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    Ensemble propagations
    -../_images/6e6a62c14e57f13d28a9e74d541b1e0c3e10a00f7b9dae1733d5bd99cf523cc6.png +../_images/4eaaa9cdba19e7de39bfcd4e8246dfb478888a831740b1fa62f7e0b8e838fdaa.png
    diff --git a/notebooks/Customising the adaptive integrator.html b/notebooks/Customising the adaptive integrator.html index 5cb0e931..fe6ed3fb 100644 --- a/notebooks/Customising the adaptive integrator.html +++ b/notebooks/Customising the adaptive integrator.html @@ -636,8 +636,8 @@

    Compact mode -
    CPU times: user 6.04 s, sys: 57.4 ms, total: 6.09 s
    -Wall time: 6.09 s
    +
    CPU times: user 6.48 s, sys: 72.2 ms, total: 6.55 s
    +Wall time: 6.55 s
     
    @@ -652,8 +652,10 @@

    Compact mode -

    We see a net advantage in timings using the Taylor integration scheme. Note we are here not using batch propagation, which would add an additional 2-4 factor speedup in performances.

    diff --git a/notebooks/Optimal Control of the Lotka-Volterra equations.html b/notebooks/Optimal Control of the Lotka-Volterra equations.html index 55eb7de5..6a0122f6 100644 --- a/notebooks/Optimal Control of the Lotka-Volterra equations.html +++ b/notebooks/Optimal Control of the Lotka-Volterra equations.html @@ -1098,9 +1098,9 @@

    Implementing a single shooting method -
    /tmp/ipykernel_10690/2413872175.py:11: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
    +
    /tmp/ipykernel_10695/2413872175.py:11: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
       ta.pars[6] = np.heaviside(switching_function(x_0,y_0,lx_0,ly_0, ps), 1.)
    -/tmp/ipykernel_10690/2413872175.py:14: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
    +/tmp/ipykernel_10695/2413872175.py:14: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
       ta.state[0] = x_0; ta.state[1] = y_0; ta.state[2] = lx_0; ta.state[3] = ly_0
     
    @@ -1142,7 +1142,7 @@

    Implementing a single shooting method -
    /tmp/ipykernel_10690/3578120629.py:12: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
    +
    /tmp/ipykernel_10695/3578120629.py:12: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
       ta.pars[6] = np.heaviside(switching_function(x_0,y_0,lx_0,ly_0, ps), 1.)
     
    diff --git a/notebooks/Periodic orbits in the CR3BP.html b/notebooks/Periodic orbits in the CR3BP.html index 04dc0461..0b5e14ba 100644 --- a/notebooks/Periodic orbits in the CR3BP.html +++ b/notebooks/Periodic orbits in the CR3BP.html @@ -735,7 +735,7 @@

    Putting all together and integrating some initial conditions -
    --- 14.274664640426636 seconds --- to build the Taylor integrator
    +
    --- 13.061972618103027 seconds --- to build the Taylor integrator
     
    @@ -766,7 +766,7 @@

    Putting all together and integrating some initial conditions -
    --- 0.05044221878051758 seconds --- to propagate
    +
    --- 0.04901456832885742 seconds --- to propagate
     
    @@ -824,7 +824,7 @@

    Putting all together and integrating some initial conditions - diff --git a/notebooks/ffnn.html b/notebooks/ffnn.html index 0c1e314f..a7c7d397 100644 --- a/notebooks/ffnn.html +++ b/notebooks/ffnn.html @@ -617,7 +617,7 @@

    Inference -
    array([ 0.16446752, -0.67900669])
    +
    array([-0.03372767,  0.03050241])
     
    @@ -631,7 +631,7 @@

    Inference -
    [((0.022528761908604866 * tanh((-0.44711154732304215 - (0.046638901949726086 * x) - (0.0037584771852179344 * y)))) + (0.15408516526118221 * tanh(((0.10147494033503690 * y) - 0.19134591770711273 - (0.31974946294429185 * x)))) + (0.16358146212747970 * tanh((0.41956559127694715 + (0.46038126200921425 * x) - (0.39021292429519605 * y)))) + (0.17046165527471135 * tanh((0.47275650298592409 + (0.41746338079148004 * y) - (0.37909132226147713 * x)))) + (0.17435992269215261 * tanh((-0.44536474879122490 - (0.35126735319689983 * y) - (0.34514031609557472 * x)))) + (0.19171572053929964 * tanh((-0.13239834075862689 - (0.48887490109632170 * x) - (0.36914815876512064 * y)))) + (0.22600043566582839 * tanh((0.38530525760927314 + (0.13723440797107977 * x) - (0.083786566260100948 * y)))) + (0.25435923181532694 * tanh((-0.34872312084995272 - (0.41746140170887291 * y) - (0.018157260685927823 * x)))) + (0.27597269409920833 * tanh((0.21895194297341081 - (0.28762397501808401 * x) - (0.25329631005102737 * y)))) + ..., (0.20030724507482511 + (0.0073033243880175069 * tanh((0.30575208615657179 + (0.036146467325952059 * x) - (0.015898987129201791 * y)))) + (0.014117370308742827 * tanh((-0.25269072180974006 - (0.25439823732692224 * y) - (0.23273899186130442 * x)))) + (0.039389439518354941 * tanh((0.47532292549039290 + (0.32189249935781539 * y) - (0.12721941410966642 * x)))) + (0.046879725707853592 * tanh(((0.30036512424821260 * x) - 0.41650705172183977 - (0.16242746401087904 * y)))) + (0.050950752346306860 * tanh(((0.18290324163847338 * x) - 0.074098516117613311 - (0.39748961899193269 * y)))) + (0.079687236549878526 * tanh((0.075837081633515435 + (0.0069992660315134625 * y) + (0.080509708739007313 * x)))) + (0.12955241342081913 * tanh((0.41956559127694715 + (0.46038126200921425 * x) - (0.39021292429519605 * y)))) + (0.13980744578091819 * tanh((-0.20029826026245501 - (0.37995687318024285 * x) - (0.36421547249297703 * y)))) + (0.18916185875041358 * tanh((-0.48365181480399788 - (0.36252487150566937 * y) - (0.30514735465426202 * ...]
    +
    [((0.0048053678368830122 * tanh((-0.33579700285353653 - (0.35111183936010637 * y) - (0.10381357617924780 * x)))) + (0.028595893703249664 * tanh(((0.078139409081563915 * y) + (0.17499737560735029 * x) - 0.21000737408614867))) + (0.030129936109455580 * tanh((0.32232705770892078 - (0.32900781999661055 * x) - (0.046269771202279597 * y)))) + (0.066764267463296556 * tanh((0.22777501771099262 - (0.25412253845360666 * y) - (0.067359176108984675 * x)))) + (0.073240398872319257 * tanh((0.30426522199809469 - (0.18460404120684326 * x) - (0.12472602260285925 * y)))) + (0.078974328334058264 * tanh((0.44246432931267210 + (0.00077450772258691458 * y) + (0.47735971355506435 * x)))) + (0.085193785007156686 * tanh((0.43364537459452801 - (0.37280713397039733 * y) - (0.32012575795208831 * x)))) + (0.10088939471641711 * tanh(((0.39112498874616941 * x) - 0.18904249283170338 - (0.13257522218476159 * y)))) + (0.12193952760263993 * tanh((0.12158018548133775 + (0.10661244976450646 * x) + (0.42022601450221886 * y)))) + ..., (0.10518113037957810 + (0.0092634792563579538 * tanh((0.37020016409997258 - (0.34927592126801854 * y) - (0.25448200476644212 * x)))) + (0.075328310841195067 * tanh((0.055020502853538877 - (0.22690745267971735 * y) - (0.0084469241399355299 * x)))) + (0.098523169080268924 * tanh(((0.078139409081563915 * y) + (0.17499737560735029 * x) - 0.21000737408614867))) + (0.098659708604166396 * tanh((0.40949433645498634 + (0.0022917217932006961 * y) - (0.16676945487184724 * x)))) + (0.16918854450083320 * tanh((0.38391483355111866 + (0.40808502142044967 * y) - (0.34928328694299748 * x)))) + (0.18944759508338127 * tanh(((0.20423919457037865 * y) + (0.45344116108174048 * x) - 0.28782716986377022))) + (0.23160482212655453 * tanh(((0.21422780529594176 * x) - 0.23826579254336389 - (0.34632401371875898 * y)))) + (0.24176221529038966 * tanh((0.29135570069084182 + (0.013561077790746001 * x) + (0.49475460291288720 * y)))) + (0.25821214020706662 * tanh((-0.15834847999729118 - (0.29231921911790038 * x) - (0.11202278807605992 * ...]
     
