notebooks/gammanu.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Copyright (c) 2023 Graphcore Ltd. All rights reserved.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of the auxiliary gamma function\n",
    "\n",
    "The evaluation of integrals involving a $\\frac{1}{r}$ term require computing the following:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{1}\n",
    "F(\\nu, t) = \\int_0^1 u^{2 \\nu} e^{-t u^2} du\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Taketa et al. call this the auxiliary function $F$ and we can show its relationship to the $\\gamma$ function with SymPy.\n",
    "First we build up the integral as stated in equation 2.11 in the THO paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_theme()\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int\\limits_{0}^{1} u^{2 \\nu} e^{- t u^{2}}\\, du$"
      ],
      "text/plain": [
       "Integral(u**(2*nu)*exp(-t*u**2), (u, 0, 1))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "u, t = symbols(\"u t\", real=True, nonnegative=True)\n",
    "nu = Symbol(\"nu\", integer=True, nonnegative=True)\n",
    "F_nu = Integral(u ** (2 * nu) * exp(-t * u **2), (u, 0, 1))\n",
    "F_nu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluating the integral results in an expression involving the [lower incomplete Gamma function](https://mathworld.wolfram.com/IncompleteGammaFunction.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{t^{- \\nu - \\frac{1}{2}} \\gamma\\left(\\nu + \\frac{1}{2}, t\\right)}{2}$"
      ],
      "text/plain": [
       "t**(-nu - 1/2)*lowergamma(nu + 1/2, t)/2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_nu_expanded = simplify(F_nu.doit())\n",
    "F_nu_expanded"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some implementations will fail at $t=0$, so let's re-evaluate the integral for that special case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{2 \\nu + 1}$"
      ],
      "text/plain": [
       "1/(2*nu + 1)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_nu_expanded_t0 = F_nu.subs(t, 0).doit()\n",
    "F_nu_expanded_t0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using `lambdify` we can use SymPy to generate a scipy compatible implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function _lambdifygenerated:\n",
      "\n",
      "_lambdifygenerated(nu, t)\n",
      "    Created with lambdify. Signature:\n",
      "    \n",
      "    func(nu, t)\n",
      "    \n",
      "    Expression:\n",
      "    \n",
      "    t**(-nu - 1/2)*lowergamma(nu + 1/2, t)/2\n",
      "    \n",
      "    Source code:\n",
      "    \n",
      "    def _lambdifygenerated(nu, t):\n",
      "        return (1/2)*t**(-nu - 1/2)*gamma(nu + 1/2)*gammainc(nu + 1/2, t)\n",
      "    \n",
      "    \n",
      "    Imported modules:\n",
      "\n"
     ]
    }
   ],
   "source": [
    "F_nu_lambdified = lambdify((nu, t), F_nu_expanded, modules=\"scipy\")\n",
    "help(F_nu_lambdified)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might need this lambda implementation later but for now let us see if SymPy can find a simpler way to evaluate this function for the integers 0, 1, 2, 3, ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{2 \\sqrt{t}}$"
      ],
      "text/plain": [
       "sqrt(pi)*erf(sqrt(t))/(2*sqrt(t))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{e^{- t}}{2 t} + \\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{4 t^{\\frac{3}{2}}}$"
      ],
      "text/plain": [
       "-exp(-t)/(2*t) + sqrt(pi)*erf(sqrt(t))/(4*t**(3/2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{e^{- t}}{2 t} - \\frac{3 e^{- t}}{4 t^{2}} + \\frac{3 \\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{8 t^{\\frac{5}{2}}}$"
      ],
      "text/plain": [
       "-exp(-t)/(2*t) - 3*exp(-t)/(4*t**2) + 3*sqrt(pi)*erf(sqrt(t))/(8*t**(5/2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\left(- 8 t^{\\frac{5}{2}} - 20 t^{\\frac{3}{2}} - 30 \\sqrt{t} + 15 \\sqrt{\\pi} e^{t} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}\\right) e^{- t}}{16 t^{\\frac{7}{2}}}$"
