diff --git a/.gitignore b/.gitignore index 8a9f724..011cb6a 100644 --- a/.gitignore +++ b/.gitignore @@ -137,3 +137,5 @@ dmypy.json # Cython debug symbols cython_debug/ + +notebooks/figures/* diff --git a/notebooks/action_sampling.ipynb b/notebooks/action_sampling.ipynb deleted file mode 100644 index 17d3315..0000000 --- a/notebooks/action_sampling.ipynb +++ /dev/null @@ -1,510 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "ccd85cd9", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "/Users/annalena/miniconda3/envs/phoenix/bin/python\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/__init__.py\n" - ] - } - ], - "source": [ - "import sys; print(sys.executable) # should be the env where you ran pip\n", - "import phoenix; print(phoenix.__file__)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "140735c3", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:9: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:15: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:23: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:28: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:39: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:48: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:73: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:78: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:83: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:88: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:95: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:129: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions.py:142: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/actionsampling.py:22: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/actionsampling.py:28: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/actionsampling.py:56: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n" - ] - } - ], - "source": [ - "from phoenix.potentials import miyamoto_nagai_potential as Phi\n", - "from phoenix.actionsampling import sample_actions_batch" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "c47be4cd", - "metadata": {}, - "outputs": [], - "source": [ - "# Miyamoto–Nagai params (example numbers)\n", - "M, a, b = 1.0, 6.0, 0.3" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "0fc174a9", - "metadata": {}, - "outputs": [], - "source": [ - "JR, Jz, Jphi, Rc, kap, nu = sample_actions_batch(\n", - " Phi, M, a, b,\n", - " N=200_000, seed=42,\n", - " R0=8.0, Rd=2.6, Sigma0=1000.0,\n", - " RsigR=7.0, RsigZ=7.0,\n", - " sigmaR0_R0=35.0, sigmaz0_R0=20.0,\n", - " Rmin=0.2, Rmax=30.0\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "fb235ddd", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot histograms of the actions\n", - "import matplotlib.pyplot as plt\n", - "\n", - "plt.figure(figsize=(12, 4))\n", - "plt.subplot(1, 3, 1)\n", - "plt.hist(JR, bins=100)#, density=True)\n", - "plt.xlabel(r\"$J_R$\")\n", - "plt.subplot(1, 3, 2)\n", - "plt.hist(Jz, bins=100)#, density=True)\n", - "plt.xlabel(r\"$J_z$\")\n", - "plt.subplot(1, 3, 3)\n", - "plt.hist(Jphi, bins=100)#, density=True)\n", - "plt.xlabel(r\"$J_\\phi$\")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "phoenix", - "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": "3.12.0" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/components_disk.ipynb b/notebooks/components_disk.ipynb index 87fd604..f4d1a1a 100644 --- a/notebooks/components_disk.ipynb +++ b/notebooks/components_disk.ipynb @@ -32,14 +32,13 @@ "params = {\n", " \"R0\": 8.0, # for actions to phase space\n", " \"Rinit\": 8.0, # for sampling\n", - " \"R0\": 5.0,\n", " \"Rd\": 2.5,\n", " \"Sigma0\": 100.0,\n", " \"RsigR\": 18.0,\n", - " \"RsigZ\": 2.0,\n", + " \"RsigZ\": 10.0,\n", " \"sigmaR0_R0\": 140.0,\n", - " \"sigmaz0_R0\": 5.0,\n", - " \"L0\": 50.0,\n", + " \"sigmaz0_R0\": 50.0,\n", + " \"L0\": 1000.0,\n", " \"Rinit_for_Rc\": 8.0,\n", "}\n", "\n", @@ -61,7 +60,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions_disky_Binney.py:13: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:13: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", "```\n", "from jaxtyping import jaxtyped\n", "# Use your favourite typechecker: usually one of the two lines below.\n", @@ -85,7 +84,7 @@ "```\n", "\n", " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions_disky_Binney.py:37: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:37: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", "```\n", "from jaxtyping import jaxtyped\n", "# Use your favourite typechecker: usually one of the two lines below.\n", @@ -109,7 +108,7 @@ "```\n", "\n", " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions_disky_Binney.py:62: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:62: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", "```\n", "from jaxtyping import jaxtyped\n", "# Use your favourite typechecker: usually one of the two lines below.\n", @@ -133,7 +132,7 @@ "```\n", "\n", " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions_disky_Binney.py:87: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:87: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", "```\n", "from jaxtyping import jaxtyped\n", "# Use your favourite typechecker: usually one of the two lines below.\n", @@ -157,7 +156,7 @@ "```\n", "\n", " @jaxtyped\n", - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions_disky_Binney.py:115: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:115: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", "```\n", "from jaxtyping import jaxtyped\n", "# Use your favourite typechecker: usually one of the two lines below.