    @@ -647,8 +647,8 @@

    Inference
    C++ datatype: double
     Variables: [x, y]
    -Output #0: ((0.022528761908604866 * tanh((-0.44711154732304215 - (0.046638901949726086 * x) - (0.0037584771852179344 * y)))) + (0.15408516526118221 * tanh(((0.10147494033503690 * y) - 0.19134591770711273 - (0.31974946294429185 * x)))) + (0.16358146212747970 * tanh((0.41956559127694715 + (0.46038126200921425 * x) - (0.39021292429519605 * y)))) + (0.17046165527471135 * tanh((0.47275650298592409 + (0.41746338079148004 * y) - (0.37909132226147713 * x)))) + (0.17435992269215261 * tanh((-0.44536474879122490 - (0.35126735319689983 * y) - (0.34514031609557472 * x)))) + (0.19171572053929964 * tanh((-0.13239834075862689 - (0.48887490109632170 * x) - (0.36914815876512064 * y)))) + (0.22600043566582839 * tanh((0.38530525760927314 + (0.13723440797107977 * x) - (0.083786566260100948 * y)))) + (0.25435923181532694 * tanh((-0.34872312084995272 - (0.41746140170887291 * y) - (0.018157260685927823 * x)))) + (0.27597269409920833 * tanh((0.21895194297341081 - (0.28762397501808401 * x) - (0.25329631005102737 * y)))) + ...
    -Output #1: (0.20030724507482511 + (0.0073033243880175069 * tanh((0.30575208615657179 + (0.036146467325952059 * x) - (0.015898987129201791 * y)))) + (0.014117370308742827 * tanh((-0.25269072180974006 - (0.25439823732692224 * y) - (0.23273899186130442 * x)))) + (0.039389439518354941 * tanh((0.47532292549039290 + (0.32189249935781539 * y) - (0.12721941410966642 * x)))) + (0.046879725707853592 * tanh(((0.30036512424821260 * x) - 0.41650705172183977 - (0.16242746401087904 * y)))) + (0.050950752346306860 * tanh(((0.18290324163847338 * x) - 0.074098516117613311 - (0.39748961899193269 * y)))) + (0.079687236549878526 * tanh((0.075837081633515435 + (0.0069992660315134625 * y) + (0.080509708739007313 * x)))) + (0.12955241342081913 * tanh((0.41956559127694715 + (0.46038126200921425 * x) - (0.39021292429519605 * y)))) + (0.13980744578091819 * tanh((-0.20029826026245501 - (0.37995687318024285 * x) - (0.36421547249297703 * y)))) + (0.18916185875041358 * tanh((-0.48365181480399788 - (0.36252487150566937 * y) - (0.30514735465426202 * ...
    +Output #0: ((0.0048053678368830122 * tanh((-0.33579700285353653 - (0.35111183936010637 * y) - (0.10381357617924780 * x)))) + (0.028595893703249664 * tanh(((0.078139409081563915 * y) + (0.17499737560735029 * x) - 0.21000737408614867))) + (0.030129936109455580 * tanh((0.32232705770892078 - (0.32900781999661055 * x) - (0.046269771202279597 * y)))) + (0.066764267463296556 * tanh((0.22777501771099262 - (0.25412253845360666 * y) - (0.067359176108984675 * x)))) + (0.073240398872319257 * tanh((0.30426522199809469 - (0.18460404120684326 * x) - (0.12472602260285925 * y)))) + (0.078974328334058264 * tanh((0.44246432931267210 + (0.00077450772258691458 * y) + (0.47735971355506435 * x)))) + (0.085193785007156686 * tanh((0.43364537459452801 - (0.37280713397039733 * y) - (0.32012575795208831 * x)))) + (0.10088939471641711 * tanh(((0.39112498874616941 * x) - 0.18904249283170338 - (0.13257522218476159 * y)))) + (0.12193952760263993 * tanh((0.12158018548133775 + (0.10661244976450646 * x) + (0.42022601450221886 * y)))) + ...
    +Output #1: (0.10518113037957810 + (0.0092634792563579538 * tanh((0.37020016409997258 - (0.34927592126801854 * y) - (0.25448200476644212 * x)))) + (0.075328310841195067 * tanh((0.055020502853538877 - (0.22690745267971735 * y) - (0.0084469241399355299 * x)))) + (0.098523169080268924 * tanh(((0.078139409081563915 * y) + (0.17499737560735029 * x) - 0.21000737408614867))) + (0.098659708604166396 * tanh((0.40949433645498634 + (0.0022917217932006961 * y) - (0.16676945487184724 * x)))) + (0.16918854450083320 * tanh((0.38391483355111866 + (0.40808502142044967 * y) - (0.34928328694299748 * x)))) + (0.18944759508338127 * tanh(((0.20423919457037865 * y) + (0.45344116108174048 * x) - 0.28782716986377022))) + (0.23160482212655453 * tanh(((0.21422780529594176 * x) - 0.23826579254336389 - (0.34632401371875898 * y)))) + (0.24176221529038966 * tanh((0.29135570069084182 + (0.013561077790746001 * x) + (0.49475460291288720 * y)))) + (0.25821214020706662 * tanh((-0.15834847999729118 - (0.29231921911790038 * x) - (0.11202278807605992 * ...
     

    @@ -661,7 +661,7 @@

    Inference - @@ -121740,9 +121740,9 @@

    Adding a spring and damping -
    CPU times: user 102 ms, sys: 0 ns, total: 102 ms
    -Wall time: 104 ms
    +
    CPU times: user 81.4 ms, sys: 0 ns, total: 81.4 ms
    +Wall time: 81.4 ms
     
    @@ -515,8 +515,8 @@

    JIT compilation and caching -
    CPU times: user 3.39 ms, sys: 0 ns, total: 3.39 ms
    -Wall time: 2.72 ms
    +
    CPU times: user 3.57 ms, sys: 0 ns, total: 3.57 ms
    +Wall time: 2.83 ms
     
    @@ -530,8 +530,8 @@

    JIT compilation and caching -
    CPU times: user 14.7 ms, sys: 0 ns, total: 14.7 ms
    -Wall time: 14.1 ms
    +
    CPU times: user 15.7 ms, sys: 0 ns, total: 15.7 ms
    +Wall time: 15 ms
     
    (<taylor_outcome.time_limit: -4294967299>,
    @@ -560,8 +560,8 @@ 

    JIT compilation and caching -
    CPU times: user 1.35 ms, sys: 0 ns, total: 1.35 ms
    -Wall time: 966 µs
    +
    CPU times: user 1.74 ms, sys: 0 ns, total: 1.74 ms
    +Wall time: 1.1 ms
     
    @@ -913,9 +913,9 @@

    Pendulum on a movable support
    - +
    - + oninput="anim6ec30c31d34141748229183d5b741746.set_frame(parseInt(this.value));">
    - - - - - - - - -
    -
    - - - Once + - - Loop + - +
    @@ -73085,9 +73085,9 @@

    Adding a friction term Contents

    Lagrange propagation and the state transition matrix#

    In the gravitational two-body problem it is possible to compute the state of the system at an arbitrary time from an initial state \(\left( \boldsymbol{r}_0, \boldsymbol{v}_0 \right)\) via the so-called Lagrange coefficients \(F\), \(G\), \(F_t\) and \(G_t\):

    -
    -(1)#\[\begin{equation} +
    +(1)#\[\begin{equation} \begin{cases} \boldsymbol{r} & = F \boldsymbol{r}_0 + G \boldsymbol{v}_0 \\ \boldsymbol{v} & = F_t \boldsymbol{r}_0 + G_t \boldsymbol{v}_0 diff --git a/notebooks/projection.html b/notebooks/projection.html index c89d8e09..444d3596 100644 --- a/notebooks/projection.html +++ b/notebooks/projection.html @@ -637,7 +637,7 @@

    Setting things up

    -../_images/8a5b41c83e2c821239a180523bfff903c3d3addc185dc616684fb7e2bb59e99a.png +../_images/f9b3dd4c175a0f83b648ee303f90299d472b1eed058d1dcbf67738952b759fe5.png

    This Poincare’ section is suggesting that the integral of motion \(\mathcal{C}\) does indeed exist, because the intersections of all random orbits are clearly tracing curves on the \(x=0\) plane.

    @@ -684,7 +684,7 @@

    Running the experiments

    -../_images/708cf7839f129f1423c854150c1af418c3f66be46ee6bc90db5a8874ebd37ab8.png +../_images/7b2874c5d84cd85715d7b4b576a9abd8c715c554fdbca30f2c18dbbb5311fcf4.png

    The qualitative picture is now radically different. Although islands of stable motion persist, now most trajectories seem to be densely filling the plane, rather than tracing curves on it. Let us further increase the energy level:

    @@ -695,7 +695,7 @@

    Running the experiments

    -../_images/c295b6d5a09154356f0acd61606581ce9ae6d8e962a6b9474a2de541878244b4.png +../_images/8bdfc4b9cfd8cddca6a51391a225711f1ffe432cfb256c6b6ce95029b0d75501.png

    At higher energies, the densely-filling behaviour (which Henon and Heiles call ergodic) is even more prevalent than before.

    diff --git a/notebooks/sympy_interop.html b/notebooks/sympy_interop.html index 6d9b2674..92d7b7c2 100644 --- a/notebooks/sympy_interop.html +++ b/notebooks/sympy_interop.html @@ -658,8 +658,8 @@

    Interoperability with SymPy -
    CPU times: user 2.38 s, sys: 0 ns, total: 2.38 s
    -Wall time: 2.38 s
    +
    CPU times: user 2.47 s, sys: 0 ns, total: 2.47 s
    +Wall time: 2.48 s
     
    (<taylor_outcome.time_limit: -4294967299>,
    @@ -679,8 +679,8 @@ 

    Interoperability with SymPy -
    CPU times: user 2.42 s, sys: 0 ns, total: 2.42 s
    -Wall time: 2.42 s
    +
    CPU times: user 2.8 s, sys: 56.4 ms, total: 2.86 s
    +Wall time: 2.89 s
     