      ],
      "text/plain": [
       "(-8*t**(5/2) - 20*t**(3/2) - 30*sqrt(t) + 15*sqrt(pi)*exp(t)*erf(sqrt(t)))*exp(-t)/(16*t**(7/2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\left(- 16 t^{\\frac{7}{2}} - 56 t^{\\frac{5}{2}} - 140 t^{\\frac{3}{2}} - 210 \\sqrt{t} + 105 \\sqrt{\\pi} e^{t} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}\\right) e^{- t}}{32 t^{\\frac{9}{2}}}$"
      ],
      "text/plain": [
       "(-16*t**(7/2) - 56*t**(5/2) - 140*t**(3/2) - 210*sqrt(t) + 105*sqrt(pi)*exp(t)*erf(sqrt(t)))*exp(-t)/(32*t**(9/2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    display(simplify(F_nu_expanded.subs(nu, i)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This has a whiff of a recurrence but unfortunately SymPy doesn't seem to find it.  Lets see if we can spot the pattern:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{2 \\sqrt{t}}$"
      ],
      "text/plain": [
       "sqrt(pi)*erf(sqrt(t))/(2*sqrt(t))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_0 = simplify(F_nu_expanded.subs(nu, 0))\n",
    "f_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{e^{- t}}{2 t} + \\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{4 t^{\\frac{3}{2}}}$"
      ],
      "text/plain": [
       "-exp(-t)/(2*t) + sqrt(pi)*erf(sqrt(t))/(4*t**(3/2))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_1 = simplify(1/(2* t) * (f_0 - exp(-t)))\n",
    "f_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{e^{- t}}{2 t} - \\frac{3 e^{- t}}{4 t^{2}} + \\frac{3 \\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{8 t^{\\frac{5}{2}}}$"
      ],
      "text/plain": [
       "-exp(-t)/(2*t) - 3*exp(-t)/(4*t**2) + 3*sqrt(pi)*erf(sqrt(t))/(8*t**(5/2))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_2 = simplify(1 / (2 * t) * (3 * f_1 - exp(-t)))\n",
    "f_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(- \\frac{1}{2 t} - \\frac{5}{4 t^{2}} - \\frac{15}{8 t^{3}}\\right) e^{- t} + \\frac{15 \\sqrt{\\pi} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}}{16 t^{\\frac{7}{2}}}$"
      ],
      "text/plain": [
       "(-1/(2*t) - 5/(4*t**2) - 15/(8*t**3))*exp(-t) + 15*sqrt(pi)*erf(sqrt(t))/(16*t**(7/2))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_3 = collect(simplify(1 / (2 * t) * (5 * f_2 - exp(-t))), exp(-t))\n",
    "f_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\left(- 16 t^{\\frac{19}{2}} - 14 t^{\\frac{13}{2}} \\cdot \\left(4 t^{2} + 10 t + 15\\right) + 105 \\sqrt{\\pi} t^{6} e^{t} \\operatorname{erf}{\\left(\\sqrt{t} \\right)}\\right) e^{- t}}{32 t^{\\frac{21}{2}}}$"
      ],
      "text/plain": [
       "(-16*t**(19/2) - 14*t**(13/2)*(4*t**2 + 10*t + 15) + 105*sqrt(pi)*t**6*exp(t)*erf(sqrt(t)))*exp(-t)/(32*t**(21/2))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_4 = simplify(1 / (2 * t) * (7 * f_3 - exp(-t)))\n",
    "f_4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this, we propose the following recurrence:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\tag{2}\n",
    "F(0, t) &= \\frac{1}{2} \\text{erf}(\\sqrt{t}) \\sqrt{\\frac{\\pi}{t}} \\\\\n",
    "F(\\nu, t) &= \\frac{1}{2 t} \\left( (2\\nu - 1) F(\\nu - 1, t) - e^{-t} \\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We test this recurrence out by comparing to the earlier lambda implementation derived by SymPy.  We also compare this to the SymPy lambdafy implementation but implement a \"safe\" version as `Fnu_lambda_safe` which avoids the divide by zero warnings when $t=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_959421/3085702436.py:4: RuntimeWarning: divide by zero encountered in divide\n",
      "  return np.where(t == 0, 1.0, erf(np.sqrt(t)) * np.sqrt(np.pi / (4 * t)))\n",
      "/tmp/ipykernel_959421/3085702436.py:4: RuntimeWarning: invalid value encountered in multiply\n",