\n", @@ -215,7 +214,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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", 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" ] @@ -301,7 +300,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -395,414 +394,6 @@ "plt.tight_layout()\n", "plt.show()" ] - }, - { - "cell_type": "markdown", - "id": "70e7f102", - "metadata": {}, - "source": [ - "# Spheroid distribution function" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "c2f67b12", - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " \"R0\": 8.0, # for actions to phase space\n", - " \"N0_spheroid\": 1e6,\n", - " \"J0_spheroid\": 50.0,\n", - " \"Gamma_spheroid\": 2.5,\n", - " \"Beta_spheroid\": 3.5,\n", - "}\n", - "\n", - "envelope_max = 3.0\n", - "n_candidates = 250_000\n", - "key = jax.random.PRNGKey(42)\n", - "# Js are max 400, 400, 2000\n", - "\n", - "Phi_spheroid = plummer_potential\n", - "theta_spheroid = jnp.array([1e12, 30.0]) # (M, a) z.B. für Plummer" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "11117be1", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/annalena/Documents/GitHub/phoenix/phoenix/distributionfunctions_spheroidal.py:13: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", - "```\n", - "from jaxtyping import jaxtyped\n", - "# Use your favourite typechecker: usually one of the two lines below.\n", - "from typeguard import typechecked as typechecker\n", - "from beartype import beartype as typechecker\n", - "\n", - "@jaxtyped(typechecker=typechecker)\n", - "def foo(...):\n", - "```\n", - "and the old double-decorator syntax\n", - "```\n", - "@jaxtyped\n", - "@typechecker\n", - "def foo(...):\n", - "```\n", - "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", - "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", - "```\n", - "@jaxtyped(typechecker)\n", - "def foo(...):\n", - "```\n", - "\n", - " @jaxtyped\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of candidate actions: 250000\n" - ] - } - ], - "source": [ - "#Generate candidate actions\n", - "from phoenix.distributionfunctions_spheroidal import f_double_power_law as df_spheroid\n", - "candidates, samples, soft_weights2 = sampling.sample_df_potential(df_spheroid, key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, tau=0.01)\n", - "print(\"Number of candidate actions:\", candidates.shape[0])\n", - "\n", - "#Map the candidate actions to phase-space coordinates\n", - "phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi_spheroid, theta_spheroid)\n", - "x2 = phase_space_coords[:, 0]\n", - "y2 = phase_space_coords[:, 1]\n", - "z2 = phase_space_coords[:, 2]\n", - "v_x2 = phase_space_coords[:, 3]\n", - "v_y2 = phase_space_coords[:, 4]\n", - "v_z2 = phase_space_coords[:, 5]" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "31da2be2", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Visualize the distribution of candidate actions\n", - "fig, axs = plt.subplots(1, 3, figsize=(15, 4))\n", - "axs[0].hist(samples[:, 0], bins=50, weights=soft_weights)\n", - "axs[0].set_xlabel(r\"$J_r$\")\n", - "axs[1].hist(samples[:, 1], bins=50, weights=soft_weights)\n", - "axs[1].set_xlabel(r\"$J_z$\")\n", - "axs[2].hist(samples[:, 2], bins=50, weights=soft_weights)\n", - "axs[2].set_xlabel(r\"$L_z$\")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "3fbdb10f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "import matplotlib.colors as colors\n", - "plt.figure(figsize=(12,6))\n", - "plt.subplot(231)\n", - "plt.hist2d(x2, y2, bins=50, cmap=\"viridis\", weights=soft_weights2)#, norm=colors.LogNorm(), cmin=1, weights=soft_weights)\n", - "plt.xlabel('x [kpc]')\n", - "plt.ylabel('y [kpc]')\n", - "plt.axis('equal')\n", - "plt.subplot(232)\n", - "plt.hist2d(x2, z2, bins=50, cmap=\"viridis\", weights=soft_weights2)\n", - "plt.xlabel('x [kpc]')\n", - "plt.ylabel('z [kpc]')\n", - "plt.axis('equal')\n", - "plt.subplot(233)\n", - "plt.hist2d(y2, z2, bins=50, cmap=\"viridis\", weights=soft_weights2)\n", - "plt.xlabel('y [kpc]')\n", - "plt.ylabel('z [kpc]')\n", - "plt.axis('equal')\n", - "\n", - "\n", - "plt.subplot(234)\n", - "plt.hist(v_x2, bins=50, weights=soft_weights2)#, range=(-2000, 2000))\n", - "plt.xlabel(r\"$v_\\text{x}$ (km/s)\")\n", - "plt.ylabel(\"Number of stars\")\n", - "\n", - "plt.subplot(235)\n", - "plt.hist(v_y2, bins=50, weights=soft_weights2)#, range=(-2000, 2000))\n", - "plt.xlabel(r\"$v_\\text{y}$ (km/s)\")\n", - "plt.ylabel(\"Number of stars\")\n", - "\n", - "plt.subplot(236)\n", - "plt.hist(v_z2, bins=50, weights=soft_weights2)\n", - "plt.xlabel(r\"$v_\\text{z}$ (km/s)\")\n", - "plt.ylabel(\"Number of stars\")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "fc1be153", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib.colors as mcolors\n", - "from scipy.stats import binned_statistic_2d\n", - "\n", - "# Helper function to calculate weighted mean\n", - "def weighted_mean_2d(x_pos, y_pos, values, weights, x_bins, y_bins):\n", - " # Sum of (value * weight) in each bin\n", - " weighted_sum, _, _, _ = binned_statistic_2d(\n", - " x_pos, y_pos, values * weights, statistic='sum', bins=[x_bins, y_bins]\n", - " )\n", - " # Sum of weights in each bin\n", - " sum_of_weights, _, _, _ = binned_statistic_2d(\n", - " x_pos, y_pos, weights, statistic='sum', bins=[x_bins, y_bins]\n", - " )\n", - " \n", - " # Divide, handling division by zero (where sum_of_weights is 0)\n", - " with np.errstate(divide='ignore', invalid='ignore'):\n", - " result = weighted_sum / sum_of_weights\n", - " \n", - " return result\n", - "\n", - "num_bins_x = 40\n", - "num_bins_y = 40\n", - "num_bins_z = 40 \n", - "\n", - "# Example: x, z, v_y are 1D arrays of particle positions and velocities\n", - "# Define bin edges\n", - "x_bins = np.linspace(x2.min(), x2.max(), num_bins_x + 1)\n", - "y_bins = np.linspace(y2.min(), y2.max(), num_bins_y + 1)\n", - "z_bins = np.linspace(z2.min(), z2.max(), num_bins_z + 1)\n", - "\n", - "# Digitize positions to bin indices\n", - "x_idx = np.digitize(x2, x_bins) - 1\n", - "y_idx = np.digitize(y2, y_bins) - 1\n", - "z_idx = np.digitize(z2, z_bins) - 1\n", - "\n", - "# Initialize array for mean v_y\n", - "mean_vx = np.full((num_bins_y, num_bins_z), np.nan)\n", - "mean_vy = np.full((num_bins_x, num_bins_z), np.nan)\n", - "mean_vz = np.full((num_bins_x, num_bins_y), np.nan)\n", - "\n", - "# 1. Mean v_x (y vs z)\n", - "mean_vx = weighted_mean_2d(y2, z2, v_x2, soft_weights2, y_bins, z_bins)\n", - "\n", - "# 