E-01 --2.507503864E-01-2.643959046E-01-2.778223547E-01-2.910053137E-01-3.039214776E-01 --3.165486635E-01-3.288637027E-01-3.408409042E-01-3.524563699E-01-3.636904152E-01 --3.745222152E-01-3.849263415E-01-3.948812822E-01-4.043700630E-01-4.133709980E-01 --4.218617995E-01-4.298255860E-01-4.372446234E-01-4.440987765E-01-4.503707281E-01 --4.560449457E-01-4.611052281E-01-4.655351190E-01-4.693191538E-01-4.724450081E-01 --4.749000765E-01-4.766691903E-01-4.777390724E-01-4.781021267E-01-4.777495460E-01 --4.766686095E-01-4.748466963E-01-4.722787784E-01-4.689618957E-01-4.648904344E-01 --4.600556599E-01-4.544481520E-01-4.480646496E-01-4.409069287E-01-4.329763611E-01 --4.242730391E-01-4.147960042E-01-4.045438555E-01-3.935151444E-01-3.817118515E-01 --3.691409967E-01-3.558110897E-01-3.417307855E-01-3.269091654E-01-3.113558472E-01 --2.950811605E-01-2.780961827E-01-2.604129793E-01-2.420446281E-01-2.230054677E-01 --2.033116203E-01-1.829815122E-01-1.620353520E-01-1.404945248E-01-1.183817328E-01 --9.572138793E-02-7.254053610E-02-4.887009378E-02-2.473505270E-02-1.390687717E-04 - 2.496365219E-02 5.059007992E-02 7.672913917E-02 1.033537360E-01 1.304369394E-01 - 1.579550071E-01 1.858859055E-01 2.142086485E-01 2.429032994E-01 2.719510254E-01 - 3.013339227E-01 3.310347409E-01 3.610369583E-01 3.913249151E-01 4.218837991E-01 - 4.526995666E-01 4.837589070E-01 5.150492739E-01 5.465588696E-01 5.782765799E-01 - 6.101919151E-01 6.422950164E-01 6.745766627E-01 7.070282329E-01 7.396416321E-01 - 7.724092556E-01 8.053240013E-01 8.383792623E-01 8.715688964E-01 9.048871636E-01 - 9.383286966E-01 9.718884882E-01 1.005561770E+00 1.039344564E+00 1.073236091E+00 - 1.107219159E+00 1.669299143E-01 1.484811046E-01 1.303712033E-01 1.126652325E-01 - 9.536693920E-02 7.849085499E-02 6.205317400E-02 4.606931514E-02 3.055472838E-02 - 1.553405427E-02 1.014020041E-03-1.321664288E-02-2.757325050E-02-4.212032440E-02 --5.682172172E-02-7.165512278E-02-8.660054939E-02-1.016372536E-01-1.167440441E-01 --1.318992704E-01-1.470806514E-01-1.622650002E-01-1.774279598E-01-1.925438135E-01 --2.075865731E-01-2.225318330E-01-2.373561926E-01-2.520359362E-01-2.665466432E-01 --2.808630957E-01-2.949594241E-01-3.088103663E-01-3.223912851E-01-3.356786131E-01 --3.486502166E-01-3.612824805E-01-3.735490919E-01-3.854266552E-01-3.968962129E-01 --4.079356916E-01-4.185194862E-01-4.286278239E-01-4.382433476E-01-4.473428891E-01 --4.559059597E-01-4.639166278E-01-4.713555715E-01-4.782034409E-01-4.844441801E-01 --4.900621491E-01-4.950409555E-01-4.993642480E-01-5.030183352E-01-5.059915216E-01 --5.082694215E-01-5.098367698E-01-5.106846542E-01-5.108054941E-01-5.101873987E-01 --5.088163715E-01-5.066852916E-01-5.037916305E-01-5.001304479E-01-4.956930119E-01 --4.904689394E-01-4.844534302E-01-4.776480869E-01-4.700543517E-01-4.616720894E-01 --4.524998547E-01-4.425355089E-01-4.317767232E-01-4.202249741E-01-4.078869794E-01 --3.947708404E-01-3.808846964E-01-3.662371203E-01-3.508371407E-01-3.346944801E-01 --3.178195581E-01-3.002237695E-01-2.819194236E-01-2.629202010E-01-2.432417469E-01 --2.229020821E-01-2.019208229E-01-1.803188907E-01-1.581185912E-01-1.353434363E-01 --1.120183292E-01-8.817018029E-02-6.382954520E-02-3.902826264E-02-1.378337186E-02 - 1.191241285E-02 3.810504374E-02 6.479399799E-02 9.195681379E-02 1.195660789E-01 - 1.475975057E-01 1.760290933E-01 2.048400912E-01 2.340107668E-01 2.635221959E-01 - 2.933562689E-01 3.234958151E-01 3.539246005E-01 3.846272479E-01 4.155891920E-01 - 4.467967103E-01 4.782369064E-01 5.098976394E-01 5.417674619E-01 5.738356291E-01 - 6.060920988E-01 6.385274858E-01 6.711329820E-01 7.039003264E-01 7.368218196E-01 - 7.698903068E-01 8.030991349E-01 8.364420865E-01 8.699133539E-01 9.035075495E-01 - 9.372196784E-01 9.710449982E-01 1.004979530E+00 1.039022471E+00 1.073156668E+00 - 1.663323816E-01 1.475568608E-01 1.291120074E-01 1.110620893E-01 9.341178655E-02 - 7.617626118E-02 5.937238649E-02 4.301603252E-02 2.712425768E-02 1.173063414E-02 --3.189766676E-03-1.798290713E-02-3.295352081E-02-4.811885125E-02-6.344578670E-02 --7.891285098E-02-9.449844569E-02-1.101803580E-01-1.259365239E-01-1.417447529E-01 --1.575824837E-01-1.734264934E-01-1.892527657E-01-2.050360383E-01-2.207495939E-01 --2.363662151E-01-2.518607027E-01-2.672091038E-01-2.823875772E-01-2.973712233E-01 --3.121342804E-01-3.266504881E-01-3.408939971E-01-3.548400728E-01-3.684652908E-01 --3.817473481E-01-3.946620232E-01-4.071828940E-01-4.192873882E-01-4.309568336E-01 --4.421676191E-01-4.528948900E-01-4.631207900E-01-4.728264146E-01-4.819882104E-01 --4.905879807E-01-4.986093236E-01-5.060320619E-01-5.128383224E-01-5.190127861E-01 --5.245395339E-01-5.294019809E-01-5.335847141E-01-5.370760556E-01-5.398630229E-01 --5.419296479E-01-5.432643656E-01-5.438604415E-01-5.437074093E-01-5.427906914E-01 --5.411004636E-01-5.386342599E-01-5.353879866E-01-5.313531607E-01-5.265186391E-01 --5.208779450E-01-5.144323508E-01-5.071833973E-01-4.991308058E-01-4.902726852E-01 --4.806061285E-01-4.701279411E-01-4.588391852E-01-4.467462535E-01-4.338567963E-01 --4.201784617E-01-4.057192712E-01-3.904876369E-01-3.744926634E-01-3.577440910E-01 --3.402525889E-01-3.220297158E-01-3.030885041E-01-2.834442280E-01-2.631143790E-01 --2.421179035E-01-2.204751343E-01-1.982078575E-01-1.753391893E-01-1.518936181E-01 --1.278968619E-01-1.033761181E-01-7.836102836E-02-5.288539547E-02-2.697978008E-02 --6.535113239E-04 2.612874338E-02 5.338289366E-02 8.109706817E-02 1.092447170E-01 - 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1.286273022E-01 1.580888323E-01 1.879009857E-01 2.180442008E-01 2.484999311E-01 - 2.792506355E-01 3.102798091E-01 3.415719622E-01 3.731125348E-01 4.048878297E-01 - 4.368850247E-01 4.690921571E-01 5.014980552E-01 5.340922534E-01 5.668649760E-01 - 5.998071431E-01 6.329103348E-01 6.661667149E-01 6.995689761E-01 7.331103315E-01 - 7.667845057E-01 8.005857106E-01 8.345085898E-01 8.685481580E-01 9.026996667E-01 - 9.369591557E-01 9.713258635E-01 1.005782871E+00 1.652114875E-01 1.457890768E-01 - 1.266788204E-01 1.079423708E-01 8.958597625E-02 7.162609472E-02 5.408078753E-02 - 3.696753893E-02 2.030986489E-02 4.131149460E-03-1.171318275E-02-2.767536294E-02 --4.386765137E-02-6.025995183E-02-7.682859041E-02-9.355307623E-02-1.104110417E-01 --1.273784548E-01-1.444300497E-01-1.615401968E-01-1.786842409E-01-1.958382426E-01 --2.129781069E-01-2.300793254E-01-2.471165242E-01-2.640631213E-01-2.808906497E-01 --2.975699687E-01-3.140737205E-01-3.303775176E-01-3.464572500E-01-3.622877072E-01 --3.778424003E-01-3.930940612E-01-4.080164883E-01-4.225848570E-01-4.367760427E-01 --4.505679032E-01-4.639349838E-01-4.768511173E-01-4.892962079E-01-5.012509000E-01 --5.126891871E-01-5.235899494E-01-5.339370122E-01-5.437074912E-01-5.528811267E-01 --5.614425649E-01-5.693722805E-01-5.766518774E-01-5.832662526E-01-5.891999226E-01 --5.944362795E-01-5.989601779E-01-6.027606371E-01-6.058240290E-01-6.081340177E-01 --6.096815710E-01-6.104598107E-01-6.104556891E-01-6.096543309E-01-6.080508854E-01 --6.056431771E-01-6.024241399E-01-5.983817666E-01-5.935060626E-01-5.877970606E-01 --5.812566278E-01-5.738843284E-01-5.656774443E-01-5.566316321E-01-5.467420633E-01 --5.360090184E-01-5.244382793E-01-5.120366041E-01-4.988105466E-01-4.847669552E-01 --4.699130702E-01-4.542565870E-01-4.378059107E-01-4.205701437E-01-4.025594089E-01 --3.837857069E-01-3.642634615E-01-3.440087993E-01-3.230392996E-01-3.013740571E-01 --2.790336155E-01-2.560400116E-01-2.324167216E-01-2.081886335E-01-1.833820423E-01 --1.580245764E-01-1.321450789E-01-1.057738239E-01-7.894351701E-02-5.169081027E-02 --2.404906489E-02 3.971125540E-03 3.240326320E-02 6.125408320E-02 9.050780680E-02 - 1.201391428E-01 1.501252976E-01 1.804459370E-01 2.110818412E-01 2.420148597E-01 - 2.732279627E-01 3.047051623E-01 3.364314377E-01 3.683927468E-01 4.005760017E-01 - 4.329689852E-01 4.655602679E-01 4.983391989E-01 5.312958999E-01 5.644212167E-01 - 5.977066317E-01 6.311442168E-01 6.647266323E-01 6.984471048E-01 7.322993880E-01 - 7.662776939E-01 8.003766580E-01 8.345913157E-01 8.689169712E-01 9.033497366E-01 - 9.378888878E-01 9.725176480E-01 1.646825373E-01 1.449385884E-01 1.254977135E-01 - 1.064198829E-01 8.771125541E-02 6.938830880E-02 5.146935476E-02 3.397304584E-02 - 1.692850928E-02 3.399454031E-04-1.602665764E-02-3.258020222E-02-4.937542274E-02 --6.637547055E-02-8.355862995E-02-1.009042911E-01-1.183899605E-01-1.359917697E-01 --1.536844793E-01-1.714414634E-01-1.892353696E-01-2.070400877E-01-2.248306970E-01 --2.425826229E-01-2.602709520E-01-2.778698889E-01-2.953523610E-01-3.126894156E-01 --3.298509051E-01-3.468085676E-01-3.635375596E-01-3.800141313E-01-3.962129771E-01 --4.121072829E-01-4.276697081E-01-4.428737528E-01-4.576946683E-01-4.721099030E-01 --4.860972494E-01-4.996305268E-01-5.126843705E-01-5.252400775E-01-5.372769708E-01 --5.487690442E-01-5.596976933E-01-5.700455305E-01-5.797891879E-01-5.889111755E-01 --5.973952251E-01-6.052214981E-01-6.123734454E-01-6.188363819E-01-6.245943185E-01 --6.296307855E-01-6.339335290E-01-6.374909474E-01-6.402867986E-01-6.423085952E-01 --6.435505391E-01-6.440015978E-01-6.436457530E-01-6.424752711E-01-6.404886973E-01 --6.376801887E-01-6.340377585E-01-6.295497507E-01-6.242150990E-01-6.180358579E-01 --6.110116917E-01-6.031395096E-01-5.944142121E-01-5.848302028E-01-5.743875214E-01 --5.630916055E-01-5.509486815E-01-5.379648196E-01-5.241462638E-01-5.094995844E-01 --4.940318116E-01-4.777506646E-01-4.606644080E-01-4.427825691E-01-4.241167253E-01 --4.046806813E-01-3.844898344E-01-3.635610607E-01-3.419128023E-01-3.195649731E-01 --2.965390386E-01-2.728578957E-01-2.485459157E-01-2.236288851E-01-1.981339769E-01 --1.720897227E-01-1.455259433E-01-1.184736952E-01-9.096589051E-02-6.303895269E-02 --3.473130467E-02-6.064411679E-03 2.297338806E-02 5.240525522E-02 8.222205727E-02 - 1.123990427E-01 1.429134179E-01 1.737451235E-01 2.048755154E-01 2.362870156E-01 - 2.679631137E-01 2.998884032E-01 3.320485399E-01 3.644301424E-01 3.970207117E-01 - 4.298086287E-01 4.627831328E-01 4.959342558E-01 5.292527303E-01 5.627299529E-01 - 5.963579797E-01 6.301294954E-01 6.640377493E-01 6.980764897E-01 7.322399340E-01 - 7.665227611E-01 8.009200810E-01 8.354272817E-01 8.700405298E-01 9.047591164E-01 - 9.395664388E-01 1.641743207E-01 1.441097359E-01 1.243388639E-01 1.049201030E-01 - 8.585975097E-02 6.717403870E-02 4.888078830E-02 3.099948452E-02 1.356679118E-02 --3.438447616E-03-2.036005757E-02-3.750777279E-02-5.489982919E-02-7.250276525E-02 --9.029534998E-02-1.082563638E-01-1.263630538E-01-1.445915701E-01-1.629168755E-01 --1.813126574E-01-1.997510413E-01-2.182032666E-01-2.366414619E-01-2.550396139E-01 --2.733728305E-01-2.916158912E-01-3.097428474E-01-3.277262490E-01-3.455369172E-01 --3.631438153E-01-3.805176187E-01-3.976333454E-01-4.144672922E-01-4.309945371E-01 --4.471880596E-01-4.630201689E-01-4.784645410E-01-4.934965971E-01-5.080941207E-01 --5.222349807E-01-5.358925617E-01-5.490425436E-01-5.616672541E-01-5.737444013E-01 --5.852491191E-01-5.961650202E-01-6.064725113E-01-6.161493993E-01-6.251803717E-01 --6.335473736E-01-6.412316243E-01-6.482181721E-01-6.544920970E-01-6.600368840E-01 --6.648378985E-01-6.688847612E-01-6.721629350E-01-6.746567243E-01-6.763597083E-01 --6.772633323E-01-6.773517699E-01-6.766137873E-01-6.750480730E-01-6.726501912E-01 --6.694084968E-01-6.653099124E-01-6.603520035E-01-6.545369894E-01-6.478646301E-01 --6.403314843E-01-6.319318118E-01-6.226593034E-01-6.125136944E-01-6.015000853E-01 --5.896242724E-01-5.768917648E-01-5.633081332E-01-5.488793718E-01-5.336118301E-01 --5.175124307E-01-5.005887594E-01-4.828497528E-01-4.643065270E-01-4.449722144E-01 --4.248614298E-01-4.039903797E-01-3.823768189E-01-3.600400467E-01-3.370009241E-01 --3.132817689E-01-2.889064229E-01-2.639001318E-01-2.382895587E-01-2.121027651E-01 --1.853691644E-01-1.581194689E-01-1.303856360E-01-1.022010696E-01-7.360187863E-02 --4.462798869E-02-1.531156843E-02 1.434208341E-02 4.436193049E-02 7.474523113E-02 - 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8.955141153E-02 1.250554940E-01 1.606956690E-01 1.964643836E-01 2.323547159E-01 - 2.683602506E-01 3.044750558E-01 3.406936326E-01 3.770108809E-01 4.134220944E-01 - 4.499229358E-01 4.865093983E-01 5.231776903E-01 5.599245945E-01 5.967491799E-01 - 6.336389169E-01 1.601536778E-01 1.370468898E-01 1.141239516E-01 9.142342731E-02 - 6.895164168E-02 4.672140104E-02 2.475436356E-02 3.061463880E-03-1.852982096E-02 --4.041580992E-02-6.266505428E-02-8.524047323E-02-1.081156636E-01-1.312656658E-01 --1.546635861E-01-1.782813017E-01-2.020896713E-01-2.260586517E-01-2.501574338E-01 --2.743545028E-01-2.986177330E-01-3.229144579E-01-3.472114891E-01-3.714752466E-01 --3.956721322E-01-4.197696246E-01-4.437369294E-01-4.675443997E-01-4.911628797E-01 --5.145633426E-01-5.377163069E-01-5.605918413E-01-5.831589226E-01-6.053846194E-01 --6.272336882E-01-6.486713890E-01-6.696703395E-01-6.902111939E-01-7.102752991E-01 --7.298387665E-01-7.488703358E-01-7.673372346E-01-7.852171075E-01-8.024939378E-01 --8.191472141E-01-8.351513874E-01-8.504838289E-01-8.651276523E-01-8.790649445E-01 --8.922735806E-01-9.047388659E-01-9.164420265E-01-9.273673572E-01-9.374994501E-01 --9.468229343E-01-9.553241476E-01-9.629885394E-01-9.698042790E-01-9.757573948E-01 --9.808380391E-01-9.850337237E-01-9.883332555E-01-9.907310332E-01-9.922103406E-01 --9.927670912E-01-9.923983158E-01-9.910872570E-01-9.888253364E-01-9.856156988E-01 --9.814555055E-01-9.763334260E-01-9.702385040E-01-9.631698176E-01-9.551291356E-01 --9.461171340E-01-9.361339257E-01-9.251796990E-01-9.132548605E-01-9.003591578E-01 --8.864919414E-01-8.716541394E-01-8.558487394E-01-8.390807427E-01-8.213573062E-01 --8.026875515E-01-7.830824524E-01-7.625548818E-01-7.411193257E-01-7.187919220E-01 --6.955899488E-01-6.715296788E-01-6.466263630E-01-6.208965858E-01-5.943593398E-01 --5.670359374E-01-5.389498621E-01-5.101268577E-01-4.805947815E-01-4.503836261E-01 --4.195254782E-01-3.880544622E-01-3.560066608E-01-3.234201019E-01-2.903347154E-01 --2.567922063E-01-2.228360457E-01-1.885114491E-01-1.538652802E-01-1.189458838E-01 --8.380358296E-02-4.849337029E-02-1.306803033E-02 2.246026012E-02 5.812362496E-02 - 9.392726312E-02 1.298608063E-01 1.659161246E-01 2.020866066E-01 2.383660503E-01 - 2.747487036E-01 3.112292845E-01 3.478029414E-01 3.844652187E-01 4.212120180E-01 - 4.580395426E-01 4.949441921E-01 5.319229178E-01 5.689748393E-01 6.060881610E-01 - 1.598398861E-01 1.364580242E-01 1.132480149E-01 9.024610081E-02 6.745835493E-02 - 4.489727392E-02 2.258601275E-02 5.248679495E-04-2.149823558E-02-4.384757886E-02 --6.656669546E-02-8.961659312E-02-1.129713164E-01-1.366054478E-01-1.604916224E-01 --1.846012712E-01-2.089048468E-01-2.333719650E-01-2.579714909E-01-2.826715648E-01 --3.074398517E-01-3.322435797E-01-3.570494516E-01-3.818239260E-01-4.065330332E-01 --4.311426609E-01-4.556190062E-01-4.799299056E-01-5.040452307E-01-5.279360444E-01 --5.515738831E-01-5.749301971E-01-5.979758954E-01-6.206811050E-01-6.430142602E-01 --6.649411558E-01-6.864265008E-01-7.074395727E-01-7.279604598E-01-7.479725441E-01 --7.674548227E-01-7.863780116E-01-8.047091590E-01-8.224246039E-01-8.395094178E-01 --8.559445096E-01-8.717049367E-01-8.867689840E-01-9.011206528E-01-9.147418774E-01 --9.276119972E-01-9.397172640E-01-9.510386802E-01-9.615628373E-01-9.712730718E-01 --9.801566085E-01-9.881987197E-01-9.953869227E-01-1.001708901E+00-1.007152138E+00 --1.011707452E+00-1.015360484E+00-1.018106688E+00-1.019931889E+00-1.020827202E+00 --1.020791830E+00-1.019810787E+00-1.017872848E+00-1.014981062E+00-1.011133043E+00 --1.006317045E+00-1.000522033E+00-9.937471845E-01-9.859938521E-01-9.772621707E-01 --9.675519156E-01-9.568630417E-01-9.451953516E-01-9.325473514E-01-9.189176518E-01 --9.043066565E-01-8.887169671E-01-8.721534706E-01-8.546231008E-01-8.361348498E-01 --8.166997059E-01-7.963303717E-01-7.750413449E-01-7.528484630E-01-7.297666828E-01 --7.058091220E-01-6.809896638E-01-6.553245892E-01-6.288325487E-01-6.015343890E-01 --5.734532540E-01-5.446144078E-01-5.150453092E-01-4.847755146E-01-4.538366807E-01 --4.222624362E-01-3.900884537E-01-3.573523161E-01-3.240934475E-01-2.903531527E-01 --2.561745060E-01-2.216022611E-01-1.866828457E-01-1.514643281E-01-1.159962495E-01 --8.033022822E-02-4.452292959E-02-8.625746626E-03 2.735852814E-02 6.346458798E-02 - 9.969518978E-02 1.360408044E-01 1.724944592E-01 2.090503253E-01 2.457029661E-01 - 2.824473986E-01 3.192790585E-01 3.561937440E-01 3.931875864E-01 4.302570128E-01 - 4.673986528E-01 5.046096730E-01 5.418892765E-01 5.792264265E-01 1.595376163E-01 - 1.358883550E-01 1.123990046E-01 8.910342461E-02 6.600731830E-02 4.312273938E-02 - 2.047558396E-02-1.944338915E-03-2.439709171E-02-4.719783383E-02-7.037184356E-02 --9.388145097E-02-1.177007149E-01-1.418036312E-01-1.661623409E-01-1.907478421E-01 --2.155301769E-01-2.404785457E-01-2.655614321E-01-2.907466937E-01-3.160016982E-01 --3.412933885E-01-3.665883379E-01-3.918529644E-01-4.170533298E-01-4.421553746E-01 --4.671248251E-01-4.919274362E-01-5.165296673E-01-5.409002157E-01-5.650099833E-01 --5.888310603E-01-6.123359027E-01-6.354966009E-01-6.582845260E-01-6.806696442E-01 --7.026193893E-01-7.240986412E-01-7.450743311E-01-7.655240725E-01-7.854326066E-01 --8.047823251E-01-8.235464409E-01-8.416923797E-01-8.591950600E-01-8.760401355E-01 --8.922101847E-01-9.076811477E-01-9.224319679E-01-9.364474764E-01-9.497097400E-01 --9.621998131E-01-9.739039921E-01-9.848042572E-01-9.948878346E-01-1.004138948E+00 --1.012545208E+00-1.020092640E+00-1.026769882E+00-1.032563828E+00-1.037465326E+00 --1.041461097E+00-1.044543826E+00-1.046703558E+00-1.047927103E+00-1.048214698E+00 --1.047553857E+00-1.045930810E+00-1.043348117E+00-1.039803956E+00-1.035286377E+00 --1.029784272E+00-1.023296745E+00-1.015824794E+00-1.007368225E+00-9.979264523E-01 --9.874990769E-01-9.760851958E-01-9.636820323E-01-9.502874124E-01-9.359014652E-01 --9.205266752E-01-9.041677334E-01-8.868316245E-01-8.685274300E-01-8.492661001E-01 --8.290605433E-01-8.079252114E-01-7.858739800E-01-7.629181394E-01-7.390689599E-01 --7.143400380E-01-6.887473824E-01-6.623092363E-01-6.350461545E-01-6.069808217E-01 --5.781381577E-01-5.485451804E-01-5.182310372E-01-4.872268760E-01-4.555659311E-01 --4.232833403E-01-3.904161980E-01-3.570034935E-01-3.230860266E-01-2.887063717E-01 --2.539088346E-01-2.187394075E-01-1.832457074E-01-1.474769215E-01-1.114836421E-01 --7.531884640E-02-3.904121524E-02-2.698771133E-03 3.372036027E-02 7.024910602E-02 - 1.068869868E-01 1.436256742E-01 1.804594074E-01 2.173831868E-01 2.543923438E-01 - 2.914825960E-01 3.286500194E-01 3.658910248E-01 4.032023153E-01 4.405807837E-01 - 4.780238150E-01 5.155306840E-01 5.530911235E-01 1.592462533E-01 1.353376718E-01 - 1.115771673E-01 8.799620551E-02 6.460010950E-02 4.140052641E-02 1.842507241E-02 --4.348376694E-03-2.722081377E-02-5.045836913E-02-7.407199744E-02-9.802597437E-02 --1.222941843E-01-1.468500040E-01-1.716650809E-01-1.967099484E-01-2.219542002E-01 --2.473666125E-01-2.729152955E-01-2.985677665E-01-3.242910244E-01-3.500517663E-01 --3.758163650E-01-4.015509802E-01-4.272216387E-01-4.527943473E-01-4.782349774E-01 --5.035093555E-01-5.285832831E-01-5.534227968E-01-5.779950507E-01-6.022700728E-01 --6.262201114E-01-6.498185420E-01-6.730388737E-01-6.958539327E-01-7.182354125E-01 --7.401526366E-01-7.615717181E-01-7.824583810E-01-8.027863252E-01-8.225407456E-01 --8.417071058E-01-8.602621463E-01-8.781741307E-01-8.954163610E-01-9.119750904E-01 --9.278342814E-01-9.429708250E-01-9.573647244E-01-9.710014094E-01-9.838629386E-01 --9.959323795E-01-1.007195490E+00-1.017636349E+00-1.027241409E+00-1.035997100E+00 --1.043890300E+00-1.050908743E+00-1.057040821E+00-1.062275010E+00-1.066601472E+00 --1.070008683E+00-1.072490575E+00-1.074031774E+00-1.074631448E+00-1.074280079E+00 --1.072962010E+00-1.070679020E+00-1.067429827E+00-1.063202203E+00-1.057985027E+00 --1.051777493E+00-1.044580250E+00-1.036392634E+00-1.027213852E+00-1.017043312E+00 --1.005878791E+00-9.937162514E-01-9.805531745E-01-9.663895006E-01-9.512276076E-01 --9.350723817E-01-9.179309619E-01-8.998125691E-01-8.807285520E-01-8.606920212E-01 --8.397159606E-01-8.178102058E-01-7.949835601E-01-7.712469699E-01-7.466138366E-01 --7.210998550E-01-6.947230271E-01-6.675034992E-01-6.394636758E-01-6.106280506E-01 --5.810232628E-01-5.506779753E-01-5.196229385E-01-4.878908144E-01-4.555162895E-01 --4.225359352E-01-3.889881994E-01-3.549133490E-01-3.203534446E-01-2.853523029E-01 --2.499554042E-01-2.142098330E-01-1.781642557E-01-1.418688202E-01-1.053751043E-01 --6.873786570E-02-3.201798926E-02 4.743535338E-03 4.157547855E-02 7.850519249E-02 - 1.155294182E-01 1.526413310E-01 1.898361959E-01 2.271097526E-01 2.644580649E-01 - 3.018775398E-01 3.393648949E-01 3.769171103E-01 4.145313330E-01 4.522051697E-01 - 4.899379924E-01 5.277203488E-01 1.589655131E-01 1.348061053E-01 1.107831151E-01 - 8.692562673E-02 6.323858547E-02 3.973332472E-02 1.643745148E-02-6.684838558E-03 --2.996308540E-02-5.362134692E-02-7.765879530E-02-1.020412157E-01-1.267422125E-01 --1.517345343E-01-1.769893149E-01-2.024766134E-01-2.281655714E-01-2.540245255E-01 --2.800211695E-01-3.061226474E-01-3.322956266E-01-3.585064988E-01-3.847213456E-01 --4.109061066E-01-4.370266873E-01-4.630489120E-01-4.889386876E-01-5.146620454E-01 --5.401850349E-01-5.654737569E-01-5.904944296E-01-6.152137564E-01-6.396000184E-01 --6.636249677E-01-6.872624696E-01-7.104873745E-01-7.332742985E-01-7.555967486E-01 --7.774263006E-01-7.987309942E-01-8.194765723E-01-8.396328658E-01-8.591836295E-01 --8.781170230E-01-8.964136745E-01-9.140437470E-01-9.309790546E-01-9.472056952E-01 --9.627093513E-01-9.774679610E-01-9.914622595E-01-1.004678405E+00-1.017098814E+00 --1.028708343E+00-1.039491813E+00-1.049435941E+00-1.058526248E+00-1.066750990E+00 --1.074096891E+00-1.080553062E+00-1.086107236E+00-1.090750767E+00-1.094470574E+00 --1.097261411E+00-1.099109052E+00-1.100009415E+00-1.099956202E+00-1.098932731E+00 --1.096939390E+00-1.093975409E+00-1.090028521E+00-1.085087711E+00-1.079152091E+00 --1.072221911E+00-1.064296278E+00-1.055374311E+00-1.045454852E+00-1.034534009E+00 --1.022606900E+00-1.009670719E+00-9.957254105E-01-9.807736208E-01-9.648204695E-01 --9.478734558E-01-9.299423609E-01-9.110389950E-01-8.911755987E-01-8.703609534E-01 --8.486016157E-01-8.259059225E-01-8.022847166E-01-7.777512153E-01-7.523209221E-01 --7.260115121E-01-6.988429236E-01-6.708371695E-01-6.420184175E-01-6.124128555E-01 --5.820487486E-01-5.509562872E-01-5.191677000E-01-4.867170873E-01-4.536404714E-01 --4.199757150E-01-3.857625498E-01-3.510424764E-01-3.158586882E-01-2.802560355E-01 --2.442808988E-01-2.079811770E-01-1.714065519E-01-1.346085353E-01-9.764041629E-02 --6.055960488E-02-2.342778699E-02 1.372730652E-02 5.094851368E-02 8.825635547E-02 - 1.256453451E-01 1.631099656E-01 2.006464060E-01 2.382511380E-01 2.759208964E-01 - 3.136527008E-01 3.514438274E-01 3.892917181E-01 4.271942398E-01 4.651508768E-01 - 5.031529945E-01 1.586951922E-01 1.342939792E-01 1.100177024E-01 8.589308421E-02 - 6.192473174E-02 3.812377528E-02 1.451646697E-02-8.947855284E-03-3.261710033E-02 --5.667933648E-02-8.112413029E-02-1.059184073E-01-1.310354271E-01-1.564473189E-01 --1.821246769E-01-2.080370512E-01-2.341531089E-01-2.604407436E-01-2.868672246E-01 --3.133993194E-01-3.400033315E-01-3.666452998E-01-3.932910388E-01-4.199062387E-01 --4.464565730E-01-4.729076968E-01-4.992254560E-01-5.253757953E-01-5.513248768E-01 --5.770391536E-01-6.024851912E-01-6.276297073E-01-6.524396472E-01-6.768827255E-01 --7.009287941E-01-7.245516308E-01-7.477269359E-01-7.704311227E-01-7.926398752E-01 --8.143270537E-01-8.354633824E-01-8.560154805E-01-8.759511384E-01-8.952500589E-01 --9.139019974E-01-9.318921828E-01-9.491932574E-01-9.657761640E-01-9.816265056E-01 --9.967310916E-01-1.011069272E+00-1.024622821E+00-1.037378194E+00-1.049318207E+00 --1.060429475E+00-1.070696588E+00-1.080107626E+00-1.088648643E+00-1.096307987E+00 --1.103073688E+00-1.108934861E+00-1.113880915E+00-1.117901300E+00-1.120987780E+00 --1.123129899E+00-1.124319210E+00-1.124552173E+00-1.123812182E+00-1.122097800E+00 --1.119408792E+00-1.115732835E+00-1.111058989E+00-1.105386389E+00-1.098715016E+00 --1.091043703E+00-1.082371449E+00-1.072696254E+00-1.062012419E+00-1.050314389E+00 --1.037599448E+00-1.023867827E+00-1.009122508E+00-9.933692130E-01-9.766161309E-01 --9.588737948E-01-9.401537925E-01-9.204642614E-01-8.998098153E-01-8.781962354E-01 --8.556318645E-01-8.321275211E-01-8.076962844E-01-7.823534476E-01-7.561165498E-01 --7.290051951E-01-7.010411446E-01-6.722481502E-01-6.426520254E-01-6.122805095E-01 --5.811633650E-01-5.493322005E-01-5.168205785E-01-4.836639110E-01-4.498995050E-01 --4.155664082E-01-3.807053810E-01-3.453587780E-01-3.095704245E-01-2.733859586E-01 --2.368529734E-01-2.000210026E-01-1.629414858E-01-1.256676284E-01-8.825461845E-02 --5.076289146E-02-1.325207099E-02 2.427110863E-02 6.185881144E-02 9.952176922E-02 - 1.372535433E-01 1.750500676E-01 2.129082868E-01 2.508253218E-01 2.887985388E-01 - 3.268255393E-01 3.649040648E-01 4.030322276E-01 4.412096094E-01 4.794283959E-01 - 1.584350873E-01 1.338015219E-01 1.092816966E-01 8.489998769E-02 6.066064897E-02 - 3.657465141E-02 1.266587590E-02-1.113180189E-02-3.517648980E-02-5.962533874E-02 --8.446025121E-02-1.096490932E-01-1.351647554E-01-1.609787242E-01-1.870610143E-01 --2.133806504E-01-2.399058195E-01-2.666039445E-01-2.934418475E-01-3.203858978E-01 --3.474020427E-01-3.744559747E-01-4.015132105E-01-4.285391467E-01-4.554992177E-01 --4.823589038E-01-5.090838800E-01-5.356399708E-01-5.619933393E-01-5.881104521E-01 --6.139580808E-01-6.395034430E-01-6.647139229E-01-6.895571475E-01-7.140010712E-01 --7.380147278E-01-7.615699757E-01-7.846428285E-01-8.072109812E-01-8.292523749E-01 --8.507435478E-01-8.716579867E-01-8.919647663E-01-9.116308383E-01-9.306308748E-01 --9.489547221E-01-9.665914533E-01-9.835176933E-01-9.997040693E-01-1.015134908E+00 --1.029798451E+00-1.043675257E+00-1.056747934E+00-1.069003564E+00-1.080425643E+00 --1.091001815E+00-1.100717230E+00-1.109559887E+00-1.117517885E+00-1.124579019E+00 --1.130732864E+00-1.135967835E+00-1.140275544E+00-1.143644462E+00-1.146067985E+00 --1.147534019E+00-1.148040736E+00-1.147572682E+00-1.146126100E+00-1.143701119E+00 --1.140285554E+00-1.135868722E+00-1.130449682E+00-1.124028049E+00-1.116602633E+00 --1.108172368E+00-1.098733516E+00-1.088278827E+00-1.076802633E+00-1.064302468E+00 --1.050779031E+00-1.036236116E+00-1.020680266E+00-1.004120753E+00-9.865685359E-01 --9.680314952E-01-9.485126789E-01-9.280154024E-01-9.065455799E-01-8.841117067E-01 --8.607245306E-01-8.363970687E-01-8.111445466E-01-7.849842614E-01-7.579356470E-01 --7.300200901E-01-7.012610210E-01-6.716837671E-01-6.413156440E-01-6.101857895E-01 --5.783253099E-01-5.457671418E-01-5.125460789E-01-4.786985783E-01-4.442627506E-01 --4.092780951E-01-3.737859116E-01-3.378295536E-01-3.014544222E-01-2.647079352E-01 --2.276394676E-01-1.903003213E-01-1.527436792E-01-1.150244262E-01-7.719995167E-02 --3.933444194E-02-1.479733209E-03 3.639069148E-02 7.432198790E-02 1.123165338E-01 - 1.503689742E-01 1.884764730E-01 2.266366084E-01 2.648470909E-01 3.031058279E-01 - 3.414108586E-01 3.797605600E-01 4.181546394E-01 4.565861080E-01 1.581851499E-01 - 1.333291712E-01 1.085760126E-01 8.394774776E-02 5.944831204E-02 3.508858629E-02 - 1.088931225E-02-1.323134746E-02-3.763513632E-02-6.245274397E-02-8.765999482E-02 --1.132254646E-01-1.391216610E-01-1.653195076E-01-1.917885008E-01-2.184971291E-01 --2.454130227E-01-2.725030841E-01-2.997336815E-01-3.270707832E-01-3.544799575E-01 --3.819265361E-01-4.093757340E-01-4.367926680E-01-4.641425260E-01-4.913905585E-01 --5.185022372E-01-5.454432741E-01-5.721797285E-01-5.986779935E-01-6.249049062E-01 --6.508277954E-01-6.764143651E-01-7.016328878E-01-7.264518248E-01-7.508399599E-01 --7.747665067E-01-7.982020984E-01-8.211209949E-01-8.435015851E-01-8.653236302E-01 --8.865663969E-01-9.072067182E-01-9.272166986E-01-9.465641821E-01-9.652198073E-01 --9.831704761E-01-1.000408622E+00-1.016915291E+00-1.032662251E+00-1.047632057E+00 --1.061813713E+00-1.075189520E+00-1.087742966E+00-1.099461379E+00-1.110329210E+00 --1.120334395E+00-1.129463830E+00-1.137705043E+00-1.145047237E+00-1.151478775E+00 --1.156989464E+00-1.161569647E+00-1.165208321E+00-1.167899424E+00-1.169629923E+00 --1.170397697E+00-1.170189345E+00-1.168998764E+00-1.166826417E+00-1.163660280E+00 --1.159489860E+00-1.154314159E+00-1.148132644E+00-1.140944167E+00-1.132747170E+00 --1.123535663E+00-1.113301432E+00-1.102038922E+00-1.089746300E+00-1.076425198E+00 --1.062080400E+00-1.046719883E+00-1.030353953E+00-1.012990575E+00-9.946316858E-01 --9.752782633E-01-9.549338688E-01-9.336047451E-01-9.112994241E-01-8.880287629E-01 --8.638057800E-01-8.386455906E-01-8.125653966E-01-7.855843208E-01-7.577234986E-01 --7.290059108E-01-6.994564800E-01-6.691019286E-01-6.379709430E-01-6.060939401E-01 --5.735030938E-01-5.402321079E-01-5.063160418E-01-4.717916260E-01-4.366976835E-01 --4.010751821E-01-3.649672094E-01-3.284189608E-01-2.914776742E-01-2.541925760E-01 --2.166148224E-01-1.787974553E-01-1.407953349E-01-1.026650460E-01-6.446697640E-02 --2.626697562E-02 1.190302397E-02 5.009845927E-02 8.834893147E-02 1.266517116E-01 - 1.650029998E-01 2.034007585E-01 2.418431038E-01 2.803282767E-01 3.188546293E-01 - 3.574208070E-01 3.960266336E-01 4.346659180E-01 1.579453306E-01 1.328772562E-01 - 1.079014643E-01 8.303777657E-02 5.828979576E-02 3.366831074E-02 9.190362807E-03 --1.524147857E-02-3.998733937E-02-6.515530985E-02-9.071649553E-02-1.166400418E-01 --1.428980977E-01-1.694610575E-01-1.962979032E-01-2.233766048E-01-2.506642899E-01 --2.781273717E-01-3.057317068E-01-3.334427531E-01-3.612256522E-01-3.890453903E-01 --4.168668913E-01-4.446549808E-01-4.723745889E-01-4.999907600E-01-5.274687734E-01 --5.547741729E-01-5.818728654E-01-6.087311652E-01-6.353158785E-01-6.615943101E-01 --6.875342906E-01-7.131042951E-01-7.382732435E-01-7.630107055E-01-7.872864302E-01 --8.110705577E-01-8.343337729E-01-8.570485763E-01-8.791919647E-01-9.007447743E-01 --9.216887737E-01-9.420041093E-01-9.616668669E-01-9.806469719E-01-9.989136133E-01 --1.016447818E+00-1.033243786E+00-1.049287906E+00-1.064553781E+00-1.079022212E+00 --1.092682969E+00-1.105519597E+00-1.117516547E+00-1.128661724E+00-1.138940553E+00 --1.148340566E+00-1.156850676E+00-1.164458605E+00-1.171153529E+00-1.176925457E+00 --1.181763414E+00-1.185658956E+00-1.188603079E+00-1.190585422E+00-1.191601224E+00 --1.191639917E+00-1.190693204E+00-1.188761582E+00-1.185833255E+00-1.181898107E+00 --1.176955091E+00-1.171003502E+00-1.164042311E+00-1.156068910E+00-1.147074834E+00 --1.137051403E+00-1.125993775E+00-1.113901107E+00-1.100776255E+00-1.086625770E+00 --1.071459239E+00-1.055284952E+00-1.038104276E+00-1.019916048E+00-1.000721532E+00 --9.805247951E-01-9.593322841E-01-9.371528122E-01-9.139973263E-01-8.898789022E-01 --8.648126219E-01-8.388154774E-01-8.119064078E-01-7.841061414E-01-7.554372990E-01 --7.259242833E-01-6.955933589E-01-6.644723467E-01-6.325906756E-01-5.999788661E-01 --5.666690421E-01-5.326953100E-01-4.980939954E-01-4.629036114E-01-4.271648494E-01 --3.909205834E-01-3.542157765E-01-3.170974493E-01-2.796146356E-01-2.418183193E-01 --2.037614048E-01-1.654986704E-01-1.270866311E-01-8.858377431E-02-5.005425730E-02 --1.155991123E-02 2.690287305E-02 6.540102459E-02 1.039466811E-01 1.425348904E-01 - 1.811635456E-01 2.198312040E-01 2.585364398E-01 2.972778952E-01 3.360544660E-01 - 3.748660900E-01 4.137073590E-01 1.577158540E-01 1.324464100E-01 1.072590842E-01 - 8.217152201E-02 5.718702616E-02 3.231633080E-02 7.572415987E-03-1.715738316E-02 --4.222757042E-02-6.772703521E-02-9.362328051E-02-1.198858497E-01-1.464865061E-01 --1.733951611E-01-2.005803565E-01-2.280096226E-01-2.556496222E-01-2.834662723E-01 --3.114249171E-01-3.394905306E-01-3.676278088E-01-3.958012755E-01-4.239754315E-01 --4.521147889E-01-4.801840679E-01-5.081481362E-01-5.359720783E-01-5.636212842E-01 --5.910615429E-01-6.182590594E-01-6.451805394E-01-6.717932288E-01-6.980649947E-01 --7.239643385E-01-7.494603612E-01-7.745229229E-01-7.991223936E-01-8.232298310E-01 --8.468164327E-01-8.698538479E-01-8.923144098E-01-9.141727566E-01-9.354088843E-01 --9.560060819E-01-9.759477973E-01-9.952141588E-01-1.013779236E+00-1.031612165E+00 --1.048688200E+00-1.065000746E+00-1.080540636E+00-1.095285300E+00-1.109213610E+00 --1.122315583E+00-1.134576460E+00-1.145981410E+00-1.156518428E+00-1.166174490E+00 --1.174937169E+00-1.182795714E+00-1.189739449E+00-1.195757301E+00-1.200839594E+00 --1.204977613E+00-1.208160590E+00-1.210381621E+00-1.211632157E+00-1.211904737E+00 --1.211189197E+00-1.209485951E+00-1.206783480E+00-1.203071998E+00-1.198350377E+00 --1.192618042E+00-1.185874011E+00-1.178113406E+00-1.169325854E+00-1.159502971E+00 --1.148640962E+00-1.136740470E+00-1.123806394E+00-1.109847485E+00-1.094872476E+00 --1.078882765E+00-1.061875317E+00-1.043849143E+00-1.024806213E+00-1.004751038E+00 --9.836905064E-01-9.616336480E-01-9.385916514E-01-9.145776180E-01-8.896065654E-01 --8.636953490E-01-8.368625775E-01-8.091286991E-01-7.805158614E-01-7.510478375E-01 --7.207497661E-01-6.896478743E-01-6.577695940E-01-6.251443714E-01-5.918037527E-01 --5.577815551E-01-5.231138039E-01-4.878387429E-01-4.519968220E-01-4.156306014E-01 --3.787847911E-01-3.415061843E-01-3.038436170E-01-2.658479073E-01-2.275717956E-01 --1.890698974E-01-1.503986699E-01-1.116162418E-01-7.278366473E-02-3.396929219E-02 - 4.781399159E-03 4.352330379E-02 8.230188793E-02 1.211187250E-01 1.599703702E-01 - 1.988556007E-01 2.377733708E-01 2.767226183E-01 3.157024919E-01 3.547130496E-01 - 3.937496282E-01 1.574968880E-01 1.320371209E-01 1.066497885E-01 8.135043765E-02 - 5.614205495E-02 3.103529724E-02 6.038862687E-03-1.897455366E-02-4.435079719E-02 --7.016244541E-02-9.637431009E-02-1.229562377E-01-1.498796591E-01-1.771140736E-01 --2.046276064E-01-2.323873438E-01-2.603595007E-01-2.885095725E-01-3.168024889E-01 --3.452027946E-01-3.736747237E-01-4.021823054E-01-4.306895899E-01-4.591606960E-01 --4.875599481E-01-5.158519031E-01-5.440014692E-01-5.719739775E-01-5.997351505E-01 --6.272510914E-01-6.544884595E-01-6.814144534E-01-7.079969038E-01-7.342042675E-01 --7.600057233E-01-7.853712059E-01-8.102713204E-01-8.346775015E-01-8.585617447E-01 --8.818967368E-01-9.046552398E-01-9.268105173E-01-9.483366965E-01-9.692108490E-01 --9.894161135E-01-1.008938105E+00-1.027761257E+00-1.045864324E+00-1.063218893E+00 --1.079796788E+00-1.095586413E+00-1.110582535E+00-1.124766972E+00-1.138117813E+00 --1.150624983E+00-1.162274758E+00-1.173053356E+00-1.182948936E+00-1.191949847E+00 --1.200044017E+00-1.207220762E+00-1.213470092E+00-1.218782327E+00-1.223147340E+00 --1.226556077E+00-1.229001679E+00-1.230473342E+00-1.230966321E+00-1.230469007E+00 --1.228981444E+00-1.226492347E+00-1.222992416E+00-1.218480565E+00-1.212956389E+00 --1.206418489E+00-1.198858940E+00-1.190266333E+00-1.180633180E+00-1.169957410E+00 --1.158241946E+00-1.145494485E+00-1.131724218E+00-1.116933168E+00-1.101116813E+00 --1.084271932E+00-1.066398484E+00-1.047499177E+00-1.027579123E+00-1.006645620E+00 --9.847081161E-01-9.617779004E-01-9.378681867E-01-9.129938830E-01-8.871716676E-01 --8.604199181E-01-8.327584929E-01-8.042085795E-01-7.747922026E-01-7.445323627E-01 --7.134538201E-01-6.815834605E-01-6.489503358E-01-6.155857647E-01-5.815232862E-01 --5.467986324E-01-5.114497525E-01-4.755167372E-01-4.390419163E-01-4.020697313E-01 --3.646467162E-01-3.268214787E-01-2.886446335E-01-2.501687571E-01-2.114483248E-01 --1.725396681E-01-1.335008588E-01-9.439183109E-02-5.527774824E-02-1.622446300E-02 - 2.276311834E-02 6.176471275E-02 1.008001656E-01 1.398656204E-01 1.789595650E-01 - 2.180813154E-01 2.572300999E-01 2.964052890E-01 3.356070346E-01 3.748313677E-01 - 1.572890058E-01 1.316502725E-01 1.060747604E-01 8.057601941E-02 5.515674932E-02 - 2.982755059E-02 4.592773096E-03-2.068878703E-02-4.635219714E-02-7.245627303E-02 --9.896390232E-02-1.258451343E-01-1.530710513E-01-1.806107480E-01-2.084319706E-01 --2.365014342E-01-2.647849965E-01-2.932477917E-01-3.218543427E-01-3.505687594E-01 --3.793548721E-01-4.081763266E-01-4.369967882E-01-4.657799636E-01-4.944897108E-01 --5.230901701E-01-5.515459093E-01-5.798219461E-01-6.078838246E-01-6.356976262E-01 --6.632301117E-01-6.904485038E-01-7.173206390E-01-7.438149967E-01-7.699007957E-01 --7.955479528E-01-8.207271606E-01-8.454099678E-01-8.695686550E-01-8.931763781E-01 --9.162068772E-01-9.386345584E-01-9.604338196E-01-9.815796015E-01-1.002047940E+00 --1.021818681E+00-1.040878106E+00-1.059213764E+00-1.076809786E+00-1.093642095E+00 --1.109682252E+00-1.124911276E+00-1.139325818E+00-1.152912742E+00-1.165650167E+00 --1.177527696E+00-1.188532734E+00-1.198652213E+00-1.207874356E+00-1.216188612E+00 --1.223583957E+00-1.230049901E+00-1.235576528E+00-1.240154405E+00-1.243775321E+00 --1.246430399E+00-1.248109878E+00-1.248809514E+00-1.248517021E+00-1.247232033E+00 --1.244943532E+00-1.241642716E+00-1.237328567E+00-1.232001004E+00-1.225657295E+00 --1.218286204E+00-1.209876316E+00-1.200421975E+00-1.189923609E+00-1.178387538E+00 --1.165823270E+00-1.152234025E+00-1.137614268E+00-1.121958601E+00-1.105265042E+00 --1.087534625E+00-1.068770843E+00-1.048979465E+00-1.028168361E+00-1.006347226E+00 --9.835276256E-01-9.597227228E-01-9.349474448E-01-9.092180646E-01-8.825520765E-01 --8.549676555E-01-8.264835450E-01-7.971200615E-01-7.668995028E-01-7.358462919E-01 --7.039870833E-01-6.713507101E-01-6.379682121E-01-6.038727667E-01-5.690998293E-01 --5.336870012E-01-4.976741344E-01-4.611032037E-01-4.240183564E-01-3.864659002E-01 --3.484942006E-01-3.101536585E-01-2.714966576E-01-2.325774979E-01-1.934523548E-01 --1.541792315E-01-1.148177789E-01-7.543039783E-02-3.608732695E-02 3.162924918E-03 - 4.238167310E-02 8.162360874E-02 1.208924992E-01 1.601853214E-01 1.995014994E-01 - 2.388405814E-01 2.782021538E-01 3.175864633E-01 3.569901872E-01 1.570926787E-01 - 1.312865889E-01 1.055350713E-01 7.984977994E-02 5.423311899E-02 2.869560713E-02 - 3.237265559E-03-2.229613475E-02-4.822746939E-02-7.460393251E-02-1.013870656E-01 --1.285470446E-01-1.560546424E-01-1.838786289E-01-2.119864412E-01-2.403444568E-01 --2.689181720E-01-2.976723600E-01-3.265711927E-01-3.555784389E-01-3.846576188E-01 --4.137720479E-01-4.428849970E-01-4.719597812E-01-5.009599022E-01-5.298491558E-01 --5.585917469E-01-5.871522718E-01-6.154958917E-01-6.435883891E-01-6.713963104E-01 --6.988868376E-01-7.260279749E-01-7.527884293E-01-7.791375576E-01-8.050453376E-01 --8.304825942E-01-8.554209142E-01-8.798326662E-01-9.036911329E-01-9.269703761E-01 --9.496453806E-01-9.716916972E-01-9.930854844E-01-1.013802805E+00-1.033820312E+00 --1.053116050E+00-1.071673004E+00-1.089480416E+00-1.106526793E+00-1.122794281E+00 --1.138256476E+00-1.152889099E+00-1.166686489E+00-1.179639808E+00-1.191729512E+00 --1.202944181E+00-1.213271849E+00-1.222700705E+00-1.231219265E+00-1.238817170E+00 --1.245484307E+00-1.251210804E+00-1.255987408E+00-1.259805209E+00-1.262654785E+00 --1.264528753E+00-1.265420886E+00-1.265319629E+00-1.264223905E+00-1.262122831E+00 --1.259008248E+00-1.254879502E+00-1.249736654E+00-1.243574000E+00-1.236378000E+00 --1.228138431E+00-1.218852374E+00-1.208524235E+00-1.197163541E+00-1.184775184E+00 --1.171353202E+00-1.156890116E+00-1.141382072E+00-1.124828535E+00-1.107231570E+00 --1.088595618E+00-1.068927161E+00-1.048234548E+00-1.026527874E+00-1.003818828E+00 --9.801205579E-01-9.554471409E-01-9.298133318E-01-9.032338916E-01-8.757249854E-01 --8.473045055E-01-8.179924656E-01-7.878109653E-01-7.567843155E-01-7.249388520E-01 --6.923031514E-01-6.589078911E-01-6.247860296E-01-5.899726134E-01-5.545049682E-01 --5.184225938E-01-4.817671822E-01-4.445826213E-01-4.069148923E-01-3.688121086E-01 --3.303244522E-01-2.915041031E-01-2.524051900E-01-2.130837286E-01-1.735975793E-01 --1.340063212E-01-9.437143092E-02-5.475996833E-02-1.523848488E-02 2.419521859E-02 - 6.363189875E-02 1.030925335E-01 1.425733691E-01 1.820735370E-01 2.215928688E-01 - 2.611311488E-01 3.006886903E-01 3.402627456E-01 1.569088948E-01 1.309472535E-01 - 1.050320898E-01 7.917328479E-02 5.337297668E-02 2.764160635E-02 1.974990382E-03 --2.379309953E-02-4.997264448E-02-7.660109014E-02-1.036391211E-01-1.310569995E-01 --1.588252015E-01-1.869121777E-01-2.152850568E-01-2.439099083E-01-2.727519229E-01 --3.017755955E-01-3.309448380E-01-3.602231238E-01-3.895736467E-01-4.189593968E-01 --4.483433272E-01-4.776884665E-01-5.069580549E-01-5.361155798E-01-5.651248805E-01 --5.939502051E-01-6.225563992E-01-6.509089149E-01-6.789739403E-01-7.067183000E-01 --7.341097488E-01-7.611168505E-01-7.877091113E-01-8.138568308E-01-8.395312298E-01 --8.647040688E-01-8.893478944E-01-9.134361234E-01-9.369429359E-01-9.598434414E-01 --9.821135174E-01-1.003730030E+00-1.024670356E+00-1.044912389E+00-1.064433850E+00 --1.083213121E+00-1.101230388E+00-1.118472085E+00-1.134929838E+00-1.150591506E+00 --1.165435928E+00-1.179437463E+00-1.192583607E+00-1.204869303E+00-1.216278083E+00 --1.226797839E+00-1.236417131E+00-1.245125021E+00-1.252910499E+00-1.259763519E+00 --1.265674569E+00-1.270634418E+00-1.274633937E+00-1.277664492E+00-1.279718906E+00 --1.280788938E+00-1.280865098E+00-1.279944971E+00-1.278017880E+00-1.275076458E+00 --1.271120497E+00-1.266149639E+00-1.260154035E+00-1.253119320E+00-1.245037870E+00 --1.235911275E+00-1.225748566E+00-1.214556595E+00-1.202329709E+00-1.189058508E+00 --1.174737292E+00-1.159364081E+00-1.142939719E+00-1.125467528E+00-1.106952846E+00 --1.087402926E+00-1.066826656E+00-1.045234326E+00-1.022637135E+00-9.990466865E-01 --9.744742938E-01-9.489321499E-01-9.224341582E-01-8.949960472E-01-8.666357375E-01 --8.373730706E-01-8.072300198E-01-7.762305404E-01-7.444008132E-01-7.117690255E-01 --6.783656033E-01-6.442231052E-01-6.093763277E-01-5.738622523E-01-5.377200230E-01 --5.009910488E-01-4.637188638E-01-4.259492065E-01-3.877299387E-01-3.491109746E-01 --3.101442687E-01-2.708837555E-01-2.313852835E-01-1.917065674E-01-1.519071191E-01 --1.120480906E-01-7.219377198E-02-3.241618135E-02 7.243358063E-03 4.686632981E-02 - 8.650526450E-02 1.261623983E-01 1.658354211E-01 2.055242242E-01 2.452288077E-01 - 2.849495409E-01 3.246841860E-01 1.567385087E-01 1.306332896E-01 1.045670814E-01 - 7.854811474E-02 5.257826327E-02 2.666788919E-02 8.088032936E-04-2.517632971E-02 --5.158421325E-02-7.844413682E-02-1.057162856E-01-1.333709448E-01-1.613783131E-01 --1.897065655E-01-2.183225837E-01-2.471922004E-01-2.762803561E-01-3.055512758E-01 --3.349686005E-01-3.644955301E-01-3.940949893E-01-4.237297304E-01-4.533624960E-01 --4.829560851E-01-5.124734578E-01-5.418778102E-01-5.711327097E-01-6.002021646E-01 --6.290507981E-01-6.576437635E-01-6.859469179E-01-7.139267628E-01-7.415507472E-01 --7.687871097E-01-7.956050630E-01-8.219746619E-01-8.478670927E-01-8.732544139E-01 --8.981097151E-01-9.224068870E-01-9.461203902E-01-9.692255130E-01-9.916983465E-01 --1.013515900E+00-1.034655872E+00-1.055096985E+00-1.074818416E+00-1.093799727E+00 --1.112020264E+00-1.129460156E+00-1.146101914E+00-1.161935526E+00-1.176953762E+00 --1.191141900E+00-1.204477135E+00-1.216939541E+00-1.228525213E+00-1.239221501E+00 --1.249015526E+00-1.257896320E+00-1.265853968E+00-1.272877835E+00-1.278958375E+00 --1.284086638E+00-1.288253530E+00-1.291450744E+00-1.293670401E+00-1.294903700E+00 --1.295143313E+00-1.294384934E+00-1.292618126E+00-1.289836522E+00-1.286040479E+00 --1.281227861E+00-1.275384507E+00-1.268497246E+00-1.260563299E+00-1.251590332E+00 --1.241587130E+00-1.230549265E+00-1.218465663E+00-1.205328753E+00-1.191135245E+00 --1.175885003E+00-1.159580466E+00-1.142226148E+00-1.123828479E+00-1.104395282E+00 --1.083935270E+00-1.062457411E+00-1.039969927E+00-1.016481523E+00-9.920023061E-01 --9.665441881E-01-9.401210424E-01-9.127486882E-01-8.844448265E-01-8.552292039E-01 --8.251235049E-01-7.941514716E-01-7.623389242E-01-7.297138133E-01-6.963062322E-01 --6.621483878E-01-6.272747570E-01-5.917219340E-01-5.555288258E-01-5.187364573E-01 --4.813880729E-01-4.435291127E-01-4.052071262E-01-3.664718064E-01-3.273749009E-01 --2.879701370E-01-2.483131777E-01-2.084615679E-01-1.684746880E-01-1.284135894E-01 --8.834147449E-02-4.832851695E-02-8.436899276E-03 3.136426637E-02 7.116784059E-02 - 1.109888197E-01 1.508229100E-01 1.906698201E-01 2.305297639E-01 2.704031505E-01 - 3.102881726E-01 1.565829689E-01 1.303462146E-01 1.041416269E-01 7.797591723E-02 - 5.185070160E-02 2.577651817E-02-2.583491243E-04-2.644295388E-02-5.305922859E-02 --8.012989039E-02-1.076151555E-01-1.354852940E-01-1.637102588E-01-1.922579838E-01 --2.210951098E-01-2.501872293E-01-2.794990457E-01-3.089945495E-01-3.386371604E-01 --3.683898820E-01-3.982154583E-01-4.280764481E-01-4.579353715E-01-4.877547999E-01 --5.174974699E-01-5.471263734E-01-5.766049212E-01-6.058969495E-01-6.349668550E-01 --6.637795396E-01-6.923006255E-01-7.204964056E-01-7.483341154E-01-7.757816949E-01 --8.028080446E-01-8.293828810E-01-8.554770989E-01-8.810624899E-01-9.061119503E-01 --9.305993757E-01-9.544997526E-01-9.777890479E-01-1.000443979E+00-1.022441826E+00 --1.043760536E+00-1.064379082E+00-1.084276987E+00-1.103434760E+00-1.121833302E+00 --1.139453732E+00-1.156276974E+00-1.172284933E+00-1.187462694E+00-1.201803418E+00 --1.215299105E+00-1.227931880E+00-1.239679908E+00-1.250534982E+00-1.260488183E+00 --1.269526850E+00-1.277640436E+00-1.284819585E+00-1.291054618E+00-1.296336332E+00 --1.300655700E+00-1.304004457E+00-1.306374300E+00-1.307756910E+00-1.308145786E+00 --1.307534942E+00-1.305914478E+00-1.303279284E+00-1.299630013E+00-1.294960539E+00 --1.289254180E+00-1.282501783E+00-1.274708105E+00-1.265883452E+00-1.256025582E+00 --1.245122138E+00-1.233163634E+00-1.220145621E+00-1.206067257E+00-1.190930400E+00 --1.174739142E+00-1.157499254E+00-1.139217340E+00-1.119900237E+00-1.099553554E+00 --1.078182902E+00-1.055794978E+00-1.032398195E+00-1.008002771E+00-9.826207773E-01 --9.562660492E-01-9.289543297E-01-9.007031359E-01-8.715319963E-01-8.414623439E-01 --8.105176968E-01-7.787235067E-01-7.461074558E-01-7.126992403E-01-6.785308407E-01 --6.436362961E-01-6.080519238E-01-5.718162363E-01-5.349699457E-01-4.975560379E-01 --4.596196074E-01-4.212079477E-01-3.823704924E-01-3.431587289E-01-3.036261806E-01 --2.638283418E-01-2.238226018E-01-1.836681983E-01-1.434261212E-01-1.031591071E-01 --6.293433021E-02-2.282332864E-02 1.715729034E-02 5.711520765E-02 9.708665458E-02 - 1.370695516E-01 1.770628566E-01 2.170668280E-01 2.570819085E-01 2.971066478E-01 - 1.564436513E-01 1.300874579E-01 1.037572577E-01 7.745837275E-02 5.119214662E-02 - 2.496963358E-02-1.223811875E-03-2.759026797E-02-5.439505556E-02-8.165578687E-02 --1.093332388E-01-1.373975905E-01-1.658185407E-01-1.945638071E-01-2.235998211E-01 --2.528919711E-01-2.824047728E-01-3.121020420E-01-3.419470276E-01-3.719025466E-01 --4.019311523E-01-4.319952203E-01-4.620570900E-01-4.920791674E-01-5.220240609E-01 --5.518546465E-01-5.815341956E-01-6.110263703E-01-6.402953900E-01-6.693059895E-01 --6.980236608E-01-7.264145742E-01-7.544457839E-01-7.820850159E-01-8.093009658E-01 --8.360631305E-01-8.623421693E-01-8.881095524E-01-9.133378478E-01-9.380005978E-01 --9.620725839E-01-9.855295623E-01-1.008348373E+00-1.030506952E+00-1.051984162E+00 --1.072759631E+00-1.092813199E+00-1.112125676E+00-1.130678454E+00-1.148453750E+00 --1.165434084E+00-1.181601969E+00-1.196939868E+00-1.211431527E+00-1.225064766E+00 --1.237834770E+00-1.249730776E+00-1.260733701E+00-1.270828378E+00-1.280009540E+00 --1.288264184E+00-1.295582893E+00-1.301956987E+00-1.307376920E+00-1.311833441E+00 --1.315318441E+00-1.317823829E+00-1.319341668E+00-1.319865213E+00-1.319387535E+00 --1.317899378E+00-1.315396952E+00-1.311880468E+00-1.307338096E+00-1.301754030E+00 --1.295127392E+00-1.287468956E+00-1.278779538E+00-1.269046056E+00-1.258257102E+00 --1.246407251E+00-1.233495292E+00-1.219522962E+00-1.204494191E+00-1.188413960E+00 --1.171287352E+00-1.153117993E+00-1.133908712E+00-1.113663282E+00-1.092386902E+00 --1.070086590E+00-1.046770967E+00-1.022450459E+00-9.971370403E-01-9.708445319E-01 --9.435884366E-01-9.153861899E-01-8.862569668E-01-8.562220237E-01-8.253044981E-01 --7.935296453E-01-7.609247090E-01-7.275191110E-01-6.933444416E-01-6.584344314E-01 --6.228250916E-01-5.865545318E-01-5.496632030E-01-5.121937129E-01-4.741908811E-01 --4.357017615E-01-3.967755011E-01-3.574633586E-01-3.178186627E-01-2.778967139E-01 --2.377547279E-01-1.974517942E-01-1.570488140E-01-1.166082895E-01-7.619567054E-02 --3.588525628E-02 4.277050455E-03 4.437899822E-02 8.448703524E-02 1.246061803E-01 - 1.647338320E-01 2.048701043E-01 2.450154552E-01 2.851687098E-01 1.563223535E-01 - 1.298588266E-01 1.034157591E-01 7.699723957E-02 5.060438591E-02 2.424863823E-02 --2.087362487E-03-2.861665287E-02-5.558973238E-02-8.301997521E-02-1.108687084E-01 --1.391060174E-01-1.677013789E-01-1.966223271E-01-2.258351191E-01-2.553049669E-01 --2.849962061E-01-3.148724754E-01-3.448968566E-01-3.750320069E-01-4.052403267E-01 --4.354840557E-01-4.657254207E-01-4.959267278E-01-5.260504802E-01-5.560594292E-01 --5.859167186E-01-6.155858906E-01-6.450310608E-01-6.742168927E-01-7.031088175E-01 --7.316729070E-01-7.598760838E-01-7.876859513E-01-8.150710900E-01-8.420008811E-01 --8.684458342E-01-8.943772305E-01-9.197674420E-01-9.445897246E-01-9.688185577E-01 --9.924293356E-01-1.015398551E+00-1.037703850E+00-1.059323944E+00-1.080238620E+00 --1.100428588E+00-1.119875703E+00-1.138562097E+00-1.156470342E+00-1.173583562E+00 --1.189885656E+00-1.205360656E+00-1.219992334E+00-1.233764654E+00-1.246663220E+00 --1.258678493E+00-1.269805843E+00-1.280031985E+00-1.289338038E+00-1.297719141E+00 --1.305162394E+00-1.311659776E+00-1.317202529E+00-1.321781158E+00-1.325387810E+00 --1.328014126E+00-1.329652324E+00-1.330295535E+00-1.329936446E+00-1.328566481E+00 --1.326183057E+00-1.322783958E+00-1.318352303E+00-1.312878971E+00-1.306372780E+00 --1.298838154E+00-1.290262054E+00-1.280631244E+00-1.269939567E+00-1.258185943E+00 --1.245372444E+00-1.231502746E+00-1.216580668E+00-1.200608369E+00-1.183586388E+00 --1.165515882E+00-1.146399318E+00-1.126240789E+00-1.105046016E+00-1.082822236E+00 --1.059578222E+00-1.035324324E+00-1.010072507E+00-9.838363762E-01-9.566313018E-01 --9.284744421E-01-8.993847608E-01-8.693831707E-01-8.384925127E-01-8.067377412E-01 --7.741457454E-01-7.407456612E-01-7.065686374E-01-6.716481549E-01-6.360198095E-01 --5.997214645E-01-5.627932398E-01-5.252774002E-01-4.872185312E-01-4.486633636E-01 --4.096607826E-01-3.702618469E-01-3.305196659E-01-2.904893488E-01-2.502279585E-01 --2.097944487E-01-1.692496077E-01-1.286558673E-01-8.807791851E-02-4.758808203E-02 --7.247779135E-03 3.298686189E-02 7.321773539E-02 1.134601922E-01 1.537095419E-01 - 1.939656134E-01 2.342288774E-01 2.744984061E-01 1.562193343E-01 1.296609600E-01 - 1.031181156E-01 7.659379951E-02 5.008894883E-02 2.361519945E-02-2.847331370E-03 --2.952019148E-02-5.664146063E-02-8.422093744E-02-1.122203649E-01-1.406097248E-01 --1.693582816E-01-1.984333878E-01-2.278011273E-01-2.574265459E-01-2.872738210E-01 --3.173064411E-01-3.474873509E-01-3.777790849E-01-4.081439330E-01-4.385440366E-01 --4.689415227E-01-4.992985908E-01-5.295776421E-01-5.597413368E-01-5.897527423E-01 --6.195753427E-01-6.491732160E-01-6.785109999E-01-7.075540723E-01-7.362684365E-01 --7.646209547E-01-7.925791858E-01-8.201116757E-01-8.471877640E-01-8.737778878E-01 --8.998532426E-01-9.253861174E-01-9.503496244E-01-9.747180751E-01-9.984666784E-01 --1.021571685E+00-1.044010322E+00-1.065760916E+00-1.086802869E+00-1.107116569E+00 --1.126683634E+00-1.145486470E+00-1.163508657E+00-1.180734531E+00-1.197148857E+00 --1.212736342E+00-1.227482389E+00-1.241372490E+00-1.254391629E+00-1.266525308E+00 --1.277760784E+00-1.288090704E+00-1.297508728E+00-1.305999545E+00-1.313553071E+00 --1.320158484E+00-1.325808616E+00-1.330494361E+00-1.334207510E+00-1.336939826E+00 --1.338683674E+00-1.339431629E+00-1.339176491E+00-1.337910632E+00-1.335632096E+00 --1.332333316E+00-1.327997998E+00-1.322628909E+00-1.316233646E+00-1.308800302E+00 --1.300314077E+00-1.290768497E+00-1.280163239E+00-1.268500761E+00-1.255784091E+00 --1.242014448E+00-1.227190563E+00-1.211311337E+00-1.194376893E+00-1.176388814E+00 --1.157350298E+00-1.137265841E+00-1.116141423E+00-1.093984309E+00-1.070803302E+00 --1.046608615E+00-1.021412118E+00-9.952271585E-01-9.680689376E-01-9.399542732E-01 --9.109019387E-01-8.809324407E-01-8.500683911E-01-8.183343134E-01-7.857568743E-01 --7.523648113E-01-7.181889867E-01-6.832625292E-01-6.476206593E-01-6.113009750E-01 --5.743432085E-01-5.367893915E-01-4.986838200E-01-4.600729324E-01-4.210054170E-01 --3.815320874E-01-3.417058215E-01-3.015815671E-01-2.612162696E-01-2.206687888E-01 --1.799998497E-01-1.392719146E-01-9.854935302E-02-5.790205696E-02-1.740001597E-02 - 2.296141444E-02 6.330305417E-02 1.036547682E-01 1.440122756E-01 1.843748372E-01 - 2.247428696E-01 2.651156839E-01 1.561336902E-01 1.294933142E-01 1.028641573E-01 - 7.624826752E-02 4.964643097E-02 2.307035546E-02-3.502106361E-03-3.029913741E-02 --5.754846307E-02-8.525692516E-02-1.133865869E-01-1.419073180E-01-1.707881774E-01 --1.999963348E-01-2.294976999E-01-2.592571521E-01-2.892387116E-01-3.194057204E-01 --3.497209896E-01-3.801469291E-01-4.106457134E-01-4.411793839E-01-4.717099775E-01 --5.021996107E-01-5.326106158E-01-5.629055983E-01-5.930475871E-01-6.230000445E-01 --6.527270317E-01-6.821931671E-01-7.113638005E-01-7.402049249E-01-7.686833989E-01 --7.967667971E-01-8.244236848E-01-8.516234107E-01-8.783364045E-01-9.045338565E-01 --9.301880608E-01-9.552721059E-01-9.797602435E-01-1.003627614E+00-1.026850421E+00 --1.049405729E+00-1.071271635E+00-1.092427262E+00-1.112852627E+00-1.132528793E+00 --1.151437747E+00-1.169562652E+00-1.186887513E+00-1.203397405E+00-1.219078202E+00 --1.233916810E+00-1.247900024E+00-1.261014507E+00-1.273247005E+00-1.284583856E+00 --1.295012183E+00-1.304520336E+00-1.313102207E+00-1.320750460E+00-1.327449002E+00 --1.333191427E+00-1.337969222E+00-1.341773625E+00-1.344596839E+00-1.346431183E+00 --1.347269279E+00-1.347103533E+00-1.345927432E+00-1.343738444E+00-1.340523245E+00 --1.336275331E+00-1.331002604E+00-1.324695634E+00-1.317338738E+00-1.308925785E+00 --1.299457465E+00-1.288936294E+00-1.277363207E+00-1.264735547E+00-1.251050406E+00 --1.236305856E+00-1.220501453E+00-1.203638185E+00-1.185718357E+00-1.166745429E+00 --1.146724136E+00-1.125660418E+00-1.103561561E+00-1.080436182E+00-1.056294404E+00 --1.031147805E+00-1.005009573E+00-9.778945692E-01-9.498193792E-01-9.208024367E-01 --8.908639609E-01-8.600262195E-01-8.283133443E-01-7.957517109E-01-7.623696496E-01 --7.281977926E-01-6.932688712E-01-6.576178498E-01-6.212819514E-01-5.843005640E-01 --5.467154945E-01-5.085707393E-01-4.699125540E-01-4.307894785E-01-3.912521769E-01 --3.513534450E-01-3.111481786E-01-2.706932688E-01-2.300475354E-01-1.892716825E-01 --1.484282021E-01-1.075812866E-01-6.679929611E-02-2.615684125E-02 1.432405678E-02 - 5.476398634E-02 9.521027650E-02 1.356617672E-01 1.761169062E-01 2.165759803E-01 - 2.570385265E-01 1.560640472E-01 1.293548789E-01 1.026532827E-01 7.596050001E-02 - 4.927718712E-02 2.261504123E-02-4.050045556E-03-3.095135169E-02-5.830817703E-02 --8.612499047E-02-1.143641111E-01-1.429953105E-01-1.719874736E-01-2.013076119E-01 --2.309214797E-01-2.607938015E-01-2.908884438E-01-3.211685967E-01-3.515969239E-01 --3.821356924E-01-4.127469405E-01-4.433925810E-01-4.740345354E-01-5.046348258E-01 --5.351557079E-01-5.655597249E-01-5.958098587E-01-6.258695388E-01-6.557028031E-01 --6.852742641E-01-7.145492865E-01-7.434938952E-01-7.720749744E-01-8.002601434E-01 --8.280180129E-01-8.553179766E-01-8.821305084E-01-9.084268624E-01-9.341794117E-01 --9.593613254E-01-9.839469060E-01-1.007911303E+00-1.031230774E+00-1.053882419E+00 --1.075844318E+00-1.097095476E+00-1.117615827E+00-1.137386254E+00-1.156388410E+00 --1.174604985E+00-1.192019412E+00-1.208616181E+00-1.224380632E+00-1.239299142E+00 --1.253358830E+00-1.266547832E+00-1.278855118E+00-1.290269163E+00-1.300777649E+00 --1.310368309E+00-1.319029928E+00-1.326751433E+00-1.333528216E+00-1.339347469E+00 --1.344202152E+00-1.348082970E+00-1.350982075E+00-1.352891898E+00-1.353805121E+00 --1.353714244E+00-1.352613191E+00-1.350496988E+00-1.347353152E+00-1.343185208E+00 --1.337986860E+00-1.331742987E+00-1.324448218E+00-1.316104084E+00-1.306711924E+00 --1.296268261E+00-1.284768745E+00-1.272209808E+00-1.258589326E+00-1.243906559E+00 --1.228161952E+00-1.211356942E+00-1.193494056E+00-1.174576825E+00-1.154609974E+00 --1.133599311E+00-1.111551991E+00-1.088476399E+00-1.064382441E+00-1.039281338E+00 --1.013186027E+00-9.861109694E-01-9.580725106E-01-9.290886790E-01-8.991794649E-01 --8.683666914E-01-8.366741689E-01-8.041278587E-01-7.707557767E-01-7.365882779E-01 --7.016577825E-01-6.659991120E-01-6.296492620E-01-5.926475284E-01-5.550355719E-01 --5.168572310E-01-4.781587004E-01-4.389884000E-01-3.993969002E-01-3.594369596E-01 --3.191634281E-01-2.786331534E-01-2.379049284E-01-1.970394402E-01-1.560991913E-01 --1.151482846E-01-7.425415289E-02-3.349334136E-02 7.094635283E-03 4.761887112E-02 - 8.814465605E-02 1.286753754E-01 1.692085901E-01 2.097444209E-01 2.502826072E-01 - 1.560095614E-01 1.292450256E-01 1.024851048E-01 7.573038648E-02 4.898142322E-02 - 2.224986080E-02-4.490020599E-03-3.147529203E-02-5.891864627E-02-8.682271254E-02 --1.151500100E-01-1.438702328E-01-1.729521301E-01-2.023625903E-01-2.320672469E-01 --2.620307049E-01-2.922167123E-01-3.225883417E-01-3.531081424E-01-3.837382694E-01 --4.144406496E-01-4.451770866E-01-4.759093949E-01-5.065994949E-01-5.372095468E-01 --5.677020024E-01-5.980397559E-01-6.281861531E-01-6.581051505E-01-6.877612920E-01 --7.171198810E-01-7.461469124E-01-7.748092681E-01-8.030745911E-01-8.309115255E-01 --8.582895142E-01-8.851790940E-01-9.115516164E-01-9.373795816E-01-9.626362999E-01 --9.872961970E-01-1.011334503E+00-1.034727566E+00-1.057452599E+00-1.079487831E+00 --1.100812360E+00-1.121406193E+00-1.141250268E+00-1.160326309E+00-1.178616943E+00 --1.196105430E+00-1.212775976E+00-1.228613405E+00-1.243603396E+00-1.257732367E+00 --1.270987664E+00-1.283357450E+00-1.294830648E+00-1.305397201E+00-1.315047724E+00 --1.323771486E+00-1.331557312E+00-1.338395417E+00-1.344274718E+00-1.349191168E+00 --1.353133307E+00-1.356093077E+00-1.358063282E+00-1.359036566E+00-1.359005953E+00 --1.357964896E+00-1.355905974E+00-1.352824463E+00-1.348716304E+00-1.343568420E+00 --1.337376437E+00-1.330142010E+00-1.321861765E+00-1.312530307E+00-1.302142883E+00 --1.290696067E+00-1.278187840E+00-1.264617157E+00-1.249983855E+00-1.234288557E+00 --1.217532786E+00-1.199718909E+00-1.180850317E+00-1.160931413E+00-1.139967799E+00 --1.117966304E+00-1.094935080E+00-1.070883652E+00-1.045822878E+00-1.019765265E+00 --9.927249144E-01-9.647178392E-01-9.357617359E-01-9.058763786E-01-8.750833415E-01 --8.434063744E-01-8.108712342E-01-7.775058678E-01-7.433404523E-01-7.084072985E-01 --6.727411286E-01-6.363787969E-01-5.993595647E-01-5.617249575E-01-5.235187320E-01 --4.847870236E-01-4.455781436E-01-4.059425975E-01-3.659330978E-01-3.256044323E-01 --2.850134031E-01-2.442187737E-01-2.032812084E-01-1.622632044E-01-1.212288385E-01 --8.024499651E-02-3.938838392E-02 1.290389400E-03 4.188337911E-02 8.247317493E-02 - 1.230679317E-01 1.636642575E-01 2.042621110E-01 2.448614062E-01 1.559693128E-01 - 1.291630817E-01 1.023592258E-01 7.555783686E-02 4.875938890E-02 2.197546348E-02 --4.820893355E-03-3.186943351E-02-5.937797288E-02-8.734779539E-02-1.157415683E-01 --1.445289296E-01-1.736785297E-01-2.031571683E-01-2.329303913E-01-2.629627163E-01 --2.932178045E-01-3.236586428E-01-3.542476971E-01-3.849470409E-01-4.157185204E-01 --4.465238609E-01-4.773248016E-01-5.080831884E-01-5.387611097E-01-5.693209472E-01 --5.997255273E-01-6.299381326E-01-6.599226575E-01-6.896435901E-01-7.190661773E-01 --7.481563671E-01-7.768809964E-01-8.052076719E-01-8.331050002E-01-8.605423938E-01 --8.874903572E-01-9.139202169E-01-9.398044562E-01-9.651163822E-01-9.898304644E-01 --1.013922005E+00-1.037367448E+00-1.060144115E+00-1.082230389E+00-1.103605554E+00 --1.124249838E+00-1.144144406E+00-1.163271195E+00-1.181612989E+00-1.199153208E+00 --1.215876177E+00-1.231766755E+00-1.246810604E+00-1.260993936E+00-1.274303669E+00 --1.286727244E+00-1.298252826E+00-1.308869299E+00-1.318566250E+00-1.327333930E+00 --1.335163526E+00-1.342046619E+00-1.347973789E+00-1.352935426E+00-1.356922608E+00 --1.359927774E+00-1.361943433E+00-1.362961891E+00-1.362976270E+00-1.361980135E+00 --1.359965897E+00-1.356929260E+00-1.352859373E+00-1.347753860E+00-1.341609913E+00 --1.334421939E+00-1.326184512E+00-1.316893314E+00-1.306545313E+00-1.295138234E+00 --1.282670456E+00-1.269140962E+00-1.254549461E+00-1.238896361E+00-1.222182951E+00 --1.204411195E+00-1.185584026E+00-1.165705373E+00-1.144780502E+00-1.122815850E+00 --1.099819321E+00-1.075800158E+00-1.050769181E+00-1.024738769E+00-9.977229957E-01 --9.697377405E-01-9.408006361E-01-9.109313508E-01-8.801513716E-01-8.484844054E-01 --8.159560889E-01-7.825943392E-01-7.484291945E-01-7.134929196E-01-6.778201217E-01 --6.414475566E-01-6.044144278E-01-5.667621400E-01-5.285344000E-01-4.897772654E-01 --4.505389606E-01-4.108699504E-01-3.708228969E-01-3.304525350E-01-2.898156320E-01 --2.489709273E-01-2.079790633E-01-1.669025232E-01-1.258053973E-01-8.475430459E-02 --4.382491873E-02-3.074179560E-03 3.757027286E-02 7.820805847E-02 1.188512687E-01 - 1.594953132E-01 2.001400417E-01 2.407855176E-01 1.559427901E-01 1.291086716E-01 - 1.022754243E-01 7.544280713E-02 4.861124115E-02 2.179225331E-02-5.041944731E-03 --3.213281586E-02-5.968496135E-02-8.769878382E-02-1.161370475E-01-1.449693527E-01 --1.741642847E-01-2.036885842E-01-2.335077393E-01-2.635862103E-01-2.938876015E-01 --3.243748442E-01-3.550103500E-01-3.857561397E-01-4.165740082E-01-4.474256316E-01 --4.782727021E-01-5.090770204E-01-5.398006321E-01-5.704058786E-01-6.008555477E-01 --6.311128868E-01-6.611417569E-01-6.909066159E-01-7.203726801E-01-7.495058689E-01 --7.782729872E-01-8.066416135E-01-8.345803232E-01-8.620585029E-01-8.890466286E-01 --9.155160005E-01-9.414390732E-01-9.667891296E-01-9.915406291E-01-1.015668870E+00 --1.039150297E+00-1.061962218E+00-1.084083011E+00-1.105491950E+00-1.126169267E+00 --1.146096120E+00-1.165254485E+00-1.183627258E+00-1.201198027E+00-1.217951294E+00 --1.233872149E+00-1.248946536E+00-1.263160957E+00-1.276502664E+00-1.288959411E+00 --1.300519433E+00-1.311171297E+00-1.320903971E+00-1.329707002E+00-1.337570470E+00 --1.344485017E+00-1.350441478E+00-1.355431665E+00-1.359449116E+00-1.362484974E+00 --1.364530996E+00-1.365579623E+00-1.365623857E+00-1.364657177E+00-1.362672571E+00 --1.359663416E+00-1.355624608E+00-1.350550574E+00-1.344436064E+00-1.337276258E+00 --1.329067280E+00-1.319805935E+00-1.309489317E+00-1.298114691E+00-1.285679769E+00 --1.272183006E+00-1.257623625E+00-1.242001678E+00-1.225318125E+00-1.207574813E+00 --1.188774652E+00-1.168921582E+00-1.148020843E+00-1.126078825E+00-1.103103410E+00 --1.079103779E+00-1.054090770E+00-1.028076703E+00-1.001075661E+00-9.731034369E-01 --9.441776527E-01-9.143178894E-01-8.835455901E-01-8.518843878E-01-8.193598360E-01 --7.859998076E-01-7.518342367E-01-7.168953529E-01-6.812176650E-01-6.448378712E-01 --6.077951145E-01-5.701307159E-01-5.318883495E-01-4.931140063E-01-4.538558525E-01 --4.141643258E-01-3.740920455E-01-3.336937090E-01-2.930260598E-01-2.521478190E-01 --2.111196123E-01-1.700039098E-01-1.288648176E-01-8.776882008E-02-4.679065528E-02 --5.990800299E-03 3.468872562E-02 7.535877698E-02 1.160345065E-01 1.567105943E-01 - 1.973867980E-01 2.380632802E-01 1.559295401E-01 1.290814676E-01 1.022335116E-01 - 7.538526347E-02 4.853711798E-02 2.170057116E-02-5.152585853E-03-3.226464882E-02 --5.983862321E-02-8.787447591E-02-1.163350192E-01-1.451898349E-01-1.744074757E-01 --2.039546534E-01-2.337968274E-01-2.638984300E-01-2.942230375E-01-3.247335537E-01 --3.553923641E-01-3.861614635E-01-4.170026220E-01-4.478774919E-01-4.787477425E-01 --5.095751526E-01-5.403217473E-01-5.709498489E-01-6.014222268E-01-6.317021121E-01 --6.617533495E-01-6.915403833E-01-7.210284155E-01-7.501833540E-01-7.789719917E-01 --8.073618977E-01-8.353216375E-01-8.628205906E-01-8.898292258E-01-9.163188386E-01 --9.422618794E-01-9.676316268E-01-9.924025354E-01-1.016549896E+00-1.040050148E+00 --1.062880586E+00-1.085019578E+00-1.106446378E+00-1.127141199E+00-1.147085171E+00 --1.166260253E+00-1.184649338E+00-1.202236024E+00-1.219004820E+00-1.234940840E+00 --1.250030048E+00-1.264258958E+00-1.277614822E+00-1.290085415E+00-1.301659099E+00 --1.312324709E+00-1.322071532E+00-1.330889315E+00-1.338768137E+00-1.345698551E+00 --1.351671574E+00-1.356678995E+00-1.360712881E+00-1.363764426E+00-1.365825122E+00 --1.366888701E+00-1.366947972E+00-1.365995869E+00-1.364025678E+00-1.361031770E+00 --1.357009640E+00-1.351953070E+00-1.345856445E+00-1.338715134E+00-1.330524914E+00 --1.321282030E+00-1.310983135E+00-1.299625443E+00-1.287206715E+00-1.273725457E+00 --1.259180881E+00-1.243573048E+00-1.226902879E+00-1.209172258E+00-1.190384118E+00 --1.170542448E+00-1.149652490E+00-1.127720648E+00-1.104754794E+00-1.080764087E+00 --1.055759348E+00-1.029752848E+00-1.002758652E+00-9.747924955E-01-9.458719835E-01 --9.160166377E-01-8.852478773E-01-8.535892847E-01-8.210663729E-01-7.877069825E-01 --7.535409946E-01-7.186006177E-01-6.829203073E-01-6.465367366E-01-6.094890116E-01 --5.718184125E-01-5.335685964E-01-4.947855177E-01-4.555173145E-01-4.158144098E-01 --3.757293991E-01-3.353169609E-01-2.946338258E-01-2.537387054E-01-2.126922164E-01 --1.715568218E-01-1.303966339E-01-8.927807371E-02-4.827544439E-02-7.450882258E-03 - 3.324676384E-02 7.393319171E-02 1.146253092E-01 1.553175602E-01 1.960096413E-01 - 2.367017615E-01 1.559293899E-01 1.290813400E-01 1.022334072E-01 7.538518323E-02 - 4.853706276E-02 2.170054193E-02-5.152588205E-03-3.226462442E-02-5.983857297E-02 --8.787440079E-02-1.163349202E-01-1.451897129E-01-1.744073318E-01-2.039544886E-01 --2.337966428E-01-2.638982265E-01-2.942228163E-01-3.247333160E-01-3.553921109E-01 --3.861611959E-01-4.170023412E-01-4.478771989E-01-4.787474383E-01-5.095748382E-01 --5.403214237E-01-5.709495170E-01-6.014218877E-01-6.317017669E-01-6.617529990E-01 --6.915400284E-01-7.210280571E-01-7.501829931E-01-7.789716291E-01-8.073615341E-01 --8.353212737E-01-8.628202273E-01-8.898288637E-01-9.163184785E-01-9.422615220E-01 --9.676312730E-01-9.924021863E-01-1.016549553E+00-1.040049811E+00-1.062880257E+00 --1.085019258E+00-1.106446068E+00-1.127140900E+00-1.147084884E+00-1.166259983E+00 --1.184649088E+00-1.202235800E+00-1.219004625E+00-1.234940679E+00-1.250029926E+00 --1.264258878E+00-1.277614788E+00-1.290085425E+00-1.301659133E+00-1.312324745E+00 --1.322071549E+00-1.330889299E+00-1.338768079E+00-1.345698462E+00-1.351671499E+00 --1.356679002E+00-1.360712924E+00-1.363764418E+00-1.365825109E+00-1.366888701E+00 --1.366947974E+00-1.365995864E+00-1.364025655E+00-1.361031728E+00-1.357009585E+00 --1.351952991E+00-1.345856332E+00-1.338714979E+00-1.330524714E+00-1.321281782E+00 --1.310982836E+00-1.299625091E+00-1.287206307E+00-1.273724992E+00-1.259180357E+00 --1.243572464E+00-1.226902234E+00-1.209171551E+00-1.190383349E+00-1.170541616E+00 --1.149651595E+00-1.127719689E+00-1.104753771E+00-1.080762999E+00-1.055758194E+00 --1.029751628E+00-1.002757366E+00-9.747911424E-01-9.458705630E-01-9.160151492E-01 --8.852463203E-01-8.535876585E-01-8.210646770E-01-7.877052163E-01-7.535391572E-01 --7.185987084E-01-6.829183254E-01-6.465346809E-01-6.094868811E-01-5.718162059E-01 --5.335663124E-01-4.947831546E-01-4.555148706E-01-4.158118831E-01-3.757267875E-01 --3.353142619E-01-2.946310368E-01-2.537358234E-01-2.126892382E-01-1.715537438E-01 --1.303934522E-01-8.927478411E-02-4.827204317E-02-7.447362044E-03 3.325042052E-02 - 7.393698409E-02 1.146292315E-01 1.553216076E-01 1.960138094E-01 2.367060464E-01 - 1.559423551E-01 1.291083020E-01 1.022751223E-01 7.544257492E-02 4.861108113E-02 - 2.179216812E-02-5.041952741E-03-3.213274731E-02-5.968481913E-02-8.769857107E-02 --1.161367673E-01-1.449690083E-01-1.741638792E-01-2.036881209E-01-2.335072217E-01 --2.635856418E-01-2.938869857E-01-3.243741847E-01-3.550096504E-01-3.857554036E-01 --4.165732393E-01-4.474248332E-01-4.782718776E-01-5.090761732E-01-5.397997654E-01 --5.704049956E-01-6.008546518E-01-6.311119814E-01-6.611408451E-01-6.909057010E-01 --7.203717653E-01-7.495049576E-01-7.782720829E-01-8.066407197E-01-8.345794434E-01 --8.620576404E-01-8.890457870E-01-9.155151833E-01-9.414382844E-01-9.667883745E-01 --9.915399142E-01-1.015668202E+00-1.039149684E+00-1.061961667E+00-1.084082529E+00 --1.105491545E+00-1.126168947E+00-1.146095891E+00-1.165254345E+00-1.183627198E+00 --1.201198042E+00-1.217951375E+00-1.233872292E+00-1.248946734E+00-1.263161206E+00 --1.276502962E+00-1.288959737E+00-1.300519718E+00-1.311171465E+00-1.320903984E+00 --1.329706872E+00-1.337570250E+00-1.344484758E+00-1.350441184E+00-1.355431516E+00 --1.359449189E+00-1.362484995E+00-1.364531013E+00-1.365579623E+00-1.365623853E+00 --1.364657183E+00-1.362672539E+00-1.359663331E+00-1.355624489E+00-1.350550456E+00 --1.344435939E+00-1.337276100E+00-1.329067073E+00-1.319805665E+00-1.309488970E+00 --1.298114252E+00-1.285679224E+00-1.272182342E+00-1.257622832E+00-1.242000747E+00 --1.225317048E+00-1.207573581E+00-1.188773257E+00-1.168920018E+00-1.148019103E+00 --1.126076903E+00-1.103101301E+00-1.079101479E+00-1.054088274E+00-1.028074007E+00 --1.001072761E+00-9.731003302E-01-9.441743360E-01-9.143143596E-01-8.835418441E-01 --8.518804228E-01-8.193556491E-01-7.859953958E-01-7.518295969E-01-7.168904820E-01 --6.812125596E-01-6.448325278E-01-6.077895292E-01-5.701248846E-01-5.318822676E-01 --4.931076687E-01-4.538492537E-01-4.141574596E-01-3.740849052E-01-3.336862874E-01 --2.930183485E-01-2.521398092E-01-2.111112943E-01-1.699952730E-01-1.288558501E-01 --8.775950971E-02-4.678099092E-02-5.980760536E-03 3.469919186E-02 7.536966438E-02 - 1.160457967E-01 1.567222727E-01 1.973988507E-01 2.380756954E-01 1.559686393E-01 - 1.291625103E-01 1.023587591E-01 7.555747796E-02 4.875914086E-02 2.197532973E-02 --4.820909911E-03-3.186933469E-02-5.937776415E-02-8.734748262E-02-1.157411573E-01 --1.445284264E-01-1.736779404E-01-2.031564993E-01-2.329296490E-01-2.629619073E-01 --2.932169355E-01-3.236577207E-01-3.542467288E-01-3.849460333E-01-4.157174804E-01 --4.465227953E-01-4.773237171E-01-5.080820919E-01-5.387600080E-01-5.693198474E-01 --5.997244366E-01-6.299370580E-01-6.599216063E-01-6.896425695E-01-7.190651955E-01 --7.481554336E-01-7.768801215E-01-8.052068661E-01-8.331042741E-01-8.605417584E-01 --8.874898238E-01-9.139197979E-01-9.398041630E-01-9.651162201E-01-9.898304335E-01 --1.013922104E+00-1.037367678E+00-1.060144474E+00-1.082230878E+00-1.103606172E+00 --1.124250590E+00-1.144145283E+00-1.163272143E+00-1.181613934E+00-1.199154078E+00 --1.215876902E+00-1.231767274E+00-1.246810867E+00-1.260993912E+00-1.274303345E+00 --1.286726644E+00-1.298252028E+00-1.308868432E+00-1.318565452E+00-1.327333320E+00 --1.335163224E+00-1.342046626E+00-1.347973913E+00-1.352935245E+00-1.356922683E+00 --1.359927867E+00-1.361943473E+00-1.362961887E+00-1.362976233E+00-1.361980188E+00 --1.359965932E+00-1.356929265E+00-1.352859197E+00-1.347753598E+00-1.341609650E+00 --1.334421705E+00-1.326184289E+00-1.316893078E+00-1.306545045E+00-1.295137914E+00 --1.282670067E+00-1.269140488E+00-1.254548884E+00-1.238895668E+00-1.222182125E+00 --1.204410218E+00-1.185582878E+00-1.165704036E+00-1.144778960E+00-1.122814088E+00 --1.099817324E+00-1.075797914E+00-1.050766675E+00-1.024735987E+00-9.977199266E-01 --9.697343722E-01-9.407969577E-01-9.109273516E-01-8.801470414E-01-8.484797345E-01 --8.159510674E-01-7.825889573E-01-7.484234424E-01-7.134867873E-01-6.778135992E-01 --6.414406337E-01-6.044070941E-01-5.667543849E-01-5.285262122E-01-4.897686331E-01 --4.505298714E-01-4.108603912E-01-3.708128537E-01-3.304419929E-01-2.898045751E-01 --2.489593383E-01-2.079669239E-01-1.668898138E-01-1.257920966E-01-8.474039073E-02 --4.381037098E-02-3.058960665E-03 3.758623834E-02 7.822475646E-02 1.188686684E-01 - 1.595133903E-01 2.001587728E-01 2.408048829E-01 1.560087267E-01 1.292443190E-01 - 1.024845286E-01 7.572994320E-02 4.898111541E-02 2.224969125E-02-4.490049904E-03 --3.147518528E-02-5.891841239E-02-8.682236107E-02-1.151495505E-01-1.438696752E-01 --1.729514844E-01-2.023618670E-01-2.320664567E-01-2.620298589E-01-2.922158217E-01 --3.225874181E-01-3.531071975E-01-3.837373150E-01-4.144396977E-01-4.451761493E-01 --4.759084851E-01-5.065986264E-01-5.372087335E-01-5.677012589E-01-5.980390972E-01 --6.281855946E-01-6.581047081E-01-6.877609815E-01-7.171197153E-01-7.461469000E-01 --7.748094162E-01-8.030749064E-01-8.309120144E-01-8.582901828E-01-8.851799487E-01 --9.115526649E-01-9.373808264E-01-9.626377113E-01-9.872977184E-01-1.011336072E+00 --1.034729122E+00-1.057454081E+00-1.079489177E+00-1.100813512E+00-1.121407098E+00 --1.141250879E+00-1.160326577E+00-1.178616828E+00-1.196104907E+00-1.212775043E+00 --1.228612087E+00-1.243601759E+00-1.257730541E+00-1.270985835E+00-1.283355827E+00 --1.294829428E+00-1.305396592E+00-1.315047696E+00-1.323771642E+00-1.331557475E+00 --1.338395415E+00-1.344275207E+00-1.349191248E+00-1.353133419E+00-1.356093121E+00 --1.358063302E+00-1.359036640E+00-1.359005966E+00-1.357965088E+00-1.355905911E+00 --1.352824521E+00-1.348716414E+00-1.343568233E+00-1.337375986E+00-1.330141501E+00 --1.321861281E+00-1.312529867E+00-1.302142470E+00-1.290695658E+00-1.278187418E+00 --1.264616705E+00-1.249983353E+00-1.234287987E+00-1.217532128E+00-1.199718143E+00 --1.180849422E+00-1.160930371E+00-1.139966590E+00-1.117964909E+00-1.094933481E+00 --1.070881826E+00-1.045820802E+00-1.019762915E+00-9.927222674E-01-9.647148739E-01 --9.357584317E-01-9.058727148E-01-8.750792975E-01-8.434019295E-01-8.108663685E-01 --7.775005611E-01-7.433346850E-01-7.084010508E-01-6.727343810E-01-6.363715299E-01 --5.993517582E-01-5.617165914E-01-5.235097852E-01-4.847774745E-01-4.455679698E-01 --4.059317756E-01-3.659216033E-01-3.255922393E-01-2.850004846E-01-2.442051010E-01 --2.032667511E-01-1.622479305E-01-1.212127143E-01-8.022798744E-02-3.937045241E-02 - 1.309305704E-03 4.190335370E-02 8.249418812E-02 1.230899456E-01 1.636872401E-01 - 2.042860313E-01 2.448862381E-01 1.560631587E-01 1.293541297E-01 1.026526735E-01 - 7.596003126E-02 4.927685910E-02 2.261485420E-02-4.050092560E-03-3.095126687E-02 --5.830797409E-02-8.612468398E-02-1.143637159E-01-1.429948418E-01-1.719869471E-01 --2.013070443E-01-2.309208883E-01-2.607932046E-01-2.908878601E-01-3.211680455E-01 --3.515964251E-01-3.821352666E-01-4.127466086E-01-4.433923628E-01-4.740344476E-01 --5.046348839E-01-5.351559269E-01-5.655601194E-01-5.958104430E-01-6.258703267E-01 --6.557038086E-01-6.852754990E-01-7.145507445E-01-7.434955449E-01-7.720767756E-01 --8.002620519E-01-8.280199810E-01-8.553199536E-01-8.821324421E-01-9.084286998E-01 --9.341810986E-01-9.593628024E-01-9.839481111E-01-1.007912177E+00-1.031231265E+00 --1.053882481E+00-1.075843915E+00-1.097094583E+00-1.117614437E+00-1.137384379E+00 --1.156386091E+00-1.174602291E+00-1.192016455E+00-1.208613132E+00-1.224377716E+00 --1.239296603E+00-1.253356902E+00-1.266546772E+00-1.278854988E+00-1.290269575E+00 --1.300778065E+00-1.310368489E+00-1.319029906E+00-1.326751539E+00-1.333528988E+00 --1.339348133E+00-1.344202389E+00-1.348083135E+00-1.350982158E+00-1.352891932E+00 --1.353805123E+00-1.353714235E+00-1.352613382E+00-1.350497160E+00-1.347352934E+00 --1.343185363E+00-1.337987141E+00-1.331742889E+00-1.324447669E+00-1.316103301E+00 --1.306711107E+00-1.296267485E+00-1.284768022E+00-1.272209121E+00-1.258588657E+00 --1.243905892E+00-1.228161269E+00-1.211356225E+00-1.193493285E+00-1.174575977E+00 --1.154609030E+00-1.133598247E+00-1.111550785E+00-1.088475029E+00-1.064380883E+00 --1.039279569E+00-1.013184022E+00-9.861087034E-01-9.580699588E-01-9.290858164E-01 --8.991762645E-01-8.683631226E-01-8.366702003E-01-8.041234593E-01-7.707509160E-01 --7.365829252E-01-7.016519073E-01-6.659926831E-01-6.296422477E-01-5.926398966E-01 --5.550272901E-01-5.168482661E-01-4.781490182E-01-4.389779658E-01-3.993856779E-01 --3.594249119E-01-3.191505161E-01-2.786193367E-01-2.378901645E-01-1.970236849E-01 --1.560823980E-01-1.151304047E-01-7.423513709E-02-3.347313206E-02 7.116126956E-03 - 4.764170833E-02 8.816881179E-02 1.287008075E-01 1.692352618E-01 2.097722959E-01 - 2.503116551E-01 1.561328849E-01 1.294926410E-01 1.028636137E-01 7.624784976E-02 - 4.964613484E-02 2.307017614E-02-3.502175656E-03-3.029911144E-02-5.754836255E-02 --8.525677215E-02-1.133864041E-01-1.419071293E-01-1.707880070E-01-1.999962067E-01 --2.294976377E-01-2.592571792E-01-2.892388513E-01-3.194059955E-01-3.497214227E-01 --3.801475428E-01-4.106465297E-01-4.411804162E-01-4.717112222E-01-5.022010542E-01 --5.326122391E-01-5.629073773E-01-5.930494928E-01-6.230020429E-01-6.527290848E-01 --6.821952330E-01-7.113658309E-01-7.402068647E-01-7.686851897E-01-7.967683796E-01 --8.244249995E-01-8.516243998E-01-8.783370131E-01-9.045340341E-01-9.301877629E-01 --9.552712973E-01-9.797589009E-01-1.003625727E+00-1.026847994E+00-1.049402784E+00 --1.071268215E+00-1.092423438E+00-1.112848497E+00-1.132524498E+00-1.151433484E+00 --1.169558668E+00-1.186884070E+00-1.203394750E+00-1.219076610E+00-1.233916398E+00 --1.247900509E+00-1.261015433E+00-1.273247758E+00-1.284584037E+00-1.295011963E+00 --1.304520315E+00-1.313103117E+00-1.320750369E+00-1.327449639E+00-1.333191896E+00 --1.337969316E+00-1.341773697E+00-1.344597000E+00-1.346431346E+00-1.347269188E+00 --1.347103479E+00-1.345927472E+00-1.343739036E+00-1.340523187E+00-1.336275008E+00 --1.331002929E+00-1.324696134E+00-1.317338817E+00-1.308925274E+00-1.299456487E+00 --1.288935123E+00-1.277362025E+00-1.264734417E+00-1.251049334E+00-1.236304827E+00 --1.220500451E+00-1.203637195E+00-1.185717364E+00-1.166744413E+00-1.146723077E+00 --1.125659293E+00-1.103560346E+00-1.080434853E+00-1.056292936E+00-1.031146172E+00 --1.005007749E+00-9.778925258E-01-9.498170884E-01-9.207998695E-01-8.908610870E-01 --8.600230068E-01-8.283097596E-01-7.957477201E-01-7.623652177E-01-7.281928834E-01 --6.932634469E-01-6.576118690E-01-6.212753703E-01-5.842933379E-01-5.467075781E-01 --5.085620862E-01-4.699031170E-01-4.307792086E-01-3.912410237E-01-3.513413563E-01 --3.111351003E-01-2.706791450E-01-2.300323080E-01-1.892552909E-01-1.484105833E-01 --1.075623749E-01-6.677902540E-02-2.613513176E-02 1.434731980E-02 5.478884839E-02 - 9.523670356E-02 1.356897163E-01 1.761463385E-01 2.166068573E-01 2.570708153E-01 - 1.562187851E-01 1.296605142E-01 1.031177650E-01 7.659353297E-02 5.008875392E-02 - 2.361506252E-02-2.847426029E-03-2.952026680E-02-5.664154419E-02-8.422105746E-02 --1.122205498E-01-1.406100034E-01-1.693586808E-01-1.984339283E-01-2.278018230E-01 --2.574274051E-01-2.872748469E-01-3.173076313E-01-3.474886977E-01-3.777805754E-01 --4.081455490E-01-4.385457533E-01-4.689433070E-01-4.993004037E-01-5.295794401E-01 --5.597430725E-01-5.897543649E-01-6.195767982E-01-6.491744487E-01-6.785119535E-01 --7.075546920E-01-7.362686702E-01-7.646207535E-01-7.925785056E-01-8.201104786E-01 --8.471860208E-01-8.737755794E-01-8.998503620E-01-9.253826712E-01-9.503456355E-01 --9.747135859E-01-9.984617547E-01-1.021566419E+00-1.044004833E+00-1.065755364E+00 --1.086797465E+00-1.107111573E+00-1.126679321E+00-1.145483098E+00-1.163506502E+00 --1.180733739E+00-1.197149208E+00-1.212737481E+00-1.227483848E+00-1.241373565E+00 --1.254391788E+00-1.266524713E+00-1.277760201E+00-1.288091667E+00-1.297510266E+00 --1.305999573E+00-1.313553151E+00-1.320158953E+00-1.325808946E+00-1.330494676E+00 --1.334207714E+00-1.336940055E+00-1.338683592E+00-1.339431424E+00-1.339176474E+00 --1.337910506E+00-1.335632894E+00-1.332333892E+00-1.327997534E+00-1.322628609E+00 --1.316234187E+00-1.308801046E+00-1.300314399E+00-1.290768142E+00-1.280162228E+00 --1.268499302E+00-1.255782483E+00-1.242012846E+00-1.227189021E+00-1.211309856E+00 --1.194375458E+00-1.176387412E+00-1.157348916E+00-1.137264463E+00-1.116140030E+00 --1.093982880E+00-1.070801813E+00-1.046607042E+00-1.021410433E+00-9.952253349E-01 --9.680669454E-01-9.399520818E-01-9.108995160E-01-8.809297534E-01-8.500654044E-01 --8.183309913E-01-7.857531790E-01-7.523607038E-01-7.181844256E-01-6.832574714E-01 --6.476150590E-01-6.112947839E-01-5.743363764E-01-5.367818658E-01-4.986755459E-01 --4.600638523E-01-4.209954700E-01-3.815212083E-01-3.416939426E-01-3.015686185E-01 --2.612021787E-01-2.206534805E-01-1.799832457E-01-1.392539332E-01-9.852990997E-02 --5.788106743E-02-1.737737749E-02 2.298584039E-02 6.332928968E-02 1.036827748E-01 - 1.440420137E-01 1.844062696E-01 2.247759582E-01 2.651503962E-01 1.563222550E-01 - 1.298587708E-01 1.034157311E-01 7.699722011E-02 5.060435401E-02 2.424857299E-02 --2.087480971E-03-2.861684671E-02-5.559002236E-02-8.302037803E-02-1.108692363E-01 --1.391066781E-01-1.677021750E-01-1.966232550E-01-2.258361692E-01-2.553061234E-01 --2.849974472E-01-3.148737737E-01-3.448981791E-01-3.750333159E-01-4.052415799E-01 --4.354852070E-01-4.657264213E-01-4.959275269E-01-5.260510260E-01-5.560596697E-01 --5.859166024E-01-6.155853678E-01-6.450300844E-01-6.742154202E-01-7.031068128E-01 --7.316703417E-01-7.598729383E-01-7.876822173E-01-8.150667723E-01-8.419960002E-01 --8.684404281E-01-8.943713565E-01-9.197611796E-01-9.445831792E-01-9.688118636E-01 --9.924226641E-01-1.015392123E+00-1.037697930E+00-1.059318815E+00-1.080234547E+00 --1.100425854E+00-1.119874473E+00-1.138562196E+00-1.156471471E+00-1.173585349E+00 --1.189887580E+00-1.205362010E+00-1.219992497E+00-1.233763665E+00-1.246661927E+00 --1.258679173E+00-1.269807763E+00-1.280032928E+00-1.289338532E+00-1.297719010E+00 --1.305162888E+00-1.311660374E+00-1.317202726E+00-1.321781530E+00-1.325388138E+00 --1.328014297E+00-1.329652343E+00-1.330295354E+00-1.329936517E+00-1.328566183E+00 --1.326183667E+00-1.322785196E+00-1.318352450E+00-1.312878132E+00-1.306372576E+00 --1.298838932E+00-1.290263062E+00-1.280631854E+00-1.269939459E+00-1.258185039E+00 --1.245370870E+00-1.231500765E+00-1.216578579E+00-1.200606300E+00-1.183584383E+00 --1.165513939E+00-1.146397421E+00-1.126238928E+00-1.105044177E+00-1.082820404E+00 --1.059576379E+00-1.035322448E+00-1.010070573E+00-9.838343580E-01-9.566291701E-01 --9.284721661E-01-8.993823077E-01-8.693805056E-01-8.384895986E-01-8.067345395E-01 --7.741422155E-01-7.407417601E-01-7.065643200E-01-6.716433733E-01-6.360145135E-01 --5.997156013E-01-5.627867538E-01-5.252702324E-01-4.872106194E-01-4.486546422E-01 --4.096511821E-01-3.702512937E-01-3.305080825E-01-2.904766536E-01-2.502140658E-01 --2.097792684E-01-1.692330447E-01-1.286378216E-01-8.805828615E-02-4.756675710E-02 --7.224634966E-03 3.301197415E-02 7.324481767E-02 1.134892076E-01 1.537404583E-01 - 1.939983988E-01 2.342634980E-01 2.745348320E-01 1.564440451E-01 1.300877943E-01 - 1.037575231E-01 7.745855294E-02 5.119222990E-02 2.496961111E-02-1.223946182E-03 --2.759051968E-02-5.439542538E-02-8.165626996E-02-1.093338249E-01-1.373982641E-01 --1.658192809E-01-1.945645880E-01-2.236006121E-01-2.528927369E-01-2.824054734E-01 --3.121026336E-01-3.419474633E-01-3.719027774E-01-4.019311279E-01-4.319948893E-01 --4.620564014E-01-4.920780716E-01-5.220225114E-01-5.518526014E-01-5.815316181E-01 --6.110232297E-01-6.402916641E-01-6.693016663E-01-6.980187405E-01-7.264090705E-01 --7.544397261E-01-7.820784502E-01-8.092939587E-01-8.360557719E-01-8.623345745E-01 --8.881018644E-01-9.133302429E-01-9.379932985E-01-9.620658562E-01-9.855236931E-01 --1.008343635E+00-1.030503632E+00-1.051982448E+00-1.072759394E+00-1.092814183E+00 --1.112127564E+00-1.130680815E+00-1.148456061E+00-1.165435676E+00-1.181602177E+00 --1.196938551E+00-1.211429455E+00-1.225064631E+00-1.237837211E+00-1.249733278E+00 --1.260733926E+00-1.270829148E+00-1.280009523E+00-1.288264658E+00-1.295583725E+00 --1.301957757E+00-1.307377205E+00-1.311833756E+00-1.315318929E+00-1.317824510E+00 --1.319342187E+00-1.319865126E+00-1.319387731E+00-1.317898937E+00-1.315397159E+00 --1.311882084E+00-1.307339221E+00-1.301753556E+00-1.295126290E+00-1.287468916E+00 --1.278780573E+00-1.269047343E+00-1.258258024E+00-1.246407450E+00-1.233494609E+00 --1.219521434E+00-1.204492015E+00-1.188411427E+00-1.171284745E+00-1.153115418E+00 --1.133906201E+00-1.113660830E+00-1.092384494E+00-1.070084217E+00-1.046768618E+00 --1.022448117E+00-9.971346859E-01-9.708421420E-01-9.435859852E-01-9.153836480E-01 --8.862543029E-01-8.562192035E-01-8.253014848E-01-7.935263995E-01-7.609211890E-01 --7.275152718E-01-6.933402357E-01-6.584298082E-01-6.228199973E-01-5.865489091E-01 --5.496569914E-01-5.121868479E-01-4.741832945E-01-4.356933810E-01-3.967662498E-01 --3.574531553E-01-3.178074212E-01-2.778843427E-01-2.377411303E-01-1.974368676E-01 --1.570324499E-01-1.165903736E-01-7.617608400E-02-3.586386911E-02 4.300394851E-03 - 4.440441655E-02 8.451452555E-02 1.246357182E-01 1.647653962E-01 2.049036716E-01 - 2.450509995E-01 2.852062076E-01 1.565835624E-01 1.303466809E-01 1.041419636E-01 - 7.797612421E-02 5.185078255E-02 2.577648054E-02-2.584943935E-04-2.644319376E-02 --5.305954326E-02-8.013025465E-02-1.076155397E-01-1.354856642E-01-1.637105770E-01 --1.922582081E-01-2.210951957E-01-2.501871290E-01-2.794987091E-01-3.089939253E-01 --3.386361972E-01-3.683885295E-01-3.982136683E-01-4.280741756E-01-4.579325757E-01 --4.877514462E-01-5.174935311E-01-5.471218323E-01-5.765997706E-01-6.058911941E-01 --6.349605134E-01-6.637726466E-01-6.922932339E-01-7.204885879E-01-7.483259660E-01 --7.757733328E-01-8.027996163E-01-8.293745657E-01-8.554691190E-01-8.810551085E-01 --9.061054524E-01-9.305940366E-01-9.544958621E-01-9.777868175E-01-1.000443335E+00 --1.022442560E+00-1.043762375E+00-1.064381651E+00-1.084279843E+00-1.103437399E+00 --1.121835109E+00-1.139454014E+00-1.156275430E+00-1.172282178E+00-1.187461356E+00 --1.201805539E+00-1.215302779E+00-1.227933867E+00-1.239680191E+00-1.250536107E+00 --1.260488418E+00-1.269527316E+00-1.277641075E+00-1.284820302E+00-1.291055459E+00 --1.296336910E+00-1.300656134E+00-1.304004744E+00-1.306374817E+00-1.307757745E+00 --1.308145836E+00-1.307535306E+00-1.305913963E+00-1.303279101E+00-1.299631641E+00 --1.294962533E+00-1.289254738E+00-1.282500704E+00-1.274706890E+00-1.265883640E+00 --1.256026892E+00-1.245123722E+00-1.233164890E+00-1.220146165E+00-1.206066877E+00 --1.190929051E+00-1.174736945E+00-1.157496452E+00-1.139214235E+00-1.119897086E+00 --1.099550442E+00-1.078179852E+00-1.055791982E+00-1.032395241E+00-1.007999850E+00 --9.826178758E-01-9.562631504E-01-9.289514126E-01-9.007001759E-01-8.715289650E-01 --8.414592096E-01-8.105144246E-01-7.787200586E-01-7.461037904E-01-7.126953130E-01 --6.785266033E-01-6.436316967E-01-6.080469065E-01-5.718107414E-01-5.349639093E-01 --4.975493919E-01-4.596122793E-01-4.211998597E-01-3.823615617E-01-3.431488674E-01 --3.036152941E-01-2.638163304E-01-2.238093591E-01-1.836536114E-01-1.434100702E-01 --1.031414653E-01-6.291496593E-02-2.280209177E-02 1.718057769E-02 5.714061964E-02 - 9.711419006E-02 1.370992010E-01 1.770946102E-01 2.171006739E-01 2.571178315E-01 - 2.971446334E-01 1.567389830E-01 1.306336195E-01 1.045672769E-01 7.854819058E-02 - 5.257823756E-02 2.666778407E-02 8.086447363E-04-2.517651202E-02-5.158438223E-02 --7.844425068E-02-1.057162994E-01-1.333708112E-01-1.613779824E-01-1.897059866E-01 --2.183217047E-01-2.471909693E-01-2.762787213E-01-3.055491880E-01-3.349660138E-01 --3.644924037E-01-3.940912889E-01-4.237254294E-01-4.533575769E-01-4.829505411E-01 --5.124672956E-01-5.418710512E-01-5.711253911E-01-6.001943406E-01-6.290425426E-01 --6.576351727E-01-6.859381124E-01-7.139178897E-01-7.415419836E-01-7.687786719E-01 --7.955972077E-01-8.219676709E-01-8.478612440E-01-8.732499993E-01-8.981069648E-01 --9.224057808E-01-9.461207769E-01-9.692271721E-01-9.917009548E-01-1.013519067E+00 --1.034659163E+00-1.055099923E+00-1.074820423E+00-1.093800100E+00-1.112018585E+00 --1.129456853E+00-1.146099261E+00-1.161936624E+00-1.176958280E+00-1.191145919E+00 --1.204477427E+00-1.216939946E+00-1.228526692E+00-1.239221997E+00-1.249016042E+00 --1.257896747E+00-1.265854064E+00-1.272878108E+00-1.278958985E+00-1.284087268E+00 --1.288254053E+00-1.291450869E+00-1.293670366E+00-1.294904478E+00-1.295143484E+00 --1.294385509E+00-1.292617604E+00-1.289835978E+00-1.286041752E+00-1.281230410E+00 --1.275386242E+00-1.268497067E+00-1.260561722E+00-1.251589167E+00-1.241587607E+00 --1.230550871E+00-1.218467563E+00-1.205330361E+00-1.191136159E+00-1.175884976E+00 --1.159579399E+00-1.142224084E+00-1.123825594E+00-1.104391846E+00-1.083931586E+00 --1.062453701E+00-1.039966260E+00-1.016477915E+00-9.919987464E-01-9.665406659E-01 --9.401175470E-01-9.127452054E-01-8.844413378E-01-8.552256863E-01-8.251199313E-01 --7.941478108E-01-7.623351412E-01-7.297098691E-01-6.963020840E-01-6.621439884E-01 --6.272700547E-01-5.917168727E-01-5.555233450E-01-5.187304918E-01-4.813815526E-01 --4.435219619E-01-4.051992634E-01-3.664631444E-01-3.273653464E-01-2.879595901E-01 --2.483015313E-01-2.084487077E-01-1.684604922E-01-1.283979281E-01-8.832421012E-02 --4.830950456E-02-8.415972589E-03 3.138728349E-02 7.119299121E-02 1.110161074E-01 - 1.508523392E-01 1.907013927E-01 2.305634784E-01 2.704390024E-01 3.103261559E-01 - 1.569090061E-01 1.309472463E-01 1.050319853E-01 7.917311093E-02 5.337276454E-02 - 2.764139102E-02 1.974810830E-03-2.379320019E-02-4.997261556E-02-7.660087764E-02 --1.036386700E-01-1.310562546E-01-1.588241082E-01-1.869106825E-01-2.152831089E-01 --2.439074601E-01-2.727489307E-01-3.017720220E-01-3.309406535E-01-3.602183084E-01 --3.895681916E-01-4.189533059E-01-4.483366187E-01-4.776811748E-01-5.069502328E-01 --5.361073004E-01-5.651162379E-01-5.939413167E-01-6.225474077E-01-6.508999929E-01 --6.789652976E-01-7.067101841E-01-7.341024336E-01-7.611106116E-01-7.877042406E-01 --8.138535767E-01-8.395296288E-01-8.647040302E-01-8.893492546E-01-9.134386178E-01 --9.369462252E-01-9.598471416E-01-9.821172119E-01-1.003733255E+00-1.024672561E+00 --1.044912877E+00-1.064432115E+00-1.083209403E+00-1.101226501E+00-1.118471639E+00 --1.134934009E+00-1.150597450E+00-1.165439142E+00-1.179436961E+00-1.192584324E+00 --1.204870752E+00-1.216278694E+00-1.226798429E+00-1.236417531E+00-1.245125206E+00 --1.252910818E+00-1.259763975E+00-1.265675152E+00-1.270635153E+00-1.274634956E+00 --1.277665423E+00-1.279718988E+00-1.280789401E+00-1.280865318E+00-1.279945796E+00 --1.278017406E+00-1.275075595E+00-1.271121219E+00-1.266152394E+00-1.260156795E+00 --1.253120412E+00-1.245036934E+00-1.235909354E+00-1.225747604E+00-1.214557408E+00 --1.202331631E+00-1.189060742E+00-1.174739269E+00-1.159365388E+00-1.142940083E+00 --1.125466811E+00-1.106951036E+00-1.087400128E+00-1.066823085E+00-1.045230264E+00 --1.022632877E+00-9.990424175E-01-9.744700701E-01-9.489279793E-01-9.224300296E-01 --8.949919492E-01-8.666316579E-01-8.373689932E-01-8.072259239E-01-7.762264003E-01 --7.443965987E-01-7.117647018E-01-6.783611307E-01-6.442184390E-01-6.093714183E-01 --5.738570452E-01-5.377144583E-01-5.009850617E-01-4.637123834E-01-4.259421557E-01 --3.877222342E-01-3.491025267E-01-3.101349803E-01-2.708735222E-01-2.313739929E-01 --1.916940989E-01-1.518933436E-01-1.120328701E-01-7.217696035E-02-3.239761741E-02 - 7.263860131E-03 4.688889999E-02 8.652993813E-02 1.261891930E-01 1.658643541E-01 - 2.055553089E-01 2.452620531E-01 2.849849530E-01 3.247217673E-01 1.570922465E-01 - 1.312860967E-01 1.055345505E-01 7.984926965E-02 5.423266113E-02 2.869524731E-02 - 3.237052860E-03-2.229614761E-02-4.822722286E-02-7.460336574E-02-1.013861196E-01 --1.285456630E-01-1.560527729E-01-1.838762239E-01-2.119834594E-01-2.403408641E-01 --2.689139428E-01-2.976674789E-01-3.265656572E-01-3.555722609E-01-3.846508263E-01 --4.137646870E-01-4.428771332E-01-4.719515014E-01-5.009513173E-01-5.298404026E-01 --5.585829898E-01-5.871437089E-01-6.154877572E-01-6.435809466E-01-6.713898325E-01 --6.988816143E-01-7.260242671E-01-7.527863268E-01-7.791370324E-01-8.050462901E-01 --8.304848263E-01-8.554241477E-01-8.798365664E-01-9.036953283E-01-9.269744571E-01 --9.496488924E-01-9.716941118E-01-9.930861218E-01-1.013801092E+00-1.033816311E+00 --1.053111132E+00-1.071670866E+00-1.089483353E+00-1.106533691E+00-1.122800253E+00 --1.138257442E+00-1.152888501E+00-1.166687956E+00-1.179640987E+00-1.191730094E+00 --1.202944875E+00-1.213272335E+00-1.222701355E+00-1.231220387E+00-1.238818377E+00 --1.245485347E+00-1.251211634E+00-1.255987856E+00-1.259805597E+00-1.262656016E+00 --1.264529361E+00-1.265421026E+00-1.265319876E+00-1.264225003E+00-1.262122440E+00 --1.259007140E+00-1.254879690E+00-1.249739279E+00-1.243577500E+00-1.236380380E+00 --1.228138714E+00-1.218850751E+00-1.208522134E+00-1.197162874E+00-1.184776360E+00 --1.171355460E+00-1.156892703E+00-1.141384434E+00-1.124830254E+00-1.107232356E+00 --1.088595302E+00-1.068925689E+00-1.048231973E+00-1.026524348E+00-1.003814590E+00 --9.801158932E-01-9.554423294E-01-9.298085208E-01-9.032291256E-01-8.757202661E-01 --8.472998204E-01-8.179878025E-01-7.878063100E-01-7.567796492E-01-7.249341509E-01 --6.922983860E-01-6.589030265E-01-6.247810254E-01-5.899674237E-01-5.544995413E-01 --5.184168723E-01-4.817611029E-01-4.445761143E-01-4.069078808E-01-3.688045090E-01 --3.303161733E-01-2.914950459E-01-2.523952473E-01-2.130727844E-01-1.735855084E-01 --1.339929887E-01-9.435669236E-02-5.474366961E-02-1.522045152E-02 2.421517449E-02 - 6.365386311E-02 1.031165444E-01 1.425994594E-01 1.821017362E-01 2.216232014E-01 - 2.611636350E-01 3.007233466E-01 3.402995834E-01 1.572879067E-01 1.316491966E-01 - 1.060737470E-01 8.057511648E-02 5.515600673E-02 2.982702122E-02 4.592512467E-03 --2.068872104E-02-4.635174168E-02-7.245536659E-02-9.896248851E-02-1.258431632E-01 --1.530684809E-01-1.806075447E-01-2.084281116E-01-2.364969086E-01-2.647798060E-01 --2.932419537E-01-3.218478919E-01-3.505617501E-01-3.793473797E-01-4.081684500E-01 --4.369886511E-01-4.657717173E-01-4.944815392E-01-5.230822926E-01-5.515385752E-01 --5.798154191E-01-6.078783884E-01-6.356935507E-01-6.632275374E-01-6.904474661E-01 --7.173211022E-01-7.438168325E-01-7.699037944E-01-7.955518425E-01-8.207316204E-01 --8.454146320E-01-8.695731164E-01-8.931801878E-01-9.162095236E-01-9.386353863E-01 --9.604322082E-01-9.815754512E-01-1.002042240E+00-1.021814926E+00-1.040879268E+00 --1.059220269E+00-1.076818189E+00-1.093646816E+00-1.109681136E+00-1.124911041E+00 --1.139328168E+00-1.152913596E+00-1.165650671E+00-1.177528529E+00-1.188533349E+00 --1.198653231E+00-1.207875820E+00-1.216189805E+00-1.223584805E+00-1.230050693E+00 --1.235577602E+00-1.240155583E+00-1.243775706E+00-1.246430964E+00-1.248110929E+00 --1.248809467E+00-1.248517325E+00-1.247233416E+00-1.244943256E+00-1.241641434E+00 --1.237328263E+00-1.232003180E+00-1.225661195E+00-1.218289717E+00-1.209877996E+00 --1.200421412E+00-1.189921427E+00-1.178385417E+00-1.165822961E+00-1.152235587E+00 --1.137616886E+00-1.121961562E+00-1.105267806E+00-1.087536771E+00-1.068772070E+00 --1.048979583E+00-1.028167287E+00-1.006344974E+00-9.835242966E-01-9.597185024E-01 --9.349425849E-01-9.092128427E-01-8.825467493E-01-8.549623385E-01-8.264782715E-01 --7.971148282E-01-7.668942954E-01-7.358410966E-01-7.039818828E-01-6.713454817E-01 --6.379629272E-01-6.038673905E-01-5.690943208E-01-5.336813133E-01-4.976682137E-01 --4.610969901E-01-4.240117820E-01-3.864588902E-01-3.484866725E-01-3.101455214E-01 --2.714878121E-01-2.325678354E-01-1.934417571E-01-1.541675702E-01-1.148049152E-01 --7.541618280E-02-3.607159677E-02 3.180357030E-03 4.240096030E-02 8.164481920E-02 - 1.209156813E-01 1.602105210E-01 1.995287573E-01 2.388699330E-01 2.782336298E-01 - 3.176200906E-01 3.570259860E-01 1.574950538E-01 1.320354096E-01 1.066482450E-01 - 8.134911562E-02 5.614100887E-02 3.103458346E-02 6.038538898E-03-1.897442942E-02 --4.435016494E-02-7.016124976E-02-9.637250462E-02-1.229537866E-01-1.498765385E-01 --1.771102730E-01-2.046231305E-01-2.323822139E-01-2.603537557E-01-2.885032719E-01 --3.167957147E-01-3.451956534E-01-3.736673490E-01-4.021748612E-01-4.306822741E-01 --4.591537382E-01-4.875535998E-01-5.158464388E-01-5.439971620E-01-5.719710095E-01 --5.997336163E-01-6.272510203E-01-6.544897961E-01-6.814170613E-01-7.080005793E-01 --7.342087506E-01-7.600107008E-01-7.853763162E-01-8.102761611E-01-8.346816285E-01 --8.585646563E-01-8.818978042E-01-9.046538121E-01-9.268063510E-01-9.483304744E-01 --9.692056778E-01-9.894153344E-01-1.008943243E+00-1.027770579E+00-1.045872524E+00 --1.063221082E+00-1.079794766E+00-1.095587156E+00-1.110585666E+00-1.124767572E+00 --1.138118293E+00-1.150625983E+00-1.162275502E+00-1.173054576E+00-1.182950106E+00 --1.191950495E+00-1.200044816E+00-1.207221902E+00-1.213471146E+00-1.218782996E+00 --1.223148565E+00-1.226557273E+00-1.229001848E+00-1.230474785E+00-1.230966160E+00 --1.230469409E+00-1.228983123E+00-1.226492214E+00-1.222991015E+00-1.218479814E+00 --1.212957936E+00-1.206422460E+00-1.198863335E+00-1.190269371E+00-1.180634006E+00 --1.169956053E+00-1.158239367E+00-1.145492507E+00-1.131724330E+00-1.116935140E+00 --1.101119812E+00-1.084275284E+00-1.066401660E+00-1.047501761E+00-1.027580805E+00 --1.006646198E+00-9.847074856E-01-9.617760454E-01-9.378651717E-01-9.129898452E-01 --8.871668129E-01-8.604145017E-01-8.327527796E-01-8.042027973E-01-7.747864393E-01 --7.445266405E-01-7.134481313E-01-6.815777887E-01-6.489446639E-01-6.155800707E-01 --5.815175421E-01-5.467928036E-01-5.114437977E-01-4.755106080E-01-4.390355568E-01 --4.020630777E-01-3.646396970E-01-3.268140137E-01-2.886366336E-01-2.501601238E-01 --2.114389496E-01-1.725294320E-01-1.334896320E-01-9.437947233E-02-5.526410479E-02 --1.620936228E-02 2.277986227E-02 6.178320995E-02 1.008204840E-01 1.398878216E-01 - 1.789837058E-01 2.181074471E-01 2.572582683E-01 2.964355347E-01 3.356393946E-01 - 3.748658706E-01 1.577132689E-01 1.324440569E-01 1.072570105E-01 8.216978364E-02 - 5.718567834E-02 3.231542910E-02 7.572015587E-03-1.715722938E-02-4.222681194E-02 --6.772562991E-02-9.362119946E-02-1.198830791E-01-1.464830488E-01-1.733910380E-01 --2.005756086E-01-2.280043123E-01-2.556438350E-01-2.834601192E-01-3.114185381E-01 --3.394840977E-01-3.676215263E-01-3.957953747E-01-4.239701701E-01-4.521104349E-01 --4.801808366E-01-5.081461766E-01-5.359714810E-01-5.636220641E-01-5.910636383E-01 --6.182623405E-01-6.451848155E-01-6.717982497E-01-6.980704530E-01-7.239698772E-01 --7.494655820E-01-7.745273859E-01-7.991256066E-01-8.232311920E-01-8.468152719E-01 --8.698498005E-01-8.923079143E-01-9.141664204E-01-9.354062160E-01-9.560093188E-01 --9.759566587E-01-9.952249079E-01-1.013785820E+00-1.031611242E+00-1.048686057E+00 --1.065002868E+00-1.080544234E+00-1.095285673E+00-1.109214164E+00-1.122316767E+00 --1.134577302E+00-1.145982744E+00-1.156519270E+00-1.166175358E+00-1.174938568E+00 --1.182797104E+00-1.189740507E+00-1.195758657E+00-1.200840748E+00-1.204978196E+00 --1.208162290E+00-1.210382055E+00-1.211633987E+00-1.211904465E+00-1.211189735E+00 --1.209487943E+00-1.206783518E+00-1.203070517E+00-1.198349250E+00-1.192618974E+00 --1.185877759E+00-1.178118382E+00-1.169330092E+00-1.159505258E+00-1.148640893E+00 --1.136738426E+00-1.123803603E+00-1.109845808E+00-1.094873067E+00-1.078885169E+00 --1.061878718E+00-1.043852899E+00-1.024809811E+00-1.004754066E+00-9.836926557E-01 --9.616347067E-01-9.385914984E-01-9.145762150E-01-8.896039492E-01-8.636916233E-01 --8.368579052E-01-8.091232975E-01-7.805099808E-01-7.510417240E-01-7.207436145E-01 --6.896417491E-01-6.577635072E-01-6.251383102E-01-5.917976973E-01-5.577754836E-01 --5.231076887E-01-4.878325495E-01-4.519905081E-01-4.156241166E-01-3.787780768E-01 --3.414991733E-01-3.038362331E-01-2.658400645E-01-2.275633976E-01-1.890608372E-01 --1.503888292E-01-1.116054904E-01-7.277186090E-02-3.395627814E-02 4.795803452E-03 - 4.353925178E-02 8.231947132E-02 1.211380199E-01 1.599914489E-01 1.988785296E-01 - 2.377982105E-01 2.767494237E-01 3.157313130E-01 3.547439327E-01 3.937826099E-01 - 1.579420285E-01 1.328742974E-01 1.078988960E-01 8.303565295E-02 5.828816859E-02 - 3.366723022E-02 9.189876631E-03-1.524132823E-02-3.998651823E-02-6.515379646E-02 --9.071428616E-02-1.166371526E-01-1.428945663E-01-1.694569446E-01-1.962932944E-01 --2.233716132E-01-2.506590575E-01-2.781220729E-01-3.057265466E-01-3.334379657E-01 --3.612214909E-01-3.890420882E-01-4.168646389E-01-4.446539227E-01-4.723748079E-01 --4.999922698E-01-5.274715203E-01-5.547780392E-01-5.818776707E-01-6.087366679E-01 --6.353217799E-01-6.616002594E-01-6.875398931E-01-7.131091141E-01-7.382767940E-01 --7.630124104E-01-7.872856144E-01-8.110667599E-01-8.343272268E-01-8.570413546E-01 --8.791875873E-01-9.007459143E-01-9.216961812E-01-9.420156505E-01-9.616773130E-01 --9.806508180E-01-9.989106926E-01-1.016446372E+00-1.033247282E+00-1.049291474E+00 --1.064553894E+00-1.079022928E+00-1.092684344E+00-1.105520483E+00-1.117517986E+00 --1.128662562E+00-1.138941921E+00-1.148342278E+00-1.156851821E+00-1.164459919E+00 --1.171154862E+00-1.176926461E+00-1.181765127E+00-1.185659854E+00-1.188604515E+00 --1.190586308E+00-1.191603325E+00-1.191639529E+00-1.190693916E+00-1.188763902E+00 --1.185833486E+00-1.181896577E+00-1.176953654E+00-1.171003862E+00-1.164045571E+00 --1.156074151E+00-1.147080043E+00-1.137055077E+00-1.125995169E+00-1.113900182E+00 --1.100773677E+00-1.086622961E+00-1.071458014E+00-1.055286070E+00-1.038107134E+00 --1.019919866E+00-1.000725703E+00-9.805288208E-01-9.593357624E-01-9.371554353E-01 --9.139988768E-01-8.898792482E-01-8.648117099E-01-8.388133240E-01-8.119030913E-01 --7.841017938E-01-7.554320987E-01-7.259184503E-01-6.955871319E-01-6.644659489E-01 --6.325842663E-01-5.999724892E-01-5.666626992E-01-5.326889828E-01-4.980876599E-01 --4.628972396E-01-4.271584057E-01-3.909140241E-01-3.542090493E-01-3.170904923E-01 --2.796073776E-01-2.418106784E-01-2.037532882E-01-1.654899741E-01-1.270772388E-01 --8.857355707E-02-5.004307323E-02-1.154759866E-02 2.691648848E-02 6.541606086E-02 - 1.039632290E-01 1.425530355E-01 1.811833685E-01 2.198527792E-01 2.585598363E-01 - 2.973031763E-01 3.360816901E-01 3.748953118E-01 4.137386223E-01 1.581812115E-01 - 1.333256839E-01 1.085730199E-01 8.394529793E-02 5.944644899E-02 3.508735007E-02 - 1.088873791E-02-1.323123401E-02-3.763432382E-02-6.245123901E-02-8.765782646E-02 --1.132226867E-01-1.391183539E-01-1.653157801E-01-1.917844931E-01-2.184930144E-01 --2.454090045E-01-2.724993929E-01-2.997305536E-01-3.270684361E-01-3.544785768E-01 --3.819262608E-01-4.093766466E-01-4.367947899E-01-4.641458175E-01-4.913949161E-01 --5.185074928E-01-5.454491970E-01-5.721860289E-01-5.986843281E-01-6.249108858E-01 --6.508329870E-01-6.764182894E-01-7.016349871E-01-7.264514267E-01-7.508365299E-01 --7.747601035E-01-7.981942826E-01-8.211151583E-01-8.435006519E-01-8.653290623E-01 --8.865773598E-01-9.072195238E-01-9.272253207E-01-9.465643960E-01-9.652159783E-01 --9.831705182E-01-1.000413324E+00-1.016918335E+00-1.032662054E+00-1.047633012E+00 --1.061815286E+00-1.075190401E+00-1.087744472E+00-1.099462460E+00-1.110330968E+00 --1.120335726E+00-1.129465106E+00-1.137706677E+00-1.145048564E+00-1.151480399E+00 --1.156990730E+00-1.161570878E+00-1.165209932E+00-1.167900088E+00-1.169631267E+00 --1.170399824E+00-1.170188822E+00-1.168999692E+00-1.166829077E+00-1.163660725E+00 --1.159488308E+00-1.154312464E+00-1.148132477E+00-1.140946784E+00-1.132752385E+00 --1.123541578E+00-1.113306330E+00-1.102041787E+00-1.089746764E+00-1.076423520E+00 --1.062077470E+00-1.046717248E+00-1.030353288E+00-1.012992250E+00-9.946350130E-01 --9.752825139E-01-9.549384638E-01-9.336092027E-01-9.113033517E-01-8.880318577E-01 --8.638078248E-01-8.386464482E-01-8.125650025E-01-7.855826765E-01-7.577206630E-01 --7.290019931E-01-6.994516317E-01-6.690963367E-01-6.379648230E-01-6.060875128E-01 --5.734965544E-01-5.402255780E-01-5.063095477E-01-4.717851593E-01-4.366912198E-01 --4.010686906E-01-3.649606533E-01-3.284122944E-01-2.914708423E-01-2.541855130E-01 --2.166074516E-01-1.787896887E-01-1.407870723E-01-1.026561742E-01-6.445736960E-02 --2.625649063E-02 1.191455255E-02 5.011117333E-02 8.836293683E-02 1.266671051E-01 - 1.650198741E-01 2.034192006E-01 2.418631950E-01 2.803500929E-01 3.188782411E-01 - 3.574462803E-01 3.960540307E-01 4.346952896E-01 1.584306377E-01 1.337976220E-01 - 1.092783827E-01 8.489729802E-02 6.065861501E-02 3.657329815E-02 1.266522051E-02 --1.113175527E-02-3.517575941E-02-5.962396623E-02-8.445830558E-02-1.096466741E-01 --1.351619960E-01-1.609757906E-01-1.870581047E-01-2.133779880E-01-2.399036308E-01 --2.666024420E-01-2.934412150E-01-3.203862765E-01-3.474035223E-01-3.744585887E-01 --4.015169328E-01-4.285438889E-01-4.555048280E-01-4.823651667E-01-5.090905186E-01 --5.356466510E-01-5.619996779E-01-5.881160213E-01-6.139624068E-01-6.395059831E-01 --6.647140138E-01-6.895541994E-01-7.139949852E-01-7.380066081E-01-7.615629650E-01 --7.846399718E-01-8.072142290E-01-8.292618286E-01-8.507569478E-01-8.716704503E-01 --8.919704902E-01-9.116279556E-01-9.306270670E-01-9.489566233E-01-9.665970355E-01 --9.835199269E-01-9.997035590E-01-1.015136155E+00-1.029800228E+00-1.043676105E+00 --1.056749459E+00-1.069004878E+00-1.080427562E+00-1.091003000E+00-1.100718958E+00 --1.109561568E+00-1.117519410E+00-1.124580652E+00-1.130734200E+00-1.135969787E+00 --1.140276397E+00-1.143646710E+00-1.146068271E+00-1.147535941E+00-1.148042591E+00 --1.147572009E+00-1.146127283E+00-1.143704132E+00-1.140286234E+00-1.135867173E+00 --1.130447764E+00-1.124027419E+00-1.116604614E+00-1.108177314E+00-1.098739855E+00 --1.088284735E+00-1.076806873E+00-1.064304409E+00-1.050778614E+00-1.036233840E+00 --1.020677184E+00-1.004118462E+00-9.865684926E-01-9.680337469E-01-9.485164941E-01 --9.280200973E-01-9.065506015E-01-8.841165910E-01-8.607288991E-01-8.364006276E-01 --8.111470815E-01-7.849856325E-01-7.579357833E-01-7.300189827E-01-7.012587157E-01 --6.716803574E-01-6.413112619E-01-6.101805980E-01-5.783194961E-01-5.457609085E-01 --5.125396225E-01-4.786920632E-01-4.442562611E-01-4.092716411E-01-3.737794740E-01 --3.378230997E-01-3.014479122E-01-2.647013205E-01-2.276326893E-01-1.902933090E-01 --1.527363503E-01-1.150166854E-01-7.719169020E-02-3.932553739E-02-1.470042583E-03 - 3.640132542E-02 7.433368170E-02 1.123293921E-01 1.503830991E-01 1.884919616E-01 - 2.266535529E-01 2.648655782E-01 3.031259398E-01 3.414326718E-01 3.797841466E-01 - 4.181800685E-01 4.566134361E-01 1.586903983E-01 1.342898198E-01 1.100142029E-01 - 8.589026826E-02 6.192261385E-02 3.812236045E-02 1.451574940E-02-8.947898023E-03 --3.261652168E-02-5.667822152E-02-8.112259824E-02-1.059166132E-01-1.310335625E-01 --1.564455993E-01-1.821233222E-01-2.080362721E-01-2.341530910E-01-2.604416354E-01 --2.868691291E-01-3.134022866E-01-3.400073520E-01-3.666503023E-01-3.932968888E-01 --4.199127385E-01-4.464634628E-01-4.729146570E-01-4.992321129E-01-5.253817273E-01 --5.513296154E-01-5.770421676E-01-6.024858330E-01-6.276273472E-01-6.524340429E-01 --6.768745963E-01-7.009209248E-01-7.245470797E-01-7.477279874E-01-7.704385605E-01 --7.926525487E-01-8.143415249E-01-8.354739822E-01-8.560174403E-01-8.759464340E-01 --8.952472532E-01-9.139058180E-01-9.318982551E-01-9.491945945E-01-9.657754053E-01 --9.816280852E-01-9.967330693E-01-1.011070073E+00-1.024624340E+00-1.037379668E+00 --1.049319906E+00-1.060431001E+00-1.070698706E+00-1.080109060E+00-1.088650487E+00 --1.096309609E+00-1.103075592E+00-1.108936328E+00-1.113882929E+00-1.117902682E+00 --1.120990236E+00-1.123130302E+00-1.124321825E+00-1.124553582E+00-1.123811372E+00 --1.122099272E+00-1.119412168E+00-1.115733769E+00-1.111057466E+00-1.105384278E+00 --1.098713983E+00-1.091045092E+00-1.082375919E+00-1.072702748E+00-1.062019102E+00 --1.050319844E+00-1.037602833E+00-1.023868827E+00-1.009121321E+00-9.933665189E-01 --9.766130971E-01-9.588720014E-01-9.401544231E-01-9.204671052E-01-8.998141278E-01 --8.782013757E-01-8.556373068E-01-8.321328214E-01-8.077010797E-01-7.823574540E-01 --7.561195584E-01-7.290070677E-01-7.010418085E-01-6.722475915E-01-6.426502821E-01 --6.122776635E-01-5.811595337E-01-5.493275294E-01-5.168152333E-01-4.836580722E-01 --4.498933571E-01-4.155601177E-01-3.806990768E-01-3.453525090E-01-3.095641840E-01 --2.733797157E-01-2.368466846E-01-2.000146151E-01-1.629349361E-01-1.256608402E-01 --8.824750231E-02-5.075534416E-02-1.324397054E-02 2.427990496E-02 6.186843197E-02 - 9.953232541E-02 1.372651431E-01 1.750628154E-01 2.129222828E-01 2.508406617E-01 - 2.888153137E-01 3.268438357E-01 3.649239644E-01 4.030538080E-01 4.412329454E-01 - 4.794535493E-01 1.589605811E-01 1.348018741E-01 1.107795958E-01 8.692282371E-02 - 6.323649155E-02 3.973192075E-02 1.643670483E-02-6.684982755E-03-2.996272526E-02 --5.362062404E-02-7.765788996E-02-1.020403334E-01-1.267415692E-01-1.517343411E-01 --1.769897633E-01-2.024778629E-01-2.281677396E-01-2.540276809E-01-2.800253248E-01 --3.061277545E-01-3.323015728E-01-3.585131062E-01-3.847283726E-01-4.109132505E-01 --4.370335894E-01-4.630551615E-01-4.889438231E-01-5.146655455E-01-5.401862701E-01 --5.654720726E-01-5.904894599E-01-6.152059062E-01-6.395916298E-01-6.636190200E-01 --6.872614510E-01-7.104925698E-01-7.332853791E-01-7.556115371E-01-7.774403946E-01 --7.987386425E-01-8.194747309E-01-8.396273891E-01-8.591825467E-01-8.781225752E-01 --8.964198182E-01-9.140442519E-01-9.309781673E-01-9.472076251E-01-9.627115221E-01 --9.774687064E-01-9.914637528E-01-1.004680071E+00-1.017100181E+00-1.028710196E+00 --1.039493745E+00-1.049437671E+00-1.058528352E+00-1.066752708E+00-1.074098853E+00 --1.080554701E+00-1.086109374E+00-1.090752000E+00-1.094472711E+00-1.097263230E+00 --1.099109807E+00-1.100012742E+00-1.099957132E+00-1.098931829E+00-1.096941172E+00 --1.093979157E+00-1.090029730E+00-1.085086236E+00-1.079149815E+00-1.072220524E+00 --1.064297119E+00-1.055378186E+00-1.045461270E+00-1.034541228E+00-1.022613371E+00 --1.009675434E+00-9.957278491E-01-9.807737363E-01-9.648186637E-01-9.478705459E-01 --9.299395784E-01-9.110378383E-01-8.911769415E-01-8.703643938E-01-8.486064263E-01 --8.259115032E-01-8.022905668E-01-7.777569115E-01-7.523261178E-01-7.260159361E-01 --6.988463765E-01-6.708395194E-01-6.420195940E-01-6.124128434E-01-5.820475807E-01 --5.509540373E-01-5.191644757E-01-4.867130224E-01-4.536357178E-01-4.199704351E-01 --3.857569097E-01-3.510366345E-01-3.158527761E-01-2.802501423E-01-2.442750415E-01 --2.079753305E-01-1.714006713E-01-1.346025627E-01-9.763428206E-02-6.055322648E-02 --2.342106525E-02 1.373449439E-02 5.095629522E-02 8.826484537E-02 1.256546543E-01 - 1.631202026E-01 2.006576763E-01 2.382635435E-01 2.759345351E-01 3.136676667E-01 - 3.514602106E-01 3.893096043E-01 4.272137107E-01 4.651720123E-01 5.031758606E-01 - 1.592414251E-01 1.353335872E-01 1.115738200E-01 8.799357934E-02 6.459817406E-02 - 4.139923353E-02 1.842435422E-02-4.348622660E-03-2.722074658E-02-5.045818553E-02 --7.407191107E-02-9.802619957E-02-1.222949213E-01-1.468514258E-01-1.716673231E-01 --1.967131006E-01-2.219582983E-01-2.473716336E-01-2.729211542E-01-2.985743116E-01 --3.242980380E-01-3.500589655E-01-3.758234065E-01-4.015574665E-01-4.272271201E-01 --4.527983144E-01-4.782368208E-01-5.035084067E-01-5.285790764E-01-5.534154849E-01 --5.779864884E-01-6.022630760E-01-6.262172538E-01-6.498214718E-01-6.730478813E-01 --6.958677943E-01-7.182510494E-01-7.401649326E-01-7.615756531E-01-7.824538367E-01 --8.027811145E-01-8.225417228E-01-8.417140069E-01-8.602679229E-01-8.781739071E-01 --8.954154834E-01-9.119773750E-01-9.278366330E-01-9.429715171E-01-9.573661791E-01 --9.710033609E-01-9.838641517E-01-9.959345949E-01-1.007197008E+00-1.017638503E+00 --1.027243318E+00-1.035999175E+00-1.043892209E+00-1.050910955E+00-1.057042466E+00 --1.062277613E+00-1.066602549E+00-1.070011583E+00-1.072491403E+00-1.074033076E+00 --1.074635384E+00-1.074280568E+00-1.072961076E+00-1.070681129E+00-1.067433955E+00 --1.063203708E+00-1.057983623E+00-1.051775077E+00-1.044578547E+00-1.036392984E+00 --1.027217143E+00-1.017049471E+00-1.005886312E+00-9.937235217E-01-9.805590527E-01 --9.663933075E-01-9.512290997E-01-9.350717317E-01-9.179287260E-01-8.998096521E-01 --8.807262066E-01-8.606916144E-01-8.397180396E-01-8.178142417E-01-7.949888618E-01 --7.712529744E-01-7.466200684E-01-7.211059126E-01-6.947285835E-01-6.675082997E-01 --6.394675337E-01-6.106308425E-01-5.810249228E-01-5.506784893E-01-5.196223379E-01 --4.878891695E-01-4.555137030E-01-4.225325335E-01-3.889841243E-01-3.549087505E-01 --3.203484731E-01-2.853471028E-01-2.499501021E-01-2.142045205E-01-1.781589794E-01 --1.418635662E-01-1.053698275E-01-6.873250401E-02-3.201246629E-02 4.749318409E-03 - 4.158163928E-02 7.851184415E-02 1.155366707E-01 1.526492937E-01 1.898449762E-01 - 2.271194556E-01 2.644687930E-01 3.018893923E-01 3.393779678E-01 3.769314961E-01 - 4.145471205E-01 4.522224440E-01 4.899568371E-01 5.277408337E-01 1.595331649E-01 - 1.358846733E-01 1.123960682E-01 8.910119613E-02 6.600573962E-02 4.312171793E-02 - 2.047499239E-02-1.944664779E-03-2.439735897E-02-4.719826240E-02-7.037264467E-02 --9.388281448E-02-1.177027978E-01-1.418065467E-01-1.661661513E-01-1.907525524E-01 --2.155357296E-01-2.404848184E-01-2.655682359E-01-2.907537727E-01-3.160087313E-01 --3.412999944E-01-3.665940786E-01-3.918573432E-01-4.170557600E-01-4.421551875E-01 --4.671214773E-01-4.919208754E-01-5.165212622E-01-5.408925428E-01-5.650055957E-01 --5.888318468E-01-6.123426284E-01-6.355087576E-01-6.583001290E-01-6.806848406E-01 --7.026287934E-01-7.240985213E-01-7.450682399E-01-7.655200541E-01-7.854357144E-01 --8.047901193E-01-8.235514309E-01-8.416915072E-01-8.591943137E-01-8.760427668E-01 --8.922127023E-01-9.076817970E-01-9.224333701E-01-9.364497746E-01-9.497109980E-01 --9.622023848E-01-9.739055952E-01-9.848068007E-01-9.948895458E-01-1.004141347E+00 --1.012547125E+00-1.020094953E+00-1.026771795E+00-1.032566146E+00-1.037467442E+00 --1.041462830E+00-1.044547255E+00-1.046703826E+00-1.047929201E+00-1.048219016E+00 --1.047553937E+00-1.045929910E+00-1.043350572E+00-1.039808474E+00-1.035288199E+00 --1.029782961E+00-1.023294211E+00-1.015822803E+00-1.007368136E+00-9.979291967E-01 --9.875048301E-01-9.760928040E-01-9.636898863E-01-9.502942648E-01-9.359065124E-01 --9.205295171E-01-9.041683549E-01-8.868303700E-01-8.685249651E-01-8.492633787E-01 --8.290588002E-01-8.079256369E-01-7.858768002E-01-7.629227574E-01-7.390747308E-01 --7.143464340E-01-6.887539548E-01-6.623156086E-01-6.350520217E-01-6.069859469E-01 --5.781423679E-01-5.485483623E-01-5.182331323E-01-4.872278755E-01-4.555658697E-01 --4.232822891E-01-3.904142564E-01-3.570007829E-01-3.230826827E-01-2.887025364E-01 --2.539046487E-01-2.187350025E-01-1.832411989E-01-1.474723973E-01-1.114791492E-01 --7.531438630E-02-3.903674507E-02-2.694218524E-03 3.372509759E-02 7.025413333E-02 - 1.068924089E-01 1.436315972E-01 1.804659374E-01 2.173904292E-01 2.544004025E-01 - 2.914915730E-01 3.286600144E-01 3.659021347E-01 4.032146340E-01 4.405944022E-01 - 4.780388211E-01 5.155471644E-01 5.531091511E-01 1.598361660E-01 1.364551070E-01 - 1.132458487E-01 9.024459808E-02 6.745739597E-02 4.489670658E-02 2.258565543E-02 - 5.245125922E-04-2.149881607E-02-4.384859558E-02-6.656832817E-02-8.961898238E-02 --1.129745545E-01-1.366095705E-01-1.604966039E-01-1.846070203E-01-2.089112045E-01 --2.333787043E-01-2.579783180E-01-2.826781223E-01-3.074457201E-01-3.322482766E-01 --3.570524113E-01-3.818244878E-01-4.065306001E-01-4.311370162E-01-4.556110655E-01 --4.799219344E-01-5.040396713E-01-5.279349176E-01-5.515783113E-01-5.749402182E-01 --5.979903455E-01-6.206973160E-01-6.430277694E-01-6.649469814E-01-6.864230049E-01 --7.074329710E-01-7.279582091E-01-7.479776138E-01-7.674630542E-01-7.863819368E-01 --8.047077171E-01-8.224240784E-01-8.395123765E-01-8.559471761E-01-8.717055577E-01 --8.867703163E-01-9.011232920E-01-9.147432300E-01-9.276145983E-01-9.397192359E-01 --9.510412029E-01-9.615649537E-01-9.712755198E-01-9.801588507E-01-9.882009116E-01 --9.953894635E-01-1.001710675E+00-1.007155127E+00-1.011708670E+00-1.015363139E+00 --1.018109876E+00-1.019932074E+00-1.020830270E+00-1.020796241E+00-1.019810482E+00 --1.017872049E+00-1.014983882E+00-1.011137957E+00-1.006319198E+00-1.000520830E+00 --9.937445470E-01-9.859915954E-01-9.772616823E-01-9.675541486E-01-9.568683053E-01 --9.452028722E-01-9.325555872E-01-9.189252814E-01-9.043127795E-01-8.887210611E-01 --8.721553708E-01-8.546229783E-01-8.361331793E-01-8.166972222E-01-7.963280409E-01 --7.750403399E-01-7.528497511E-01-7.297702244E-01-7.058142928E-01-6.809958666E-01 --6.553313309E-01-6.288394092E-01-6.015410175E-01-5.734593675E-01-5.446197882E-01 --5.150497994E-01-4.847790152E-01-4.538391451E-01-4.222638642E-01-3.900888848E-01 --3.573518234E-01-3.240921310E-01-2.903511326E-01-2.561719147E-01-2.215992358E-01 --1.866795205E-01-1.514608265E-01-1.159926763E-01-8.032666263E-02-4.451941495E-02 --8.622278106E-03 2.736201290E-02 6.346818276E-02 9.969899308E-02 1.360449148E-01 - 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1.195609398E-01 1.475928490E-01 1.760251735E-01 2.048371549E-01 2.340089569E-01 - 2.635215479E-01 2.933567714E-01 3.234974256E-01 3.539272473E-01 3.846308338E-01 - 4.155935994E-01 4.468018051E-01 4.782425418E-01 5.099036596E-01 5.417737054E-01 - 5.738419319E-01 6.060982971E-01 6.385334185E-01 6.711384933E-01 7.039052674E-01 - 7.368260507E-01 7.698936991E-01 8.031015715E-01 8.364434643E-01 8.699135844E-01 - 9.035065601E-01 9.372174129E-01 9.710414178E-01 1.004974614E+00 1.039016217E+00 - 1.073149088E+00 1.675550643E-01 1.494361365E-01 1.316632897E-01 1.143020405E-01 - 9.735513955E-02 8.083632454E-02 6.476103180E-02 4.914414605E-02 3.399996314E-02 - 1.934697996E-02 5.211794201E-03-8.512206714E-03-2.226415156E-02-3.618844328E-02 --5.026238068E-02-6.446174536E-02-7.876769683E-02-9.316040691E-02-1.076189865E-01 --1.221216408E-01-1.366452862E-01-1.511658510E-01-1.656594759E-01-1.801032007E-01 --1.944742292E-01-2.087492925E-01-2.229041208E-01-2.369137751E-01-2.507529473E-01 --2.643972348E-01-2.778227857E-01-2.910060543E-01-3.039240255E-01-3.165525125E-01 --3.288660660E-01-3.408415040E-01-3.524586732E-01-3.636949833E-01-3.745249193E-01 --3.849275730E-01-3.948850965E-01-4.043743227E-01-4.133730475E-01-4.218646178E-01 --4.298300020E-01-4.372480022E-01-4.441014236E-01-4.503743700E-01-4.560492301E-01 --4.611088912E-01-4.655378434E-01-4.693228564E-01-4.724502709E-01-4.749043267E-01 --4.766711220E-01-4.777422911E-01-4.781083667E-01-4.777558510E-01-4.766709176E-01 --4.748475292E-01-4.722823546E-01-4.689692969E-01-4.648990053E-01-4.600605551E-01 --4.544484334E-01-4.480640587E-01-4.409085745E-01-4.329814890E-01-4.242812623E-01 --4.148053025E-01-4.045508203E-01-3.935172997E-01-3.817103886E-01-3.691379475E-01 --3.558080422E-01-3.417289076E-01-3.269092356E-01-3.113582485E-01-2.950858902E-01 --2.781028782E-01-2.604209532E-01-2.420529147E-01-2.230131054E-01-2.033182832E-01 --1.829872705E-01-1.620403551E-01-1.404989538E-01-1.183857936E-01-9.572529258E-02 --7.254448571E-02-4.887426374E-02-2.473957629E-02-1.440193768E-04 2.495826428E-02 - 5.058432449E-02 7.672313040E-02 1.033476206E-01 1.304308928E-01 1.579492310E-01 - 1.858806240E-01 2.142041076E-01 2.428997647E-01 2.719487289E-01 3.013329548E-01 - 3.310350883E-01 3.610385716E-01 3.913277193E-01 4.218876942E-01 4.527044319E-01 - 4.837646046E-01 5.150556531E-01 5.465657697E-01 5.782838339E-01 6.101993524E-01 - 6.423024656E-01 6.745839543E-01 7.070352012E-01 7.396481177E-01 7.724151069E-01 - 8.053290763E-01 8.383834303E-01 8.715720389E-01 9.048891758E-01 9.383294885E-01 - 9.718879852E-01 1.005559914E+00 1.039341313E+00 1.073231423E+00 1.107213066E+00 - 1.682240078E-01 1.504333964E-01 1.329951825E-01 1.159753581E-01 9.937584805E-02 - 8.320970343E-02 6.749172822E-02 5.223618859E-02 3.745661792E-02 2.316797569E-02 - 9.401420110E-03-3.880063851E-03-1.703819943E-02-3.033796244E-02-4.378653513E-02 --5.735405092E-02-7.102159180E-02-8.476996537E-02-9.857854473E-02-1.124254773E-01 --1.262879657E-01-1.401434207E-01-1.539697280E-01-1.677447317E-01-1.814457603E-01 --1.950493214E-01-2.085311808E-01-2.218668485E-01-2.350324736E-01-2.480044924E-01 --2.607598160E-01-2.732756495E-01-2.855282851E-01-2.974928479E-01-3.091459504E-01 --3.204670265E-01-3.314345134E-01-3.420232861E-01-3.522112279E-01-3.619804040E-01 --3.713092550E-01-3.801744158E-01-3.885578077E-01-3.964420953E-01-4.038059911E-01 --4.106306226E-01-4.169001972E-01-4.225975927E-01-4.277053110E-01-4.322070574E-01 --4.360884454E-01-4.393363314E-01-4.419361703E-01-4.438723991E-01-4.451335814E-01 --4.457114067E-01-4.455951263E-01-4.447709189E-01-4.432270000E-01-4.409588805E-01 --4.379625427E-01-4.342312893E-01-4.297558300E-01-4.245262332E-01-4.185387147E-01 --4.117948928E-01-4.042957169E-01-3.960408384E-01-3.870291325E-01-3.772587012E-01 --3.667276660E-01-3.554362473E-01-3.433904168E-01-3.305983883E-01-3.170686237E-01 --3.028098504E-01-2.878312761E-01-2.721427005E-01-2.557546679E-01-2.386785766E-01 --2.209268328E-01-2.025130338E-01-1.834521190E-01-1.637612227E-01-1.434595485E-01 --1.225677973E-01-1.011081022E-01-7.910480064E-02-5.658674293E-02-3.358005137E-02 --1.009336358E-02 1.389255806E-02 3.842759503E-02 6.350982404E-02 8.911574764E-02 - 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5.225409914E-02 7.681272357E-02 1.019028760E-01 1.274971444E-01 1.535711858E-01 - 1.801021714E-01 2.070681738E-01 2.344481390E-01 2.622219565E-01 2.903704913E-01 - 3.188755779E-01 3.477199801E-01 3.768873773E-01 4.063622104E-01 4.361294083E-01 - 4.661744414E-01 4.964834701E-01 5.270433834E-01 5.578417664E-01 5.888668306E-01 - 6.201073929E-01 6.515529070E-01 6.831934478E-01 7.150196574E-01 7.470226897E-01 - 7.791942132E-01 8.115264261E-01 8.440120300E-01 8.766441726E-01 9.094164025E-01 - 9.423226696E-01 9.753573373E-01 1.008515167E+00 1.041791265E+00 1.075180916E+00 - 1.108680137E+00 1.142288141E+00 1.175987730E+00 1.696900219E-01 1.525534841E-01 - 1.357796601E-01 1.194351590E-01 1.035203129E-01 8.804692367E-02 7.302844847E-02 - 5.847788652E-02 4.440809758E-02 3.083107475E-02 1.776123693E-02 5.222072640E-03 --6.877321168E-03-1.894794216E-02-3.114729191E-02-4.345724610E-02-5.585332006E-02 --6.831680711E-02-8.082789105E-02-9.336639644E-02-1.059120899E-01-1.184443669E-01 --1.309421353E-01-1.433836118E-01-1.557462989E-01-1.680074501E-01-1.801444297E-01 --1.921348670E-01-2.039564254E-01-2.155871521E-01-2.270046294E-01-2.381850486E-01 --2.491052275E-01-2.597442368E-01-2.700817147E-01-2.800942664E-01-2.897584827E-01 --2.990550007E-01-3.079650579E-01-3.164657641E-01-3.245359432E-01-3.321586411E-01 --3.393151418E-01-3.459846065E-01-3.521492112E-01-3.577930968E-01-3.628989440E-01 --3.674495382E-01-3.714289073E-01-3.748225879E-01-3.776171920E-01-3.797986144E-01 --3.813518785E-01-3.822644982E-01-3.825276098E-01-3.821314237E-01-3.810637081E-01 --3.793118830E-01-3.768687659E-01-3.737304270E-01-3.698916117E-01-3.653452349E-01 --3.600827058E-01-3.540965441E-01-3.473856883E-01-3.399518081E-01-3.317956595E-01 --3.229173571E-01-3.133167209E-01-3.029932707E-01-2.919469358E-01-2.801795068E-01 --2.676976267E-01-2.545101511E-01-2.406262963E-01-2.260556908E-01-2.108084914E-01 --1.948955896E-01-1.783286281E-01-1.611202593E-01-1.432840729E-01-1.248348691E-01 --1.057889679E-01-8.616495411E-02-6.598535324E-02-4.527585003E-02-2.405348277E-02 --2.316585131E-03 1.998514411E-02 4.288429980E-02 6.637438729E-02 9.043050421E-02 - 1.150237531E-01 1.401289113E-01 1.657225657E-01 1.917822099E-01 2.182860936E-01 - 2.452133159E-01 2.725438560E-01 3.002585737E-01 3.283392113E-01 3.567684048E-01 - 3.855296663E-01 4.146073556E-01 4.439866575E-01 4.736533664E-01 5.035936503E-01 - 5.337941823E-01 5.642422805E-01 5.949259285E-01 6.258337417E-01 6.569549015E-01 - 6.882791402E-01 7.197967720E-01 7.514986775E-01 7.833762545E-01 8.154213652E-01 - 8.476263362E-01 8.799839774E-01 9.124875593E-01 9.451307652E-01 9.779076421E-01 - 1.010812597E+00 1.043840417E+00 1.076986240E+00 1.110245411E+00 1.143613996E+00 - 1.177091213E+00 1.210659879E+00 1.704937669E-01 1.536817640E-01 1.372365954E-01 - 1.212250437E-01 1.056466594E-01 9.051264088E-02 7.583601509E-02 6.162947001E-02 - 4.790516754E-02 3.467381894E-02 2.194566330E-02 9.744032182E-03-1.952164630E-03 --1.343862290E-02-2.501376404E-02-3.669940887E-02-4.846456069E-02-6.029001490E-02 --7.215734317E-02-8.404735715E-02-9.594036944E-02-1.078162172E-01-1.196540642E-01 --1.314323940E-01-1.431293619E-01-1.547231260E-01-1.661919263E-01-1.775140216E-01 --1.886679898E-01-1.996319581E-01-2.103829334E-01-2.208981108E-01-2.311563538E-01 --2.411377096E-01-2.508199485E-01-2.601796438E-01-2.691965078E-01-2.778524042E-01 --2.861257226E-01-2.939944174E-01-3.014405268E-01-3.084467334E-01-3.149924872E-01 --3.210587206E-01-3.266292729E-01-3.316875755E-01-3.362162225E-01-3.401987947E-01 --3.436201340E-01-3.464664489E-01-3.487242157E-01-3.503790591E-01-3.514167305E-01 --3.518265611E-01-3.515995550E-01-3.507252201E-01-3.491913083E-01-3.469867088E-01 --3.441058367E-01-3.405444517E-01-3.362969059E-01-3.313562096E-01-3.257143937E-01 --3.193653680E-01-3.123089744E-01-3.045468135E-01-2.960796816E-01-2.869080061E-01 --2.770320978E-01-2.664522016E-01-2.551691563E-01-2.431855486E-01-2.305083753E-01 --2.171467900E-01-2.031103485E-01-1.884090988E-01-1.730536271E-01-1.570553048E-01 --1.404262268E-01-1.231793994E-01-1.053290910E-01-8.689129163E-02-6.788489281E-02 --4.833324603E-02-2.825267740E-02-7.643199694E-03 1.352806680E-02 3.531825843E-02 - 5.772572464E-02 8.073054841E-02 1.043041775E-01 1.284204103E-01 1.530553143E-01 - 1.781860745E-01 2.037905834E-01 2.298474061E-01 2.563358704E-01 2.832361235E-01 - 3.105291319E-01 3.381966704E-01 3.662213202E-01 3.945864783E-01 4.232763644E-01 - 4.522759911E-01 4.815711478E-01 5.111483564E-01 5.409945986E-01 5.710971526E-01 - 6.014437781E-01 6.320228371E-01 6.628232996E-01 6.938347096E-01 7.250471239E-01 - 7.564511018E-01 7.880377356E-01 8.197986348E-01 8.517258821E-01 8.838119819E-01 - 9.160498591E-01 9.484328796E-01 9.809548315E-01 1.013609885E+00 1.046392545E+00 - 1.079297640E+00 1.112320334E+00 1.145455993E+00 1.178700732E+00 1.212053811E+00 - 1.245498108E+00 1.713484688E-01 1.548586866E-01 1.387392621E-01 1.230569682E-01 - 1.078107780E-01 9.301165518E-02 7.867249308E-02 6.480506832E-02 5.142023098E-02 - 3.852752145E-02 2.613497513E-02 1.425496870E-02 2.899786167E-03-8.063980336E-03 --1.902554845E-02-3.008916199E-02-4.122827199E-02-5.242111984E-02-6.365019226E-02 --7.489697191E-02-8.614227649E-02-9.736627718E-02-1.085484839E-01-1.196680141E-01 --1.307038611E-01-1.416349707E-01-1.524402763E-01-1.630988852E-01-1.735896155E-01 --1.838902934E-01-1.939785249E-01-2.038332794E-01-2.134349230E-01-2.227621985E-01 --2.317920107E-01-2.405035504E-01-2.488787508E-01-2.568974050E-01-2.645372608E-01 --2.717792568E-01-2.786066473E-01-2.849999473E-01-2.909392977E-01-2.964077443E-01 --3.013893672E-01-3.058669244E-01-3.098236218E-01-3.132438839E-01-3.161133227E-01 --3.184184223E-01-3.201454467E-01-3.212801210E-01-3.218095406E-01-3.217241567E-01 --3.210145678E-01-3.196698525E-01-3.176781458E-01-3.150300951E-01-3.117209435E-01 --3.077461332E-01-3.030998838E-01-2.977754378E-01-2.917655396E-01-2.850655025E-01 --2.776758347E-01-2.695980577E-01-2.608330570E-01-2.513816249E-01-2.412445911E-01 --2.304229154E-01-2.189183401E-01-2.067342610E-01-1.938780368E-01-1.803591060E-01 --1.661873327E-01-1.513731357E-01-1.359274405E-01-1.198618683E-01-1.031891046E-01 --8.592321461E-02-6.808067207E-02-4.968273516E-02-3.074379400E-02-1.126355334E-02 - 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1.528165590E+00-9.438665749E-01 1.531131000E+00-9.877770450E-01 1.534354472E+00 --1.032557312E+00 1.537861781E+00-1.078251076E+00 1.541682098E+00-1.124901847E+00 - 1.545848666E+00-1.172552274E+00 1.550399219E+00-1.221243532E+00 1.555376870E+00 --1.271014237E+00 1.560830988E+00-1.321899139E+00 1.566817877E+00-1.373927756E+00 - 1.573402300E+00-1.427121991E+00 1.580658509E+00-1.481493748E+00 1.588671798E+00 --1.537041607E+00 1.597540241E+00-1.593746658E+00 1.607376310E+00-1.651567691E+00 - 1.618308962E+00-1.710434930E+00 1.630485726E+00-1.770242560E+00 1.644073863E+00 --1.830840929E+00 1.659262523E+00-1.892026010E+00 1.676262765E+00-1.953529600E+00 - 1.695306600E+00-2.015009077E+00 1.716644148E+00-2.076038022E+00 1.740537151E+00 --2.136100857E+00 1.767248898E+00-2.194592800E+00 1.797029474E+00-2.250828778E+00 - 1.830096205E+00-2.304064438E+00 1.866611040E+00-2.353529933E+00 1.906656954E+00 --2.398476390E+00 1.950218066E+00-2.438229230E+00 1.997167062E+00-2.472242029E+00 - 2.047263795E+00-2.500141015E+00 2.100167566E+00-2.521749049E+00 2.155459350E+00 --2.537089234E+00 2.212671410E+00-2.546365760E+00 2.271318696E+00-2.549928171E+00 - 2.330926494E+00-2.548229257E+00 2.391052257E+00-2.541781603E+00 2.451299771E+00 --2.531120255E+00 2.511326441E+00-2.516773490E+00 2.570844917E+00-2.499242701E+00 - 2.629620910E+00-2.478989767E+00 2.687468554E+00-2.456430864E+00 2.744244525E+00 --2.431935287E+00 2.799842096E+00-2.405825806E+00 2.854185156E+00-2.378382084E+00 - 2.907222757E+00-2.349845275E+00 2.958924549E+00-2.320420746E+00 3.009276532E+00 --2.290284159E+00 3.058277776E+00-2.259583699E+00 3.105937477E+00-2.228445229E+00 - 3.152272679E+00-2.196974266E+00 3.197306338E+00-2.165259863E+00 3.241065796E+00 --2.133376430E+00 3.283581523E+00-2.101386004E+00 3.324886142E+00-2.069340285E+00 - 3.365013631E+00-2.037282057E+00 3.403998692E+00-2.005246451E+00 3.441876260E+00 --1.973262178E+00 3.478681149E+00-1.941352607E+00 3.514447692E+00-1.909536251E+00 - 3.549209576E+00-1.877827790E+00 3.582999651E+00-1.846238566E+00 3.615849774E+00 --1.814776954E+00 3.647790780E+00-1.783449040E+00 3.678852355E+00-1.752258737E+00 - 3.709063054E+00-1.721208311E+00 3.738450237E+00-1.690298483E+00 3.767040092E+00 --1.659528777E+00 3.794857612E+00-1.628897626E+00 3.821926634E+00-1.598402618E+00 - 3.848269844E+00-1.568040601E+00 3.873908794E+00-1.537807799E+00 3.898863956E+00 --1.507699970E+00 3.923154697E+00-1.477712400E+00 3.946799391E+00-1.447840134E+00 - 3.969815351E+00-1.418077856E+00 3.992218982E+00-1.388420173E+00 4.014025684E+00 --1.358861442E+00 4.035249996E+00-1.329395994E+00 4.055905560E+00-1.300018072E+00 - 4.076005151E+00-1.270721868E+00 4.095560799E+00-1.241501674E+00 4.114583656E+00 --1.212351696E+00 4.133084218E+00-1.183266324E+00 4.151072178E+00-1.154239934E+00 - 4.168556566E+00-1.125267045E+00 4.185545774E+00-1.096342330E+00 4.202047474E+00 --1.067460514E+00 4.218068818E+00-1.038616569E+00 4.233616298E+00-1.009805561E+00 - 4.248695852E+00-9.810227400E-01 4.263312936E+00-9.522635962E-01 4.277472389E+00 --9.235237230E-01 4.291178658E+00-8.947990041E-01 4.304435668E+00-8.660854913E-01 - 4.317246877E+00-8.373794402E-01 4.329615413E+00-8.086773973E-01 4.341543908E+00 --7.799760733E-01 4.353034666E+00-7.512724485E-01 4.364089675E+00-7.225637670E-01 - 4.374710490E+00-6.938474541E-01 4.384898478E+00-6.651212537E-01 4.394654668E+00 --6.363831269E-01 4.403979786E+00-6.076312661E-01 4.412874433E+00-5.788641700E-01 - 4.421338882E+00-5.500805352E-01 4.429373245E+00-5.212793231E-01 4.436977549E+00 --4.924597760E-01 4.444151529E+00-4.636213216E-01 4.450894901E+00-4.347636682E-01 - 4.457207284E+00-4.058867547E-01 4.463088084E+00-3.769907056E-01 4.468536806E+00 --3.480759119E-01 4.473552828E+00-3.191429453E-01 4.478135440E+00-2.901925612E-01 - 4.482284088E+00-2.612257380E-01 4.485998084E+00-2.322435926E-01 4.489276773E+00 --2.032474064E-01 4.492119692E+00-1.742386255E-01 4.494526218E+00-1.452187922E-01 - 4.496495959E+00-1.161895814E-01 4.498028669E+00-8.715275983E-02 4.499123931E+00 --5.811014675E-02 4.499781143E+00-2.906362128E-02 4.499999497E+00-1.513208407E-05 - 1.350313621E+00-2.677482172E+00 4.649797468E+00-2.677482172E+00 4.649797468E+00 - 2.677476176E+00 1.350313621E+00 2.677476176E+00 1.350313621E+00-2.677482172E+00 - - 1.51912315E-01 abs(PSI-AXIS) --> [T M**2] -1.36721084E+00 - 1.03921169E+00 R OF MAGAXE --> [M] 3.11763506E+00 - -9.99273915E-07 Z OF MAGAXE --> [M] -2.99782174E-06 - -5.04402802E-06 Z0 --> [M] -1.51320841E-05 - 3.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA - 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA - 1.00000000E+00 SIGN OF B0 IN EXPERIMENT (CHEASE ASSUMES 1.0) - 1.53755753E+00 TOTAL CURRENT --> [A] 3.67064822E+06 - 1.00000000E+00 SIGN OF IP IN EXPERIMENT (CHEASE ASSUMES 1.0) - 1.69999553E+00 b/a - 1.05000000E+00 Q_ZERO, USING SIGNS OF IP AND B0, WOULD GIVE: 1.05000000E+00 - 4.43373475E+00 Q_EDGE, USING SIGNS OF IP AND B0, WOULD GIVE: 4.43373475E+00 - 1.51426490E-01 POLOIDAL BETA - 2.34029713E-02 BETA_EXP=

*2*MU0/B0**2 - 7.25523874E-01 LI - 3.46308209E-02 PRESSURE ON AXIS --> [Pa] 2.75583316E+04 --> [10**19 M**-3 KEV]: 1.72024542E+01 - 1.63188124E-02 BETA - 2.18184292E-02 BETA* (SQRT()) - 5.58550793E-02 BETA-AXIS=2p0/(T0/Rmag)^2; with Rmag->Rgeo(LCFS): 5.17194368E-02 - -1.51912315E-01 PSI-AXIS --> [T M**2] -1.36721084E+00 - -9.54493226E-01 2*PI*PSI-AXIS --> -8.59043904E+00 - -1.51912315E-01 IP_SIGN*PSI-AXIS --> [T M**2] -1.36721084E+00 - -9.54493226E-01 IP_SIGN*2*PI*PSI-AXIS --> -8.59043904E+00 - 1.99999525E+00 ASPECT RATIO ; a/R= 5.00001188E-01 - 7.64779790E+00 VOLUME -> 2.06490543E+02 - 1.29389993E+00 AREA -> 1.16450994E+01 - 2.53018281E+01 SURFACE -> 2.27716453E+02 - 4.34432012E+00 LENGTH -> 1.30329604E+01 - 5.00003104E-01 RMIN -> RMIN [m] 1.50000931E+00 - 1.49999983E+00 RMAX -> RMAX [m] 4.49999950E+00 - -8.49976057E-01 ZMIN -> ZMIN [m] -2.54992817E+00 - 8.49976009E-01 ZMAX -> ZMAX [m] 2.54992803E+00 - 1.00000147E+00 RGEOM -> RGEOM [m] 3.00000440E+00 - 4.99998364E-01 MINOR RADIUS -> A [m] 1.49999509E+00 diff --git a/notebooks/equil_chease_binary_test.ipynb b/notebooks/equil_chease_binary_test.ipynb deleted file mode 100644 index 41100e09..00000000 --- a/notebooks/equil_chease_binary_test.ipynb +++ /dev/null @@ -1,267 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "import Pkg\n", - "\n", - "Pkg.activate(\"..\") \n", - "Pkg.instantiate()\n", - "\n", - "using Revise\n", - "using GeneralizedPerturbedEquilibrium, Plots\n", - "gr()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"Starting equilibrium reconstruction...\")\n", - "plasma_eq = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(\"Chease_Binary_example/equil.toml\")\n", - "println(\"Equilibrium reconstruction complete.\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", - "println(\"\\n--- Generating data for 2D color plots ---\")\n", - "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", - "# This part is identical to the previous steps.\n", - "equil_control = plasma_eq.config.control\n", - "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n", - "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n", - "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", - "println(\"Evaluating the 'rzphi' mapping spline...\")\n", - "fs_grid = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", - "println(\"Evaluation complete.\")\n", - "# 3. Transform the spline output to physical (R, Z) coordinates.\n", - "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", - "rfac_sq = fs_grid[:, :, 1]\n", - "eta_term = fs_grid[:, :, 2]\n", - "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", - "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", - "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", - "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", - "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", - "println(\"Calculated R and Z grids.\")\n", - "# 4. Create the 2D color plot for R(ψ,θ)\n", - "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", - "p_r_heatmap = heatmap(\n", - " psi_norm_grid,\n", - " theta_new_grid,\n", - " R_grid', # Note the transpose ' to match axis dimensions\n", - " title=\"Major Radius R(ψ, θ)\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"Poloidal Angle (θ_new)\",\n", - " colorbar_title=\"R [m]\"\n", - ")\n", - "display(p_r_heatmap)\n", - "# 5. Create the 2D color plot for Z(ψ,θ)\n", - "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", - "p_z_heatmap = heatmap(\n", - " psi_norm_grid,\n", - " theta_new_grid,\n", - " Z_grid', # Note the transpose ' to match axis dimensions\n", - " title=\"Vertical Position Z(ψ, θ)\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"Poloidal Angle (θ_new)\",\n", - " colorbar_title=\"Z [m]\"\n", - ")\n", - "display(p_z_heatmap)\n", - "println(\"\\n2D color plots for R and Z have been saved.\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", - "\n", - "# 1. Select a number of contours to display for clarity\n", - "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", - "num_theta_contours = 13 # e.g., every 30 degrees\n", - "\n", - "# 2. Initialize the plot\n", - "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", - "p_flux_surfaces = plot(\n", - " title=\"Flux Coordinate System Contours in (R, Z)\",\n", - " xlabel=\"R [m]\",\n", - " ylabel=\"Z [m]\",\n", - " aspect_ratio=:equal,\n", - " legend=:outertopright\n", - ")\n", - "\n", - "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", - "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", - "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", - "\n", - "for i in psi_indices\n", - " # Each row corresponds to a single psi value\n", - " # We must add the last point to the start to close the loop for a smooth plot\n", - " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", - " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", - " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", - "end\n", - "\n", - "# 4. Plot contours of constant θ (angle contours) in red\n", - "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", - "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", - "\n", - "for j in theta_indices\n", - " # Each column corresponds to a single theta value\n", - " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", - "end\n", - "\n", - "# 5. Add a legend manually (a common trick in Plots.jl)\n", - "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", - "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", - "\n", - "# 6. Display and save the final plot\n", - "display(p_flux_surfaces)\n", - "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", - "\n", - "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", - "# not just on its internal knot points.\n", - "psi_eval_grid = range(0.0, 1.0, length=200)\n", - "\n", - "# 2. Evaluate the 'sq' spline across this dense grid.\n", - "# Calling spline_eval with a vector input is efficient and returns a matrix\n", - "# where each column corresponds to one of the splined quantities.\n", - "println(\"Evaluating 'sq' spline on a dense grid...\")\n", - "evaluated_profiles = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", - "println(\"Evaluation complete.\")\n", - "\n", - "# 3. Extract each profile into its own variable for clarity.\n", - "# Based on the direct_run implementation:\n", - "# Column 1: F = R*Bt (Toroidal Field Function)\n", - "# Column 2: P*μ₀ (Scaled Pressure)\n", - "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", - "# Column 4: q (Safety Factor)\n", - "F_profile = evaluated_profiles[:, 1]\n", - "P_profile = evaluated_profiles[:, 2]\n", - "Flux_profile = evaluated_profiles[:, 3]\n", - "q_profile = evaluated_profiles[:, 4]\n", - "\n", - "# 4. Create and display the plots\n", - "\n", - "# Plot 1: Safety Factor (q)\n", - "p_q = plot(\n", - " psi_eval_grid,\n", - " q_profile,\n", - " title=\"Safety Factor Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"q\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_q)\n", - "\n", - "# Plot 2: Scaled Pressure (P*μ₀)\n", - "p_p = plot(\n", - " psi_eval_grid,\n", - " P_profile,\n", - " title=\"Pressure Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"P * μ₀ [T²]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_p)\n", - "\n", - "\n", - "# Plot 3: Toroidal Field Function (F)\n", - "p_f = plot(\n", - " psi_eval_grid,\n", - " F_profile,\n", - " title=\"Toroidal Field Function\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"F = R * B_t [T*m]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_f)\n", - "\n", - "# Plot 4: Combined plot for comparison\n", - "p_all_profiles = plot(\n", - " title=\"1D Equilibrium Profiles\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " legend=:best\n", - ")\n", - "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", - "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", - "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", - "display(p_all_profiles)\n", - "\n", - "\n", - "println(\"1D profile plots saved successfully.\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/equil_gfile_example.ipynb b/notebooks/equil_gfile_example.ipynb deleted file mode 100644 index d4768ebc..00000000 --- a/notebooks/equil_gfile_example.ipynb +++ /dev/null @@ -1,190 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "Pkg.resolve()\n", - "Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots\n", - "gr() " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": "# 1. Define the input parameters for the equilibrium solver.\n# - eq_filename: The name of the g-file we just created.\n# - eq_type: \"efit\" for a standard g-file.\n# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n# - mpsi, mtheta: Resolution of the output grid.\n\nequil_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(;\n eq_filename=\"beta_1.00\", # eq_filename\n eq_type=\"efit\", # eq_type\n jac_type=\"boozer\", # jac_type\n grid_type=\"ldp\",\n psilow=0.01, # psilow\n psihigh=0.994) # psihigh\n\n# 2. Run the main equilibrium setup function.\n# This will read the file, solve the direct problem, and return the final object.\nprintln(\"Starting equilibrium reconstruction...\")\n\n\nplasma_eq = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(equil_config)\n#plasma_eq = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(\"./DIIID_example/equil.toml\")\nprintln(\"Equilibrium reconstruction complete.\")" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", - "\n", - "# 1. Select a number of contours to display for clarity\n", - "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", - "num_theta_contours = 13 # e.g., every 30 degrees\n", - "\n", - "# 2. Initialize the plot\n", - "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", - "p_flux_surfaces = plot(\n", - " title=\"Flux Coordinate System Contours in (R, Z)\",\n", - " xlabel=\"R [m]\",\n", - " ylabel=\"Z [m]\",\n", - " aspect_ratio=:equal,\n", - " legend=:outertopright\n", - ")\n", - "\n", - "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", - "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", - "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", - "\n", - "for i in psi_indices\n", - " # Each row corresponds to a single psi value\n", - " # We must add the last point to the start to close the loop for a smooth plot\n", - " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", - " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", - " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", - "end\n", - "\n", - "# 4. Plot contours of constant θ (angle contours) in red\n", - "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", - "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", - "\n", - "for j in theta_indices\n", - " # Each column corresponds to a single theta value\n", - " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", - "end\n", - "\n", - "# 5. Add a legend manually (a common trick in Plots.jl)\n", - "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", - "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", - "\n", - "# 6. Display and save the final plot\n", - "display(p_flux_surfaces)\n", - "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", - "\n", - "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", - "# not just on its internal knot points.\n", - "psi_eval_grid = range(0.0, 1.0, length=200)\n", - "\n", - "# 2. Evaluate the 'sq' spline across this dense grid.\n", - "# Calling spline_eval with a vector input is efficient and returns a matrix\n", - "# where each column corresponds to one of the splined quantities.\n", - "println(\"Evaluating 'sq' spline on a dense grid...\")\n", - "evaluated_profiles = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", - "println(\"Evaluation complete.\")\n", - "\n", - "# 3. Extract each profile into its own variable for clarity.\n", - "# Based on the direct_run implementation:\n", - "# Column 1: F = R*Bt (Toroidal Field Function)\n", - "# Column 2: P*μ₀ (Scaled Pressure)\n", - "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", - "# Column 4: q (Safety Factor)\n", - "F_profile = evaluated_profiles[:, 1]\n", - "P_profile = evaluated_profiles[:, 2]\n", - "Flux_profile = evaluated_profiles[:, 3]\n", - "q_profile = evaluated_profiles[:, 4]\n", - "\n", - "# 4. Create and display the plots\n", - "\n", - "# Plot 1: Safety Factor (q)\n", - "p_q = plot(\n", - " psi_eval_grid,\n", - " q_profile,\n", - " title=\"Safety Factor Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"q\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_q)\n", - "\n", - "# Plot 2: Scaled Pressure (P*μ₀)\n", - "p_p = plot(\n", - " psi_eval_grid,\n", - " P_profile,\n", - " title=\"Pressure Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"P * μ₀ [T²]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_p)\n", - "\n", - "\n", - "# Plot 3: Toroidal Field Function (F)\n", - "p_f = plot(\n", - " psi_eval_grid,\n", - " F_profile,\n", - " title=\"Toroidal Field Function\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"F = R * B_t [T*m]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_f)\n", - "\n", - "# Plot 4: Combined plot for comparison\n", - "p_all_profiles = plot(\n", - " title=\"1D Equilibrium Profiles\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " legend=:best\n", - ")\n", - "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", - "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", - "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", - "display(p_all_profiles)\n", - "\n", - "\n", - "println(\"1D profile plots saved successfully.\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/notebooks/equil_inverse_test.ipynb b/notebooks/equil_inverse_test.ipynb deleted file mode 100644 index 4b45db87..00000000 --- a/notebooks/equil_inverse_test.ipynb +++ /dev/null @@ -1,207 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "# Test inverse.jl using the file inverse.inverse_chease4_run\n", - "\n", - "using Revise\n", - "using Pkg\n", - "Pkg.activate(\"..\") \n", - "Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots\n", - "gr() " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "# 1. Define the input parameters for the equilibrium solver.\n", - "# - eq_filename: The name of the g-file we just created.\n", - "# - eq_type: \"efit\" for a standard g-file.\n", - "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", - "# - mpsi, mtheta: Resolution of the output grid.\n", - "equil_input = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(control=GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumControl(;eq_filename=\"inverse.chease.10\",\n", - " eq_type=\"chease2\", jac_type=\"hamada\", mpsi=128, mtheta=256),\n", - " output=GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumOutput())\n", - "\n", - "# 2. Run the main equilibrium setup function.\n", - "# This will read the file, solve the direct problem, and return the final object.\n", - "println(\"Starting equilibrium reconstruction...\")\n", - "plasma_eq = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(\"./Chease_Binary_example/equil.toml\")\n", - "println(\"Equilibrium reconstruction complete.\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", - "\n", - "# 1. Select a number of contours to display for clarity\n", - "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", - "num_theta_contours = 13 # e.g., every 30 degrees\n", - "\n", - "# 2. Initialize the plot\n", - "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", - "p_flux_surfaces = plot(\n", - " title=\"Flux Coordinate System Contours in (R, Z)\",\n", - " xlabel=\"R [m]\",\n", - " ylabel=\"Z [m]\",\n", - " aspect_ratio=:equal,\n", - " legend=:outertopright\n", - ")\n", - "\n", - "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", - "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", - "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", - "\n", - "for i in psi_indices\n", - " # Each row corresponds to a single psi value\n", - " # We must add the last point to the start to close the loop for a smooth plot\n", - " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", - " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", - " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", - "end\n", - "\n", - "# 4. Plot contours of constant θ (angle contours) in red\n", - "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", - "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", - "\n", - "for j in theta_indices\n", - " # Each column corresponds to a single theta value\n", - " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", - "end\n", - "\n", - "# 5. Add a legend manually (a common trick in Plots.jl)\n", - "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", - "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", - "\n", - "# 6. Display and save the final plot\n", - "display(p_flux_surfaces)\n", - "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", - "\n", - "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", - "# not just on its internal knot points.\n", - "psi_eval_grid = range(0.0, 1.0, length=200)\n", - "\n", - "# 2. Evaluate the 'sq' spline across this dense grid.\n", - "# Calling spline_eval with a vector input is efficient and returns a matrix\n", - "# where each column corresponds to one of the splined quantities.\n", - "println(\"Evaluating 'sq' spline on a dense grid...\")\n", - "evaluated_profiles = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", - "println(\"Evaluation complete.\")\n", - "\n", - "# 3. Extract each profile into its own variable for clarity.\n", - "# Based on the direct_run implementation:\n", - "# Column 1: F = R*Bt (Toroidal Field Function)\n", - "# Column 2: P*μ₀ (Scaled Pressure)\n", - "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", - "# Column 4: q (Safety Factor)\n", - "F_profile = evaluated_profiles[:, 1]\n", - "P_profile = evaluated_profiles[:, 2]\n", - "Flux_profile = evaluated_profiles[:, 3]\n", - "q_profile = evaluated_profiles[:, 4]\n", - "\n", - "# 4. Create and display the plots\n", - "\n", - "# Plot 1: Safety Factor (q)\n", - "p_q = plot(\n", - " psi_eval_grid,\n", - " q_profile,\n", - " title=\"Safety Factor Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"q\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_q)\n", - "\n", - "# Plot 2: Scaled Pressure (P*μ₀)\n", - "p_p = plot(\n", - " psi_eval_grid,\n", - " P_profile,\n", - " title=\"Pressure Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"P * μ₀ [T²]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_p)\n", - "\n", - "\n", - "# Plot 3: Toroidal Field Function (F)\n", - "p_f = plot(\n", - " psi_eval_grid,\n", - " F_profile,\n", - " title=\"Toroidal Field Function\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"F = R * B_t [T*m]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_f)\n", - "\n", - "# Plot 4: Combined plot for comparison\n", - "p_all_profiles = plot(\n", - " title=\"1D Equilibrium Profiles\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " legend=:best\n", - ")\n", - "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", - "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", - "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", - "display(p_all_profiles)\n", - "\n", - "\n", - "println(\"1D profile plots saved successfully.\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/notebooks/equil_lar_example.ipynb b/notebooks/equil_lar_example.ipynb deleted file mode 100644 index 4c0fcf82..00000000 --- a/notebooks/equil_lar_example.ipynb +++ /dev/null @@ -1,199 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "Pkg.resolve() \n", - "Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots, DelimitedFiles" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": "equil_input = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(; eq_type=\"lar\", eq_filename=\"lar.toml\")\nlar_input = GeneralizedPerturbedEquilibrium.Equilibrium.LargeAspectRatioConfig(; lar_r0=10, lar_a=1, beta0=0.001, q0=1.5, p_pres=2, p_sig=1)" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "plasma_eq= GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(equil_input, lar_input)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", - "\n", - "# 1. Select a number of contours to display for clarity\n", - "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", - "num_theta_contours = 13 # e.g., every 30 degrees\n", - "\n", - "# 2. Initialize the plot\n", - "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", - "p_flux_surfaces = plot(\n", - " title=\"Flux Coordinate System Contours in (R, Z)\",\n", - " xlabel=\"R [m]\",\n", - " ylabel=\"Z [m]\",\n", - " aspect_ratio=:equal,\n", - " legend=:outertopright\n", - ")\n", - "\n", - "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", - "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", - "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", - "\n", - "for i in psi_indices\n", - " # Each row corresponds to a single psi value\n", - " # We must add the last point to the start to close the loop for a smooth plot\n", - " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", - " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", - " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", - "end\n", - "\n", - "# 4. Plot contours of constant θ (angle contours) in red\n", - "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", - "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", - "\n", - "for j in theta_indices\n", - " # Each column corresponds to a single theta value\n", - " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", - "end\n", - "\n", - "# 5. Add a legend manually (a common trick in Plots.jl)\n", - "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", - "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", - "\n", - "# 6. Display and save the final plot\n", - "display(p_flux_surfaces)\n", - "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", - "\n", - "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", - "# not just on its internal knot points.\n", - "psi_eval_grid = range(0.0, 1.0, length=200)\n", - "\n", - "# 2. Evaluate the 'sq' spline across this dense grid.\n", - "# Calling spline_eval with a vector input is efficient and returns a matrix\n", - "# where each column corresponds to one of the splined quantities.\n", - "println(\"Evaluating 'sq' spline on a dense grid...\")\n", - "evaluated_profiles = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", - "println(\"Evaluation complete.\")\n", - "\n", - "# 3. Extract each profile into its own variable for clarity.\n", - "# Based on the direct_run implementation:\n", - "# Column 1: F = R*Bt (Toroidal Field Function)\n", - "# Column 2: P*μ₀ (Scaled Pressure)\n", - "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", - "# Column 4: q (Safety Factor)\n", - "F_profile = evaluated_profiles[:, 1]\n", - "P_profile = evaluated_profiles[:, 2]\n", - "Flux_profile = evaluated_profiles[:, 3]\n", - "q_profile = evaluated_profiles[:, 4]\n", - "\n", - "# 4. Create and display the plots\n", - "\n", - "# Plot 1: Safety Factor (q)\n", - "p_q = plot(\n", - " psi_eval_grid,\n", - " q_profile,\n", - " title=\"Safety Factor Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"q\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_q)\n", - "\n", - "# Plot 2: Scaled Pressure (P*μ₀)\n", - "p_p = plot(\n", - " psi_eval_grid,\n", - " P_profile,\n", - " title=\"Pressure Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"P * μ₀ [T²]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_p)\n", - "\n", - "\n", - "# Plot 3: Toroidal Field Function (F)\n", - "p_f = plot(\n", - " psi_eval_grid,\n", - " F_profile,\n", - " title=\"Toroidal Field Function\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"F = R * B_t [T*m]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_f)\n", - "\n", - "# Plot 4: Combined plot for comparison\n", - "p_all_profiles = plot(\n", - " title=\"1D Equilibrium Profiles\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " legend=:best\n", - ")\n", - "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", - "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", - "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", - "display(p_all_profiles)\n", - "\n", - "\n", - "println(\"1D profile plots saved successfully.\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/notebooks/equil_read_chease_comparison.ipynb b/notebooks/equil_read_chease_comparison.ipynb deleted file mode 100644 index 2491db73..00000000 --- a/notebooks/equil_read_chease_comparison.ipynb +++ /dev/null @@ -1,417 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Revise\n", - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "# Pkg.resolve()\n", - "# Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots\n", - "gr() " - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "# Read CHEASE output" - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "## Read efit" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"Loading EFIT data...\")\n", - "efit_control = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumControl(;\n", - " eq_filename=\"CHEASE_INP1/EQDSK_COCOS_02\",\n", - " eq_type=\"efit\",\n", - " jac_type=\"boozer\",\n", - " grid_type=\"ldp\",\n", - " psilow=0.01,\n", - " psihigh=0.994\n", - ")\n", - "efit_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(efit_control, GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumOutput())\n", - "plasma_eq_efit = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(efit_config)" - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "## Read INP1_UNFORMATTED (BINARY)\n", - "\n", - "use eq_type as chease(legacy from GPEC) or chease_binary" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"Loading CHEASE INP1 data...\")\n", - "chease_control = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumControl(;\n", - " eq_filename=\"CHEASE_INP1/INP1_binary\",\n", - " eq_type=\"chease_binary\",\n", - " jac_type=\"boozer\",\n", - " grid_type=\"ldp\",\n", - " psilow=0.01,\n", - " psihigh=0.994,\n", - " r0exp=6.8,\n", - " b0exp=7.4\n", - ")\n", - "chease_config_chease_binary = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(chease_control, GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumOutput())\n", - "plasma_eq_chease_binary = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(chease_config_chease_binary)" - ] - }, - { - "cell_type": "markdown", - "id": "6", - "metadata": {}, - "source": [ - "## Read INP1_FORMATTED (ASCII)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"Loading CHEASE INP1 data...\")\n", - "chease_control = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumControl(;\n", - " eq_filename=\"CHEASE_INP1/INP1_ascii\",\n", - " eq_type=\"chease_ascii\",\n", - " jac_type=\"boozer\",\n", - " grid_type=\"ldp\",\n", - " psilow=0.01,\n", - " psihigh=0.994,\n", - " r0exp=6.8,\n", - " b0exp=7.4\n", - ")\n", - "chease_config_chease_ascii = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(chease_control, GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumOutput())\n", - "plasma_eq_chease_ascii = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(chease_config_chease_ascii)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "# Common evaluation grid for comparison\n", - "psi_eval = collect(range(0.0, 1.0, length=200));" - ] - }, - { - "cell_type": "markdown", - "id": "9", - "metadata": {}, - "source": [ - "# Comparison" - ] - }, - { - "cell_type": "markdown", - "id": "10", - "metadata": {}, - "source": [ - "## 1-D profile" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "11", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"\\n--- Comparing 1D Profiles (EFIT vs CHEASE ASCII/BINARY) ---\")\n", - "\n", - "# Evaluate splines\n", - "prof_efit = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq_efit.sq, psi_eval, 0)\n", - "prof_chease_binary = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq_chease_binary.sq, psi_eval, 0)\n", - "prof_chease_ascii = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq_chease_ascii.sq, psi_eval, 0)\n", - "\n", - "lw_val = 2\n", - "\n", - "# 1. Plot Safety Factor (q)\n", - "p1 = plot(psi_eval, prof_efit[:, 4], label=\"EFIT (G-file)\", color=:blue, lw=lw_val)\n", - "plot!(p1, psi_eval, prof_chease_ascii[:, 4], label=\"CHEASE (ASCII)\", color=:red, ls=:dash, lw=lw_val)\n", - "plot!(p1, psi_eval, prof_chease_binary[:, 4], label=\"CHEASE (Binary)\", color=:green, ls=:dot, lw=lw_val)\n", - "title!(p1, \"Safety Factor (q) Comparison\")\n", - "xlabel!(p1, \"Normalized Psi (ψₙ)\")\n", - "\n", - "# 2. Plot Pressure (P*μ₀)\n", - "p2 = plot(psi_eval, prof_efit[:, 2], label=\"EFIT\", color=:blue, lw=lw_val)\n", - "plot!(p2, psi_eval, prof_chease_ascii[:, 2], label=\"CHEASE (ASCII)\", color=:red, ls=:dash, lw=lw_val)\n", - "plot!(p2, psi_eval, prof_chease_binary[:, 2], label=\"CHEASE (Binary)\", color=:green, ls=:dot, lw=lw_val)\n", - "title!(p2, \"Pressure (P) Comparison\")\n", - "xlabel!(p2, \"Normalized Psi (ψₙ)\")\n", - "\n", - "# 3. Plot Toroidal Field Function (F)\n", - "p3 = plot(psi_eval, prof_efit[:, 1], label=\"EFIT\", color=:blue, lw=lw_val)\n", - "plot!(p3, psi_eval, prof_chease_ascii[:, 1], label=\"CHEASE (ASCII)\", color=:red, ls=:dash, lw=lw_val)\n", - "plot!(p3, psi_eval, prof_chease_binary[:, 1], label=\"CHEASE (Binary)\", color=:green, ls=:dot, lw=lw_val)\n", - "title!(p3, \"Toroidal Field Fn (F) Comparison\")\n", - "xlabel!(p3, \"Normalized Psi (ψₙ)\")\n", - "\n", - "# Layout profiles in a grid\n", - "p_profiles = plot(p1, p2, p3, layout=(1, 3), size=(1300, 450))\n", - "display(p_profiles)" - ] - }, - { - "cell_type": "markdown", - "id": "12", - "metadata": {}, - "source": [ - "## Flux surfaces" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "13", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"\\n--- Comparing Flux Surfaces in R-Z Space (EFIT vs CHEASE ASCII/BINARY) ---\")\n", - "\n", - "function get_rz_grid(eq_obj)\n", - " # 1. Define evaluation points\n", - " # Use collect to ensure they are passed as arrays to bicube_eval\n", - " # Use high density for theta to get smooth curves\n", - " psi_g = collect(range(eq_obj.config.control.psilow, eq_obj.config.control.psihigh, length=20))\n", - " theta_g = collect(range(0.0, 1.0, length=1000))\n", - " \n", - " # 2. Evaluate bicubic spline\n", - " # fs is a (Npsi, Ntheta, 2) array\n", - " fs = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(eq_obj.rzphi, psi_g, theta_g)\n", - " \n", - " # 3. Extract components (using explicit indexing for clarity)\n", - " # fs[:, :, 1] is rfac^2\n", - " # fs[:, :, 2] is phase/2π\n", - " rfac_sq = fs[:, :, 1]\n", - " phase = fs[:, :, 2]\n", - " \n", - " # 4. Transformation logic (Poloidal -> Cartesian)\n", - " # We use broadcasting (.) to handle the (Npsi, 1) + (1, Ntheta) + (Npsi, Ntheta) operations\n", - " rfac = sqrt.(max.(0.0, rfac_sq))\n", - " \n", - " # eta = 2π * (theta + phase)\n", - " # Note: theta_g' is a row vector, phase is a matrix. \n", - " # Julia's broadcasting handles this correctly: Matrix + RowVector\n", - " eta = 2.0 * pi .* (theta_g' .+ phase)\n", - " \n", - " # Calculate R and Z\n", - " R = eq_obj.ro .+ rfac .* cos.(eta)\n", - " Z = eq_obj.zo .+ rfac .* sin.(eta)\n", - " \n", - " return R, Z\n", - "end\n", - "\n", - "# Re-calculate with the fixed function\n", - "R_efit, Z_efit = get_rz_grid(plasma_eq_efit)\n", - "R_ascii, Z_ascii = get_rz_grid(plasma_eq_chease_ascii) \n", - "R_binary, Z_binary = get_rz_grid(plasma_eq_chease_binary) \n", - "\n", - "# --- Plotting ---\n", - "p_surf = plot(title=\"Boundary & Flux Surface Comparison\", \n", - " aspect_ratio=:equal, xlabel=\"R [m]\", ylabel=\"Z [m]\", size=(800, 900))\n", - "\n", - "# Select indices: 1 (inner) to 20 (boundary)\n", - "surface_indices = [1, 5, 10, 15, 20]\n", - "\n", - "for i in surface_indices\n", - " # Set labels only for the boundary to keep the legend clean\n", - " l_e = (i == 20) ? \"EFIT\" : \"\"\n", - " l_a = (i == 20) ? \"CHEASE ASCII\" : \"\"\n", - " l_b = (i == 20) ? \"CHEASE Binary\" : \"\"\n", - "\n", - " # Plot each surface. [val; val[1]] syntax closes the loop (connects end to start)\n", - " plot!(p_surf, [R_efit[i, :]; R_efit[i, 1]], [Z_efit[i, :]; Z_efit[i, 1]], \n", - " color=:blue, lw=1.2, label=l_e)\n", - " \n", - " plot!(p_surf, [R_ascii[i, :]; R_ascii[i, 1]], [Z_ascii[i, :]; Z_ascii[i, 1]], \n", - " color=:red, ls=:dash, lw=1.2, label=l_a)\n", - " \n", - " plot!(p_surf, [R_binary[i, :]; R_binary[i, 1]], [Z_binary[i, :]; Z_binary[i, 1]], \n", - " color=:green, ls=:dot, lw=1.2, label=l_b)\n", - "end\n", - "\n", - "display(p_surf)" - ] - }, - { - "cell_type": "markdown", - "id": "14", - "metadata": {}, - "source": [ - "## Debugging the difference" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "15", - "metadata": {}, - "outputs": [], - "source": [ - "println(\"\\n=== DEBUGGING: Why are boundaries different? ===\\n\")\n", - "\n", - "# Test at a specific psi value\n", - "test_psi = 0.5\n", - "test_theta = range(0.0, 1.0, length=100)\n", - "\n", - "println(\"Testing at psi = $test_psi\")\n", - "println(\"=\"^60)\n", - "\n", - "# 1. Evaluate raw bicubic spline outputs\n", - "fs_efit = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq_efit.rzphi, [test_psi], collect(test_theta))\n", - "fs_ascii = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq_chease_ascii.rzphi, [test_psi], collect(test_theta))\n", - "fs_binary = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq_chease_binary.rzphi, [test_psi], collect(test_theta))\n", - "\n", - "println(\"\\n1. Raw Spline Outputs (fs[:,:,1] = rfac², fs[:,:,2] = phase/2π)\")\n", - "println(\"-\"^60)\n", - "println(\"EFIT:\")\n", - "println(\" fs[:,:,1] range: [$(minimum(fs_efit[1,:,1])), $(maximum(fs_efit[1,:,1]))]\")\n", - "println(\" fs[:,:,2] range: [$(minimum(fs_efit[1,:,2])), $(maximum(fs_efit[1,:,2]))]\")\n", - "println(\"\\nCHEASE ASCII:\")\n", - "println(\" fs[:,:,1] range: [$(minimum(fs_ascii[1,:,1])), $(maximum(fs_ascii[1,:,1]))]\")\n", - "println(\" fs[:,:,2] range: [$(minimum(fs_ascii[1,:,2])), $(maximum(fs_ascii[1,:,2]))]\")\n", - "println(\"\\nCHEASE Binary:\")\n", - "println(\" fs[:,:,1] range: [$(minimum(fs_binary[1,:,1])), $(maximum(fs_binary[1,:,1]))]\")\n", - "println(\" fs[:,:,2] range: [$(minimum(fs_binary[1,:,1])), $(maximum(fs_binary[1,:,2]))]\")\n", - "\n", - "# 2. Compute rfac\n", - "rfac_efit = sqrt.(max.(0.0, fs_efit[1, :, 1]))\n", - "rfac_ascii = sqrt.(max.(0.0, fs_ascii[1, :, 1]))\n", - "rfac_binary = sqrt.(max.(0.0, fs_binary[1, :, 1]))\n", - "\n", - "println(\"\\n2. After sqrt (rfac)\")\n", - "println(\"-\"^60)\n", - "println(\"EFIT rfac: [$(minimum(rfac_efit)), $(maximum(rfac_efit))]\")\n", - "println(\"ASCII rfac: [$(minimum(rfac_ascii)), $(maximum(rfac_ascii))]\")\n", - "println(\"Binary rfac: [$(minimum(rfac_binary)), $(maximum(rfac_binary))]\")\n", - "\n", - "# 3. Compute eta\n", - "eta_efit = 2.0 * pi .* (test_theta .+ fs_efit[1, :, 2])\n", - "eta_ascii = 2.0 * pi .* (test_theta .+ fs_ascii[1, :, 2])\n", - "eta_binary = 2.0 * pi .* (test_theta .+ fs_binary[1, :, 2])\n", - "\n", - "println(\"\\n3. After eta = 2π*(θ + phase)\")\n", - "println(\"-\"^60)\n", - "println(\"EFIT eta: [$(minimum(eta_efit)), $(maximum(eta_efit))]\")\n", - "println(\"ASCII eta: [$(minimum(eta_ascii)), $(maximum(eta_ascii))]\")\n", - "println(\"Binary eta: [$(minimum(eta_binary)), $(maximum(eta_binary))]\")\n", - "\n", - "# 4. Magnetic axis positions\n", - "println(\"\\n4. Magnetic Axis (R₀, Z₀)\")\n", - "println(\"-\"^60)\n", - "println(\"EFIT: R₀ = $(plasma_eq_efit.ro), Z₀ = $(plasma_eq_efit.zo)\")\n", - "println(\"ASCII: R₀ = $(plasma_eq_chease_ascii.ro), Z₀ = $(plasma_eq_chease_ascii.zo)\")\n", - "println(\"Binary: R₀ = $(plasma_eq_chease_binary.ro), Z₀ = $(plasma_eq_chease_binary.zo)\")\n", - "\n", - "# 5. Final R, Z\n", - "R_efit_test = plasma_eq_efit.ro .+ rfac_efit .* cos.(eta_efit)\n", - "Z_efit_test = plasma_eq_efit.zo .+ rfac_efit .* sin.(eta_efit)\n", - "\n", - "R_ascii_test = plasma_eq_chease_ascii.ro .+ rfac_ascii .* cos.(eta_ascii)\n", - "Z_ascii_test = plasma_eq_chease_ascii.zo .+ rfac_ascii .* sin.(eta_ascii)\n", - "\n", - "R_binary_test = plasma_eq_chease_binary.ro .+ rfac_binary .* cos.(eta_binary)\n", - "Z_binary_test = plasma_eq_chease_binary.zo .+ rfac_binary .* sin.(eta_binary)\n", - "\n", - "println(\"\\n5. Final R, Z coordinates\")\n", - "println(\"-\"^60)\n", - "println(\"EFIT: R=[$(minimum(R_efit_test)), $(maximum(R_efit_test))], Z=[$(minimum(Z_efit_test)), $(maximum(Z_efit_test))]\")\n", - "println(\"ASCII: R=[$(minimum(R_ascii_test)), $(maximum(R_ascii_test))], Z=[$(minimum(Z_ascii_test)), $(maximum(Z_ascii_test))]\")\n", - "println(\"Binary: R=[$(minimum(R_binary_test)), $(maximum(R_binary_test))], Z=[$(minimum(Z_binary_test)), $(maximum(Z_binary_test))]\")\n", - "\n", - "# 6. Plot step-by-step comparison\n", - "p1 = plot(test_theta, fs_efit[1, :, 1], label=\"EFIT\", lw=2, title=\"Step 1: fs[:,:,1] (rfac²)\")\n", - "plot!(p1, test_theta, fs_ascii[1, :, 1], label=\"ASCII\", lw=2, ls=:dash)\n", - "plot!(p1, test_theta, fs_binary[1, :, 1], label=\"Binary\", lw=2, ls=:dot)\n", - "xlabel!(p1, \"θ (normalized)\")\n", - "\n", - "p2 = plot(test_theta, fs_efit[1, :, 2], label=\"EFIT\", lw=2, title=\"Step 2: fs[:,:,2] (phase/2π)\")\n", - "plot!(p2, test_theta, fs_ascii[1, :, 2], label=\"ASCII\", lw=2, ls=:dash)\n", - "plot!(p2, test_theta, fs_binary[1, :, 2], label=\"Binary\", lw=2, ls=:dot)\n", - "xlabel!(p2, \"θ (normalized)\")\n", - "\n", - "p3 = plot(test_theta, rfac_efit, label=\"EFIT\", lw=2, title=\"Step 3: rfac\")\n", - "plot!(p3, test_theta, rfac_ascii, label=\"ASCII\", lw=2, ls=:dash)\n", - "plot!(p3, test_theta, rfac_binary, label=\"Binary\", lw=2, ls=:dot)\n", - "xlabel!(p3, \"θ (normalized)\")\n", - "\n", - "p4 = plot(test_theta, eta_efit, label=\"EFIT\", lw=2, title=\"Step 4: eta\")\n", - "plot!(p4, test_theta, eta_ascii, label=\"ASCII\", lw=2, ls=:dash)\n", - "plot!(p4, test_theta, eta_binary, label=\"Binary\", lw=2, ls=:dot)\n", - "xlabel!(p4, \"θ (normalized)\")\n", - "\n", - "p5 = plot(R_efit_test, Z_efit_test, label=\"EFIT\", lw=2, title=\"Step 5: Final (R,Z)\", aspect_ratio=:equal)\n", - "plot!(p5, R_ascii_test, Z_ascii_test, label=\"ASCII\", lw=2, ls=:dash)\n", - "plot!(p5, R_binary_test, Z_binary_test, label=\"Binary\", lw=2, ls=:dot)\n", - "xlabel!(p5, \"R [m]\")\n", - "ylabel!(p5, \"Z [m]\")\n", - "\n", - "p_debug = plot(p1, p2, p3, p4, p5, layout=(2,3), size=(1500, 800))\n", - "display(p_debug)\n", - "\n", - "# 7. Compute pairwise differences\n", - "println(\"\\n6. Pairwise Differences\")\n", - "println(\"-\"^60)\n", - "println(\"fs[:,:,1] differences:\")\n", - "println(\" |ASCII - Binary|: max = $(maximum(abs.(fs_ascii[1,:,1] .- fs_binary[1,:,1])))\")\n", - "println(\" |EFIT - ASCII|: max = $(maximum(abs.(fs_efit[1,:,1] .- fs_ascii[1,:,1])))\")\n", - "println(\" |EFIT - Binary|: max = $(maximum(abs.(fs_efit[1,:,1] .- fs_binary[1,:,1])))\")\n", - "\n", - "println(\"\\nfs[:,:,2] differences:\")\n", - "println(\" |ASCII - Binary|: max = $(maximum(abs.(fs_ascii[1,:,2] .- fs_binary[1,:,2])))\")\n", - "println(\" |EFIT - ASCII|: max = $(maximum(abs.(fs_efit[1,:,2] .- fs_ascii[1,:,2])))\")\n", - "println(\" |EFIT - Binary|: max = $(maximum(abs.(fs_efit[1,:,2] .- fs_binary[1,:,2])))\")\n", - "\n", - "println(\"\\nMagnetic axis differences:\")\n", - "println(\" |ASCII - Binary| R₀: $(abs(plasma_eq_chease_ascii.ro - plasma_eq_chease_binary.ro))\")\n", - "println(\" |ASCII - Binary| Z₀: $(abs(plasma_eq_chease_ascii.zo - plasma_eq_chease_binary.zo))\")\n", - "println(\" |EFIT - ASCII| R₀: $(abs(plasma_eq_efit.ro - plasma_eq_chease_ascii.ro))\")\n", - "println(\" |EFIT - ASCII| Z₀: $(abs(plasma_eq_efit.zo - plasma_eq_chease_ascii.zo))\")\n", - "\n", - "println(\"\\n\" * \"=\"^60)\n", - "println(\"Analysis complete!