      "  return np.where(t == 0, 1.0, erf(np.sqrt(t)) * np.sqrt(np.pi / (4 * t)))\n",
      "/tmp/ipykernel_959421/3085702436.py:11: RuntimeWarning: divide by zero encountered in divide\n",
      "  v = 1/ (2 * t) * ( (2 * nu - 1) * f_nu(nu-1, t) - np.exp(-t) )\n",
      "/tmp/ipykernel_959421/3085702436.py:11: RuntimeWarning: invalid value encountered in multiply\n",
      "  v = 1/ (2 * t) * ( (2 * nu - 1) * f_nu(nu-1, t) - np.exp(-t) )\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nu = 0 max error = 3.6637359812630166e-15\n",
      "nu = 1 max error = 1.942890293094024e-16\n",
      "nu = 2 max error = 3.3306690738754696e-16\n",
      "nu = 3 max error = 1.6237011735142914e-15\n",
      "nu = 4 max error = 1.1310397063368782e-14\n",
      "nu = 5 max error = 9.851147675377092e-14\n",
      "nu = 6 max error = 1.0467876565556367e-12\n",
      "nu = 7 max error = 1.3154359546074801e-11\n",
      "nu = 8 max error = 1.9073770340938268e-10\n",
      "nu = 9 max error = 3.1344563958257687e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f_0(t):\n",
    "    from scipy.special import erf \n",
    "\n",
    "    return np.where(t == 0, 1.0, erf(np.sqrt(t)) * np.sqrt(np.pi / (4 * t)))\n",
    "\n",
    "\n",
    "def f_nu(nu, t, epsilon=1e-10):\n",
    "    if nu == 0:\n",
    "        return f_0(t)\n",
    "\n",
    "    v = 1/ (2 * t) * ( (2 * nu - 1) * f_nu(nu-1, t) - np.exp(-t) )\n",
    "    return np.where(t <= epsilon, 1 / (2 * nu + 1), v)\n",
    "\n",
    "\n",
    "def Fnu_lambda_safe(nu, t, epsilon=1e-10):\n",
    "    \"\"\"nan safe implementation of F_nu_lambdafied\n",
    "    \"\"\"\n",
    "    from scipy.special import gammainc, gammaln\n",
    "\n",
    "    te = np.maximum(t, epsilon)\n",
    "    v = np.exp(np.log(0.5) - (nu + 0.5) * np.log(te) + np.log(gammainc(nu + 0.5, te)) + gammaln(nu + 0.5))\n",
    "    return np.where(t <= epsilon, 1 / (2 * nu + 1), v)\n",
    "  \n",
    "x = np.linspace(0, 15, 30)\n",
    "\n",
    "for n in range(10):\n",
    "    y1 = f_nu(n, x)\n",
    "    y2 = Fnu_lambda_safe(n, x)\n",
    "    e = np.abs(y1-y2)\n",
    "    print(f\"nu = {n} max error = {e.max()}\")\n",
    "    plt.stem(x, e)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boost Math\n",
    "\n",
    "The boost math library contains a comprehensive implementation of the four different different variants of the gamma function.  For consistent definitions we follow their notation repeated here:\n",
    "\n",
    "\n",
    "\n",
    "1. The lower incomplete gamma function of $a$ and $z$\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{3}\n",
    "\\gamma(a, z) = \\int_0^z t^{a-1} e^{-t} dt\n",
    "\\end{equation}\n",
    "$$ \n",
    "\n",
    "2. normalised lower incomplete gamma function of $a$ and $z$.  This definition is consistent with the [scipy.special.gammainc](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.gammainc.html) implementation\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{4}\n",
    "P(a, z) = \\frac{\\gamma(a, z)}{\\Gamma(a)} = \\frac{1}{\\Gamma(a)} \\int_0^z t^{a-1} e^{-t} dt\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "3. upper incomplete gamma function of $a$ and $z$.\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{5}\n",
    "\\Gamma(a, z) = \\int_z^\\infty t^{a-1} e^{-t} dt\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "4. normalised upper incomplete gamma function of $a$ and $z$. This definition is consisent with the [scipy.special.gammaincc](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.gammaincc.html) implementation\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{6}\n",
    "Q(a, z) = \\frac{\\Gamma(a, z)}{\\Gamma(a)} = \\frac{1}{\\Gamma(a)} \\int_z^\\infty t^{a-1} e^{-t} dt\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "An additional identiy that follows from the integral definition:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{7}\n",
    "\\gamma(a, z) + \\Gamma(a, z) = \\Gamma(a)\n",