2. Mean v_y (x vs z)\n", - "mean_vy = weighted_mean_2d(x2, z2, v_y2, soft_weights2, x_bins, z_bins)\n", - "\n", - "# 3. Mean v_z (x vs y)\n", - "mean_vz = weighted_mean_2d(x2, y2, v_z2, soft_weights2, x_bins, y_bins)\n", - "\n", - " \n", - "# Plot mean velocity maps side-by-side (y vs z, x vs z, x vs y)\n", - "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n", - "# mean_vx: y vs z\n", - "im0 = axs[0].imshow(mean_vx.T, origin='lower', aspect='auto',\n", - " extent=[y_bins[0], y_bins[-1], z_bins[0], z_bins[-1]],\n", - " cmap='RdBu')\n", - "axs[0].set_xlabel('y')\n", - "axs[0].set_ylabel('z')\n", - "axs[0].set_title('Mean $v_x$ (y vs z)')\n", - "axs[0].axis('equal')\n", - "plt.colorbar(im0, ax=axs[0], label='Mean $v_x$')\n", - "# mean_vy: x vs z\n", - "im1 = axs[1].imshow(mean_vy.T, origin='lower', aspect='auto',\n", - " extent=[x_bins[0], x_bins[-1], z_bins[0], z_bins[-1]],\n", - " cmap='RdBu')\n", - "axs[1].set_xlabel('x')\n", - "axs[1].set_ylabel('z')\n", - "axs[1].set_title('Mean $v_y$ (x vs z)')\n", - "axs[1].axis('equal')\n", - "plt.colorbar(im1, ax=axs[1], label='Mean $v_y$')\n", - "# mean_vz: x vs y\n", - "im2 = axs[2].imshow(mean_vz.T, origin='lower', aspect='auto',\n", - " extent=[x_bins[0], x_bins[-1], y_bins[0], y_bins[-1]],\n", - " cmap='RdBu')\n", - "axs[2].set_xlabel('x')\n", - "axs[2].set_ylabel('y')\n", - "axs[2].set_title('Mean $v_z$ (x vs y)')\n", - "plt.colorbar(im2, ax=axs[2], label='Mean $v_z$')\n", - "axs[2].axis('equal')\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "3c1ffb51", - "metadata": {}, - "source": [ - "# Combine disk and spheroid" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "f7801296", - "metadata": {}, - "outputs": [], - "source": [ - "x_tot = jnp.concatenate([x, x2])\n", - "y_tot = jnp.concatenate([y, y2])\n", - "z_tot = jnp.concatenate([z, z2])\n", - "v_x_tot = jnp.concatenate([v_x, v_x2])\n", - "v_y_tot = jnp.concatenate([v_y, v_y2])\n", - "v_z_tot = jnp.concatenate([v_z, v_z2]) \n", - "soft_weights_tot = jnp.concatenate([soft_weights, soft_weights2])" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "641c002b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib.colors as mcolors\n", - "from scipy.stats import binned_statistic_2d\n", - "\n", - "# Helper function to calculate weighted mean\n", - "def weighted_mean_2d(x_pos, y_pos, values, weights, x_bins, y_bins):\n", - " # Sum of (value * weight) in each bin\n", - " weighted_sum, _, _, _ = binned_statistic_2d(\n", - " x_pos, y_pos, values * weights, statistic='sum', bins=[x_bins, y_bins]\n", - " )\n", - " # Sum of weights in each bin\n", - " sum_of_weights, _, _, _ = binned_statistic_2d(\n", - " x_pos, y_pos, weights, statistic='sum', bins=[x_bins, y_bins]\n", - " )\n", - " \n", - " # Divide, handling division by zero (where sum_of_weights is 0)\n", - " with np.errstate(divide='ignore', invalid='ignore'):\n", - " result = weighted_sum / sum_of_weights\n", - " \n", - " return result\n", - "\n", - "num_bins_x = 40\n", - "num_bins_y = 40\n", - "num_bins_z = 40 \n", - "\n", - "# Example: x, z, v_y are 1D arrays of particle positions and velocities\n", - "# Define bin edges\n", - "x_bins = np.linspace(x_tot.min(), x_tot.max(), num_bins_x + 1)\n", - "y_bins = np.linspace(y_tot.min(), y_tot.max(), num_bins_y + 1)\n", - "z_bins = np.linspace(z_tot.min(), z_tot.max(), num_bins_z + 1)\n", - "\n", - "# Digitize positions to bin indices\n", - "x_idx = np.digitize(x_tot, x_bins) - 1\n", - "y_idx = np.digitize(y_tot, y_bins) - 1\n", - "z_idx = np.digitize(z_tot, z_bins) - 1\n", - "\n", - "# Initialize array for mean v_y\n", - "mean_vx = np.full((num_bins_y, num_bins_z), np.nan)\n", - "mean_vy = np.full((num_bins_x, num_bins_z), np.nan)\n", - "mean_vz = np.full((num_bins_x, num_bins_y), np.nan)\n", - "\n", - "# 1. Mean v_x (y vs z)\n", - "mean_vx = weighted_mean_2d(y_tot, z_tot, v_x_tot, soft_weights_tot, y_bins, z_bins)\n", - "\n", - "# 2. Mean v_y (x vs z)\n", - "mean_vy = weighted_mean_2d(x_tot, z_tot, v_y_tot, soft_weights_tot, x_bins, z_bins)\n", - "\n", - "# 3. Mean v_z (x vs y)\n", - "mean_vz = weighted_mean_2d(x_tot, y_tot, v_z_tot, soft_weights_tot, x_bins, y_bins)\n", - "\n", - " \n", - "# Plot mean velocity maps side-by-side (y vs z, x vs z, x vs y)\n", - "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n", - "# mean_vx: y vs z\n", - "im0 = axs[0].imshow(mean_vx.T, origin='lower', aspect='auto',\n", - " extent=[y_bins[0], y_bins[-1], z_bins[0], z_bins[-1]],\n", - " cmap='RdBu')\n", - "axs[0].set_xlabel('y')\n", - "axs[0].set_ylabel('z')\n", - "axs[0].set_title('Mean $v_x$ (y vs z)')\n", - "axs[0].axis('equal')\n", - "plt.colorbar(im0, ax=axs[0], label='Mean $v_x$')\n", - "# mean_vy: x vs z\n", - "im1 = axs[1].imshow(mean_vy.T, origin='lower', aspect='auto',\n", - " extent=[x_bins[0], x_bins[-1], z_bins[0], z_bins[-1]],\n", - " cmap='RdBu')\n", - "axs[1].set_xlabel('x')\n", - "axs[1].set_ylabel('z')\n", - "axs[1].set_title('Mean $v_y$ (x vs z)')\n", - "axs[1].axis('equal')\n", - "plt.colorbar(im1, ax=axs[1], label='Mean $v_y$')\n", - "# mean_vz: x vs y\n", - "im2 = axs[2].imshow(mean_vz.T, origin='lower', aspect='auto',\n", - " extent=[x_bins[0], x_bins[-1], y_bins[0], y_bins[-1]],\n", - " cmap='RdBu')\n", - "axs[2].set_xlabel('x')\n", - "axs[2].set_ylabel('y')\n", - "axs[2].set_title('Mean $v_z$ (x vs y)')\n", - "plt.colorbar(im2, ax=axs[2], label='Mean $v_z$')\n", - "axs[2].axis('equal')\n", - "plt.tight_layout()\n", - "plt.show()" - ] } ], "metadata": { @@ -821,7 +412,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.0" + "version": "3.12.12" } }, "nbformat": 4, diff --git a/notebooks/components_disk_spheroid.ipynb b/notebooks/components_disk_spheroid.ipynb new file mode 100644 index 0000000..beb4bdc --- /dev/null +++ b/notebooks/components_disk_spheroid.ipynb @@ -0,0 +1,805 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "eb6c2e6b", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix import sampling, actions_to_phase_space\n", + "from