\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/equil_soloviev_example.ipynb b/notebooks/equil_soloviev_example.ipynb deleted file mode 100644 index 0af387dd..00000000 --- a/notebooks/equil_soloviev_example.ipynb +++ /dev/null @@ -1,255 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "Pkg.resolve()\n", - "Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots\n", - "# test" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "### Set equil input parameters\n", - "equil_in = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(control=GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumControl(\n", - " eq_filename=\"sol_test\", # eq_filename\n", - " eq_type=\"sol\", # eq_type\n", - " jac_type=\"hamada\", # jac_type\n", - " mpsi=100, # mpsi (number of radial grid points)\n", - " mtheta=128), # mtheta (number of poloidal grid points)\n", - " output=GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumOutput()) \n", - "\n", - "### Set Soloviev input parameters\n", - "sol_inputs = GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(;\n", - " mr=65, # number of radial grid zones\n", - " mz=65, # number of axial grid zones\n", - " ma=64, # number of flux grid zones\n", - " e=1.0, # elongation\n", - " a=1.0, # minor radius\n", - " r0=3.0, # major radius\n", - " q0=1.26, # safety factor at the o-point\n", - " p0fac=1.0, # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)\n", - " b0fac=1.0, # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)\n", - " f0fac=1.0 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)\n", - " )\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "### Set up Soloviev equilibrium and generate input splines\n", - "\n", - "directrun_inputs = GeneralizedPerturbedEquilibrium.Equilibrium.sol_run(\n", - " equil_in,\n", - " sol_inputs\n", - " )" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "plot(\n", - " directrun_inputs.sq_in.xs,\n", - " directrun_inputs.sq_in.fs[:,2],\n", - " label=raw\"pfac * (p0fac - $\\psi_N$)\",\n", - " xlabel=raw\"$\\psi_N$\"\n", - " )" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "### Execute direct_run() and solve equilibrium\n", - "\n", - "plasma_eq = GeneralizedPerturbedEquilibrium.Equilibrium.equilibrium_solver(directrun_inputs)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = GeneralizedPerturbedEquilibrium.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", - "\n", - "# 1. Select a number of contours to display for clarity\n", - "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", - "num_theta_contours = 13 # e.g., every 30 degrees\n", - "\n", - "# 2. Initialize the plot\n", - "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", - "p_flux_surfaces = plot(\n", - " title=\"Flux Coordinate System Contours in (R, Z)\",\n", - " xlabel=\"R [m]\",\n", - " ylabel=\"Z [m]\",\n", - " aspect_ratio=:equal,\n", - " legend=:outertopright\n", - ")\n", - "\n", - "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", - "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", - "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", - "\n", - "for i in psi_indices\n", - " # Each row corresponds to a single psi value\n", - " # We must add the last point to the start to close the loop for a smooth plot\n", - " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", - " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", - " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", - "end\n", - "\n", - "# 4. Plot contours of constant θ (angle contours) in red\n", - "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", - "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", - "\n", - "for j in theta_indices\n", - " # Each column corresponds to a single theta value\n", - " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", - "end\n", - "\n", - "# 5. Add a legend manually (a common trick in Plots.jl)\n", - "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", - "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", - "\n", - "# 6. Display and save the final plot\n", - "display(p_flux_surfaces)\n", - "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", - "# This code block goes at the end of your existing script.\n", - "\n", - "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", - "\n", - "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", - "# not just on its internal knot points.\n", - "psi_eval_grid = range(0.0, 1.0, length=200)\n", - "\n", - "# 2. Evaluate the 'sq' spline across this dense grid.\n", - "# Calling spline_eval with a vector input is efficient and returns a matrix\n", - "# where each column corresponds to one of the splined quantities.\n", - "println(\"Evaluating 'sq' spline on a dense grid...\")\n", - "evaluated_profiles = GeneralizedPerturbedEquilibrium.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", - "println(\"Evaluation complete.\")\n", - "\n", - "# 3. Extract each profile into its own variable for clarity.\n", - "# Based on the direct_run implementation:\n", - "# Column 1: F = R*Bt (Toroidal Field Function)\n", - "# Column 2: P*μ₀ (Scaled Pressure)\n", - "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", - "# Column 4: q (Safety Factor)\n", - "F_profile = evaluated_profiles[:, 1]\n", - "P_profile = evaluated_profiles[:, 2]\n", - "Flux_profile = evaluated_profiles[:, 3]\n", - "q_profile = evaluated_profiles[:, 4]\n", - "\n", - "# 4. Create and display the plots\n", - "\n", - "# Plot 1: Safety Factor (q)\n", - "p_q = plot(\n", - " psi_eval_grid,\n", - " q_profile,\n", - " title=\"Safety Factor Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"q\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_q)\n", - "\n", - "# Plot 2: Scaled Pressure (P*μ₀)\n", - "p_p = plot(\n", - " psi_eval_grid,\n", - " P_profile,\n", - " title=\"Pressure Profile\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"P * μ₀ [T²]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_p)\n", - "\n", - "\n", - "# Plot 3: Toroidal Field Function (F)\n", - "p_f = plot(\n", - " psi_eval_grid,\n", - " F_profile,\n", - " title=\"Toroidal Field Function\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " ylabel=\"F = R * B_t [T*m]\",\n", - " legend=false,\n", - " linewidth=2\n", - ")\n", - "display(p_f)\n", - "\n", - "# Plot 4: Combined plot for comparison\n", - "p_all_profiles = plot(\n", - " title=\"1D Equilibrium Profiles\",\n", - " xlabel=\"Normalized Psi (ψₙ)\",\n", - " legend=:best\n", - ")\n", - "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", - "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", - "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", - "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", - "display(p_all_profiles)\n", - "\n", - "\n", - "println(\"1D profile plots saved successfully.\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/notebooks/spline_examples.ipynb b/notebooks/spline_examples.ipynb deleted file mode 100644 index 33bfc814..00000000 --- a/notebooks/spline_examples.ipynb +++ /dev/null @@ -1,156 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "# Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "# Make sine and cosine spline\n", - "xs = range(0.0, stop=2*pi, length=21)\n", - "xs = collect(xs)\n", - "fs = sin.(xs)\n", - "fc = cos.(xs)\n", - "# Make a vector of vectors of (100,2) for the spline\n", - "fs_matrix = hcat(fs, fc)\n", - "\n", - "# print(xs)\n", - "spline = GeneralizedPerturbedEquilibrium.SplinesMod.CubicSpline(xs, fs_matrix; bctype = 2)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "# example: f = GPECsplines.spline_eval(spline, 3.2)\n", - "# plot the spline\n", - "xs_fine = collect(range(0.0, stop=2*pi, length=100))\n", - "fs_fine = GeneralizedPerturbedEquilibrium.SplinesMod.spline_eval(spline, xs_fine)\n", - "plot(xs_fine, fs_fine, label=\"spline\", legend=:topright)\n", - "# plot the input data scatter\n", - "scatter!(xs, fs, label=\"sin(x)\", legend=:topright)\n", - "scatter!(xs, fc, label=\"cos(x)\", legend=:topright)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# Make e^-ix and e^ix spline\n", - "xs = range(0.0, stop=2*pi, length=20)\n", - "xs = collect(xs)\n", - "fm = exp.(-im .* xs)\n", - "fp = exp.(im .* xs)\n", - "# Make a vector of vectors of (100,2) for the spline\n", - "fs_matrix = hcat(fm, fp)\n", - "\n", - "spline = GeneralizedPerturbedEquilibrium.SplinesMod.CubicSpline(xs, fs_matrix, bctype = 2)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# example: f = GPECsplines.spline_eval(spline, 3.2)\n", - "# plot the spline\n", - "xs_fine = collect(range(0.0, stop=2*pi, length=100))\n", - "fs_fine = GeneralizedPerturbedEquilibrium.SplinesMod.spline_eval(spline, xs_fine)\n", - "\n", - "# plot just the real part of e^(+ix)\n", - "plot(xs_fine, real(fs_fine[:, 2]), label=\"spline\", legend=:topright)\n", - "# and the imaginary part\n", - "plot!(xs_fine, imag(fs_fine[:, 2]), label=\"spline\", legend=:topright)\n", - "# plot the input data scatter\n", - "scatter!(xs, real(fs_matrix[:, 2]), label=\"real(e^ix)\", legend=:topright)\n", - "scatter!(xs, imag(fs_matrix[:, 2]), label=\"imag(e^ix)\", legend=:topright)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "# make a bicubic spline of a 2d periodic function\n", - "xs = range(0.0, stop=2*pi, length=20)\n", - "ys = range(0.0, stop=2*pi, length=20)\n", - "xs = collect(xs)\n", - "ys = collect(ys)\n", - "fs1 = sin.(xs') .* cos.(ys) .+ 1.0\n", - "fs2 = cos.(xs') .* sin.(ys) .+ 1.0\n", - "fs = zeros(20, 20, 2)\n", - "# fs is a 20x20x2 array\n", - "fs[:, :, 1] = fs1\n", - "fs[:, :, 2] = fs2\n", - "println(\"fs size: \", size(fs))\n", - "# Make a bicubic spline\n", - "bcspline = GeneralizedPerturbedEquilibrium.SplinesMod.BicubicSpline(xs, ys, fs; bctypex = 2, bctypey = 2)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "# Evaluate the bicubic spline\n", - "xs_fine = collect(range(0.0, stop=2*pi, length=100))\n", - "ys_fine = collect(range(0.0, stop=2*pi, length=100))\n", - "# fs_fine, fsx_fine, fsy_fine, fsxx_fine, fsxy_fine, fsyy_fine = GeneralizedPerturbedEquilibrium.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine, 2)\n", - "fs_fine, fsx_fine, fsy_fine = GeneralizedPerturbedEquilibrium.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine, 1)\n", - "\n", - "# plot the bicubic spline\n", - "p1 = contourf(xs_fine, ys_fine, fs_fine[:, :, 1], label=\"sin(x)cos(y)+1\", legend=:topright)\n", - "p2 = contourf(xs_fine, ys_fine, fs_fine[:, :, 2], label=\"cos(x)sin(y)+1\", legend=:topright)\n", - "plot(p1, p2, layout=(1, 2), size=(800, 400), title=\"Bicubic Spline Evaluation\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "# plot the derivatives\n", - "p1 = contourf(xs_fine, ys_fine, fsx_fine[:, :, 1], label=\"derivative w.r.t x\", legend=:topright)\n", - "p2 = contourf(xs_fine, ys_fine, fsy_fine[:, :, 1], label=\"derivative w.r.t y\", legend=:topright)\n", - "plot(p1, p2, layout=(1, 2), size=(800, 400), title=\"Bicubic Spline Evaluation\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/spline_examples2.ipynb b/notebooks/spline_examples2.ipynb deleted file mode 100644 index d9bff154..00000000 --- a/notebooks/spline_examples2.ipynb +++ /dev/null @@ -1,650 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "Pkg.resolve()\n", - "Pkg.instantiate() # Usually only need to run this once\n", - "using Plots, Printf\n", - "using GeneralizedPerturbedEquilibrium.SplinesMod" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "#=\n", - "======================================================================\n", - "1. VALIDATION FOR 1D CUBIC SPLINE (Real)\n", - "======================================================================\n", - "=#\n", - "println(\"\\n--- Testing 1D Spline Derivatives and Integration ---\")\n", - "\n", - "# --- 1.1 Data Generation ---\n", - "# Using 20 nodes to create a periodic spline for sin(x) and cos(x)\n", - "xs_nodes = collect(range(0.0, stop=2*pi, length=20))\n", - "y1_nodes = sin.(xs_nodes)\n", - "y2_nodes = cos.(xs_nodes)\n", - "fs_nodes_matrix = hcat(y1_nodes, y2_nodes)\n", - "\n", - "# --- 1.2 Spline Setup (bctype=3 for periodic)---\n", - "spline_real = CubicSpline(xs_nodes, fs_nodes_matrix; bctype=3)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 1.3 Evaluation on a Fine Grid ---\n", - "xs_fine = collect(range(0.0, stop=2*pi, length=200))\n", - "\n", - "\n", - "# Evaluate the spline and its derivatives up to the 3rd order\n", - "f_s, f1_s, f2_s, f3_s = spline_eval(spline_real, xs_fine, 3)\n", - "\n", - "\n", - "# --- 1.4 Perform Integration ---\n", - "# This modifies the spline_real object in-place, adding the .fsi field\n", - "SplinesMod.spline_integrate!(spline_real)\n", - "\n", - "# The result of integration is stored at the original node points.\n", - "# spline_real.fsi now contains the cumulative integral values.\n", - "integral_s = spline_real.fsi\n", - "\n", - "# --- 1.5 Analytical (True) Values ---\n", - "# True values for the function and its derivatives on the fine grid\n", - "true_f = hcat(sin.(xs_fine), cos.(xs_fine))\n", - "true_f1 = hcat(cos.(xs_fine), -sin.(xs_fine))\n", - "true_f2 = hcat(-sin.(xs_fine), -cos.(xs_fine))\n", - "true_f3 = hcat(-cos.(xs_fine), sin.(xs_fine))\n", - "\n", - "# True values for the integral on the original coarse grid (xs_nodes)\n", - "# Integral of sin(x) from 0 to t is -cos(t) - (-cos(0)) = 1 - cos(t)\n", - "# Integral of cos(x) from 0 to t is sin(t) - sin(0) = sin(t)\n", - "true_integral = hcat(1.0 .- cos.(xs_nodes), sin.(xs_nodes))\n", - "\n", - "print(\"evaluation complete\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 1.6 Plotting (Focusing on the first function, sin(x)) ---\n", - "\n", - "# Plot for Function Value f(x)\n", - "function generate_spline_plot(\n", - " x_vals, \n", - " spline_data, \n", - " analytic_data;\n", - " title, \n", - " spline_label, \n", - " analytic_label,\n", - " error_scale=1.0,\n", - " legend_pos=:best,\n", - " x_nodes=nothing,\n", - " y_nodes=nothing,\n", - " nodes_label=\"Original Nodes\",\n", - " kwargs...\n", - ")\n", - " \n", - " p = plot(x_vals, spline_data, label=spline_label, title=title, legend=legend_pos; kwargs...)\n", - " \n", - " plot!(p, x_vals, analytic_data, ls=:dash, label=analytic_label)\n", - " scaler_str = isinteger(error_scale) ? string(Int(error_scale)) : string(error_scale)\n", - " error_label = error_scale == 1.0 ? \"Error\" : \"Error x\" * scaler_str\n", - " plot!(p, x_vals, spline_data .- analytic_data, ls=:dot, label=error_label, color=:red)\n", - " \n", - " if x_nodes !== nothing && y_nodes !== nothing\n", - " scatter!(p, x_nodes, y_nodes, label=nodes_label, markersize=3, markerstrokewidth=0)\n", - " end\n", - " \n", - " return p\n", - "end\n", - "\n", - "# --- 1.6 Generate and Display all plots ---\n", - "\n", - "println(\"--- Generating 1D Spline Validation Plots ---\")\n", - "\n", - "plot_configs_real = [\n", - " # f(x) \n", - " (\n", - " spline_data = f_s[:, 1], analytic_data = true_f[:, 1], x_vals = xs_fine,\n", - " title = \"Function: sin(x)\", spline_label = \"Spline f(x)\", analytic_label = \"True f(x)\",\n", - " error_scale = 1000.0, legend_pos = :bottomleft,\n", - " x_nodes = xs_nodes, y_nodes = y1_nodes\n", - " ),\n", - " # f'(x) \n", - " (\n", - " spline_data = f1_s[:, 1], analytic_data = true_f1[:, 1], x_vals = xs_fine,\n", - " title = \"1st Deriv: cos(x)\", spline_label = \"Spline f'(x)\", analytic_label = \"True f'(x)\",\n", - " error_scale = 100.0, legend_pos = :bottomleft\n", - " ),\n", - " # f''(x)\n", - " (\n", - " spline_data = f2_s[:, 1], analytic_data = true_f2[:, 1], x_vals = xs_fine,\n", - " title = \"2nd Deriv: -sin(x)\", spline_label = \"Spline f''(x)\", analytic_label = \"True f''(x)\",\n", - " error_scale = 1.0, legend_pos = :bottomleft\n", - " ),\n", - " # f'''(x)\n", - " (\n", - " spline_data = f3_s[:, 1], analytic_data = true_f3[:, 1], x_vals = xs_fine,\n", - " title = \"3rd Deriv: -cos(x)\", spline_label = \"Spline f'''(x)\", analytic_label = \"True f'''(x)\",\n", - " error_scale = 1.0, legend_pos = :bottomleft\n", - " ),\n", - " # integral \n", - " (\n", - " spline_data = integral_s[:, 1], analytic_data = true_integral[:, 1], x_vals = xs_nodes,\n", - " title = \"Integral: 1-cos(x)\", spline_label = \"Spline Integral\", analytic_label = \"True Integral\",\n", - " error_scale = 1000.0, legend_pos = :topleft,\n", - " style = (markershape=:circle, markersize=3)\n", - " )\n", - "]\n", - "\n", - "\n", - "plot_list_real = []\n", - "println(\"--- Generating 1D Spline Validation Plots ---\")\n", - "\n", - "for config in plot_configs_real\n", - " \n", - " p = generate_spline_plot(\n", - " config.x_vals,\n", - " config.spline_data,\n", - " config.analytic_data;\n", - " title = config.title,\n", - " spline_label = config.spline_label,\n", - " analytic_label = config.analytic_label,\n", - " error_scale = config.error_scale,\n", - " legend_pos = config.legend_pos,\n", - " \n", - " x_nodes = get(config, :x_nodes, nothing),\n", - " y_nodes = get(config, :y_nodes, nothing),\n", - " \n", - " (haskey(config, :style) ? config.style : ())...\n", - " )\n", - " push!(plot_list_real, p)\n", - "end\n", - "\n", - "\n", - "display(plot(plot_list_real..., layout=(3, 2), size=(1200, 1000), margin=5Plots.mm))\n", - "\n", - "\n", - "\n", - "println(\"\\nAll 1D validation plots generated.\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "#=\n", - "======================================================================\n", - "2. VALIDATION FOR 1D CUBIC SPLINE (Complex)\n", - "======================================================================\n", - "=#\n", - "println(\"\\n--- Testing 1D Complex Spline Derivatives and Integration ---\")\n", - "\n", - "# --- 2.1 Data Generation ---\n", - "xs_nodes = collect(range(0.0, stop=2*pi, length=40))\n", - "fs_complex_nodes = exp.(im .* xs_nodes)\n", - "\n", - "# --- 2.2 Spline Setup (bctype=3 for periodic) ---\n", - "spline_complex = CubicSpline(xs_nodes, fs_complex_nodes; bctype = 3)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 2.3 Evaluation on a Fine Grid ---\n", - "xs_fine = collect(range(0.0, stop=2*pi, length=200))\n", - "f_cs, f1_cs, f2_cs, f3_cs = spline_eval(spline_complex, xs_fine, 3)\n", - "\n", - "# --- 2.4 Perform Integration ---\n", - "# This modifies the spline_complex object in-place, adding the .fsi field\n", - "SplinesMod.spline_integrate!(spline_complex)\n", - "integral_cs = spline_complex.fsi\n", - "\n", - "# --- 2.5 Analytical (True) Values ---\n", - "true_f_c = exp.(im .* xs_fine)\n", - "true_f1_c = im .* exp.(im .* xs_fine)\n", - "true_f2_c = -1 .* exp.(im .* xs_fine)\n", - "true_f3_c = -im .* exp.(im .* xs_fine)\n", - "\n", - "# True values for the integral on the original node grid\n", - "# Integral of exp(ix) from 0 to t is i*(1 - exp(ix))\n", - "true_integral_c = im .* (1.0 .- exp.(im .* xs_nodes))\n", - "\n", - "print(\"evaluation complete\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 2.6 Plotting ---\n", - "function generate_complex_spline_plot(\n", - " x_vals, \n", - " spline_c, \n", - " analytic_c; \n", - " part, \n", - " title, \n", - " kwargs...\n", - " )\n", - " func = (part == :real) ? real : imag\n", - " \n", - " spline_data = func(spline_c)\n", - " analytic_data = func(analytic_c)\n", - " error_data = spline_data .- analytic_data\n", - " \n", - " p = plot(x_vals, analytic_data, ls=:dash, label=\"True\", title=title; kwargs...)\n", - " \n", - " plot!(p, x_vals, spline_data, label=\"Spline\")\n", - " \n", - " plot!(p, x_vals, error_data, ls=:dot, label=\"Error\", color=:red)\n", - " \n", - " return p\n", - "end\n", - "\n", - "\n", - "\n", - "plot_configs = [\n", - " (label=\"f(x)\", data_s=f_cs, data_t=true_f_c, formula=\"e^ix\", re_res=\"cos(x)\", im_res=\"sin(x)\", x_vals=xs_fine),\n", - " (label=\"f'(x)\", data_s=f1_cs, data_t=true_f1_c, formula=\"ie^ix\", re_res=\"-sin(x)\", im_res=\"cos(x)\", x_vals=xs_fine),\n", - " (label=\"f''(x)\", data_s=f2_cs, data_t=true_f2_c, formula=\"-e^ix\", re_res=\"-cos(x)\", im_res=\"-sin(x)\", x_vals=xs_fine),\n", - " (label=\"f'''(x)\",data_s=f3_cs, data_t=true_f3_c, formula=\"-ie^ix\", re_res=\"sin(x)\", im_res=\"-cos(x)\", x_vals=xs_fine),\n", - " (label=\"∫f dt\", data_s=integral_cs, data_t=true_integral_c, formula=\"i(1-e^ix)\", re_res=\"sin(x)\", im_res=\"1-cos(x)\", x_vals=xs_nodes, style=(markershape=:circle, markersize=2)),\n", - "]\n", - "\n", - "plot_list = []\n", - "println(\"--- Generating Complex Spline Validation Plots ---\")\n", - "\n", - "\n", - "for config in plot_configs\n", - " for part_info in ((part=:real, name=\"Re\", res=config.re_res), \n", - " (part=:imag, name=\"Im\", res=config.im_res))\n", - " \n", - " title = \"$(config.label) = $(part_info.name)($(config.formula)) = $(part_info.res)\"\n", - " \n", - " plot_style = haskey(config, :style) ? config.style : (legend=:bottomleft,)\n", - "\n", - " p = generate_complex_spline_plot(\n", - " config.x_vals, \n", - " config.data_s, \n", - " config.data_t;\n", - " part=part_info.part,\n", - " title=title,\n", - " plot_style... \n", - " )\n", - " push!(plot_list, p)\n", - " end\n", - "end\n", - "\n", - "display(plot(plot_list..., layout=(5, 2), size=(1000, 1500),\n", - " plot_title=\"Complex Spline: f(x) = e^(ix), Derivatives, and Integral\",\n", - " margin=4Plots.mm))\n", - "\n", - "println(\"\\nAll complex validation plots generated.\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "#=\n", - "======================================================================\n", - "3. VALIDATION FOR 2D BICUBIC SPLINE\n", - "======================================================================\n", - "=#\n", - "println(\"\\n--- Testing 2D Bicubic Spline Derivatives ---\")\n", - "\n", - "# --- 3.1 Data Generation (for fitting) ---\n", - "nx_nodes, ny_nodes = 20, 20\n", - "x_nodes = collect(range(0.0, stop=2*pi, length=nx_nodes))\n", - "y_nodes = collect(range(0.0, stop=2*pi, length=ny_nodes))\n", - "\n", - "f_nodes = zeros(nx_nodes, ny_nodes, 1) # n_qty = 1 for this test\n", - "for j in 1:ny_nodes, i in 1:nx_nodes\n", - " f_nodes[i, j, 1] = sin(x_nodes[i]) * cos(y_nodes[j])\n", - "end\n", - "\n", - "# --- 3.2 Spline Setup (bctype=2 for periodic in both dimensions) ---\n", - "bcspline = BicubicSpline(x_nodes, y_nodes, f_nodes, bctypex=2, bctypey= 2)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 3.3 Evaluation ---\n", - "nx_fine, ny_fine = 50, 50\n", - "x_fine = collect(range(0.0, stop=2*pi, length=nx_fine))\n", - "y_fine = collect(range(0.0, stop=2*pi, length=ny_fine))\n", - "\n", - "# Get derivatives up to 2nd order\n", - "f_s, fx_s, fy_s, fxx_s, fxy_s, fyy_s = bicube_eval(bcspline, x_fine, y_fine, 2)\n", - "\n", - "\n", - "# --- 3.4 Analytical (True) Functions ---\n", - "f_analytic(x, y) = sin(x) * cos(y)\n", - "fx_analytic(x, y) = cos(x) * cos(y)\n", - "fy_analytic(x, y) = -sin(x) * sin(y)\n", - "fxx_analytic(x, y) = -sin(x) * cos(y)\n", - "fyy_analytic(x, y) = -sin(x) * cos(y)\n", - "fxy_analytic(x, y) = -cos(x) * sin(y)\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "9", - "metadata": {}, - "outputs": [], - "source": [ - "# --- 3.5 Plotting Helper Function ---\n", - "function generate_bicube_plots(name, spline_data, analytic_func, x_grid, y_grid)\n", - " \n", - " analytical_data = [analytic_func(x, y) for x in x_grid, y in y_grid]\n", - " spline_slice = spline_data[:, :, 1]\n", - " error_data = spline_slice - analytical_data\n", - " max_abs_error = maximum(abs, error_data)\n", - " \n", - " p1 = heatmap(x_grid, y_grid, spline_slice', title=\"Spline: $name\", c=:viridis)\n", - " p2 = heatmap(x_grid, y_grid, analytical_data', title=\"Analytical: $name\", c=:viridis)\n", - " p3 = heatmap(x_grid, y_grid, error_data', title=\"Error (Max Abs: $(@sprintf(\"%.2e\", max_abs_error)))\", c=:bwr)\n", - "\n", - " return plot(p1, p2, p3, layout=(1, 3), size=(1000, 300), aspect_ratio=:equal)\n", - "end\n", - "\n", - "# --- 3.6 Generate and Display all plots ---\n", - "display(generate_bicube_plots(\"f\", f_s, f_analytic, x_fine, y_fine))\n", - "display(generate_bicube_plots(\"fx\", fx_s, fx_analytic, x_fine, y_fine))\n", - "display(generate_bicube_plots(\"fy\", fy_s, fy_analytic, x_fine, y_fine))\n", - "display(generate_bicube_plots(\"fxx\", fxx_s, fxx_analytic, x_fine, y_fine)) \n", - "display(generate_bicube_plots(\"fyy\", fyy_s, fyy_analytic, x_fine, y_fine)) \n", - "display(generate_bicube_plots(\"fxy\", fxy_s, fxy_analytic, x_fine, y_fine))\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "10", - "metadata": {}, - "outputs": [], - "source": [ - "#=\n", - "======================================================================\n", - "4. VALIDATION FOR 2D FOURIER SPLINE (CUBIC-X, FOURIER-Y)\n", - "======================================================================\n", - "=#\n", - "# Assuming FourierSpline is where the module is located\n", - "# For standalone testing, you might need:\n", - "# include(\"FourierSpline.jl\")\n", - "# using .FourierSpline\n", - "\n", - "println(\"\\n--- Testing 2D Fourier-Spline Derivatives ---\")\n", - "\n", - "\n", - "\n", - "# --- 4.1 Data Generation (for fitting) ---\n", - "# For fit_method=2 (FFT), my_nodes must be a power of 2.\n", - "# We use mx+1 points for x and my+1 points for y.\n", - "# The grid is [0, mx] and [0, my].\n", - "mx_nodes, my_nodes = 32, 32 # my_nodes must be a power of 2 for FFT test\n", - "x_nodes = collect(range(0.0, stop=3.0, length=mx_nodes + 1))\n", - "# y is periodic from 0 to 2pi. The last point y_nodes[my+1] should equal the first y_nodes[1] + 2pi\n", - "y_nodes = collect(range(0.0, stop=2*pi, length=my_nodes + 1))\n", - "\n", - "f_nodes = zeros(mx_nodes + 1, my_nodes + 1, 1) # n_qty = 1\n", - "for j in 1:(my_nodes + 1), i in 1:(mx_nodes + 1)\n", - " f_nodes[i, j, 1] = x_nodes[i]^2 * cos(2 * y_nodes[j])\n", - "end\n", - "\n", - "# --- 4.2 Spline Setup ---\n", - "# Use bctype=1 (natural) for x-direction as it's not periodic.\n", - "# The y-direction is inherently periodic.\n", - "# mband determines how many Fourier modes are used. A higher number gives more accuracy.\n", - "mband_val = 10\n", - "\n", - "# Test both fit methods\n", - "println(\"\\n--- Setting up with fit_method=1 (Integral) ---\")\n", - "fspline_m1 = FourierSpline(x_nodes, y_nodes, f_nodes, mband_val, bctype=4, fit_method=1,fit_flag=true)\n", - "\n", - "println(\"\\n--- Setting up with fit_method=2 (FFT) ---\")\n", - "# This requires my_nodes to be a power of 2.\n", - "fspline_m2 = FourierSpline(x_nodes, y_nodes, f_nodes, mband_val, bctype=2, fit_method=2,fit_flag=true)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "11", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 4.3 Evaluation ---\n", - "# We will evaluate using the FFT-fitted spline (method 2) as it's generally faster if applicable.\n", - "# You can switch to fspline_m1 to compare.\n", - "chosen_fspline = fspline_m1\n", - "\n", - "nx_fine, ny_fine = 60, 60\n", - "x_fine = collect(range(0.0, stop=3.0, length=nx_fine))\n", - "y_fine = collect(range(0.0, stop=2*pi, length=ny_fine))\n", - "\n", - "# Get derivatives up to 2nd order\n", - "f_s, fx_s, fy_s, fxx_s, fxy_s, fyy_s = fspline_eval(chosen_fspline, x_fine, y_fine, Int(2))\n", - "\n", - "\n", - "# --- 4.4 Analytical (True) Functions (Periodic in y) ---\n", - "f_analytic(x, y) = x^2 * cos(2*y)\n", - "fx_analytic(x, y) = 2*x * cos(2*y)\n", - "fy_analytic(x, y) = -2 * x^2 * sin(2*y)\n", - "fxx_analytic(x, y) = 2 * cos(2*y)\n", - "fyy_analytic(x, y) = -4 * x^2 * cos(2*y)\n", - "fxy_analytic(x, y) = -4 * x * sin(2*y)\n", - "\n", - "print(\"evaluation complete\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "12", - "metadata": {}, - "outputs": [], - "source": [ - "function generate_fspline_plot(name, spline_data, analytic_func, x_grid, y_grid)\n", - "\n", - " \n", - " # 1. Generate the analytical data on the fine grid\n", - " analytical_data = [analytic_func(x, y) for x in x_grid, y in y_grid]\n", - " \n", - " # 2. Extract the 2D slice from the 3D spline output array (n_qty=1)\n", - " spline_slice = spline_data[:, :, 1]\n", - " \n", - " # 3. Calculate the error between the spline and analytical data\n", - " error_data = spline_slice - analytical_data\n", - " max_abs_error = maximum(abs, error_data)\n", - " \n", - " # 4. Create three separate heatmaps for comparison\n", - " # Note: We transpose the data (') because Plots.jl heatmap expects (y, x) data layout\n", - " p1 = heatmap(x_grid, y_grid, spline_slice', \n", - " title=\"Spline: $name\", c=:viridis, aspect_ratio=:equal)\n", - " \n", - " p2 = heatmap(x_grid, y_grid, analytical_data', \n", - " title=\"Analytical: $name\", c=:viridis, aspect_ratio=:equal)\n", - " \n", - " p3 = heatmap(x_grid, y_grid, error_data', \n", - " title=\"Error (Max Abs: $(@sprintf(\"%.2e\", max_abs_error)))\", c=:bwr, aspect_ratio=:equal)\n", - "\n", - " # 5. Combine the three heatmaps into a single plot object with a 1x3 layout\n", - " return plot(p1, p2, p3, layout=(1, 3), size=(800, 400), margin=4Plots.mm)\n", - "end\n", - "\n", - "\n", - "# --- 4.5 Generate all plots ---\n", - "# This section calls the helper function for the main function and each derivative,\n", - "# displaying each result as a separate row of plots.\n", - "\n", - "display(generate_fspline_plot(\"f\", f_s, f_analytic, x_fine, y_fine))\n", - "display(generate_fspline_plot(\"fx\", fx_s, fx_analytic, x_fine, y_fine))\n", - "display(generate_fspline_plot(\"fy\", fy_s, fy_analytic, x_fine, y_fine))\n", - "display(generate_fspline_plot(\"fxx\", fxx_s, fxx_analytic, x_fine, y_fine))\n", - "display(generate_fspline_plot(\"fyy\", fyy_s, fyy_analytic, x_fine, y_fine))\n", - "display(generate_fspline_plot(\"fxy\", fxy_s, fxy_analytic, x_fine, y_fine))\n", - "\n", - "println(\"\\nAll Fourier Spline validation plots generated.\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "13", - "metadata": {}, - "outputs": [], - "source": [ - "coeffs = chosen_fspline.cs.fs\n", - "num_x, num_modes = size(coeffs)\n", - "\n", - "for ix in 1:num_x # Loop over x-coordinate indices\n", - " for m_idx in 1:num_modes # Loop over Fourier mode indices\n", - " # Since the mode index (m_idx) is 1-based, the actual mode (m) is m_idx - 1\n", - " m = m_idx - 1\n", - " \n", - " # Retrieve the current coefficient value\n", - " val = coeffs[ix, m_idx]\n", - " \n", - " # Print results with formatted real and imaginary parts\n", - " @printf(\"x_index=%2d, mode=%2d (coeffs[%2d, %2d]): Re = %+.4e, Im = %+.4e\\n\", \n", - " ix, m, ix, m_idx, real(val), imag(val))\n", - " end\n", - " # Add a separator line between each x-point group\n", - " println(\"-\"^20) \n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "14", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Block 5: Validation of Fourier Coefficients ---\n", - "\n", - "println(\"\\n--- Validating Fourier Coefficients c_m(x) ---\")\n", - "\n", - "# Evaluate the spline of coefficients on the fine x-grid\n", - "# The result is a matrix of size (nx_fine, cs_nqty)\n", - "coeffs_spline_fine = spline_eval(chosen_fspline.cs, x_fine)\n", - "\n", - "# Define the analytical functions for the first few coefficients\n", - "# c0_analytic(x) = 0.0 + 0.0im\n", - "c0_analytic(x) = 0.0 + 0.0im + 1e-15 # Add a tiny epsilon to avoid \"No strict ticks found\" warning in Plots.jl\n", - "c1_analytic(x) = 0.0 + 0.0im\n", - "c2_analytic(x) = (x^2 / 2.0) + 0.0im # This is the only non-zero one\n", - "c3_analytic(x) = 0.0 + 0.0im\n", - "c4_analytic(x) = 0.0 + 0.0im\n", - "\n", - "analytic_funcs = [c0_analytic, c1_analytic, c2_analytic, c3_analytic, c4_analytic]\n", - "\n", - "# Create a list to hold the plot objects\n", - "coefficient_plots = []\n", - "\n", - "\n", - "num_modes_to_plot = min(5, chosen_fspline.cs.nqty)\n", - "\n", - "for m_idx in 1:num_modes_to_plot\n", - " m = m_idx - 1 # Current mode number (m=0, 1, 2, ...)\n", - " \n", - " # Extract the data for the m-th mode from the spline evaluation result\n", - " spline_c_m = coeffs_spline_fine[:, m_idx]\n", - " \n", - " # Generate the analytical data for the m-th mode\n", - " analytic_c_m = [analytic_funcs[m_idx](x) for x in x_fine]\n", - " \n", - " # Plot the real part\n", - " p_real = generate_complex_spline_plot(\n", - " x_fine,\n", - " spline_c_m,\n", - " analytic_c_m,\n", - " part=:real,\n", - " title=\"Re(c_$m(x))\"\n", - " )\n", - " \n", - " # Plot the imaginary part\n", - " p_imag = generate_complex_spline_plot(\n", - " x_fine,\n", - " spline_c_m,\n", - " analytic_c_m,\n", - " part=:imag,\n", - " title=\"Im(c_$m(x))\"\n", - " )\n", - " \n", - " # Add the pair of plots to our list\n", - " push!(coefficient_plots, p_real)\n", - " push!(coefficient_plots, p_imag)\n", - "end\n", - "\n", - "# Combine all coefficient plots into a single figure with a readable layout\n", - "# The layout will be (num_modes_to_plot x 2 columns)\n", - "coeff_plot_layout = (num_modes_to_plot, 2)\n", - "final_coeff_plot = plot(coefficient_plots..., layout=coeff_plot_layout, size=(800, 250 * num_modes_to_plot))\n", - "\n", - "# Display the final combined plot\n", - "display(final_coeff_plot)\n", - "\n", - "println(\"\\nFourier coefficient validation plots generated.\")" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/vac_fourier.ipynb b/notebooks/vac_fourier.ipynb deleted file mode 100644 index 0c710f8a..00000000 --- a/notebooks/vac_fourier.ipynb +++ /dev/null @@ -1,311 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"..\")\n", - "Pkg.instantiate()\n", - "using GeneralizedPerturbedEquilibrium, Plots" - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "# Fourier Analysis Routines\n", - "\n", - "This notebook demonstrates two core routines: **`fouran!`** (Fourier analysis) and **`foranv!`** (inverse Fourier analysis). \n", - "Both functions operate on matrices representing discretized angular grids and Fourier coefficients.\n", - "\n", - "---\n", - "\n", - "## 1. `fouran!` — Forward Fourier Analysis\n", - "\n", - "This routine computes Fourier-transformed coefficients from an input matrix.\n", - "\n", - "**Mathematical form:**\n", - "\n", - "For each mode index $l_1$ in the range \n", - "$j_{\\max} = l_{\\max} - l_{\\min} + 1$, \n", - "\n", - "$$\n", - "gil[m_{00}+i, \\, l_{00}+l_1] \n", - "= \\sum_{j=1}^{m_{th}} cs[j, l_1] \\cdot gij[i, j], \n", - "\\quad i = 1, \\dots, m_{th}.\n", - "$$\n", - "\n", - "- `gij` : input matrix in real space \n", - "- `cs` : Fourier basis coefficients \n", - "- `gil` : output Fourier coefficient matrix \n", - "- $(m_{00}, l_{00})$ : index offsets \n", - "- $m_{th}$ : number of angular grid points \n", - "\n", - "---\n", - "\n", - "## 2. `foranv!` — Inverse Fourier Analysis\n", - "\n", - "This routine reconstructs a real-space matrix from the Fourier coefficients.\n", - "\n", - "**Mathematical form:**\n", - "\n", - "For each pair of mode indices $(l_1, l_2)$ in \n", - "$j_{\\max} = l_{\\max} - l_{\\min} + 1$, \n", - "\n", - "$$\n", - "gll[l_2, l_1] \n", - "= \\sum_{i=1}^{m_{th}} \n", - "d\\theta \\cdot 2\\pi \\cdot cs[i, l_2] \\cdot gil[m_{00}+i, l_{00}+l_1],\n", - "$$\n", - "\n", - "where \n", - "\n", - "- $d\\theta = \\dfrac{2\\pi}{m_{th}}$ is the angular step size, \n", - "- `gll` : reconstructed matrix in real space \n", - "- `gil` : Fourier coefficients from `fouran!` \n", - "- `cs` : Fourier basis coefficients \n", - "\n", - "---\n", - "\n", - "## Workflow Summary\n", - "\n", - "1. Start with $gij$ (real-space values). \n", - "2. Call **`fouran!`** → produces `gil` (Fourier coefficients). \n", - "3. Call **`foranv!`** → reconstructs `gll` (approximation of original $gij$). \n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "function fouran!(\n", - " gij::Matrix{Float64},\n", - " gil::Matrix{Float64},\n", - " cs::Matrix{Float64},\n", - " m00::Int,\n", - " l00::Int,\n", - " lmin::Vector{Int},\n", - " lmax::Vector{Int},\n", - " mth::Int\n", - ")\n", - "\n", - " # -------------------------------------------------------------------------\n", - " # Purpose:\n", - " # This routine performs a truncated Fourier transform of gij onto gil\n", - " # using Fourier coefficients stored in cs.\n", - " #\n", - " # Inputs:\n", - " # gij(i,j) : input matrix of size (mth × mth), the \"physical-space\" data\n", - " # cs(j,l) : Fourier coefficient matrix (mth × jmax1)\n", - " # m00, l00 : integer offsets in the gil matrix\n", - " # lmin, lmax : define the active range of Fourier mode indices\n", - " # mth : number of θ-grid points (dimension of gij along i, j)\n", - " #\n", - " # Output:\n", - " # gil(i', l') : matrix updated in-place, where i' = m00 + i and l' = l00 + l\n", - " #\n", - " # -------------------------------------------------------------------------\n", - "\n", - " # Compute jmax1 like Fortran\n", - " jmax1 = lmax[1] - lmin[1] + 1\n", - "\n", - " # Zero out relevant gil block\n", - " for l1 in 1:jmax1\n", - " for i in 1:mth\n", - " gil[m00 + i, l00 + l1] = 0.0\n", - " end\n", - " end\n", - "\n", - " # Accumulate with ll offset (critical to match Fortran)\n", - " for l1 in 1:jmax1\n", - " ll = l1 - 1 + lmin[1]\n", - " for j in 1:mth\n", - " for i in 1:mth\n", - " gil[m00 + i, l00 + l1] += cs[j, l1] * gij[i, j]\n", - " end\n", - " end\n", - " end\n", - "\n", - " return nothing\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "function foranv!(gil::Matrix{Float64}, gll::Matrix{Float64}, cs::Matrix{Float64},\n", - " m00::Int, l00::Int, mth::Int, lmin::Int, lmax::Int,\n", - " dth::Float64)\n", - " \n", - " # -------------------------------------------------------------------------\n", - " # Purpose:\n", - " # This routine performs the inverse Fourier transform of gil using the\n", - " # coefficient matrix cs, producing the real-space matrix gll.\n", - " #\n", - " # Notes:\n", - " # • The summation is over the θ-grid index i.\n", - " # • The factor (dth ⋅ twopi) accounts for the discretized integration\n", - " # over poloidal angle θ (with spacing dth and full 2π periodicity).\n", - " # • gll is symmetric in the sense that its block depends on l1, l2\n", - " # but the roles of l1 and l2 are not interchangeable here because\n", - " # cs is indexed by (i, l2) and gil by (i, l1).\n", - " #\n", - " # Inputs:\n", - " # gil(i', l') : input Fourier-space data, dimensions (nths2 × nfm2)\n", - " # cs(i, l2) : Fourier coefficient matrix (mth × jmax1)\n", - " # m00, l00 : integer offsets into gil\n", - " # mth : number of θ-grid points\n", - " # lmin, lmax : Fourier mode index bounds\n", - " # dth : angular spacing (2π / mth)\n", - " #\n", - " # Output:\n", - " # gll(l2, l1) : jmax1 × jmax1 real-space block\n", - " #\n", - " # -------------------------------------------------------------------------\n", - "\n", - " jmax1 = lmax - lmin + 1\n", - "\n", - " # Zero out gll block\n", - " for l1 in 1:jmax1\n", - " for l2 in 1:jmax1\n", - " gll[l2, l1] = 0.0\n", - " end\n", - " end\n", - "\n", - " # Main accumulation (note: gll[l2, l1], not gll[l1, l2])\n", - " for l1 in 1:jmax1\n", - " for l2 in 1:jmax1\n", - " for i in 1:mth\n", - " gll[l2, l1] += dth * cs[i, l2] * gil[m00+i, l00+l1] * 2π\n", - " end\n", - " end\n", - " end\n", - "\n", - " return gll\n", - "end\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "function test_fourier()\n", - " # Parameters\n", - " mtheta = 200\n", - " mthvac = 900\n", - " mpert = 34\n", - "\n", - " # After defglo/global_alloc\n", - " nths = 905\n", - " nths2 = 1810\n", - " nfm = 34\n", - " nfm2 = 68\n", - "\n", - " m00 = 0\n", - " l00 = 34\n", - "\n", - " # Define lmin/lmax like in arrays.f (dummy example: from 1 to nfm)\n", - " lmin = [1]\n", - " lmax = [nfm]\n", - "\n", - " # Allocate arrays\n", - " gij = zeros(Float64, nths, nths)\n", - " gil = zeros(Float64, nths2, nfm2)\n", - " cs = zeros(Float64, nths, nfm)\n", - " x = zeros(Float64, nths)\n", - "\n", - " # Allocate gll for foranv test\n", - " gll = zeros(Float64, nfm, nfm)\n", - "\n", - " # Fill x(i) = 6.28 / i\n", - " for i in 1:nths\n", - " x[i] = 6.28 / i\n", - " end\n", - "\n", - " # Fill gij(i,j) and cs(i,j)\n", - " for i in 1:nths\n", - " for j in 1:nths\n", - " gij[i,j] = sin(x[i] + x[j])\n", - " end\n", - " for j in 1:nfm\n", - " cs[i,j] = (sin(j * x[i]))^2\n", - " end\n", - " end\n", - "\n", - " # Call your Fourier routine\n", - " fouran!(gij, gil, cs, m00, l00, lmin, lmax, nths)\n", - "\n", - " println(\"gil(1:5,1:5) submatrix starting at (109+1,33+1):\")\n", - " for i in 1:5\n", - " println([gil[109+i, 33+j] for j in 1:5])\n", - " end\n", - "\n", - " mth = nths\n", - " dth = 2π / mth\n", - " gll = zeros(Float64, nfm, nfm)\n", - "\n", - " foranv!(gil, gll, cs, m00, l00, mth, lmin[1], lmax[1], dth)\n", - "\n", - " println(\"gll(1:5,1:5) matrix:\")\n", - " for i in 1:5\n", - " println([gll[i,j] for j in 1:5])\n", - " end\n", - "\n", - "end\n", - "\n", - "test_fourier()\n" - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "## ✅ Verification\n", - "\n", - "All test cases **match** with the Fortran version of the code.\n", - "\n", - "**Fortran Reference Output**\n", - "\n", - "```Test 2: Fourier and Inverse Fourier\n", - "gil(1:5,1:5) submatrix starting at (109+1,33+1):\n", - "0.000000 5.758477 8.519921 10.099648 11.729998\n", - "0.000000 5.756084 8.512475 10.087153 11.712772\n", - "0.000000 5.753733 8.505160 10.074878 11.695851\n", - "0.000000 5.751421 8.497972 10.062818 11.679226\n", - "0.000000 5.749149 8.490908 10.050967 11.662890\n", - "gll(1:5,1:5) matrix:\n", - "2.378815 5.239105 7.825739 10.283557 12.793731\n", - "5.239105 10.009040 13.985464 17.811371 21.749000\n", - "7.825739 13.985464 18.839502 23.552753 28.430625\n", - "10.283557 17.811371 23.552753 29.158460 34.979160\n", - "12.793731 21.749000 28.430625 34.979160 41.794207```\n" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/vac_wall.ipynb b/notebooks/vac_wall.ipynb deleted file mode 100644 index b03e25ef..00000000 --- a/notebooks/vac_wall.ipynb +++ /dev/null @@ -1,393 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "# Load required packages\n", - "using DelimitedFiles\n", - "using LinearAlgebra\n", - "using Plots\n", - "using Plots.PlotMeasures\n", - "using Revise\n", - "# using Revise\n", - "gr()\n", - "\n", - "# Add GPEC to path and load\n", - "push!(LOAD_PATH, joinpath(@__DIR__, \"..\"))\n", - "using GeneralizedPerturbedEquilibrium\n", - "\n", - "# Initialize globals with proper grid parameters\n", - "# The kernel function expects coordinates on a regular theta grid\n", - "mth = 512 # Number of poloidal grid points\n", - "inputs = GeneralizedPerturbedEquilibrium.Vacuum.VacuumInput(\n", - " mtheta=mth,\n", - " n=1\n", - ")\n", - "shapings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings()" - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "# Make virtual plasma boundary" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "using Plots\n", - "\n", - "# 1. Grid setup\n", - "mth = inputs.mtheta\n", - "theta = range(0, 1, length=mth+1)[1:mth] \n", - "dtheta_val = 2π / mth\n", - "\n", - "# 2. Physical parameters\n", - "R0 = 6.0 \n", - "a = 2.0 \n", - "kappa = 2.0 \n", - "delta_tri = 0.6 # This 'delta' is the actual Triangularity for the D-shape\n", - "n = 1 \n", - "qa = 4.3 \n", - "\n", - "# 3. Coordinate and derivative calculations with Triangularity (D-shape)\n", - "alpha = 2π .* theta\n", - "x = R0 .+ a .* cos.(alpha .+ asin(delta_tri) .* sin.(alpha))\n", - "z = kappa .* a .* sin.(alpha)\n", - "\n", - "# Derivatives (Chain rule applied)\n", - "common_slope = 2π .* (1 .+ asin(delta_tri) .* cos.(alpha))\n", - "dx_dtheta = -a .* sin.(alpha .+ asin(delta_tri) .* sin.(alpha)) .* common_slope\n", - "dz_dtheta = 2π .* kappa .* a .* cos.(alpha)\n", - "\n", - "# 4. Phase offset 'delta' (Set to 0 as it's a coordinate phase, not triangularity)\n", - "delta_vec = zeros(mth) # Now 0-filled, delta_param removed\n", - "cnqd = cos.(n * qa .* delta_vec) # will be 1.0\n", - "snqd = sin.(n * qa .* delta_vec) # will be 0.0\n", - "\n", - "# 5. Mode setup\n", - "mlow, mhigh = -10, 10\n", - "l_modes = mlow:mhigh\n", - "mpert = length(l_modes)\n", - "\n", - "# 6. Basis function matrices calculation\n", - "sinlt = zeros(mth, mpert)\n", - "coslt = zeros(mth, mpert)\n", - "snlth = zeros(mth, mpert)\n", - "cslth = zeros(mth, mpert)\n", - "\n", - "for (j, l) in enumerate(l_modes)\n", - " angle_pure = 2π * l .* theta\n", - " # Since delta_vec is 0, angle_with_delta == angle_pure\n", - " angle_with_delta = angle_pure .+ (n * qa .* delta_vec)\n", - " \n", - " sinlt[:, j] = sin.(angle_pure)\n", - " coslt[:, j] = cos.(angle_pure)\n", - " snlth[:, j] = sin.(angle_with_delta)\n", - " cslth[:, j] = cos.(angle_with_delta)\n", - "end\n", - "\n", - "# 7. Construct PlasmaGeometry\n", - "plasma = GeneralizedPerturbedEquilibrium.Vacuum.PlasmaGeometry(\n", - " x,\n", - " z,\n", - " delta_vec,\n", - " dx_dtheta,\n", - " dz_dtheta,\n", - " cnqd,\n", - " snqd,\n", - " sinlt,\n", - " coslt,\n", - " snlth,\n", - " cslth\n", - ")\n", - "\n", - "\n", - "println(\"Plasma Geometry setup complete with Triangularity δ = $delta_tri\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# --- Visualization ---\n", - "\n", - "# Plot 1: Poloidal Cross-section (Showing the D-shape)\n", - "p1 = plot(x, z, label=\"D-shaped Surface\", lw=2, aspect_ratio=:equal,\n", - " title=\"Poloidal Cross-section (δ=$delta_tri)\",\n", - " xlabel=\"R [m]\", ylabel=\"Z [m]\")\n", - "scatter!([R0], [0], label=\"Geometric Center\", color=:red)\n", - "\n", - "# Plot 2: Tangent Vectors\n", - "step = 8\n", - "p2 = quiver(x[1:step:end], z[1:step:end], \n", - " quiver=(dx_dtheta[1:step:end].*0.05, dz_dtheta[1:step:end].*0.05),\n", - " label=\"Tangent Vectors\", color=:blue)\n", - "plot!(x, z, label=\"\", color=:black, alpha=0.3, aspect_ratio=:equal)\n", - "title!(p2, \"Surface Derivatives\")\n", - "\n", - "plot(p1, p2, layout=(1, 2), size=(900, 450))" - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "# Various wall options " - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "## Conformal option" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "shapings.shape = \"conformal\"\n", - "shapings.a = 0.2\n", - "settings = GeneralizedPerturbedEquilibrium.Vacuum.initialize_wall(inputs, plasma, shapings);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "# 1. Plot settings\n", - "p = plot(aspect_ratio=:equal, size=(600, 800), legend=:outerright)\n", - "\n", - "# 2. Plot Plasma Surface (Inner curve)\n", - "plot!(p, plasma.x, plasma.z, label=\"Plasma Surface\", \n", - " lw=2, color=:red, linestyle=:dash)\n", - "\n", - "# 3. Plot Vacuum Wall (Outer curve)\n", - "# Since the wall coordinates often return one extra point to close the loop (mth+1 or mth+2),\n", - "# it will automatically draw a closed line.\n", - "plot!(p, settings.x, settings.z, label=\"Vacuum Wall ($(shapings.shape))\", \n", - " lw=3, color=:black)\n", - "\n", - "# 4. Decoration\n", - "title!(p, \"Plasma and Vacuum Wall Geometry\")\n", - "xlabel!(p, \"R [m]\")\n", - "ylabel!(p, \"Z [m]\")\n", - "\n", - "# Optional: Add geometric center for reference\n", - "scatter!(p, [6.0], [0.0], label=\"Geometric Center\", color=:blue, markersize=3)\n", - "\n", - "display(p)" - ] - }, - { - "cell_type": "markdown", - "id": "8", - "metadata": {}, - "source": [ - "## Dee or Mod-Dee option" - ] - }, - { - "cell_type": "markdown", - "id": "9", - "metadata": {}, - "source": [ - "### Dee" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "10", - "metadata": {}, - "outputs": [], - "source": [ - "shapings.shape = \"dee\"\n", - "shapings.a = 1.2 # Wall minor radius scale factor (1.2 times the plasma radius)\n", - "shapings.bw = 2.2 # Elongation (slightly longer than plasma's kappa=2.0)\n", - "shapings.dw = 0.7 # Triangularity (shaper D-shape than plasma's 0.6)\n", - "shapings.tw = 0.1 # Squareness (bulge at the 'shoulder' of the D-shape)\n", - "shapings.cw = 0.0 # Radial center offset relative to plasma center\n", - "dee_settings = GeneralizedPerturbedEquilibrium.Vacuum.initialize_wall(inputs, plasma, shapings);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "11", - "metadata": {}, - "outputs": [], - "source": [ - "# 2. Visualization\n", - "p_dee = plot(aspect_ratio=:equal, size=(600, 800), legend=:outerright)\n", - "plot!(p_dee, plasma.x, plasma.z, label=\"Plasma Surface\", lw=2, color=:red, linestyle=:dash)\n", - "plot!(p_dee, dee_settings.x, dee_settings.z, label=\"Dee Shape Wall\", lw=3, color=:black)\n", - "title!(p_dee, \"Dee Shape Wall (Relative to Plasma)\")\n", - "display(p_dee)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "12", - "metadata": {}, - "outputs": [], - "source": [ - "shapings.shape = \"mod_dee\"\n", - "shapings.a = 3.5 # Wall minor radius scale factor (1.2 times the plasma radius)\n", - "shapings.bw = 1.8 # Elongation (slightly longer than plasma's kappa=2.0)\n", - "shapings.dw = 0.5 # Triangularity (shaper D-shape than plasma's 0.6)\n", - "shapings.tw = 0.05 # Squareness (bulge at the 'shoulder' of the D-shape)\n", - "shapings.cw = 6.2 # Radial center offset relative to plasma center\n", - "mod_dee_settings = GeneralizedPerturbedEquilibrium.Vacuum.initialize_wall(inputs, plasma, shapings);\n", - "\n", - "# 2. Visualization\n", - "p_mod = plot(aspect_ratio=:equal, size=(600, 800), legend=:outerright)\n", - "plot!(p_mod, plasma.x, plasma.z, label=\"Plasma Surface\", lw=2, color=:red, linestyle=:dash)\n", - "plot!(p_mod, mod_dee_settings.x, mod_dee_settings.z, label=\"Mod-Dee Shape Wall\", lw=3, color=:blue)\n", - "title!(p_mod, \"Mod-Dee Shape Wall (Absolute Coordinates)\")\n", - "display(p_mod)" - ] - }, - { - "cell_type": "markdown", - "id": "13", - "metadata": {}, - "source": [ - "# Elliptical" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "14", - "metadata": {}, - "outputs": [], - "source": [ - "shapings.shape = \"elliptical\"\n", - "shapings.a = 4.0\n", - "elliptical_settings = GeneralizedPerturbedEquilibrium.Vacuum.initialize_wall(inputs, plasma, shapings);\n", - "\n", - "\n", - "# 2. Visualization\n", - "p_ell = plot(aspect_ratio=:equal, size=(600, 800), legend=:outerright)\n", - "\n", - "# Plot Plasma Surface\n", - "plot!(p_ell, plasma.x, plasma.z, label=\"Plasma Surface\", \n", - " lw=2, color=:red, linestyle=:dash)\n", - "\n", - "# Plot Elliptical Wall\n", - "plot!(p_ell, elliptical_settings.x, elliptical_settings.z, label=\"Elliptical Wall\", \n", - " lw=3, color=:green)\n", - "\n", - "title!(p_ell, \"Elliptical Wall Geometry\")\n", - "xlabel!(p_ell, \"R [m]\")\n", - "ylabel!(p_ell, \"Z [m]\")\n", - "\n", - "display(p_ell)" - ] - }, - { - "cell_type": "markdown", - "id": "15", - "metadata": {}, - "source": [ - "## from_file" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "16", - "metadata": {}, - "outputs": [], - "source": [ - "# --- 1. Create a dummy \"wall_geo.in\" file ---\n", - "# In a real scenario, this file would come from CAD data or external diagnostic coordinates.\n", - "mtheta_val = 512\n", - "open(\"wall_geo.in\", \"w\") do io\n", - " println(io, mtheta_val) # Row 1: Number of points (npots0)\n", - " println(io, 6.2) # Row 2: R-coordinate of the wall center (wcentr)\n", - " println(io, \"# index R Z\") # Row 3: Header/Comment line (skipped by the reader)\n", - " \n", - " # Generate a sample D-shaped wall boundary numerically\n", - " for i in 1:mtheta_val\n", - " # Calculate theta from 0 to 2π (Counter-Clockwise)\n", - " theta = 2π * (i-1) / (mtheta_val-1)\n", - " \n", - " r = 6.2 + 3.0 * cos(theta + 0.3 * sin(theta))\n", - " z = 4.5 * sin(theta)\n", - "\n", - " println(io, \"$i $r $z\")\n", - " end\n", - "end\n", - "\n", - "# --- 2. Configure Wall Settings ---\n", - "\n", - "shapings.shape = \"./wall_geo.in\"\n", - "shapings.a = 4.0\n", - "shapings.equal_arc_wall = false\n", - "fromfile_settings = GeneralizedPerturbedEquilibrium.Vacuum.initialize_wall(inputs, plasma, shapings);\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "17", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "# --- 4. Visualization ---\n", - "p = plot(aspect_ratio=:equal, size=(600, 800), legend=:outerright)\n", - "\n", - "# Plot the Plasma Boundary for reference\n", - "plot!(p, plasma.x, plasma.z, label=\"Plasma Surface\", \n", - " lw=2, color=:red, linestyle=:dash)\n", - "\n", - "# Plot the Vacuum Vessel Wall loaded from the file\n", - "plot!(p, fromfile_settings.x, fromfile_settings.z, label=\"Wall (from_file)\", \n", - " lw=3, color=:darkgreen)\n", - "\n", - "# Add plot labels and title\n", - "title!(p, \"External Wall Geometry (from_file)\")\n", - "xlabel!(p, \"R [m]\")\n", - "ylabel!(p, \"Z [m]\")\n", - "\n", - "# Display the final plot\n", - "display(p)" - ] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/vacuum_tests/grdgre_output.txt b/notebooks/vacuum_tests/grdgre_output.txt deleted file mode 100644 index 58f4b974..00000000 --- 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-1,1,-1,1,1,0 diff --git a/notebooks/vacuum_tests/test_fourier.jl b/notebooks/vacuum_tests/test_fourier.jl deleted file mode 100644 index 200a045c..00000000 --- a/notebooks/vacuum_tests/test_fourier.jl +++ /dev/null @@ -1,412 +0,0 @@ -""" -Test script to verify that the refactored Fourier transform functions -produce identical results to the original nested-loop versions. -Written by Claude. -""" - -using LinearAlgebra -using Printf - -# Try to load FFTW for FFT-based implementations -const USE_FFT = try - using FFTW - true -catch - @warn "FFTW not available. Run `import Pkg; Pkg.add(\"FFTW\")` to enable FFT tests." - false -end - -# ============================================================================ -# Original versions (nested loops) -# ============================================================================ - -function fourier_transform_old!( - gil::Matrix{Float64}, - gij::Matrix{Float64}, - cs::Matrix{Float64}, - m00::Int, - l00::Int, - mth::Int, - mpert::Int -) - # Zero out relevant gil block - for l1 in 1:mpert - for i in 1:mth - gil[m00+i, l00+l1] = 0.0 - end - end - - # Accumulate with nested loops - for l1 in 1:mpert - for j in 1:mth - for i in 1:mth - gil[m00+i, l00+l1] += cs[j, l1] * gij[i, j] - end - end - end -end - -function fourier_inverse_transform_old!( - gll::Matrix{Float64}, - gil::Matrix{Float64}, - cs::Matrix{Float64}, - m00::Int, - l00::Int, - mth::Int, - mpert::Int -) - # Zero out gll block - for l1 in 1:mpert - for l2 in 1:mpert - gll[l2, l1] = 0.0 - end - end - - # Main accumulation - dth = 2π / mth - for l1 in 1:mpert - for l2 in 1:mpert - gll[l2, l1] = dth * sum(cs[i, l2] * gil[m00+i, l00+l1] for i in 1:mth) * 2π - end - end -end - -# ============================================================================ -# New versions (vectorized) -# ============================================================================ - -function fourier_transform_new!( - gil::Matrix{Float64}, - gij::Matrix{Float64}, - cs::Matrix{Float64}, - m00::Int, - l00::Int, - mth::Int, - mpert::Int -) - # Zero out relevant gil block - gil[(m00+1):(m00+mth), (l00+1):(l00+mpert)] .= 0.0 - - # Accumulate Fourier transform via matrix multiply - mul!(view(gil, (m00+1):(m00+mth), (l00+1):(l00+mpert)), gij, cs) -end - -function fourier_inverse_transform_new!( - gll::Matrix{Float64}, - gil::Matrix{Float64}, - cs::Matrix{Float64}, - m00::Int, - l00::Int, - mth::Int, - mpert::Int -) - # Zero out gll block - fill!(view(gll, 1:mpert, 1:mpert), 0.0) - - # Inverse Fourier transform via matrix multiply: gll = cs^T * gil * (2π * dth) - # This computes: gll[l2, l1] = (2π * dth) * Σ_i cs[i, l2] * gil[i, l1] - dth = 2π / mth - mul!(gll, cs', view(gil, (m00+1):(m00+mth), (l00+1):(l00+mpert)), 2π * dth, 0.0) -end - -# ============================================================================ -# FFT-based versions (only if FFTW is available) -# ============================================================================ - -if USE_FFT - function fourier_transform_fft!( - gil::Matrix{Float64}, - gij::Matrix{Float64}, - cs::Matrix{Float64}, - m00::Int, - l00::Int, - mth::Int, - mpert::Int - ) - # Zero out relevant gil block - gil[(m00+1):(m00+mth), (l00+1):(l00+mpert)] .= 0.0 - - # For each row, compute FFT along columns and extract modes - for i in 1:mth - # Take FFT of row i across all theta points - fft_result = fft(gij[i, :]) - - # Extract the first mpert Fourier modes and store - # Note: This assumes cs represents standard Fourier basis - for l in 1:min(mpert, length(fft_result)) - gil[m00+i, l00+l] = real(fft_result[l]) / mth - end - end - end - - function fourier_inverse_transform_fft!( - gll::Matrix{Float64}, - gil::Matrix{Float64}, - cs::Matrix{Float64}, - m00::Int, - l00::Int, - mth::Int, - mpert::Int - ) - # Zero out gll block - gll[1:mpert, 1:mpert] .= 0.0 - - dth = 2π / mth - - # For each mode pair, compute inverse FFT - for l1 in 1:mpert - for l2 in 1:mpert - # Extract spectral coefficients from gil - spectral_data = Complex{Float64}[gil[m00+i, l00+l1] for i in 1:mth] - - # Pad to full size if needed - if length(spectral_data) < mth - append!(spectral_data, zeros(Complex{Float64}, mth - length(spectral_data))) - end - - # Inverse FFT - physical_data = ifft(spectral_data) - - # Accumulate contribution (simplified - actual implementation depends on cs structure) - gll[l2, l1] += dth * 2π * sum(abs.(physical_data)) - end - end - end -end # if USE_FFT - -# ============================================================================ -# Test functions -# ============================================================================ - -function test_fourier_transform() - println("\n" * "="^70) - println("Testing fourier_transform!") - println("="^70) - - # Test parameters - mth = 64 - mpert = 10 - m00 = 5 - l00 = 3 - - # Create test data - gij = randn(mth, mth) - cs = randn(mth, mpert) - - # Allocate output matrices - gil_old = zeros(m00 + mth + 10, l00 + mpert + 10) - gil_new = zeros(m00 + mth + 10, l00 + mpert + 10) - gil_fft = zeros(m00 + mth + 10, l00 + mpert + 10) - - # Run old version - print(" Old (nested loops): ") - @time fourier_transform_old!(gil_old, gij, cs, m00, l00, mth, mpert) - - # Run new version - print(" New (vectorized): ") - @time fourier_transform_new!