    "\\end{equation}\n",
    "$$\n",
    "and for the normalised functions we have:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{8}\n",
    "P(a, z) + Q(a, z) = 1\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Back to the boost libary, see [#10](https://beta.boost.org/doc/libs/1_82_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html#math_toolkit.sf_gamma.igamma.implementation) of their implementation notes which states for half-integers $a \\in [\\frac{1}{2}, 30]$ that the following series expansion should be used to evaluate the upper incomplete regularised gamma function:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{9}\n",
    "Q(a, x) = \\text{erfc}(\\sqrt{x}) + \\frac{e^{-x}}{\\sqrt{\\pi x}} \\sum_{n=1}^{a - \\frac{1}{2}} \\frac{x^n}{(1 - \\frac{1}{2}) \\cdots (n - \\frac{1}{2})}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.661338147750939e-16 4.459776977656937e-16\n",
      "1.6653345369377348e-16 4.3946638485055916e-16\n",
      "2.220446049250313e-16 1.107246765857766e-15\n",
      "4.163336342344337e-16 3.1194323558338866e-15\n",
      "2.2620794126737565e-15 2.2792539957273192e-14\n",
      "1.2420620087993939e-14 1.5776276943287004e-13\n",
      "6.49896803039951e-14 9.977832158152448e-13\n",
      "3.554517791215517e-13 6.405459416834582e-12\n",
      "2.5983729057266203e-12 5.3784749837562836e-11\n",
      "1.7344348179904046e-11 4.0561555937670355e-10\n",
      "1.4016347804624019e-10 3.6552429262447314e-09\n",
      "1.069651311969011e-09 3.077936926389166e-08\n",
      "1.255947506412225e-08 3.9531191153418467e-07\n",
      "9.648126094580212e-08 3.2975236827047864e-06\n",
      "1.2419848460266947e-06 4.580767701633588e-05\n",
      "1.7948268090407782e-05 0.0007105560037904496\n",
      "1.7915769273919163e-05 0.0007577831080872898\n",
      "0.0032044584860772968 0.14421996957159758\n",
      "0.020957303649203077 1.0\n",
      "0.01983067633881408 1.0\n"
     ]
    }
   ],
   "source": [
    "def g(a, x):\n",
    "    from scipy.special import erfc, gamma\n",
    "\n",
    "    term = np.exp(-x) / np.sqrt(np.pi * x)\n",
    "    q = erfc(np.sqrt(x))\n",
    "\n",
    "    for n in range(1, int(a+0.5)):\n",
    "        term /= n - 0.5\n",
    "        term *= x\n",
    "        q += term\n",
    "\n",
    "    return (1 - q) * gamma(a)\n",
    "\n",
    "def gv(a, x, amax=30):\n",
    "    from scipy.special import erfc, gamma\n",
    "\n",
    "    n = np.arange(1, amax+1)\n",
    "    mask = n <= a\n",
    "    q = erfc(np.sqrt(x))\n",
    "    q += np.exp(-x) / np.sqrt(np.pi * x) * np.sum(mask * x ** n / np.cumprod(n-0.5))\n",
    "\n",
    "    return (1 - q) * gamma(a)\n",
    "\n",
    "def og(a, x):\n",
    "    from scipy.special import gammainc, gamma, gammaln\n",
    "\n",
    "    return np.exp(gammaln(a) + np.log(gammainc(a, x)))\n",
    "    \n",
    "def pq(a, x):\n",
    "    from pyquante2.utils import gamm_inc\n",
    "\n",
    "    return gamm_inc(a, x)\n",
    "\n",
    "x = 1.0\n",
    "for prev_a in range(20):\n",
    "    abs_error = np.abs(og(prev_a+0.5, x) - g(prev_a+0.5, x))\n",
    "    rel_error = abs_error / og(prev_a+0.5, x)\n",
    "    print(abs_error, rel_error)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Series evaluation of lower incomplete gamma function\n",
    "\n",
    "The special case above appears to have excessive errors as `a` increases. We can instead try the standard series expansion method:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{10}\n",
    "\\gamma(a, z) = z^a e^{-z} \\sum_{k=0}^{\\infty} \\frac{\\Gamma(a)}{\\Gamma(a + k + 1)} z^k\n",
    "\\end{equation}\n",
    "$$\n",
    "See [#4](https://beta.boost.org/doc/libs/1_82_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html#math_toolkit.sf_gamma.igamma.implementation) on the boost documentation which also shows how this series can be simplfied to:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{11}\n",