phoenix.potentials import miyamoto_nagai_potential, plummer_potential\n", + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "19b33a08", + "metadata": {}, + "source": [ + "# Disk distribution function" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "8194b8f7", + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " \"R0\": 8.0, # for actions to phase space\n", + " \"Rinit\": 8.0, # for sampling\n", + " \"R0\": 5.0,\n", + " \"Rd\": 2.5,\n", + " \"Sigma0\": 100.0,\n", + " \"RsigR\": 18.0,\n", + " \"RsigZ\": 2.0,\n", + " \"sigmaR0_R0\": 140.0,\n", + " \"sigmaz0_R0\": 5.0,\n", + " \"L0\": 50.0,\n", + " \"Rinit_for_Rc\": 8.0,\n", + "}\n", + "\n", + "envelope_max = 3.0\n", + "n_candidates = 250_000\n", + "key = jax.random.PRNGKey(42)\n", + "\n", + "Phi_spheroid = miyamoto_nagai_potential\n", + "theta_spheroid = jnp.array([1e12, 60.0, 0.01]) # (M, a, b) z.B. für Miyamoto-Nagai" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f98cca27", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:13: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:37: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:62: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:87: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:115: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of candidate actions: 250000\n" + ] + } + ], + "source": [ + "#Generate candidate actions\n", + "from phoenix.distributionfunctions_disky_Binney import f_disc_from_params\n", + "candidates, samples, soft_weights = sampling.sample_df_potential(f_disc_from_params, key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, tau=0.01)\n", + "print(\"Number of candidate actions:\", samples.shape[0])\n", + "\n", + "#Map the candidate actions to phase-space coordinates\n", + "phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi_spheroid, theta_spheroid)\n", + "x = phase_space_coords[:, 0]\n", + "y = phase_space_coords[:, 1]\n", + "z = phase_space_coords[:, 2]\n", + "v_x = phase_space_coords[:, 3]\n", + "v_y = phase_space_coords[:, 4]\n", + "v_z = phase_space_coords[:, 5]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9ffdb3ec", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Visualize the distribution of candidate actions\n", + "fig, axs = plt.subplots(1, 3, figsize=(15, 4))\n", + "axs[0].hist(samples[:, 0], bins=50, weights=soft_weights)\n", + "axs[0].set_xlabel(r\"$J_r$\")\n", + "axs[1].hist(samples[:, 1], bins=50, weights=soft_weights)\n", + "axs[1].set_xlabel(r\"$J_z$\")\n", + "axs[2].hist(samples[:, 2], bins=50, weights=soft_weights)\n", + "axs[2].set_xlabel(r\"$L_z$\")\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/disc_sampled_actions.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "4c883b89", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors\n", + "plt.figure(figsize=(12,6))\n", + "plt.subplot(231)\n", + "plt.hist2d(x, y, bins=50, cmap=\"viridis\", weights=soft_weights)#, norm=colors.LogNorm(), cmin=1, weights=soft_weights)\n", + "plt.xlabel('x [kpc]')\n", + "plt.ylabel('y [kpc]')\n", + "plt.axis('equal')\n", + "plt.subplot(232)\n", + "plt.hist2d(x, z, bins=50, cmap=\"viridis\", weights=soft_weights)\n", + "plt.xlabel('x [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.axis('equal')\n", + "plt.subplot(233)\n", + "plt.hist2d(y, z, bins=50, cmap=\"viridis\", weights=soft_weights)\n", + "plt.xlabel('y [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.axis('equal')\n", + "\n", + "\n", + "plt.subplot(234)\n", + "plt.hist(v_x, bins=50, weights=soft_weights)#, range=(-2000, 2000))\n", + "plt.xlabel(r\"$v_\\text{x}$ (km/s)\")\n", + "plt.ylabel(\"Number of stars\")\n", + "\n", + "plt.subplot(235)\n", + "plt.hist(v_y, bins=50, weights=soft_weights)#, range=(-2000, 2000))\n", + "plt.xlabel(r\"$v_\\text{y}$ (km/s)\")\n", + "plt.ylabel(\"Number of stars\")\n", + "\n", + "plt.subplot(236)\n", + "plt.hist(v_z, bins=50, weights=soft_weights)\n", + "plt.xlabel(r\"$v_\\text{z}$ (km/s)\")\n", + "plt.ylabel(\"Number of stars\")\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/disc_phasespace.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "a4d8948d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as mcolors\n", + "from scipy.stats import binned_statistic_2d\n", + "\n", + "# Helper function to calculate weighted mean\n", + "def weighted_mean_2d(x_pos, y_pos, values, weights, x_bins, y_bins):\n", + " # Sum of (value * weight) in each bin\n", + " weighted_sum, _, _, _ = binned_statistic_2d(\n", + " x_pos, y_pos, values * weights, statistic='sum', bins=[x_bins, y_bins]\n", + " )\n", + " # Sum of weights in each bin\n", + " sum_of_weights, _, _, _ = binned_statistic_2d(\n", + " x_pos, y_pos, weights, statistic='sum', bins=[x_bins, y_bins]\n", + " )\n", + " \n", + " # Divide, handling division by zero (where sum_of_weights is 0)\n", + " with np.errstate(divide='ignore', invalid='ignore'):\n", + " result = weighted_sum / sum_of_weights\n", + " \n", + " return result\n", + "\n", + "num_bins_x = 40\n", + "num_bins_y = 40\n", + "num_bins_z = 40 \n", + "\n", + "# Example: x, z, v_y are 1D arrays of particle positions and velocities\n", + "# Define bin edges\n", + "x_bins = np.linspace(x.min(), x.max(), num_bins_x + 1)\n", + "y_bins = np.linspace(y.min(), y.max(), num_bins_x + 1)\n", + "z_bins = np.linspace(z.min(), z.max(), num_bins_z + 1)\n", + "\n", + "# Digitize positions to bin indices\n", + "x_idx = np.digitize(x, x_bins) - 1\n", + "y_idx = np.digitize(y, y_bins) - 1\n", + "z_idx = np.digitize(z, z_bins) - 1\n", + "\n", + "# Initialize array for mean v_y\n", + "mean_vx = np.full((num_bins_y, num_bins_z), np.nan)\n", + "mean_vy = np.full((num_bins_x, num_bins_z), np.nan)\n", + "mean_vz = np.full((num_bins_x, num_bins_y), np.nan)\n", + "\n", + "# 1. Mean v_x (y vs z)\n", + "mean_vx = weighted_mean_2d(y, z, v_x, soft_weights, y_bins, z_bins)\n", + "\n", + "# 2. Mean v_y (x vs z)\n", + "mean_vy = weighted_mean_2d(x, z, v_y, soft_weights, x_bins, z_bins)\n", + "\n", + "# 3. Mean v_z (x vs y)\n", + "mean_vz = weighted_mean_2d(x, y, v_z, soft_weights, x_bins, y_bins)\n", + "\n", + " \n", + "# Plot mean velocity maps side-by-side (y vs z, x vs z, x vs y)\n", + "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n", + "# mean_vx: y vs z\n", + "im0 = axs[0].imshow(mean_vx.T, origin='lower', aspect='auto',\n", + " extent=[y_bins[0], y_bins[-1], z_bins[0], z_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[0].set_xlabel('y')\n", + "axs[0].set_ylabel('z')\n", + "axs[0].set_title('Mean $v_x$ (y vs z)')\n", + "axs[0].axis('equal')\n", + "plt.colorbar(im0, ax=axs[0], label='Mean $v_x$')\n", + "# mean_vy: x vs z\n", + "im1 = axs[1].imshow(mean_vy.T, origin='lower', aspect='auto',\n", + " extent=[x_bins[0], x_bins[-1], z_bins[0], z_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[1].set_xlabel('x')\n", + "axs[1].set_ylabel('z')\n", + "axs[1].set_title('Mean $v_y$ (x vs z)')\n", + "axs[1].axis('equal')\n", + "plt.colorbar(im1, ax=axs[1], label='Mean $v_y$')\n", + "# mean_vz: x vs y\n", + "im2 = axs[2].imshow(mean_vz.T, origin='lower', aspect='auto',\n", + " extent=[x_bins[0], x_bins[-1], y_bins[0], y_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[2].set_xlabel('x')\n", + "axs[2].set_ylabel('y')\n", + "axs[2].set_title('Mean $v_z$ (x vs y)')\n", + "plt.colorbar(im2, ax=axs[2], label='Mean $v_z$')\n", + "axs[2].axis('equal')\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/disc_velocities.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "70e7f102", + "metadata": {}, + "source": [ + "# Spheroid distribution function" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "c2f67b12", + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " \"R0\": 8.0, # for actions to phase space\n", + " \"N0_spheroid\": 1e6,\n", + " \"J0_spheroid\": 50.0,\n", + " \"Gamma_spheroid\": 2.5,\n", + " \"Beta_spheroid\": 3.5,\n", + "}\n", + "\n", + "envelope_max = 3.0\n", + "n_candidates = 250_000\n", + "key = jax.random.PRNGKey(42)\n", + "# Js are max 400, 400, 2000\n", + "\n", + "Phi_spheroid = plummer_potential\n", + "theta_spheroid = jnp.array([1e12, 30.0]) # (M, a) z.B. für Plummer" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "11117be1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of candidate actions: 250000\n" + ] + } + ], + "source": [ + "#Generate candidate actions\n", + "from phoenix.distributionfunctions_spheroidal import f_double_power_law as df_spheroid\n", + "candidates, samples, soft_weights2 = sampling.sample_df_potential(df_spheroid, key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, tau=0.01)\n", + "print(\"Number of candidate actions:\", candidates.shape[0])\n", + "\n", + "#Map the candidate actions to phase-space coordinates\n", + "phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi_spheroid, theta_spheroid)\n", + "x2 = phase_space_coords[:, 0]\n", + "y2 = phase_space_coords[:, 1]\n", + "z2 = phase_space_coords[:, 2]\n", + "v_x2 = phase_space_coords[:, 3]\n", + "v_y2 = phase_space_coords[:, 4]\n", + "v_z2 = phase_space_coords[:, 5]" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "31da2be2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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A9s4KAAAAOqjt27fHTTfdFBdffHFqidOGhobo2bNnWr+CgoIoLS1NTWzLpK6uLoqLi1Nb7969WzR2AGhv9nsG+pAhQyJJkt2276ntA6WlpTF79uz9/dMAAADQqX2wbGqSJDFjxoyDPl5tbW1MmDAh9bixsVERHQD+TtbXQAcAAACy74Pi+VtvvRVPPfVUavZ5RER5eXls3Lgxrf/OnTtj06ZNUV5evttjFhYWRmFhYYvFDADt3X4v4QIAAAC0rg+K56tXr45//dd/jR49eqS1V1VVxebNm2PZsmWpfU899VQ0NzfH4MGDWztcAOgwzEAHAACAHNu6dWusWbMm9Xjt2rWxYsWKKC0tjV69esWXv/zlWL58ecybNy927dqVWte8tLQ0unbtGv369Yvhw4fH2LFjY+bMmbFjx44YP358jB49OioqKnJ1WgDQ7imgAwAAQI4tXbo0zjnnnNTjD9YlHzNmTHzve9+LJ554IiIiBgwYkPa8p59+OoYMGRIREbNmzYrx48fH0KFDIz8/P0aNGhVTp05tlfgBoKNSQAcAAIAcGzJkSCRJstv2PbV9oLS0NGbPnp3NsACg07MGOgAAAAAAZKCADgAAAAAAGSigAwAAAABABgroAAAAAACQgQI6AAAAAABkoIAOAAAAAAAZKKADAAAAAEAGCugAAAAAAJCBAjoAAAAAAGSggA4AAAAAABkooANAB7Vo0aI4//zzo6KiIvLy8mLu3Llp7UmSxKRJk6JXr17RvXv3qK6ujtWrV6f12bRpU9TU1ERRUVGUlJTE5ZdfHlu3bm3FswAAAIDcKch1AABAy9i2bVuccsopcdlll8VFF130kfa77747pk6dGg8//HBUVlbGxIkTY9iwYfHqq69Gt27dIiKipqYm/vSnP8WCBQtix44dcemll8a4ceNi9uzZrX06++WYm3+127Y37xzZipEAAADQnimgA0AHNWLEiBgxYkTGtiRJYsqUKXHLLbfEBRdcEBERjzzySJSVlcXcuXNj9OjR8dprr8X8+fNjyZIlMWjQoIiImDZtWpx77rlxzz33REVFRaudCwAAAOSCJVwAoBNau3ZtNDQ0RHV1dWpfcXFxDB48OOrr6yMior6+PkpKSlLF84iI6urqyM/Pj8WLF+/22E1NTdHY2Ji2AQAAQHukgA4AnVBDQ0NERJSVlaXtLysrS7U1NDREz54909oLCgqitLQ01SeTurq6KC4uTm29e/fOcvQAAADQOhTQAYCsqq2tjS1btqS29evX5zokAAAAOCAK6ADQCZWXl0dExIYNG9L2b9iwIdVWXl4eGzduTGvfuXNnbNq0KdUnk8LCwigqKkrbAAAAoD1SQAeATqiysjLKy8tj4cKFqX2NjY2xePHiqKqqioiIqqqq2Lx5cyxbtizV56mnnorm5uYYPHhwq8cMAAAAra0g1wEAAC1j69atsWbNmtTjtWvXxooVK6K0tDT69OkT1157bdx2221x3HHHRWVlZUycODEqKiriwgsvjIiIfv36xfDhw2Ps2LExc+bM2LFjR4wfPz5Gjx4dFRUVOTorAAAAaD0K6ADQQS1dujTOOeec1OMJEyZERMSYMWPioYceihtvvDG2bdsW48aNi82bN8fZZ58d8+fPj27duqWeM2vWrBg/fnwMHTo08vPzY9SoUTF16tRWPxcAAADIBQX0fXTMzb/aY/ubd45spUgAYN8MGTIkkiTZbXteXl5Mnjw5Jk+evNs+paWlMXv27JYIDwAAANo8a6ADAAAAAEAGCugAAAAAAJCBAjoAAAAAAGSggA4AAAAAABkooAMAAAAAQAYK6AAAAAAAkIECOgAAAAAAZKCADgAAAAAAGex3AX3RokVx/vnnR0VFReTl5cXcuXPT2pMkiUmTJkWvXr2ie/fuUV1dHatXr07rs2nTpqipqYmioqIoKSmJyy+/PLZu3XpQJwIAAAAAANm03wX0bdu2xSmnnBLTp0/P2H733XfH1KlTY+bMmbF48eI47LDDYtiwYbF9+/ZUn5qamnjllVdiwYIFMW/evFi0aFGMGzfuwM8CAAAAAACyrGB/nzBixIgYMWJExrYkSWLKlClxyy23xAUXXBAREY888kiUlZXF3LlzY/To0fHaa6/F/PnzY8mSJTFo0KCIiJg2bVqce+65cc8990RFRcVBnA4AAAAAAGRHVtdAX7t2bTQ0NER1dXVqX3FxcQwePDjq6+sjIqK+vj5KSkpSxfOIiOrq6sjPz4/FixdnPG5TU1M0NjambQAAAAAA0JKyWkBvaGiIiIiysrK0/WVlZam2hoaG6NmzZ1p7QUFBlJaWpvp8WF1dXRQXF6e23r17ZzNsAAAAyCn3GwOAtimrBfSWUltbG1u2bElt69evz3VIAAAAkDXuNwYAbdN+r4G+J+Xl5RERsWHDhujVq1dq/4YNG2LAgAGpPhs3bkx73s6dO2PTpk2p539YYWFhFBYWZjNUAAAAaDPcbwwA2qaszkCvrKyM8vLyWLhwYWpfY2NjLF68OKqqqiIioqqqKjZv3hzLli1L9Xnqqaeiubk5Bg8enM1wAAAAoN1rqfuNRbjnGADszX7PQN+6dWusWbMm9Xjt2rWxYsWKKC0tjT59+sS1114bt912Wxx33HFRWVkZEydOjIqKirjwwgsjIqJfv34xfPjwGDt2bMycOTN27NgR48ePj9GjR/tFHAAAAD6kpe43FvG3e47deuutWY4YADqO/S6gL126NM4555zU4wkTJkRExJgxY+Khhx6KG2+8MbZt2xbjxo2LzZs3x9lnnx3z58+Pbt26pZ4za9asGD9+fAwdOjTy