    (<taylor_outcome.time_limit: -4294967299>,
    diff --git a/searchindex.js b/searchindex.js
    index d9b7fefd..32ce1f92 100644
    --- a/searchindex.js
    +++ b/searchindex.js
    @@ -1 +1 @@
    -Search.setIndex({"docnames": ["acknowledgement", "advanced_tutorials", "api_exsys", "api_integrators", "api_lagham", "autosummary_generated/heyoka.diff_args", "autosummary_generated/heyoka.diff_tensors", "autosummary_generated/heyoka.dtens", "autosummary_generated/heyoka.expression", "autosummary_generated/heyoka.hamiltonian", "autosummary_generated/heyoka.lagrangian", "autosummary_generated/heyoka.make_vars", "autosummary_generated/heyoka.taylor_adaptive", "basic_tutorials", "benchmarks", "breaking_changes", "changelog", "examples_astro", "examples_event", "examples_ml", "examples_others", "index", "install", "notebooks/Batch mode overview", "notebooks/Box control for Formation Flying Satellites", "notebooks/Comparing coordinate systems", "notebooks/Customising the adaptive integrator", "notebooks/Dense output", "notebooks/Event detection", "notebooks/Inverting Kepler's equation in ODEs", "notebooks/Long term stability of Trappist-1", "notebooks/NeuralHamiltonianODEs", "notebooks/NeuralODEs", "notebooks/Non-autonomous systems", "notebooks/ODEs with parameters", "notebooks/Optimal Control of the Lotka-Volterra equations", "notebooks/Outer Solar System", "notebooks/Periodic orbits in the CR3BP", "notebooks/Planetary embryos", "notebooks/Poincar\u00e9 sections", "notebooks/Pseudo arc-length continuation in the CR3BP", "notebooks/Sampling events", "notebooks/The Keplerian billiard", "notebooks/The Maxwell-Boltzmann distribution", "notebooks/The adaptive integrator", "notebooks/The expression system", "notebooks/The restricted three-body problem", "notebooks/The two-fixed elliptic billiard", "notebooks/The variational equations", "notebooks/The wavy ramp", "notebooks/arbitrary_precision", "notebooks/compiled_functions", "notebooks/computing_derivatives", "notebooks/definite_integrals", "notebooks/differentiable_atmosphere", "notebooks/elp2000", "notebooks/ensemble_batch_perf", "notebooks/ensemble_mode", "notebooks/ev_sensitivity", "notebooks/ex_system_revisited", "notebooks/ext_precision", "notebooks/ffnn", "notebooks/gg_stab", "notebooks/jit_caching", "notebooks/lagrangian", "notebooks/lagrangian_propagator", "notebooks/mercury_precession", "notebooks/parallel_mode", "notebooks/pickling", "notebooks/projection", "notebooks/second_integral", "notebooks/single_precision", "notebooks/sympy_interop", "notebooks/tides_spokes", "notebooks/torch_and_heyoka", "notebooks/ttv", "notebooks/vsop2013", "tut_taylor_method"], "filenames": ["acknowledgement.rst", "advanced_tutorials.rst", "api_exsys.rst", "api_integrators.rst", "api_lagham.rst", "autosummary_generated/heyoka.diff_args.rst", "autosummary_generated/heyoka.diff_tensors.rst", "autosummary_generated/heyoka.dtens.rst", "autosummary_generated/heyoka.expression.rst", "autosummary_generated/heyoka.hamiltonian.rst", "autosummary_generated/heyoka.lagrangian.rst", "autosummary_generated/heyoka.make_vars.rst", "autosummary_generated/heyoka.taylor_adaptive.rst", "basic_tutorials.rst", "benchmarks.rst", "breaking_changes.rst", "changelog.rst", "examples_astro.rst", "examples_event.rst", "examples_ml.rst", "examples_others.rst", "index.md", "install.rst", "notebooks/Batch mode overview.ipynb", "notebooks/Box control for Formation Flying Satellites.ipynb", "notebooks/Comparing coordinate systems.ipynb", "notebooks/Customising the adaptive integrator.ipynb", "notebooks/Dense output.ipynb", "notebooks/Event detection.ipynb", "notebooks/Inverting Kepler's equation in ODEs.ipynb", "notebooks/Long term stability of Trappist-1.ipynb", "notebooks/NeuralHamiltonianODEs.ipynb", "notebooks/NeuralODEs.ipynb", "notebooks/Non-autonomous systems.ipynb", "notebooks/ODEs with parameters.ipynb", "notebooks/Optimal Control of the Lotka-Volterra equations.ipynb", "notebooks/Outer Solar System.ipynb", "notebooks/Periodic orbits in the CR3BP.ipynb", "notebooks/Planetary embryos.ipynb", "notebooks/Poincar\u00e9 sections.ipynb", "notebooks/Pseudo arc-length 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72, 73, 74, 75, 76], "import": [7, 11, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76], "hy": [7, 15, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76], "x": [7, 11, 15, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "y": [7, 11, 23, 24, 25, 29, 30, 31, 32, 35, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 61, 62, 64, 66, 69, 70, 72, 73, 75, 76], "make_var": [7, 16, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 70, 71, 72, 74, 76], "dt": [7, 25, 30, 32, 35, 37, 38, 40, 41, 43, 48, 52, 53, 65, 77], "2": [7, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "fetch": [7, 15, 16, 23, 25, 27, 28, 36, 42, 43, 47, 51, 52, 57, 63], "jacobian": [7, 16, 32, 52, 62, 64, 65], "0": [7, 10, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77], "0000000000000000": [7, 25, 45, 51, 52, 54, 55, 59, 69, 72], "gradient": [7, 16, 17, 21, 23, 32, 40, 47, 49, 52, 58, 69], "first": [7, 15, 16, 17, 21, 23, 24, 26, 27, 28, 30, 31, 34, 35, 36, 37, 40, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 72, 74, 75, 76], "ha": [7, 15, 16, 22, 23, 25, 26, 27, 28, 32, 35, 37, 38, 40, 42, 44, 45, 46, 52, 55, 59, 61, 62, 63, 65, 69, 74], "exactli": [7, 16, 28, 36, 43, 50, 61, 72, 76], "index_of": 7, "vidx": 7, "posit": [7, 15, 24, 25, 28, 30, 33, 37, 38, 40, 41, 42, 43, 47, 55, 62, 64, 65, 66, 67, 69, 70, 73, 75, 76], "suppli": [7, 11, 15, 16, 45, 51, 64, 69], "dens": [7, 13, 16, 21, 28, 44, 47, 52, 63, 70, 75], "spars": [7, 52], "format": [7, 17, 21, 23, 25, 27, 28, 30, 38, 40, 43, 44, 45, 49, 50, 52, 55, 60, 61, 67, 68, 69, 73, 76], "2d": [7, 23, 27, 42, 43, 44, 49, 52, 56, 62, 70, 73], "arrai": [7, 15, 16, 23, 24, 27, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 61, 65, 66, 69, 70, 71, 73, 74, 75, 76], "numpi": [7, 15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 53, 54, 55, 56, 57, 58, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76], "ndarrai": 7, 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26, 35, 37, 38, 39, 41, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 74], "have": [9, 10, 15, 16, 23, 24, 25, 26, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 44, 45, 48, 49, 51, 52, 54, 55, 57, 58, 61, 62, 64, 66, 68, 72, 74, 75, 76, 77], "same": [9, 10, 15, 16, 22, 23, 26, 28, 31, 32, 35, 36, 37, 40, 44, 51, 54, 56, 57, 59, 61, 62, 63, 67, 68, 69, 70, 72, 73, 74], "appear": [9, 10, 23, 25, 33, 40, 52, 58, 59, 77], "other": [9, 10, 15, 21, 22, 23, 25, 26, 27, 28, 35, 36, 37, 38, 40, 42, 44, 46, 48, 49, 50, 51, 52, 54, 56, 57, 59, 61, 66, 67, 69, 70, 72, 74, 77], "depend": [9, 10, 16, 25, 30, 32, 33, 36, 40, 43, 45, 46, 52, 53, 54, 55, 57, 58, 60, 66, 68, 76, 77], "l": [10, 24, 25, 29, 31, 32, 35, 37, 40, 54, 61, 62, 64, 73], "qdot": 10, "d": [10, 25, 30, 32, 35, 37, 40, 48, 58, 62, 64, 73, 77], "euler": [10, 62, 64, 70, 73], "lagrang": [10, 16, 17, 21, 35, 62, 64, 73], "veloc": [10, 23, 24, 28, 33, 36, 37, 38, 42, 43, 46, 47, 49, 58, 62, 64, 65, 66, 67, 69, 73, 75], "option": [10, 15, 16, 22, 23, 26, 27, 28, 35, 38, 44, 51, 57, 61, 64], "rayleigh": [10, 62, 64], "dissip": [10, 49, 61, 62, 64, 73], "quadrat": [10, 52, 59, 62, 64], "form": [10, 23, 28, 30, 32, 35, 37, 38, 40, 45, 54, 57, 61, 64, 73, 77], "add": [10, 16, 22, 24, 28, 32, 36, 37, 38, 39, 40, 41, 42, 62, 70, 73], "forc": [10, 23, 25, 33, 42, 46, 47, 51, 54, 62, 64, 73], "dynam": [10, 16, 23, 24, 25, 28, 30, 31, 32, 33, 38, 40, 41, 42, 43, 46, 47, 49, 50, 53, 54, 55, 56, 58, 60, 61, 62, 64, 69, 70, 71, 72, 73, 76], "explicit": [10, 29, 33, 50, 58, 60, 73, 77], "str": [11, 30, 32, 37, 40], "creat": [11, 16, 22, 23, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76], "from": [11, 15, 16, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "string": [11, 50, 57, 60], "instanc": [11, 15, 23, 28, 30, 44, 45, 50, 51, 52, 53, 55, 56, 57, 59, 60, 63, 65, 69, 71, 73, 76], "otherwis": [11, 25, 28, 32, 43, 44, 60, 61, 66, 70, 71, 72, 73], "z": [11, 24, 25, 29, 37, 39, 40, 45, 46, 51, 52, 54, 55, 59, 66, 70, 72, 76], "sy": [12, 15, 26, 29, 33, 36, 38, 39, 42, 44, 48, 50, 56, 57, 60, 62, 63, 64, 67, 68, 69, 72, 75], "kwarg": [12, 32, 61], "taylor": [13, 16, 21, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 40, 43, 44, 48, 50, 51, 54, 57, 61, 67, 71, 72, 73], "adapt": [13, 15, 16, 21, 25, 28, 30, 32, 51, 57, 60, 61, 63, 71, 77], "integr": [13, 14, 15, 16, 17, 18, 20, 21, 22, 25, 27, 28, 29, 30, 31, 33, 34, 35, 39, 40, 41, 42, 43, 46, 47, 48, 49, 51, 52, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77], "customis": [13, 16, 21, 28, 72], "od": [13, 16, 17, 19, 21, 23, 25, 26, 27, 28, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 55, 56, 57, 58, 61, 67, 68, 69, 71, 72, 73, 76, 77], "autonom": [13, 21, 48, 51, 70], "continu": [13, 15, 16, 17, 21, 22, 28, 30, 35, 42, 43, 44, 50, 57, 63], "output": [13, 15, 16, 21, 22, 28, 31, 34, 35, 44, 50, 51, 52, 57, 59, 61, 63, 69, 71, 74, 75, 76], "event": [13, 16, 21, 24, 35, 38, 39, 42, 43, 47, 49, 50, 57, 60, 70, 71, 75], "detect": [13, 16, 21, 24, 30, 34, 35, 38, 39, 41, 42, 43, 44, 47, 50, 57, 58, 70, 75], "see": [14, 16, 22, 23, 25, 27, 28, 30, 32, 33, 34, 35, 38, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76], "section": [14, 16, 18, 21, 25, 26, 27, 28, 33, 45, 50, 54, 65, 70], "document": [14, 15, 16, 22, 28, 75], "c": [14, 16, 21, 22, 24, 26, 27, 30, 33, 34, 35, 37, 40, 44, 45, 47, 48, 50, 51, 57, 60, 61, 62, 63, 66, 68, 70, 71, 72, 75], "librari": [14, 16, 21, 22, 28, 44, 45, 50, 60, 68, 74], "comparison": [14, 16, 29, 32, 36, 40, 50, 51, 54, 69], "popular": [14, 32, 54, 77], "numer": [14, 16, 21, 23, 24, 25, 26, 28, 29, 31, 32, 34, 35, 36, 37, 40, 42, 43, 45, 47, 48, 51, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 76, 77], "packag": [14, 54, 55, 61, 65, 68, 75, 76], "evalu": [14, 20, 21, 26, 27, 29, 32, 35, 37, 40, 50, 52, 55, 59, 61, 63, 65, 69, 76, 77], "perform": [14, 16, 20, 21, 23, 24, 25, 26, 28, 35, 36, 37, 43, 44, 45, 48, 50, 52, 53, 54, 55, 57, 60, 61, 62, 63, 67, 68, 69, 71, 72, 73, 74, 76, 77], "parallelis": [14, 16, 21, 30, 57, 67], "also": [14, 16, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 57, 59, 60, 61, 62, 63, 65, 66, 68, 69, 71, 73, 74, 75, 76, 77], "includ": [15, 16, 21, 22, 25, 28, 30, 36, 37, 40, 48, 57, 58, 72, 76], "backward": [15, 23, 28, 44, 53], "incompat": 15, "been": [15, 16, 25, 26, 27, 28, 32, 37, 42, 44, 46, 52, 54, 55, 59, 61, 62, 63, 64, 65, 66, 68, 72], "explicitli": [15, 25, 29, 32, 33, 41, 50, 54, 59], "requir": [15, 16, 22, 23, 24, 25, 27, 28, 32, 35, 36, 37, 44, 50, 67, 69, 71, 73, 76, 77], 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71, 72, 73, 74, 75], "alwai": [15, 16, 23, 27, 28, 32, 40, 42, 44, 45, 50, 52, 53, 54, 59, 60, 70, 73], "updat": [15, 22, 23, 24, 26, 38, 41, 43, 44, 49, 69, 75], "accordingli": [15, 30, 35], "mean": [15, 16, 25, 26, 27, 30, 34, 36, 38, 40, 43, 49, 51, 52, 54, 55, 56, 64, 65, 67, 76], "code": [15, 16, 22, 23, 24, 26, 28, 30, 32, 36, 37, 40, 41, 43, 47, 49, 51, 57, 59, 60, 61, 63, 68, 76, 77], "need": [15, 22, 23, 24, 25, 27, 28, 30, 32, 35, 36, 37, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 54, 55, 58, 59, 60, 61, 62, 63, 67, 68, 69, 72, 73, 74, 76, 77], "rewritten": [15, 77], "second": [15, 18, 21, 27, 28, 30, 32, 36, 37, 40, 42, 44, 47, 50, 51, 52, 54, 55, 56, 57, 59, 62, 67, 73, 76], "signatur": [15, 16, 23, 28], "bool": [15, 28], "convention": [15, 72], "call": [15, 16, 23, 24, 25, 27, 28, 31, 32, 33, 35, 37, 40, 42, 44, 51, 57, 59, 61, 65, 70, 72, 73], "mr": 15, "remov": [15, 16, 25, 28, 59, 63, 75], "flag": [15, 22, 23, 27, 28, 44, 51, 59, 63, 67], "meant": [15, 28, 74], "signal": 15, "possibl": [15, 16, 22, 23, 25, 28, 30, 31, 34, 35, 37, 42, 44, 45, 48, 50, 51, 52, 53, 55, 57, 58, 60, 65, 69, 70, 72, 73, 74, 76], "multipl": [15, 23, 30, 35, 36, 51, 52, 56, 57, 58, 59, 67, 73], "root": [15, 28, 35, 36, 37, 40, 43, 45], "within": [15, 25, 27, 28, 35, 52, 53, 59, 70], "cooldown": [15, 24, 43, 60, 71], "period": [15, 16, 17, 21, 23, 25, 28, 29, 30, 32, 33, 46, 54, 62, 65, 66, 73], "never": [15, 33, 57], "intend": [15, 50, 60], "drop": [15, 23, 55, 73, 76], "exist": [15, 35, 70], "straightforward": [15, 35, 52, 57], "you": [15, 21, 22, 27, 28, 32, 34, 35, 36, 37, 40, 44, 50, 51, 59, 60, 61, 64, 67, 68, 70, 72], "just": [15, 16, 21, 22, 23, 26, 27, 28, 32, 37, 39, 41, 48, 51, 52, 60, 62, 63, 69, 70, 73, 74, 77], "part": [15, 21, 24, 27, 35, 49, 59, 69], "scalar": [15, 16, 23, 35, 44, 51, 52, 59, 60, 71], "propagate_for": [15, 16, 23, 27, 44, 67], "propagate_until": [15, 23, 26, 27, 28, 30, 32, 37, 39, 40, 44, 48, 50, 53, 56, 57, 58, 63, 69, 70, 72, 75], "sixth": [15, 44], "element": [15, 16, 23, 26, 27, 29, 32, 35, 36, 38, 51, 57, 59, 62, 64, 65, 66, 73, 75, 76], "while": [15, 23, 24, 25, 26, 28, 33, 36, 37, 38, 44, 45, 46, 50, 58, 59, 61, 67, 69, 70, 73, 74, 75], "variant": 15, "fifth": [15, 27, 44], "modifi": [15, 16, 28, 57], "analog": 15, "wai": [15, 16, 25, 26, 28, 31, 36, 42, 44, 45, 48, 50, 52, 54, 57, 67, 68, 73, 74], "new": [15, 22, 25, 35, 36, 37, 40, 41, 46, 48, 51, 52, 53, 56, 57, 59, 62, 63, 64, 68, 70, 72, 73], "should": [15, 23, 27, 28, 30, 37, 42, 44, 51, 52, 55, 57, 69, 71, 72, 73, 76], "In": [15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "case": [15, 16, 17, 21, 23, 25, 26, 27, 28, 32, 33, 34, 35, 36, 37, 39, 41, 42, 43, 44, 45, 47, 48, 50, 51, 54, 58, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74], "matter": [15, 26, 52, 60, 73], "unpack": [15, 22], "declar": 15, "account": [15, 24, 25, 28, 32, 43, 54, 56, 66, 73], "adjust": [15, 41, 75], "when": [15, 16, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 61, 64, 67, 70, 71, 72, 73, 75, 76], "fact": [15, 16, 24, 25, 29, 32, 37, 49, 50, 55, 63, 67, 76], "two": [15, 16, 18, 21, 23, 24, 25, 27, 28, 32, 35, 36, 37, 43, 46, 48, 49, 51, 52, 55, 57, 58, 59, 62, 65, 66, 70, 73, 74, 75], "time": [15, 16, 17, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 77], "grid": [15, 16, 23, 24, 25, 27, 28, 29, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 50, 51, 57, 60, 62, 69, 71, 73], "equal": [15, 16, 25, 26, 30, 37, 41, 42, 43, 44, 46, 47, 62, 64, 69, 73, 74], "previous": [15, 37, 69], "differ": [15, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 40, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 62, 65, 67, 68, 70, 73, 74, 76], "between": [15, 24, 25, 28, 35, 37, 38, 52, 53, 54, 55, 62, 65, 69, 73, 76], "point": [15, 16, 21, 23, 24, 26, 27, 28, 30, 32, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 47, 49, 50, 51, 55, 56, 59, 60, 61, 67, 68, 69, 70, 71, 72, 73, 76], "want": [15, 22, 24, 30, 34, 35, 37, 40, 41, 49, 51, 52, 55, 58, 60, 61, 62, 69, 76], "recov": [15, 40], "invok": [15, 16, 23, 27, 28, 42, 44, 50, 57, 59, 69, 72, 73, 75], "manual": [15, 28, 50, 73], "vsop2013": [15, 16, 17, 21], "move": [15, 16, 21, 28, 34, 37, 44, 46, 47, 64, 69, 70, 73], "model": [15, 16, 21, 26, 30, 31, 32, 36, 38, 42, 51, 54, 55, 56, 61, 63, 67, 69, 71, 73, 74, 75, 76], "submodul": [15, 16, 55, 76], "semant": [15, 16, 73], "make_nbody_si": [15, 16], "replac": [15, 16, 23, 25, 26, 55, 60, 73, 76], "nbodi": [15, 26, 30, 36, 38, 42, 56, 67, 69, 75], "ident": [15, 23, 32, 37, 40, 74], "quadrupl": [15, 16, 22, 45, 67], "via": [15, 16, 17, 21, 22, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 72, 73, 75, 76, 77], "real128": [15, 16, 22, 45, 50, 60, 67], "float": [15, 16, 21, 23, 24, 26, 28, 35, 36, 37, 40, 43, 45, 50, 51, 59, 60, 67, 71, 72], "longdoubl": [15, 16, 45, 50, 53, 60], "addition": [15, 27, 28, 41, 43, 49, 50], "enabl": [15, 16, 22, 23, 26, 27, 43, 44, 51, 60, 65, 67, 71], "inform": [15, 16, 27, 30, 31, 32, 40, 43, 49, 52, 57], "strict": [15, 16, 22], "convers": [15, 16, 24, 25, 35, 50, 54, 60, 76], "For": [15, 21, 23, 25, 26, 28, 29, 30, 32, 34, 36, 42, 43, 45, 48, 50, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 65, 68, 70, 72, 73, 74, 76], "attempt": [15, 43, 68, 69, 73], "integ": [15, 52, 57], "ta": [15, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 75], "taylor_adapt": [15, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 75], "typeerror": 15, "solut": [15, 16, 24, 25, 26, 27, 29, 32, 35, 37, 39, 40, 41, 44, 48, 53, 54, 55, 56, 58, 76, 77], "here": [15, 23, 24, 25, 26, 28, 29, 30, 32, 33, 35, 37, 38, 40, 48, 50, 52, 54, 57, 58, 60, 61, 62, 65, 69, 72, 73, 74, 77], "initi": [15, 16, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 77], "instead": [15, 16, 22, 23, 24, 25, 26, 28, 29, 30, 32, 34, 40, 41, 44, 45, 49, 51, 52, 57, 59, 60, 64, 68, 70, 76], "similarli": [15, 23, 28, 44, 50, 51, 59, 60, 64, 71, 72], "again": [15, 23, 24, 28, 33, 34, 35, 40, 41, 44, 54, 56, 62, 63, 64, 68, 69, 70, 71], "problem": [15, 16, 17, 21, 23, 24, 25, 26, 28, 29, 30, 35, 36, 40, 42, 47, 51, 52, 65, 69, 70], "expect": [15, 23, 27, 28, 32, 37, 51, 53, 57, 58, 62, 65], "similar": [15, 23, 27, 32, 36, 48, 51, 54, 55, 69, 76, 77], "fashion": [15, 21, 38, 42, 47, 55, 69, 76], "your": [15, 21, 22, 30, 35, 60], "except": [15, 25, 30, 40, 45, 54, 59, 60, 67, 76], "correct": [15, 24, 37, 54, 55, 59, 76], "especi": [15, 72, 77], "whenev": [15, 22, 