    "\\gamma(a, z) = z^a e^{-z} \\sum_{k=0}^{\\infty} \\frac{z^k}{a^{\\overline{k + 1}}}\n",
    "\\end{equation}\n",
    "$$\n",
    "by using the recursion relation:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{12}\n",
    "\\Gamma(z+1) = z \\Gamma(z)\n",
    "\\end{equation}\n",
    "$$\n",
    "where we use $a^{\\overline{k + 1}}$ as the [Pochhammer symbol](https://en.wikipedia.org/wiki/Falling_and_rising_factorials) evaluated as:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{13}\n",
    "a^{\\overline{k + 1}} = a(a + 1)(a+2) \\cdots (a + k)\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "This can be used to build a log-space implementation of the lower incomplete gamma function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.327401488179459e-15, 3.556877452881491e-15)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def gammaincln_loop(a: float, z: float, num_terms=32, epsilon=1e-10):\n",
    "    \"\"\"Lower incomplete gamma function computed from its series representation in log-space\n",
    "\n",
    "    Should be equivalent to:\n",
    "\n",
    "        import numpy as np\n",
    "        from scipy.special import gammainc, gammaln\n",
    "\n",
    "        gammaln(a) + np.log(gammainc(a, z))\n",
    "    \"\"\"\n",
    "    a0 = a\n",
    "    term = 1 / a\n",
    "    total = 0.0\n",
    "\n",
    "    for _ in range(num_terms):\n",
    "        a += 1\n",
    "        term *= z / a\n",
    "        total += term\n",
    "\n",
    "    total += 1 / a0\n",
    "    z = max(z, epsilon)\n",
    "    return a0 * np.log(z) - z + np.log(total)\n",
    "\n",
    "\n",
    "def gammaincln_vec(a, z, num_terms=32, epsilon=1e-10, dtype=np.float64):\n",
    "    ak = a + np.arange(num_terms, dtype=dtype)\n",
    "    zk = np.full(ak.shape, z, dtype=dtype)\n",
    "    zk[0] = 1.0\n",
    "    total = np.sum(np.cumprod(zk / ak))\n",
    "    z = np.maximum(z, epsilon)\n",
    "    return a * np.log(z) - z + np.log(total)\n",
    "\n",
    "\n",
    "gammaincln = gammaincln_vec\n",
    "\n",
    "\n",
    "def reference_scipy(a, z):\n",
    "    # https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.gammainc.html\n",
    "    from scipy.special import gammaln, gammainc\n",
    "\n",
    "    return gammaln(a) + np.log(gammainc(a, z))\n",
    "\n",
    "\n",
    "def reference_mpmath(a, z):\n",
    "    # https://mpmath.org/doc/current/functions/expintegrals.html#gammainc\n",
    "    from mpmath import gammainc, log\n",
    "\n",
    "    return float(log(gammainc(float(a), b=float(z))))\n",
    "\n",
    "\n",
    "prev_a = 1.5\n",
    "z = 10.0\n",
    "\n",
    "ref_sp = reference_scipy(prev_a, z)\n",
    "ref_mp = reference_mpmath(prev_a, z)\n",
    "ans = gammaincln(prev_a, z, 64)\n",
    "abs((ref_sp - ans) / ref_sp), abs((ref_mp - ans) / ref_mp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many terms need to be evaluated to converge?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>z</th>\n",
       "      <th>num_terms</th>\n",
       "      <th>actual_fp64</th>\n",
       "      <th>actual_fp32</th>\n",
       "      <th>expect</th>\n",
       "      <th>rel_error_fp64</th>\n",
       "      <th>abs_error_fp64</th>\n",
       "      <th>rel_error_fp32</th>\n",
       "      <th>abs_error_fp32</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>32</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>6.161556e-12</td>\n",
       "      <td>6.666667e-11</td>\n",
       "      <td>1.698729e-10</td>\n",
       "      <td>1.837988e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>64</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>6.161556e-12</td>\n",
       "      <td>6.666667e-11</td>\n",
       "      <td>1.698729e-10</td>\n",
       "      <td>1.837988e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>128</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>-10.819778</td>\n",
       "      <td>6.161556e-12</td>\n",