8/Nj1KhRMXXq1CycDgAAALCvamtrU9/rI/52FXnv3r1b7e8fc/Ov9tj+5p0jWykSAMhsvwvoQ4YMiSRJdtuel5cXkydPjsmTJ++2T2lpacyePXt//zQAAAB0Oi11v7EI9xwDgL3J6hroAAAAQHa53xgA5M5+z0AHAAAAssv9xgCgbVJABwAAgBxzvzEAaJsU0AEAACDH3G8MANoma6ADAAAAAEAGZqADAJ3KMTf/ao/tb945spUiAQAAoK0zAx0AAAAAADJQQAcAAAAAgAwU0AEAAAAAIAMFdAAAAAAAyEABHQAAAAAAMlBABwAAAACADBTQAQAAAAAgAwV0AAAAAADIoCDXAXQUx9z8qz22v3nnyFaKBAAAAACAbDADHQAAAAAAMlBABwAAAACADBTQAQAAAAAgAwV0AAAAAADIQAEdADqxXbt2xcSJE6OysjK6d+8exx57bHz/+9+PJElSfZIkiUmTJkWvXr2ie/fuUV1dHatXr85h1AAAANA6FNABoBO76667YsaMGXHffffFa6+9FnfddVfcfffdMW3atFSfu+++O6ZOnRozZ86MxYsXx2GHHRbDhg2L7du35zByAAAAaHkFuQ4AAMid3/3ud3HBBRfEyJEjIyLimGOOiZ/97GfxwgsvRMTfZp9PmTIlbrnllrjgggsiIuKRRx6JsrKymDt3bowePTpnsQMAAEBLMwMdADqxM888MxYuXBivv/56RES89NJL8dxzz8WIESMiImLt2rXR0NAQ1dXVqecUFxfH4MGDo76+PuMxm5qaorGxMW0DAACA9sgMdADoxG6++eZobGyMvn37RpcuXWLXrl1x++23R01NTURENDQ0REREWVlZ2vPKyspSbR9WV1cXt956a8sGnkPH3PyrPba/eefIVooEAACAlmYGOgB0Yj//+c9j1qxZMXv27Fi+fHk8/PDDcc8998TDDz98wMesra2NLVu2pLb169dnMWIAAABoPWagA0AndsMNN8TNN9+cWsu8f//+8dZbb0VdXV2MGTMmysvLIyJiw4YN0atXr9TzNmzYEAMGDMh4zMLCwigsLGzx2AEAAKClKaADQCf23nvvRX5++gVpXbp0iebm5oiIqKysjPLy8li4cGGqYN7Y2BiLFy+OK664orXDBQA6GUunAZBrCugA0Imdf/75cfvtt0efPn3ixBNPjBdffDHuvffeuOyyyyIiIi8vL6699tq47bbb4rjjjovKysqYOHFiVFRUxIUXXpjb4AEAAKCFKaADQCc2bdq0mDhxYnz729+OjRs3RkVFRfzjP/5jTJo0KdXnxhtvjG3btsW4ceNi8+bNcfbZZ8f8+fOjW7duOYwcAAAAWp4COgB0YocffnhMmTIlpkyZsts+eXl5MXny5Jg8eXLrBZZDe7tUHAAAgM4jf+9dAAAAAACg81FABwAAAACADBTQAQAAAAAgAwV0AAAAAADIIOsF9F27dsXEiROjsrIyunfvHscee2x8//vfjyRJUn2SJIlJkyZFr169onv37lFdXR2rV6/OdigAAAAAAHDAsl5Av+uuu2LGjBlx3333xWuvvRZ33XVX3H333TFt2rRUn7vvvjumTp0aM2fOjMWLF8dhhx0Ww4YNi+3bt2c7HAAAAAAAOCAF2T7g7373u7jgggti5MiRERFxzDHHxM9+9rN44YUXIuJvs8+nTJkSt9xyS1xwwQUREfHII49EWVlZzJ07N0aPHp3tkAAAAAAAYL9lfQb6mWeeGQsXLozXX389IiJeeumleO6552LEiBEREbF27dpoaGiI6urq1HOKi4tj8ODBUV9fn/GYTU1N0djYmLYBAABAZ2G5VADIjazPQL/55pujsbEx+vbtG126dIldu3bF7bffHjU1NRER0dDQEBERZWVlac8rKytLtX1YXV1d3HrrrdkOFQAAANqFD5ZLffjhh+PEE0+MpUuXxqWXXhrFxcVx9dVXR8R/LZf68MMPR2VlZUycODGGDRsWr776anTr1i3HZwAA7VPWC+g///nPY9asWTF79uw48cQTY8WKFXHttddGRUVFjBkz5oCOWVtbGxMmTEg9bmxsjN69e2crZAAAAGjTLJea2TE3/2qP7W/eObKVIgGgo8p6Af2GG26Im2++OZWc+/fvH2+99VbU1dXFmDFjory8PCIiNmzYEL169Uo9b8OGDTFgwICMxywsLIzCwsJshwoAAADtwplnnhkPPPBAvP766/HpT386tVzqvffeGxF7Xy61oxbQ90aBHYCDlfUC+nvvvRf5+elLq3fp0iWam5sjIqKysjLKy8tj4cKFqYJ5Y2NjLF68OK644opshwMAAADtXksslxrxt3uONTU1pR675xgApMt6Af3888+P22+/Pfr06RMnnnhivPjii3HvvffGZZddFhEReXl5ce2118Ztt90Wxx13XGpdtoqKirjwwguzHQ4AAAC0ey2xXGqEe44BwN5kvYA+bdq0mDhxYnz729+OjRs3RkVFRfzjP/5jTJo0KdXnxhtvjG3btsW4ceNi8+bNcfbZZ8f8+fM79E1N9nTZmEvGAAAA2JOWWC41wj3HAGBvsl5AP/zww2PKlCkxZcqU3fbJy8uLyZMnx+TJk7P95wEAAKDDaanlUt1zDAD2LOsFdACAzszNygBoCZZLBYDcUEAHAACANs5yqQCQGwroAAAA0MZZLhUAciN/710AAAAAAKDzUUAHAAAAAIAMFNABAAAAACADBXQAAAAAAMhAAR0AAAAAADJQQAcAAAAAgAwU0AEAAAAAIAMFdAAAAAAAyEABHQAAAAAAMlBABwAAAACADBTQAQAAAAAgAwV0AAAAAADIoCDXAbB3x9z8qz22v3nnyFaKBAAAAACg81BAbwP2ViAHADoPP5wDAAC0HZZwAQAAAACADBTQAQAAAAAgAwV0AAAAAADIwBroAACtyL1PAAAA2g8F9A7AzcYAoPOQ9wEAAFqPJVwAAAAAACADBXQA6OTefvvt+PrXvx49evSI7t27R//+/WPp0qWp9iRJYtKkSdGrV6/o3r17VFdXx+rVq3MYMQAAALQOS7jgUnCATuwvf/lLnHXWWXHOOefEb37zmzjqqKNi9erVccQRR6T63H333TF16tR4+OGHo7KyMiZOnBjDhg2LV199Nbp165bD6AEAAKBlKaADQCd21113Re/evePBBx9M7ausrEz9O0mSmDJlStxyyy1xwQUXRETEI488EmVlZTF37twYPXp0q8cMAAAArcUSLgDQiT3xxBMxaNCg+MpXvhI9e/aMgQMHxo9//ONU+9q1a6OhoSGqq6tT+4qLi2Pw4MFRX1+f8ZhNTU3R2NiYtgEAAEB7pIAOAJ3YG2+8ETNmzIjjjjsunnzyybjiiivi6quvjocffjgiIhoaGiIioqysLO15ZWVlqbYPq6uri+Li4tTWu3fvlj0JAAAAaCGWcAGATqy5uTkGDRoUd9xxR0REDBw4MFauXBkzZ86MMWPGHNAxa2trY8KECanHjY2NiugAQLvknmEAmIEOAJ1Yr1694oQTTkjb169fv1i3bl1ERJSXl0dExIYNG9L6bNiwIdX2YYWFhVFUVJS2AQAAQHukgA4AndhZZ50Vq1atStv3+uuvx9FHHx0Rf7uhaHl5eSxcuDDV3tjYGIsXL46qqqpWjRUAAABamyVcAKATu+666+LMM8+MO+64I7761a/GCy+8EA888EA88MADERGRl5cX1157bdx2221x3HHHRWVlZUycODEqKiriwgsvzG3wAAAA0MIU0AGgEzv99NPj8ccfj9ra2pg8eXJUVlbGlClToqamJtXnxhtvjG3btsW4ceNi8+bNcfbZZ8f8+fOjW7duOYwcAODg7W2NcwBQQAeATu68886L8847b7fteXl5MXny5Jg8eXIrRgUAAAC51yJroL/99tvx9a9/PXr06BHdu3eP/v37x9KlS1PtSZLEpEmTolevXtG9e/eorq6O1atXt0QoAAAAAABwQLI+A/0vf/lLnHXWWXHOOefEb37zmzjqqKNi9erVccQRR6T63H333TF16tR4+OGHU2upDhs2LF599VWXgwMAtKC9Xar+5p0jWykSAGj/5FWAji/rM9Dvuuuu6N27dzz44INxxhlnRGVlZXzhC1+IY489NiL+Nvt8ypQpccstt8QFF1wQJ598cjzyyCPxzjvvxNy5c7MdDgAAAHQIrvYGgNaX9QL6E088EYMGDYqvfOUr0bNnzxg4cGD8+Mc/TrWvXbs2Ghoaorq6OrWvuLg4Bg8eHPX19dkOBwAAANq9D672PuSQQ+I3v/lNvPrqq/E//+f/zHi198yZM2Px4sVx2GGHxbBhw2L79u05jBwA2resL+HyxhtvxIwZM2LChAnxne98J5YsWRJXX311dO3aNcaMGRMNDQ0REVFWVpb2vLKyslTbhzU1NUVTU1PqcWNjY7bDBgAAgDbr76/2/kBlZWXq3x++2jsi4pFHHomysrKYO3dujB49utVjBoCOIOsz0Jubm+PUU0+NO+64IwYOHBjjxo2LsWPHxsyZMw/4mHV1dVFcXJzaevfuncWIAQAAoG1ztTcA5EbWZ6D36tUrTjjhhLR9/fr1i//7f/9vRESUl5dHRMSGDRuiV69eqT4bNmyIAQMGZDxmbW1tTJgwIfW4sbFREX0/7O2mJgAAALRtLXG1d4QrvgFgb7I+A/2ss86KVatWpe17/fXX4+ijj46Iv11iVl5eHgsXLky1NzY2xuLFi6OqqirjMQsLC6OoqChtAwAAgM6iJa72jnDFNwDsTdYL6Nddd108//zzcccdd8SaNWti9uzZ8cADD8SVV14ZERF5eXlx7bXXxm233RZPPPFEvPzyy/GNb3wjKioq4sILL8x2OAAAANDu7e5q73Xr1kVE+tXef2/Dhg2ptkxqa2tjy5YtqW39+vVZjhwA2resL+Fy+umnx+OPPx61tbUxefLkqKysjClTpkRNTU2qz4033hjbtm2LcePGxebNm+Pss8+O+fPnR7du3bIdDgAAALR7+3O19wfLo35wtfcVV1yx2+MWFhZGYWFhi8UNAO1d1gvoERHnnXdenHfeebttz8vLi8mTJ8fkyZNb4s8DAABAh3LdddfFmWeeGXfccUd89atfjRdeeCEeeOCBeOCBByIi/Wrv4447LiorK2PixImu9gaAg9QiBXQAAHLDzcMBOiZXe3dMe8rbb945shUjAWB3FNABAACgHXC1NwC0vqzfRBQAAAAAADoCBXQAAAAAAMhAAR0AAAAAADKwBjoAAABAC3Bzb4D2TwEdAAAAoI3ZW/H9zTtHtlIkAJ2bJVwAAAAAACADBXQAAAAAAMhAAR0AAAAAADJQQAcAAAAAgAzcRBQAgDbBzdIAAIC2xgx0AAAAAADIQAEdAAAAAAAyUEAHAAAAAIAMrIHOQbNeKQAAAADQESmgAwDQKvb2ozsAAEBbo4DOXvmyCwAAAG2Lq8EBWocCOgAAWeFHdwAAoKNxE1EAAAAAAMjADHRanMvKAAAAAID2SAGdnNtTgV1xHQAAAADIFQV0AABS/LANAES4mhzgA9ZABwAAAACADMxABwBgn+xtJhoAAEBHYwY6AAAAAABkYAY6ABAREXfeeWfU1tbGNddcE1OmTImIiO3bt8f1118fc+bMiaamphg2bFjcf//9UVZWlttgAQDIKWukA52FGegAQCxZsiR+9KMfxcknn5y2/7rrrotf/vKX8eijj8azzz4b77zzTlx00UU5ihIAAABalwI6AHRyW7dujZqamvjxj38cRxxxRGr/li1b4ic/+Unce++98fnPfz5OO+20ePDBB+N3v/tdPP/88zmMGAAAAFqHJVxgD1ySBnQGV155ZYwcOTKqq6vjtttuS+1ftmxZ7NixI6qrq1P7+vbtG3369In6+vr4zGc+k4tw4YDJ6wAAwP5SQAeATmzOnDmxfPnyWLJkyUfaGhoaomvXrlFSUpK2v6ysLBoaGnZ7zKampmhqako9bmxszFq8sCd7K5ADAADsLwV02jQzxQBazvr16+Oaa66JBQsWRLdu3bJ23Lq6urj11luzdjwAAPaf79MA2WENdADopJYtWxYbN26MU089NQoKCqKgoCCeffbZmDp1ahQUFERZWVm8//77sXnz5rTnbdiwIcrLy3d73Nra2tiyZUtqW79+fQufCQAAALQMM9Bp1w72Um2/uAOd2dChQ+Pll19O23fppZdG375946abborevXvHIYccEgsXLoxRo0ZFRMSqVati3bp1UVVVtdvjFhYWRmFhYYvGDgDAwbH0GcC+afEC+p133hm1tbVxzTXXxJQpUyIiYvv27XH99dfHnDlzoqmpKYYNGxb3339/lJWVtXQ4AMD/7/DDD4+TTjopbd9hhx0WPXr0SO2//PLLY8KECVFaWhpFRUVx1VVXRVVVlRuIAgCwR5aQATqKFl3CZcmSJfGjH/0oTj755LT91113Xfzyl7+MRx99NJ599tl455134qKLLmrJUACAA/CDH/wgzjvvvBg1alR89rOfjfLy8njsscdyHRYAAAC0ihabgb5169aoqamJH//4x3Hbbbel9m/ZsiV+8pOfxOzZs+Pzn/98REQ8+OCD0a9fv3j++efNaKNVuWQNIN0zzzyT9rhbt24xffr0mD59em4CAgAycrU3ALSOFpuBfuWVV8bIkSOjuro6bf+yZctix44dafv79u0bffr0ifr6+pYKBwAAADoEV3sDQOtpkRnoc+bMieXLl8eSJUs+0tbQ0BBdu3aNkpKStP1lZWXR0NCQ8XhNTU3R1NSUetzY2JjVeAEAAKA9cLU3ALSurM9AX79+fVxzzTUxa9as6NatW1aOWVdXF8XFxamtd+/eWTkuAAAAtCfZvtq7qakpGhsb0zYA4L9kfQb6smXLYuPGjXHqqaem9u3atSsWLVoU9913Xzz55JPx/vvvx+bNm9NmoW/YsCHKy8szHrO2tjYmTJiQetzY2KiIDgDQybh3CdDZZftq74i/TVi79dZbsx0qAHQYWS+gDx06NF5++eW0fZdeemn07ds3brrppujdu3cccsghsXDhwhg1alRERKxatSrWrVsXVVVVGY9ZWFgYhYWF2Q4VAABS9lagf/POka0UCcBHfXC194IFC7J2tXeECWsAsDdZL6AffvjhcdJJJ6XtO+yww6JHjx6p/ZdffnlMmDAhSktLo6ioKK666qqoqqqyJhsAAABk0BJXe0eYsAYAe9MiNxHdmx/84AeRn58fo0aNiqamphg2bFjcf//9uQgFAAAA2ryWuNobANi7VimgP/PMM2mPu3XrFtOnT4/p06e3xp8HAACAds3V3gCQGzmZgQ4AAABkl6u9ASD7FNDhILjZGAB0HnvK+3I+kAuu9gaAlpef6wAAAAAAAKAtMgMd2jAz3AEAAOiIfN8F2gsz0AEAAAAAIAMz0KEF+UUdAMgGnykA6GzkPqCtMAMdAAAAAAAyUEAHAAAAAIAMLOECObS3S9IAAAAAgNxRQAcAgBZmHVcAAGifLOECAAAAAAAZmIEOAAAAQLuyp6u7XNkFZJMZ6AAAAAAAkIEZ6NBBWWsVAAAAAA6OGegAAAAAAJCBGejQSZmhDgAAAAB7poAOAAAAQIdhwhiQTQroAABwkPb2Rb2lnw8AZI8CPPD3FNABAAAAYB8psEPnooAOtAgfKAAAAABo7xTQoR1zuTcAAAAAtJz8XAcAAAAAAABtkRnoAADQyVl6DQAAMlNABzLyRRoA2g/LugEAQMtQQAcAAA6KH94BAOioFNCBNskXcQBoO8xwBwCgs1JABwAAcsaP5gAAtGUK6MABMRMNAAAAPsqPw9CxKKADOaEADwAAAB+lAA9tiwI6AAAAALQTCuzQuvJzHQAAkDt1dXVx+umnx+GHHx49e/aMCy+8MFatWpXWZ/v27XHllVdGjx494mMf+1iMGjUqNmzYkKOIAQAAoPUooANAJ/bss8/GlVdeGc8//3wsWLAgduzYEV/4whdi27ZtqT7XXXdd/PKXv4xHH300nn322XjnnXfioosuymHUAAAA0Dos4QIAndj8+fPTHj/00EPRs2fPWLZsWXz2s5+NLVu2xE9+8pOYPXt2fP7zn4+IiAcffDD69esXzz//fHzmM5/JRdgAAHDA3JML2B8K6ABAypYtWyIiorS0NCIili1bFjt27Ijq6upUn759+0afPn2ivr5eAR0AAPaTAj60L1lfwsVaqgDQPjU3N8e1114bZ511Vpx00kkREdHQ0BBdu3aNkpKStL5lZWXR0NCQ8ThNTU3R2NiYtgEAAEB7lPUZ6B+spXr66afHzp074zvf+U584QtfiFdffTUOO+ywiPjbWqq/+tWv4tFHH43i4uIYP358XHTRRfFv//Zv2Q4HANhHV155ZaxcuTKee+65gzpOXV1d3HrrrVmKCugI2vJMu73F9uadI1spEti7urq6eOyxx+IPf/hDdO/ePc4888y466674vjjj0/12b59e1x//fUxZ86caGpqimHDhsX9998fZWVlOYwcaCvkPdh/WS+gW0sVANqf8ePHx7x582LRokXxiU98IrW/vLw83n///di8eXPaLPQNGzZEeXl5xmPV1tbGhAkTUo8bGxujd+/eLRY7AHQWJqwBLU2BHT6qxddAt5Yq0BIkdciOJEniqquuiscffzyeeeaZqKysTGs/7bTT4pBDDomFCxfGqFGjIiJi1apVsW7duqiqqsp4zMLCwigsLGzx2AGgszFhDejofNenLWrRAno211JtampKPbaWKgBkx5VXXhmzZ8+OX/ziF3H44YencnFxcXF07949iouL4/LLL48JEyZEaWlpFBUVxVVXXRVVVVW+hANAjmVjwprv29DxtOTSaQd7bAVw2qOs30T0732wluqcOXMO6jh1dXVRXFyc2lwGDgDZMWPGjNiyZUsMGTIkevXqldr+5V/+JdXnBz/4QZx33nkxatSo+OxnPxvl5eXx2GOP5TBqACBbE9Z83waAPWuxAvoHa6k+/fTTu11L9e/tbS3VLVu2pLb169e3VNgA0KkkSZJx++Y3v5nq061bt5g+fXps2rQptm3bFo899thuczYA0DqyNWHN920A2LOsL+FiLVUAAABoOdm8+bfv2wCwZ1kvoFtLFWgP9rRumzXZAKDjaMl1YKG1tcSENQBgz7JeQJ8xY0ZERAwZMiRt/4MPPpi6HPwHP/hB5Ofnx6hRo6KpqSmGDRsW999/f7ZDAQAAgA7DhDUAaH0tsoTL3nywlur06dOz/ecBAACgQzJhDQBaX9YL6ADt3d4u9bbECwAAuWDCGgC0PgV0AACgzbKGOQAAuaSADgAAAAC0eQd7xbgrzjkQCuhAh5TL2WoSMgAAAHxUS39Xd+UaLSE/1wEAAAAAAEBbZAY6QCszQx0AAACgfTADHQAAAAAAMjADHQAAAADo9PZ0xbirxTsvBXSA/eSmJADAByzNBgDQsSmgAwAA7IYfzgEAOjdroAMAAAAAQAZmoAO0MS4FBwA+YC1WAGgbfFfvvBTQAQAA2iFf5AEAWp4lXAAAAAAAIAMz0AEAAFqIWeIAAO2bAjoAAECO7K3ADgBAbimgA7DPzKIDAAAAOhMFdIB2RhEbAMgGnykAoPXIu+2XAjpAByMpAwAAAGRHfq4DAAAAAACAtsgMdIBOxgx1AOgc3KAUADoP3/VbjgI6AAAA+80XdQCgM7CECwAAAAAAZGAGOgBpXO4NAAAAbcvBfld35diBU0AHAADgI/yoDgD7Tt7suBTQAciag/1F2y/iAAAAdEYK8G2XAjoArcYHAgAAAKA9UUAHoN0wQx0AAACyz/ft3VNABwAAoM3xRR4AaAsU0AEAAMg6BXAAoCNQQAcAAKDd2VOBXnEeAFpXR87LCugAdBhmugFA++Hm4gBAe6CADgAAAADAbnXmH74V0AHoNMxQBwAAgNbV3r+L5+fqD0+fPj2OOeaY6NatWwwePDheeOGFXIUCABHxt6S+p60zk7cBoP2QtwEge3JSQP+Xf/mXmDBhQnz3u9+N5cuXxymnnBLDhg2LjRs35iIcAGAP5G0AaD/kbQDIrpwU0O+9994YO3ZsXHrppXHCCSfEzJkz49BDD42f/vSnuQgHANgDeRsA2g95GwCyq9UL6O+//34sW7Ysqqur/yuI/Pyorq6O+vr61g4HANgDeRsA2g95GwCyr9VvIvqf//mfsWvXrigrK0vbX1ZWFn/4wx8yPqepqSmamppSj7ds2RIREY2NjVmLq7npvawdC4COKVt554PjJEmSleO1JHkbgPYomzlH3j44cjYAe9PW83arF9APRF1dXdx6660f2d+7d+8cRANAZ1U8JbvHe/fdd6O4uDi7B20D5G0Aci3bOTtC3gaAltLW83arF9CPPPLI6NKlS2zYsCFt/4YNG6K8vDzjc2pra2PChAmpx83NzbFp06bo0aNH5OXlHXRMjY2N0bt371i/fn0UFRUd9PE6G+N3cIzfwTF+B8f4HZwDHb8kSeLdd9+NioqKFowuO+TtjskYZodxzA7jePCMYXbsbhzl7QPntZnOeKQzHumMRzrjkc54pNvTeLRE3m71AnrXrl3jtNNOi4ULF8aFF14YEX9L0AsXLozx48dnfE5hYWEUFham7SspKcl6bEVFRV6EB8H4HRzjd3CM38ExfgfnQMavvcxgk7c7NmOYHcYxO4zjwTOG2ZFpHOXtg+O1mc54pDMe6YxHOuORznik2914ZDtv52QJlwkTJsSYMWNi0KBBccYZZ8SUKVNi27Ztcemll+YiHABgD+RtAGg/5G0AyK6cFNC/9rWvxX/8x3/EpEmToqGhIQYMGBDz58//yI1OAIDck7cBoP2QtwEgu3J2E9Hx48fv9hKy1lZYWBjf/e53P3LZGvvG+B0c43dwjN/BMX4HpzONn7zdsRjD7DCO2WEcD54xzI6ONI5tJW93pDHNBuORznikMx7pjEc645GutccjL0mSpFX+EgAAAAAAtCP5uQ4AAAAAAADaIgV0AAAAAADIQAEdAAAAAAAy6PQF9OnTp8cxxxwT3bp1i8GDB8cLL7yQ65DapLq6ujj99NPj8MMPj549e8aFF14Yq1atSuuzffv2uPLKK6NHjx7xsY99LEaNGhUbNmzIUcRt25133hl5eXlx7bXXpvYZvz17++234+tf/3r06NEjunfvHv3794+lS5em2pMkiUmTJkWvXr2ie/fuUV1dHatXr85hxG3Hrl27YuLEiVFZWRndu3ePY489Nr7//e/H398Cw/j9l0WLFsX5558fFRUVkZeXF3Pnzk1r35ex2rRpU9TU1ERRUVGUlJTE5ZdfHlu3bm3Fs+i45O39I39nnxx+4OTygyenHxi5PXc6Q97+3ve+F3l5eWlb3759U+37kiPWrVsXI0eOjEMPPTR69uwZN9xwQ+zcubO1T+WAtNb76/e//338wz/8Q3Tr1i169+4dd999d0uf2gHZ23h885vf/MjrZfjw4Wl9OtJ4ZOuz6L68R5555pk49dRTo7CwMD71qU/FQw891NKnt9/2ZTyGDBnykdfIt771rbQ+HWU8ZsyYESeffHIUFRVFUVFRVFVVxW9+85tUe5t6bSSd2Jw5c5KuXbsmP/3pT5NXXnklGTt2bFJSUpJs2LAh16G1OcOGDUsefPDBZOXKlcmKFSuSc889N+nTp0+ydevWVJ9vfetbSe/evZOFCxcmS5cuTT7zmc8kZ555Zg6jbpteeOGF5JhjjklOPvnk5JprrkntN367t2nTpuToo49OvvnNbyaLFy9O3njjjeTJJ59M1qxZk+pz5513JsXFxcncuXOTl156KfniF7+YVFZWJn/9619zGHnbcPvttyc9evRI5s2bl6xduzZ59NFHk4997GPJD3/4w1Qf4/dffv3rXyf/9E//lDz22GNJRCSPP/54Wvu+jNXw4cOTU045JXn++eeT3/72t8mnPvWp5OKLL27lM+l45O39J39nlxx+4OTy7JDTD4zcnhudJW9/97vfTU488cTkT3/6