28, 32, 35, 47, 50, 69, 75], "until": [15, 16, 23, 27, 28, 44, 50, 58, 69], "5": [15, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 50, 51, 54, 55, 56, 57, 59, 61, 62, 64, 65, 69, 70, 72, 73, 75, 76], "assum": [15, 35, 37, 40, 54, 55, 58, 60, 61, 70, 73, 74, 75, 76], "size": [15, 16, 23, 24, 28, 30, 32, 37, 38, 42, 43, 44, 47, 51, 55, 56, 57, 63, 72, 73, 76, 77], "r0": [15, 65, 66], "r1": [15, 75], "r2": [15, 24, 66, 72, 75], "r3": 15, "fix": [15, 18, 21, 23, 32, 34, 37, 40, 46, 52, 54, 58, 59, 61, 70, 76], "g": [15, 16, 22, 23, 25, 26, 27, 28, 29, 30, 32, 34, 36, 37, 38, 40, 43, 45, 48, 51, 52, 56, 57, 58, 59, 60, 63, 64, 65, 67, 69, 70, 72, 73, 75, 77], "r4": 15, "noth": [15, 27, 37, 65], "request": [15, 23, 35, 37, 40, 44, 50, 57, 59], "whether": [15, 52, 60, 67], "append": [15, 23, 25, 28, 30, 31, 32, 35, 37, 38, 39, 40, 41, 43, 48, 49, 52, 57, 61, 70, 74, 75], "repres": [15, 23, 25, 26, 28, 29, 32, 33, 34, 35, 36, 38, 42, 44, 45, 50, 51, 52, 54, 55, 56, 59, 61, 62, 64, 69, 70, 71, 73, 76, 77], "sign": [15, 28, 35, 70], "trigger": [15, 23, 24, 28, 32, 35, 39, 42, 43, 47, 49, 50, 58, 70, 75], "its": [15, 16, 24, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 44, 45, 46, 47, 49, 52, 57, 58, 61, 62, 63, 68, 69, 73, 74], "neg": [15, 16, 23, 24, 28, 37, 38, 42, 43, 46, 47, 49, 70, 73, 75], "graviti": [16, 17, 21, 34, 44, 47, 56, 66, 67, 73], "stabilis": [16, 62], "159": 16, "156": [16, 54], "It": [16, 23, 27, 28, 29, 32, 37, 40, 44, 45, 51, 52, 55, 59, 60, 61, 73, 76], "step": [16, 25, 28, 35, 36, 37, 38, 40, 41, 44, 47, 56, 57, 63, 67, 68, 69, 73, 75, 77], "callback": [16, 23, 24, 25, 27, 28, 29, 35, 38, 39, 41, 42, 43, 44, 47, 49, 50, 57, 69, 70, 75], "propagate_": 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"mandatori": [16, 22, 23, 28, 44, 51, 57, 64], "164": 16, "improv": [16, 25, 50, 52, 54, 66], "162": [16, 61], "161": 16, "termin": [16, 23, 35, 38, 39, 41, 42, 49, 50, 60, 69, 71], "simplifi": [16, 32, 35, 37, 45, 59, 66, 72, 73], "158": 16, "propagate_grid": [16, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 49, 54, 60, 61, 62, 64, 66, 69, 71, 73], "154": 16, "binari": [16, 50, 52, 59, 68], "wheel": 16, "built": [16, 27, 29, 30, 61], "manylinux2014": 16, "153": [16, 30], "build": [16, 22, 25, 30, 32, 35, 37, 38, 40, 52, 54, 55, 59, 76], "atmospher": [16, 19, 21], "neural": [16, 19, 21, 54, 71, 74], "network": [16, 19, 21, 31, 32, 54, 74], "151": 16, "interfac": [16, 19, 21, 44, 54, 61], "pytorch": [16, 54, 61], "python": [16, 21, 22, 30, 35, 50, 51, 57, 60, 68, 77], "150": [16, 37, 38, 73], "implement": [16, 23, 24, 25, 28, 29, 30, 34, 36, 37, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 58, 59, 60, 61, 63, 64, 65, 77], "elp2000": [16, 17, 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69, 72, 73], "larg": [16, 25, 26, 38, 43, 50, 51, 55, 58, 67, 71, 72, 73, 76, 77], "144": 16, "against": [16, 23, 42, 47, 49], "139": 16, "137": 16, "circular": [16, 24, 25, 40, 46, 54, 62, 65, 67, 73, 75], "restrict": [16, 17, 21, 40, 51], "three": [16, 17, 21, 23, 28, 35, 37, 40, 47, 51, 57, 59, 70, 76], "bodi": [16, 17, 21, 24, 25, 26, 28, 36, 38, 40, 42, 51, 54, 56, 65, 66, 67, 69, 70, 75, 76], "135": 16, "llvm": [16, 21, 30, 32, 50, 63, 68, 77], "slp": 16, "134": 16, "opt": [16, 26], "due": [16, 23, 28, 49, 50, 51, 54, 57, 58, 59, 62, 66, 67, 73], "consider": [16, 51, 57, 62, 72], "increas": [16, 23, 27, 28, 36, 37, 38, 40, 47, 51, 55, 56, 61, 70, 71, 72, 73, 76], "memori": [16, 23, 26, 27, 50, 51, 63, 67, 71, 73], "llvm_state": [16, 63], "avoid": [16, 23, 24, 25, 28, 32, 33, 40, 42, 43, 47, 49, 50, 51, 52, 54, 57, 59, 63, 68, 72], "re": [16, 23, 24, 28, 35, 36, 38, 42, 43, 49, 59, 62, 63, 64, 65, 69, 70, 73], "optimis": [16, 22, 26, 52], "alreadi": [16, 32, 33, 42, 51, 59, 63, 67, 73], "dure": [16, 23, 27, 28, 30, 38, 50, 51, 54, 57, 60, 63, 69, 71, 73], "program": [16, 26, 63], "132": 16, "bitcod": 16, "pre_hook": [16, 44], "taken": [16, 23, 27, 28, 29, 32, 35, 36, 44, 56, 62, 67, 69], "128": [16, 21, 50], "introduc": [16, 24, 25, 31, 33, 35, 36, 37, 42, 43, 47, 48, 50, 54, 56, 61, 62, 64, 65, 67, 73], "vectoris": [16, 36, 65], "overload": 16, "api": [16, 22, 23, 27, 32, 57, 71], "These": [16, 25, 30, 32, 33, 35, 36, 37, 40, 42, 44, 48, 55, 56, 59, 67, 70, 76], "allow": [16, 23, 24, 25, 27, 32, 35, 36, 40, 43, 55, 59, 61, 76], "oper": [16, 22, 23, 25, 27, 32, 35, 37, 40, 44, 45, 46, 50, 52, 57, 59, 60, 67, 69, 71, 77], "effici": [16, 27, 30, 35, 42, 43, 44, 55, 56, 57, 61, 67, 72, 73, 76], "repeatedli": [16, 44, 51], "individu": [16, 35, 36, 50, 67], "127": 16, "high": [16, 21, 23, 29, 32, 33, 34, 35, 36, 37, 38, 40, 43, 44, 45, 46, 48, 50, 54, 55, 57, 60, 69, 71, 73, 74, 76, 77], "substitut": [16, 35, 58, 59, 72, 73], "gener": [16, 22, 23, 24, 25, 26, 27, 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"api-overview"]], "Precision and truncation threshold": [[55, "precision-and-truncation-threshold"], [76, "precision-and-truncation-threshold"]], "Time coordinate": [[55, "time-coordinate"], [76, "time-coordinate"]], "Checking the implementation": [[55, "checking-the-implementation"], [76, "checking-the-implementation"]], "Evaluating the performance of ensemble & batch mode": [[56, "evaluating-the-performance-of-ensemble-batch-mode"]], "The scalar, serial baseline": [[56, "the-scalar-serial-baseline"]], "Parallelisation with ensemble propagation": [[56, "parallelisation-with-ensemble-propagation"]], "Vectorisation with batch mode": [[56, "vectorisation-with-batch-mode"]], "Choosing between threads and processes": [[57, "choosing-between-threads-and-processes"]], "Computing event sensitivity": [[58, "computing-event-sensitivity"]], "The analytical approach": [[58, "the-analytical-approach"]], "The numerical approach": [[58, "the-numerical-approach"]], "Application to optimisation 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"handling-rational-numbers"]], "Elastic tides": [[73, "elastic-tides"]], "What to expect?": [[73, "what-to-expect"]], "Spokes on the wheel": [[73, "spokes-on-the-wheel"]], "The first Lagrangian": [[73, "the-first-lagrangian"]], "Adding damping": [[73, "adding-damping"]], "Adding a moon": [[73, "adding-a-moon"]], "Analysing the bulge": [[73, "analysing-the-bulge"]], "Interfacing torch to heyoka.py": [[74, "interfacing-torch-to-heyoka-py"]], "Calculating transit timing variations": [[75, "calculating-transit-timing-variations"]], "Introduction to the VSOP2013 planetary theory": [[76, "introduction-to-the-vsop2013-planetary-theory"]], "Taylor\u2019s method": [[77, "taylor-s-method"]]}, "indexentries": {"diff_args (class in heyoka)": [[5, "heyoka.diff_args"]], "diff_tensors() (in module heyoka)": [[6, "heyoka.diff_tensors"]], "__init__() (heyoka.dtens method)": [[7, "heyoka.dtens.__init__"]], "args (heyoka.dtens property)": [[7, "heyoka.dtens.args"]], "dtens (class in heyoka)": [[7, 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    \ No newline at end of file
    +Search.setIndex({"docnames": ["acknowledgement", "advanced_tutorials", "api_exsys", "api_integrators", "api_lagham", "autosummary_generated/heyoka.diff_args", "autosummary_generated/heyoka.diff_tensors", "autosummary_generated/heyoka.dtens", "autosummary_generated/heyoka.expression", "autosummary_generated/heyoka.hamiltonian", "autosummary_generated/heyoka.lagrangian", "autosummary_generated/heyoka.make_vars", "autosummary_generated/heyoka.taylor_adaptive", "basic_tutorials", "benchmarks", "breaking_changes", "changelog", "examples_astro", "examples_event", "examples_ml", "examples_others", "index", "install", "notebooks/Batch mode overview", "notebooks/Box control for Formation Flying Satellites", "notebooks/Comparing coordinate systems", "notebooks/Customising the adaptive integrator", "notebooks/Dense output", "notebooks/Event detection", "notebooks/Inverting Kepler's equation in ODEs", "notebooks/Long term stability of Trappist-1", "notebooks/NeuralHamiltonianODEs", 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72, 73, 74, 75, 76], "import": [7, 11, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76], "hy": [7, 15, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76], "x": [7, 11, 15, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "y": [7, 11, 23, 24, 25, 29, 30, 31, 32, 35, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 61, 62, 64, 66, 69, 70, 72, 73, 75, 76], "make_var": [7, 16, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 70, 71, 72, 74, 76], "dt": [7, 25, 30, 32, 35, 37, 38, 40, 41, 43, 48, 52, 53, 65, 77], "2": [7, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "fetch": [7, 15, 16, 23, 25, 27, 