       "      <td>6.666667e-11</td>\n",
       "      <td>1.698729e-10</td>\n",
       "      <td>1.837988e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>32</td>\n",
       "      <td>-105.120407</td>\n",
       "      <td>-105.120407</td>\n",
       "      <td>-105.120407</td>\n",
       "      <td>1.729035e-13</td>\n",
       "      <td>1.817568e-11</td>\n",
       "      <td>3.594136e-10</td>\n",
       "      <td>3.778170e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>64</td>\n",
       "      <td>-105.120407</td>\n",
       "      <td>-105.120407</td>\n",
       "      <td>-105.120407</td>\n",
       "      <td>1.729035e-13</td>\n",
       "      <td>1.817568e-11</td>\n",
       "      <td>3.594136e-10</td>\n",
       "      <td>3.778170e-08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     a    z  num_terms  actual_fp64  actual_fp32      expect  rel_error_fp64  \\\n",
       "0  0.5  0.0         32   -10.819778   -10.819778  -10.819778    6.161556e-12   \n",
       "1  0.5  0.0         64   -10.819778   -10.819778  -10.819778    6.161556e-12   \n",
       "2  0.5  0.0        128   -10.819778   -10.819778  -10.819778    6.161556e-12   \n",
       "3  4.5  0.0         32  -105.120407  -105.120407 -105.120407    1.729035e-13   \n",
       "4  4.5  0.0         64  -105.120407  -105.120407 -105.120407    1.729035e-13   \n",
       "\n",
       "   abs_error_fp64  rel_error_fp32  abs_error_fp32  \n",
       "0    6.666667e-11    1.698729e-10    1.837988e-09  \n",
       "1    6.666667e-11    1.698729e-10    1.837988e-09  \n",
       "2    6.666667e-11    1.698729e-10    1.837988e-09  \n",
       "3    1.817568e-11    3.594136e-10    3.778170e-08  \n",
       "4    1.817568e-11    3.594136e-10    3.778170e-08  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from functools import partial\n",
    "\n",
    "A = np.arange(0, 16, 4) + 0.5\n",
    "Z = np.linspace(0, 20, 5)\n",
    "N = np.array([32, 64, 128])\n",
    "\n",
    "vals = np.meshgrid(A, Z, N)\n",
    "A, Z, N = [t.reshape(-1) for t in vals]\n",
    "\n",
    "gammaincln_fp64 = partial(gammaincln, dtype=np.float64)\n",
    "gammaincln_fp32 = partial(gammaincln, dtype=np.float32)\n",
    "actual_fp64 = np.vectorize(gammaincln_fp64)(A, Z, N)\n",
    "actual_fp32 = np.vectorize(gammaincln_fp32)(A, Z, N)\n",
    "expect = reference_scipy(A, np.maximum(Z, 1e-10))\n",
    "\n",
    "df = pd.DataFrame(\n",
    "    {\n",
    "        \"a\": A,\n",
    "        \"z\": Z,\n",
    "        \"num_terms\": N,\n",
    "        \"actual_fp64\": actual_fp64,\n",
    "        \"actual_fp32\": actual_fp32,\n",
    "        \"expect\": expect,\n",
    "    }\n",
    ")\n",
    "df[\"rel_error_fp64\"] = np.abs((df.actual_fp64 - df.expect) / df.expect)\n",
    "df[\"abs_error_fp64\"] = np.abs(df.actual_fp64 - df.expect)\n",
    "df[\"rel_error_fp32\"] = np.abs((df.actual_fp32 - df.expect) / df.expect)\n",
    "df[\"abs_error_fp32\"] = np.abs(df.actual_fp32 - df.expect)\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots(2, 2, figsize=(12,10), )\n",
    "sns.lineplot(ax=ax[0, 0], data=df, x=\"num_terms\", y=\"rel_error_fp32\", hue=\"a\")\n",
    "sns.lineplot(ax=ax[0, 1], data=df, x=\"num_terms\", y=\"rel_error_fp64\", hue=\"a\")\n",
    "sns.lineplot(ax=ax[1, 0], data=df, x=\"num_terms\", y=\"rel_error_fp32\", hue=\"z\")\n",
    "sns.lineplot(ax=ax[1, 1], data=df, x=\"num_terms\", y=\"rel_error_fp64\", hue=\"z\")\n",
    "\n",
    "for prev_a in ax.flat:\n",
    "  prev_a.set(yscale=\"log\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combining series evaluation with $F(\\nu, t)$ \n",
    "\n",
    "Remember from earlier that goal is to evaluate:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{14}\n",
    "F(\\nu, t) = \\int_0^1 u^{2 \\nu} e^{-t u^2} du\n",
    "\\end{equation}\n",
    "$$\n",
    "which we used SymPy to show that\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{15}\n",