(gil_new, gij, cs, m00, l00, mth, mpert) - - # Run FFT version if available - if USE_FFT - print(" FFT (built-in): ") - @time fourier_transform_fft!(gil_fft, gij, cs, m00, l00, mth, mpert) - end - - # Compare results: old vs new - diff = gil_old .- gil_new - max_diff = maximum(abs.(diff)) - rel_diff = max_diff / (maximum(abs.(gil_old)) + 1e-10) - - println("\nResults (Old vs New):") - println(" Max absolute difference: ", @sprintf("%.2e", max_diff)) - println(" Max relative difference: ", @sprintf("%.2e", rel_diff)) - - # Check relevant block - block_old = gil_old[(m00+1):(m00+mth), (l00+1):(l00+mpert)] - block_new = gil_new[(m00+1):(m00+mth), (l00+1):(l00+mpert)] - block_fft = gil_fft[(m00+1):(m00+mth), (l00+1):(l00+mpert)] - block_diff = maximum(abs.(block_old .- block_new)) - - println(" Block max difference: ", @sprintf("%.2e", block_diff)) - println(" Block norm (old): ", @sprintf("%.6f", norm(block_old))) - println(" Block norm (new): ", @sprintf("%.6f", norm(block_new))) - - # Compare FFT version if available (note: may differ due to different basis) - if USE_FFT - diff_fft = block_old .- block_fft - max_diff_fft = maximum(abs.(diff_fft)) - println("\nFFT Comparison (informational - may use different basis):") - println(" FFT vs Old max diff: ", @sprintf("%.2e", max_diff_fft)) - println(" Block norm (FFT): ", @sprintf("%.6f", norm(block_fft))) - end - - if max_diff < 1e-10 - println("\n✓ PASS: Results are identical (within machine precision)") - else - println("\n✗ FAIL: Results differ by more than tolerance") - println("\nFirst 5x5 of OLD result:") - display(block_old[1:5, 1:5]) - println("\nFirst 5x5 of NEW result:") - display(block_new[1:5, 1:5]) - println("\nFirst 5x5 of DIFFERENCE:") - display((block_old .- block_new)[1:5, 1:5]) - end - - return max_diff < 1e-10 -end - -function test_fourier_inverse_transform() - println("\n" * "="^70) - println("Testing fourier_inverse_transform!") - println("="^70) - - # Test parameters - mth = 64 - mpert = 10 - m00 = 5 - l00 = 3 - - # Create test data - gil = randn(m00 + mth + 10, l00 + mpert + 10) - cs = randn(mth, mpert) - - # Allocate output matrices - gll_old = zeros(mpert, mpert) - gll_new = zeros(mpert, mpert) - gll_fft = zeros(mpert, mpert) - - # Run old version - print(" Old (nested loops): ") - @time fourier_inverse_transform_old!(gll_old, gil, cs, m00, l00, mth, mpert) - - # Run new version - print(" New (vectorized): ") - @time fourier_inverse_transform_new!(gll_new, gil, cs, m00, l00, mth, mpert) - - # Run FFT version if available - if USE_FFT - print(" FFT (built-in): ") - @time fourier_inverse_transform_fft!(gll_fft, gil, cs, m00, l00, mth, mpert) - end - - # Compare results: old vs new - diff = gll_old .- gll_new - max_diff = maximum(abs.(diff)) - rel_diff = max_diff / (maximum(abs.(gll_old)) + 1e-10) - - println("\nResults (Old vs New):") - println(" Max absolute difference: ", @sprintf("%.2e", max_diff)) - println(" Max relative difference: ", @sprintf("%.2e", rel_diff)) - println(" Matrix norm (old): ", @sprintf("%.6f", norm(gll_old))) - println(" Matrix norm (new): ", @sprintf("%.6f", norm(gll_new))) - - # Compare FFT version if available - if USE_FFT - diff_fft = gll_old .- gll_fft - max_diff_fft = maximum(abs.(diff_fft)) - println("\nFFT Comparison (informational - may use different basis):") - println(" FFT vs Old max diff: ", @sprintf("%.2e", max_diff_fft)) - println(" Matrix norm (FFT): ", @sprintf("%.6f", norm(gll_fft))) - end - - if max_diff < 1e-10 - println("\n✓ PASS: Results are identical (within machine precision)") - else - println("\n✗ FAIL: Results differ by more than tolerance") - println("\nFirst 5x5 of OLD result:") - display(gll_old[1:5, 1:5]) - println("\nFirst 5x5 of NEW result:") - display(gll_new[1:5, 1:5]) - println("\nFirst 5x5 of DIFFERENCE:") - display(diff[1:5, 1:5]) - end - - return max_diff < 1e-10 -end - -function benchmark_comparison() - println("\n" * "="^70) - println("Performance Comparison") - println("="^70) - - mth = 512 - mpert = 50 - m00 = 10 - l00 = 5 - - # Test data - gij = randn(mth, mth) - cs = randn(mth, mpert) - gil_old = zeros(m00 + mth + 20, l00 + mpert + 20) - gil_new = zeros(m00 + mth + 20, l00 + mpert + 20) - gil_fft = zeros(m00 + mth + 20, l00 + mpert + 20) - - println("\nFourier Transform (mth=$mth, mpert=$mpert):") - print(" Old (nested loops): ") - @time fourier_transform_old!(gil_old, gij, cs, m00, l00, mth, mpert) - - print(" New (vectorized): ") - @time fourier_transform_new!(gil_new, gij, cs, m00, l00, mth, mpert) - - if USE_FFT - print(" FFT (built-in): ") - @time fourier_transform_fft!(gil_fft, gij, cs, m00, l00, mth, mpert) - end - - # Inverse transform - gil = randn(m00 + mth + 20, l00 + mpert + 20) - gll_old = zeros(mpert, mpert) - gll_new = zeros(mpert, mpert) - gll_fft = zeros(mpert, mpert) - - println("\nInverse Fourier Transform (mth=$mth, mpert=$mpert):") - print(" Old (nested loops): ") - @time fourier_inverse_transform_old!(gll_old, gil, cs, m00, l00, mth, mpert) - - print(" New (vectorized): ") - @time fourier_inverse_transform_new!(gll_new, gil, cs, m00, l00, mth, mpert) - - if USE_FFT - print(" FFT (built-in): ") - @time fourier_inverse_transform_fft!(gll_fft, gil, cs, m00, l00, mth, mpert) - end -end - -# ============================================================================ -# Main test runner -# ============================================================================ - -function run_all_tests() - println("\n") - println("╔" * "="^68 * "╗") - println("║" * " "^15 * "FOURIER TRANSFORM TEST SUITE" * " "^25 * "║") - println("╚" * "="^68 * "╝") - - test1_pass = test_fourier_transform() - test2_pass = test_fourier_inverse_transform() - - # Benchmark - benchmark_comparison() - - # Summary - println("\n" * "="^70) - println("TEST SUMMARY") - println("="^70) - println(" fourier_transform!: ", test1_pass ? "✓ PASS" : "✗ FAIL") - println(" fourier_inverse_transform!: ", test2_pass ? "✓ PASS" : "✗ FAIL") - println() - - if test1_pass && test2_pass - println("🎉 All tests passed!") - else - println("⚠️ Some tests failed - review output above") - end - println("="^70 * "\n") - - return test1_pass && test2_pass -end - -# Run tests -if abspath(PROGRAM_FILE) == @__FILE__ - run_all_tests() -end diff --git a/notebooks/vacuum_tests/test_trig_basis.jl b/notebooks/vacuum_tests/test_trig_basis.jl deleted file mode 100644 index 740c2855..00000000 --- a/notebooks/vacuum_tests/test_trig_basis.jl +++ /dev/null @@ -1,219 +0,0 @@ -""" -Test script to verify vectorized trigonometric basis initialization -produces identical results to the original nested loop version. -Written by Claude. -""" - -using Printf -using LinearAlgebra - -# ============================================================================ -# Original version (nested loops) -# ============================================================================ - -function init_trig_basis_old(mtheta::Int, n::Int, qa::Float64, delta::Vector{Float64}, - mlow::Int, mpert::Int) - cos_nqdelta = zeros(mtheta) - sin_nqdelta = zeros(mtheta) - sin_mstheta = zeros(mtheta, mpert) - cos_mstheta = zeros(mtheta, mpert) - sin_mstheta_arg = zeros(mtheta, mpert) - cos_mstheta_arg = zeros(mtheta, mpert) - - for is in 1:mtheta - theta = (is-1) * 2π / mtheta - nqdelta = n * qa * delta[is] - cos_nqdelta[is] = cos(nqdelta) - sin_nqdelta[is] = sin(nqdelta) - for l1 in 1:mpert - mi = mlow - 1 + l1 - mitheta = mi * theta - mitheta_arg = mi * theta + nqdelta - sin_mstheta[is, l1] = sin(mitheta) - cos_mstheta[is, l1] = cos(mitheta) - sin_mstheta_arg[is, l1] = sin(mitheta_arg) - cos_mstheta_arg[is, l1] = cos(mitheta_arg) - end - end - - return (cos_nqdelta, sin_nqdelta, sin_mstheta, cos_mstheta, - sin_mstheta_arg, cos_mstheta_arg) -end - -# ============================================================================ -# New version (vectorized) -# ============================================================================ - -function init_trig_basis_new(mtheta::Int, n::Int, qa::Float64, delta::Vector{Float64}, - mlow::Int, mpert::Int) - # Theta grid - theta_grid = range(0; stop=2π, length=mtheta + 1)[1:(end-1)] - - # Compute n*q*δ phase term for each poloidal angle - nqdelta = n .* qa .* delta - - # Basis functions for the phase factor - cos_nqdelta = cos.(nqdelta) - sin_nqdelta = sin.(nqdelta) - - # Mode numbers: m = mlow, mlow+1, ..., mlow+mpert-1 - mode_numbers = (mlow-1) .+ (1:mpert)' # Row vector for broadcasting - - # Outer product: theta_grid (column) × mode_numbers (row) → (mtheta × mpert) matrix - mitheta = theta_grid * mode_numbers # Broadcasting: m*θ for all combinations - - # Compute basis functions without phase (pure harmonics) - sin_mstheta = sin.(mitheta) - cos_mstheta = cos.(mitheta) - - # Add phase factor: m*θ + n*q*δ (broadcast nqdelta column-wise across modes) - mitheta_arg = mitheta .+ nqdelta - sin_mstheta_arg = sin.(mitheta_arg) - cos_mstheta_arg = cos.(mitheta_arg) - - return (cos_nqdelta, sin_nqdelta, sin_mstheta, cos_mstheta, - sin_mstheta_arg, cos_mstheta_arg) -end - -# ============================================================================ -# Test function -# ============================================================================ - -function test_trig_basis() - println("\n" * "="^70) - println("Testing Trigonometric Basis Initialization") - println("="^70) - - # Test parameters (typical tokamak values) - mtheta = 512 - mpert = 50 - mlow = 1 - n = 1 - qa = 2.5 - delta = 0.3 .* sin.(range(0, 2π; length=mtheta+1)[1:(end-1)]) # Typical triangularity profile - - println("\nTest configuration:") - println(" mtheta = $mtheta (poloidal grid points)") - println(" mpert = $mpert (Fourier modes)") - println(" mlow = $mlow (lowest mode number)") - println(" n = $n (toroidal mode number)") - println(" qa = $qa (edge safety factor)") - println(" delta = triangularity profile (sinusoidal)") - - # Run old version - print("\nOld (nested loops): ") - @time (cos_nqd_old, sin_nqd_old, sin_ms_old, cos_ms_old, - sin_msa_old, cos_msa_old) = init_trig_basis_old(mtheta, n, qa, delta, mlow, mpert) - - # Run new version - print("New (vectorized): ") - @time (cos_nqd_new, sin_nqd_new, sin_ms_new, cos_ms_new, - sin_msa_new, cos_msa_new) = init_trig_basis_new(mtheta, n, qa, delta, mlow, mpert) - - # Compare results - println("\n" * "-"^70) - println("RESULTS") - println("-"^70) - - arrays = [ - ("cos(n*q*δ)", cos_nqd_old, cos_nqd_new), - ("sin(n*q*δ)", sin_nqd_old, sin_nqd_new), - ("sin(m*θ)", sin_ms_old, sin_ms_new), - ("cos(m*θ)", cos_ms_old, cos_ms_new), - ("sin(m*θ + n*q*δ)", sin_msa_old, sin_msa_new), - ("cos(m*θ + n*q*δ)", cos_msa_old, cos_msa_new) - ] - - all_pass = true - for (name, old, new) in arrays - diff = old .- new - max_diff = maximum(abs.(diff)) - rel_diff = max_diff / (maximum(abs.(old)) + 1e-16) - - pass = max_diff < 1e-14 - status = pass ? "✓ PASS" : "✗ FAIL" - all_pass = all_pass && pass - - @printf("%-20s: max_diff = %.2e, rel_diff = %.2e %s\n", - name, max_diff, rel_diff, status) - end - - println("-"^70) - - if all_pass - println("\n🎉 All arrays match within machine precision!") - else - println("\n⚠️ Some arrays differ - review output above") - end - - return all_pass -end - -# ============================================================================ -# Benchmark comparison -# ============================================================================ - -function benchmark_trig_basis() - println("\n" * "="^70) - println("Performance Benchmark") - println("="^70) - - test_sizes = [(128, 20), (256, 30), (512, 50), (1024, 100)] - - for (mtheta, mpert) in test_sizes - println("\nmtheta = $mtheta, mpert = $mpert:") - - # Setup - mlow = 1 - n = 1 - qa = 2.5 - delta = 0.3 .* sin.(range(0, 2π; length=mtheta+1)[1:(end-1)]) - - # Warm-up - init_trig_basis_old(mtheta, n, qa, delta, mlow, mpert) - init_trig_basis_new(mtheta, n, qa, delta, mlow, mpert) - - # Benchmark - print(" Old (nested loops): ") - t_old = @elapsed for _ in 1:100 - init_trig_basis_old(mtheta, n, qa, delta, mlow, mpert) - end - @printf("%.3f ms/call\n", t_old * 10) - - print(" New (vectorized): ") - t_new = @elapsed for _ in 1:100 - init_trig_basis_new(mtheta, n, qa, delta, mlow, mpert) - end - @printf("%.3f ms/call\n", t_new * 10) - - speedup = t_old / t_new - @printf(" Speedup: %.1fx\n", speedup) - end -end - -# ============================================================================ -# Main -# ============================================================================ - -function run_tests() - println("\n") - println("╔" * "="^68 * "╗") - println("║" * " "^12 * "TRIGONOMETRIC BASIS INITIALIZATION TEST" * " "^17 * "║") - println("╚" * "="^68 * "╝") - - pass = test_trig_basis() - benchmark_trig_basis() - - println("\n" * "="^70) - println("TEST SUMMARY") - println("="^70) - println(pass ? "✓ All tests passed!" : "✗ Some tests failed") - println("="^70 * "\n") - - return pass -end - -# Run tests -if abspath(PROGRAM_FILE) == @__FILE__ - run_tests() -end diff --git a/notebooks/vacuum_tests/vac_test.ipynb b/notebooks/vacuum_tests/vac_test.ipynb deleted file mode 100644 index a594ff3c..00000000 --- a/notebooks/vacuum_tests/vac_test.ipynb +++ /dev/null @@ -1,149 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "0", - "metadata": {}, - "outputs": [], - "source": [ - "# Load required packages\n", - "using DelimitedFiles\n", - "using LinearAlgebra\n", - "using Plots\n", - "using Plots.PlotMeasures\n", - "# using Revise\n", - "gr()\n", - "\n", - "# Add GPEC to path and load\n", - "push!(LOAD_PATH, joinpath(@__DIR__, \"../..\"))\n", - "using GeneralizedPerturbedEquilibrium\n", - "\n", - "# Initialize globals with proper grid parameters\n", - "# The kernel function expects coordinates on a regular theta grid\n", - "mth = 512 # Number of poloidal grid points\n", - "inputs = GeneralizedPerturbedEquilibrium.Vacuum.VacuumInput(\n", - " mtheta=mth,\n", - " n=1,\n", - ")\n", - "settings = GeneralizedPerturbedEquilibrium.Vacuum.WallGeometry()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1", - "metadata": {}, - "outputs": [], - "source": [ - "gren = readdlm(\"gren_output.txt\")\n", - "grdgre = readdlm(\"grdgre_output.txt\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "gren_fortran = readdlm(\"../../src/Vacuum/fortran/test_kernel_gren_output.txt\")\n", - "grdgre_fortran = readdlm(\"../../src/Vacuum/fortran/test_kernel_grdgre_output.txt\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# Plot comparison of the two results, log scaled, equal aspect ratio\n", - "# set figsize = (600, 600) for square output\n", - "\n", - "p = heatmap(range(1,mth), \n", - "\t\t\trange(1,mth), \n", - "\t\t\tlog10.(abs.(gren - gren_fortran[1:mth, 1:mth]) .+ eps()), \n", - "\t\t\ttitle=\"Log-scaled difference in gren\", \n", - "\t\t\txlabel=\"Column Index\", \n", - "\t\t\tylabel=\"Row Index\", \n", - "\t\t\tcolorbar_title=\"Log10 Difference\",\n", - "\t\t\tantialiasing=false,\n", - "\t\t\tclims = (-10, 0)\n", - "\t\t\t)\n", - "\n", - "porig = heatmap(range(1,mth), \n", - "\t\t\trange(1,mth), \n", - "\t\t\tlog10.(abs.(gren_fortran[1:mth, 1:mth]) .+ eps()), \n", - "\t\t\ttitle=\"Log-scaled gren from Fortran\", \n", - "\t\t\txlabel=\"Column Index\", \n", - "\t\t\tylabel=\"Row Index\", \n", - "\t\t\tcolorbar_title=\"Log10 Value\",\n", - "\t\t\tantialiasing=false,\n", - "\t\t\tclims = (-10, 0)\n", - "\t\t\t)\n", - "\n", - "plot!(p, aspect_ratio=1, size=(600,600), dpi=100, )\n", - "plot!(porig, aspect_ratio=1, size=(600,600), dpi=100, )\n", - "p = plot(p, porig, layout=(1,2), size=(1200,600))\n", - "yflip!()\n", - "savefig(p, \"gren_comparison.pdf\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# The same thing for grdgre\n", - "p2 = heatmap(range(1,mth), \n", - "\t\t\t range(1,mth), \n", - "\t\t\t log10.(abs.(grdgre[1:mth, 1:mth] - grdgre_fortran[1:mth, 1:mth]) .+ eps()), \n", - "\t\t\t title=\"Log-scaled difference in grdgre\", \n", - "\t\t\t xlabel=\"Column Index\", \n", - "\t\t\t ylabel=\"Row Index\", \n", - "\t\t\t# colorbar_title=\"Log10 Difference\",\n", - "\t\t\t right_margin=10Plots.mm,\n", - "\t\t\t clims = (-10, 0)\n", - "\t\t\t )\n", - "\n", - "porig2 = heatmap(range(1,mth), \n", - "\t\t\t range(1,mth), \n", - "\t\t\t log10.(abs.(grdgre_fortran[1:mth, 1:mth]) .+ eps()), \n", - "\t\t\t title=\"Log-scaled grdgre from Fortran\", \n", - "\t\t\t xlabel=\"Column Index\", \n", - "\t\t\t ylabel=\"Row Index\", \n", - "\t\t\t# colorbar_title=\"Log10 Value\",\n", - "\t\t\t right_margin=10Plots.mm,\n", - "\t\t\t clims = (-10, 0)\n", - "\t\t\t )\n", - "\n", - "plot!(p2, aspect_ratio=1, size=(600,600), dpi=100, )\n", - "plot!(porig2, aspect_ratio=1, size=(600,600), dpi=100, )\n", - "p2 = plot(p2, porig2, layout=(1,2), size=(1200,600))\n", - "yflip!()\n", - "savefig(p2, \"grdgre_comparison.pdf\")\n", - "display(p2)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/vacuum_tests/vacuum_debug_julia.jl b/notebooks/vacuum_tests/vacuum_debug_julia.jl deleted file mode 100644 index fda6df3e..00000000 --- a/notebooks/vacuum_tests/vacuum_debug_julia.jl +++ /dev/null @@ -1,311 +0,0 @@ -using DelimitedFiles -using Printf -using LinearAlgebra -using Profile -push!(LOAD_PATH, joinpath(@__DIR__, "../..")) -using GeneralizedPerturbedEquilibrium -mth = 512 # Number of poloidal grid points -inputs = GeneralizedPerturbedEquilibrium.Vacuum.VacuumInput(; - mtheta=mth, - n=1 -) -# settings = GeneralizedPerturbedEquilibrium.Vacuum.WallGeometry() - -#--------------------------------------------------------------- -# Read the output_data.txt file -#--------------------------------------------------------------- -data_file = joinpath(@__DIR__, "output_data.txt") - -println("Reading file: $data_file") -println("File exists: $(isfile(data_file))") -println() - -# Read all lines -lines = readlines(data_file) -println("Total lines in file: $(length(lines))") - -# Helper function to parse a line of comma-separated numbers -function parse_number_line(line) - tokens = split(line, ',') - return [parse(Float64, strip(token)) for token in tokens if !isempty(strip(token))] -end - -# Parse the five lines -if length(lines) < 5 - error("Expected 5 lines in output_data.txt, but found only $(length(lines)) lines!") -end - -# println("\nParsing data from first 5 lines:") -xobs = parse_number_line(lines[1]) -# println(" Line 1 (xobs): $(length(xobs)) values") - -zobs = parse_number_line(lines[2]) -# println(" Line 2 (zobs): $(length(zobs)) values") - -xsce = parse_number_line(lines[3]) -# println(" Line 3 (xsce): $(length(xsce)) values") - -zsce = parse_number_line(lines[4]) -# println(" Line 4 (zsce): $(length(zsce)) values") - -params = parse_number_line(lines[5]) -# println(" Line 5 (params): $(length(params)) values") - -xobs = xobs[1:mth] -zobs = zobs[1:mth] -xsce = xsce[1:mth] -zsce = zsce[1:mth] - -# println("\n✓ Successfully parsed all data!") -# println("\nData summary:") -# println(" xobs: $(length(xobs)) points, range [$(minimum(xobs)), $(maximum(xobs))]") -# println(" zobs: $(length(zobs)) points, range [$(minimum(zobs)), $(maximum(zobs))]") -# println(" xsce: $(length(xsce)) points, range [$(minimum(xsce)), $(maximum(xsce))]") -# println(" zsce: $(length(zsce)) points, range [$(minimum(zsce)), $(maximum(zsce))]") -# println(" params: $(params)") - -# Extract kernel function parameters -j1_input = Int(params[1]) -j2_input = Int(params[2]) -isgn_input = Int(params[3]) -iopw_input = Int(params[4]) -iops_input = Int(params[5]) -wall_flag_input = params[6] != 0 # Convert to boolean - -# println("\nKernel parameters:") -# println(" j1 = $j1_input") -# println(" j2 = $j2_input") -# println(" isgn = $isgn_input") -# println(" iopw = $iopw_input") -# println(" iops = $iops_input") -# println(" wall_flag = $wall_flag_input") - -#--------------------------------------------------------------- -# Set up Kernel Function Parameters -#--------------------------------------------------------------- - -# Set up parameters for kernel function test -nobs = length(xobs) -nsrc = length(xsce) - -# Validate data consistency -if length(xobs) != length(zobs) - error("xobs and zobs have different lengths: $(length(xobs)) vs $(length(zobs))") -end -if length(xsce) != length(zsce) - error("xsce and zsce have different lengths: $(length(xsce)) vs $(length(zsce))") -end - -println("Data validation passed!") -println() - -# Initialize output matrices -grdgre = zeros(Float64, 2*nobs, 2*nsrc) -gren = zeros(Float64, nobs, nsrc) - -# Use parameters loaded from input file -j1 = j1_input -j2 = j2_input -isgn = isgn_input -iopw = iopw_input -iops = iops_input -wall_flag = wall_flag_input - -println("Test configuration:") -println(" Observer points: $nobs") -println(" Source points: $nsrc") -println(" Observer type (j1): $j1 (1=plasma, 2=wall)") -println(" Source type (j2): $j2 (1=plasma, 2=wall)") -println(" Sign parameter (isgn): $isgn") -println(" Wall option (iopw): $iopw") -println(" Log singularity option (iops): $iops") -println(" Wall flag: $wall_flag") -println() -println("Output matrix dimensions:") -println(" grdgre: $(size(grdgre))") -println(" gren: $(size(gren))") - -#--------------------------------------------------------------- -# Call the kernel function -#--------------------------------------------------------------- - -# Run the kernel function -# Note: This may fail if additional setup/initialization is required -try - GeneralizedPerturbedEquilibrium.Vacuum.kernel!( - grdgre, gren, - xobs[1:mth], zobs[1:mth], - xsce[1:mth], zsce[1:mth], - j1, j2, isgn, iopw, iops, wall_flag, inputs #settings - ) - - println("✓ Kernel function executed successfully!") - # println() - # println("Result statistics:") - # println(" grdgre: min=$(minimum(grdgre)), max=$(maximum(grdgre)), mean=$(sum(grdgre)/length(grdgre))") - # println(" gren: min=$(minimum(gren)), max=$(maximum(gren)), mean=$(sum(gren)/length(gren))") - -catch e - println("✗ Error running kernel function.") - # println(e) - println() - println("Stack trace:") - for (exc, bt) in Base.catch_stack() - showerror(stdout, exc, bt) - println() - end - println() -end - -#--------------------------------------------------------------- -# Print a small portion of the output matrices for inspection -#--------------------------------------------------------------- - -# Debug: Check what's in the result matrices -println("===== RESULT DIAGNOSTICS =====") -# println("grdgre exists: $(isdefined(Main, :grdgre))") -# println("gren exists: $(isdefined(Main, :gren))") -# println() - -if isdefined(Main, :grdgre) && isdefined(Main, :gren) - - writedlm("gren_output.txt", gren) - writedlm("grdgre_output.txt", grdgre) - - println("grdgre size: $(size(grdgre))") - println("gren size: $(size(gren))") - println() - - println("gren first 5x5:") - # display(gren[1:min(5,size(gren,1)), 1:min(5,size(gren,2))]) - for i in 1:min(5, size(gren, 1)) - for j in 1:min(5, size(gren, 2)) - @printf("%12.9f ", gren[i, j]) - end - println() - end - println() - println("grdgre first 5x5:") - for i in 1:min(5, size(grdgre, 1)) - for j in 1:min(5, size(grdgre, 2)) - @printf("%12.9f ", grdgre[i, j]) - end - println() - end - - # println("grdgre first 5x5:") - # display(grdgre[1:min(5,size(grdgre,1)), 1:min(5,size(grdgre,2))]) - println() - -else - println("ERROR: Result matrices not defined!") - println("Make sure to run the kernel execution cell first.") -end - -#--------------------------------------------------------------- -# Profile kernel! performance -#--------------------------------------------------------------- - -# Toggle profiling; set to false to skip -do_profile = false - -if do_profile - println("===== PROFILING kernel! =====") - # Clear any prior profiling data - Profile.clear() - # Increase buffer size and adjust sampling delay (Julia 1.11 compatible) - try - Profile.init(10^8, 0.005) # (buffer size, delay in seconds) - catch - # If init signature differs, continue with defaults - end - - # Warm-up run to compile and avoid JIT in profile - try - GeneralizedPerturbedEquilibrium.Vacuum.kernel!( - grdgre, gren, - xobs[1:mth], zobs[1:mth], - xsce[1:mth], zsce[1:mth], - j1, j2, isgn, iopw, iops, wall_flag, - inputs #settings - ) - catch e - println("Warm-up failed: ", e) - end - - # Collect profile across multiple iterations to gather samples - n_profile_iters = 20 - @profile for _ in 1:n_profile_iters - GeneralizedPerturbedEquilibrium.Vacuum.kernel!( - grdgre, gren, - xobs[1:mth], zobs[1:mth], - xsce[1:mth], zsce[1:mth], - j1, j2, isgn, iopw, iops, wall_flag, - inputs #settings - ) - end - - # Also record wall-clock timing for reference - total_time = @elapsed begin - for _ in 1:n_profile_iters - GeneralizedPerturbedEquilibrium.Vacuum.kernel!( - grdgre, gren, - xobs[1:mth], zobs[1:mth], - xsce[1:mth], zsce[1:mth], - j1, j2, isgn, iopw, iops, wall_flag, - inputs #settings - ) - end - end - - # Print a concise summary to stdout - println("\n===== Profile summary (top frames) =====") - try - # Print using default signature (Julia 1.11 compatible) - Profile.print() - catch e - println("Profile.print failed: ", e) - end - - # Save a longer summary to file - try - open(joinpath(@__DIR__, "profile_summary.txt"), "w") do io - println(io, "kernel! profiling summary") - println(io, "mth=$mth, iters=$n_profile_iters, total_time=$(round(total_time, digits=6)) s, avg=$(round(total_time/n_profile_iters, digits=6)) s/iter") - println(io) - # Use default print signature without kwargs - Profile.print(io; groupby=:task, sortedby=:time) - end - println("Saved detailed profile to: ", joinpath(@__DIR__, "profile_summary.txt")) - catch e - println("Failed to write profile_summary.txt: ", e) - end - - # # Generate an HTML flamegraph/profile (StatProfilerHTML) - # try - # # Try to import; if absent, activate project root and add it - # try - # import StatProfilerHTML - # catch - # # Ensure we add to the project at repo root - # Base.require(Base.PkgId(Base.UUID("44cfe95a-1eb2-52ea-b672-e2afdf69b78f"), "Pkg")) - # local Pkg = Base.loaded_modules[Base.PkgId(Base.UUID("44cfe95a-1eb2-52ea-b672-e2afdf69b78f"), "Pkg")] - # Pkg.activate(joinpath(@__DIR__, "../..")) - # Pkg.add(name="StatProfilerHTML") - # import StatProfilerHTML - # end - - # # Create HTML profile in this folder - # outpath = joinpath(@__DIR__, "profile.html") - # try - # StatProfilerHTML.statprofilehtml(outpath) - # catch - # # Fallback to default path if method signature differs - # StatProfilerHTML.statprofilehtml() - # outpath = abspath("profile.html") - # end - # println("Saved HTML profile to: ", outpath) - # catch e - # println("Failed to generate HTML profile: ", e) - # end -end diff --git a/notebooks/wall_geo.in b/notebooks/wall_geo.in deleted file mode 100644 index 3424fb41..00000000 --- a/notebooks/wall_geo.in +++ /dev/null @@ -1,515 +0,0 @@ -512 -6.2 -# index R Z -1 9.2 0.0 -2 9.199616750495267 0.055329983229003295 -3 9.198467153376706 0.11065160132205983 -4 9.196551662721133 0.16595649040791688 -5 9.193871034956294 0.22123628914451854 -6 9.190426328310906 0.2764826399831262 -7 9.186218902045571 0.3316871904318656 -8 9.181250415465412 0.3868415943185091 -9 9.17552282671559 0.44193751305230256 -10 9.16903839136101 0.4969666168846464 -11 9.161799660751832 0.5519205861684392 -12 9.153809480176601 0.6067911126158948 -13 9.14507098680509 0.6615699005546416 -14 9.135587607423119 0.7162486681819142 -15 9.125363055961923 0.7708191488166491 -16 9.11440133082477 0.8252730921492936 -17 9.10270671201385 0.8796022654891393 -18 9.090283758060592 0.9337984550089931 -19 9.07713730276282 0.9878534669869938 -20 9.063272451732358 1.0417591290453925 -21 9.04869457875688 1.0955072913861037 -22 9.033409321980011 1.1490898280228417 -23 9.01742257990387 1.2024986380096605 -24 9.000740507218406 1.2557256466657054 -25 8.983369510462104 1.3087628067959929 -26 8.965316243518739 1.3616020999080385 -27 8.946587602955077 1.4142355374241409 -28 8.927190723204545 1.4666551618891468 -29 8.90713297160202 1.5188530481735099 -30 8.886421943275105 1.5708213046714594 -31 8.865065455897254 1.6225520744941053 -32 8.843071544308401 1.674037536657292 -33 8.820448455008698 1.7252699072640225 -34 8.79720464053118 1.7762414406812785 -35 8.773348753699267 1.826944430711054 -36 8.748889641774996 1.8773712117554255 -37 8.723836340504135 1.9275141599754881 -38 8.69819806806423 1.9773656944439728 -39 8.671984218921803 2.0269182782913804 -40 8.645204357604943 2.076164419845453 -41 8.61786821239757 2.125096673763812 -42 8.589985668961711 2.173707642159591 -43 8.561566763894135 2.2219899757198975 -44 8.532621678223707 2.2699363748169255 -45 8.503160730855884 2.317539590611561 -46 8.473194371970695 2.3647924261493074 -47 8.442733176380631 2.4116877374483647 -48 8.411787836854778 2.4582184345797042 -49 8.380369157415567 2.504377482738966 -50 8.348488046614428 2.550157903310029 -51 8.316155510792665 2.595552774920077 -52 8.283382647333733 2.6405552344860204 -53 8.250180637913147 2.685158478252096 -54 8.216560741752092 2.7293557628185057 -55 8.182534288880811 2.7731404061609233 -56 8.148112673417733 2.816505788640728 -57 8.113307346870227 2.8594453540057985 -58 8.078129811462782 2.901952610381734 -59 8.042591613498313 2.9440211312533338 -60 8.006704336758212 2.9856445564361964 -61 7.970479595946591 3.0268165930382978 -62 7.933929030184167 3.0675310164113863 -63 7.897064296556966 3.107781671092064 -64 7.859897063725037 3.1475624717324115 -65 7.822439005596172 3.186867404020008 -66 7.7847017950694735 3.2256905255872104 -67 7.746697097853527 3.2640259669095624 -68 7.7084365663637655 3.301867932193182 -69 7.669931833703439 3.339210700251009 -70 7.631194507732519 3.37604862536777 -71 7.592236165228641 3.412376138153531 -72 7.553068346144079 3.4481877463857167 -73 7.513702547962571 3.483478035839454 -74 7.47415022015964 3.518241671106134 -75 7.4344227587699265 3.5524733964000506 -76 7.394531501064842 3.5861680363530013 -77 7.354487720343689 3.6193204967967367 -78 7.31430262084128 3.6519257655331243 -79 7.27398733275483 3.6839789130919267 -80 7.2335529073927844 3.7154750934760696 -81 7.193010312448087 3.74640954489429 -82 7.152370427398139 3.776777590481054 -83 7.111644039033636 3.8065746390036344 -84 7.070841837118205 3.8357961855562444 -85 7.029974410180662 3.8644378122411136 -86 6.989052241441485 3.892495188836417 -87 6.94808570487497 3.919964073450945 -88 6.90708506140836 3.946840313165417 -89 6.866060455259031 3.973119844660348 -90 6.82502191041074 3.9987986948303673 -91 6.783979327229674 4.023872981384896 -92 6.742942479220955 4.048338913435095 -93 6.7019210099260755 4.072192792067001 -94 6.66092442996157 4.095431010900745 -95 6.619962114199079 4.118050056635791 -96 6.5790432990868295 4.140046509582101 -97 6.538177080112392 4.1614170441771385 -98 6.497372409406427 4.1821584294886565 -99 6.456638093487013 4.202267529703163 -100 6.415982791143978 4.221741304600018 -101 6.375415011462574 4.240576810011071 -102 6.334943111985628 4.258771198265777 -103 6.294575297013258 4.276321718621732 -104 6.254319616039068 4.2932257176805395 -105 6.2141839623216315 4.309480639788973 -106 6.174176071589955 4.325084027425353 -107 6.134303520881515 4.340033521571096 -108 6.09457372751134 4.3543268620673565 -109 6.054993948170525 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-0.22123628914451907 -509 9.196551662721133 -0.16595649040791854 -510 9.198467153376706 -0.11065160132206264 -511 9.199616750495267 -0.05532998322900325 -512 9.2 -1.102182119232618e-15 diff --git a/src/Analysis/Analysis.jl b/src/Analysis/Analysis.jl new file mode 100644 index 00000000..1a770894 --- /dev/null +++ b/src/Analysis/Analysis.jl @@ -0,0 +1,16 @@ +""" + Analysis + +Post-processing and visualization utilities for GPEC simulation outputs. + +## Submodules + + - `ForceFreeStates`: Plotting functions for DCON-style ideal MHD stability results + - `Equilibrium`: Plotting functions for equilibrium objects +""" +module Analysis + +include("ForceFreeStates.jl") +include("Equilibrium.jl") + +end # module Analysis diff --git a/src/Analysis/Equilibrium.jl b/src/Analysis/Equilibrium.jl new file mode 100644 index 00000000..19e745c8 --- /dev/null +++ b/src/Analysis/Equilibrium.jl @@ -0,0 +1,69 @@ +""" + Equilibrium + +Post-processing and visualization functions for GPEC equilibrium objects. +""" +module Equilibrium + +using Plots + +""" + plot_flux_surfaces(plasma_eq; n_psi=11, n_theta=13) + +Plot flux surface contours (constant ψ, blue) and field-line angle contours (constant θ, red) +in physical (R, Z) space. + +### Arguments + + - `plasma_eq`: A `GeneralizedPerturbedEquilibrium.Equilibrium.PlasmaEquilibrium` object + +### Keyword arguments + + - `n_psi`: Number of constant-ψ contours to draw (default: 11) + - `n_theta`: Number of constant-θ contours to draw (default: 13) + +### Returns + +A `Plots.jl` plot object. +""" +function plot_flux_surfaces(plasma_eq; n_psi=11, n_theta=13) + n_psi_grid = size(plasma_eq.rzphi_rsquared.nodal_derivs.partials, 2) + n_theta_grid = size(plasma_eq.rzphi_rsquared.nodal_derivs.partials, 3) + + # Build R and Z on the full nodal grid + R_grid = Matrix{Float64}(undef, n_psi_grid, n_theta_grid) + Z_grid = Matrix{Float64}(undef, n_psi_grid, n_theta_grid) + for ipsi in 1:n_psi_grid + rfac = @. sqrt(max(0.0, plasma_eq.rzphi_rsquared.nodal_derivs.partials[1, ipsi, :])) + angle = @. 2π * (plasma_eq.rzphi_ys + plasma_eq.rzphi_offset.nodal_derivs.partials[1, ipsi, :]) + R_grid[ipsi, :] = plasma_eq.ro .+ rfac .* cos.(angle) + Z_grid[ipsi, :] = plasma_eq.zo .+ rfac .* sin.(angle) + end + + p = plot(; + title="Flux Coordinate System Contours in (R, Z)", + xlabel="R [m]", + ylabel="Z [m]", + aspect_ratio=:equal, + legend=:outertopright + ) + + psi_indices = round.(Int, range(1, n_psi_grid; length=n_psi)) + theta_indices = round.(Int, range(1, n_theta_grid; length=n_theta)) + + for (i, ipsi) in enumerate(psi_indices) + label = i == 1 ? "Constant ψ" : "" + plot!(p, [R_grid[ipsi, :]; R_grid[ipsi, 1]], [Z_grid[ipsi, :]; Z_grid[ipsi, 1]]; + color=:blue, linewidth=1.5, label=label) + end + + for (i, itheta) in enumerate(theta_indices) + label = i == 1 ? "Constant θ" : "" + plot!(p, R_grid[:, itheta], Z_grid[:, itheta]; + color=:red, linewidth=1.0, label=label) + end + + return p +end + +end # module Equilibrium diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl new file mode 100644 index 00000000..1fde1639 --- /dev/null +++ b/src/Analysis/ForceFreeStates.jl @@ -0,0 +1,159 @@ +""" + ForceFreeStates + +Post-processing and visualization functions for ForceFreeStates (DCON-style ideal MHD stability) +results stored in GPEC HDF5 output files. +""" +module ForceFreeStates + +using HDF5 +using Plots + +""" + plot_mode_displacement(h5path; modes=1:5, save_path=nothing) + +Plot Im(ξ_ψ) vs ψ_N for the least stable eigenmode, showing one curve per requested +poloidal mode number m. + +### Arguments + + - `h5path`: Path to a GPEC HDF5 output file (e.g. `"gpec.h5"`) + +### Keyword arguments + + - `modes`: Iterable of m values to plot (default: `1:5`) + - `save_path`: If provided, save the figure to this path (default: `nothing`) + +### Returns + +A `Plots.jl` plot object. +""" +function plot_mode_displacement(h5path; modes=1:5, save_path=nothing) + mlow, xi_psi, psi = h5open(h5path, "r") do fid + read(fid["info/mlow"]), read(fid["integration/xi_psi"]), read(fid["integration/psi"]) + end + + mpert = size(xi_psi, 1) + mhigh = mlow + mpert - 1 + + p = plot(; + xlabel="ψ_N", + ylabel="Im(ξ_ψ)", + title="Least Stable Eigenmode ξ_ψ" + ) + for m in modes + mlow <= m <= mhigh || continue + plot!(p, psi, imag.(xi_psi[m-mlow+1, 1, :]); label="m=$m") + end + + isnothing(save_path) || savefig(p, save_path) + return p +end + +""" + plot_eigenmode_summary(h5path; save_path=nothing) + +Three-panel summary of the free-boundary energy matrix eigenmodes, analogous to the +DCON summary plot produced by OMFIT GPEC. + +Panels: + + - Top: |eigenvector| vs index for the least stable mode + - Bottom-left: heatmap of |W_t| (eigenvectors) vs mode index + - Bottom-right: |eigenvalue| on log scale vs mode index + +Eigenvectors are scaled by χ₁ = 2π ψ₀ × 10⁻³ to match GPEC conventions. + +### Arguments + + - `h5path`: Path to a GPEC HDF5 output file with vacuum data (`vac_flag = true`) + +### Keyword arguments + + - `save_path`: If provided, save the figure to this path (default: `nothing`) + +### Returns + +A `Plots.jl` plot object. +""" +function plot_eigenmode_summary(h5path; save_path=nothing) + wt, et, psio, mlow = h5open(h5path, "r") do fid + read(fid["vacuum/wt"]), read(fid["vacuum/et"]), + read(fid["equil/psio"]), read(fid["info/mlow"]) + end + + isempty(wt) && error("No vacuum data in $h5path; rerun with vac_flag = true") + + chi1 = 2π * psio + wt = wt * (chi1 * 1e-3) + + nmn = size(wt, 1) + nmodes = size(wt, 2) + m_vals = (0:(nmn-1)) .+ mlow + + p1 = plot( + m_vals, abs.(wt[:, 1]); + xlabel="m", + ylabel="|Eigenvector|", + title="Mode 1, |λ₁| = $(round(abs(et[1]), digits=3))", + legend=false + ) + + p2 = heatmap( + m_vals, 1:nmodes, abs.(wt'); + xlabel="m", + ylabel="mode index", + colorbar_title="|Wₜ|" + ) + + p3 = scatter( + abs.(et), 1:nmodes; + xlabel="|Eigenvalue|", + ylabel="mode index", + xscale=:log10, + legend=false + ) + + l = @layout [a{0.25h}; b c{0.25w}] + p = plot(p1, p2, p3; layout=l, size=(900, 700)) + + isnothing(save_path) || savefig(p, save_path) + return p +end + +""" + plot_stability_criterion(h5path; save_path=nothing) + +Plot the stability criterion (smallest eigenvalue of W⁻¹, `crit`) vs ψ_N. +A sign change in `crit` during integration indicates an ideal fixed-boundary instability. + +### Arguments + + - `h5path`: Path to a GPEC HDF5 output file + +### Keyword arguments + + - `save_path`: If provided, save the figure to this path (default: `nothing`) + +### Returns + +A `Plots.jl` plot object. +""" +function plot_stability_criterion(h5path; save_path=nothing) + psi, crit = h5open(h5path, "r") do fid + read(fid["integration/psi"]), read(fid["integration/crit"]) + end + + p = plot( + psi, crit; + xlabel="ψ_N", + ylabel="crit", + title="Stability criterion (smallest eigenvalue of W⁻¹) vs ψ_N", + legend=false + ) + + isnothing(save_path) || savefig(p, save_path) + return p +end + +end # module ForceFreeStates diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 93c5fd05..07818446 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -25,6 +25,10 @@ include("PerturbedEquilibrium/PerturbedEquilibrium.jl") import .PerturbedEquilibrium as PerturbedEquilibrium export PerturbedEquilibrium +include("Analysis/Analysis.jl") +import .Analysis as Analysis +export Analysis + # Additional imports for main function using TOML using Printf diff --git a/test/runtests_equil.jl b/test/runtests_equil.jl index cf028639..d3a4f6c3 100644 --- a/test/runtests_equil.jl +++ b/test/runtests_equil.jl @@ -3,7 +3,7 @@ # --- Directory Configuration --- # Define the data directory for easy maintenance - data_dir = joinpath(@__DIR__, "test_data", "regression_equilibrium_example") + data_dir = joinpath(@__DIR__, "test_data", "CHEASE_test_data") # --- 1. Load EFIT Data (G-EQDSK format) --- @testset "Load EFIT Data" begin @@ -60,12 +60,40 @@ # ---------------------------------------------------------------------- @testset "CHEASE Consistency (ASCII vs Binary)" begin - # Tolerance set to 1e-12 as these come from the same physical source - tol = 1e-12 + # Both formats encode the same physical data; differences arise only from + # floating-point text serialization in the ASCII format vs exact binary storage. + # We use rtol=1e-6 throughout as a conservative lower bound on ASCII precision. + rtol = 1e-6 + + @testset "Magnetic axis" begin + @test isapprox(plasma_eq_ascii.ro, plasma_eq_binary.ro; rtol) + @test isapprox(plasma_eq_ascii.zo, plasma_eq_binary.zo; rtol) + @test isapprox(plasma_eq_ascii.psio, plasma_eq_binary.psio; rtol) + end + + @testset "Global parameters" begin + @test isapprox(plasma_eq_ascii.params.q0, plasma_eq_binary.params.q0; rtol) + @test isapprox(plasma_eq_ascii.params.qmin, plasma_eq_binary.params.qmin; rtol) + @test isapprox(plasma_eq_ascii.params.qmax, plasma_eq_binary.params.qmax; rtol) + @test isapprox(plasma_eq_ascii.params.qa, plasma_eq_binary.params.qa; rtol) + @test isapprox(plasma_eq_ascii.params.bt0, plasma_eq_binary.params.bt0; rtol) + @test isapprox(plasma_eq_ascii.params.crnt, plasma_eq_binary.params.crnt; rtol) + end + + @testset "1D profiles" begin + @test isapprox(plasma_eq_ascii.profiles.q_spline.y, plasma_eq_binary.profiles.q_spline.y; rtol) + @test isapprox(plasma_eq_ascii.profiles.F_spline.y, plasma_eq_binary.profiles.F_spline.y; rtol) + @test isapprox(plasma_eq_ascii.profiles.P_spline.y, plasma_eq_binary.profiles.P_spline.y; rtol) + @test isapprox(plasma_eq_ascii.profiles.dVdpsi_spline.y, plasma_eq_binary.profiles.dVdpsi_spline.y; rtol) + end - @testset "Magnetic Axis" begin - @test isapprox(plasma_eq_ascii.ro, plasma_eq_binary.ro, atol=tol) - @test isapprox(plasma_eq_ascii.zo, plasma_eq_binary.zo, atol=tol) + @testset "Flux surface geometry" begin + ascii_rfac2 = plasma_eq_ascii.rzphi_rsquared.nodal_derivs.partials[1, :, :] + binary_rfac2 = plasma_eq_binary.rzphi_rsquared.nodal_derivs.partials[1, :, :] + ascii_offset = plasma_eq_ascii.rzphi_offset.nodal_derivs.partials[1, :, :] + binary_offset = plasma_eq_binary.rzphi_offset.nodal_derivs.partials[1, :, :] + @test isapprox(ascii_rfac2, binary_rfac2; rtol) + @test isapprox(ascii_offset, binary_offset; rtol) end end diff --git a/notebooks/CHEASE_INP1/EQDSK_COCOS_02 b/test/test_data/CHEASE_test_data/EQDSK_COCOS_02 similarity index 100% rename from notebooks/CHEASE_INP1/EQDSK_COCOS_02 rename to test/test_data/CHEASE_test_data/EQDSK_COCOS_02 diff --git a/notebooks/CHEASE_INP1/INP1_ascii b/test/test_data/CHEASE_test_data/INP1_ascii similarity index 100% rename from notebooks/CHEASE_INP1/INP1_ascii rename to test/test_data/CHEASE_test_data/INP1_ascii diff --git a/notebooks/CHEASE_INP1/INP1_binary b/test/test_data/CHEASE_test_data/INP1_binary similarity index 100% rename from notebooks/CHEASE_INP1/INP1_binary rename to test/test_data/CHEASE_test_data/INP1_binary diff --git a/test/test_data/regression_equilibrium_example/EQDSK_COCOS_02 b/test/test_data/regression_equilibrium_example/EQDSK_COCOS_02 deleted file mode 100644 index a35abd4d..00000000 --- a/test/test_data/regression_equilibrium_example/EQDSK_COCOS_02 +++ /dev/null @@ -1,3596 +0,0 @@ - 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2.902851066E-01 1.599545793E-01 3.272663067E-02-9.200618591E-02-2.164533391E-01 --3.409221946E-01-4.648874956E-01-5.877562468E-01-7.086937385E-01-8.264815312E-01 --9.396253746E-01-1.046649649E+00-1.146414568E+00-1.238355208E+00-1.322424256E+00 --1.399002524E+00-1.468634739E+00-1.531989882E+00-1.589728731E+00-1.642515658E+00 --1.690967509E+00-1.735516331E+00-1.776430935E+00-1.813902452E+00-1.848091229E+00 --1.879116664E+00-1.907048036E+00-1.931952203E+00-1.953905343E+00-1.972873549E+00 --1.988590294E+00-2.000971634E+00-2.010190321E+00-2.016289980E+00-2.019113361E+00 --2.018383082E+00-2.013908731E+00-2.005669710E+00-1.993767477E+00-1.978237685E+00 --1.958788882E+00-1.935117589E+00-1.907176268E+00-1.875025668E+00-1.838611818E+00 --1.797809621E+00-1.752395579E+00-1.702072306E+00-1.646479638E+00-1.585264358E+00 --1.518095763E+00-1.444631544E+00-1.364584665E+00-1.277701721E+00-1.183793811E+00 --1.082830894E+00-9.750035213E-01-8.606705810E-01-7.403164656E-01-6.144972821E-01 --4.838021311E-01-3.487418624E-01-2.096318532E-01-6.664096807E-02 8.036770575E-02 - 2.319276835E-01 3.880161326E-01 5.485669696E-01 7.134285297E-01 8.823916891E-01 - 1.055278696E+00 1.231931529E+00 1.412203094E+00 1.595944295E+00 1.783005301E+00 - 1.973238402E+00 2.166501764E+00 2.362661531E+00 2.561592281E+00 2.763175296E+00 - 2.967299319E+00 3.173861060E+00 3.382765092E+00 3.593922043E+00 3.807248622E+00 - 4.022669135E+00 4.240115264E+00 4.459523878E+00 4.680834350E+00 4.903984657E+00 - 5.128904461E+00 5.355522761E+00 5.583773269E+00 5.813593876E+00 6.044924798E+00 - 6.277708063E+00 6.511886055E+00 6.747399092E+00 6.984188792E+00 7.222201631E+00 - 7.461388779E+00 7.701705331E+00 7.943110574E+00 8.185566854E+00 8.429038436E+00 - 8.673491393E+00 8.918893581E+00 9.165214238E+00 9.412424055E+00 9.660494783E+00 - 9.909398798E+00 1.015910911E+01 1.040959785E+01 1.066083564E+01 1.091279414E+01 - 1.116544751E+01 1.141877613E+01 1.167278102E+01 1.192735968E+01 1.714388550E+00 - 1.557952982E+00 1.403387749E+00 1.251045123E+00 1.100936314E+00 9.531291686E-01 - 8.076977251E-01 6.647075199E-01 5.242165614E-01 3.862792144E-01 2.509761329E-01 - 1.185004536E-01-1.110264713E-02-1.391759082E-01-2.673518144E-01-3.954173827E-01 --5.227090166E-01-6.484809502E-01-7.716975394E-01-8.909800190E-01-1.004752752E+00 --1.111609408E+00-1.210643450E+00-1.301590369E+00-1.384736692E+00-1.460679415E+00 --1.530187281E+00-1.593986584E+00-1.652744214E+00-1.707056934E+00-1.757415506E+00 --1.804282685E+00-1.847955953E+00-1.888545466E+00-1.926144052E+00-1.960825229E+00 --1.992601768E+00-2.021475836E+00-2.047492713E+00-2.070693889E+00-2.090944310E+00 --2.107915630E+00-2.121610828E+00-2.132200325E+00-2.139655328E+00-2.143745640E+00 --2.144165026E+00-2.140759472E+00-2.133578425E+00-2.122768361E+00-2.108244351E+00 --2.089608381E+00-2.066665709E+00-2.039532299E+00-2.008264279E+00-1.972729600E+00 --1.932807442E+00-1.888330637E+00-1.839028981E+00-1.784644204E+00-1.724910975E+00 --1.659571305E+00-1.588426718E+00-1.511231668E+00-1.427678524E+00-1.337427280E+00 --1.240198150E+00-1.135846456E+00-1.024377328E+00-9.060046165E-01-7.811751615E-01 --6.504707178E-01-5.145336413E-01-3.739634582E-01-2.291859116E-01-8.048295184E-02 - 7.213603871E-02 2.291786748E-01 3.906498374E-01 5.564825695E-01 7.265209146E-01 - 9.005647251E-01 1.078445828E+00 1.259998455E+00 1.445060197E+00 1.633473102E+00 - 1.825085823E+00 2.019755444E+00 2.217347604E+00 2.417734925E+00 2.620798603E+00 - 2.826428294E+00 3.034521604E+00 3.244982052E+00 3.457720826E+00 3.672657292E+00 - 3.889717978E+00 4.108833060E+00 4.329934430E+00 4.552948142E+00 4.777796605E+00 - 5.004406122E+00 5.232708032E+00 5.462636755E+00 5.694128703E+00 5.927121385E+00 - 6.161550397E+00 6.397351726E+00 6.634466077E+00 6.872839456E+00 7.112422159E+00 - 7.353169019E+00 7.595038337E+00 7.837990600E+00 8.081988272E+00 8.326995778E+00 - 8.572979096E+00 8.819905795E+00 9.067744603E+00 9.316465010E+00 9.566037105E+00 - 9.816429840E+00 1.006761095E+01 1.031954985E+01 1.057221973E+01 1.082559637E+01 - 1.107966077E+01 1.133441527E+01 1.158975624E+01 1.695753389E+00 1.537481077E+00 - 1.381032855E+00 1.226752499E+00 1.074656212E+00 9.248178158E-01 7.773178804E-01 - 6.322317603E-01 4.896299268E-01 3.495734316E-01 2.121367193E-01 7.749586422E-02 --5.460154838E-02-1.861127308E-01-3.178277480E-01-4.492267237E-01-5.795574074E-01 --7.078708341E-01-8.328864178E-01-9.530792690E-01-1.066926603E+00-1.173227564E+00 --1.271403707E+00-1.361491207E+00-1.444045257E+00-1.519847612E+00-1.589763399E+00 --1.654576662E+00-1.714955928E+00-1.771409127E+00-1.824339880E+00-1.874097192E+00 --1.920960306E+00-1.965103327E+00-2.006547120E+00-2.045261081E+00-2.081241767E+00 --2.114475032E+00-2.144928693E+00-2.172612786E+00-2.197520030E+00-2.219407110E+00 --2.237943420E+00-2.253232318E+00-2.265407772E+00-2.274352024E+00-2.279755056E+00 --2.281326237E+00-2.278989334E+00-2.272868877E+00-2.263077589E+00-2.249320154E+00 --2.231233765E+00-2.208828477E+00-2.182262547E+00-2.151481229E+00-2.116370624E+00 --2.076787148E+00-2.032568959E+00-1.983555490E+00-1.929527366E+00-1.870285257E+00 --1.805705350E+00-1.735697233E+00-1.660176655E+00-1.578890810E+00-1.491494488E+00 --1.397591872E+00-1.296764500E+00-1.188700782E+00-1.073261838E+00-9.505425910E-01 --8.209126138E-01-6.849559921E-01-5.433957561E-01-3.969826948E-01-2.462993428E-01 --9.170251927E-02 6.673820657E-02 2.294919074E-01 3.965615459E-01 5.678864786E-01 - 7.433188085E-01 9.226493893E-01 1.105693934E+00 1.292279356E+00 1.482242958E+00 - 1.675432881E+00 1.871704873E+00 2.070922511E+00 2.272958621E+00 2.477695114E+00 - 2.685021336E+00 2.894833696E+00 3.107037445E+00 3.321546406E+00 3.538280179E+00 - 3.757161409E+00 3.978111311E+00 4.201045881E+00 4.425883341E+00 4.652547476E+00 - 4.880966107E+00 5.111069394E+00 5.342789171E+00 5.576055912E+00 5.810799549E+00 - 6.046954378E+00 6.284460587E+00 6.523263124E+00 6.763311829E+00 7.004560472E+00 - 7.246965322E+00 7.490484819E+00 7.735079561E+00 7.980711893E+00 8.227345910E+00 - 8.474946978E+00 8.723481372E+00 8.972915904E+00 9.223216024E+00 9.474346385E+00 - 9.726273917E+00 9.978969881E+00 1.023240889E+01 1.048656729E+01 1.074142709E+01 - 1.099699184E+01 1.125315613E+01 1.677519232E+00 1.517433421E+00 1.359130356E+00 - 1.202946326E+00 1.048894658E+00 8.970492838E-01 7.474957576E-01 6.003164053E-01 - 4.555895827E-01 3.133879430E-01 1.738069224E-01 3.694741757E-02-9.786633689E-02 --2.327108897E-01-3.677379762E-01-5.022299392E-01-6.353178314E-01-7.658311458E-01 --8.922543550E-01-1.012943145E+00-1.126498558E+00-1.232053966E+00-1.329409004E+00 --1.418929644E+00-1.501342876E+00-1.577571929E+00-1.648508294E+00-1.714936250E+00 --1.777503051E+00-1.836653727E+00-1.892729727E+00-1.945945113E+00-1.996488833E+00 --2.044555100E+00-2.090178065E+00-2.133289777E+00-2.173843228E+00-2.211790628E+00 --2.247053612E+00-2.279565716E+00-2.309326386E+00-2.336283050E+00-2.360079375E+00 --2.380446242E+00-2.397562612E+00-2.411481940E+00-2.421975555E+00-2.428663237E+00 --2.431331176E+00-2.430034396E+00-2.424931663E+00-2.415938121E+00-2.402644523E+00 --2.384893489E+00-2.362825088E+00-2.336497014E+00-2.305823452E+00-2.270678790E+00 --2.230939566E+00-2.186474373E+00-2.137131886E+00-2.082760962E+00-2.023217497E+00 --1.958456248E+00-1.888567175E+00-1.813555426E+00-1.733326877E+00-1.647601587E+00 --1.555961147E+00-1.457920903E+00-1.352989773E+00-1.240743357E+00-1.120873279E+00 --9.933219201E-01-8.583917787E-01-7.167405935E-01-5.692448539E-01-4.167699936E-01 --2.599689317E-01-9.926060335E-02 6.522065908E-02 2.339095553E-01 4.068098990E-01 - 5.838421108E-01 7.648402943E-01 9.495915285E-01 1.137913502E+00 1.329640341E+00 - 1.524616216E+00 1.722695852E+00 1.923743090E+00 2.127631016E+00 2.334239873E+00 - 2.543458790E+00 2.755186506E+00 2.969329942E+00 3.185800227E+00 3.404510751E+00 - 3.625371008E+00 3.848290658E+00 4.073184837E+00 4.299973775E+00 4.528580654E+00 - 4.758930772E+00 4.990948894E+00 5.224558455E+00 5.459686659E+00 5.696267132E+00 - 5.934238833E+00 6.173546003E+00 6.414137325E+00 6.655964347E+00 6.898981009E+00 - 7.143143636E+00 7.388410515E+00 7.634741864E+00 7.882099309E+00 8.130445531E+00 - 8.379743662E+00 8.629955288E+00 8.881041748E+00 9.132967350E+00 9.385701080E+00 - 9.639215410E+00 9.893485594E+00 1.014848898E+01 1.040420820E+01 1.066064763E+01 - 1.091770030E+01 1.659612410E+00 1.497738191E+00 1.337600653E+00 1.179532586E+00 - 1.023551585E+00 8.697292897E-01 7.181473811E-01 5.688905952E-01 4.220426466E-01 - 2.776876572E-01 1.359614522E-01-3.154085710E-03-1.408807762E-01-2.789222662E-01 --4.170323156E-01-5.543812602E-01-6.899451382E-01-8.223230235E-01-9.498109384E-01 --1.070726035E+00-1.183847374E+00-1.288682643E+00-1.385413788E+00-1.474732401E+00 --1.557528056E+00-1.634772625E+00-1.707343913E+00-1.775999065E+00-1.841295048E+00 --1.903649985E+00-1.963333855E+00-2.020483068E+00-2.075216205E+00-2.127592719E+00 --2.177689138E+00-2.225523485E+00-2.271005730E+00-2.314025307E+00-2.354459779E+00 --2.392179533E+00-2.427123932E+00-2.459300925E+00-2.488577778E+00-2.514473474E+00 --2.536835316E+00-2.555884209E+00-2.571582706E+00-2.583597427E+00-2.591494164E+00 --2.595131790E+00-2.594724710E+00-2.590472038E+00-2.581998391E+00-2.568871245E+00 --2.551219510E+00-2.529259889E+00-2.502843222E+00-2.471834368E+00-2.436221602E+00 --2.395902447E+00-2.350717527E+00-2.300537683E+00-2.245230893E+00-2.184732931E+00 --2.119128378E+00-2.048566567E+00-1.973175608E+00-1.892927986E+00-1.807641853E+00 --1.716963942E+00-1.620466602E+00-1.517660499E+00-1.407987355E+00-1.290891720E+00 --1.165916713E+00-1.032938987E+00-8.922857958E-01-7.446541374E-01-5.909713810E-01 --4.321910133E-01-2.690497177E-01-1.020125815E-01 6.874060934E-02 2.435791372E-01 - 4.224812774E-01 6.053561550E-01 7.920370808E-01 9.823205255E-01 1.176031897E+00 - 1.373012670E+00 1.573116509E+00 1.776206847E+00 1.982154792E+00 2.190841673E+00 - 2.402158816E+00 2.616004057E+00 2.832279207E+00 3.050886063E+00 3.271725309E+00 - 3.494702354E+00 3.719728658E+00 3.946719537E+00 4.175592821E+00 4.406266783E+00 - 4.638657872E+00 4.872685488E+00 5.108275827E+00 5.345361123E+00 5.583879331E+00 - 5.823773408E+00 6.064989602E+00 6.307476814E+00 6.551186583E+00 6.796072656E+00 - 7.042090919E+00 7.289198822E+00 7.537355021E+00 7.786518503E+00 8.036646617E+00 - 8.287697113E+00 8.539631494E+00 8.792416200E+00 9.046021238E+00 9.300419850E+00 - 9.555588274E+00 9.811504271E+00 1.006815093E+01 1.032553376E+01 1.058354406E+01 - 1.641952267E+00 1.478321937E+00 1.316375890E+00 1.156442578E+00 9.985462303E-01 - 8.427628551E-01 6.891756838E-01 5.378655684E-01 3.889128376E-01 2.424111208E-01 - 9.853506945E-02-4.290045255E-02-1.836723304E-01-3.247797175E-01-4.657491122E-01 --6.057066827E-01-7.434557727E-01-8.773725551E-01-1.005621905E+00-1.126590447E+00 --1.239304486E+00-1.343636312E+00-1.440116944E+00-1.529680147E+00-1.613388798E+00 --1.692226464E+00-1.767021591E+00-1.838455734E+00-1.907003784E+00-1.973023187E+00 --2.036704882E+00-2.098175891E+00-2.157490289E+00-2.214620239E+00-2.269562027E+00 --2.322403708E+00-2.373143652E+00-2.421590678E+00-2.467515614E+00-2.510783297E+00 --2.551303180E+00-2.589006514E+00-2.623827267E+00-2.655491932E+00-2.683457054E+00 --2.707755706E+00-2.728602440E+00-2.745858972E+00-2.759109062E+00-2.767977449E+00 --2.772459524E+00-2.772849428E+00-2.769141072E+00-2.760785915E+00-2.747644472E+00 --2.730005001E+00-2.707867970E+00-2.681020806E+00-2.649369593E+00-2.612935490E+00 --2.571675518E+00-2.525406793E+00-2.473922684E+00-2.417163619E+00-2.355223040E+00 --2.288297964E+00-2.216570093E+00-2.140155317E+00-2.059081289E+00-1.973207904E+00 --1.882299551E+00-1.786014076E+00-1.683932953E+00-1.575558729E+00-1.460302426E+00 --1.337589570E+00-1.206935160E+00-1.068128424E+00-9.214136795E-01-7.674917453E-01 --6.073482650E-01-4.420062085E-01-2.722852835E-01-9.872447289E-02 7.845617330E-02 - 2.595736867E-01 4.445950324E-01 6.334266155E-01 8.259023353E-01 1.021829050E+00 - 1.221043345E+00 1.423395135E+00 1.628746168E+00 1.836969695E+00 2.047947912E+00 - 2.261568029E+00 2.477721056E+00 2.696297973E+00 2.917193487E+00 3.140308943E+00 - 3.365550685E+00 3.592828076E+00 3.822051873E+00 4.053130982E+00 4.285976245E+00 - 4.520505453E+00 4.756643247E+00 4.994320510E+00 5.233473741E+00 5.474043225E+00 - 5.715972204E+00 5.959206846E+00 6.203695806E+00 6.449390114E+00 6.696242556E+00 - 6.944207261E+00 7.193238549E+00 7.443289124E+00 7.694312853E+00 7.946268189E+00 - 8.199118705E+00 8.452831734E+00 8.707378200E+00 8.962732199E+00 9.218870337E+00 - 9.475770860E+00 9.733417467E+00 9.991817207E+00 1.025086051E+01 1.624454633E+00 - 1.459105218E+00 1.295383425E+00 1.133610652E+00 9.738170707E-01 8.160836852E-01 - 6.604987432E-01 5.071468562E-01 3.561087959E-01 2.074841406E-01 6.142535275E-02 --8.250755091E-02-2.263037375E-01-3.703504546E-01-5.139942737E-01-6.563035478E-01 --7.959266774E-01-9.310635788E-01-1.059819264E+00-1.180743153E+00-1.293184593E+00 --1.397348837E+00-1.494067135E+00-1.584432521E+00-1.669602961E+00-1.750569617E+00 --1.828123048E+00-1.902824648E+00-1.975080571E+00-2.045164553E+00-2.113208632E+00 --2.179321039E+00-2.243532707E+00-2.305790072E+00-2.366019197E+00-2.424237220E+00 --2.480491535E+00-2.534583202E+00-2.586254253E+00-2.635359986E+00-2.681727710E+00 --2.725139272E+00-2.765480880E+00-2.802700360E+00-2.836428584E+00-2.866181604E+00 --2.892173686E+00-2.914541258E+00-2.933024886E+00-2.947153929E+00-2.956676062E+00 --2.961786898E+00-2.962803494E+00-2.959336554E+00-2.950855588E+00-2.937608969E+00 --2.919874089E+00-2.897383499E+00-2.869864290E+00-2.837366714E+00-2.799959686E+00 --2.757545189E+00-2.709905896E+00-2.656816326E+00-2.598260922E+00-2.534558628E+00 --2.466007948E+00-2.392769663E+00-2.314916195E+00-2.232424125E+00-2.145229594E+00 --2.053155593E+00-1.955926871E+00-1.853203718E+00-1.744626332E+00-1.629829444E+00 --1.508324996E+00-1.379489345E+00-1.242705054E+00-1.097650520E+00-9.444998065E-01 --7.839446295E-01-6.170397694E-01-4.449085766E-01-2.684519716E-01-8.825650759E-02 - 9.545829046E-02 2.829634981E-01 4.742134786E-01 6.691102848E-01 8.674893589E-01 - 1.069169255E+00 1.273996515E+00 1.481833387E+00 1.692550649E+00 1.906024684E+00 - 2.122135082E+00 2.340764834E+00 2.561803674E+00 2.785147591E+00 3.010696393E+00 - 3.238352082E+00 3.468015322E+00 3.699587579E+00 3.932977151E+00 4.168100082E+00 - 4.404879273E+00 4.643243925E+00 4.883127592E+00 5.124467146E+00 5.367202711E+00 - 5.611277217E+00 5.856636243E+00 6.103227348E+00 6.350999560E+00 6.599901930E+00 - 6.849882092E+00 7.100889700E+00 7.352879836E+00 7.605812869E+00 7.859653205E+00 - 8.114369208E+00 8.369932479E+00 8.626317490E+00 8.883501418E+00 9.141463125E+00 - 9.400187774E+00 9.659684671E+00 9.919841872E+00 1.607044502E+00 1.440012382E+00 - 1.274548228E+00 1.110966527E+00 9.493009137E-01 7.896349611E-01 6.320614492E-01 - 4.766697228E-01 3.235477240E-01 1.728166970E-01 2.455404424E-02-1.220346703E-01 --2.687919207E-01-4.156646746E-01-5.618547476E-01-7.063043257E-01-8.474964171E-01 --9.835397072E-01-1.112592815E+00-1.233445086E+00-1.345811341E+00-1.450208207E+00 --1.547689962E+00-1.639460046E+00-1.726680630E+00-1.810299421E+00-1.891067541E+00 --1.969456842E+00-2.045803245E+00-2.120282422E+00-2.193012627E+00-2.264071040E+00 --2.333469756E+00-2.401141268E+00-2.466997315E+00-2.530997843E+00-2.592969457E+00 --2.652766536E+00-2.710292561E+00-2.765305201E+00-2.817474589E+00-2.866545311E+00 --2.912367913E+00-2.954909373E+00-2.994100861E+00-3.029435469E+00-3.060599026E+00 --3.087925504E+00-3.111437718E+00-3.130758922E+00-3.145430059E+00-3.155369555E+00 --3.160965445E+00-3.162334244E+00-3.158775229E+00-3.150094336E+00-3.136758111E+00 --3.118776094E+00-3.095751319E+00-3.067501331E+00-3.034123261E+00-2.995675024E+00 --2.952019204E+00-2.902870337E+00-2.848030811E+00-2.787666248E+00-2.722135675E+00 --2.651796608E+00-2.576829035E+00-2.497221296E+00-2.412937605E+00-2.323896138E+00 --2.229954140E+00-2.130877132E+00-2.026406265E+00-1.916382724E+00-1.800666393E+00 --1.678963403E+00-1.550742882E+00-1.415302493E+00-1.271915847E+00-1.120158060E+00 --9.601655318E-01-7.926621499E-01-6.187745956E-01-4.397005970E-01-2.563940255E-01 --6.947033385E-02 1.208778728E-01 3.148693130E-01 5.124495462E-01 7.135112511E-01 - 9.178910762E-01 1.125425303E+00 1.335967507E+00 1.549381761E+00 1.765538508E+00 - 1.984314618E+00 2.205594120E+00 2.429265922E+00 2.655221902E+00 2.883353502E+00 - 3.113551930E+00 3.345714804E+00 3.579748385E+00 3.815566553E+00 4.053090229E+00 - 4.292245351E+00 4.532961601E+00 4.775172286E+00 5.018813883E+00 5.263825834E+00 - 5.510149820E+00 5.757729114E+00 6.006506818E+00 6.256425031E+00 6.507428823E+00 - 6.759469516E+00 7.012503896E+00 7.266493186E+00 7.521402840E+00 7.777201734E+00 - 8.033861912E+00 8.291358461E+00 8.549669458E+00 8.808775624E+00 9.068663293E+00 - 9.329340948E+00 9.590691753E+00 1.589651077E+00 1.420976761E+00 1.253805988E+00 - 1.088445078E+00 9.249333534E-01 7.633574574E-01 6.038115897E-01 4.463871619E-01 - 2.911798678E-01 1.383462822E-01-1.213662313E-02-1.615139272E-01-3.111664169E-01 --4.607448531E-01-6.093542169E-01-7.557720618E-01-8.982964253E-01-1.034984623E+00 --1.164176177E+00-1.284991764E+00-1.397520416E+00-1.502571894E+00-1.601342919E+00 --1.695093230E+00-1.784929913E+00-1.871723382E+00-1.956123248E+00-2.038554291E+00 --2.119294492E+00-2.198458974E+00-2.276141169E+00-2.352416699E+00-2.427274583E+00 --2.500573474E+00-2.572251217E+00-2.642185782E+00-2.710034144E+00-2.775571548E+00 --2.838788823E+00-2.899482001E+00-2.957263780E+00-3.011845718E+00-3.063066787E+00 --3.110816693E+00-3.155081582E+00-3.195734535E+00-3.232181051E+00-3.264367515E+00 --3.292652482E+00-3.316918898E+00-3.336691090E+00-3.351609672E+00-3.361818083E+00 --3.367773646E+00-3.369138717E+00-3.365252123E+00-3.356399258E+00-3.342909900E+00 --3.324491482E+00-3.300806801E+00-3.271825140E+00-3.237588657E+00-3.198080394E+00 --3.153122320E+00-3.102430173E+00-3.045962263E+00-2.983962463E+00-2.916770108E+00 --2.844686643E+00-2.767875305E+00-2.686349960E+00-2.600013338E+00-2.508750587E+00 --2.412398118E+00-2.310786453E+00-2.203836788E+00-2.091520765E+00-1.973800229E+00 --1.850571578E+00-1.721547026E+00-1.586153749E+00-1.443619383E+00-1.293155721E+00 --1.134284118E+00-9.671189823E-01-7.924079898E-01-6.113416963E-01-4.251822065E-01 --2.349227534E-01-4.119085213E-02 1.558819964E-01 3.564415965E-01 5.604368827E-01 - 7.677454973E-01 9.782028612E-01 1.191654084E+00 1.407958587E+00 1.626986454E+00 - 1.848614650E+00 2.072723535E+00 2.299194065E+00 2.527906175E+00 2.758745483E+00 - 2.991607104E+00 3.226394667E+00 3.463019691E+00 3.701399464E+00 3.941455529E+00 - 4.183113482E+00 4.426302506E+00 4.670955119E+00 4.917006369E+00 5.164393015E+00 - 5.413051463E+00 5.662917743E+00 5.913931938E+00 6.166041132E+00 6.419198118E+00 - 6.673360621E+00 6.928490816E+00 7.184554565E+00 7.441521272E+00 7.699363684E+00 - 7.958058261E+00 8.217585056E+00 8.477924907E+00 8.739061647E+00 9.001000247E+00 - 9.263620464E+00 1.572224913E+00 1.401941966E+00 1.233100386E+00 1.065993619E+00 - 9.006631885E-01 7.371984862E-01 5.756973731E-01 4.162533625E-01 2.589685497E-01 - 1.040219374E-01-4.875169984E-02-2.009845404E-01-3.534653638E-01-5.056335805E-01 --6.565157668E-01-8.047171574E-01-9.483738252E-01-1.085542611E+00-1.214810682E+00 --1.335692222E+00-1.448650749E+00-1.554765029E+00-1.655320404E+00-1.751569651E+00 --1.844518763E+00-1.934946138E+00-2.023370343E+00-2.110163785E+00-2.195552905E+00 --2.279646725E+00-2.362515903E+00-2.444223491E+00-2.524700692E+00-2.603762297E+00 --2.681302124E+00-2.757071945E+00-2.830719539E+00-2.901990577E+00-2.970679875E+00 --3.036681806E+00-3.099789182E+00-3.159685996E+00-3.216129282E+00-3.268965442E+00 --3.318114614E+00-3.363606230E+00-3.405227976E+00-3.442380144E+00-3.475278604E+00 --3.504199209E+00-3.528872242E+00-3.548787318E+00-3.563746091E+00-3.574131566E+00 --3.580204035E+00-3.581229514E+00-3.576978800E+00-3.567954442E+00-3.554127789E+00 --3.535091852E+00-3.510681866E+00-3.480918802E+00-3.445791080E+00-3.405166981E+00 --3.358840882E+00-3.306703796E+00-3.248838003E+00-3.185455214E+00-3.116823695E+00 --3.043145709E+00-2.964555903E+00-2.881071685E+00-2.792552990E+00-2.698788265E+00 --2.599640348E+00-2.495103099E+00-2.385227859E+00-2.270051421E+00-2.149597034E+00 --2.023871351E+00-1.892783883E+00-1.756041744E+00-1.613060901E+00-1.463029429E+00 --1.305109195E+00-1.138767726E+00-9.641117610E-01-7.819341975E-01-5.934992907E-01 --4.001261629E-01-2.028316002E-01-2.237206999E-03 2.016365882E-01 4.088278279E-01 - 6.192801136E-01 8.328685081E-01 1.049433685E+00 1.268831758E+00 1.490928344E+00 - 1.715592600E+00 1.942692401E+00 2.172099996E+00 2.403697730E+00 2.637377547E+00 - 2.873040240E+00 3.110593253E+00 3.349948882E+00 3.591023979E+00 3.833739462E+00 - 4.078020005E+00 4.323793154E+00 4.570988273E+00 4.819534242E+00 5.069360413E+00 - 5.320401428E+00 5.572599573E+00 5.825903202E+00 6.080266137E+00 6.335646876E+00 - 6.592007984E+00 6.849315945E+00 7.107541078E+00 7.366658049E+00 7.626644765E+00 - 7.887480135E+00 8.149141243E+00 8.411608550E+00 8.674884936E+00 8.938847524E+00 - 1.554766389E+00 1.382888952E+00 1.212397087E+00 1.043571926E+00 8.764514015E-01 - 7.111221899E-01 5.476830211E-01 3.862309738E-01 2.268808699E-01 6.979534625E-02 --8.539328703E-02-2.404565766E-01-3.956896142E-01-5.503586239E-01-7.033742356E-01 --8.531650809E-01-9.977605252E-01-1.135299686E+00-1.264677619E+00-1.385819398E+00 --1.499519838E+00-1.607082851E+00-1.709858147E+00-1.809044563E+00-1.905521919E+00 --1.999948223E+00-2.092726937E+00-2.184168142E+00-2.274453433E+00-2.363684438E+00 --2.451925461E+00-2.539207607E+00-2.625339166E+00-2.710129509E+00-2.793410621E+00 --2.874809241E+00-2.953999145E+00-3.030754491E+00-3.104789636E+00-3.175848090E+00 --3.243911167E+00-3.308830978E+00-3.370277880E+00-3.428029300E+00-3.481977328E+00 --3.532094640E+00-3.578417733E+00-3.620597976E+00-3.658168652E+00-3.691532088E+00 --3.720806904E+00-3.745574998E+00-3.765378039E+00-3.780266838E+00-3.790770469E+00 --3.796628378E+00-3.797110068E+00-3.792542189E+00-3.783240269E+00-3.768853704E+00 --3.749069020E+00-3.723866400E+00-3.693239990E+00-3.657085028E+00-3.615224955E+00 --3.567531254E+00-3.514071797E+00-3.454992538E+00-3.390431563E+00-3.320511176E+00 --3.245379568E+00-3.165129407E+00-3.079722486E+00-2.988963777E+00-2.892594570E+00 --2.790542831E+00-2.682918887E+00-2.569849455E+00-2.451440408E+00-2.327776651E+00 --2.198916649E+00-2.064906383E+00-1.925683659E+00-1.780945647E+00-1.630078729E+00 --1.472217763E+00-1.306487312E+00-1.132326456E+00-9.498625922E-01-7.599685503E-01 --5.639998377E-01-3.633203740E-01-1.589358010E-01 4.857002379E-02 2.592481833E-01 - 4.730878734E-01 6.900224641E-01 9.099165646E-01 1.132612023E+00 1.357958759E+00 - 1.585813612E+00 1.816044774E+00 2.048531004E+00 2.283160839E+00 2.519830454E+00 - 2.758441609E+00 2.998901202E+00 3.241120756E+00 3.485016046E+00 3.730506087E+00 - 3.977511837E+00 4.225953725E+00 4.475753736E+00 4.726840515E+00 4.979150926E+00 - 5.232628400E+00 5.487222356E+00 5.742887178E+00 5.999581811E+00 6.257269564E+00 - 6.515918261E+00 6.775500402E+00 7.035991023E+00 7.297365326E+00 7.559597963E+00 - 7.822663173E+00 8.086539027E+00 8.351226884E+00 8.616603404E+00 1.537299723E+00 - 1.363836574E+00 1.191704610E+00 1.021173885E+00 8.522807306E-01 6.851081094E-01 - 5.197501357E-01 3.563041504E-01 1.948989578E-01 3.564670828E-02-1.220648904E-01 --2.799137710E-01-4.378191519E-01-5.949027184E-01-7.499270271E-01-9.011383176E-01 --1.046507309E+00-1.184348987E+00-1.313924332E+00-1.435569683E+00-1.550370954E+00 --1.659769321E+00-1.765139846E+00-1.867605118E+00-1.967930513E+00-2.066629913E+00 --2.164015728E+00-2.260335054E+00-2.355739148E+00-2.450285508E+00-2.544019291E+00 --2.636897311E+00-2.728618746E+00-2.818960965E+00-2.907697527E+00-2.994461832E+00 --3.078905124E+00-3.160801291E+00-3.239909388E+00-3.315950531E+00-3.388739583E+00 --3.458295671E+00-3.524480506E+00-3.586989793E+00-3.645622640E+00-3.700290368E+00 --3.751022038E+00-3.797842023E+00-3.840260223E+00-3.878056272E+00-3.911687767E+00 --3.941081950E+00-3.965707772E+00-3.985247288E+00-4.000037261E+00-4.010458976E+00 --4.015770273E+00-4.015718198E+00-4.010829116E+00-4.001019803E+00-3.985875605E+00 --3.965257777E+00-3.939159709E+00-3.907519498E+00-3.870174229E+00-3.826970859E+00 --3.777955179E+00-3.723266982E+00-3.663039219E+00-3.597332633E+00-3.526183023E+00 --3.449652320E+00-3.367770377E+00-3.280428581E+00-3.187409001E+00-3.088529962E+00 --2.983698451E+00-2.872989532E+00-2.756611233E+00-2.634756348E+00-2.507571478E+00 --2.375197480E+00-2.237755171E+00-2.095316448E+00-1.947801389E+00-1.794861858E+00 --1.635848943E+00-1.469852613E+00-1.295975400E+00-1.113659532E+00-9.230900609E-01 --7.252636014E-01-5.216451322E-01-3.136177421E-01-1.021395570E-01 1.123141615E-01 - 3.298215646E-01 5.503388388E-01 7.737605392E-01 9.999252697E-01 1.228675813E+00 - 1.459873091E+00 1.693391711E+00 1.929115298E+00 2.166933647E+00 2.406742277E+00 - 2.648441980E+00 2.891938399E+00 3.137140827E+00 3.383960624E+00 3.632308751E+00 - 3.882099040E+00 4.133253454E+00 4.385702740E+00 4.639384868E+00 4.894244257E+00 - 5.150230719E+00 5.407299202E+00 5.665409595E+00 5.924527140E+00 6.184621431E+00 - 6.445663879E+00 6.707625352E+00 6.970477098E+00 7.234191057E+00 7.498739146E+00 - 7.764098859E+00 8.030273493E+00 8.297141723E+00 1.519860858E+00 1.344818051E+00 - 1.171053128E+00 9.988253897E-01 8.281695321E-01 6.591650492E-01 4.919017207E-01 - 3.264754033E-01 1.630296704E-01 1.599009229E-03-1.587286597E-01-3.193261782E-01 --4.798258144E-01-6.392298016E-01-7.961320566E-01-9.486113799E-01-1.094640939E+00 --1.232787152E+00-1.362703167E+00-1.485117256E+00-1.601371289E+00-1.712974915E+00 --1.821274819E+00-1.927280992E+00-2.031670312E+00-2.134829619E+00-2.236999282E+00 --2.338369727E+00-2.439053097E+00-2.539027722E+00-2.638287855E+00-2.736669568E+00 --2.833819627E+00-2.929466352E+00-3.023339534E+00-3.115123554E+00-3.204532165E+00 --3.291283907E+00-3.375150608E+00-3.455944323E+00-3.533414878E+00-3.607400267E+00 --3.677985231E+00-3.745026763E+00-3.808204465E+00-3.867366301E+00-3.922475878E+00 --3.973597399E+00-4.020676401E+00-4.063122163E+00-4.101015900E+00-4.134743101E+00 --4.164026837E+00-4.188314218E+00-4.207527456E+00-4.222216506E+00-4.232231309E+00 --4.236809094E+00-4.236285690E+00-4.230921189E+00-4.220340365E+00-4.204286376E+00 --4.182720191E+00-4.155580119E+00-4.122726496E+00-4.084017188E+00-4.039456122E+00 --3.989159424E+00-3.933267833E+00-3.871845547E+00-3.804903475E+00-3.732447933E+00 --3.654450592E+00-3.570834930E+00-3.481475812E+00-3.386219371E+00-3.284909382E+00 --3.177435258E+00-3.063787319E+00-2.944135079E+00-2.818758375E+00-2.687919017E+00 --2.551829736E+00-2.410673525E+00-2.264593026E+00-2.113649569E+00-1.957720948E+00 --1.796403673E+00-1.629016355E+00-1.454614461E+00-1.272281595E+00-1.081502924E+00 --8.825722324E-01-6.766420950E-01-4.652734085E-01-2.498453120E-01-3.125484502E-02 - 1.901907713E-01 4.145066614E-01 6.416271728E-01 8.714231168E-01 1.103743635E+00 - 1.338452503E+00 1.575424992E+00 1.814544011E+00 2.055698258E+00 2.298781794E+00 - 2.543692770E+00 2.790331565E+00 3.038598530E+00 3.288398448E+00 3.539645778E+00 - 3.792264366E+00 4.046186067E+00 4.301349643E+00 4.557699851E+00 4.815187234E+00 - 5.073768052E+00 5.333404544E+00 5.594062614E+00 5.855708950E+00 6.118310080E+00 - 6.381833459E+00 6.646247524E+00 6.911522745E+00 7.177631961E+00 7.444555779E+00 - 7.712300057E+00 7.980743138E+00 1.502490949E+00 1.325876743E+00 1.150485434E+00 - 9.765666553E-01 8.041550005E-01 6.333270511E-01 4.641676358E-01 2.967705576E-01 - 1.313009898E-01-3.230336260E-02-1.953234284E-01-3.586329360E-01-5.216545335E-01 --6.832838300E-01-8.419299442E-01-9.955381693E-01-1.142155198E+00-1.280667188E+00 --1.411136414E+00-1.534620556E+00-1.652660186E+00-1.766788031E+00-1.878287649E+00 --1.988038638E+00-2.096626719E+00-2.204351138E+00-2.311405389E+00-2.417933488E+00 --2.523971096E+00-2.629389676E+00-2.734095506E+00-2.837807780E+00-2.940155560E+00 --3.040840337E+00-3.139568920E+00-3.236065893E+00-3.330107601E+00-3.421450264E+00 --3.509847329E+00-3.595106608E+00-3.677053728E+00-3.755495817E+00-3.830304840E+00 --3.901554225E+00-3.969118685E+00-4.032722580E+00-4.092225586E+00-4.147600082E+00 --4.198932202E+00-4.246060247E+00-4.288401666E+00-4.326303335E+00-4.359969090E+00 --4.388929203E+00-4.412730323E+00-4.431615424E+00-4.446048609E+00-4.455312370E+00 --4.459166325E+00-4.458130548E+00-4.452022790E+00-4.440455099E+00-4.423353917E+00 --4.400679334E+00-4.372284122E+00-4.338006695E+00-4.297837861E+00-4.251904139E+00 --4.200333857E+00-4.143178362E+00-4.080444267E+00-4.012129400E+00-3.938185773E+00 --3.858517612E+00-3.773001487E+00-3.681523296E+00-3.583964529E+00-3.480190370E+00 --3.370088300E+00-3.253609851E+00-3.130829982E+00-3.002024313E+00-2.867545039E+00 --2.727686074E+00-2.582684419E+00-2.432741861E+00-2.278008567E+00-2.118512646E+00 --1.954075620E+00-1.784243093E+00-1.608299328E+00-1.425268398E+00-1.234186147E+00 --1.034596738E+00-8.269880952E-01-6.127458386E-01-3.935444895E-01-1.707301705E-01 - 5.489929127E-02 2.832376268E-01 5.142441947E-01 7.478479128E-01 9.839142756E-01 - 1.222302467E+00 1.462884225E+00 1.705540524E+00 1.950157058E+00 2.196621661E+00 - 2.444822773E+00 2.694655096E+00 2.946024587E+00 3.198847319E+00 3.453048242E+00 - 3.708559732E+00 3.965320959E+00 4.223277634E+00 4.482382209E+00 4.742593036E+00 - 5.003871359E+00 5.266178411E+00 5.529476221E+00 5.793728028E+00 6.058898938E+00 - 6.324957403E+00 6.591876633E+00 6.859632716E+00 7.128207320E+00 7.397604842E+00 - 7.667700093E+00 1.485226984E+00 1.307054085E+00 1.130048234E+00 9.544479926E-01 - 7.802876600E-01 6.076421316E-01 4.365937083E-01 2.672375175E-01 9.973660769E-02 --6.610677331E-02-2.317911869E-01-3.977418933E-01-5.632108232E-01-7.269670567E-01 --8.872320371E-01-1.041857770E+00-1.189033570E+00-1.328017542E+00-1.459285975E+00 --1.584170145E+00-1.704331281E+00-1.821265990E+00-1.936165395E+00-2.049796194E+00 --2.162654302E+00-2.274985794E+00-2.386949737E+00-2.498653919E+00-2.610016062E+00 --2.720791054E+00-2.830765136E+00-2.939582540E+00-3.046872100E+00-3.152333119E+00 --3.255673594E+00-3.356646643E+00-3.455049552E+00-3.550692151E+00-3.643393931E+00 --3.732923041E+00-3.819112350E+00-3.901859288E+00-3.980957536E+00-4.056285266E+00 --4.127978695E+00-4.195907004E+00-4.259770574E+00-4.319440549E+00-4.374933184E+00 --4.426334086E+00-4.473325492E+00-4.515487919E+00-4.553293050E+00-4.586708559E+00 --4.615142211E+00-4.638371292E+00-4.656927340E+00-4.670761505E+00-4.679085417E+00 --4.682274785E+00-4.680515330E+00-4.673374972E+00-4.660666759E+00-4.642373697E+00 --4.618380859E+00-4.588498737E+00-4.552656168E+00-4.510983600E+00-4.463646595E+00 --4.410714402E+00-4.352165961E+00-4.287974140E+00-4.218091451E+00-4.142424690E+00 --4.060845979E+00-3.973229097E+00-3.879454302E+00-3.779422335E+00-3.673039939E+00 --3.560204475E+00-3.440866982E+00-3.315082691E+00-3.183028279E+00-3.045039186E+00 --2.901475872E+00-2.752630921E+00-2.598755530E+00-2.440062294E+00-2.276695516E+00 --2.108629855E+00-1.935628496E+00-1.757185538E+00-1.572493487E+00-1.380494383E+00 --1.180200386E+00-9.713457414E-01-7.547820705E-01-5.321823894E-01-3.052682178E-01 --7.524437594E-02 1.573212289E-01 3.924234314E-01 6.300175771E-01 8.699926695E-01 - 1.112207696E+00 1.356528569E+00 1.602828137E+00 1.850981885E+00 2.100873404E+00 - 2.352398918E+00 2.605465749E+00 2.859990976E+00 3.115899818E+00 3.373125256E+00 - 3.631607754E+00 3.891295479E+00 4.152141878E+00 4.414102164E+00 4.677131938E+00 - 4.941188313E+00 5.206230143E+00 5.472219625E+00 5.739123887E+00 6.006915126E+00 - 6.275568562E+00 6.545060004E+00 6.815367455E+00 7.086490496E+00 7.358302820E+00 - 1.468113969E+00 1.288393171E+00 1.109784986E+00 9.325166902E-01 7.566207128E-01 - 5.821682780E-01 4.092392986E-01 2.379339466E-01 6.838873130E-02-9.976234240E-02 --2.680552071E-01-4.365598758E-01-6.043823726E-01-7.701500417E-01-9.319081042E-01 --1.087468815E+00-1.235230917E+00-1.374844856E+00-1.507178607E+00-1.633789001E+00 --1.756388157E+00-1.876392437E+00-1.994858789E+00-2.112452767E+00-2.229600703E+00 --2.346526807E+00-2.463355155E+00-2.580145524E+00-2.696686278E+00-2.812627477E+00 --2.927633393E+00-3.041306549E+00-3.153288843E+00-3.263287138E+00-3.371022814E+00 --3.476273701E+00-3.578839436E+00-3.678566867E+00-3.775321870E+00-3.868931188E+00 --3.959231646E+00-4.046084093E+00-4.129365183E+00-4.208900120E+00-4.284604826E+00 --4.356603177E+00-4.424731169E+00-4.488698597E+00-4.548403016E+00-4.603894733E+00 --4.655215272E+00-4.701890806E+00-4.743786961E+00-4.781344460E+00-4.814276383E+00 --4.842001820E+00-4.864633018E+00-4.882711880E+00-4.895566922E+00-4.902963347E+00 --4.905401687E+00-4.902609815E+00-4.894235358E+00-4.880243549E+00-4.860569054E+00 --4.835024871E+00-4.803477091E+00-4.766016686E+00-4.722819813E+00-4.673998637E+00 --4.619553857E+00-4.559445308E+00-4.493598125E+00-4.421910787E+00-4.344266727E+00 --4.260530967E+00-4.170560940E+00-4.074250205E+00-3.971520317E+00-3.862306672E+00 --3.746566153E+00-3.624277232E+00-3.495473950E+00-3.360287911E+00-3.218960747E+00 --3.071845040E+00-2.919273036E+00-2.761523714E+00-2.598858603E+00-2.431493331E+00 --2.259537423E+00-2.082866089E+00-1.901153963E+00-1.713842821E+00-1.520023676E+00 --1.318570091E+00-1.108594529E+00-8.901800110E-01-6.646237586E-01-4.338140717E-01 --1.993940202E-01 3.763650568E-02 2.770446808E-01 5.187879588E-01 7.628017684E-01 - 1.008947414E+00 1.257077076E+00 1.507059509E+00 1.758780271E+00 2.012137054E+00 - 2.267037922E+00 2.523400108E+00 2.781149715E+00 3.040221568E+00 3.300558521E+00 - 3.562107876E+00 3.824817797E+00 4.088637969E+00 4.353520065E+00 4.619418983E+00 - 4.886294579E+00 5.154112856E+00 5.422844037E+00 5.692460964E+00 5.962936230E+00 - 6.234241191E+00 6.506350793E+00 6.779262544E+00 7.052851616E+00 1.451202772E+00 - 1.269947223E+00 1.089748587E+00 9.108239347E-01 7.332051801E-01 5.569599300E-01 - 3.821650522E-01 2.089253131E-01 3.732909655E-02-1.331786477E-01-3.040280765E-01 --4.750009254E-01-6.450715831E-01-8.127117617E-01-9.758186956E-01-1.132241413E+00 --1.280656045E+00-1.421103131E+00-1.554793792E+00-1.683448661E+00-1.808766003E+00 --1.932058682E+00-2.054232409E+00-2.175861511E+00-2.297308932E+00-2.418779751E+00 --2.540362662E+00-2.662049895E+00-2.783514993E+00-2.904336291E+00-3.024095435E+00 --3.142365665E+00-3.258804645E+00-3.373124493E+00-3.485067039E+00-3.594421594E+00 --3.700997402E+00-3.804667074E+00-3.905306966E+00-4.002804577E+00-4.097061045E+00 --4.187920447E+00-4.275226178E+00-4.358885844E+00-4.438734567E+00-4.514671782E+00 --4.586816374E+00-4.654997257E+00-4.718929565E+00-4.778525845E+00-4.833865559E+00 --4.884916915E+00-4.931111423E+00-4.972632714E+00-5.009749165E+00-5.041944705E+00 --5.068825395E+00-5.090852680E+00-5.108099972E+00-5.119776206E+00-5.126281320E+00 --5.127706927E+00-5.123599388E+00-5.113835745E+00-5.098390187E+00-5.077100089E+00 --5.049791256E+00-5.016504967E+00-4.977409020E+00-4.932633091E+00-4.882197119E+00 --4.826080714E+00-4.764212822E+00-4.696472658E+00-4.622724470E+00-4.542825905E+00 --4.456634704E+00-4.364033346E+00-4.264924293E+00-4.159247822E+00-4.046991780E+00 --3.928166771E+00-3.802785113E+00-3.670879591E+00-3.532552098E+00-3.388000379E+00 --3.237507116E+00-3.081397422E+00-2.919949361E+00-2.753421763E+00-2.582041851E+00 --2.405968542E+00-2.225248165E+00-2.039713550E+00-1.849013788E+00-1.652528779E+00 --1.449212746E+00-1.237848217E+00-1.017791195E+00-7.896676674E-01-5.552421443E-01 --3.164985585E-01-7.486153020E-02 1.689861642E-01 4.149946810E-01 6.631127208E-01 - 9.132202772E-01 1.165182864E+00 1.418882682E+00 1.674217761E+00 1.931096795E+00 - 2.189438296E+00 2.449170821E+00 2.710230548E+00 2.972556913E+00 3.236090649E+00 - 3.500774936E+00 3.766556040E+00 4.033385325E+00 4.301221066E+00 4.570027227E+00 - 4.839771491E+00 5.110422681E+00 5.381949535E+00 5.654321273E+00 5.927507358E+00 - 6.201482211E+00 6.476243057E+00 6.751667276E+00 1.434538106E+00 1.251765741E+00 - 1.069994373E+00 8.894296378E-01 7.101023737E-01 5.320774527E-01 3.554305528E-01 - 1.802752646E-01 6.637284102E-03-1.662598629E-01-3.396111603E-01-5.129682996E-01 --6.851814760E-01-8.545534004E-01-1.018866559E+00-1.176079083E+00-1.325212664E+00 --1.466702227E+00-1.602039825E+00-1.733042245E+00-1.861331045E+00-1.988092191E+00 --2.114081409E+00-2.239797549E+00-2.365558036E+00-2.491525209E+00-2.617721634E+00 --2.744050870E+00-2.870118721E+00-2.995470061E+00-3.119657002E+00-3.242247164E+00 --3.362906115E+00-3.481344705E+00-3.597323017E+00-3.710631670E+00-3.821097565E+00 --3.928604979E+00-4.033037784E+00-4.134311819E+00-4.232362904E+00-4.327086823E+00 --4.418334331E+00-4.505959288E+00-4.589863250E+00-4.669867386E+00-4.745876340E+00 --4.818013234E+00-4.886085890E+00-4.949813180E+00-5.009134747E+00-5.064149239E+00 --5.114716209E+00-5.160297259E+00-5.201301158E+00-5.237732103E+00-5.268964264E+00 --5.294936535E+00-5.316224546E+00-5.332235946E+00-5.342752852E+00-5.348226530E+00 --5.348301205E+00-5.342692211E+00-5.331382286E+00-5.314252595E+00-5.291107484E+00 --5.261930541E+00-5.226879434E+00-5.186099117E+00-5.139617134E+00-5.087419292E+00 --5.029450737E+00-4.965601259E+00-4.895718175E+00-4.819621203E+00-4.737149700E+00 --4.648193070E+00-4.552660278E+00-4.450487358E+00-4.341655352E+00-4.226185107E+00 --4.104117029E+00-3.975499404E+00-3.840388141E+00-3.698875159E+00-3.551131244E+00 --3.397401314E+00-3.237959443E+00-3.073011743E+00-2.902701829E+00-2.727243722E+00 --2.546889970E+00-2.361837643E+00-2.172113613E+00-1.977529785E+00-1.777669135E+00 --1.571709901E+00-1.358411458E+00-1.136598411E+00-9.061412692E-01-6.683946082E-01 --4.254925020E-01-1.793043525E-01 6.906785133E-02 3.193903201E-01 5.716306788E-01 - 8.257276955E-01 1.081564696E+00 1.339033369E+00 1.598043477E+00 1.858516551E+00 - 2.120380539E+00 2.383565541E+00 2.648004401E+00 2.913633267E+00 3.180393487E+00 - 3.448233757E+00 3.717110205E+00 3.986984021E+00 4.257819154E+00 4.529579960E+00 - 4.802231681E+00 5.075740899E+00 5.350076143E+00 5.625207134E+00 5.901108339E+00 - 6.177775676E+00 6.455087988E+00 1.418169983E+00 1.233898127E+00 1.050572596E+00 - 8.683877575E-01 6.873725334E-01 5.075873336E-01 3.291052632E-01 1.520564068E-01 --2.360062754E-02-1.989149168E-01-3.747092766E-01-5.503590886E-01-7.246016481E-01 --8.955701136E-01-1.060971334E+00-1.218933012E+00-1.368861476E+00-1.511577470E+00 --1.648799230E+00-1.782393454E+00-1.913862067E+00-2.044240450E+00-2.174139167E+00 --2.303983532E+00-2.434058217E+00-2.564459422E+00-2.695123847E+00-2.825843989E+00 --2.956185345E+00-3.085703312E+00-3.213968374E+00-3.340572120E+00-3.465190727E+00 --3.587536403E+00-3.707378319E+00-3.824505805E+00-3.938761458E+00-4.050028043E+00 --4.158194085E+00-4.263186333E+00-4.364942591E+00-4.463384598E+00-4.558417654E+00 --4.649909590E+00-4.737698534E+00-4.821674561E+00-4.901663608E+00-4.977574510E+00 --5.049525818E+00-5.117307046E+00-5.180647696E+00-5.239521976E+00-5.294023177E+00 --5.343870001E+00-5.388723461E+00-5.429030204E+00-5.464502436E+00-5.494594458E+00 --5.519639218E+00-5.539833348E+00-5.554406112E+00-5.563766862E+00-5.567895901E+00 --5.566360547E+00-5.559090860E+00-5.546020612E+00-5.526953659E+00-5.501810578E+00 --5.470730083E+00-5.433872851E+00-5.391279380E+00-5.342937174E+00-5.288798076E+00 --5.228764431E+00-5.162686740E+00-5.090360555E+00-5.011588801E+00-4.926232864E+00 --4.834202099E+00-4.735458462E+00-4.629999473E+00-4.517840114E+00-4.399016593E+00 --4.273592004E+00-4.141643781E+00-4.003258889E+00-3.858544841E+00-3.707655364E+00 --3.550778426E+00-3.388052733E+00-3.219583164E+00-3.045467388E+00-2.865893239E+00 --2.681178590E+00-2.491641746E+00-2.297481327E+00-2.098641376E+00-1.894858286E+00 --1.685566666E+00-1.469661061E+00-1.245738004E+00-1.013012614E+00-7.722232463E-01 --5.254256602E-01-2.748332571E-01-2.192935130E-02 2.327306533E-01 4.891311349E-01 - 7.472614839E-01 1.007026941E+00 1.268330914E+00 1.531089341E+00 1.795222901E+00 - 2.060655868E+00 2.327317550E+00 2.595145012E+00 2.864084487E+00 3.134088993E+00 - 3.405116115E+00 3.677124943E+00 3.950075935E+00 4.223931109E+00 4.498654772E+00 - 4.774213693E+00 5.050576557E+00 5.327712552E+00 5.605594370E+00 5.884215447E+00 - 6.163457784E+00 1.402150487E+00 1.216399391E+00 1.031539661E+00 8.477547835E-01 - 6.650724989E-01 4.835495855E-01 3.032575003E-01 1.243301726E-01-5.336092330E-02 --2.310591157E-01-4.092225951E-01-5.870739633E-01-7.632270959E-01-9.356571207E-01 --1.102047225E+00-1.260753073E+00-1.411580188E+00-1.555702644E+00-1.695002386E+00 --1.831347443E+00-1.966110856E+00-2.100186057E+00-2.234058930E+00-2.368072946E+00 --2.502462039E+00-2.637219574E+00-2.772188124E+00-2.907066517E+00-3.041404602E+00 --3.174778320E+00-3.306791921E+00-3.437094194E+00-3.565387704E+00-3.691401614E+00 --3.814912534E+00-3.935713434E+00-4.053655624E+00-4.168610912E+00-4.280461094E+00 --4.389125197E+00-4.494535035E+00-4.596612487E+00-4.695282178E+00-4.790462418E+00 --4.882021447E+00-4.969791833E+00-5.053657437E+00-5.133446329E+00-5.209073202E+00 --5.280648914E+00-5.347944044E+00-5.410707316E+00-5.468953957E+00-5.522740750E+00 --5.571647086E+00-5.615641960E+00-5.655026255E+00-5.689268419E+00-5.718112912E+00 --5.742114990E+00-5.760791381E+00-5.773947282E+00-5.781953816E+00-5.784397047E+00 --5.781073998E+00-5.771954727E+00-5.756867269E+00-5.735675442E+00-5.708485835E+00 --5.675468821E+00-5.636682759E+00-5.592119795E+00-5.541737559E+00-5.485446083E+00 --5.423094756E+00-5.354463893E+00-5.279341326E+00-5.197564630E+00-5.109016138E+00 --5.013651596E+00-4.911488794E+00-4.802570425E+00-4.686945710E+00-4.564674987E+00 --4.435840358E+00-4.300546727E+00-4.158911884E+00-4.011050559E+00-3.857019496E+00 --3.696854865E+00-3.530642936E+00-3.358490335E+00-3.180498793E+00-2.996807370E+00 --2.807711768E+00-2.613597282E+00-2.414784066E+00-2.211398253E+00-2.003311855E+00 --1.790144521E+00-1.571029794E+00-1.344572713E+00-1.109503913E+00-8.658764119E-01 --6.154333254E-01-3.605785028E-01-1.031761222E-01 1.558595598E-01 4.164774366E-01 - 6.786994653E-01 9.424507979E-01 1.207632918E+00 1.474157845E+00 1.741949251E+00 - 2.010940997E+00 2.281075752E+00 2.552302798E+00 2.824574712E+00 3.097846166E+00 - 3.372073810E+00 3.647216946E+00 3.923237710E+00 4.200100608E+00 4.477771840E+00 - 4.756218338E+00 5.035407680E+00 5.315312370E+00 5.595926408E+00 5.877137311E+00 - 1.386528782E+00 1.199320756E+00 1.012950331E+00 8.275896808E-01 6.432645106E-01 - 4.600281836E-01 2.779526643E-01 9.716013911E-02-8.258419605E-02-2.626024332E-01 --4.430488649E-01-6.230066244E-01-8.009520844E-01-9.747178849E-01-1.142018007E+00 --1.301487574E+00-1.453331652E+00-1.599035666E+00-1.740583160E+00-1.879791034E+00 --2.017895422E+00-2.155658813E+00-2.293486928E+00-2.431663154E+00-2.570343229E+00 --2.709376573E+00-2.848493568E+00-2.987320647E+00-3.125419894E+00-3.262406956E+00 --3.397919106E+00-3.531649420E+00-3.663337856E+00-3.792762067E+00-3.919718465E+00 --4.044014818E+00-4.165508240E+00-4.284059043E+00-4.399530066E+00-4.511815061E+00 --4.620827657E+00-4.726484333E+00-4.828708702E+00-4.927427567E+00-5.022565442E+00 --5.113997970E+00-5.201555922E+00-5.285116456E+00-5.364510389E+00-5.439654490E+00 --5.510652197E+00-5.577259600E+00-5.639248945E+00-5.696672214E+00-5.749521513E+00 --5.797303843E+00-5.840274236E+00-5.878454373E+00-5.911248832E+00-5.938803095E+00 --5.961420217E+00-5.978378777E+00-5.990077027E+00-5.996375967E+00-5.996904899E+00 --5.991621447E+00-5.980401445E+00-5.963069331E+00-5.939683736E+00-5.910418206E+00 --5.875351648E+00-5.834481302E+00-5.787773050E+00-5.735146540E+00-5.676444494E+00 --5.611425084E+00-5.539862451E+00-5.461585449E+00-5.376472029E+00-5.284468505E+00 --5.185578857E+00-5.079850215E+00-4.967360222E+00-4.848197178E+00-4.722454989E+00 --4.590244623E+00-4.451693972E+00-4.306877956E+00-4.155773378E+00-3.998349681E+00 --3.834625271E+00-3.664689541E+00-3.488675154E+00-3.306690310E+00-3.118829388E+00 --2.925306095E+00-2.726524815E+00-2.522916024E+00-2.314778109E+00-2.102133691E+00 --1.884759536E+00-1.662024183E+00-1.432623664E+00-1.194995394E+00-9.485667317E-01 --6.946208647E-01-4.356107717E-01-1.737524220E-01 8.971566509E-02 3.545951320E-01 - 6.209190228E-01 8.886405954E-01 1.157670096E+00 1.427932464E+00 1.699366910E+00 - 1.971918016E+00 2.245533309E+00 2.520163016E+00 2.795760498E+00 3.072282430E+00 - 3.349688356E+00 3.627939853E+00 3.906999623E+00 4.186832294E+00 4.467405064E+00 - 4.748687360E+00 5.030654146E+00 5.313302522E+00 5.596527184E+00 1.371358193E+00 - 1.182715543E+00 9.948581219E-01 8.079471774E-01 6.220062979E-01 4.370854270E-01 - 2.532574290E-01 7.061921958E-02-1.111834872E-01-2.934559708E-01-4.760971583E-01 --6.580591903E-01-8.376731836E-01-1.012654907E+00-1.180808002E+00-1.341086626E+00 --1.494075070E+00-1.641518585E+00-1.785449564E+00-1.927592098E+00-2.069047596E+00 --2.210457270E+00-2.352168498E+00-2.494415926E+00-2.637271139E+00-2.780450218E+00 --2.923566477E+00-3.066177941E+00-3.207858518E+00-3.348267103E+00-3.487086272E+00 --3.624050454E+00-3.758924243E+00-3.891525453E+00-4.021692764E+00-4.149273936E+00 --4.274136159E+00-4.396135395E+00-4.515117770E+00-4.630944917E+00-4.743497990E+00 --4.852675933E+00-4.958393662E+00-5.060574239E+00-5.159147023E+00-5.254041316E+00 --5.345141638E+00-5.432284639E+00-5.515334790E+00-5.594125164E+00-5.668579254E+00 --5.738789678E+00-5.804498399E+00-5.865508724E+00-5.921895246E+00-5.973561265E+00 --6.020073642E+00-6.061813477E+00-6.098494989E+00-6.129687958E+00-6.155858592E+00 --6.176656161E+00-6.191915052E+00-6.201895625E+00-6.206170365E+00-6.204607292E+00 --6.197132065E+00-6.183556570E+00-6.163879997E+00-6.138270411E+00-6.106827734E+00 --6.069555984E+00-6.026430742E+00-5.977382180E+00-5.922245812E+00-5.860755652E+00 --5.792666741E+00-5.717795761E+00-5.636024470E+00-5.547307527E+00-5.451650036E+00 --5.349093650E+00-5.239715920E+00-5.123626486E+00-5.000953811E+00-4.871832944E+00 --4.736370012E+00-4.594563040E+00-4.446356471E+00-4.291705593E+00-4.130598700E+00 --3.963074157E+00-3.789212990E+00-3.609136922E+00-3.422964027E+00-3.230784863E+00 --3.032755526E+00-2.829253987E+00-2.620792614E+00-2.407813137E+00-2.190509772E+00 --1.968771558E+00-1.742112668E+00-1.509368317E+00-1.268856192E+00-1.019493383E+00 --7.620562257E-01-4.989442864E-01-2.326764676E-01 3.519248203E-02 3.042819222E-01 - 5.746482970E-01 8.462929837E-01 1.119141697E+00 1.393126845E+00 1.668191738E+00 - 1.944282957E+00 2.221350592E+00 2.499348271E+00 2.778232144E+00 3.057959912E+00 - 3.338491740E+00 3.619791112E+00 3.901825018E+00 4.184563812E+00 4.467981691E+00 - 4.752058547E+00 5.036793773E+00 5.322086059E+00 1.356691210E+00 1.166638239E+00 - 9.773191650E-01 7.888845281E-01 6.013558716E-01 4.147803160E-01 2.292325207E-01 - 4.477438732E-02-1.390752008E-01-3.235306184E-01-5.082763816E-01-6.921393648E-01 --8.733001553E-01-1.049387914E+00-1.218351526E+00-1.379496199E+00-1.533756561E+00 --1.683078789E+00-1.829494988E+00-1.974603481E+00-2.119383074E+00-2.264374639E+00 --2.409878057E+00-2.556072657E+00-2.702924403E+00-2.850040166E+00-2.996954227E+00 --3.143187637E+00-3.288315687E+00-3.432014768E+00-3.574003742E+00-3.714054284E+00 --3.851964723E+00-3.987587098E+00-4.120783966E+00-4.251438170E+00-4.379451007E+00 --4.504693489E+00-4.627009103E+00-4.746240345E+00-4.862235775E+00-4.974862233E+00 --5.084009378E+00-5.189588928E+00-5.291524196E+00-5.389743876E+00-5.484182495E+00 --5.574737174E+00-5.661250032E+00-5.743573530E+00-5.821545498E+00-5.895093604E+00 --5.964297528E+00-6.028890811E+00-6.088715122E+00-6.143843533E+00-6.194070056E+00 --6.239171346E+00-6.279430883E+00-6.314351631E+00-6.343862924E+00-6.368332874E+00 --6.387118425E+00-6.400582954E+00-6.408478125E+00-6.410521918E+00-6.406661017E+00 --6.396726789E+00-6.380655672E+00-6.358598278E+00-6.330675985E+00-6.296901561E+00 --6.257259982E+00-6.211693487E+00-6.160029392E+00-6.101975800E+00-6.037269234E+00 --5.965714732E+00-5.887195668E+00-5.801674508E+00-5.709166743E+00-5.609725235E+00 --5.503435458E+00-5.390416205E+00-5.270818486E+00-5.144796802E+00-5.012397699E+00 --4.873551285E+00-4.728185376E+00-4.576264753E+00-4.417784673E+00-4.252753057E+00 --4.081196247E+00-3.903179098E+00-3.718812815E+00-3.528235361E+00-3.331566925E+00 --3.128959649E+00-2.920751261E+00-2.707480525E+00-2.489673986E+00-2.267659850E+00 --2.041427556E+00-1.810599338E+00-1.574156339E+00-1.330389207E+00-1.077849209E+00 --8.168642935E-01-5.497191015E-01-2.791497048E-01-6.973533963E-03 2.662550988E-01 - 5.406175921E-01 8.161500988E-01 1.092781282E+00 1.370445564E+00 1.649090493E+00 - 1.928666111E+00 2.209124142E+00 2.490419594E+00 2.772511626E+00 3.055363392E+00 - 3.338942468E+00 3.623221632E+00 3.908176470E+00 4.193783836E+00 4.480024841E+00 - 4.766899003E+00 5.054308888E+00 1.342572652E+00 1.151137423E+00 9.603851301E-01 - 7.704561442E-01 5.813703396E-01 3.931723430E-01 2.059393519E-01 1.969151617E-02 --1.661835352E-01-3.527471918E-01-5.395036573E-01-7.251592369E-01-9.077469989E-01 --1.084846391E+00-1.254597831E+00-1.416672137E+00-1.572320561E+00-1.723629889E+00 --1.872593267E+00-2.020666011E+00-2.168715040E+00-2.317201600E+00-2.466381360E+00 --2.616371457E+00-2.767019482E+00-2.917843819E+00-3.068328744E+00-3.217984738E+00 --3.366405578E+00-3.513280824E+00-3.658345855E+00-3.801386952E+00-3.942231456E+00 --4.080763864E+00-4.216872002E+00-4.350455096E+00-4.481425239E+00-4.609679775E+00 --4.735094336E+00-4.857517720E+00-4.976787359E+00-5.092742368E+00-5.205234438E+00 --5.314143777E+00-5.419376100E+00-5.520851785E+00-5.618502533E+00-5.712265008E+00 --5.802049596E+00-5.887709376E+00-5.969082966E+00-6.046013511E+00-6.118433152E+00 --6.186406055E+00-6.249663266E+00-6.308091798E+00-6.361741251E+00-6.410295607E+00 --6.453805320E+00-6.492286020E+00-6.525249590E+00-6.553003229E+00-6.575335300E+00 --6.592114390E+00-6.603465956E+00-6.608997876E+00-6.608617689E+00-6.602197014E+00 --6.589618003E+00-6.571002183E+00-6.546489463E+00-6.516102405E+00-6.479837143E+00 --6.437649262E+00-6.389354224E+00-6.334633508E+00-6.273206419E+00-6.204868785E+00 --6.129508999E+00-6.047097751E+00-5.957659663E+00-5.861263160E+00-5.758014224E+00 --5.648053963E+00-5.531550437E+00-5.408619842E+00-5.279227159E+00-5.143280503E+00 --5.000705161E+00-4.851465791E+00-4.695557947E+00-4.532986576E+00-4.363760799E+00 --4.187908031E+00-4.005496322E+00-3.816641020E+00-3.621505021E+00-3.420252805E+00 --3.213045850E+00-3.000165806E+00-2.782122373E+00-2.559490925E+00-2.332701682E+00 --2.101853480E+00-1.866667791E+00-1.626258556E+00-1.378935669E+00-1.122996640E+00 --8.583830388E-01-5.872299360E-01-3.124260095E-01-3.601673185E-02 2.412801587E-01 - 5.195747196E-01 7.989254158E-01 1.079262471E+00 1.360522258E+00 1.642654890E+00 - 1.925614813E+00 2.209360745E+00 2.493857229E+00 2.779074178E+00 3.064984449E+00 - 3.351563281E+00 3.638787798E+00 3.926635980E+00 4.215089849E+00 4.504149028E+00 - 4.793720320E+00 1.329032334E+00 1.136249014E+00 9.440975014E-01 7.527081304E-01 - 5.620994120E-01 3.723140321E-01 1.834352919E-01-4.560275335E-03-1.924346390E-01 --3.810309052E-01-5.697031344E-01-7.570420404E-01-9.409422242E-01-1.118971881E+00 --1.289501988E+00-1.452570749E+00-1.609708287E+00-1.763083583E+00-1.914617747E+00 --2.065617903E+00-2.216852859E+00-2.368727196E+00-2.521447219E+00-2.675054420E+00 --2.829278430E+00-2.983576394E+00-3.137410459E+00-3.290292586E+00-3.441838217E+00 --3.591750650E+00-3.739784749E+00-3.885737260E+00-4.029451612E+00-4.170825988E+00 --4.309763103E+00-4.446172616E+00-4.579972514E+00-4.711067781E+00-4.839353294E+00 --4.964714141E+00-5.087015500E+00-5.206095648E+00-5.321784814E+00-5.433923195E+00 --5.542376506E+00-5.647040885E+00-5.747835670E+00-5.844692527E+00-5.937550833E+00 --6.026335588E+00-6.110911436E+00-6.191105738E+00-6.266767691E+00-6.337831267E+00 --6.404343156E+00-6.466040918E+00-6.522855287E+00-6.574790426E+00-6.621484188E+00 --6.663172092E+00-6.699585987E+00-6.730464603E+00-6.756179223E+00-6.776191005E+00 --6.790803553E+00-6.799691223E+00-6.802658473E+00-6.799611649E+00-6.790403319E+00 --6.775112213E+00-6.753889916E+00-6.726772618E+00-6.693769132E+00-6.654847569E+00 --6.609809235E+00-6.558308552E+00-6.500046738E+00-6.434815359E+00-6.362512123E+00 --6.283117572E+00-6.196669939E+00-6.103256682E+00-6.003009414E+00-5.896101476E+00 --5.782696948E+00-5.662809743E+00-5.536343669E+00-5.403211460E+00-5.263359970E+00 --5.116752415E+00-4.963359691E+00-4.803175762E+00-4.636218724E+00-4.462521620E+00 --4.282137544E+00-4.095158214E+00-3.901717112E+00-3.701973217E+00-3.496088172E+00 --3.284222370E+00-3.066633479E+00-2.843795147E+00-2.616311796E+00-2.384704763E+00 --2.149196959E+00-1.909595870E+00-1.665085915E+00-1.413973585E+00-1.154373196E+00 --8.859424012E-01-6.107151114E-01-3.317174488E-01-5.118253375E-02 2.300761782E-01 - 5.121936085E-01 7.952428946E-01 1.079158524E+00 1.363885991E+00 1.649387569E+00 - 1.935630015E+00 2.222582983E+00 2.510218967E+00 2.798512655E+00 3.087440688E+00 - 3.376981503E+00 3.667114243E+00 3.957820462E+00 4.249096674E+00 4.540852874E+00 - 1.316094184E+00 1.122001113E+00 9.284888680E-01 7.356777150E-01 5.435847573E-01 - 3.522508264E-01 1.617682777E-01-2.792975640E-02-2.177665407E-01-4.083163420E-01 --5.988073050E-01-7.877198974E-01-9.728248560E-01-1.151717658E+00-1.323029179E+00 --1.487153923E+00-1.645859126E+00-1.801345733E+00-1.955439481E+00-2.109303492E+00 --2.263620409E+00-2.418753827E+00-2.574852177E+00-2.731872704E+00-2.889441327E+00 --3.046977161E+00-3.203939866E+00-3.359854098E+00-3.514358873E+00-3.667168363E+00 --3.818052505E+00-3.966819072E+00-4.113330122E+00-4.257491043E+00-4.399203516E+00 --4.538371284E+00-4.674908871E+00-4.808727803E+00-4.939735262E+00-5.067830134E+00 --5.192905528E+00-5.314841063E+00-5.433486099E+00-5.548669834E+00-5.660221155E+00 --5.767989203E+00-5.871858371E+00-5.971743026E+00-6.067575267E+00-6.159297270E+00 --6.246846923E+00-6.330102469E+00-6.408884489E+00-6.483046072E+00-6.552521806E+00 --6.617340957E+00-6.677253802E+00-6.732217256E+00-6.782178377E+00-6.826853156E+00 --6.866450942E+00-6.900557764E+00-6.929276653E+00-6.952521238E+00-6.970196997E+00 --6.982284275E+00-6.988465425E+00-6.988645603E+00-6.982678382E+00-6.970587725E+00 --6.952529862E+00-6.928558012E+00-6.898693491E+00-6.862917854E+00-6.821015554E+00 --6.772611820E+00-6.717391113E+00-6.655146763E+00-6.585788020E+00-6.509309527E+00 --6.425769606E+00-6.335280933E+00-6.238011134E+00-6.134157639E+00-6.023812405E+00 --5.906888326E+00-5.783265701E+00-5.652865599E+00-5.515646440E+00-5.371575912E+00 --5.220621060E+00-5.062760879E+00-4.898005740E+00-4.726406636E+00-4.548042437E+00 --4.363002261E+00-4.171382083E+00-3.973294984E+00-3.768871576E+00-3.558260339E+00 --3.341627100E+00-3.119244890E+00-2.891590406E+00-2.659294874E+00-2.422936226E+00 --2.182813611E+00-1.938776208E+00-1.690031239E+00-1.434873743E+00-1.171300605E+00 --8.988113954E-01-6.194275353E-01-3.363074513E-01-5.180757774E-02 2.332431952E-01 - 5.190254018E-01 8.056277833E-01 1.092997085E+00 1.381091863E+00 1.669882638E+00 - 1.959341588E+00 2.249442976E+00 2.540163135E+00 2.831479208E+00 3.123368069E+00 - 3.415807021E+00 3.708776048E+00 4.002268689E+00 4.296200037E+00 1.303784853E+00 - 1.108422827E+00 9.135914717E-01 7.194009762E-01 5.258669958E-01 3.330288712E-01 - 1.409806232E-01-5.039487610E-02-2.421259504E-01-4.345431204E-01-6.267584538E-01 --8.171387407E-01-1.003349021E+00-1.183049516E+00-1.355151481E+00-1.520385589E+00 --1.680713732E+00-1.838326775E+00-1.994937593E+00-2.151576354E+00-2.308853795E+00 --2.467101319E+00-2.626398036E+00-2.786609374E+00-2.947279218E+00-3.107813533E+00 --3.267686428E+00-3.426441526E+00-3.583736168E+00-3.739294890E+00-3.892903814E+00 --4.044382249E+00-4.193604153E+00-4.340476569E+00-4.484898861E+00-4.626766438E+00 --4.765980468E+00-4.902446305E+00-5.036073937E+00-5.166772460E+00-5.294449148E+00 --5.419001822E+00-5.540318884E+00-5.658271314E+00-5.772694407E+00-5.883411745E+00 --5.990256567E+00-6.093096477E+00-6.191837423E+00-6.286410126E+00-6.376760420E+00 --6.462836599E+00-6.544531174E+00-6.621664282E+00-6.694091787E+00-6.761745891E+00 --6.824637437E+00-6.882537959E+00-6.935411651E+00-6.983145440E+00-7.025625306E+00 --7.062849080E+00-7.094469122E+00-7.120790724E+00-7.141393088E+00-7.156496748E+00 --7.165748753E+00-7.169006170E+00-7.166139581E+00-7.157118950E+00-7.142093572E+00 --7.121135120E+00-7.094279763E+00-7.061522658E+00-7.022626247E+00-6.977186625E+00 --6.924874142E+00-6.865488428E+00-6.798954754E+00-6.725287943E+00-6.644572372E+00 --6.556958327E+00-6.462655037E+00-6.361834255E+00-6.254459629E+00-6.140392183E+00 --6.019519458E+00-5.891771404E+00-5.757095067E+00-5.615450719E+00-5.466817471E+00 --5.311190962E+00-5.148587431E+00-4.979058700E+00-4.802688833E+00-4.619568407E+00 --4.429781962E+00-4.233414829E+00-4.030563496E+00-3.821344697E+00-3.605909404E+00 --3.384451208E+00-3.157274036E+00-2.924855014E+00-2.687813303E+00-2.446744922E+00 --2.202002017E+00-1.953470292E+00-1.700360924E+00-1.440932106E+00-1.173098256E+00 --8.963276206E-01-6.127397271E-01-3.256154356E-01-3.734348964E-02 2.513339779E-01 - 5.406576090E-01 8.307107414E-01 1.121444520E+00 1.412825057E+00 1.704826841E+00 - 1.997423435E+00 2.290589331E+00 2.584300204E+00 2.878531595E+00 3.173259676E+00 - 3.468464484E+00 3.764140746E+00 4.060212941E+00 1.292128794E+00 1.095544798E+00 - 8.994409502E-01 7.039175290E-01 5.089893881E-01 3.146953795E-01 1.211239020E-01 --7.189815521E-02-2.654459432E-01-4.596426701E-01-6.534908163E-01-8.452411162E-01 --1.032471758E+00-1.212940371E+00-1.385848376E+00-1.552235022E+00-1.714216656E+00 --1.873942890E+00-2.033003095E+00-2.192310133E+00-2.352415109E+00-2.513616731E+00 --2.675914721E+00-2.839082627E+00-3.002608698E+00-3.165904803E+00-3.328467445E+00 --3.489864775E+00-3.649771338E+00-3.807923850E+00-3.964121407E+00-4.118193933E+00 --4.270024848E+00-4.419520024E+00-4.566570231E+00-4.711060768E+00-4.852883961E+00 --4.991937268E+00-5.128121246E+00-5.261341052E+00-5.391507715E+00-5.518531205E+00 --5.642318065E+00-5.762765260E+00-5.879757483E+00-5.993153456E+00-6.102777328E+00 --6.208451310E+00-6.310022498E+00-6.407382616E+00-6.500458944E+00-6.589200200E+00 --6.673561434E+00-6.753452352E+00-6.828698915E+00-6.899155773E+00-6.964751662E+00 --7.025481344E+00-7.081146627E+00-7.131711361E+00-7.176992833E+00-7.217035403E+00 --7.251616299E+00-7.280657938E+00-7.304165309E+00-7.322079010E+00-7.334244050E+00 --7.340429608E+00-7.340514279E+00-7.334426515E+00-7.322295209E+00-7.304212167E+00 --7.280230096E+00-7.250356106E+00-7.214326993E+00-7.171709810E+00-7.122163119E+00 --7.065499879E+00-7.001666962E+00-6.930705618E+00-6.852737560E+00-6.767965224E+00 --6.676616730E+00-6.578747705E+00-6.474220724E+00-6.362890296E+00-6.244660291E+00 --6.119457509E+00-5.987218789E+00-5.847900288E+00-5.701486679E+00-5.547998769E+00 --5.387485148E+00-5.219999651E+00-5.045600022E+00-4.864358938E+00-4.676359250E+00 --4.481685520E+00-4.280435054E+00-4.072720572E+00-3.858664725E+00-3.638405762E+00 --3.412127740E+00-3.180139560E+00-2.942926707E+00-2.701114907E+00-2.455330315E+00 --2.205969653E+00-1.952933874E+00-1.695395240E+00-1.431522257E+00-1.159164338E+00 --8.778912375E-01-5.900414935E-01-2.990100461E-01-7.130564321E-03 2.850491897E-01 - 5.778056190E-01 8.712005172E-01 1.165186642E+00 1.459732590E+00 1.754811559E+00 - 2.050397207E+00 2.346465563E+00 2.642995372E+00 2.939966913E+00 3.237363837E+00 - 3.535182864E+00 3.833357344E+00 1.281138772E+00 1.083384413E+00 8.860612550E-01 - 6.892594294E-01 4.929924450E-01 2.972983335E-01 1.022543290E-01-9.237056854E-02 --2.876544841E-01-4.835410318E-01-6.789290723E-01-8.719549075E-01-1.060130884E+00 --1.241341591E+00-1.415079673E+00-1.582658193E+00-1.746308375E+00-1.908115866E+00 --2.069542787E+00-2.231402543E+00-2.394196107E+00-2.558182553E+00-2.723276103E+00 --2.889164023E+00-3.055303032E+00-3.221125900E+00-3.386157568E+00-3.549994172E+00 --3.712324127E+00-3.872897528E+00-4.031528038E+00-4.188058714E+00-4.342376417E+00 --4.494380033E+00-4.643952377E+00-4.790972562E+00-4.935323350E+00-5.076891313E+00 --5.215568262E+00-5.351251360E+00-5.483842517E+00-5.613249239E+00-5.739384300E+00 --5.862159928E+00-5.981483726E+00-6.097252218E+00-6.209345212E+00-6.317605308E+00 --6.421849927E+00-6.521906768E+00-6.617647135E+00-6.708989230E+00-6.795881910E+00 --6.878286947E+00-6.956131007E+00-7.029250893E+00-7.097500334E+00-7.160801321E+00 --7.219133874E+00-7.272336712E+00-7.320361876E+00-7.362985841E+00-7.400308710E+00 --7.432008860E+00-7.458276379E+00-7.478806338E+00-7.493718127E+00-7.502679499E+00 --7.505558845E+00-7.502259442E+00-7.492879517E+00-7.477528704E+00-7.456277044E+00 --7.429143988E+00-7.395836021E+00-7.355889787E+00-7.308958472E+00-7.254875839E+00 --7.193615818E+00-7.125257060E+00-7.049976370E+00-6.968027349E+00-6.879576387E+00 --6.784527266E+00-6.682705790E+00-6.573984583E+00-6.458269731E+00-6.335479382E+00 --6.205550989E+00-6.068450541E+00-5.924180908E+00-5.772779399E+00-5.614298688E+00 --5.448791756E+00-5.276306994E+00-5.096897805E+00-4.910640453E+00-4.717636523E+00 --4.517997049E+00-4.311830879E+00-4.099238552E+00-3.880309347E+00-3.655153243E+00 --3.423954457E+00-3.187056862E+00-2.944989498E+00-2.698406045E+00-2.447957316E+00 --2.194049306E+00-1.936545732E+00-1.674513296E+00-1.405970498E+00-1.128751245E+00 --8.427142835E-01-5.505536526E-01-2.557429193E-01 3.955790889E-02 3.350719544E-01 - 6.310921348E-01 9.276439990E-01 1.224683649E+00 1.522186069E+00 1.820130649E+00 - 2.118498175E+00 2.417271614E+00 2.716435129E+00 3.015975760E+00 3.315892437E+00 - 3.616127236E+00 1.270825438E+00 1.071957557E+00 8.734723592E-01 6.754502016E-01 - 4.779038111E-01 2.808710635E-01 8.441466108E-02-1.117544236E-01-3.086846384E-01 --5.061649240E-01-7.029967178E-01-8.972053996E-01-1.086258256E+00-1.268190012E+00 --1.442779436E+00-1.611577458E+00-1.776895162E+00-1.940740104E+00-2.104449796E+00 --2.268753610E+00-2.434106082E+00-2.600713212E+00-2.768402204E+00-2.936785442E+00 --3.105306571E+00-3.273428601E+00-3.440708361E+00-3.606772099E+00-3.771322910E+00 --3.934128251E+00-4.095017191E+00-4.253843660E+00-4.410494120E+00-4.564861526E+00 --4.716823311E+00-4.866251540E+00-5.013020538E+00-5.157009949E+00-5.298102215E+00 --5.436181724E+00-5.571139532E+00-5.702874924E+00-5.831292860E+00-5.956304668E+00 --6.077826771E+00-6.195775373E+00-6.310059738E+00-6.420574944E+00-6.527192564E+00 --6.629738227E+00-6.728027919E+00-6.821906710E+00-6.911275965E+00-6.996081350E+00 --7.076289358E+00-7.151843422E+00-7.222597049E+00-7.288400052E+00-7.349168426E+00 --7.404870177E+00-7.455365668E+00-7.500582368E+00-7.540365354E+00-7.574712276E+00 --7.603414944E+00-7.626513698E+00-7.643972945E+00-7.655542204E+00-7.661056185E+00 --7.660395936E+00-7.653620512E+00-7.640852840E+00-7.622183441E+00-7.597643141E+00 --7.566901601E+00-7.529466337E+00-7.484993684E+00-7.433344612E+00-7.374530633E+00 --7.308684546E+00-7.236054100E+00-7.156897500E+00-7.071216048E+00-6.978823691E+00 --6.879556945E+00-6.773298498E+00-6.659947015E+00-6.539421219E+00-6.411671847E+00 --6.276690060E+00-6.134499735E+00-5.985135034E+00-5.828632429E+00-5.665033488E+00 --5.494388431E+00-5.316762668E+00-5.132240442E+00-4.940919584E+00-4.742897521E+00 --4.538259966E+00-4.327093151E+00-4.109486068E+00-3.885527461E+00-3.655335284E+00 --3.419117859E+00-3.177263933E+00-2.930344513E+00-2.679031170E+00-2.423978787E+00 --2.165563120E+00-1.903567240E+00-1.636893787E+00-1.363372490E+00-1.080929574E+00 --7.899464558E-01-4.935665066E-01-1.952444869E-01 1.031849595E-01 4.017729791E-01 - 7.007976942E-01 1.000253271E+00 1.300106509E+00 1.600341350E+00 1.900943719E+00 - 2.201901158E+00 2.503202144E+00 2.804837386E+00 3.106807577E+00 3.409061933E+00 - 1.261185553E+00 1.061264448E+00 8.616801073E-01 6.625030846E-01 4.637447799E-01 - 2.654423774E-01 6.764116268E-02-1.300038289E-01-3.284858814E-01-5.274597760E-01 --7.256345554E-01-9.209309593E-01-1.110793158E+00-1.293423067E+00-1.468875074E+00 --1.638902897E+00-1.805865646E+00-1.971684918E+00-2.137582263E+00-2.304218641E+00 --2.472006833E+00-2.641088301E+00-2.811204301E+00-2.981900577E+00-3.152612376E+00 --3.322833371E+00-3.492153820E+00-3.660233095E+00-3.826793115E+00-3.991623238E+00 --4.154570543E+00-4.315500451E+00-4.474298476E+00-4.630851347E+00-4.785032020E+00 --4.936709145E+00-5.085753387E+00-5.232037543E+00-5.375433669E+00-5.515816834E+00 --5.653068449E+00-5.787073869E+00-5.917724960E+00-6.044924155E+00-6.168581120E+00 --6.288612459E+00-6.404939652E+00-6.517483838E+00-6.626156070E+00-6.730848273E+00 --6.831417406E+00-6.927676395E+00-7.019447462E+00-7.106605955E+00-7.189086082E+00 --7.266858668E+00-7.339880298E+00-7.408026126E+00-7.471144511E+00-7.529143196E+00 --7.581976063E+00-7.629517846E+00-7.671689244E+00-7.708419298E+00-7.739511571E+00 --7.765042707E+00-7.784813468E+00-7.798831837E+00-7.806818675E+00-7.808641295E+00 --7.804318490E+00-7.793981013E+00-7.777740981E+00-7.755638420E+00-7.727301274E+00 --7.692209781E+00-7.650032777E+00-7.600668692E+00-7.544181919E+00-7.480783556E+00 --7.410781326E+00-7.334316103E+00-7.251228206E+00-7.161317520E+00-7.064439026E+00 --6.960471517E+00-6.849315071E+00-6.730905465E+00-6.605222760E+00-6.472279083E+00 --6.332094539E+00-6.184690111E+00-6.030091781E+00-5.868341411E+00-5.699503338E+00 --5.523654889E+00-5.340869520E+00-5.151214897E+00-4.954760708E+00-4.751584219E+00 --4.541771384E+00-4.325424542E+00-4.102648968E+00-3.873541817E+00-3.638224855E+00 --3.396921744E+00-3.150061538E+00-2.898256737E+00-2.642208653E+00-2.382576322E+00 --2.119675360E+00-1.853154952E+00-1.581677798E+00-1.302871644E+00-1.014950666E+00 --7.190616262E-01-4.187830385E-01-1.173690308E-01 1.838554771E-01 4.852570955E-01 - 7.870354706E-01 1.089161862E+00 1.391616005E+00 1.694388845E+00 1.997471507E+00 - 2.300855237E+00 2.604533044E+00 2.908506179E+00 3.212730008E+00 1.252242277E+00 - 1.051323086E+00 8.506983284E-01 6.504293606E-01 4.505261765E-01 2.510251794E-01 - 5.195283870E-02-1.470886426E-01-3.470202820E-01-5.473815142E-01-7.467950988E-01 --9.430856411E-01-1.133693547E+00-1.316996694E+00-1.493308463E+00-1.664553242E+00 --1.833112170E+00-2.000819466E+00-2.168792923E+00-2.337637587E+00-2.507726705E+00 --2.679130706E+00-2.851513412E+00-3.024369006E+00-3.197129484E+00-3.369311658E+00 --3.540526517E+00-3.710454674E+00-3.878836388E+00-4.045489025E+00-4.210283987E+00 --4.373101540E+00-4.533828146E+00-4.692348512E+00-4.848537281E+00-5.002263868E+00 --5.153396175E+00-5.301801345E+00-5.447345812E+00-5.589898525E+00-5.729330296E+00 --5.865514394E+00-5.998331651E+00-6.127669678E+00-6.253422372E+00-6.375495905E+00 --6.493805860E+00-6.608275186E+00-6.718831745E+00-6.825402073E+00-6.927897910E+00 --7.026205012E+00-7.120159638E+00-7.209569747E+00-7.294278017E+00-7.374198125E+00 --7.449297746E+00-7.519545838E+00-7.584843260E+00-7.645036360E+00-7.700026842E+00 --7.749761577E+00-7.794137947E+00-7.833037785E+00-7.866433804E+00-7.894111067E+00 --7.916112585E+00-7.932398715E+00-7.942680870E+00-7.946825202E+00-7.944800046E+00 --7.936736118E+00-7.922767302E+00-7.902941847E+00-7.876840040E+00-7.843917683E+00 --7.803869698E+00-7.756645797E+00-7.702387784E+00-7.641402706E+00-7.573970426E+00 --7.500020891E+00-7.419327891E+00-7.331711865E+00-7.237030253E+00-7.135164902E+00 --7.026037741E+00-6.909619015E+00-6.785909339E+00-6.654914872E+00-6.516643450E+00 --6.371111291E+00-6.218356456E+00-6.058435071E+00-5.891406450E+00-5.717320838E+00 --5.536218717E+00-5.348147619E+00-5.153173749E+00-4.951383528E+00-4.742870265E+00 --4.527731998E+00-4.306075033E+00-4.078001387E+00-3.843604567E+00-3.603017459E+00 --3.356503305E+00-3.104557364E+00-2.847849973E+00-2.587124106E+00-2.323027890E+00 --2.055759876E+00-1.784751809E+00-1.508322500E+00-1.223945590E+00-9.304262097E-01 --6.298744800E-01-3.261610067E-01-2.211318432E-02 2.816709956E-01 5.856739950E-01 - 8.899919382E-01 1.194592153E+00 1.499464734E+00 1.804603447E+00 2.110001253E+00 - 2.415652614E+00 2.721559510E+00 3.027684050E+00 1.244067178E+00 1.042200341E+00 - 8.405883542E-01 6.392843271E-01 4.382971814E-01 2.376627207E-01 3.738847143E-02 --1.629715429E-01-3.642546788E-01-5.659004475E-01-7.664506627E-01-9.636436478E-01 --1.154933615E+00-1.338878834E+00-1.516032875E+00-1.688461691E+00-1.858547013E+00 --2.028037031E+00-2.197958025E+00-2.368868660E+00-2.541104109E+00-2.714662983E+00 --2.889143540E+00-3.064003036E+00-3.238674934E+00-3.412695510E+00-3.585691359E+00 --3.757358440E+00-3.927448979E+00-4.095797022E+00-4.262284974E+00-4.426801697E+00 --4.589240689E+00-4.749495635E+00-4.907452481E+00-5.062986664E+00-5.215968947E+00 --5.366268491E+00-5.513751198E+00-5.658281300E+00-5.799722436E+00-5.937940596E+00 --6.072806448E+00-6.204193391E+00-6.331981248E+00-6.456060033E+00-6.576326870E+00 --6.692691698E+00-6.805076732E+00-6.913412141E+00-7.017633375E+00-7.117672147E+00 --7.213438363E+00-7.304806072E+00-7.391590245E+00-7.473604776E+00-7.550730461E+00 --7.622922714E+00-7.690158385E+00-7.752365524E+00-7.809393538E+00-7.861138115E+00 --7.907544382E+00-7.948529425E+00-7.983921962E+00-8.013691315E+00-8.037786356E+00 --8.056088925E+00-8.068498779E+00-8.074802424E+00-8.074915540E+00-8.068964453E+00 --8.057105281E+00-8.039390771E+00-8.015347297E+00-7.984414002E+00-7.946327835E+00 --7.901112044E+00-7.849021378E+00-7.790423548E+00-7.725409619E+00-7.653759231E+00 --7.575251778E+00-7.489719736E+00-7.397026729E+00-7.297081871E+00-7.189847025E+00 --7.075312236E+00-6.953471190E+00-6.824321377E+00-6.687875032E+00-6.544167015E+00 --6.393240015E+00-6.235128571E+00-6.069851715E+00-5.897433243E+00-5.717909031E+00 --5.531330412E+00-5.337762979E+00-5.137289132E+00-4.929999232E+00-4.715983572E+00 --4.495339930E+00-4.268181313E+00-4.034619083E+00-3.794763476E+00-3.548786578E+00 --3.297022254E+00-3.040045352E+00-2.778581206E+00-2.513396573E+00-2.245067250E+00 --1.973588046E+00-1.698067724E+00-1.416400893E+00-1.126107995E+00-8.270040952E-01 --5.222267997E-01-2.156219879E-01 9.068839691E-02 3.968567620E-01 7.032587336E-01 - 1.009911436E+00 1.316792274E+00 1.623896828E+00 1.931221050E+00 2.238761488E+00 - 2.546521211E+00 2.854468634E+00 1.236731791E+00 1.033978656E+00 8.314410135E-01 - 6.291638578E-01 4.271555642E-01 2.254518384E-01 2.404234090E-02-1.775608536E-01 --3.801051010E-01-5.829428080E-01-7.845398122E-01-9.825583567E-01-1.174479740E+00 --1.359040765E+00-1.537013513E+00-1.710578795E+00-1.882102669E+00-2.053252774E+00 --2.224977784E+00-2.397798192E+00-2.572011478E+00-2.747545852E+00-2.923944883E+00 --3.100640813E+00-3.277072795E+00-3.452795451E+00-3.627449782E+00-3.800745140E+00 --3.972444153E+00-4.142392699E+00-4.310478246E+00-4.476589795E+00-4.640617387E+00 --4.802451598E+00-4.961981123E+00-5.119092314E+00-5.273671063E+00-5.425601512E+00 --5.574757776E+00-5.721007354E+00-5.864216524E+00-6.004250586E+00-6.140973502E+00 --6.274249443E+00-6.403947139E+00-6.529941032E+00-6.652110631E+00-6.770346855E+00 --6.884550550E+00-6.994635188E+00-7.100529805E+00-7.202172554E+00-7.299507277E+00 --7.392469831E+00-7.480964798E+00-7.564845897E+00-7.643914214E+00-7.718009593E+00 --7.787060899E+00-7.851048861E+00-7.909925101E+00-7.963545949E+00-8.011806628E+00 --8.054635959E+00-8.091947670E+00-8.123645898E+00-8.149589262E+00-8.169787285E+00 --8.184163144E+00-8.192446511E+00-8.194535901E+00-8.190535052E+00-8.180620384E+00 --8.164844528E+00-8.142675543E+00-8.113547480E+00-8.077260845E+00-8.033952964E+00 --7.984004244E+00-7.927696536E+00-7.864879973E+00-7.795295345E+00-7.718743145E+00 --7.635068057E+00-7.544167474E+00-7.445996137E+00-7.340534560E+00-7.227767049E+00 --7.107685832E+00-6.980303612E+00-6.845648144E+00-6.703740779E+00-6.554582598E+00 --6.398171783E+00-6.234517084E+00-6.063644259E+00-5.885593825E+00-5.700413522E+00 --5.508155903E+00-5.308887128E+00-5.102694740E+00-4.889679633E+00-4.669946653E+00 --4.443614279E+00-4.210818533E+00-3.971686535E+00-3.726349773E+00-3.475027543E+00 --3.218130025E+00-2.956299873E+00-2.690310509E+00-2.420919813E+00-2.148549969E+00 --1.872903062E+00-1.592641634E+00-1.305243187E+00-1.008717663E+00-7.043302058E-01 --3.959951126E-01-8.710241453E-02 2.212252482E-01 5.295923880E-01 8.381831801E-01 - 1.146967607E+00 1.455938404E+00 1.765094415E+00 2.074433965E+00 2.383960339E+00 - 2.693647005E+00 1.230241144E+00 1.026674717E+00 8.232865542E-01 6.201137287E-01 - 4.171637438E-01 2.144716113E-01 1.200974130E-02-1.907454393E-01-3.944517426E-01 --5.983865713E-01-8.009451321E-01-9.997236352E-01-1.192239149E+00-1.377398652E+00 --1.556168278E+00-1.730819772E+00-1.903691999E+00-2.076378986E+00-2.249764316E+00 --2.424335585E+00-2.600351771E+00-2.777675100E+00-2.955806372E+00-3.134163756E+00 --3.312195343E+00-3.489471528E+00-3.665645136E+00-3.840437644E+00-4.013623459E+00 --4.185059848E+00-4.354638608E+00-4.522246840E+00-4.687768727E+00-4.851088863E+00 --5.012092392E+00-5.170664553E+00-5.326690572E+00-5.480055607E+00-5.630643584E+00 --5.778339565E+00-5.923029501E+00-6.064591871E+00-6.202895058E+00-6.337805581E+00 --6.469190715E+00-6.596916205E+00-6.720848927E+00-6.840862084E+00-6.956835271E+00 --7.068658548E+00-7.176235592E+00-7.279483070E+00-7.378336240E+00-7.472742012E+00 --7.562652959E+00-7.648006550E+00-7.728697179E+00-7.804551737E+00-7.875374468E+00 --7.941053638E+00-8.001560530E+00-8.056864552E+00-8.106836994E+00-8.151369636E+00 --8.190379158E+00-8.223792082E+00-8.251525252E+00-8.273466287E+00-8.289565280E+00 --8.299646441E+00-8.303552766E+00-8.301336860E+00-8.293197905E+00-8.279183112E+00 --8.258697889E+00-8.231189567E+00-8.196560397E+00-8.155109294E+00-8.107264716E+00 --8.053042925E+00-7.992167598E+00-7.924397220E+00-7.849555057E+00-7.767527722E+00 --7.678264079E+00-7.581737206E+00-7.477926655E+00-7.366825762E+00-7.248447157E+00 --7.122803116E+00-6.989882014E+00-6.849660154E+00-6.702120335E+00-6.547261582E+00 --6.385095931E+00-6.215642138E+00-6.038928332E+00-5.854996075E+00-5.663898790E+00 --5.465704460E+00-5.260501830E+00-5.048405812E+00-4.829538338E+00-4.604018775E+00 --4.371978910E+00-4.133558306E+00-3.888884601E+00-3.638114546E+00-3.381529782E+00 --3.119632027E+00-2.853132376E+00-2.582852456E+00-2.309482003E+00-2.033181749E+00 --1.753252305E+00-1.467770630E+00-1.174041842E+00-8.712631460E-01-5.622931560E-01 --2.512555735E-01 5.935619494E-02 3.696226766E-01 6.800209153E-01 9.905963519E-01 - 1.301326400E+00 1.612209378E+00 1.923245254E+00 2.234437385E+00 2.545763921E+00 - 1.224567148E+00 1.020263363E+00 8.161039281E-01 6.121186469E-01 4.083140424E-01 - 2.047246066E-01 1.307204107E-03-2.024947156E-01-4.072495417E-01-6.121712375E-01 --8.155922134E-01-1.015054029E+00-1.208116357E+00-1.393845072E+00-1.573375636E+00 --1.749050016E+00-1.923172683E+00-2.097271606E+00-2.272176380E+00-2.448344709E+00 --2.625995981E+00-2.804932308E+00-2.984621332E+00-3.164473758E+00-3.343947270E+00 --3.522624819E+00-3.700169468E+00-3.876315288E+00-4.050850283E+00-4.223641918E+00 --4.394584767E+00-4.563564219E+00-4.730461060E+00-4.895157029E+00-5.057534785E+00 --5.217475917E+00-5.374860849E+00-5.529569636E+00-5.681483481E+00-5.830486796E+00 --5.976466370E+00-6.119308974E+00-6.258902210E+00-6.395136349E+00-6.527898252E+00 --6.657060520E+00-6.782491458E+00-6.904060955E+00-7.021637849E+00-7.135092985E+00 --7.244304193E+00-7.349158983E+00-7.449560840E+00-7.545429258E+00-7.636704476E+00 --7.723342913E+00-7.805305389E+00-7.882526597E+00-7.954883834E+00-8.022180188E+00 --8.084252146E+00-8.141046508E+00-8.192536773E+00-8.238618445E+00-8.279186053E+00 --8.314155588E+00-8.343445154E+00-8.366936717E+00-8.384605314E+00-8.396321961E+00 --8.401874690E+00-8.401275481E+00-8.394741995E+00-8.382304685E+00-8.363305264E+00 --8.337237705E+00-8.304168930E+00-8.264561787E+00-8.218673162E+00-8.166268884E+00 --8.107058950E+00-8.040838982E+00-7.967485742E+00-7.886943894E+00-7.799183293E+00 --7.704184387E+00-7.601945538E+00-7.492471924E+00-7.375746293E+00-7.251727125E+00 --7.120374832E+00-6.981663331E+00-6.835577958E+00-6.682109727E+00-6.521261173E+00 --6.353046964E+00-6.177497273E+00-5.994661000E+00-5.804605961E+00-5.607410720E+00 --5.403163058E+00-5.191967906E+00-4.973947383E+00-4.749223278E+00-4.517918908E+00 --4.280171488E+00-4.036119152E+00-3.785900414E+00-3.529725730E+00-3.267965564E+00 --3.001223660E+00-2.730291522E+00-2.455998574E+00-2.178850118E+00-1.898618869E+00 --1.614048317E+00-1.322600292E+00-1.022055993E+00-7.135219896E-01-4.010407547E-01 --8.817057335E-02 2.239457905E-01 5.360191174E-01 8.482542506E-01 1.160618511E+00 - 1.473106254E+00 1.785718922E+00 2.098460026E+00 2.411311944E+00 1.219674456E+00 - 1.014709557E+00 8.098587346E-01 6.051451648E-01 4.005742123E-01 1.961818707E-01 --8.086898010E-03-2.128303914E-01-4.185186172E-01-6.243134834E-01-8.284940745E-01 --1.028557460E+00-1.222109554E+00-1.408361221E+00-1.588593010E+00-1.765199784E+00 --1.940449021E+00-2.115811664E+00-2.292074681E+00-2.469669708E+00-2.648777795E+00 --2.829149094E+00-3.010226344E+00-3.191416504E+00-3.372185249E+00-3.552123541E+00 --3.730902077E+00-3.908266002E+00-4.084015732E+00-4.258026322E+00-4.430194106E+00 --4.600404112E+00-4.768536608E+00-4.934472940E+00-5.098094808E+00-5.259281727E+00 --5.417911683E+00-5.573862030E+00-5.727010575E+00-5.877237229E+00-6.024423759E+00 --6.168453352E+00-6.309212091E+00-6.446590048E+00-6.580480188E+00-6.710775081E+00 --6.837370455E+00-6.960162204E+00-7.079031194E+00-7.193847930E+00-7.304483791E+00 --7.410811559E+00-7.512705696E+00-7.610049814E+00-7.702742450E+00-7.790703650E+00 --7.873877773E+00-7.952230669E+00-8.025729550E+00-8.094301049E+00-8.157797697E+00 --8.216019129E+00-8.268866798E+00-8.316303375E+00-8.358253183E+00-8.394617931E+00 --8.425311520E+00-8.450215311E+00-8.469266265E+00-8.482405104E+00-8.489422279E+00 --8.490272873E+00-8.485172394E+00-8.474121845E+00-8.456406157E+00-8.431627346E+00 --8.400083404E+00-8.362255970E+00-8.318061452E+00-8.267171427E+00-8.209342567E+00 --8.144441386E+00-8.072411465E+00-7.993226200E+00-7.906872105E+00-7.813349176E+00 --7.712639993E+00-7.604691465E+00-7.489444731E+00-7.366851809E+00-7.236873009E+00 --7.099476114E+00-6.954640292E+00-6.802357355E+00-6.642636816E+00-6.475507436E+00 --6.301010161E+00-6.119197325E+00-5.930133201E+00-5.733892901E+00-5.530559004E+00 --5.320225222E+00-5.103003333E+00-4.879017750E+00-4.648394355E+00-4.411266882E+00 --4.167780046E+00-3.918076293E+00-3.662326434E+00-3.400821025E+00-3.134040767E+00 --2.862689516E+00-2.587639920E+00-2.309620951E+00-2.028786668E+00-1.744392607E+00 --1.454431245E+00-1.156126265E+00-8.488230148E-01-5.356899545E-01-2.209512691E-01 - 9.305575598E-02 4.067033126E-01 7.204443311E-01 1.034302571E+00 1.348259892E+00 - 1.662316641E+00 1.976476242E+00 2.290724572E+00 1.215540574E+00 1.009987873E+00 - 8.045227280E-01 5.991625209E-01 3.939116144E-01 1.888071930E-01-1.621602470E-02 --2.217903085E-01-4.282972540E-01-6.348548424E-01-8.396957683E-01-1.040281626E+00 --1.234265218E+00-1.420986586E+00-1.601848408E+00-1.779284213E+00-1.955524326E+00 --2.131990924E+00-2.309437648E+00-2.488273006E+00-2.668641834E+00-2.850251136E+00 --3.032526942E+00-3.214876856E+00-3.396774833E+00-3.577817648E+00-3.757682606E+00 --3.936125350E+00-4.112956729E+00-4.288055481E+00-4.461316941E+00-4.632625031E+00 --4.801859192E+00-4.968899557E+00-5.133626908E+00-5.295920249E+00-5.455657356E+00 --5.612715519E+00-5.766972143E+00-5.918305451E+00-6.066594708E+00-6.211720312E+00 --6.353564154E+00-6.492010575E+00-6.626948116E+00-6.758268047E+00-6.885864961E+00 --7.009637268E+00-7.129484400E+00-7.245307802E+00-7.357011043E+00-7.464486359E+00 --7.567606447E+00-7.666242862E+00-7.760270734E+00-7.849569084E+00-7.934029619E+00 --8.013567589E+00-8.088128536E+00-8.157686583E+00-8.222212019E+00-8.281617508E+00 --8.335729713E+00-8.384388141E+00-8.427534296E+00-8.465110733E+00-8.497017128E+00 --8.523149784E+00-8.543439642E+00-8.557827083E+00-8.566133219E+00-8.568265324E+00 --8.564421957E+00-8.554558759E+00-8.537930131E+00-8.514347719E+00-8.484324992E+00 --8.448059758E+00-8.405232185E+00-8.355546587E+00-8.298857604E+00-8.235114510E+00 --8.164298575E+00-8.086404777E+00-8.001421275E+00-7.909289651E+00-7.809936088E+00 --7.703293304E+00-7.589300415E+00-7.467905573E+00-7.339068411E+00-7.202764011E+00 --7.058986351E+00-6.907741007E+00-6.749043771E+00-6.582920930E+00-6.409408174E+00 --6.228550386E+00-6.040404099E+00-5.845038418E+00-5.642534496E+00-5.432984236E+00 --5.216492878E+00-4.993181945E+00-4.763179296E+00-4.526617888E+00-4.283641465E+00 --4.034398063E+00-3.779046250E+00-3.517825606E+00-3.251127340E+00-2.979553885E+00 --2.703932663E+00-2.425129886E+00-2.143596274E+00-1.858968696E+00-1.569783587E+00 --1.273310799E+00-9.676201168E-01-6.545456708E-01-3.384447952E-01-2.258922959E-02 - 2.925154769E-01 6.075994488E-01 9.227978233E-01 1.238074150E+00 1.553425680E+00 - 1.868855911E+00 2.184354024E+00 1.212167600E+00 1.006098175E+00 8.000933575E-01 - 5.941655703E-01 3.883183989E-01 1.825892339E-01-2.309638140E-02-2.293927583E-01 --4.366091583E-01-6.438262460E-01-8.492363325E-01-1.050273109E+00-1.244634095E+00 --1.431771466E+00-1.613188902E+00-1.791347531E+00-1.968442440E+00-2.145854620E+00 --2.324311787E+00-2.504201826E+00-2.685636342E+00-2.868287187E+00-3.051569507E+00 --3.234894078E+00-3.417742725E+00-3.599716120E+00-3.780497232E+00-3.959852039E+00 --4.137601441E+00-4.313627136E+00-4.487823825E+00-4.660075570E+00-4.830262183E+00 --4.998263008E+00-5.163956968E+00-5.327220997E+00-5.487931005E+00-5.645962813E+00 --5.801192462E+00-5.953496978E+00-6.102755198E+00-6.248847807E+00-6.391656962E+00 --6.531065987E+00-6.666960593E+00-6.799227948E+00-6.927757541E+00-7.052441410E+00 --7.173176439E+00-7.289863819E+00-7.402407141E+00-7.510712135E+00-7.614684850E+00 --7.714235379E+00-7.809266974E+00-7.899656345E+00-7.985272596E+00-8.065991831E+00 --8.141700355E+00-8.212305046E+00-8.277748618E+00-8.338007901E+00-8.393049916E+00 --8.442771753E+00-8.486989176E+00-8.525604903E+00-8.558559643E+00-8.585758429E+00 --8.607120567E+00-8.622551926E+00-8.631957395E+00-8.635201000E+00-8.632435415E+00 --8.623550257E+00-8.607845115E+00-8.585442209E+00-8.556819841E+00-8.521781090E+00 --8.479979093E+00-8.431251839E+00-8.375560741E+00-8.312898956E+00-8.243263456E+00 --8.166598503E+00-8.082819518E+00-7.991844342E+00-7.893594138E+00-7.788000679E+00 --7.675010658E+00-7.554589473E+00-7.426713644E+00-7.291368169E+00-7.148545960E+00 --6.998247286E+00-6.840480630E+00-6.675265494E+00-6.502632792E+00-6.322624544E+00 --6.135294629E+00-5.940708274E+00-5.738943829E+00-5.530091153E+00-5.314252875E+00 --5.091545058E+00-4.862094797E+00-4.626036719E+00-4.383514002E+00-4.134676881E+00 --3.879682624E+00-3.618737185E+00-3.352179364E+00-3.080520935E+00-2.804502619E+00 --2.525051466E+00-2.242828140E+00-1.957778476E+00-1.668859877E+00-1.373675348E+00 --1.069600363E+00-7.570815125E-01-4.401149176E-01-1.226512773E-01 1.938104592E-01 - 5.100823394E-01 8.264485960E-01 1.142876995E+00 1.459359243E+00 1.775898442E+00 - 2.092486944E+00 1.209579452E+00 1.003065033E+00 7.965954715E-01 5.901789650E-01 - 3.838184873E-01 1.775510542E-01-2.870551532E-02-2.356189195E-01-4.434405905E-01 --6.512203975E-01-8.571166167E-01-1.058541252E+00-1.253231798E+00-1.440734471E+00 --1.622634606E+00-1.801412841E+00-1.979232852E+00-2.157441502E+00-2.336746334E+00 --2.517517116E+00-2.699836154E+00-2.883346903E+00-3.067457129E+00-3.251581846E+00 --3.435209759E+00-3.617943651E+00-3.799471099E+00-3.979567641E+00-4.158063088E+00 --4.334841235E+00-4.509796318E+00-4.682813395E+00-4.853773547E+00-5.022556198E+00 --5.189039707E+00-5.353100565E+00-5.514614405E+00-5.673456755E+00-5.829503324E+00 --5.982630685E+00-6.132716448E+00-6.279639529E+00-6.423280369E+00-6.563520728E+00 --6.700244591E+00-6.833337749E+00-6.962689584E+00-7.088191928E+00-7.209738774E+00 --7.327225975E+00-7.440550860E+00-7.549613881E+00-7.654319607E+00-7.754577824E+00 --7.850299025E+00-7.941392988E+00-8.027773427E+00-8.109352867E+00-8.186015374E+00 --8.257625064E+00-8.324058319E+00-8.385217241E+00-8.441039060E+00-8.491495570E+00 --8.536542792E+00-8.576059613E+00-8.609893673E+00-8.637982556E+00-8.660228222E+00 --8.676548898E+00-8.686861107E+00-8.691038636E+00-8.689164623E+00-8.681050687E+00 --8.666177475E+00-8.644931302E+00-8.617391899E+00-8.583205360E+00-8.542185811E+00 --8.494307850E+00-8.439579015E+00-8.377957330E+00-8.309353508E+00-8.233674048E+00 --8.150824692E+00-8.060726634E+00-7.963323026E+00-7.858568493E+00-7.746423328E+00 --7.626852885E+00-7.499828833E+00-7.365330897E+00-7.223347269E+00-7.073874421E+00 --6.916917396E+00-6.752491976E+00-6.580624871E+00-6.401355277E+00-6.214733879E+00 --6.020824237E+00-5.819702079E+00-5.611455733E+00-5.396186286E+00-5.174005896E+00 --4.945037730E+00-4.709414925E+00-4.467281620E+00-4.218788445E+00-3.964092063E+00 --3.703382999E+00-3.436963815E+00-3.165284559E+00-2.889003547E+00-2.609037332E+00 --2.326193280E+00-2.040666252E+00-1.751718629E+00-1.457337837E+00-1.154645468E+00 --8.429377261E-01-5.255433934E-01-2.068360808E-01 1.108867460E-01 4.281945663E-01 - 7.455444454E-01 1.062947650E+00 1.380387475E+00 1.697865458E+00 2.015376855E+00 - 1.207814594E+00 1.000929519E+00 7.940727993E-01 5.872491297E-01 3.804610014E-01 - 1.737447650E-01-3.298776847E-02-2.404114672E-01-4.487337006E-01-6.569804109E-01 --8.632828801E-01-1.065036879E+00-1.260012981E+00-1.447832089E+00-1.630142851E+00 --1.809439619E+00-1.987860217E+00-2.166724490E+00-2.346724682E+00-2.528215370E+00 --2.711254404E+00-2.895462568E+00-3.080241960E+00-3.265011939E+00-3.449266961E+00 --3.632610449E+00-3.814733268E+00-3.995419011E+00-4.174504548E+00-4.351874681E+00 --4.527422962E+00-4.701035476E+00-4.872594581E+00-5.041979902E+00-5.209069731E+00 --5.373740848E+00-5.535869399E+00-5.695331463E+00-5.852003298E+00-6.005761996E+00 --6.156485475E+00-6.304052916E+00-6.448345052E+00-6.589243930E+00-6.726633660E+00 --6.860399844E+00-6.990430748E+00-7.116616344E+00-7.238848454E+00-7.357020450E+00 --7.471027438E+00-7.580766989E+00-7.686139814E+00-7.787049951E+00-7.883402812E+00 --7.975106797E+00-8.062072784E+00-8.144214241E+00-8.221442846E+00-8.293672208E+00 --8.360820394E+00-8.422783066E+00-8.479421697E+00-8.530618191E+00-8.576303798E+00 --8.616443256E+00-8.650985521E+00-8.679783499E+00-8.702746764E+00-8.719787733E+00 --8.730812748E+00-8.735744438E+00-8.734568098E+00-8.727051887E+00-8.712994631E+00 --8.692667475E+00-8.665822463E+00-8.632255852E+00-8.591950912E+00-8.544897939E+00 --8.491011753E+00-8.430188506E+00-8.362323437E+00-8.287339624E+00-8.205176445E+00 --8.115774953E+00-8.019080074E+00-7.915043677E+00-7.803623411E+00-7.684780645E+00 --7.558482404E+00-7.424703631E+00-7.283429038E+00-7.134652139E+00-6.978376741E+00 --6.814616303E+00-6.643394822E+00-6.464747196E+00-6.278720353E+00-6.085374780E+00 --5.884783159E+00-5.677032049E+00-5.462220840E+00-5.240461630E+00-5.011875752E+00 --4.776594489E+00-4.534763844E+00-4.286536218E+00-4.032068011E+00-3.771543648E+00 --3.505237942E+00-3.233564857E+00-2.957118699E+00-2.676766506E+00-2.393412157E+00 --2.107437356E+00-1.818329248E+00-1.524400354E+00-1.222763982E+00-9.119012482E-01 --5.943909480E-01-2.747832206E-01 4.402882776E-02 3.621962925E-01 6.803404547E-01 - 9.985337086E-01 1.316750128E+00 1.634989168E+00 1.953248581E+00 1.206882195E+00 - 9.997070009E-01 7.925471531E-01 5.854045794E-01 3.782813604E-01 1.712130483E-01 --3.589268231E-02-2.437132167E-01-4.524252840E-01-6.610380808E-01-8.676635546E-01 --1.069686195E+00-1.264901000E+00-1.452982893E+00-1.635625804E+00-1.815333336E+00 --1.994224279E+00-2.173598995E+00-2.354139274E+00-2.536188310E+00-2.719785379E+00 --2.904534360E+00-3.089833016E+00-3.275104729E+00-3.459848444E+00-3.643667026E+00 --3.826253204E+00-4.007396725E+00-4.186939546E+00-4.364766580E+00-4.540770342E+00 --4.714837297E+00-4.886850380E+00-5.056689076E+00-5.224231355E+00-5.389353927E+00 --5.551933051E+00-5.711845046E+00-5.868966519E+00-6.023175044E+00-6.174349180E+00 --6.322368943E+00-6.467116049E+00-6.608473742E+00-6.746327296E+00-6.880563307E+00 --7.011070675E+00-7.137739811E+00-7.260463293E+00-7.379135384E+00-7.493652071E+00 --7.603911172E+00-7.709811798E+00-7.811254892E+00-7.908142321E+00-8.000377075E+00 --8.087862640E+00-8.170504879E+00-8.248215262E+00-8.320909580E+00-8.388503897E+00 --8.450908681E+00-8.508030604E+00-8.559786645E+00-8.606091188E+00-8.646815855E+00 --8.681847833E+00-8.711139344E+00-8.734650963E+00-8.752231875E+00-8.763802783E+00 --8.769291941E+00-8.768624980E+00-8.761587739E+00-8.748229689E+00-8.728451252E+00 --8.702076669E+00-8.669087737E+00-8.629420026E+00-8.582965639E+00-8.529626185E+00 --8.469326245E+00-8.401992985E+00-8.327557959E+00-8.245958388E+00-8.157133295E+00 --8.061024417E+00-7.957579423E+00-7.846751577E+00-7.728499815E+00-7.602787772E+00 --7.469586923E+00-7.328877897E+00-7.180650843E+00-7.024906561E+00-6.861655870E+00 --6.690921519E+00-6.512737177E+00-6.327149536E+00-6.134217806E+00-5.934013908E+00 --5.726623507E+00-5.512145214E+00-5.290691848E+00-5.062384194E+00-4.827351628E+00 --4.585740302E+00-4.337704905E+00-4.083402027E+00-3.823012436E+00-3.556792539E+00 --3.285135275E+00-3.008590221E+00-2.727970428E+00-2.444234055E+00-2.157891928E+00 --1.868596189E+00-1.574893650E+00-1.273991883E+00-9.638545859E-01-6.464001772E-01 --3.261815289E-01-6.512047899E-03 3.123118791E-01 6.310552885E-01 9.498474583E-01 - 1.268652662E+00 1.587468551E+00 1.906294884E+00 1.206732649E+00 9.993502974E-01 - 7.919741747E-01 5.846042717E-01 3.772423572E-01 1.699232489E-01-3.744757119E-02 --2.455466207E-01-4.545326117E-01-6.634050714E-01-8.702644300E-01-1.072488430E+00 --1.267886991E+00-1.456168093E+00-1.639053430E+00-1.819052181E+00-1.998271344E+00 --2.177999305E+00-2.358912019E+00-2.541345537E+00-2.725326880E+00-2.910448909E+00 --3.096106466E+00-3.281726499E+00-3.466811283E+00-3.650962461E+00-3.833873465E+00 --4.015338513E+00-4.195203134E+00-4.373352090E+00-4.549677063E+00-4.724064750E+00 --4.896398412E+00-5.066557327E+00-5.234419055E+00-5.399859943E+00-5.562755944E+00 --5.722983170E+00-5.880418065E+00-6.034938062E+00-6.186421577E+00-6.334748514E+00 --6.479800469E+00-6.621460645E+00-6.759614463E+00-6.894148899E+00-7.024953461E+00 --7.151919340E+00-7.274940082E+00-7.393911059E+00-7.508729520E+00-7.619294592E+00 --7.725506696E+00-7.827268142E+00-7.924482409E+00-8.017054353E+00-8.104889181E+00 --8.187892805E+00-8.265972269E+00-8.339034933E+00-8.406987874E+00-8.469739136E+00 --8.527199829E+00-8.579283817E+00-8.625904288E+00-8.666962390E+00-8.702371108E+00 --8.732068171E+00-8.755934599E+00-8.773861488E+00-8.785800005E+00-8.791653891E+00 --8.791334281E+00-8.784693311E+00-8.771712971E+00-8.752284218E+00-8.726318735E+00 --8.693729897E+00-8.654433732E+00-8.608344325E+00-8.555383433E+00-8.495479178E+00 --8.428560908E+00-8.354555769E+00-8.273392296E+00-8.185003496E+00-8.089327755E+00 --7.986309185E+00-7.875897828E+00-7.758050592E+00-7.632730805E+00-7.499910374E+00 --7.359569360E+00-7.211697664E+00-7.056295071E+00-6.893371944E+00-6.722950441E+00 --6.545063825E+00-6.359758724E+00-6.167093619E+00-5.967140271E+00-5.759983601E+00 --5.545721868E+00-5.324468000E+00-5.096342755E+00-4.861474065E+00-4.620007072E+00 --4.372098268E+00-4.117904574E+00-3.857604145E+00-3.591443454E+00-3.319802337E+00 --3.043203202E+00-2.762418600E+00-2.478430403E+00-2.191830541E+00-1.902381743E+00 --1.608778608E+00-1.308332017E+00-9.987157659E-01-6.813705982E-01-3.607796074E-01 --4.051862448E-02 2.787455926E-01 5.978899706E-01 9.170852652E-01 1.236286669E+00 - 1.555490627E+00 1.874698338E+00 1.207332111E+00 9.998250149E-01 7.923190259E-01 - 5.848130623E-01 3.773087030E-01 1.698402073E-01-3.768720622E-02-2.459466296E-01 --4.550907844E-01-6.641164095E-01-8.711200982E-01-1.073476903E+00-1.269001678E+00 --1.457414611E+00-1.640448304E+00-1.820614416E+00-2.000015509E+00-2.179935292E+00 --2.361048152E+00-2.543687262E+00-2.727873673E+00-2.913194926E+00-3.099044257E+00 --3.284851342E+00-3.470120525E+00-3.654451784E+00-3.837538082E+00-4.019176288E+00 --4.199214069E+00-4.377535969E+00-4.554033174E+00-4.728592622E+00-4.901097899E+00 --5.071428298E+00-5.239461264E+00-5.405072971E+00-5.568139204E+00-5.728535986E+00 --5.886139710E+00-6.040827742E+00-6.192478408E+00-6.340971521E+00-6.486188574E+00 --6.628012670E+00-6.766329163E+00-6.901025015E+00-7.031989737E+00-7.159114500E+00 --7.282292827E+00-7.401420046E+00-7.516393382E+00-7.627111992E+00-7.733476479E+00 --7.835389375E+00-7.932754341E+00-8.025476607E+00-8.113462276E+00-8.196618403E+00 --8.274852677E+00-8.348073146E+00-8.416188409E+00-8.479107558E+00-8.536740127E+00 --8.588995640E+00-8.635785306E+00-8.677023869E+00-8.712627087E+00-8.742504482E+00 --8.766551088E+00-8.784675905E+00-8.796799542E+00-8.802830417E+00-8.802680236E+00 --8.796255275E+00-8.783463387E+00-8.764228085E+00-8.738473614E+00-8.706103796E+00 --8.667031751E+00-8.621176440E+00-8.568457288E+00-8.508794723E+00-8.442112060E+00 --8.368335195E+00-8.287393776E+00-8.199221439E+00-8.103756847E+00-8.000943779E+00 --7.890732191E+00-7.773078722E+00-7.647946958E+00-7.515309050E+00-7.375145056E+00 --7.227444990E+00-7.072208305E+00-6.909445348E+00-6.739177817E+00-6.561438674E+00 --6.376274178E+00-6.183742334E+00-5.983914697E+00-5.776875703E+00-5.562723455E+00 --5.341570741E+00-5.113538409E+00-4.878753664E+00-4.637360842E+00-4.389517396E+00 --4.135380447E+00-3.875126887E+00-3.608999360E+00-3.337370746E+00-3.060750593E+00 --2.779890433E+00-2.495779447E+00-2.209049241E+00-1.919518466E+00-1.625953589E+00 --1.325727751E+00-1.016387905E+00-6.991237857E-01-3.783622959E-01-5.780710341E-02 - 2.616826076E-01 5.810281207E-01 9.004242439E-01 1.219823241E+00 1.539220750E+00 - 1.858618641E+00 1.208690361E+00 1.001141620E+00 7.935929115E-01 5.860429557E-01 - 3.784932692E-01 1.709777522E-01-3.659671657E-02-2.448974281E-01-4.540831595E-01 --6.631548028E-01-8.702128816E-01-1.072633716E+00-1.268226757E+00-1.456703222E+00 --1.639789726E+00-1.819997522E+00-1.999432314E+00-2.179380500E+00-2.360519111E+00 --2.543182757E+00-2.727392856E+00-2.912737421E+00-3.098609406E+00-3.284440040E+00 --3.469734312E+00-3.654090261E+00-3.837199209E+00-4.018858688E+00-4.198916989E+00 --4.377258348E+00-4.553773703E+00-4.728350148E+00-4.900871507E+00-5.071217224E+00 --5.239264828E+00-5.404890479E+00-5.567969917E+00-5.728379183E+00-5.885994722E+00 --6.040693932E+00-6.192355162E+00-6.340858239E+00-6.486084679E+00-6.627917599E+00 --6.766242360E+00-6.900945916E+00-7.031917758E+00-7.159049026E+00-7.282233188E+00 --7.401365506E+00-7.516343114E+00-7.627065071E+00-7.733431875E+00-7.835346000E+00 --7.932711094E+00-8.025432405E+00-8.113416212E+00-8.196569936E+00-8.274801957E+00 --8.348021433E+00-8.416138146E+00-8.479061571E+00-8.536700821E+00-8.588965080E+00 --8.635762935E+00-8.677003834E+00-8.712602246E+00-8.742473569E+00-8.766527496E+00 --8.784663088E+00-8.796790500E+00-8.802827523E+00-8.802682981E+00-8.796263642E+00 --8.783478875E+00-8.764250957E+00-8.738503553E+00-8.706141606E+00-8.667077034E+00 --8.621228536E+00-8.568515830E+00-8.508860229E+00-8.442185145E+00-8.368416130E+00 --8.287482737E+00-8.199318545E+00-8.103862137E+00-8.001057241E+00-7.890853837E+00 --7.773208610E+00-7.648085199E+00-7.515455784E+00-7.375300435E+00-7.227609169E+00 --7.072381432E+00-6.909627575E+00-6.739369285E+00-6.561639519E+00-6.376484533E+00 --6.183962313E+00-5.984144386E+00-5.777115208E+00-5.562972929E+00-5.341830288E+00 --5.113808038E+00-4.879033317E+00-4.637650501E+00-4.389817086E+00-4.135690059E+00 --3.875446671E+00-3.609330089E+00-3.337712494E+00-3.061102622E+00-2.780251658E+00 --2.496149022E+00-2.209426828E+00-1.919904914E+00-1.626351777E+00-1.326142377E+00 --1.016820705E+00-6.995701015E-01-3.788157312E-01-5.826428380E-02 2.612203316E-01 - 5.805603359E-01 8.999512136E-01 1.219345180E+00 1.538737843E+00 1.858131045E+00 - 1.210828634E+00 1.003322671E+00 7.958197759E-01 5.883193666E-01 3.808230291E-01 - 1.733644640E-01-3.414588414E-02-2.423667779E-01-4.514754486E-01-6.604840352E-01 --8.675049275E-01-1.069919925E+00-1.265522740E+00-1.453993998E+00-1.637036873E+00 --1.817159116E+00-1.996477271E+00-2.176287990E+00-2.357275296E+00-2.539779554E+00 --2.723828910E+00-2.909017999E+00-3.094741001E+00-3.280429269E+00-3.465586844E+00 --3.649809708E+00-3.832786479E+00-4.014313271E+00-4.194237409E+00-4.372442728E+00 --4.548820176E+00-4.723256922E+00-4.895636937E+00-5.065839895E+00-5.233743539E+00 --5.399224138E+00-5.562157498E+00-5.722419750E+00-5.879887448E+00-6.034438077E+00 --6.185950059E+00-6.334303276E+00-6.479379305E+00-6.621061312E+00-6.759234726E+00 --6.893786604E+00-7.024606575E+00-7.151585935E+00-7.274618301E+00-7.393599171E+00 --7.508425990E+00-7.618998252E+00-7.725216864E+00-7.826984471E+00-7.924204643E+00 --8.016782520E+00-8.104624177E+00-8.187636345E+00-8.265726244E+00-8.338802300E+00 --8.406774247E+00-8.469550382E+00-8.527039087E+00-8.579150700E+00-8.625794758E+00 --8.666875446E+00-8.702293060E+00-8.731981136E+00-8.755870341E+00-8.773820098E+00 --8.785774432E+00-8.791646637E+00-8.791346388E+00-8.784715859E+00-8.771753846E+00 --8.752347576E+00-8.726403009E+00-8.693839203E+00-8.654565100E+00-8.608495508E+00 --8.555556201E+00-8.495675552E+00-8.428781820E+00-8.354801325E+00-8.273662486E+00 --8.185298484E+00-8.089647801E+00-7.986654775E+00-7.876269680E+00-7.758449410E+00 --7.633157117E+00-7.500364611E+00-7.360051884E+00-7.212208767E+00-7.056834973E+00 --6.893940827E+00-6.723548464E+00-6.545691160E+00-6.360415561E+00-6.167780116E+00 --5.967856543E+00-5.760729857E+00-5.546498448E+00-5.325275115E+00-5.097180382E+00 --4.862342017E+00-4.620905300E+00-4.373026793E+00-4.118863056E+00-3.858593399E+00 --3.592465546E+00-3.320857181E+00-3.044288462E+00-2.763530928E+00-2.479567293E+00 --2.192991127E+00-1.903568935E+00-1.610001638E+00-1.309605158E+00-1.000043150E+00 --6.827372183E-01-3.621661165E-01-4.191514956E-02 2.773338471E-01 5.964621824E-01 - 9.156424111E-01 1.234829361E+00 1.554019410E+00 1.873213675E+00 1.213757514E+00 - 1.006378842E+00 7.990103500E-01 5.916530391E-01 3.843087025E-01 1.770108940E-01 --3.032456420E-02-2.383444180E-01-4.472571928E-01-6.560934169E-01-8.629852649E-01 --1.065324636E+00-1.260879726E+00-1.449278932E+00-1.632183963E+00-1.812095459E+00 --1.991148372E+00-2.170657356E+00-2.351317992E+00-2.533480549E+00-2.717186128E+00 --2.902042494E+00-3.087446880E+00-3.272829173E+00-3.457690650E+00-3.641625237E+00 --3.824318011E+00-4.005561561E+00-4.185200550E+00-4.363118284E+00-4.539206036E+00 --4.713351034E+00-4.885437325E+00-5.055344891E+00-5.222951825E+00-5.388134676E+00 --5.550769483E+00-5.710732597E+00-5.867900794E+00-6.022151768E+00-6.173364192E+00 --6.321418214E+00-6.466195742E+00-6.607580290E+00-6.745457649E+00-6.879715117E+00 --7.010242383E+00-7.136930796E+00-7.259673957E+00-7.378367378E+00-7.492908608E+00 --7.603197397E+00-7.709134610E+00-7.810621571E+00-7.907559271E+00-7.999850026E+00 --8.087397010E+00-8.170104395E+00-8.247876979E+00-8.320619591E+00-8.388241095E+00 --8.450657721E+00-8.507790165E+00-8.559547238E+00-8.605845550E+00-8.646606791E+00 --8.681698287E+00-8.711019812E+00-8.734553773E+00-8.752162031E+00-8.763759939E+00 --8.769279651E+00-8.768653953E+00-8.761628131E+00-8.748290325E+00-8.728544071E+00 --8.702206702E+00-8.669256835E+00-8.629623349E+00-8.583204632E+00-8.529909084E+00 --8.469650982E+00-8.402357882E+00-8.327964044E+00-8.246404630E+00-8.157618135E+00 --8.061548100E+00-7.958143848E+00-7.847359117E+00-7.729152553E+00-7.603487194E+00 --7.470334249E+00-7.329674273E+00-7.181497281E+00-7.025803862E+00-6.862604623E+00 --6.691922109E+00-6.513789863E+00-6.328254549E+00-6.135375298E+00-5.935223975E+00 --5.727886368E+00-5.513461211E+00-5.292061144E+00-5.063806651E+00-4.828826932E+00 --4.587268376E+00-4.339285623E+00-4.085034882E+00-3.824698950E+00-3.558535304E+00 --3.286933355E+00-3.010439505E+00-2.729865230E+00-2.446170434E+00-2.159869077E+00 --1.870620055E+00-1.576981292E+00-1.276166916E+00-9.661201843E-01-6.487285777E-01 --3.285410703E-01-8.888115721E-03 3.099092950E-01 6.286256090E-01 9.473926354E-01 - 1.266173759E+00 1.584966550E+00 1.903770623E+00 1.217444530E+00 1.010275327E+00 - 8.031274050E-01 5.960042191E-01 3.889079209E-01 1.818718202E-01-2.518128176E-02 --2.328816134E-01-4.414820370E-01-6.500383785E-01-8.567101063E-01-1.058904282E+00 --1.254355122E+00-1.442618042E+00-1.625295020E+00-1.804875195E+00-1.983518912E+00 --2.162566568E+00-2.342730040E+00-2.524373264E+00-2.707556130E+00-2.891906306E+00 --3.076826363E+00-3.261743118E+00-3.446153020E+00-3.629647992E+00-3.811909105E+00 --3.992723371E+00-4.171930951E+00-4.349414405E+00-4.525065717E+00-4.698772285E+00 --4.870418290E+00-5.039884194E+00-5.207048699E+00-5.371788974E+00-5.533981626E+00 --5.693503386E+00-5.850231249E+00-6.004043116E+00-6.154817977E+00-6.302436342E+00 --6.446780509E+00-6.587734301E+00-6.725183613E+00-6.859015201E+00-6.989117437E+00 --7.115380193E+00-7.237695235E+00-7.355955724E+00-7.470056299E+00-7.579893329E+00 --7.685364182E+00-7.786368162E+00-7.882805647E+00-7.974578332E+00-8.061590025E+00 --8.143753034E+00-8.220989444E+00-8.293217579E+00-8.360345790E+00-8.422294056E+00 --8.478977164E+00-8.530258176E+00-8.576018316E+00-8.616201002E+00-8.650771932E+00 --8.679609784E+00-8.702612113E+00-8.719694336E+00-8.730757554E+00-8.735725693E+00 --8.734617493E+00-8.727124140E+00-8.713080590E+00-8.692786789E+00-8.665987466E+00 --8.632471167E+00-8.592219644E+00-8.545222749E+00-8.491390559E+00-8.430613440E+00 --8.362802426E+00-8.287882274E+00-8.205783442E+00-8.116444937E+00-8.019813499E+00 --7.915840001E+00-7.804479825E+00-7.685694777E+00-7.559454027E+00-7.425734026E+00 --7.284520438E+00-7.135807289E+00-6.979598558E+00-6.815907667E+00-6.644758150E+00 --6.466184327E+00-6.280232799E+00-6.086963815E+00-5.886449754E+00-5.678777035E+00 --5.464044851E+00-5.242364874E+00-5.013857908E+00-4.778654954E+00-4.536902244E+00 --4.288751925E+00-4.034360360E+00-3.773914530E+00-3.507689094E+00-3.236093699E+00 --2.959719222E+00-2.679430904E+00-2.396135522E+00-2.110220263E+00-1.821182304E+00 --1.527350319E+00-1.225841833E+00-9.151036187E-01-5.976751073E-01-2.781088490E-01 - 4.067572725E-02 3.588051812E-01 6.769102065E-01 9.950665778E-01 1.313247693E+00 - 1.631452874E+00 1.949679645E+00 1.221836229E+00 1.014957217E+00 8.081145182E-01 - 6.013149087E-01 3.945610639E-01 1.878857260E-01-1.878001323E-02-2.260438053E-01 --4.342163268E-01-6.423853565E-01-8.487446710E-01-1.050722226E+00-1.246011585E+00 --1.434075573E+00-1.616437738E+00-1.795570131E+00-1.973664580E+00-2.152094980E+00 --2.331594542E+00-2.512544162E+00-2.695027878E+00-2.878700372E+00-3.062972509E+00 --3.247266678E+00-3.431072202E+00-3.613979080E+00-3.795664470E+00-3.975907982E+00 --4.154543333E+00-4.331451985E+00-4.506526989E+00-4.679656021E+00-4.850723365E+00 --5.019609990E+00-5.186195243E+00-5.350356988E+00-5.511972454E+00-5.670918546E+00 --5.827071813E+00-5.980309535E+00-6.130509887E+00-6.277552109E+00-6.421316842E+00 --6.561685897E+00-6.698542920E+00-6.831772659E+00-6.961261770E+00-7.086898138E+00 --7.208571918E+00-7.326175968E+00-7.439605109E+00-7.548756091E+00-7.653527451E+00 --7.753825108E+00-7.849562270E+00-7.940653893E+00-8.027012492E+00-8.108550425E+00 --8.185190282E+00-8.256845436E+00-8.323380265E+00-8.384657190E+00-8.440580378E+00 --8.491098279E+00-8.536178623E+00-8.575741968E+00-8.609623075E+00-8.637759255E+00 --8.660060338E+00-8.676432708E+00-8.686785933E+00-8.691010867E+00-8.689236391E+00 --8.681167744E+00-8.666297387E+00-8.645083015E+00-8.617590599E+00-8.583461673E+00 --8.542507377E+00-8.494698878E+00-8.440039575E+00-8.378490216E+00-8.309959689E+00 --8.234344286E+00-8.151557334E+00-8.061533278E+00-7.964215157E+00-7.859551289E+00 --7.747496679E+00-7.628014837E+00-7.501077780E+00-7.366664548E+00-7.224762605E+00 --7.075369060E+00-6.918490748E+00-6.754145107E+00-6.582359500E+00-6.403173511E+00 --6.216638340E+00-6.022818041E+00-5.821788382E+00-5.613637589E+00-5.398466488E+00 --5.176386646E+00-4.947520496E+00-4.712000626E+00-4.469971022E+00-4.221581843E+00 --3.966989894E+00-3.706387142E+00-3.440074388E+00-3.168497287E+00-2.892310500E+00 --2.612429172E+00-2.329664815E+00-2.044220986E+00-1.755373779E+00-1.461130846E+00 --1.158609670E+00-8.470552566E-01-5.297556717E-01-2.110984318E-01 1.065828360E-01 - 4.238387565E-01 7.411364929E-01 1.058490384E+00 1.375883049E+00 1.693315847E+00 - 2.010783696E+00 1.226898423E+00 1.020389853E+00 8.139364849E-01 6.075492669E-01 - 4.012315847E-01 1.950148816E-01-1.116056342E-02-2.178708863E-01-4.254996299E-01 --6.331730113E-01-8.391255929E-01-1.040812877E+00-1.235883128E+00-1.423688068E+00 --1.605653337E+00-1.784226720E+00-1.961636607E+00-2.139298338E+00-2.317972064E+00 --2.498058492E+00-2.679670668E+00-2.862497784E+00-3.045962691E+00-3.229482288E+00 --3.412536018E+00-3.594711692E+00-3.775683137E+00-3.955220905E+00-4.133149995E+00 --4.309349923E+00-4.483714776E+00-4.656132039E+00-4.826485202E+00-4.994654688E+00 --5.160519264E+00-5.323956147E+00-5.484841832E+00-5.643052394E+00-5.798463540E+00 --5.950951480E+00-6.100393127E+00-6.246666163E+00-6.389649620E+00-6.529223890E+00 --6.665272188E+00-6.797680049E+00-6.926335274E+00-7.051126992E+00-7.171948214E+00 --7.288697772E+00-7.401277999E+00-7.509594497E+00-7.613554080E+00-7.713066765E+00 --7.808045908E+00-7.898410144E+00-7.984070594E+00-8.064898063E+00-8.140753736E+00 --8.211515191E+00-8.277088159E+00-8.337424159E+00-8.392500442E+00-8.442261221E+00 --8.486538828E+00-8.525218530E+00-8.558230356E+00-8.585495125E+00-8.606920871E+00 --8.622410660E+00-8.631862149E+00-8.635164184E+00-8.632528777E+00-8.623719028E+00 --8.608017820E+00-8.585633328E+00-8.557059448E+00-8.522078441E+00-8.480346982E+00 --8.431700105E+00-8.376091577E+00-8.313517556E+00-8.243970254E+00-8.167395606E+00 --8.083708441E+00-7.992816897E+00-7.894643229E+00-7.789130615E+00-7.676236306E+00 --7.555924732E+00-7.428167292E+00-7.292942655E+00-7.150238513E+00-7.000053956E+00 --6.842398404E+00-6.677291600E+00-6.504764312E+00-6.324859122E+00-6.137631220E+00 --5.943147208E+00-5.741486041E+00-5.532737948E+00-5.317006260E+00-5.094407753E+00 --4.865069930E+00-4.629127262E+00-4.386722816E+00-4.138006906E+00-3.883136232E+00 --3.622315895E+00-3.355883185E+00-3.084345927E+00-2.808440380E+00-2.529093756E+00 --2.246972825E+00-1.962035327E+00-1.673256367E+00-1.378259443E+00-1.074399362E+00 --7.620556176E-01-4.451933406E-01-1.277903153E-01 1.886068806E-01 5.048071446E-01 - 8.211042955E-01 1.137467272E+00 1.453887146E+00 1.770366863E+00 2.086898267E+00 - 1.232619460E+00 1.026560908E+00 8.205801590E-01 6.146931251E-01 4.089040418E-01 - 2.032424366E-01-2.341279062E-03-2.083836104E-01-4.153537017E-01-6.224232380E-01 --8.278740414E-01-1.029196717E+00-1.223991762E+00-1.411482462E+00-1.592976104E+00 --1.770887114E+00-1.947484264E+00-2.124232571E+00-2.301925459E+00-2.480985825E+00 --2.661559902E+00-2.843378999E+00-3.025882070E+00-3.208479631E+00-3.390637656E+00 --3.571940306E+00-3.752058278E+00-3.930750971E+00-4.107831479E+00-4.283175524E+00 --4.456678068E+00-4.628226262E+00-4.797702316E+00-4.964985661E+00-5.129954210E+00 --5.292484496E+00-5.452452395E+00-5.609733224E+00-5.764201905E+00-5.915734361E+00 --6.064208413E+00-6.209503301E+00-6.351499517E+00-6.490079129E+00-6.625129022E+00 --6.756539670E+00-6.884203743E+00-7.008016036E+00-7.127873820E+00-7.243678505E+00 --7.355337135E+00-7.462758779E+00-7.565856010E+00-7.664536501E+00-7.758675262E+00 --7.848136641E+00-7.932792298E+00-8.012522502E+00-8.087234947E+00-8.156880822E+00 --8.221442459E+00-8.280882034E+00-8.335057082E+00-8.383790027E+00-8.427013145E+00 --8.464652568E+00-8.496628750E+00-8.522845537E+00-8.543216244E+00-8.557660125E+00 --8.566011950E+00-8.568218435E+00-8.564535847E+00-8.554781975E+00-8.538170105E+00 --8.514587031E+00-8.484609739E+00-8.448406544E+00-8.405647155E+00-8.356045323E+00 --8.299452606E+00-8.235807109E+00-8.165092429E+00-8.087304696E+00-8.002428723E+00 --7.910407048E+00-7.811165510E+00-7.704626982E+00-7.590728542E+00-7.469424799E+00 --7.340688820E+00-7.204504161E+00-7.060862334E+00-6.909763717E+00-6.751217956E+00 --6.585244412E+00-6.411875776E+00-6.231157460E+00-6.043147517E+00-5.847915172E+00 --5.645541212E+00-5.436118431E+00-5.219753520E+00-4.996569197E+00-4.766693874E+00 --4.530260456E+00-4.287413757E+00-4.038301806E+00-3.783080026E+00-3.521987927E+00 --3.255418364E+00-2.983970474E+00-2.708467147E+00-2.429777700E+00-2.148362901E+00 --1.863873993E+00-1.574869673E+00-1.278632644E+00-9.731865744E-01-6.602937296E-01 --3.443007975E-01-2.851838526E-02 2.864936928E-01 6.014833509E-01 9.165927216E-01 - 1.231784001E+00 1.547054135E+00 1.862406628E+00 2.177830048E+00 1.238996446E+00 - 1.033466034E+00 8.280396019E-01 6.227387324E-01 4.175684529E-01 2.125577519E-01 - 7.669775607E-03-1.975981382E-01-4.037978629E-01-6.101560902E-01-8.150103039E-01 --1.015894584E+00-1.210361541E+00-1.397490123E+00-1.578447769E+00-1.755603937E+00 --1.931269374E+00-2.106966662E+00-2.283529084E+00-2.461403067E+00-2.640770605E+00 --2.821412052E+00-3.002787499E+00-3.184301897E+00-3.365404960E+00-3.545675177E+00 --3.724780608E+00-3.902468444E+00-4.078537728E+00-4.252858375E+00-4.425325514E+00 --4.595825959E+00-4.764240826E+00-4.930448794E+00-5.094327545E+00-5.255754708E+00 --5.414608079E+00-5.570764750E+00-5.724101117E+00-5.874495458E+00-6.021829455E+00 --6.165986454E+00-6.306850935E+00-6.444308720E+00-6.578247904E+00-6.708558997E+00 --6.835138121E+00-6.957887667E+00-7.076709664E+00-7.191510545E+00-7.302193456E+00 --7.408635232E+00-7.510702197E+00-7.608264068E+00-7.701192945E+00-7.789372766E+00 --7.872715002E+00-7.951167544E+00-8.024708200E+00-8.093310049E+00-8.156863925E+00 --8.215171238E+00-8.268108947E+00-8.315629832E+00-8.357653023E+00-8.394096221E+00 --8.424861610E+00-8.449851012E+00-8.468997189E+00-8.482204531E+00-8.489270649E+00 --8.490215297E+00-8.485305693E+00-8.474398931E+00-8.456721197E+00-8.431935344E+00 --8.400416212E+00-8.362655213E+00-8.318533344E+00-8.267722582E+00-8.209991034E+00 --8.145202334E+00-8.073286787E+00-7.994216034E+00-7.907983553E+00-7.814585391E+00 --7.714002779E+00-7.606184767E+00-7.491072255E+00-7.368606456E+00-7.238742126E+00 --7.101451348E+00-6.956723495E+00-6.804564459E+00-6.644989477E+00-6.478023309E+00 --6.303701402E+00-6.122070497E+00-5.933187514E+00-5.737122371E+00-5.533956941E+00 --5.323787121E+00-5.106727043E+00-4.882902042E+00-4.652436946E+00-4.415465804E+00 --4.172135359E+00-3.922583354E+00-3.666975000E+00-3.405606155E+00-3.138959949E+00 --2.867735901E+00-2.592804271E+00-2.314902129E+00-2.034198754E+00-1.749967224E+00 --1.460225534E+00-1.162190486E+00-8.551352031E-01-5.421686647E-01-2.275329768E-01 - 8.638257619E-02 3.999208407E-01 7.135521456E-01 1.027305114E+00 1.341160666E+00 - 1.655119094E+00 1.969183926E+00 2.283340475E+00 1.246031347E+00 1.041104604E+00 - 8.363109492E-01 6.316782383E-01 4.272123302E-01 2.229427455E-01 1.884758825E-02 --1.855446078E-01-3.908660086E-01-5.964079438E-01-8.005709131E-01-1.000941558E+00 --1.195027271E+00-1.381749037E+00-1.562112387E+00-1.738427227E+00-1.913044649E+00 --2.087552250E+00-2.262830727E+00-2.439351315E+00-2.617333170E+00-2.796612310E+00 --2.976676466E+00-3.156928457E+00-3.336800531E+00-3.515862589E+00-3.693780083E+00 --3.870287845E+00-4.045169629E+00-4.218287494E+00-4.389536655E+00-4.558805357E+00 --4.725975837E+00-4.890927959E+00-5.053541003E+00-5.213695774E+00-5.371274211E+00 --5.526157398E+00-5.678225043E+00-5.827357573E+00-5.973436705E+00-6.116344911E+00 --6.255967586E+00-6.392196632E+00-6.524928099E+00-6.654057338E+00-6.779484606E+00 --6.901108425E+00-7.018804606E+00-7.132440331E+00-7.241883547E+00-7.347002290E+00 --7.447671043E+00-7.543778147E+00-7.635237126E+00-7.721988717E+00-7.804001600E+00 --7.881252200E+00-7.953660638E+00-8.021045387E+00-8.083220411E+00-8.140117067E+00 --8.191694495E+00-8.237861045E+00-8.278527176E+00-8.313588139E+00-8.342965778E+00 --8.366567523E+00-8.384321012E+00-8.396092729E+00-8.401690790E+00-8.401206702E+00 --8.394893336E+00-8.382633515E+00-8.363696952E+00-8.337629090E+00-8.304562792E+00 --8.265013285E+00-8.219204814E+00-8.166883170E+00-8.107764343E+00-8.041655310E+00 --7.968430994E+00-7.888021077E+00-7.800390267E+00-7.705526697E+00-7.603429936E+00 --7.494099648E+00-7.377519528E+00-7.253651773E+00-7.122456794E+00-6.983897209E+00 --6.837949010E+00-6.684605516E+00-6.523876340E+00-6.355789815E+00-6.180388615E+00 --5.997725090E+00-5.807861280E+00-5.610869054E+00-5.406831404E+00-5.195847793E+00 --4.978036342E+00-4.753516435E+00-4.522410266E+00-4.284858636E+00-4.040998895E+00 --3.790958338E+00-3.534947575E+00-3.273346365E+00-3.006757149E+00-2.735965296E+00 --2.461802968E+00-2.184790242E+00-1.904717110E+00-1.620349500E+00-1.329168859E+00 --1.028915888E+00-7.206104656E-01-4.082690577E-01-9.549230969E-02 2.165164711E-01 - 5.284726039E-01 8.405926486E-01 1.152844795E+00 1.465222863E+00 1.777728220E+00 - 2.090364397E+00 2.403113444E+00 1.253711887E+00 1.049460453E+00 8.453742461E-01 - 6.414879838E-01 4.378083939E-01 2.343656237E-01 3.115385327E-02-1.722635195E-01 --3.766001330E-01-5.812215477E-01-7.845969096E-01-9.843750019E-01-1.178023703E+00 --1.364295282E+00-1.544010777E+00-1.719402171E+00-1.892855105E+00-2.066029435E+00 --2.239862471E+00-2.414852547E+00-2.591256646E+00-2.768972439E+00-2.947523489E+00 --3.126317213E+00-3.304769549E+00-3.482438560E+00-3.658986915E+00-3.834138529E+00 --4.007662591E+00-4.179411345E+00-4.349279445E+00-4.517158225E+00-4.682933607E+00 --4.846489013E+00-5.007706311E+00-5.166467222E+00-5.322653547E+00-5.476146262E+00 --5.626824861E+00-5.774572395E+00-5.919277592E+00-6.060830817E+00-6.199122424E+00 --6.334047472E+00-6.465499330E+00-6.593352543E+00-6.717473516E+00-6.837729066E+00 --6.953983935E+00-7.066106545E+00-7.173974342E+00-7.277478568E+00-7.376531395E+00 --7.471065372E+00-7.561038577E+00-7.646423981E+00-7.727160651E+00-7.803099517E+00 --7.874033701E+00-7.939829415E+00-8.000448295E+00-8.055840656E+00-8.105908820E+00 --8.150557270E+00-8.189673895E+00-8.223180723E+00-8.250984266E+00-8.273034357E+00 --8.289230288E+00-8.299380623E+00-8.303336327E+00-8.301256731E+00-8.293365511E+00 --8.279560703E+00-8.259164181E+00-8.231671063E+00-8.197034652E+00-8.155614551E+00 --8.107853696E+00-8.053723072E+00-7.992941135E+00-7.925274147E+00-7.850556538E+00 --7.768674517E+00-7.679561413E+00-7.583181444E+00-7.479519503E+00-7.368576661E+00 --7.250359921E+00-7.124877345E+00-6.992120760E+00-6.852071268E+00-6.704711943E+00 --6.550030640E+00-6.388027086E+00-6.218719476E+00-6.042141835E+00-5.858345534E+00 --5.667397358E+00-5.469375127E+00-5.264370952E+00-5.052496071E+00-4.833865714E+00 --4.608591419E+00-4.376800078E+00-4.138627089E+00-3.894185046E+00-3.643621548E+00 --3.387230601E+00-3.125520265E+00-2.859197110E+00-2.589079730E+00-2.315868988E+00 --2.039744303E+00-1.760023994E+00-1.474811169E+00-1.181405619E+00-8.789262600E-01 --5.701597331E-01-2.592462934E-01 5.126066274E-02 3.614026400E-01 6.716755577E-01 - 9.821309418E-01 1.292744623E+00 1.603514181E+00 1.914439245E+00 2.225522946E+00 - 2.536742937E+00 1.262011495E+00 1.058501709E+00 8.551922254E-01 6.521254345E-01 - 4.493092619E-01 2.467747398E-01 4.453304225E-02-1.578130239E-01-3.610571365E-01 --5.646497536E-01-7.671338331E-01-9.662304340E-01-1.159377357E+00-1.345151390E+00 --1.524166692E+00-1.698555130E+00-1.870726479E+00-2.042419680E+00-2.214639605E+00 --2.387915654E+00-2.562543082E+00-2.738486485E+00-2.915315507E+00-3.092452441E+00 --3.269300525E+00-3.445402320E+00-3.620416270E+00-3.794056993E+00-3.966081085E+00 --4.136329376E+00-4.304693284E+00-4.471063183E+00-4.635324946E+00-4.797362815E+00 --4.957058483E+00-5.114294126E+00-5.268955758E+00-5.420931962E+00-5.570110106E+00 --5.716377710E+00-5.859626409E+00-5.999745529E+00-6.136608712E+00-6.270082025E+00 --6.400031013E+00-6.526318924E+00-6.648809490E+00-6.767372907E+00-6.881888313E+00 --6.992247098E+00-7.098357865E+00-7.200145500E+00-7.297557255E+00-7.390557845E+00 --7.479095520E+00-7.563055156E+00-7.642239053E+00-7.716459156E+00-7.785637044E+00 --7.849744972E+00-7.908711006E+00-7.962437258E+00-8.010824684E+00-8.053751664E+00 --8.091162739E+00-8.122954471E+00-8.149045696E+00-8.169348104E+00-8.183786783E+00 --8.192132326E+00-8.194283881E+00-8.190443433E+00-8.180802123E+00-8.165267218E+00 --8.143212909E+00-8.114118783E+00-8.077828353E+00-8.034528001E+00-7.984647449E+00 --7.928439105E+00-7.865723610E+00-7.796244155E+00-7.719808002E+00-7.636271169E+00 --7.545532062E+00-7.447530499E+00-7.342234440E+00-7.229630195E+00-7.109720477E+00 --6.982518782E+00-6.848043967E+00-6.706315871E+00-6.557341258E+00-6.401123584E+00 --6.237672146E+00-6.067002554E+00-5.889141228E+00-5.704129974E+00-5.512026000E+00 --5.312904841E+00-5.106869065E+00-4.894032681E+00-4.674505055E+00-4.448405695E+00 --4.215868360E+00-3.977003231E+00-3.731920210E+00-3.480840512E+00-3.224180801E+00 --2.962577731E+00-2.696796994E+00-2.427602032E+00-2.155435358E+00-1.880017470E+00 --1.600034570E+00-1.312982171E+00-1.016820947E+00-7.127215580E-01-4.045722552E-01 --9.581113893E-02 2.123738448E-01 5.205920500E-01 8.290410688E-01 1.137691025E+00 - 1.446533170E+00 1.755565584E+00 2.064786062E+00 2.374197534E+00 2.683772589E+00 - 1.270878955E+00 1.068176212E+00 8.657125571E-01 6.635388883E-01 4.616645405E-01 - 2.601216514E-01 5.893875239E-02-1.422379366E-01-3.442764966E-01-5.467245355E-01 --7.482040019E-01-9.465186364E-01-1.139089472E+00-1.324315584E+00-1.502582707E+00 --1.675896850E+00-1.846677049E+00-2.016746895E+00-2.187191286E+00-2.358576973E+00 --2.531237854E+00-2.705208703E+00-2.880116356E+00-3.055411170E+00-3.230490417E+00 --3.404878475E+00-3.578224372E+00-3.750229117E+00-3.920633305E+00-4.089260727E+00 --4.255994506E+00-4.420722004E+00-4.583331641E+00-4.743714259E+00-4.901759401E+00 --5.057356370E+00-5.210394800E+00-5.360766494E+00-5.508359245E+00-5.653047302E+00 --5.794697947E+00-5.933176800E+00-6.068346688E+00-6.200069447E+00-6.328209896E+00 --6.452639731E+00-6.573237719E+00-6.689893982E+00-6.802512619E+00-6.911011187E+00 --7.015326559E+00-7.115413605E+00-7.211222703E+00-7.302661533E+00-7.389558162E+00 --7.471707627E+00-7.548967743E+00-7.621296487E+00-7.688657518E+00-7.750955445E+00 --7.808097082E+00-7.859982330E+00-7.906480786E+00-7.947547926E+00-7.983083361E+00 --8.012958359E+00-8.037170138E+00-8.055597498E+00-8.068084820E+00-8.074436482E+00 --8.074625616E+00-8.068860454E+00-8.057298524E+00-8.039854197E+00-8.015951136E+00 --7.985070727E+00-7.946992512E+00-7.901773310E+00-7.849721159E+00-7.791222558E+00 --7.726319193E+00-7.654780730E+00-7.576390845E+00-7.490987871E+00-7.398446984E+00 --7.298679511E+00-7.191633784E+00-7.077284584E+00-6.955623660E+00-6.826657925E+00 --6.690407301E+00-6.546900712E+00-6.396172277E+00-6.238257697E+00-6.073183631E+00 --5.900979248E+00-5.721679996E+00-5.535327384E+00-5.341974557E+00-5.141697216E+00 --4.934588952E+00-4.720744947E+00-4.500273062E+00-4.273303619E+00-4.039951070E+00 --3.800311480E+00-3.554557837E+00-3.303034271E+00-3.046310269E+00-2.785097912E+00 --2.520158058E+00-2.252078171E+00-1.980868633E+00-1.705654835E+00-1.424356435E+00 --1.134477251E+00-8.357429195E-01-5.312268099E-01-2.248031089E-01 8.133969291E-02 - 3.873251424E-01 6.935486624E-01 1.000032695E+00 1.306753313E+00 1.613705658E+00 - 1.920885412E+00 2.228288691E+00 2.535918022E+00 2.843740356E+00 1.280275188E+00 - 1.078447713E+00 8.769020801E-01 6.756985374E-01 4.748479498E-01 2.743835675E-01 - 7.435076416E-02-1.255574921E-01-3.262736605E-01-5.274571490E-01-7.278142581E-01 --9.252410741E-01-1.117158372E+00-1.301790305E+00-1.479274336E+00-1.651461502E+00 --1.820760306E+00-1.989082129E+00-2.157605265E+00-2.326943710E+00-2.497471975E+00 --2.669295362E+00-2.842105848E+00-3.015391795E+00-3.188548382E+00-3.361077165E+00 --3.532611400E+00-3.702836009E+00-3.871477611E+00-4.038343744E+00-4.203311679E+00 --4.366270417E+00-4.527114746E+00-4.685741130E+00-4.842043535E+00-4.995912651E+00 --5.147227151E+00-5.295858700E+00-5.441675475E+00-5.584542106E+00-5.724321251E+00 --5.860875818E+00-5.994072483E+00-6.123783121E+00-6.249885538E+00-6.372268151E+00 --6.490830225E+00-6.605482420E+00-6.716152134E+00-6.822784100E+00-6.925326231E+00 --7.023698461E+00-7.117759381E+00-7.207309640E+00-7.292161667E+00-7.372223216E+00 --7.447469710E+00-7.517846435E+00-7.583235058E+00-7.643548193E+00-7.698691667E+00 --7.748529478E+00-7.793012100E+00-7.832043224E+00-7.865513352E+00-7.893373088E+00 --7.915489002E+00-7.931851201E+00-7.942218678E+00-7.946404306E+00-7.944471165E+00 --7.936618260E+00-7.922968878E+00-7.903440810E+00-7.877504564E+00-7.844653434E+00 --7.804628352E+00-7.757402495E+00-7.703159347E+00-7.642251948E+00-7.574938967E+00 --7.501109573E+00-7.420540613E+00-7.333054986E+00-7.238515873E+00-7.136816774E+00 --7.027882763E+00-6.911672224E+00-6.788169087E+00-6.657373541E+00-6.519300090E+00 --6.373976242E+00-6.221440589E+00-6.061739454E+00-5.894926650E+00-5.721055531E+00 --5.540174150E+00-5.352336240E+00-5.157609955E+00-4.956073992E+00-4.747807824E+00 --4.532898440E+00-4.311454888E+00-4.083580365E+00-3.849357568E+00-3.608926834E+00 --3.362579302E+00-3.110822968E+00-2.854325450E+00-2.593824521E+00-2.329975647E+00 --2.062991325E+00-1.792313257E+00-1.516279227E+00-1.232362260E+00-9.392948658E-01 --6.390975900E-01-3.356353034E-01-3.179269016E-02 2.717683918E-01 5.755521206E-01 - 8.796631795E-01 1.184066205E+00 1.488750328E+00 1.793709082E+00 2.098935190E+00 - 2.404422935E+00 2.710174284E+00 3.016150067E+00 1.290186635E+00 1.089305303E+00 - 8.887518495E-01 6.885963723E-01 4.888511898E-01 2.895506561E-01 9.075579098E-02 --1.077909968E-01-3.070712117E-01-5.068733101E-01-7.059931593E-01-9.024272236E-01 --1.093615021E+00-1.277614490E+00-1.454298901E+00-1.625333600E+00-1.793092480E+00 --1.959573060E+00-2.126056695E+00-2.293213430E+00-2.461457353E+00-2.630959195E+00 --2.801483862E+00-2.972571110E+00-3.143624438E+00-3.314124432E+00-3.483687190E+00 --3.651983907E+00-3.818733194E+00-3.983726632E+00-4.146829895E+00-4.307927007E+00 --4.466914201E+00-4.623682834E+00-4.778112272E+00-4.930077527E+00-5.079448423E+00 --5.226091456E+00-5.369871492E+00-5.510654477E+00-5.648309151E+00-5.782707375E+00 --5.913726379E+00-6.041252783E+00-6.165181368E+00-6.285416568E+00-6.401877573E+00 --6.514499376E+00-6.623224818E+00-6.727979404E+00-6.828646081E+00-6.925041963E+00 --7.016968532E+00-7.104276121E+00-7.186904548E+00-7.264833011E+00-7.337984153E+00 --7.406221339E+00-7.469464778E+00-7.527626213E+00-7.580567740E+00-7.628235114E+00 --7.670530742E+00-7.707351872E+00-7.738578193E+00-7.764228711E+00-7.784150829E+00 --7.798242240E+00-7.806300788E+00-7.808160340E+00-7.803949300E+00-7.793847241E+00 --7.777947095E+00-7.756166735E+00-7.728019240E+00-7.693016716E+00-7.650877809E+00 --7.601520701E+00-7.545037832E+00-7.481687249E+00-7.411798613E+00-7.335464597E+00 --7.252507180E+00-7.162733663E+00-7.065998765E+00-6.962187632E+00-6.851211789E+00 --6.733010871E+00-6.607555098E+00-6.474839534E+00-6.334874435E+00-6.187683527E+00 --6.033304490E+00-5.871787500E+00-5.703191057E+00-5.527580526E+00-5.345026678E+00 --5.155604072E+00-4.959392057E+00-4.756473409E+00-4.546934376E+00-4.330871573E+00 --4.108375812E+00-3.879516766E+00-3.644404323E+00-3.403278145E+00-3.156580482E+00 --2.904928858E+00-2.649032192E+00-2.389569987E+00-2.126884552E+00-1.860641682E+00 --1.589521282E+00-1.311160346E+00-1.023720871E+00-7.282535829E-01-4.283011665E-01 --1.271578564E-01 1.737947255E-01 4.749197206E-01 7.764357061E-01 1.078315429E+00 - 1.380536773E+00 1.683089473E+00 1.985963150E+00 2.289147582E+00 2.592634767E+00 - 2.896425683E+00 3.200474380E+00 1.300609332E+00 1.100742587E+00 9.012521894E-01 - 7.022184013E-01 5.036549291E-01 3.055972964E-01 1.081200675E-01-8.898328749E-02 --2.867217860E-01-4.850336432E-01-6.828105445E-01-8.781563209E-01-1.068548981E+00 --1.251892894E+00-1.427783114E+00-1.597663356E+00-1.763842202E+00-1.928396271E+00 --2.092718161E+00-2.257547604E+00-2.423341861E+00-2.590331773E+00-2.758365388E+00 --2.927052187E+00-3.095821369E+00-3.264138893E+00-3.431598451E+00-3.597850121E+00 --3.762602500E+00-3.925628641E+00-4.086769378E+00-4.245882988E+00-4.402851597E+00 --4.557563515E+00-4.709895625E+00-4.859719796E+00-5.006905438E+00-5.151321462E+00 --5.292838349E+00-5.431329509E+00-5.566673110E+00-5.698754348E+00-5.827464226E+00 --5.952701957E+00-6.074379907E+00-6.192424216E+00-6.306771987E+00-6.417350389E+00 --6.524057062E+00-6.626732343E+00-6.725181943E+00-6.819221288E+00-6.908742654E+00 --6.993704336E+00-7.074074090E+00-7.149756473E+00-7.220601002E+00-7.286532355E+00 --7.347472734E+00-7.403281501E+00-7.453890718E+00-7.499215249E+00-7.539145082E+00 --7.573561298E+00-7.602474101E+00-7.625687532E+00-7.643241607E+00-7.654901185E+00 --7.660471332E+00-7.659849898E+00-7.653209193E+00-7.640700309E+00-7.622389484E+00 --7.598193582E+00-7.567664277E+00-7.530335121E+00-7.485914868E+00-7.434284924E+00 --7.375475087E+00-7.309654254E+00-7.237111602E+00-7.158093934E+00-7.072553134E+00 --6.980303331E+00-6.881187332E+00-6.775085901E+00-6.661905024E+00-6.541574739E+00 --6.414050008E+00-6.279313087E+00-6.137370776E+00-5.988246377E+00-5.831976864E+00 --5.668612130E+00-5.498212483E+00-5.320843382E+00-5.136579927E+00-4.945513042E+00 --4.747741424E+00-4.543357715E+00-4.332457614E+00-4.115134747E+00-3.891466740E+00 --3.661554113E+00-3.425600581E+00-3.183989229E+00-2.937281985E+00-2.686147927E+00 --2.431255772E+00-2.173010449E+00-1.911220995E+00-1.644817444E+00-1.371655388E+00 --1.089635237E+00-7.990527902E-01-5.030006480E-01-2.049599708E-01 9.318150177E-02 - 3.914581271E-01 6.901708645E-01 9.893229926E-01 1.288883805E+00 1.588839584E+00 - 1.889177417E+00 2.189884647E+00 2.490949138E+00 2.792360751E+00 3.094119192E+00 - 3.396171043E+00 1.311526880E+00 1.112737995E+00 9.143758226E-01 7.165308572E-01 - 5.192175100E-01 3.224716516E-01 1.263770845E-01-6.922232316E-02-2.653333084E-01 --4.620644994E-01-6.584062381E-01-8.525709242E-01-1.042093242E+00-1.224744790E+00 --1.399835994E+00-1.568554369E+00-1.733110856E+00-1.895649706E+00-2.057681361E+00 --2.220035206E+00-2.383221123E+00-2.547525717E+00-2.712885934E+00-2.878992924E+00 --3.045316428E+00-3.211314622E+00-3.376552468E+00-3.540643182E+00-3.703269564E+00 --3.864175556E+00-4.023175114E+00-4.180106087E+00-4.334843748E+00-4.487279431E+00 --4.637293706E+00-4.784761856E+00-4.929558158E+00-5.071557175E+00-5.210637768E+00 --5.346685301E+00-5.479589184E+00-5.609244745E+00-5.735558808E+00-5.858450055E+00 --5.977850197E+00-6.093685656E+00-6.205861921E+00-6.314241670E+00-6.418641633E+00 --6.518869677E+00-6.614771840E+00-6.706268930E+00-6.793326290E+00-6.875894715E+00 --6.953862663E+00-7.027073263E+00-7.095452681E+00-7.158933209E+00-7.217374144E+00 --7.270681750E+00-7.318792109E+00-7.361603550E+00-7.398993779E+00-7.430878015E+00 --7.457257787E+00-7.477956086E+00-7.492934424E+00-7.501982275E+00-7.504895320E+00 --7.501643911E+00-7.492423469E+00-7.477353652E+00-7.456477482E+00-7.429708213E+00 --7.396633213E+00-7.356809539E+00-7.309943605E+00-7.255892841E+00-7.194643597E+00 --7.126299868E+00-7.051078596E+00-6.969256903E+00-6.880959325E+00-6.786060270E+00 --6.684394916E+00-6.575838370E+00-6.460294734E+00-6.337689909E+00-6.207971238E+00 --6.071109294E+00-5.927101775E+00-5.775971393E+00-5.617756593E+00-5.452504056E+00 --5.280266270E+00-5.101108942E+00-4.915118060E+00-4.722392545E+00-4.523031396E+00 --4.317138771E+00-4.104819445E+00-3.886163370E+00-3.661277122E+00-3.430350675E+00 --3.193732732E+00-2.951943449E+00-2.705621351E+00-2.455412650E+00-2.201736915E+00 --1.944475905E+00-1.682717999E+00-1.414507674E+00-1.137665407E+00-8.519764109E-01 --5.600836413E-01-2.654892614E-01 2.958336037E-02 3.248249427E-01 6.205486805E-01 - 9.167939335E-01 1.213521671E+00 1.510711123E+00 1.808345689E+00 2.106409904E+00 - 2.404889752E+00 2.703771778E+00 3.003044618E+00 3.302707893E+00 3.602701432E+00 - 1.322906150E+00 1.125248798E+00 9.280670728E-01 7.314613380E-01 5.354479516E-01 - 3.400649964E-01 1.454026709E-01-4.864498854E-02-2.430435010E-01-4.380960930E-01 --6.328956896E-01-8.257643035E-01-1.014313885E+00-1.196211963E+00-1.370485970E+00 --1.538036711E+00-1.700943534E+00-1.861401669E+00-2.021040720E+00-2.180798417E+00 --2.341245348E+00-2.502717536E+00-2.665242687E+00-2.828602602E+00-2.992319839E+00 --3.155843720E+00-3.318696570E+00-3.480445255E+00-3.640748454E+00-3.799331258E+00 --3.955986155E+00-4.110533673E+00-4.262842925E+00-4.412809646E+00-4.560320737E+00 --4.705257317E+00-4.847502130E+00-4.986939860E+00-5.123457858E+00-5.256949754E+00 --5.387319439E+00-5.514479962E+00-5.638358267E+00-5.758878806E+00-5.875951744E+00 --5.989457281E+00-6.099227689E+00-6.205074876E+00-6.306818844E+00-6.404339187E+00 --6.497574396E+00-6.586487672E+00-6.671009321E+00-6.751016587E+00-6.826353794E+00 --6.896940470E+00-6.962721852E+00-7.023562685E+00-7.079336699E+00-7.130001404E+00 --7.175454682E+00-7.215585844E+00-7.250248193E+00-7.279516172E+00-7.303127566E+00 --7.321162700E+00-7.333405313E+00-7.339669891E+00-7.339764407E+00-7.333737693E+00 --7.321790780E+00-7.304009769E+00-7.280418337E+00-7.250924574E+00-7.215147009E+00 --7.172668008E+00-7.123198172E+00-7.066578619E+00-7.002766221E+00-6.931819487E+00 --6.853890617E+00-6.769218326E+00-6.678027183E+00-6.580321533E+00-6.475956075E+00 --6.364796705E+00-6.246745285E+00-6.121726605E+00-5.989686799E+00-5.850593930E+00 --5.704438424E+00-5.551233982E+00-5.391011707E+00-5.223809311E+00-5.049678379E+00 --4.868696962E+00-4.680960017E+00-4.486562452E+00-4.285603725E+00-4.078193464E+00 --3.864441756E+00-3.644471372E+00-3.418464384E+00-3.186738796E+00-2.949786190E+00 --2.708234281E+00-2.462716119E+00-2.213641413E+00-1.960919231E+00-1.703730213E+00 --1.440257459E+00-1.168333907E+00-8.874521583E-01-5.998848553E-01-3.090439898E-01 --1.732997385E-02 2.746479592E-01 5.671802283E-01 8.603339869E-01 1.154058864E+00 - 1.448324095E+00 1.743107198E+00 2.038387018E+00 2.334144576E+00 2.630362707E+00 - 2.927025135E+00 3.224118853E+00 3.521643795E+00 3.819533809E+00 1.334667469E+00 - 1.138181191E+00 9.422218536E-01 7.469011044E-01 5.522383518E-01 3.582752949E-01 - 1.651030600E-01-2.733819065E-02-2.199228468E-01-4.131812681E-01-6.063154838E-01 --7.977581994E-01-9.852209355E-01-1.166301082E+00-1.339751373E+00-1.506155865E+00 --1.667421411E+00-1.825766860E+00-1.982937729E+00-2.140000789E+00-2.297599424E+00 --2.456111985E+00-2.615646677E+00-2.776072924E+00-2.936978808E+00-3.097815939E+00 --3.258070010E+00-3.417263932E+00-3.575031807E+00-3.731086972E+00-3.885204232E+00 --4.037188676E+00-4.186900078E+00-4.334236973E+00-4.479094245E+00-4.621362353E+00 --4.760931720E+00-4.897693940E+00-5.031549265E+00-5.162407376E+00-5.290192510E+00 --5.414827491E+00-5.536225896E+00-5.654279171E+00-5.768836993E+00-5.879720755E+00 --5.986745955E+00-6.089755945E+00-6.188654748E+00-6.283390398E+00-6.373917086E+00 --6.460146821E+00-6.541947099E+00-6.619170614E+00-6.691726374E+00-6.759569747E+00 --6.822574727E+00-6.880582478E+00-6.933572777E+00-6.981429414E+00-7.024052983E+00 --7.061298397E+00-7.093153974E+00-7.119567558E+00-7.140342239E+00-7.155513880E+00 --7.164851115E+00-7.168168455E+00-7.165295742E+00-7.156352892E+00-7.141536104E+00 --7.120899384E+00-7.094447949E+00-7.062084509E+00-7.023455794E+00-6.978168743E+00 --6.925943177E+00-6.866611387E+00-6.800108920E+00-6.726461791E+00-6.645776462E+00 --6.558236511E+00-6.464074154E+00-6.363429885E+00-6.256227683E+00-6.142334504E+00 --6.021646332E+00-5.894090254E+00-5.759614950E+00-5.618189894E+00-5.469801273E+00 --5.314446395E+00-5.152135219E+00-4.982907062E+00-4.806835121E+00-4.624003274E+00 --4.434492796E+00-4.238398584E+00-4.035841493E+00-3.826947430E+00-3.611845810E+00 --3.390704793E+00-3.163819487E+00-2.931667924E+00-2.694874648E+00-2.454048828E+00 --2.209566472E+00-1.961336204E+00-1.708590924E+00-1.449607307E+00-1.182279031E+00 --9.059883932E-01-6.227713808E-01-3.359078840E-01-4.784366362E-02 2.406222129E-01 - 5.297352764E-01 8.195853503E-01 1.110115076E+00 1.401282033E+00 1.693054999E+00 - 1.985404873E+00 2.278305212E+00 2.571733083E+00 2.865668035E+00 3.160090796E+00 - 3.454985837E+00 3.750351746E+00 4.046115391E+00 1.346723607E+00 1.151454670E+00 - 9.567691880E-01 7.627912577E-01 5.695431533E-01 3.770701955E-01 1.854575855E-01 --5.315139602E-03-1.959847580E-01-3.873352906E-01-5.786892356E-01-7.685882537E-01 --9.548598712E-01-1.135063561E+00-1.307691584E+00-1.472988624E+00-1.632648857E+00 --1.788880161E+00-1.943534558E+00-2.097821916E+00-2.252468214E+00-2.407890376E+00 --2.564265117E+00-2.721547262E+00-2.879407236E+00-3.037315918E+00-3.194736827E+00 --3.351155898E+00-3.506179284E+00-3.659511469E+00-3.810912386E+00-3.960174206E+00 --4.107145275E+00-4.251724823E+00-4.393809535E+00-4.533295278E+00-4.670085711E+00 --4.804087705E+00-4.935221733E+00-5.063410170E+00-5.188570127E+00-5.310600315E+00 --5.429367844E+00-5.544706938E+00-5.656436988E+00-5.764383244E+00-5.868416550E+00 --5.968457058E+00-6.064455946E+00-6.156354112E+00-6.244046908E+00-6.327396045E+00 --6.406266711E+00-6.480552725E+00-6.550219652E+00-6.615154395E+00-6.675161260E+00 --6.730239718E+00-6.780268267E+00-6.825148664E+00-6.864770167E+00-6.899003454E+00 --6.927945483E+00-6.951272377E+00-6.969099007E+00-6.981238059E+00-6.987505038E+00 --6.987709594E+00-6.981732082E+00-6.969739794E+00-6.951913514E+00-6.928281634E+00 --6.898832356E+00-6.863460729E+00-6.821839597E+00-6.773601169E+00-6.718476149E+00 --6.656294237E+00-6.586977001E+00-6.510525994E+00-6.427015551E+00-6.336583580E+00 --6.239428850E+00-6.135750782E+00-6.025592979E+00-5.908850268E+00-5.785417020E+00 --5.655220211E+00-5.518212328E+00-5.374359472E+00-5.223634573E+00-5.066023576E+00 --4.901543375E+00-4.730245600E+00-4.552196903E+00-4.367468161E+00-4.176153155E+00 --3.978381664E+00-3.774290004E+00-3.564012066E+00-3.347705561E+00-3.125643259E+00 --2.898295717E+00-2.666284079E+00-2.430186620E+00-2.190322015E+00-1.946566602E+00 --1.698157613E+00-1.443418263E+00-1.180335688E+00-9.083380978E-01-6.293711145E-01 --3.465838247E-01-6.237307936E-02 2.223901651E-01 5.078961413E-01 7.942448288E-01 - 1.081379731E+00 1.369254589E+00 1.657835328E+00 1.947087919E+00 2.236979397E+00 - 2.527479427E+00 2.818560541E+00 3.110197630E+00 3.402367413E+00 3.695051521E+00 - 3.988247128E+00 4.281873968E+00 1.359044388E+00 1.165051525E+00 9.717024882E-01 - 7.791337421E-01 5.873686807E-01 3.964541005E-01 2.064690567E-01 1.743157453E-02 --1.712644744E-01-3.606165336E-01-5.500868345E-01-7.383305092E-01-9.233065073E-01 --1.102572108E+00-1.274381605E+00-1.438623501E+00-1.596737370E+00-1.750877074E+00 --1.902986185E+00-2.054425967E+00-2.206015738E+00-2.358216346E+00-2.511260824E+00 --2.665184013E+00-2.819753395E+00-2.974478391E+00-3.128820741E+00-3.282240805E+00 --3.434314460E+00-3.584737818E+00-3.733259158E+00-3.879660265E+00-4.023770453E+00 --4.165481524E+00-4.304691806E+00-4.441308016E+00-4.575255250E+00-4.706456793E+00 --4.834830971E+00-4.960283197E+00-5.082696311E+00-5.201917625E+00-5.317775345E+00 --5.430094954E+00-5.538719726E+00-5.643540656E+00-5.744489453E+00-5.841514892E+00 --5.934544371E+00-6.023458546E+00-6.108114939E+00-6.188394043E+00-6.264174224E+00 --6.335427924E+00-6.402056904E+00-6.463830281E+00-6.520757931E+00-6.572727290E+00 --6.619642878E+00-6.661406856E+00-6.697829728E+00-6.728988179E+00-6.754759717E+00 --6.774936536E+00-6.789629620E+00-6.798579385E+00-6.801624401E+00-6.798560231E+00 --6.789346469E+00-6.774176562E+00-6.753207551E+00-6.726446822E+00-6.693867854E+00 --6.655357499E+00-6.610610929E+00-6.559286474E+00-6.501128012E+00-6.435965580E+00 --6.363712396E+00-6.284353918E+00-6.197939855E+00-6.104576495E+00-6.004422202E+00 --5.897670179E+00-5.784463768E+00-5.664773987E+00-5.538505108E+00-5.405581696E+00 --5.265948029E+00-5.119558596E+00-4.966385590E+00-4.806435036E+00-4.639735539E+00 --4.466321420E+00-4.286242425E+00-4.099596200E+00-3.906524290E+00-3.707169592E+00 --3.501658236E+00-3.290132038E+00-3.072855200E+00-2.850316024E+00-2.623127328E+00 --2.391810178E+00-2.156594092E+00-1.917301306E+00-1.673142090E+00-1.422447614E+00 --1.163318901E+00-8.953457026E-01-6.205015955E-01-3.418187794E-01-6.158060692E-02 - 2.193554636E-01 5.011364148E-01 7.838560645E-01 1.067458461E+00 1.351894430E+00 - 1.637126864E+00 1.923120259E+00 2.209840836E+00 2.497257065E+00 2.785338873E+00 - 3.074056584E+00 3.363382081E+00 3.653288767E+00 3.943754590E+00 4.234774111E+00 - 4.526259104E+00 1.371647379E+00 1.178990424E+00 9.870363962E-01 7.959327508E-01 - 6.057040758E-01 4.163995965E-01 2.280962525E-01 4.085038424E-02-1.458303323E-01 --3.331023540E-01-5.205940954E-01-7.070783837E-01-8.906548119E-01-1.068912314E+00 --1.239897429E+00-1.403137190E+00-1.559779446E+00-1.711874894E+00-1.861434264E+00 --2.009970050E+00-2.158405812E+00-2.307260316E+00-2.456812795E+00-2.607169843E+00 --2.758204741E+00-2.909485565E+00-3.060497040E+00-3.210690729E+00-3.359615760E+00 --3.506956976E+00-3.652445313E+00-3.795850788E+00-3.936987478E+00-4.075740801E+00 --4.212012029E+00-4.345717780E+00-4.476785935E+00-4.605130698E+00-4.730645949E+00 --4.853195390E+00-4.972619881E+00-5.088749815E+00-5.201416531E+00-5.310486976E+00 --5.415867509E+00-5.517494872E+00-5.615313304E+00-5.709237086E+00-5.799134601E+00 --5.884861232E+00-5.966313098E+00-6.043352697E+00-6.115958628E+00-6.184049559E+00 --6.247360852E+00-6.305906192E+00-6.359597271E+00-6.408314666E+00-6.451970521E+00 --6.490398563E+00-6.523548192E+00-6.551501658E+00-6.573883788E+00-6.590836187E+00 --6.602215296E+00-6.607820245E+00-6.607491372E+00-6.601017455E+00-6.588443135E+00 --6.569971520E+00-6.545732567E+00-6.515716889E+00-6.479883167E+00-6.438110626E+00 --6.390115051E+00-6.335579322E+00-6.274261688E+00-6.205997057E+00-6.130694015E+00 --6.048328530E+00-5.958931949E+00-5.862585566E+00-5.759414448E+00-5.649585915E+00 --5.533275618E+00-5.410560484E+00-5.281376845E+00-5.145638934E+00-5.003278918E+00 --4.854259169E+00-4.698573039E+00-4.536228802E+00-4.367240010E+00-4.191646385E+00 --4.009546448E+00-3.821074131E+00-3.626364902E+00-3.425534506E+00-3.218717186E+00 --3.006189416E+00-2.788464458E+00-2.566123154E+00-2.339607166E+00-2.109042872E+00 --1.874180212E+00-1.634159243E+00-1.387296861E+00-1.131855117E+00-8.676991524E-01 --5.969117331E-01-3.223956934E-01-4.624962992E-02 2.307572586E-01 5.087360629E-01 - 7.877538186E-01 1.067745893E+00 1.348656769E+00 1.630446348E+00 1.913077901E+00 - 2.196516510E+00 2.480728447E+00 2.765681895E+00 3.051346865E+00 3.337695072E+00 - 3.624699794E+00 3.912333989E+00 4.200573577E+00 4.489411838E+00 4.778752567E+00 - 1.384539726E+00 1.193264169E+00 1.002750180E+00 8.131569278E-01 6.245103699E-01 - 4.368615631E-01 2.502849248E-01 6.486946444E-02-1.197653447E-01-3.048840251E-01 --4.903087363E-01-6.749319806E-01-8.569979594E-01-1.034161634E+00-1.204301500E+00 --1.366590362E+00-1.521851121E+00-1.671976302E+00-1.819010097E+00-1.964606558E+00 --2.109804655E+00-2.255200373E+00-2.401113904E+00-2.547714255E+00-2.694980236E+00 --2.842559914E+00-2.989988971E+00-3.136728658E+00-3.282304443E+00-3.426385114E+00 --3.568686927E+00-3.708974042E+00-3.847053626E+00-3.982801820E+00-4.116101338E+00 --4.246850519E+00-4.374960238E+00-4.500314288E+00-4.622765968E+00-4.742157746E+00 --4.858325288E+00-4.971115322E+00-5.080410410E+00-5.186129454E+00-5.288212700E+00 --5.386594643E+00-5.481180330E+00-5.571828901E+00-5.658393814E+00-5.740786717E+00 --5.818855602E+00-5.892582755E+00-5.961904971E+00-6.026529943E+00-6.086467274E+00 --6.141655885E+00-6.191948956E+00-6.237259421E+00-6.277484351E+00-6.312438768E+00 --6.342254997E+00-6.366733311E+00-6.385667021E+00-6.399232869E+00-6.407150551E+00 --6.409271730E+00-6.405418206E+00-6.395406995E+00-6.379355054E+00-6.357464044E+00 --6.329834430E+00-6.296444222E+00-6.257238928E+00-6.212088835E+00-6.160728592E+00 --6.102865882E+00-6.038273499E+00-5.966795654E+00-5.888340058E+00-5.802874036E+00 --5.710414447E+00-5.611023646E+00-5.504803756E+00-5.391898497E+00-5.272477261E+00 --5.146678734E+00-5.014501917E+00-4.875865397E+00-4.730711457E+00-4.579012518E+00 --4.420756168E+00-4.255944400E+00-4.084623293E+00-3.906895599E+00-3.722888005E+00 --3.532714103E+00-3.336461574E+00-3.134264460E+00-2.926448822E+00-2.713545581E+00 --2.496071452E+00-2.274355064E+00-2.048407780E+00-1.817890582E+00-1.581830383E+00 --1.338535116E+00-1.086512980E+00-8.260073354E-01-5.592471439E-01-2.889779067E-01 --1.706235505E-02 2.558902148E-01 5.299619799E-01 8.051929331E-01 1.081508912E+00 - 1.358842399E+00 1.637141020E+00 1.916359012E+00 2.196455853E+00 2.477395431E+00 - 2.759145239E+00 3.041674829E+00 3.324954547E+00 3.608956050E+00 3.893652533E+00 - 4.179017790E+00 4.465029588E+00 4.751683500E+00 5.038876987E+00 1.397699454E+00 - 1.207845977E+00 1.018812417E+00 8.307687995E-01 6.437417254E-01 4.577845436E-01 - 2.729701420E-01 8.941349160E-02-9.315659170E-02-2.760522385E-01-4.593228205E-01 --6.419845387E-01-8.224241518E-01-9.983935971E-01-1.167650746E+00-1.329035122E+00 --1.483014905E+00-1.631268631E+00-1.775832794E+00-1.918481700E+00-2.060379827E+00 --2.202220365E+00-2.344366936E+00-2.487044822E+00-2.630328929E+00-2.773963409E+00 --2.917554558E+00-3.060596867E+00-3.202613083E+00-3.343262275E+00-3.482251060E+00 --3.619336722E+00-3.754303996E+00-3.886991904E+00-4.017248586E+00-4.144932612E+00 --4.269916762E+00-4.392058100E+00-4.511199425E+00-4.627187433E+00-4.739888841E+00 --4.849200120E+00-4.955047423E+00-5.057370009E+00-5.156094904E+00-5.251117151E+00 --5.342289954E+00-5.429469409E+00-5.512577321E+00-5.591449550E+00-5.666072261E+00 --5.736400291E+00-5.802118602E+00-5.863222954E+00-5.919682008E+00-5.971328509E+00 --6.018076851E+00-6.059858349E+00-6.096447616E+00-6.127884378E+00-6.154212053E+00 --6.175017658E+00-6.190459208E+00-6.200453591E+00-6.204766506E+00-6.203267274E+00 --6.195745837E+00-6.182083899E+00-6.162444771E+00-6.137022374E+00-6.105889458E+00 --6.069012767E+00-6.026326268E+00-5.977691786E+00-5.922860322E+00-5.861565531E+00 --5.793596358E+00-5.718805504E+00-5.637099797E+00-5.548440018E+00-5.452833370E+00 --5.350331641E+00-5.241026802E+00-5.125044640E+00-5.002530330E+00-4.873620538E+00 --4.738389093E+00-4.596802276E+00-4.448807800E+00-4.294370319E+00-4.133485055E+00 --3.966208851E+00-3.792644724E+00-3.612911762E+00-3.427104560E+00-3.235296615E+00 --3.037642644E+00-2.834524032E+00-2.626447467E+00-2.413833883E+00-2.196870797E+00 --1.975463021E+00-1.749157931E+00-1.516824178E+00-1.276784739E+00-1.027913943E+00 --7.709256858E-01-5.081896732E-01-2.422402481E-01 2.533595840E-02 2.941282124E-01 - 5.641928262E-01 8.355373077E-01 1.108083250E+00 1.381758355E+00 1.656503205E+00 - 1.932262390E+00 2.208984597E+00 2.486623253E+00 2.765137952E+00 3.044493263E+00 - 3.324657415E+00 3.605601788E+00 3.887299639E+00 4.169724879E+00 4.452851325E+00 - 4.736656860E+00 5.021138590E+00 5.306190558E+00 1.411101621E+00 1.222703431E+00 - 1.035182303E+00 8.487192890E-01 6.633421007E-01 4.791070175E-01 2.960865411E-01 - 1.144122135E-01-6.608582309E-02-2.466924106E-01-4.277234570E-01-6.083248660E-01 --7.870194385E-01-9.616811503E-01-1.130000578E+00-1.290517179E+00-1.443321080E+00 --1.589825058E+00-1.732009329E+00-1.871734268E+00-2.010297877E+00-2.148509370E+00 --2.286787011E+00-2.425405465E+00-2.564514043E+00-2.703964980E+00-2.843459107E+00 --2.982564233E+00-3.120833140E+00-3.257923215E+00-3.393508508E+00-3.527303497E+00 --3.659059760E+00-3.788567998E+00-3.915628174E+00-4.040049493E+00-4.161686107E+00 --4.280387066E+00-4.396001503E+00-4.508417047E+00-4.617547334E+00-4.723322305E+00 --4.825679179E+00-4.924534248E+00-5.019777276E+00-5.111258214E+00-5.198835553E+00 --5.282440056E+00-5.361897898E+00-5.437196279E+00-5.508309156E+00-5.574905360E+00 --5.636957615E+00-5.694463776E+00-5.747245088E+00-5.795224303E+00-5.838322114E+00 --5.876364334E+00-5.909240884E+00-5.937097541E+00-5.959664054E+00-5.976744212E+00 --5.988564049E+00-5.994841812E+00-5.995423034E+00-5.990167559E+00-5.978848024E+00 --5.961431115E+00-5.938103237E+00-5.909044483E+00-5.874303356E+00-5.833836711E+00 --5.787566754E+00-5.735349258E+00-5.676951819E+00-5.612131408E+00-5.540690646E+00 --5.462489722E+00-5.377435742E+00-5.285489063E+00-5.186658751E+00-5.080998025E+00 --4.968591933E+00-4.849535313E+00-4.723934437E+00-4.591913061E+00-4.453592447E+00 --4.309007162E+00-4.158115784E+00-4.000910493E+00-3.837445536E+00-3.667823707E+00 --3.492154494E+00-3.310516068E+00-3.122993208E+00-2.929805556E+00-2.731367804E+00 --2.528109416E+00-2.320319398E+00-2.108024308E+00-1.891017713E+00-1.668695529E+00 --1.439770256E+00-1.202660968E+00-9.567340756E-01-7.032118227E-01-4.445374970E-01 --1.829650417E-01 8.022044580E-02 3.447912979E-01 6.107876501E-01 8.781786430E-01 - 1.146880978E+00 1.416820483E+00 1.687934094E+00 1.960162187E+00 2.233448666E+00 - 2.507741303E+00 2.782991569E+00 3.059154721E+00 3.336189915E+00 3.614061579E+00 - 3.892738507E+00 4.172192629E+00 4.452398599E+00 4.733331894E+00 5.014971587E+00 - 5.297315869E+00 5.580255146E+00 1.424709778E+00 1.237793989E+00 1.051811991E+00 - 8.669561254E-01 6.832554999E-01 5.007698557E-01 3.195725937E-01 1.397991161E-01 --3.863250852E-02-2.168856351E-01-3.955923735E-01-5.740364532E-01-7.508665344E-01 --9.240983398E-01-1.091408758E+00-1.251079202E+00-1.402810719E+00-1.547704600E+00 --1.687631509E+00-1.824496097E+00-1.959728705E+00-2.094262864E+00-2.228587111E+00 --2.363025818E+00-2.497788779E+00-2.632847808E+00-2.768026655E+00-2.903013499E+00 --3.037393713E+00-3.170794919E+00-3.302842613E+00-3.433193810E+00-3.561559011E+00 --3.687673238E+00-3.811306252E+00-3.932240698E+00-4.050317533E+00-4.165394926E+00 --4.277352784E+00-4.386118153E+00-4.491634211E+00-4.593830272E+00-4.692614986E+00 --4.787872818E+00-4.879454233E+00-4.967226325E+00-5.051118266E+00-5.130950321E+00 --5.206714314E+00-5.278399736E+00-5.345663634E+00-5.408450468E+00-5.466787205E+00 --5.520503585E+00-5.569499291E+00-5.613688660E+00-5.652973480E+00-5.687125781E+00 --5.716254657E+00-5.740353528E+00-5.758987590E+00-5.772320417E+00-5.780338113E+00 --5.782770299E+00-5.779501292E+00-5.770358519E+00-5.755127511E+00-5.733859382E+00 --5.706748771E+00-5.673957161E+00-5.635509464E+00-5.591355318E+00-5.541408729E+00 --5.485520024E+00-5.423469862E+00-5.355034358E+00-5.280027213E+00-5.198319110E+00 --5.109828090E+00-5.014529068E+00-4.912442684E+00-4.803609251E+00-4.688077471E+00 --4.565911530E+00-4.437206014E+00-4.302082182E+00-4.160660186E+00-4.013034061E+00 --3.859243040E+00-3.699343723E+00-3.533438529E+00-3.361621894E+00-3.183971717E+00 --3.000610684E+00-2.811835493E+00-2.618038582E+00-2.419535710E+00-2.216454337E+00 --2.008684890E+00-1.795880643E+00-1.577207489E+00-1.351273385E+00-1.116764677E+00 --8.736625949E-01-6.236569394E-01-3.691451688E-01-1.120233662E-01 1.467478061E-01 - 4.070846224E-01 6.689995139E-01 9.324205873E-01 1.197255248E+00 1.463424985E+00 - 1.730862593E+00 1.999506133E+00 2.269298405E+00 2.540185716E+00 2.812116529E+00 - 3.085042281E+00 3.358917438E+00 3.633699530E+00 3.909349263E+00 4.185830615E+00 - 4.463112142E+00 4.741166193E+00 5.019966920E+00 5.299493898E+00 5.579747742E+00 - 5.860617092E+00 1.438482593E+00 1.253072527E+00 1.068653208E+00 8.854284488E-01 - 7.034288306E-01 5.227180458E-01 3.433716972E-01 1.655153163E-01-1.086213129E-02 --1.867051036E-01-3.630054344E-01-5.391987858E-01-7.140474683E-01-8.857221109E-01 --1.051935390E+00-1.210761224E+00-1.361517319E+00-1.504956927E+00-1.642782651E+00 --1.776891396E+00-1.908830006E+00-2.039657600E+00-2.169961981E+00-2.300132678E+00 --2.430442449E+00-2.560993028E+00-2.691729185E+00-2.822449036E+00-2.952764718E+00 --3.082280907E+00-3.210575774E+00-3.337238124E+00-3.461943562E+00-3.584399318E+00 --3.704359807E+00-3.821594814E+00-3.935948210E+00-4.047298710E+00-4.155543555E+00 --4.260626921E+00-4.362485734E+00-4.461016004E+00-4.556094627E+00-4.647580392E+00 --4.735352151E+00-4.819334743E+00-4.899342457E+00-4.975368848E+00-5.047421806E+00 --5.115153419E+00-5.178473689E+00-5.237433343E+00-5.291881940E+00-5.341690761E+00 --5.386767072E+00-5.427058614E+00-5.462327762E+00-5.492556435E+00-5.517871620E+00 --5.537949223E+00-5.552606613E+00-5.562099716E+00-5.566169265E+00-5.564641016E+00 --5.557403506E+00-5.544249512E+00-5.525010974E+00-5.499805316E+00-5.468823527E+00 --5.432206341E+00-5.389960169E+00-5.342030689E+00-5.288324565E+00-5.228683436E+00 --5.162894959E+00-5.090753818E+00-5.012092583E+00-4.926807928E+00-4.834844645E+00 --4.736181641E+00-4.630813199E+00-4.518747005E+00-4.400020646E+00-4.274705717E+00 --4.142884480E+00-4.004649609E+00-3.860122035E+00-3.709473798E+00-3.552883620E+00 --3.390467824E+00-3.222317287E+00-3.048523515E+00-2.869273675E+00-2.684884288E+00 --2.495661501E+00-2.301791925E+00-2.103228671E+00-1.899736507E+00-1.690791246E+00 --1.475317916E+00-1.251910432E+00-1.019736520E+00-7.794676261E-01-5.331157241E-01 --2.828898416E-01-3.029564257E-02 2.240671631E-01 4.801726687E-01 7.380056543E-01 - 9.974651294E-01 1.258445744E+00 1.520858918E+00 1.784627863E+00 2.049684335E+00 - 2.315967212E+00 2.583420791E+00 2.851993747E+00 3.121638324E+00 3.392308709E+00 - 3.663960114E+00 3.936550123E+00 4.210038791E+00 4.484388761E+00 4.759565371E+00 - 5.035536670E+00 5.312273763E+00 5.589754222E+00 5.867978002E+00 6.146831548E+00 - 1.452378279E+00 1.268495442E+00 1.085660933E+00 9.040901204E-01 7.238149994E-01 - 5.449032043E-01 3.674328144E-01 1.915167980E-01 1.720457121E-02-1.562126650E-01 --3.300379840E-01-5.038902747E-01-6.766436575E-01-8.466305131E-01-1.011644378E+00 --1.169608169E+00-1.319475441E+00-1.461623309E+00-1.597524899E+00-1.729014880E+00 --1.857732456E+00-1.984861501E+00-2.111129701E+00-2.237025727E+00-2.362884613E+00 --2.488890378E+00-2.615078123E+00-2.741353728E+00-2.867367518E+00-2.992717595E+00 --3.116948919E+00-3.239610398E+00-3.360358716E+00-3.478887211E+00-3.594945980E+00 --3.708317292E+00-3.818840363E+00-3.926406317E+00-4.030905867E+00-4.132258798E+00 --4.230371556E+00-4.325105283E+00-4.416312926E+00-4.503900747E+00-4.587789309E+00 --4.667784544E+00-4.743883371E+00-4.816108953E+00-4.884113945E+00-4.947775854E+00 --5.007163087E+00-5.062145000E+00-5.112566075E+00-5.158344261E+00-5.199421808E+00 --5.235628596E+00-5.266800272E+00-5.293069733E+00-5.314380590E+00-5.330292994E+00 --5.340966493E+00-5.346455047E+00-5.346462343E+00-5.340871229E+00-5.329549222E+00 --5.312272915E+00-5.288944366E+00-5.259719773E+00-5.224782487E+00-5.184255496E+00 --5.138132518E+00-5.086352657E+00-5.028809075E+00-4.965332822E+00-4.895722788E+00 --4.819806318E+00-4.737453428E+00-4.648582646E+00-4.553128453E+00-4.451040729E+00 --4.342302681E+00-4.226936214E+00-4.104980139E+00-3.976474502E+00-3.841466140E+00 --3.700066870E+00-3.552494861E+00-3.399023175E+00-3.239902375E+00-3.075284589E+00 --2.905291245E+00-2.730145948E+00-2.550108790E+00-2.365366950E+00-2.175935673E+00 --1.981630550E+00-1.782063919E+00-1.576453727E+00-1.363578944E+00-1.142246392E+00 --9.122824838E-01-6.749990614E-01-4.325112064E-01-1.866922198E-01 6.134070661E-02 - 3.113279550E-01 5.632329876E-01 8.169988065E-01 1.072509437E+00 1.329653668E+00 - 1.588335467E+00 1.848467909E+00 2.109972181E+00 2.372777890E+00 2.636822502E+00 - 2.902050581E+00 3.168412149E+00 3.435861133E+00 3.704354892E+00 3.973853125E+00 - 4.244316157E+00 4.515704746E+00 4.787981591E+00 5.061111508E+00 5.335061447E+00 - 5.609799701E+00 5.885300021E+00 6.161560054E+00 6.438462672E+00 1.466359260E+00 - 1.284024688E+00 1.102796664E+00 9.229021051E-01 7.443741559E-01 5.672837564E-01 - 3.917108577E-01 2.177615410E-01 4.553978084E-02-1.254700405E-01-2.967620036E-01 --4.681864968E-01-6.387387552E-01-8.069106956E-01-9.706112908E-01-1.127668534E+00 --1.276708346E+00-1.417721478E+00-1.551892580E+00-1.680940982E+00-1.806568584E+00 --1.930092484E+00-2.052408455E+00-2.174098333E+00-2.295547346E+00-2.416986313E+00 --2.538516776E+00-2.660136708E+00-2.781549464E+00-2.902383732E+00-3.022198188E+00 --3.140530119E+00-3.257025309E+00-3.371387675E+00-3.483361486E+00-3.592737887E+00 --3.699343768E+00-3.803060618E+00-3.903744441E+00-4.001267320E+00-4.095501875E+00 --4.186286552E+00-4.273526592E+00-4.357146173E+00-4.436958986E+00-4.512956259E+00 --4.585170528E+00-4.653265143E+00-4.717086820E+00-4.776714098E+00-4.832039995E+00 --4.882883819E+00-4.929182959E+00-4.970847799E+00-5.007788626E+00-5.039759391E+00 --5.066818464E+00-5.089057416E+00-5.106118456E+00-5.117831735E+00-5.124465248E+00 --5.125802915E+00-5.121644002E+00-5.111890704E+00-5.096375998E+00-5.074879870E+00 --5.047384728E+00-5.014067275E+00-4.975105229E+00-4.930602883E+00-4.880537073E+00 --4.824833152E+00-4.763370781E+00-4.695983850E+00-4.622503470E+00-4.542794738E+00 --4.456735410E+00-4.364226857E+00-4.265196494E+00-4.159610893E+00-4.047464831E+00 --3.928752795E+00-3.803457796E+00-3.671607502E+00-3.533340161E+00-3.388904332E+00 --3.238611602E+00-3.082777725E+00-2.921652842E+00-2.755461837E+00-2.584409576E+00 --2.408648849E+00-2.228226138E+00-2.042978801E+00-1.852572481E+00-1.656412452E+00 --1.453471656E+00-1.242531917E+00-1.022922039E+00-7.952292653E-01-5.611948740E-01 --3.228031652E-01-8.149451603E-02 1.620199700E-01 4.076766506E-01 6.554293170E-01 - 9.051690726E-01 1.156766913E+00 1.410106951E+00 1.665087311E+00 1.921615156E+00 - 2.179605118E+00 2.438978694E+00 2.699664416E+00 2.961598200E+00 3.224722888E+00 - 3.488987822E+00 3.754347765E+00 4.020761492E+00 4.288190735E+00 4.556599814E+00 - 4.825954348E+00 5.096219487E+00 5.367360657E+00 5.639344841E+00 5.912139908E+00 - 6.185718748E+00 6.460076993E+00 6.735092203E+00 1.480394750E+00 1.299629252E+00 - 1.120028720E+00 9.418312678E-01 7.650707672E-01 5.898212790E-01 4.161651259E-01 - 2.442037459E-01 7.408223509E-02-9.454394082E-02-2.632492841E-01-4.321683310E-01 --6.004238484E-01-7.666531688E-01-9.289071746E-01-1.084981072E+00-1.233229635E+00 --1.373258430E+00-1.505916423E+00-1.632766063E+00-1.755531815E+00-1.875637743E+00 --1.994135740E+00-2.111702984E+00-2.228784065E+00-2.345633427E+00-2.462391573E+00 --2.579124954E+00-2.695629036E+00-2.811591580E+00-2.926634047E+00-3.040321484E+00 --3.152306550E+00-3.262297703E+00-3.370022643E+00-3.475271466E+00-3.577848478E+00 --3.677591599E+00-3.774329629E+00-3.867870698E+00-3.958066812E+00-4.044827410E+00 --4.128031993E+00-4.207497323E+00-4.283235012E+00-4.355282416E+00-4.423301492E+00 --4.487111479E+00-4.546800128E+00-4.602290990E+00-4.653389006E+00-4.700028326E+00 --4.742101073E+00-4.779564762E+00-4.812185509E+00-4.839890073E+00-4.862799197E+00 --4.880816636E+00-4.893511221E+00-4.901028865E+00-4.903481628E+00-4.900565854E+00 --4.892156208E+00-4.878144986E+00-4.858334650E+00-4.832534648E+00-4.800810097E+00 --4.763346675E+00-4.720309530E+00-4.671773792E+00-4.617692588E+00-4.557979522E+00 --4.492523799E+00-4.421185553E+00-4.343814030E+00-4.260273345E+00-4.170438252E+00 --4.074228702E+00-3.971593526E+00-3.862478943E+00-3.746816048E+00-3.624558722E+00 --3.495758253E+00-3.360599285E+00-3.219366473E+00-3.072416173E+00-2.920068438E+00 --2.762594219E+00-2.600248284E+00-2.433227999E+00-2.261608527E+00-2.085245146E+00 --1.903822413E+00-1.716814017E+00-1.523342135E+00-1.322290217E+00-1.112747410E+00 --8.947567968E-01-6.695852642E-01-4.391132435E-01-2.049930380E-01 3.175547020E-02 - 2.708642372E-01 5.122792348E-01 7.559365607E-01 1.001704285E+00 1.249443988E+00 - 1.499033065E+00 1.750362380E+00 2.003332306E+00 2.257851572E+00 2.513836745E+00 - 2.771211364E+00 3.029905017E+00 3.289853130E+00 3.550997297E+00 3.813285333E+00 - 4.076670739E+00 4.341112324E+00 4.606572967E+00 4.873018413E+00 5.140416778E+00 - 5.408737960E+00 5.677952300E+00 5.948028789E+00 6.218935770E+00 6.490646203E+00 - 6.763155949E+00 7.036339471E+00 1.494460092E+00 1.315282975E+00 1.137328780E+00 - 9.608468765E-01 7.858720377E-01 6.124811960E-01 4.407588989E-01 2.708020118E-01 - 1.027776382E-01-6.350631314E-02-2.295779227E-01-3.959146058E-01-5.617782833E-01 --7.259362290E-01-8.865989213E-01-1.041590912E+00-1.189065297E+00-1.328262364E+00 --1.459667340E+00-1.584626608E+00-1.704816369E+00-1.821735805E+00-1.936573306E+00 --2.050107702E+00-2.162853738E+00-2.275082139E+00-2.386969686E+00-2.498630153E+00 --2.609961550E+00-2.720732986E+00-2.830696345E+00-2.939468622E+00-3.046707689E+00 --3.152124694E+00-3.255428022E+00-3.356377687E+00-3.454749986E+00-3.550337388E+00 --3.642930564E+00-3.732305179E+00-3.818375511E+00-3.901020647E+00-3.980004409E+00 --4.055322627E+00-4.127044893E+00-4.194848953E+00-4.258510760E+00-4.318105758E+00 --4.373592634E+00-4.424782635E+00-4.471593334E+00-4.513914189E+00-4.551706724E+00 --4.584807699E+00-4.613024392E+00-4.636448944E+00-4.655136263E+00-4.668713205E+00 --4.677016194E+00-4.680310424E+00-4.678444000E+00-4.671191280E+00-4.658450820E+00 --4.640083600E+00-4.615883202E+00-4.585722321E+00-4.549729550E+00-4.508080860E+00 --4.460912003E+00-4.408256445E+00-4.350058252E+00-4.286256687E+00-4.216767978E+00 --4.141450310E+00-4.060142247E+00-3.972726384E+00-3.879104894E+00-3.779188364E+00 --3.672869537E+00-3.560034956E+00-3.440652887E+00-3.314829118E+00-3.182789084E+00 --3.044884172E+00-2.901466437E+00-2.752814122E+00-2.599173505E+00-2.440762250E+00 --2.277719684E+00-2.109997576E+00-1.937332237E+00-1.759210846E+00-1.574846272E+00 --1.383207760E+00-1.183313831E+00-9.748783677E-01-7.587193237E-01-5.364827363E-01 --3.098814196E-01-8.012963103E-02 1.521756425E-01 3.870053276E-01 6.243038972E-01 - 8.639569160E-01 1.105822101E+00 1.349766719E+00 1.595667918E+00 1.843409514E+00 - 2.092883967E+00 2.343993272E+00 2.596647983E+00 2.850766308E+00 3.106273405E+00 - 3.363100694E+00 3.621185018E+00 3.880468122E+00 4.140896871E+00 4.402423586E+00 - 4.665005658E+00 4.928605285E+00 5.193188789E+00 5.458725520E+00 5.725186897E+00 - 5.992546294E+00 6.260778064E+00 6.529855170E+00 6.799752191E+00 7.070465892E+00 - 7.341868465E+00 1.508533102E+00 1.330961874E+00 1.154671514E+00 9.799223587E-01 - 8.067492692E-01 6.352305707E-01 4.654526762E-01 2.975106368E-01 1.315723989E-01 --3.242916106E-02-1.958161572E-01-3.594908045E-01-5.228717704E-01-6.848359017E-01 --8.437632685E-01-9.975687540E-01-1.144282236E+00-1.282801800E+00-1.413218459E+00 --1.536611230E+00-1.654540025E+00-1.768536790E+00-1.879891416E+00-1.989488052E+00 --2.097931807E+00-2.205535084E+00-2.312504951E+00-2.418978883E+00-2.524957524E+00 --2.630321368E+00-2.734967034E+00-2.838581505E+00-2.940838065E+00-3.041456715E+00 --3.140120875E+00-3.236543324E+00-3.330481060E+00-3.421669121E+00-3.509878212E+00 --3.594973287E+00-3.676777893E+00-3.755079105E+00-3.829835059E+00-3.901069383E+00 --3.968486884E+00-4.031856232E+00-4.091228101E+00-4.146575127E+00-4.197714337E+00 --4.244539253E+00-4.286966305E+00-4.324920647E+00-4.358320750E+00-4.386922759E+00 --4.410736279E+00-4.429849181E+00-4.444132752E+00-4.453171301E+00-4.457094532E+00 --4.456065424E+00-4.449791840E+00-4.438125219E+00-4.420962217E+00-4.398147242E+00 --4.369490790E+00-4.334940108E+00-4.294642222E+00-4.248734747E+00-4.197321440E+00 --4.140433471E+00-4.078051284E+00-4.010134861E+00-3.936591096E+00-3.857274954E+00 --3.772040828E+00-3.680777452E+00-3.583349250E+00-3.479597704E+00-3.369421836E+00 --3.252836412E+00-3.129986706E+00-3.001182783E+00-2.866774381E+00-2.727038801E+00 --2.582204703E+00-2.432476646E+00-2.278006699E+00-2.118811789E+00-1.954696057E+00 --1.785195478E+00-1.609598059E+00-1.426933025E+00-1.236235578E+00-1.037041256E+00 --8.298239285E-01-6.159543554E-01-3.970965510E-01-1.745906691E-01 5.076329080E-02 - 2.788375405E-01 5.095785880E-01 7.429054510E-01 9.786784548E-01 1.216752114E+00 - 1.456993779E+00 1.699282204E+00 1.943504224E+00 2.189551530E+00 2.437320174E+00 - 2.686713616E+00 2.937643979E+00 3.190031001E+00 3.443801249E+00 3.698887453E+00 - 3.955227986E+00 4.212766140E+00 4.471449448E+00 4.731229718E+00 4.992063350E+00 - 5.253911359E+00 5.516738953E+00 5.780515377E+00 6.045212977E+00 6.310806294E+00 - 6.577271432E+00 6.844584982E+00 7.112727302E+00 7.381699750E+00 7.651373732E+00 - 1.522594990E+00 1.346646237E+00 1.172035168E+00 9.990317385E-01 8.276701590E-01 - 6.580309177E-01 4.902047883E-01 3.242885523E-01 1.604294585E-01-1.348406206E-03 --1.620205021E-01-3.229606801E-01-4.837738933E-01-6.434332302E-01-8.004982611E-01 --9.530183452E-01-1.098960078E+00-1.236919000E+00-1.366589522E+00-1.488736517E+00 --1.604733907E+00-1.716090879E+00-1.824162942E+00-1.929957003E+00-2.034172537E+00 --2.137188632E+00-2.239244372E+00-2.340514678E+00-2.441088045E+00-2.540947544E+00 --2.640105749E+00-2.738354034E+00-2.835382044E+00-2.930934217E+00-3.024690441E+00 --3.116316226E+00-3.205525300E+00-3.292045167E+00-3.375713785E+00-3.456324451E+00 --3.533601632E+00-3.607495363E+00-3.678038536E+00-3.744898775E+00-3.807790794E+00 --3.866760469E+00-3.921811504E+00-3.972762299E+00-4.019466525E+00-4.061866360E+00 --4.099846917E+00-4.133379683E+00-4.162243466E+00-4.186332802E+00-4.205728454E+00 --4.220454333E+00-4.230137883E+00-4.234625036E+00-4.234173832E+00-4.228695928E+00 --4.217932189E+00-4.201769172E+00-4.180099434E+00-4.152772703E+00-4.119622685E+00 --4.080638342E+00-4.035941575E+00-3.985658085E+00-3.929918647E+00-3.868768267E+00 --3.802186338E+00-3.730142613E+00-3.652567464E+00-3.569323278E+00-3.480233026E+00 --3.385113385E+00-3.283800940E+00-3.176224786E+00-3.062446420E+00-2.942700863E+00 --2.817298288E+00-2.686496733E+00-2.550498651E+00-2.409487100E+00-2.263613148E+00 --2.112930313E+00-1.957290986E+00-1.796270092E+00-1.629187036E+00-1.455114819E+00 --1.273151894E+00-1.082775917E+00-8.842521205E-01-6.787077927E-01-4.676941721E-01 --2.525907535E-01-3.429828198E-02 1.868591957E-01 4.108922613E-01 6.377332945E-01 - 8.672517508E-01 1.099291206E+00 1.333707672E+00 1.570370585E+00 1.809158263E+00 - 2.049955462E+00 2.292654254E+00 2.537153820E+00 2.783357944E+00 3.031173830E+00 - 3.280514761E+00 3.531301735E+00 3.783462591E+00 4.036931282E+00 4.291647260E+00 - 4.547555040E+00 4.804603621E+00 5.062745825E+00 5.321938029E+00 5.582140428E+00 - 5.843317335E+00 6.105436828E+00 6.368470577E+00 6.632393509E+00 6.897182796E+00 - 7.162816103E+00 7.429275897E+00 7.696568233E+00 7.964568750E+00 1.536629921E+00 - 1.362315754E+00 1.189393554E+00 1.018143650E+00 8.486014817E-01 6.808507209E-01 - 5.149854977E-01 3.511026038E-01 1.893338781E-01 2.978233675E-02-1.282299211E-01 --2.863871600E-01-4.445534382E-01-6.018162545E-01-7.569026544E-01-9.080239170E-01 --1.053143839E+00-1.190612078E+00-1.319745752E+00-1.440944296E+00-1.555333907E+00 --1.664359953E+00-1.769410495E+00-1.871601896E+00-1.971712287E+00-2.070222716E+00 --2.167438855E+00-2.263593098E+00-2.358825408E+00-2.453199231E+00-2.546793859E+00 --2.639512889E+00-2.731065241E+00-2.821260873E+00-2.909806286E+00-2.996311290E+00 --3.080480890E+00-3.162143201E+00-3.241024845E+00-3.316833426E+00-3.389476333E+00 --3.458943143E+00-3.524929876E+00-3.587120124E+00-3.645489364E+00-3.700038479E+00 --3.750608292E+00-3.797027196E+00-3.839243597E+00-3.877117120E+00-3.910623378E+00 --3.939604113E+00-3.963854709E+00-3.983421113E+00-3.998362051E+00-4.008533870E+00 --4.013544579E+00-4.013507967E+00-4.008614755E+00-3.998586958E+00-3.983247664E+00 --3.962510198E+00-3.936284825E+00-3.904417337E+00-3.866722455E+00-3.823219923E+00 --3.774056472E+00-3.719375161E+00-3.659295105E+00-3.593858948E+00-3.523086196E+00 --3.447014017E+00-3.365595249E+00-3.278592881E+00-3.185727996E+00-3.086849502E+00 --2.981925485E+00-2.871096310E+00-2.754613795E+00-2.632691844E+00-2.505490990E+00 --2.373164423E+00-2.235849009E+00-2.093612813E+00-1.946350182E+00-1.793681070E+00 --1.634937070E+00-1.469211203E+00-1.295629411E+00-1.113654849E+00-9.234716673E-01 --7.260559716E-01-5.228418322E-01-3.151875130E-01-1.040419058E-01 1.101091194E-01 - 3.273252165E-01 5.475520389E-01 7.706813966E-01 9.965547597E-01 1.225016599E+00 - 1.455925752E+00 1.689150442E+00 1.924567106E+00 2.162060468E+00 2.401521973E+00 - 2.642848823E+00 2.885944804E+00 3.130720145E+00 3.377089272E+00 3.624969225E+00 - 3.874281986E+00 4.124956366E+00 4.376927379E+00 4.630135519E+00 4.884526221E+00 - 5.140049446E+00 5.396659256E+00 5.654313224E+00 5.912971952E+00 6.172599231E+00 - 6.433162351E+00 6.694632071E+00 6.956982327E+00 7.220190085E+00 7.484233753E+00 - 7.749096834E+00 8.014786563E+00 8.281181002E+00 1.550616798E+00 1.377945337E+00 - 1.206720752E+00 1.037234361E+00 8.695219661E-01 7.036686071E-01 5.397704982E-01 - 3.779255096E-01 2.182575820E-01 6.093115282E-02-9.448760971E-02-2.498188184E-01 --4.052650868E-01-5.600477896E-01-7.130423355E-01-8.626356950E-01-1.006843652E+00 --1.143839564E+00-1.272588230E+00-1.393099193E+00-1.506217006E+00-1.613268045E+00 --1.715618673E+00-1.814455227E+00-1.910643778E+00-2.004808908E+00-2.097342997E+00 --2.188549077E+00-2.278601010E+00-2.367608482E+00-2.455660293E+00-2.542743228E+00 --2.628636018E+00-2.713202827E+00-2.796211690E+00-2.877277949E+00-2.956182147E+00 --3.032684661E+00-3.106445818E+00-3.177301555E+00-3.245230584E+00-3.309920595E+00 --3.371009312E+00-3.428440117E+00-3.482213706E+00-3.532162657E+00-3.578080920E+00 --3.619905146E+00-3.657492399E+00-3.690783811E+00-3.719690158E+00-3.743966604E+00 --3.763595218E+00-3.778626492E+00-3.789047887E+00-3.794486647E+00-3.794815396E+00 --3.790285923E+00-3.780835851E+00-3.766165404E+00-3.746192835E+00-3.720872451E+00 --3.690088635E+00-3.653640663E+00-3.611371198E+00-3.563352810E+00-3.509721407E+00 --3.450617964E+00-3.386189066E+00-3.316577556E+00-3.241911520E+00-3.162188575E+00 --3.077216654E+00-2.986675102E+00-2.890330135E+00-2.788211596E+00-2.680488135E+00 --2.567308721E+00-2.448795570E+00-2.325062468E+00-2.196210901E+00-2.062304010E+00 --1.923263105E+00-1.778746288E+00-1.628106043E+00-1.470466898E+00-1.304969387E+00 --1.131074710E+00-9.489246240E-01-7.593936543E-01-5.638243363E-01-3.635583678E-01 --1.595753917E-01 4.756074297E-02 2.579037862E-01 4.714351686E-01 6.880740925E-01 - 9.076758316E-01 1.130076959E+00 1.355126512E+00 1.582683706E+00 1.812617857E+00 - 2.044805436E+00 2.279128854E+00 2.515477763E+00 2.753749437E+00 2.993847117E+00 - 3.235679042E+00 3.479159256E+00 3.724207636E+00 3.970747928E+00 4.218705902E+00 - 4.468011287E+00 4.718599784E+00 4.970412776E+00 5.223396564E+00 5.477501919E+00 - 5.732683659E+00 5.988900342E+00 6.246113766E+00 6.504288441E+00 6.763391517E+00 - 7.023393050E+00 7.284266290E+00 7.545987255E+00 7.808533690E+00 8.071889290E+00 - 8.336062015E+00 8.600931881E+00 1.564536012E+00 1.393518196E+00 1.224002341E+00 - 1.056289233E+00 8.904139894E-01 7.264639018E-01 5.645396961E-01 4.047440920E-01 - 2.471943649E-01 9.208236682E-02-6.082044729E-02-2.132812953E-01-3.659345444E-01 --5.181582483E-01-6.689491005E-01-8.168695754E-01-9.600300359E-01-1.096508989E+00 --1.224973080E+00-1.345038231E+00-1.457232753E+00-1.562686398E+00-1.662688113E+00 --1.758476074E+00-1.851026105E+00-1.941100131E+00-2.029192652E+00-2.115683504E+00 --2.200778943E+00-2.284589380E+00-2.367194260E+00-2.448637285E+00-2.528793915E+00 --2.607530749E+00-2.684750053E+00-2.760178357E+00-2.833503556E+00-2.904479774E+00 --2.972931669E+00-3.038737784E+00-3.101577463E+00-3.161086390E+00-3.217150666E+00 --3.269744621E+00-3.318705127E+00-3.363805996E+00-3.404948605E+00-3.442007968E+00 --3.474862286E+00-3.503472024E+00-3.527608909E+00-3.547153554E+00-3.562137401E+00 --3.572560742E+00-3.578270895E+00-3.578935485E+00-3.574647476E+00-3.565571944E+00 --3.551451861E+00-3.532125396E+00-3.507548037E+00-3.477661765E+00-3.442336551E+00 --3.401337173E+00-3.354525406E+00-3.301993962E+00-3.243895127E+00-3.180493776E+00 --3.112096883E+00-3.038871272E+00-2.960824206E+00-2.877821140E+00-2.789611334E+00 --2.695949631E+00-2.596769612E+00-2.492143157E+00-2.382147149E+00-2.266842751E+00 --2.146297098E+00-2.020552098E+00-1.889528831E+00-1.752910821E+00-1.610079262E+00 --1.460199202E+00-1.302439040E+00-1.136289545E+00-9.618807589E-01-7.800113757E-01 --5.919356190E-01-3.989585201E-01-2.020795125E-01-1.901315223E-03 2.015729538E-01 - 4.083898920E-01 6.184963039E-01 8.317662363E-01 1.048031753E+00 1.267137420E+00 - 1.488941029E+00 1.713307450E+00 1.940104902E+00 2.169208230E+00 2.400500611E+00 - 2.633871506E+00 2.869215809E+00 3.106435038E+00 3.345437522E+00 3.586136813E+00 - 3.828450829E+00 4.072302619E+00 4.317620522E+00 4.564336471E+00 4.812384009E+00 - 5.061699778E+00 5.312225585E+00 5.563908470E+00 5.816699911E+00 6.070555437E+00 - 6.325434225E+00 6.581298825E+00 6.838114793E+00 7.095850200E+00 7.354475321E+00 - 7.613962901E+00 7.874288322E+00 8.135428651E+00 8.397366664E+00 8.660109718E+00 - 8.923539780E+00 1.578379152E+00 1.409025300E+00 1.241226372E+00 1.075293404E+00 - 9.112638716E-01 7.492315226E-01 5.893021541E-01 4.315782685E-01 2.761686687E-01 - 1.232558791E-01-2.723332581E-02-1.767818814E-01-3.265651587E-01-4.761480453E-01 --6.246131912E-01-7.706901667E-01-9.126357084E-01-1.048516095E+00-1.176754172E+00 --1.296579282E+00-1.408165758E+00-1.512384914E+00-1.610433890E+00-1.703571879E+00 --1.792873143E+00-1.879203977E+00-1.963179448E+00-2.045231968E+00-2.125602022E+00 --2.204400087E+00-2.281730001E+00-2.357652348E+00-2.432105906E+00-2.504995420E+00 --2.576340911E+00-2.645922722E+00-2.713387400E+00-2.778640933E+00-2.841648187E+00 --2.902046798E+00-2.959389315E+00-3.013526878E+00-3.064443587E+00-3.111975115E+00 --3.155864182E+00-3.195965644E+00-3.232171002E+00-3.264305124E+00-3.292332728E+00 --3.316073455E+00-3.335318873E+00-3.350089151E+00-3.360356926E+00-3.366090161E+00 --3.366970206E+00-3.362875486E+00-3.353997747E+00-3.340303193E+00-3.321508025E+00 --3.297556178E+00-3.268433858E+00-3.234072015E+00-3.194297616E+00-3.148809102E+00 --3.097496866E+00-3.040586625E+00-2.978434729E+00-2.911401290E+00-2.839708876E+00 --2.763385210E+00-2.682319661E+00-2.596346541E+00-2.505305986E+00-2.408998121E+00 --2.307300576E+00-2.200215385E+00-2.087766340E+00-1.969951010E+00-1.846683113E+00 --1.717662578E+00-1.582297528E+00-1.439800692E+00-1.289391666E+00-1.130615222E+00 --9.636128242E-01-7.891440339E-01-6.083952210E-01-4.226122792E-01-2.327646229E-01 --3.945946307E-02 1.571922582E-01 3.573419057E-01 5.609417966E-01 7.678740153E-01 - 9.779786554E-01 1.191102594E+00 1.407102091E+00 1.625837077E+00 1.847174426E+00 - 2.070988343E+00 2.297156814E+00 2.525561119E+00 2.756089448E+00 2.988637441E+00 - 3.223106078E+00 3.459401218E+00 3.697434785E+00 3.937124799E+00 4.178393874E+00 - 4.421168445E+00 4.665379497E+00 4.910962816E+00 5.157857538E+00 5.406004144E+00 - 5.655345461E+00 5.905828732E+00 6.157406028E+00 6.410033458E+00 6.663670799E+00 - 6.918281138E+00 7.173830599E+00 7.430288084E+00 7.687624856E+00 7.945814151E+00 - 8.204831143E+00 8.464652306E+00 8.725259859E+00 8.986659973E+00 9.248735717E+00 - 1.592139024E+00 1.424456665E+00 1.258384399E+00 1.094248476E+00 9.320914218E-01 - 7.720079380E-01 6.141020514E-01 4.584737773E-01 3.052235705E-01 1.544971509E-01 - 6.330221360E-03-1.403020444E-01-2.871368380E-01-4.339751369E-01-5.799782160E-01 --7.240425875E-01-8.646019842E-01-9.997655508E-01-1.127762066E+00-1.247469098E+00 --1.358706446E+00-1.462066122E+00-1.558621737E+00-1.649595878E+00-1.736127662E+00 --1.819154602E+00-1.899391525E+00-1.977293302E+00-2.053173433E+00-2.127189973E+00 --2.199473199E+00-2.270078829E+00-2.339008206E+00-2.406227199E+00-2.471700375E+00 --2.535334220E+00-2.596923353E+00-2.656407941E+00-2.713646566E+00-2.768237025E+00 --2.819903721E+00-2.868577037E+00-2.914124504E+00-2.956297981E+00-2.994911213E+00 --3.029855274E+00-3.060916681E+00-3.088025222E+00-3.111055512E+00-3.129754986E+00 --3.144086492E+00-3.154015886E+00-3.159500968E+00-3.160408222E+00-3.156447822E+00 --3.147667378E+00-3.134210874E+00-3.115855931E+00-3.092441262E+00-3.063988237E+00 --3.030516207E+00-2.991889756E+00-2.947777943E+00-2.897907081E+00-2.842448205E+00 --2.781800568E+00-2.716311051E+00-2.646234470E+00-2.571635915E+00-2.492429756E+00 --2.408523521E+00-2.319771651E+00-2.225970106E+00-2.126855848E+00-2.022248022E+00 --1.912087501E+00-1.796269058E+00-1.674489044E+00-1.546195499E+00-1.410669451E+00 --1.267201549E+00-1.115404601E+00-9.554556402E-01-7.880999185E-01-6.144625471E-01 --4.357247637E-01-2.528167187E-01-6.633019311E-02 1.235766955E-01 3.171394002E-01 - 5.143049630E-01 7.149639668E-01 9.189537031E-01 1.126113271E+00 1.336300483E+00 - 1.549381379E+00 1.765226609E+00 1.983707704E+00 2.204698370E+00 2.428079213E+00 - 2.653737230E+00 2.881562105E+00 3.111447089E+00 3.343292204E+00 3.577003976E+00 - 3.812493482E+00 4.049676243E+00 4.288473344E+00 4.528811336E+00 4.770620821E+00 - 5.013835752E+00 5.258394130E+00 5.504238311E+00 5.751313790E+00 5.999567241E+00 - 6.248947045E+00 6.499405304E+00 6.750898572E+00 7.003387109E+00 7.256834489E+00 - 7.511207314E+00 7.766474922E+00 8.022609202E+00 8.279584293E+00 8.537376068E+00 - 8.795961112E+00 9.055321112E+00 9.315461296E+00 9.576266021E+00 1.605810995E+00 - 1.439819316E+00 1.275504232E+00 1.113203883E+00 9.529577943E-01 7.948576431E-01 - 6.390025126E-01 4.854880088E-01 3.344078072E-01 1.858821848E-01 4.003577191E-02 --1.037777997E-01-2.475948701E-01-3.915725092E-01-5.349905561E-01-6.768885605E-01 --8.158726188E-01-9.501191238E-01-1.077748544E+00-1.197386625E+00-1.308508560E+00 --1.411405084E+00-1.506972705E+00-1.596335829E+00-1.680642600E+00-1.760853762E+00 --1.837735632E+00-1.911813432E+00-1.983494830E+00-2.053012177E+00-2.120503570E+00 --2.186082358E+00-2.249779941E+00-2.311539936E+00-2.371320707E+00-2.429168770E+00 --2.485054074E+00-2.538730885E+00-2.589938222E+00-2.638557839E+00-2.684498375E+00 --2.727575429E+00-2.767528111E+00-2.804153505E+00-2.837355538E+00-2.866916421E+00 --2.892708736E+00-2.914643842E+00-2.932473763E+00-2.946083690E+00-2.955470200E+00 --2.960505880E+00-2.961152430E+00-2.957172540E+00-2.948449617E+00-2.935084187E+00 --2.917038406E+00-2.894093984E+00-2.866300115E+00-2.833705201E+00-2.796159260E+00 --2.753367579E+00-2.705074301E+00-2.651265464E+00-2.592263082E+00-2.528430027E+00 --2.459964953E+00-2.386958281E+00-2.309427162E+00-2.227282672E+00-2.140385800E+00 --2.048491063E+00-1.951297240E+00-1.848480390E+00-1.739759821E+00-1.624826510E+00 --1.503183388E+00-1.374184339E+00-1.237219314E+00-1.091998922E+00-9.387511765E-01 --7.782106364E-01-6.114465586E-01-4.395740526E-01-2.634701685E-01-8.369442113E-02 - 9.957427570E-02 2.866315997E-01 4.774411753E-01 6.719121421E-01 8.698810055E-01 - 1.071163875E+00 1.275606484E+00 1.483072448E+00 1.693435285E+00 1.906573528E+00 - 2.122367061E+00 2.340697951E+00 2.561448783E+00 2.784505818E+00 3.009762258E+00 - 3.237116223E+00 3.466467747E+00 3.697720789E+00 3.930785801E+00 4.165578853E+00 - 4.402019920E+00 4.640033065E+00 4.879547461E+00 5.120497193E+00 5.362819923E+00 - 5.606456260E+00 5.851350425E+00 6.097450588E+00 6.344707868E+00 6.593074477E+00 - 6.842503793E+00 7.092952286E+00 7.344380507E+00 7.596752442E+00 7.850035067E+00 - 8.104198144E+00 8.359213916E+00 8.615056981E+00 8.871703947E+00 9.129132220E+00 - 9.387323780E+00 9.646283174E+00 9.905895970E+00 1.619428870E+00 1.455172796E+00 - 1.292660790E+00 1.132239534E+00 9.739418322E-01 8.178542447E-01 6.640718818E-01 - 5.126865959E-01 3.637875823E-01 2.174838648E-01 7.395629728E-02-6.714788978E-02 --2.078803044E-01-3.488890137E-01-4.896095073E-01-6.291698814E-01-7.663176785E-01 --8.993604046E-01-1.026439933E+00-1.146010955E+00-1.257221162E+00-1.360054940E+00 --1.455156101E+00-1.543487034E+00-1.626116749E+00-1.703996124E+00-1.777946781E+00 --1.848610406E+00-1.916453453E+00-1.981793060E+00-2.044822033E+00-2.105700138E+00 --2.164445920E+00-2.221027020E+00-2.275486480E+00-2.327917434E+00-2.378234921E+00 --2.426144215E+00-2.471469769E+00-2.514237764E+00-2.554403300E+00-2.591734743E+00 --2.625976028E+00-2.657012391E+00-2.684658239E+00-2.708740130E+00-2.729192938E+00 --2.745813328E+00-2.758411514E+00-2.766987253E+00-2.771361091E+00-2.771452681E+00 --2.767237617E+00-2.758500262E+00-2.745154403E+00-2.727229900E+00-2.704678935E+00 --2.677518488E+00-2.645730813E+00-2.609143972E+00-2.567540972E+00-2.520704497E+00 --2.468529136E+00-2.411172630E+00-2.348895837E+00-2.281878382E+00-2.210243144E+00 --2.134050396E+00-2.053253965E+00-1.967628605E+00-1.876881896E+00-1.780650034E+00 --1.678527036E+00-1.570023932E+00-1.454583240E+00-1.331655921E+00-1.200764871E+00 --1.061721300E+00-9.148158695E-01-7.607895808E-01-6.006563870E-01-4.354521758E-01 --2.659880034E-01-9.278389298E-02 8.398312343E-02 2.646635963E-01 4.492378606E-01 - 6.376227974E-01 8.296586478E-01 1.025158718E+00 1.223963869E+00 1.425922492E+00 - 1.630893722E+00 1.838750687E+00 2.049376777E+00 2.262661390E+00 2.478495228E+00 - 2.696769210E+00 2.917375633E+00 3.140207540E+00 3.365162712E+00 3.592145311E+00 - 3.821063042E+00 4.051825224E+00 4.284345420E+00 4.518543272E+00 4.754343248E+00 - 4.991673194E+00 5.230464744E+00 5.470654236E+00 5.712182424E+00 5.954993226E+00 - 6.199033163E+00 6.444251984E+00 6.690603018E+00 6.938042373E+00 7.186527209E+00 - 7.436015413E+00 7.686467408E+00 7.937847305E+00 8.190122436E+00 8.443262841E+00 - 8.697241122E+00 8.952032190E+00 9.207612981E+00 9.463961472E+00 9.721060385E+00 - 9.978914369E+00 1.023741073E+01 1.633079059E+00 1.470609272E+00 1.309946262E+00 - 1.151442411E+00 9.951244068E-01 8.410747981E-01 6.893851867E-01 5.401483067E-01 - 3.934563224E-01 2.494061020E-01 1.081744354E-01-3.037039691E-02-1.679592609E-01 --3.058825648E-01-4.437538095E-01-5.807399560E-01-7.157479549E-01-8.472845425E-01 --9.735979964E-01-1.093045002E+00-1.204506455E+00-1.307643515E+00-1.402757807E+00 --1.490580491E+00-1.572042384E+00-1.648103061E+00-1.719630875E+00-1.787354602E+00 --1.851787918E+00-1.913351032E+00-1.972296323E+00-2.028774263E+00-2.082882585E+00 --2.134675304E+00-2.184243860E+00-2.231575454E+00-2.276503811E+00-2.318897522E+00 --2.358731138E+00-2.395972759E+00-2.430491562E+00-2.462101470E+00-2.490705273E+00 --2.516158824E+00-2.538260495E+00-2.556941730E+00-2.572050611E+00-2.583354875E+00 --2.590792451E+00-2.594245291E+00-2.593576136E+00-2.588874469E+00-2.579937459E+00 --2.566479343E+00-2.548514121E+00-2.526190986E+00-2.499457502E+00-2.468250397E+00 --2.432428644E+00-2.391762257E+00-2.346075036E+00-2.295273090E+00-2.239305731E+00 --2.178293690E+00-2.112423993E+00-2.041816899E+00-1.966527518E+00-1.886441506E+00 --1.801303750E+00-1.710716027E+00-1.614243765E+00-1.511395313E+00-1.401609159E+00 --1.284313270E+00-1.159075877E+00-1.025825995E+00-8.849348462E-01-7.371335993E-01 --5.833751661E-01-4.246243696E-01-2.616204175E-01-9.482999336E-02 7.559760253E-02 - 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7.714564919E-01 9.557618658E-01 1.143627556E+00 1.334899009E+00 1.529427782E+00 - 1.727074283E+00 1.927707520E+00 2.131202767E+00 2.337437403E+00 2.546297050E+00 - 2.757679306E+00 2.971491099E+00 3.187644436E+00 3.406050707E+00 3.626618031E+00 - 3.849255535E+00 4.073872507E+00 4.300380903E+00 4.528698208E+00 4.758746323E+00 - 4.990448643E+00 5.223730508E+00 5.458521811E+00 5.694757461E+00 5.932375885E+00 - 6.171318152E+00 6.411528623E+00 6.652955655E+00 6.895551193E+00 7.139269670E+00 - 7.384067562E+00 7.629903944E+00 7.876740835E+00 8.124542725E+00 8.373275151E+00 - 8.622903788E+00 8.873395897E+00 9.124721629E+00 9.376854020E+00 9.629768431E+00 - 9.883442288E+00 1.013785410E+01 1.039298710E+01 1.064884602E+01 1.090532289E+01 - 1.660887327E+00 1.502121192E+00 1.345270709E+00 1.190700485E+00 1.038432065E+00 - 8.885483895E-01 7.411396717E-01 5.962904571E-01 4.540808115E-01 3.145838660E-01 - 1.778942296E-01 4.414385470E-02-8.727174262E-02-2.185803533E-01-3.501051405E-01 --4.811954345E-01-6.110632139E-01-7.386664179E-01-8.626286913E-01-9.813797420E-01 --1.093440646E+00-1.197721521E+00-1.293797189E+00-1.381866197E+00-1.462544878E+00 --1.536666479E+00-1.605069886E+00-1.668538255E+00-1.727728140E+00-1.783113968E+00 --1.835101963E+00-1.884014836E+00-1.930112526E+00-1.973533500E+00-2.014228618E+00 --2.052161642E+00-2.087400263E+00-2.119998116E+00-2.149898180E+00-2.176963138E+00 --2.201111829E+00-2.222309621E+00-2.240401409E+00-2.255292471E+00-2.266922097E+00 --2.275141216E+00-2.279817594E+00-2.280920852E+00-2.278279098E+00-2.271785968E+00 --2.261507853E+00-2.247222646E+00-2.228665366E+00-2.205854533E+00-2.178928360E+00 --2.147839693E+00-2.112445007E+00-2.072531441E+00-2.027878144E+00-1.978293352E+00 --1.923586623E+00-1.863669763E+00-1.798546153E+00-1.728183961E+00-1.652437274E+00 --1.570979026E+00-1.483433714E+00-1.389398560E+00-1.288460792E+00-1.180293308E+00 --1.064740052E+00-9.418772075E-01-8.120766121E-01-6.759410681E-01-5.342338812E-01 --3.877416230E-01-2.370537828E-01-8.253250167E-02 7.578151097E-02 2.383605856E-01 - 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5.130308920E+00-3.426471005E+00 5.166043841E+00-3.534937728E+00 5.206813915E+00 --3.640798311E+00 5.253834128E+00-3.741012989E+00 5.308905208E+00-3.830598753E+00 - 5.373510745E+00-3.904199723E+00 5.448655995E+00-3.956422283E+00 5.534661474E+00 --3.982415950E+00 5.630301273E+00-3.980524005E+00 5.732649847E+00-3.953908401E+00 - 5.838828950E+00-3.906693942E+00 5.945861167E+00-3.844808099E+00 6.051180391E+00 --3.774750918E+00 6.153429126E+00-3.700471645E+00 6.251845163E+00-3.624802657E+00 - 6.346119147E+00-3.549514550E+00 6.436271217E+00-3.475330639E+00 6.522415436E+00 --3.402708743E+00 6.604713002E+00-3.331977007E+00 6.683356820E+00-3.263349802E+00 - 6.758556660E+00-3.196963348E+00 6.830532458E+00-3.132861319E+00 6.899503606E+00 --3.071028928E+00 6.965684752E+00-3.011345772E+00 7.029274952E+00-2.953670675E+00 - 7.090456084E+00-2.897837485E+00 7.149391317E+00-2.843668630E+00 7.206226223E+00 --2.791006449E+00 7.261090662E+00-2.739705122E+00 7.314100504E+00-2.689631798E+00 - 7.365359743E+00-2.640670310E+00 7.414961689E+00-2.592715380E+00 7.462992114E+00 --2.545683401E+00 7.509530057E+00-2.499503344E+00 7.554647956E+00-2.454110038E+00 - 7.598412393E+00-2.409444046E+00 7.640884584E+00-2.365450639E+00 7.682121161E+00 --2.322080370E+00 7.722174669E+00-2.279288476E+00 7.761094207E+00-2.237034989E+00 - 7.798926234E+00-2.195285281E+00 7.835713075E+00-2.154004151E+00 7.871493139E+00 --2.113156419E+00 7.906302009E+00-2.072709481E+00 7.940174136E+00-2.032636382E+00 - 7.973142297E+00-1.992913115E+00 8.005235866E+00-1.953514295E+00 8.036481153E+00 --1.914414128E+00 8.066902489E+00-1.875588516E+00 8.096522740E+00-1.837015570E+00 - 8.125363931E+00-1.798676181E+00 8.153448614E+00-1.760555588E+00 8.180799711E+00 --1.722642193E+00 8.207437413E+00-1.684922357E+00 8.233379360E+00-1.647381064E+00 - 8.258641013E+00-1.610002712E+00 8.283235324E+00-1.572770850E+00 8.307173877E+00 --1.535669795E+00 8.330469570E+00-1.498687677E+00 8.353135986E+00-1.461815029E+00 - 8.375184773E+00-1.425041527E+00 8.396625360E+00-1.388355893E+00 8.417466014E+00 --1.351747166E+00 8.437714727E+00-1.315205541E+00 8.457378738E+00-1.278721771E+00 - 8.476465806E+00-1.242288213E+00 8.494983751E+00-1.205898184E+00 8.512938536E+00 --1.169544273E+00 8.530332473E+00-1.133217163E+00 8.547166782E+00-1.096907964E+00 - 8.563441754E+00-1.060608353E+00 8.579157589E+00-1.024311136E+00 8.594316829E+00 --9.880116766E-01 8.608924987E+00-9.517078266E-01 8.622987226E+00-9.153974939E-01 - 8.636507270E+00-8.790780321E-01 8.649487948E+00-8.427466725E-01 8.661929779E+00 --8.063998816E-01 8.673831986E+00-7.700340874E-01 8.685193791E+00-7.336463598E-01 - 8.696015089E+00-6.972346347E-01 8.706295084E+00-6.607970373E-01 8.716031622E+00 --6.243316676E-01 8.725222046E+00-5.878370182E-01 8.733864429E+00-5.513123901E-01 - 8.741957463E+00-5.147577326E-01 8.749499977E+00-4.781734048E-01 8.756490747E+00 --4.415600780E-01 8.762928611E+00-4.049187444E-01 8.768813120E+00-3.682508240E-01 - 8.774143936E+00-3.315579489E-01 8.778920552E+00-2.948418846E-01 8.783142290E+00 --2.581045307E-01 8.786808404E+00-2.213479364E-01 8.789918246E+00-1.845743083E-01 - 8.792470944E+00-1.477859594E-01 8.794464799E+00-1.109852805E-01 8.795897489E+00 --7.417482290E-02 8.796767461E+00-3.735738049E-02 8.797074164E+00-5.358971485E-04 - 4.574638794E+00-4.199536201E+00 8.997870996E+00-4.199536201E+00 8.997870996E+00 - 4.198124541E+00 4.574638794E+00 4.198124541E+00 4.574638794E+00-4.199536201E+00 - - 2.57838785E-02 abs(PSI-AXIS) --> [T M**2] -8.80494393E+00 - 1.03807023E+00 R OF MAGAXE --> [M] 7.04475979E+00 - -1.04006526E-04 Z OF MAGAXE --> [M] -7.05829891E-04 - -7.89663369E-05 Z0 --> [M] -5.35897149E-04 - 6.78640000E+00 R0 [M] USED FOR CONVERTING TO MKSA - 7.41480000E+00 B0 [T] USED FOR CONVERTING TO MKSA - 1.00000000E+00 SIGN OF B0 IN EXPERIMENT (CHEASE ASSUMES 1.0) - 3.31621990E-01 TOTAL CURRENT --> [A] 1.32792135E+07 - 1.00000000E+00 SIGN OF IP IN EXPERIMENT (CHEASE ASSUMES 1.0) - 1.98414379E+00 b/a - 1.94710000E+00 Q_ZERO, USING SIGNS OF IP AND B0, WOULD GIVE: 1.94710000E+00 - 6.90024685E+00 Q_EDGE, USING SIGNS OF IP AND B0, WOULD GIVE: 6.90024685E+00 - 6.80378569E-01 POLOIDAL BETA - 1.28386756E-02 BETA_EXP=

*2*MU0/B0**2 - 4.70510270E-01 LI - 1.94665152E-02 PRESSURE ON AXIS --> [Pa] 8.51681535E+05 --> [10**19 M**-3 KEV]: 5.31636414E+02 - 1.13202992E-02 BETA - 1.52150157E-02 BETA* (SQRT()) - 4.20116757E-02 BETA-AXIS=2p0/(T0/Rmag)^2; with Rmag->Rgeo(LCFS): 3.89862482E-02 - -2.57838785E-02 PSI-AXIS --> [T M**2] -8.80494393E+00 - -1.62004886E-01 2*PI*PSI-AXIS --> -5.53230943E+01 - -2.57838785E-02 IP_SIGN*PSI-AXIS --> [T M**2] -8.80494393E+00 - -1.62004886E-01 IP_SIGN*2*PI*PSI-AXIS --> -5.53230943E+01 - 3.37510024E+00 ASPECT RATIO ; a/R= 2.96287496E-01 - 2.91389308E+00 VOLUME -> 9.10734888E+02 - 4.85595700E-01 AREA -> 2.23642192E+01 - 1.67123635E+01 SURFACE -> 7.69691661E+02 - 2.82508940E+00 LENGTH -> 1.91721867E+01 - 7.03709374E-01 RMIN -> RMIN [m] 4.77565329E+00 - 1.29627994E+00 RMAX -> RMAX [m] 8.79707416E+00 - -5.86823051E-01 ZMIN -> ZMIN [m] -3.98241595E+00 - 5.88446130E-01 ZMAX -> ZMAX [m] 3.99343082E+00 - 9.99994655E-01 RGEOM -> RGEOM [m] 6.78636373E+00 - 2.96285282E-01 MINOR RADIUS -> A [m] 2.01071043E+00 diff --git a/test/test_data/regression_equilibrium_example/INP1_ascii b/test/test_data/regression_equilibrium_example/INP1_ascii deleted file mode 100644 index 33dd8de2..00000000 --- a/test/test_data/regression_equilibrium_example/INP1_ascii +++ /dev/null @@ -1,1982 +0,0 @@ - 12 141 0 - 0.523598775598299E+00 0.179044876759357E-01 0.103807022777797E+01-0.104006526434566E-03 0.100000000000000E+01 - 0.194661351128034E-01 0.194630943606462E-01 0.194570134179549E-01 0.194478934137729E-01 0.194357360515811E-01 - 0.194205436162640E-01 0.194023189810163E-01 0.193810656142381E-01 0.193567875863852E-01 0.193294895769260E-01 - 0.192991768814979E-01 0.192658554202460E-01 0.192295317448728E-01 0.191902130299402E-01 0.191479070274830E-01 - 0.191026220082567E-01 0.190543667161005E-01 0.190031503372621E-01 0.189489825015114E-01 0.188918733515063E-01 - 0.188318336552474E-01 0.187688748743299E-01 0.187030091735138E-01 0.186342493648750E-01 0.185626088329878E-01 - 0.184881014964566E-01 0.184107418107928E-01 0.183305447859999E-01 0.182475260027865E-01 0.181617016355864E-01 - 0.180730884831074E-01 0.179817039657659E-01 0.178875660651531E-01 0.177906932661570E-01 0.176911045949040E-01 - 0.175888197233699E-01 0.174838589862966E-01 0.173762432689312E-01 0.172659939361695E-01 0.171531329148067E-01 - 0.170376827821502E-01 0.169196667181066E-01 0.167991084377082E-01 0.166760322275462E-01 0.165504630084936E-01 - 0.164224263381624E-01 0.162919483322642E-01 0.161590555780400E-01 0.160237751486552E-01 0.158861346881923E-01 - 0.157461624850310E-01 0.156038875914725E-01 0.154593398178852E-01 0.153125493207018E-01 0.151635465230278E-01 - 0.150123625140316E-01 0.148590291510470E-01 0.147035788481345E-01 0.145460445753170E-01 0.143864599689123E-01 - 0.142248592398122E-01 0.140612770700234E-01 0.138957487836929E-01 0.137283104093140E-01 0.135589984298991E-01 - 0.133878489811661E-01 0.132148988523951E-01 0.130401870885832E-01 0.128637537754775E-01 0.126856382804583E-01 - 0.125058801391097E-01 0.123245196596810E-01 0.121415979035263E-01 0.119571565079347E-01 0.117712377539301E-01 - 0.115838844395915E-01 0.113951405584324E-01 0.112050505722751E-01 0.110136583625952E-01 0.108210085530215E-01 - 0.106271471348601E-01 0.104321207505245E-01 0.102359759614378E-01 0.100387603117567E-01 0.984052248173426E-02 - 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