28, 36, 42, 43, 47, 51, 52, 57, 63], "jacobian": [7, 16, 32, 52, 62, 64, 65], "0": [7, 10, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77], "0000000000000000": [7, 25, 45, 51, 52, 54, 55, 59, 69, 72], "gradient": [7, 16, 17, 21, 23, 32, 40, 47, 49, 52, 58, 69], "first": [7, 15, 16, 17, 21, 23, 24, 26, 27, 28, 30, 31, 34, 35, 36, 37, 40, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 72, 74, 75, 76], "ha": [7, 15, 16, 22, 23, 25, 26, 27, 28, 32, 35, 37, 38, 40, 42, 44, 45, 46, 52, 55, 59, 61, 62, 63, 65, 69, 74], "exactli": [7, 16, 28, 36, 43, 50, 61, 72, 76], "index_of": 7, "vidx": 7, "posit": [7, 15, 24, 25, 28, 30, 33, 37, 38, 40, 41, 42, 43, 47, 55, 62, 64, 65, 66, 67, 69, 70, 73, 75, 76], "suppli": [7, 11, 15, 16, 45, 51, 64, 69], "dens": [7, 13, 16, 21, 28, 44, 47, 52, 63, 70, 75], "spars": [7, 52], "format": [7, 17, 21, 23, 25, 27, 28, 30, 38, 40, 43, 44, 45, 49, 50, 52, 55, 60, 61, 67, 68, 69, 73, 76], "2d": [7, 23, 27, 42, 43, 44, 49, 52, 56, 62, 70, 73], "arrai": [7, 15, 16, 23, 24, 27, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 61, 65, 66, 69, 70, 71, 73, 74, 75, 76], "numpi": [7, 15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 53, 54, 55, 56, 57, 58, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76], "ndarrai": 7, 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26, 35, 37, 38, 39, 41, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 74], "have": [9, 10, 15, 16, 23, 24, 25, 26, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 44, 45, 48, 49, 51, 52, 54, 55, 57, 58, 61, 62, 64, 66, 68, 72, 74, 75, 76, 77], "same": [9, 10, 15, 16, 22, 23, 26, 28, 31, 32, 35, 36, 37, 40, 44, 51, 54, 56, 57, 59, 61, 62, 63, 67, 68, 69, 70, 72, 73, 74], "appear": [9, 10, 23, 25, 33, 40, 52, 58, 59, 77], "other": [9, 10, 15, 21, 22, 23, 25, 26, 27, 28, 35, 36, 37, 38, 40, 42, 44, 46, 48, 49, 50, 51, 52, 54, 56, 57, 59, 61, 66, 67, 69, 70, 72, 74, 77], "depend": [9, 10, 16, 25, 30, 32, 33, 36, 40, 43, 45, 46, 52, 53, 54, 55, 57, 58, 60, 66, 68, 76, 77], "l": [10, 24, 25, 29, 31, 32, 35, 37, 40, 54, 61, 62, 64, 73], "qdot": 10, "d": [10, 25, 30, 32, 35, 37, 40, 48, 58, 62, 64, 73, 77], "euler": [10, 62, 64, 70, 73], "lagrang": [10, 16, 17, 21, 35, 62, 64, 73], "veloc": [10, 23, 24, 28, 33, 36, 37, 38, 42, 43, 46, 47, 49, 58, 62, 64, 65, 66, 67, 69, 73, 75], "option": [10, 15, 16, 22, 23, 26, 27, 28, 35, 38, 44, 51, 57, 61, 64], "rayleigh": [10, 62, 64], "dissip": [10, 49, 61, 62, 64, 73], "quadrat": [10, 52, 59, 62, 64], "form": [10, 23, 28, 30, 32, 35, 37, 38, 40, 45, 54, 57, 61, 64, 73, 77], "add": [10, 16, 22, 24, 28, 32, 36, 37, 38, 39, 40, 41, 42, 62, 70, 73], "forc": [10, 23, 25, 33, 42, 46, 47, 51, 54, 62, 64, 73], "dynam": [10, 16, 23, 24, 25, 28, 30, 31, 32, 33, 38, 40, 41, 42, 43, 46, 47, 49, 50, 53, 54, 55, 56, 58, 60, 61, 62, 64, 69, 70, 71, 72, 73, 76], "explicit": [10, 29, 33, 50, 58, 60, 73, 77], "str": [11, 30, 32, 37, 40], "creat": [11, 16, 22, 23, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76], "from": [11, 15, 16, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "string": [11, 50, 57, 60], "instanc": [11, 15, 23, 28, 30, 44, 45, 50, 51, 52, 53, 55, 56, 57, 59, 60, 63, 65, 69, 71, 73, 76], "otherwis": [11, 25, 28, 32, 43, 44, 60, 61, 66, 70, 71, 72, 73], "z": [11, 24, 25, 29, 37, 39, 40, 45, 46, 51, 52, 54, 55, 59, 66, 70, 72, 76], "sy": [12, 15, 26, 29, 33, 36, 38, 39, 42, 44, 48, 50, 56, 57, 60, 62, 63, 64, 67, 68, 69, 72, 75], "kwarg": [12, 32, 61], "taylor": [13, 16, 21, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 40, 43, 44, 48, 50, 51, 54, 57, 61, 67, 71, 72, 73], "adapt": [13, 15, 16, 21, 25, 28, 30, 32, 51, 57, 60, 61, 63, 71, 77], "integr": [13, 14, 15, 16, 17, 18, 20, 21, 22, 25, 27, 28, 29, 30, 31, 33, 34, 35, 39, 40, 41, 42, 43, 46, 47, 48, 49, 51, 52, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77], "customis": [13, 16, 21, 28, 72], "od": [13, 16, 17, 19, 21, 23, 25, 26, 27, 28, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 55, 56, 57, 58, 61, 67, 68, 69, 71, 72, 73, 76, 77], "autonom": [13, 21, 48, 51, 70], "continu": [13, 15, 16, 17, 21, 22, 28, 30, 35, 42, 43, 44, 50, 57, 63], "output": [13, 15, 16, 21, 22, 28, 31, 34, 35, 44, 50, 51, 52, 57, 59, 61, 63, 69, 71, 74, 75, 76], "event": [13, 16, 21, 24, 35, 38, 39, 42, 43, 47, 49, 50, 57, 60, 70, 71, 75], "detect": [13, 16, 21, 24, 30, 34, 35, 38, 39, 41, 42, 43, 44, 47, 50, 57, 58, 70, 75], "see": [14, 16, 22, 23, 25, 27, 28, 30, 32, 33, 34, 35, 38, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76], "section": [14, 16, 18, 21, 25, 26, 27, 28, 33, 45, 50, 54, 65, 70], "document": [14, 15, 16, 22, 28, 75], "c": [14, 16, 21, 22, 24, 26, 27, 30, 33, 34, 35, 37, 40, 44, 45, 47, 48, 50, 51, 57, 60, 61, 62, 63, 66, 68, 70, 71, 72, 75], "librari": [14, 16, 21, 22, 28, 44, 45, 50, 60, 68, 74], "comparison": [14, 16, 29, 32, 36, 40, 50, 51, 54, 69], "popular": [14, 32, 54, 77], "numer": [14, 16, 21, 23, 24, 25, 26, 28, 29, 31, 32, 34, 35, 36, 37, 40, 42, 43, 45, 47, 48, 51, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 76, 77], "packag": [14, 54, 55, 61, 65, 68, 75, 76], "evalu": [14, 20, 21, 26, 27, 29, 32, 35, 37, 40, 50, 52, 55, 59, 61, 63, 65, 69, 76, 77], "perform": [14, 16, 20, 21, 23, 24, 25, 26, 28, 35, 36, 37, 43, 44, 45, 48, 50, 52, 53, 54, 55, 57, 60, 61, 62, 63, 67, 68, 69, 71, 72, 73, 74, 76, 77], "parallelis": [14, 16, 21, 30, 57, 67], "also": [14, 16, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 57, 59, 60, 61, 62, 63, 65, 66, 68, 69, 71, 73, 74, 75, 76, 77], "includ": [15, 16, 21, 22, 25, 28, 30, 36, 37, 40, 48, 57, 58, 72, 76], "backward": [15, 23, 28, 44, 53], "incompat": 15, "been": [15, 16, 25, 26, 27, 28, 32, 37, 42, 44, 46, 52, 54, 55, 59, 61, 62, 63, 64, 65, 66, 68, 72], "explicitli": [15, 25, 29, 32, 33, 41, 50, 54, 59], "requir": [15, 16, 22, 23, 24, 25, 27, 28, 32, 35, 36, 37, 44, 50, 67, 69, 71, 73, 76, 77], "pass": [15, 16, 24, 27, 28, 30, 32, 33, 39, 42, 44, 50, 51, 52, 55, 57, 59, 60, 61, 65, 69, 71, 72, 73, 76], "previou": [15, 25, 26, 27, 29, 31, 35, 45, 47, 51, 60, 62, 70, 71], "where": [15, 24, 25, 26, 27, 28, 31, 32, 34, 35, 37, 40, 42, 44, 45, 46, 51, 52, 53, 54, 55, 58, 60, 61, 62, 64, 66, 70, 72, 73, 76, 77], "try": [15, 26, 27, 30, 40, 44, 48, 51, 52, 53, 59, 67, 68, 69, 70, 72, 73], "automat": [15, 16, 21, 28, 29, 43, 44, 45, 50, 52, 66, 67, 69, 72, 77], "infer": [15, 23, 50, 74], "turn": [15, 24, 25, 28, 38, 40, 43, 51, 70], "out": [15, 16, 23, 25, 28, 29, 36, 37, 38, 40, 41, 42, 43, 44, 46, 50, 54, 55, 56, 60, 61, 66, 67, 68, 71, 72, 73, 74, 76], "practic": [15, 23, 25, 26, 28, 30, 43, 49, 55, 67, 76], "confus": [15, 27, 28], "bug": [15, 27, 28, 32, 60], "affect": [15, 24, 43, 44], "now": [15, 16, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75], "alwai": [15, 16, 23, 27, 28, 32, 40, 42, 44, 45, 50, 52, 53, 54, 59, 60, 70, 73], "updat": [15, 22, 23, 24, 26, 38, 41, 43, 44, 49, 69, 75], "accordingli": [15, 30, 35], "mean": [15, 16, 25, 26, 27, 30, 34, 36, 38, 40, 43, 49, 51, 52, 54, 55, 56, 64, 65, 67, 76], "code": [15, 16, 22, 23, 24, 26, 28, 30, 32, 36, 37, 40, 41, 43, 47, 49, 51, 57, 59, 60, 61, 63, 68, 76, 77], "need": [15, 22, 23, 24, 25, 27, 28, 30, 32, 35, 36, 37, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 54, 55, 58, 59, 60, 61, 62, 63, 67, 68, 69, 72, 73, 74, 76, 77], "rewritten": [15, 77], "second": [15, 18, 21, 27, 28, 30, 32, 36, 37, 40, 42, 44, 47, 50, 51, 52, 54, 55, 56, 57, 59, 62, 67, 73, 76], "signatur": [15, 16, 23, 28], "bool": [15, 28], "convention": [15, 72], "call": [15, 16, 23, 24, 25, 27, 28, 31, 32, 33, 35, 37, 40, 42, 44, 51, 57, 59, 61, 65, 70, 72, 73], "mr": 15, "remov": [15, 16, 25, 28, 59, 63, 75], "flag": [15, 22, 23, 27, 28, 44, 51, 59, 63, 67], "meant": [15, 28, 74], "signal": 15, "possibl": [15, 16, 22, 23, 25, 28, 30, 31, 34, 35, 37, 42, 44, 45, 48, 50, 51, 52, 53, 55, 57, 58, 60, 65, 69, 70, 72, 73, 74, 76], "multipl": [15, 23, 30, 35, 36, 51, 52, 56, 57, 58, 59, 67, 73], "root": [15, 28, 35, 36, 37, 40, 43, 45], "within": [15, 25, 27, 28, 35, 52, 53, 59, 70], "cooldown": [15, 24, 43, 60, 71], "period": [15, 16, 17, 21, 23, 25, 28, 29, 30, 32, 33, 46, 54, 62, 65, 66, 73], "never": [15, 33, 57], "intend": [15, 50, 60], "drop": [15, 23, 55, 73, 76], "exist": [15, 35, 70], "straightforward": [15, 35, 52, 57], "you": [15, 21, 22, 27, 28, 32, 34, 35, 36, 37, 40, 44, 50, 51, 59, 60, 61, 64, 67, 68, 70, 72], "just": [15, 16, 21, 22, 23, 26, 27, 28, 32, 37, 39, 41, 48, 51, 52, 60, 62, 63, 69, 70, 73, 74, 77], "part": [15, 21, 24, 27, 35, 49, 59, 69], "scalar": [15, 16, 23, 35, 44, 51, 52, 59, 60, 71], "propagate_for": [15, 