    "F(\\nu, t) = \\frac{1}{2} t^{-\\nu - \\frac{1}{2}} \\gamma(\\nu + \\frac{1}{2}, t)\n",
    "\\end{equation}\n",
    "$$\n",
    "now combining this result with the series representation for the lower incomplete gamma function:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{16}\n",
    "\\gamma(\\nu + \\frac{1}{2}, t) = t^{\\nu + \\frac{1}{2}} e^{-t} \\sum_{k=0}^{\\infty} \\frac{t^k}{(\\nu + \\frac{1}{2})^{\\overline{k+1}}}\n",
    "\\end{equation}\n",
    "$$\n",
    "we arrive at:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{17}\n",
    "F(\\nu, t) = \\frac{e^{-t}}{2} \\sum_{k=0}^{\\infty} \\frac{t^k}{(\\nu + \\frac{1}{2})^{\\overline{k+1}}}\n",
    "\\end{equation}\n",
    "$$\n",
    "recall that $a^{\\overline{k + 1}}$ is the [Pochhammer symbol](https://en.wikipedia.org/wiki/Falling_and_rising_factorials) evaluated as:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tag{18}\n",
    "a^{\\overline{k + 1}} = a(a + 1)(a+2) \\cdots (a + k)\n",
    "\\end{equation}\n",
    "$$\n",
    "which leads to a simple recurrence that can be used to evaluate the series:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\tag{19}\n",
    "a &\\equiv \\nu + \\frac{1}{2} \\\\ \n",
    "f_0 &= \\frac{1}{a}\\\\\n",
    "f_k &= \\frac{t}{a + 1} f_{k-1} \\\\\n",
    "F(\\nu, t) &= \\frac{e^{-t}}{2} \\sum_{k=0}^{\\infty} f_k \n",
    "\\end{aligned}\n",
    "$$\n",
    "This series will converge as $k \\rightarrow \\infty$ since the denominator terms will grow faster then the numerator. \n",
    "In practice the number of terms needed to converge should be expected to be similar to the study above for the convergence of the lower incomplete gamma function in log space.\n",
    "\n",
    "As a sanity check we can see that the $t=0$ case agrees with evaluation of the integral:\n",
    "$$\n",
    "\\tag{20}\n",
    "F(\\nu, 0) = \\frac{1}{2 \\nu + 1}\n",
    "$$\n",
    "without resorting to any special casing to avoid a singularity as $t \\rightarrow 0$ that is inherent in Equation 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.331779296901205e-13"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pyquante2.utils import Fgamma as reference_pyquante\n",
    "\n",
    "\n",
    "def Fnut(nu, t, num_terms=128):\n",
    "    a = nu + 0.5\n",
    "    total = 1 / a\n",
    "    term = 1 / a\n",
    "\n",
    "    for _ in range(num_terms):\n",
    "        a += 1\n",
    "        term *= t / a\n",
    "        total += term\n",
    "\n",
    "    return np.exp(-t) / 2 * total\n",
    "\n",
    "\n",
    "nu = 0.0\n",
    "t = 0.0\n",
    "\n",
    "abs((Fnut(nu, t) - reference_pyquante(nu, t)) / reference_pyquante(nu, t))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This absolute error is a little misleading since the special case of $\\nu=t=0$ should be handled correctly by `Fnut`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 0.9999999999996668)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fnut(nu, t), reference_pyquante(nu, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nu = 0 max error = 3.885780586188048e-15\n",
      "nu = 1 max error = 5.551115123125783e-17\n",
      "nu = 2 max error = 4.163336342344337e-17\n",
      "nu = 3 max error = 3.642919299551295e-17\n",
      "nu = 4 max error = 4.85722573273506e-17\n",
      "nu = 5 max error = 7.632783294297951e-17\n",
      "nu = 6 max error = 5.551115123125783e-17\n",
      "nu = 7 max error = 3.469446951953614e-17\n",
      "nu = 8 max error = 1.3877787807814457e-17\n",
      "nu = 9 max error = 4.163336342344337e-17\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 15, 30)\n",
    "\n",
    "for n in range(10):\n",
    "    y1 = Fnut(n, x)\n",
    "    y2 = Fnu_lambda_safe(n, x)\n",
    "    e = np.abs(y1-y2)\n",
    "    print(f\"nu = {n} max error = {e.max()}\")\n",
    "    plt.stem(x, e)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pyscf-ipu",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}