16, 23, 27, 44, 67], "propagate_until": [15, 23, 26, 27, 28, 30, 32, 37, 39, 40, 44, 48, 50, 53, 56, 57, 58, 63, 69, 70, 72, 75], "sixth": [15, 44], "element": [15, 16, 23, 26, 27, 29, 32, 35, 36, 38, 51, 57, 59, 62, 64, 65, 66, 73, 75, 76], "while": [15, 23, 24, 25, 26, 28, 33, 36, 37, 38, 44, 45, 46, 50, 58, 59, 61, 67, 69, 70, 73, 74, 75], "variant": 15, "fifth": [15, 27, 44], "modifi": [15, 16, 28, 57], "analog": 15, "wai": [15, 16, 25, 26, 28, 31, 36, 42, 44, 45, 48, 50, 52, 54, 57, 67, 68, 73, 74], "new": [15, 22, 25, 35, 36, 37, 40, 41, 46, 48, 51, 52, 53, 56, 57, 59, 62, 63, 64, 68, 70, 72, 73], "should": [15, 23, 27, 28, 30, 37, 42, 44, 51, 52, 55, 57, 69, 71, 72, 73, 76], "In": [15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "case": [15, 16, 17, 21, 23, 25, 26, 27, 28, 32, 33, 34, 35, 36, 37, 39, 41, 42, 43, 44, 45, 47, 48, 50, 51, 54, 58, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74], "matter": [15, 26, 52, 60, 73], "unpack": [15, 22], "declar": 15, "account": [15, 24, 25, 28, 32, 43, 54, 56, 66, 73], "adjust": [15, 41, 75], "when": [15, 16, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 61, 64, 67, 70, 71, 72, 73, 75, 76], "fact": [15, 16, 24, 25, 29, 32, 37, 49, 50, 55, 63, 67, 76], "two": [15, 16, 18, 21, 23, 24, 25, 27, 28, 32, 35, 36, 37, 43, 46, 48, 49, 51, 52, 55, 57, 58, 59, 62, 65, 66, 70, 73, 74, 75], "time": [15, 16, 17, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 77], "grid": [15, 16, 23, 24, 25, 27, 28, 29, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 50, 51, 57, 60, 62, 69, 71, 73], "equal": [15, 16, 25, 26, 30, 37, 41, 42, 43, 44, 46, 47, 62, 64, 69, 73, 74], "previous": [15, 37, 69], "differ": [15, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 40, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 62, 65, 67, 68, 70, 73, 74, 76], "between": [15, 24, 25, 28, 35, 37, 38, 52, 53, 54, 55, 62, 65, 69, 73, 76], "point": [15, 16, 21, 23, 24, 26, 27, 28, 30, 32, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 47, 49, 50, 51, 55, 56, 59, 60, 61, 67, 68, 69, 70, 71, 72, 73, 76], "want": [15, 22, 24, 30, 34, 35, 37, 40, 41, 49, 51, 52, 55, 58, 60, 61, 62, 69, 76], "recov": [15, 40], "invok": [15, 16, 23, 27, 28, 42, 44, 50, 57, 59, 69, 72, 73, 75], "manual": [15, 28, 50, 73], "vsop2013": [15, 16, 17, 21], "move": [15, 16, 21, 28, 34, 37, 44, 46, 47, 64, 69, 70, 73], "model": [15, 16, 21, 26, 30, 31, 32, 36, 38, 42, 51, 54, 55, 56, 61, 63, 67, 69, 71, 73, 74, 75, 76], "submodul": [15, 16, 55, 76], "semant": [15, 16, 73], "make_nbody_si": [15, 16], "replac": [15, 16, 23, 25, 26, 55, 60, 73, 76], "nbodi": [15, 26, 30, 36, 38, 42, 56, 67, 69, 75], "ident": [15, 23, 32, 37, 40, 74], "quadrupl": [15, 16, 22, 45, 67], "via": [15, 16, 17, 21, 22, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 72, 73, 75, 76, 77], "real128": [15, 16, 22, 45, 50, 60, 67], "float": [15, 16, 21, 23, 24, 26, 28, 35, 36, 37, 40, 43, 45, 50, 51, 59, 60, 67, 71, 72], "longdoubl": [15, 16, 45, 50, 53, 60], "addition": [15, 27, 28, 41, 43, 49, 50], "enabl": [15, 16, 22, 23, 26, 27, 43, 44, 51, 60, 65, 67, 71], "inform": [15, 16, 27, 30, 31, 32, 40, 43, 49, 52, 57], "strict": [15, 16, 22], "convers": [15, 16, 24, 25, 35, 50, 54, 60, 76], "For": [15, 21, 23, 25, 26, 28, 29, 30, 32, 34, 36, 42, 43, 45, 48, 50, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 65, 68, 70, 72, 73, 74, 76], "attempt": [15, 43, 68, 69, 73], "integ": [15, 52, 57], "ta": [15, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 75], "taylor_adapt": [15, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 75], "typeerror": 15, "solut": [15, 16, 24, 25, 26, 27, 29, 32, 35, 37, 39, 40, 41, 44, 48, 53, 54, 55, 56, 58, 76, 77], "here": [15, 23, 24, 25, 26, 28, 29, 30, 32, 33, 35, 37, 38, 40, 48, 50, 52, 54, 57, 58, 60, 61, 62, 65, 69, 72, 73, 74, 77], "initi": [15, 16, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 77], "instead": [15, 16, 22, 23, 24, 25, 26, 28, 29, 30, 32, 34, 40, 41, 44, 45, 49, 51, 52, 57, 59, 60, 64, 68, 70, 76], "similarli": [15, 23, 28, 44, 50, 51, 59, 60, 64, 71, 72], "again": [15, 23, 24, 28, 33, 34, 35, 40, 41, 44, 54, 56, 62, 63, 64, 68, 69, 70, 71], "problem": [15, 16, 17, 21, 23, 24, 25, 26, 28, 29, 30, 35, 36, 40, 42, 47, 51, 52, 65, 69, 70], "expect": [15, 23, 27, 28, 32, 37, 51, 53, 57, 58, 62, 65], "similar": [15, 23, 27, 32, 36, 48, 51, 54, 55, 69, 76, 77], "fashion": [15, 21, 38, 42, 47, 55, 69, 76], "your": [15, 21, 22, 30, 35, 60], "except": [15, 25, 30, 40, 45, 54, 59, 60, 67, 76], "correct": [15, 24, 37, 54, 55, 59, 76], "especi": [15, 72, 77], "whenev": [15, 22, 28, 32, 35, 47, 50, 69, 75], "until": [15, 16, 23, 27, 28, 44, 50, 58, 69], "5": [15, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 50, 51, 54, 55, 56, 57, 59, 61, 62, 64, 65, 69, 70, 72, 73, 75, 76], "assum": [15, 35, 37, 40, 54, 55, 58, 60, 61, 70, 73, 74, 75, 76], "size": [15, 16, 23, 24, 28, 30, 32, 37, 38, 42, 43, 44, 47, 51, 55, 56, 57, 63, 72, 73, 76, 77], "r0": [15, 65, 66], "r1": [15, 75], "r2": [15, 24, 66, 72, 75], "r3": 15, "fix": [15, 18, 21, 23, 32, 34, 37, 40, 46, 52, 54, 58, 59, 61, 70, 76], "g": [15, 16, 22, 23, 25, 26, 27, 28, 29, 30, 32, 34, 36, 37, 38, 40, 43, 45, 48, 51, 52, 56, 57, 58, 59, 60, 63, 64, 65, 67, 69, 70, 72, 73, 75, 77], "r4": 15, "noth": [15, 27, 37, 65], "request": [15, 23, 35, 37, 40, 44, 50, 57, 59], "whether": [15, 52, 60, 67], "append": [15, 23, 25, 28, 30, 31, 32, 35, 37, 38, 39, 40, 41, 43, 48, 49, 52, 57, 61, 70, 74, 75], "repres": [15, 23, 25, 26, 28, 29, 32, 33, 34, 35, 36, 38, 42, 44, 45, 50, 51, 52, 54, 55, 56, 59, 61, 62, 64, 69, 70, 71, 73, 76, 77], "sign": [15, 28, 35, 70], "trigger": [15, 23, 24, 28, 32, 35, 39, 42, 43, 47, 49, 50, 58, 70, 75], "its": [15, 16, 24, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 44, 45, 46, 47, 49, 52, 57, 58, 61, 62, 63, 68, 69, 73, 74], "neg": [15, 16, 23, 24, 28, 37, 38, 42, 43, 46, 47, 49, 70, 73, 75], "graviti": [16, 17, 21, 34, 44, 47, 56, 66, 67, 73], "stabilis": [16, 62], "159": 16, "156": [16, 54], "It": [16, 23, 27, 28, 29, 32, 37, 40, 44, 45, 51, 52, 55, 59, 60, 61, 73, 76], "step": [16, 25, 28, 35, 36, 37, 38, 40, 41, 44, 47, 56, 57, 63, 67, 68, 69, 73, 75, 77], "callback": [16, 23, 24, 25, 27, 28, 29, 35, 38, 39, 41, 42, 43, 44, 47, 49, 50, 57, 69, 70, 75], "propagate_": [16, 23, 28, 44], "155": 16, "angle_reduc": 16, "reduc": [16, 23, 25, 26, 28, 29, 35, 36, 37, 39, 40, 52, 59, 71, 72, 73], "angular": [16, 24, 25, 28, 38, 62, 64, 73], "left": [16, 22, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 58, 59, 62, 64, 65, 66, 70, 72, 73, 76, 77], "pi": [16, 23, 24, 25, 29, 30, 34, 37, 38, 39, 40, 49, 53, 54, 58, 62, 65, 66, 73, 75], "right": [16, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 59, 61, 62, 64, 65, 66, 67, 70, 72, 73, 76, 77], "rang": [16, 23, 25, 27, 29, 30, 31, 32, 35, 37, 38, 40, 43, 52, 53, 54, 57, 59, 61, 63, 67, 68, 69, 70, 73, 74, 75, 76], "modul": [16, 22, 25, 28, 33, 61, 68, 73, 74, 75], "readi": [16, 22, 23, 25, 27, 28, 30, 32, 35, 36, 38, 42, 43, 46, 47, 49, 50, 51, 54, 56, 57, 62, 64, 66, 69, 73, 74, 75], "made": [16, 28, 30, 32, 35, 37, 57, 60], "break": [16, 21, 24, 30, 40, 70], "mandatori": [16, 22, 23, 28, 44, 51, 57, 64], "164": 16, "improv": [16, 25, 50, 52, 54, 66], "162": [16, 61], "161": 16, "termin": [16, 23, 35, 38, 39, 41, 42, 49, 50, 60, 69, 71], "simplifi": [16, 32, 35, 37, 45, 59, 66, 72, 73], "158": 16, "propagate_grid": [16, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 49, 54, 60, 61, 62, 64, 66, 69, 71, 73], "154": 16, "binari": [16, 50, 52, 59, 68], "wheel": 16, "built": [16, 27, 29, 30, 61], "manylinux2014": 16, "153": [16, 30], "build": [16, 22, 25, 30, 32, 35, 37, 38, 40, 52, 54, 55, 59, 76], "atmospher": [16, 19, 21], "neural": [16, 19, 21, 54, 71, 74], "network": [16, 19, 21, 31, 32, 54, 74], "151": 16, "interfac": [16, 19, 21, 44, 54, 61], "pytorch": [16, 54, 61], "python": [16, 21, 22, 30, 35, 50, 51, 57, 60, 68, 77], "150": [16, 37, 38, 73], "implement": [16, 23, 24, 25, 28, 29, 30, 34, 36, 37, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 58, 59, 60, 61, 63, 64, 65, 77], "elp2000": [16, 17, 21], "analyt": [16, 21, 25, 27, 37, 55, 65, 70, 76], "lunar": [16, 17, 21, 38], "theori": [16, 17, 21, 38], "149": 16, "wrong": 16, "truncat": [16, 26, 77], "doubl": [16, 21, 23, 26, 27, 28, 33, 34, 35, 42, 43, 44, 45, 47, 48, 49, 50, 51, 56, 57, 60, 61, 63, 67, 71], "dtime": 16, "setter": 16, "143": 16, "142": 16, "feed": [16, 19, 21, 32, 54, 74], "forward": [16, 19, 21, 23, 27, 32, 40, 44, 52, 54, 57, 63, 74], "leaki": [16, 50], "relu": 16, "141": 16, "eccentr": [16, 25, 29, 38, 65, 66, 75, 76], "longitud": [16, 25, 54, 76], "f": [16, 23, 30, 32, 35, 37, 40, 48, 50, 51, 52, 53, 54, 58, 59, 61, 62, 63, 65, 69, 70, 77], "140": [16, 54], "delta": [16, 24, 37, 40, 48, 54, 65], "anomali": [16, 25, 29, 30, 65], "conveni": [16, 30, 37, 40, 52], "orbit": [16, 17, 21, 24, 25, 29, 30, 32, 38, 42, 46, 54, 62, 65, 66, 67, 70, 72, 73, 75, 76], "cr3bp": [16, 17, 21, 32], "97": [16, 44], "slow": [16, 28, 43, 73], "veri": [16, 22, 23, 24, 25, 26, 27, 28, 31, 32, 37, 43, 45, 50, 54, 56, 63, 66, 68, 69, 72, 73], "larg": [16, 25, 26, 38, 43, 50, 51, 55, 58, 67, 71, 72, 73, 76, 77], "144": 16, "against": [16, 23, 42, 47, 49], "139": 16, "137": 16, "circular": [16, 24, 25, 40, 46, 54, 62, 65, 67, 73, 75], "restrict": [16, 17, 21, 40, 51], "three": [16, 17, 21, 23, 28, 35, 37, 40, 47, 51, 57, 59, 70, 76], "bodi": [16, 17, 21, 24, 25, 26, 28, 36, 38, 40, 42, 51, 54, 56, 65, 66, 67, 69, 70, 75, 76], "135": 16, "llvm": [16, 21, 30, 32, 50, 63, 68, 77], "slp": 16, "134": 16, "opt": [16, 26], "due": [16, 23, 28, 49, 50, 51, 54, 57, 58, 59, 62, 66, 67, 73], "consider": [16, 51, 57, 62, 72], "increas": [16, 23, 27, 28, 36, 37, 38, 40, 47, 51, 55, 56, 61, 70, 71, 72, 73, 76], "memori": [16, 23, 26, 27, 50, 51, 63, 67, 71, 73], "llvm_state": [16, 63], "avoid": [16, 23, 24, 25, 28, 32, 33, 40, 42, 43, 47, 49, 50, 51, 52, 54, 57, 59, 63, 68, 72], "re": [16, 23, 24, 28, 35, 36, 38, 42, 43, 49, 59, 62, 63, 64, 65, 69, 70, 73], "optimis": [16, 22, 26, 52], "alreadi": [16, 32, 33, 42, 51, 59, 63, 67, 73], "dure": [16, 23, 27, 28, 30, 38, 50, 51, 54, 57, 60, 63, 69, 71, 73], "program": [16, 26, 63], "132": 16, "bitcod": 16, "pre_hook": [16, 44], "taken": [16, 23, 27, 28, 29, 32, 35, 36, 44, 56, 62, 67, 69], "128": [16, 21, 50], "introduc": [16, 24, 25, 31, 33, 35, 36, 37, 42, 43, 47, 48, 50, 54, 56, 61, 62, 64, 65, 67, 73], "vectoris": [16, 36, 65], "overload": 16, "api": [16, 22, 23, 27, 32, 57, 71], "These": [16, 25, 30, 32, 33, 35, 36, 37, 40, 42, 44, 48, 55, 56, 59, 67, 70, 76], "allow": [16, 23, 24, 25, 27, 32, 35, 36, 40, 43, 55, 59, 61, 76], "oper": [16, 22, 23, 25, 27, 32, 35, 37, 40, 44, 45, 46, 50, 52, 57, 59, 60, 67, 69, 71, 77], "effici": [16, 27, 30, 35, 42, 43, 44, 55, 56, 57, 61, 67, 72, 73, 76], "repeatedli": [16, 44, 51], "individu": [16, 35, 36, 50, 67], "127": 16, "high": [16, 21, 23, 29, 32, 33, 34, 35, 36, 37, 38, 40, 43, 44, 45, 46, 48, 50, 54, 55, 57, 60, 69, 71, 73, 74, 76, 77], "substitut": [16, 35, 58, 59, 72, 73], "gener": [16, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 42, 43, 45, 46, 47, 50, 51, 55, 56, 57, 58, 60, 61, 64, 66, 70, 72, 73, 76, 77], "subexpress": [16, 52, 59, 72, 73, 77], "hand": [16, 26, 27, 28, 32, 33, 37, 45, 48, 50, 51, 58, 61, 62, 64, 67, 70, 73, 77], "side": [16, 22, 24, 25, 28, 32, 33, 37, 45, 46, 48, 50, 51, 55, 58, 61, 67, 73, 76, 77], "read": [16, 25, 27, 28, 29, 30, 33, 37, 39, 41, 44, 46, 58, 64, 66], "122": 16, "addit": [16, 22, 23, 25, 27, 28, 32, 33, 44, 45, 48, 50, 51, 57, 59, 60, 62, 64, 66, 68, 69, 70, 71, 73], "unpickl": 16, "thei": [16, 22, 23, 25, 28, 29, 32, 34, 38, 42, 44, 54, 57, 62, 67, 74], "expos": 16, "etc": [16, 22, 23, 25, 28, 50, 54, 57, 60], "120": 16, "hash": [16, 43], "119": 16, "main": [16, 22, 24, 27, 30, 31, 32, 40, 44, 54, 61, 68, 69, 77], "130": 16, "custom": [16, 28, 50, 55, 63, 72, 76], "manag": [16, 22, 44, 50, 54, 74], "prevent": [16, 25, 26, 27, 28, 52], "leak": [16, 50], "real": [16, 22, 25, 28, 35, 36, 37, 45], "disabl": [16, 28, 50, 52], "129": 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"the-variational-equations"]], "Performance test": [[32, "performance-test"]], "Taylor Integrator": [[32, "taylor-integrator"]], "Scipy Counterpart": [[32, "scipy-counterpart"]], "A note on the Adjoint Method": [[32, "a-note-on-the-adjoint-method"]], "Non-autonomous systems": [[33, "non-autonomous-systems"]], "ODEs with parameters": [[34, "odes-with-parameters"]], "Optimal Control of the Lotka-Volterra equations": [[35, "optimal-control-of-the-lotka-volterra-equations"]], "Deriving the augmented dynamics": [[35, "deriving-the-augmented-dynamics"]], "Studying the uncontrolled system": [[35, "studying-the-uncontrolled-system"]], "Controlling the prey-predator dynamics": [[35, "controlling-the-prey-predator-dynamics"]], "Implementing a single shooting method": [[35, "implementing-a-single-shooting-method"]], "Brouwer\u2019s law in the outer Solar System": [[36, "brouwer-s-law-in-the-outer-solar-system"]], "The dynamical system": [[36, "the-dynamical-system"]], "Integrating in parallel": 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problems": [[58, "application-to-optimisation-problems"]], "Using the expression system effectively": [[59, "using-the-expression-system-effectively"]], "Long sums and products": [[59, "long-sums-and-products"]], "Automatic simplifications": [[59, "automatic-simplifications"]], "Preventing automatic simplifications": [[59, "preventing-automatic-simplifications"]], "Computations in extended precision": [[60, "computations-in-extended-precision"]], "Extended-precision (80-bit) example": [[60, "extended-precision-80-bit-example"]], "Quadruple-precision (128-bit) example": [[60, "quadruple-precision-128-bit-example"]], "Other classes and functions": [[60, "other-classes-and-functions"], [71, "other-classes-and-functions"]], "Caveats, limitations & issues": [[60, "caveats-limitations-issues"]], "Initialising numbers in extended precision": [[60, "initialising-numbers-in-extended-precision"]], "NumPy issues and limitations": [[60, "numpy-issues-and-limitations"]], "Feed-Forward Neural Networks": [[61, "feed-forward-neural-networks"]], "Inference": [[61, "inference"]], "Use in numerical integration": [[61, "use-in-numerical-integration"]], "Gravity-gradient stabilization": [[62, "gravity-gradient-stabilization"]], "The initial model": [[62, "the-initial-model"]], "Adding a spring and damping": [[62, "adding-a-spring-and-damping"]], "JIT compilation and caching": [[63, "jit-compilation-and-caching"]], "Pendulum on a movable support": [[64, "pendulum-on-a-movable-support"]], "Adding a friction term": [[64, "adding-a-friction-term"]], "The spherical pendulum": [[64, "the-spherical-pendulum"]], "Lagrange propagation and the state transition matrix": [[65, "lagrange-propagation-and-the-state-transition-matrix"]], "The Lagrange propagator": [[65, "the-lagrange-propagator"]], "Constructing the STM": [[65, "constructing-the-stm"]], "Mercury\u2019s relativistic precession": [[66, "mercury-s-relativistic-precession"]], "Parallel mode": [[67, "parallel-mode"]], "Parallel planetary embryos": [[67, "parallel-planetary-embryos"]], "Pickle support": [[68, "pickle-support"]], "On the serialisation of event callbacks": [[68, "on-the-serialisation-of-event-callbacks"]], "Conserving first integrals via manifold projection": [[69, "conserving-first-integrals-via-manifold-projection"]], "Fixing the energy": [[69, "fixing-the-energy"]], "Helping the optimiser out": [[69, "helping-the-optimiser-out"]], "Packaging it all together": [[69, "packaging-it-all-together"]], "The second integral of motion": [[70, "the-second-integral-of-motion"]], "Procedure": [[70, "procedure"]], "Running the experiments": [[70, "running-the-experiments"]], "Computations in single precision": [[71, "computations-in-single-precision"]], "The pendulum example": [[71, "the-pendulum-example"]], "Interoperability with SymPy": [[72, "interoperability-with-sympy"]], "More details on the conversion process": [[72, "more-details-on-the-conversion-process"]], "Handling rational numbers": [[72, "handling-rational-numbers"]], "Elastic tides": [[73, "elastic-tides"]], "What to expect?": [[73, "what-to-expect"]], "Spokes on the wheel": [[73, "spokes-on-the-wheel"]], "The first Lagrangian": [[73, "the-first-lagrangian"]], "Adding damping": [[73, "adding-damping"]], "Adding a moon": [[73, "adding-a-moon"]], "Analysing the bulge": [[73, "analysing-the-bulge"]], "Interfacing torch to heyoka.py": [[74, "interfacing-torch-to-heyoka-py"]], "Calculating transit timing variations": [[75, "calculating-transit-timing-variations"]], "Introduction to the VSOP2013 planetary theory": [[76, "introduction-to-the-vsop2013-planetary-theory"]], "Taylor\u2019s method": [[77, "taylor-s-method"]]}, "indexentries": {"diff_args (class in heyoka)": [[5, "heyoka.diff_args"]], "diff_tensors() (in module heyoka)": [[6, "heyoka.diff_tensors"]], "__init__() (heyoka.dtens method)": [[7, "heyoka.dtens.__init__"]], "args (heyoka.dtens property)": [[7, "heyoka.dtens.args"]], "dtens (class in heyoka)": [[7, 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