U2r7j//4j1T73nLEzp07k5NOOimprq5OXnzxxeTXv/51cuSRRya1tbW5OJ391hrvry1btiRlZWVJTU1NsnLlyuRnP/tZ0r179+RHP/pRa53mPtvbeIwZMyYZPnx42utl06ZNaX060nhk47PovrxH3njjjeTQQw9NJkyYkLz66qvJtGnTki5duiTz589v1fPdm30Zj8997nPJ2LFj014jW7ZsSbV3pPF44oknkl/96lfJ66+/nqxatSr5zne+kxxyyCHJypUrkyRpW6+NTl1AP+OMM5Irr7wy9XjXrl1JRUVFUldXl8Oo2oeNGzcmEZE8++yzSZIkyebNm5NDDjkkefTRR1N9XnvttSQikvr6+lyF2ea8++67yXHHHZcsWLAg+dznPpf68m389uymm25Kzj777N22Nzc3J+Xl5cn/+B//I7Vv8+bNSWFhYfKzn/2sNUJs00aOHJlcdtllafsuuuiipKamJkkS47cnH/7Quy9j9eqrryYRkSxZsiTV5ze/+U2Sl5eXvP32260We0ckbx88+fvAyeEHRy7PDjn94Mntraez5O3vfve7ySmnnJKxbV9yxK9//eskPz8/aWhoSPWZMWNGUlRUlDQ1NbVo7NnWUu+v+++/PzniiCPSxuOmm25Kjj/++BY+o4OzuwL6BRdcsNvndOTxSJID+yy6L++RG2+8MTnxxBPT/tbXvva1ZNiwYS19Sgflw+ORJEna58xMOvJ4JEmSHHHEEcn/+l//q829NjrtEi7vv/9+LFu2LKqrq1P78vPzo7q6Ourr63MYWfuwZcuWiIgoLS2NiIhly5bFjh070sazb9++0adPH+P5d6688soYOXJk2jhFGL+9eeKJJ2LQoEHxla98JXr27BkDBw6MH//4x6n2tWvXRkNDQ9r4FRcXx+DBg41fRJx55pmxcOHCeP311yMi4qWXXornnnsuRowYERHGb3/sy1jV19dHSUlJDBo0KNWnuro68vPzY/Hixa0ec0chb2eH/H3g5PCDI5dnh5yefXJ7y+hseXv16tVRUVERn/zkJ6OmpibWrVsXEfuWI+rr66N///5RVlaW6jNs2LBobGyMV155pXVPJMuy9f6qr6+Pz372s9G1a9dUn2HDhsWqVaviL3/5SyudTfY888wz0bNnzzj++OPjiiuuiD//+c+pto4+HgfyWXRf3iP19fUf+Yw2bNiwNv//zYfH4wOzZs2KI488Mk466aSora2N9957L9XWUcdj165dMWfOnNi2bVtUVVW1uddGwYGeWHv3n//5n7Fr1660QY6IKCsriz/84Q85iqp9aG5ujmuvvTbOOuusOOmkkyIioqGhIbp27RolJSVpfcvKyqKhoSEHUbY9c+bMieXLl8eSJUs+0mb89uyNN96IGTNmxIQJE+I73/lOLFmyJK6++uro2rVrjBkzJjVGmd7Pxi/i5ptvjsbGxujbt2906dIldu3aFbfffnvU1NRERBi//bAvY9XQ0BA9e/ZMay8oKIjS0lLjeRDk7YMnfx84OfzgyeXZIadnn9zeMjpT3h48eHA89NBDcfzxx8ef/vSnuPXWW+Mf/uEfYuXKlfuUIxoaGjKO0wdt7Vm23l8NDQ1RWVn5kWN80HbEEUe0SPwtYfjw4XHRRRdFZWVl/PGPf4zvfOc7MWLEiKivr48uXbp06PE40M+i+/Ie2V2fxsbG+Otf/xrdu3dviVM6KJnGIyLiv/23/xZHH310VFRUxO9///u46aabYtWqVfHYY49FRMcbj5dffjmqqqpi+/bt8bGPfSwef/zxOOGEE2LFihVt6rXRaQvoHLgrr7wyVq5cGc8991yuQ2k31q9fH9dcc00sWLAgunXrlutw2p3m5uYYNGhQ3HHHHRERMXDgwFi5cmXMnDkzxowZk+Po2r6f//znMWvWrJg9e3aceOKJsWLFirj22mujoqLC+EEnIn8fGDk8O+Ty7JDToe354AqQiIiTTz45Bg8eHEcffXT8/Oc/b1NFKtqG0aNHp/7dv3//OPnkk+PYY4+NZ555JoYOHZrDyFqez6Lpdjce48aNS/27f//+0atXrxg6dGj88Y9/jGOPPba1w2xxxx9/fKxYsSK2bNkS/+f//J8YM2ZMPPvss7kO6yM67RIuRx55ZHTp0uUjd2/dsGFDlJeX5yiqtm/8+PExb968ePrpp+MTn/hEan95eXm8//77sXnz5rT+xvNvli1bFhs3boxTTz01CgoKoqCgIJ599tmYOnVqFBQURFlZmfHbg169esUJJ5yQtq9fv36pSyM/GCPv58xuuOGGuPnmm2P06NHRv3//uOSSS+K6666Lurq6iDB++2Nfxqq8vDw2btyY1r5z587YtGmT8TwI8vbBkb8PnByeHXJ5dsjp2Se3t4zOnLdLSkri05/+dKxZs2af8mx5eXnGcfqgrT3L1vurI4/RJz/5yTjyyCNjzZo1EdFxx+NgPovuy/nurk9RUVGb/CFrd+ORyeDBgyMi0l4jHWk8unbtGp/61KfitNNOi7q6ujjllFPihz/8YZt7bXTaAnrXrl3jtNNOi4ULF6b2NTc3x8KFC6OqqiqHkbVNSZLE+PHj4/HHH4+nnnrqI5cLnXbaaXHIIYekjeeqVati3bp1xjMihg4dGi+//HKsWLEitQ0aNChqampS/zZ+u3fWWWfFqlWr0va9/vrrcfTRR0dERGVlZZSXl6eNX2NjYyxevNj4RcR7770X+fnp/9136dIlmpubI8L47Y99GauqqqrYvHlzLFu2LNXnqaeeiubm5tSHH/afvH1g5O+DJ4dnh1yeHXJ69sntLaMz5+2tW7fGH//4x+jVq9c+5dmqqqp4+eWX04qmCxYsiKKioo/88NjeZOv9VVVVFYsWLYodO3ak+ixYsCCOP/74Nrtcyb7693//9/jzn/8cvXr1ioiONx7Z+Cy6L++RqqqqtGN80Ket/X+zt/HIZMWKFRERaa+RjjIemTQ3N0dTU1Pbe20cyB1RO4o5c+YkhYWFyUMPPZS8+uqrybhx45KSkpK0u7fyN1dccUVSXFycPPPMM8mf/vSn1Pbee++l+nzrW99K+vTpkzz11FPJ0qVLk6qqqqSqqiqHUbdtH76zsvHbvRdeeCEpKChIbr/99mT16tXJrFmzkkMPPTT53//7f6f63HnnnUlJSUnyi1/8Ivn973+fXHDBBUllZWXy17/+NYeRtw1jxoxJPv7xjyfz5s1L1q5dmzz22GPJkUcemdx4442pPsbvv7z77rvJiy++mLz44otJRCT33ntv8uKLLyZvvfVWkiT7NlbDhw9PBg4cmCxevDh57rnnkuOOOy65+OKLc3VKHYa8vf/k75Yhh+8/uTw75PQDI7fnRmfJ29dff33yzDPPJGvXrk3+7d/+Lamurk6OPPLIZOPGjUmS7D1H7Ny5MznppJOSL3zhC8mKFSuS+fPnJ0cddVRSW1ubq1PaL63x/tq8eXNSVlaWXHLJJcnKlSuTOXPmJIceemjyox/9qNXPd2/2NB7vvvtu8t//+39P6uvrk7Vr1yb/+q//mpx66qnJcccdl2zfvj11jI40Htn4LLov75E33ngjOfTQQ5Mbbrghee2115Lp06cnXbp0SebPn9+q57s3exuPNWvWJJMnT06WLl2arF27NvnFL36RfPKTn0w++9nPpo7Rkcbj5ptvTp599tlk7dq1ye9///vk5ptvTvLy8pL/9//+X5Ikbeu10akL6EmSJNOmTUv69OmTdO3aNTnjjDOS559/PtchtUkRkXF78MEHU33++te/Jt/+9reTI444Ijn00EOTL33pS8mf/vSn3AXdxn34y7fx27Nf/vKXyUknnZQUFhYmffv2TR544IG09ubm5mTixIlJWVlZUlhYmAwdOjRZtWpVjqJtWxobG5Nrrrkm6dOnT9KtW7fkk5/8ZPJP//RPSVNTU6qP8fsvTz/9dMb/78aMGZMkyb6N1Z///Ofk4osvTj72sY8lRUVFyaWXXpq8++67OTibjkfe3j/yd8uQww+MXH7w5PQDI7fnTmfI21/72teSXr16JV27dk0+/vGPJ1/72teSNWvWpNr3JUe8+eabyYgRI5Lu3bsnRx55ZHL99dcnO3bsaO1TOSCt9f566aWXkrPPPjspLCxMPv7xjyd33nlna53iftnTeLz33nvJF77wheSoo45KDjnkkOToo49Oxo4d+5EflTrSeGTrs+i+vEeefvrpZMCAAUnXrl2TT37yk2l/o63Y23isW7cu+exnP5uUlpYmhYWFyac+9ankhhtuSLZs2ZJ2nI4yHpdddlly9NFHJ127dk2OOuqoZOjQoanieZK0rddGXpIkyf7NWQcAAAAAgI6v066BDgAAAAAAe6KADgAAAAAAGSigAwAAAABABgroAAAAAACQgQI6AAAAAABkoIAOAAAAAAAZKKADAAAAAEAGCugAAAAAAJCBAjoAAAAAAGSggA4AAAAALeCss86KcePG5ToM4CAooAMfMXjw4LjiiityHQYAsBdyNgC0Xc3NzfHSSy/FqaeemutQgIOggA6k2bVrV7z88ssSPAC0cXI2ALRtq1atim3btsnV0M4poANp/vCHP8Rf//rXGDhwYK5DAQD2QM4GgLZt+fLlUVBQECeffHKuQwEOggI6kObFF1+MgoKC6N+/f65DAQD2QM4GgLZt+fLlccIJJ0S3bt1yHQpwEBTQgTQvvvhinHDCCVFYWJjrUACAPZCzAaBtW758ueVboANQQAfSvPjii7u9FHzXrl2tHA0AsDt7ytkAQO6tWLEiTjvttIxtn/vc52LAgAExYMCA6NKlSyxdurSVowP2lQI6kGbFihVpX8a/+MUvxre//e04/fTT48EHH8xhZADA3/twzvZFHADajj/+8Y+xefPm3c5Af/bZZ2PFihVxwQUXxPjx42PQoEGtHCGwrwpyHQDQdrz55pvxl7/8Je3L+MsvvxxDhw6N+++/P4eRAQB/L1POfvbZZyMi4rvf/W587nOf80UcAHJo+fLlERHRpUuXWLlyZWp/165d49Of/nREREyZMiXefPPNeOihh3IRIrCPFNCBlBdffDHy8vJiwIABERHx7rvvxq5du+Kaa67JbWAAQJoP5+wP+CIOAG3DBwX0z3zmM2n7zz777Pjtb38bDz30UCxatCgeffTRyMvLy0WIwD6yhAuQsmzZsvjUpz4VRUVFERHxyiuvxJlnnpnjqACAD/twzo6I1Bfxn/70p76IA0CO1dXVRZIkH9l++9vfxuOPPx5z5syJn/3sZ9GlS5dchwrshQI6kDJ//vyorq5OPX755Zejf//+OYwIAMjkwznbF3EAaD8uu+yyeOONN2Lw4MExYMCAmDdvXq5DAvbAEi7QySVJEm+99Vb88z//c6xcuTL++Z//OdX28ssvp305BwByZ085+7LLLoujjjoqBg8eHBERt912W5x33nm5ChUA2IO//OUvuQ4B2A8K6NDJrVy5Mj7zmc/EySefHE8++WT069cv1TZ16tQcRgYA/L095WxfxAEAoGXkJUmS5DoIAAAAAABoa6yBDgAAAAAAGSigAwAAAABABgroAAAAAACQgQI6AAAAAABkoIAOAAAAAAAZKKADAAAAAEAGCugAAAAAAJCBAjoAAAAAAGSggA4AAAAAABkooAMAAAAAQAYK6AAAAAAAkMH/B6X1WUjFpoL3AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Visualize the distribution of candidate actions\n", + "fig, axs = plt.subplots(1, 3, figsize=(15, 4))\n", + "axs[0].hist(samples[:, 0], bins=50, weights=soft_weights)\n", + "axs[0].set_xlabel(r\"$J_r$\")\n", + "axs[1].hist(samples[:, 1], bins=50, weights=soft_weights)\n", + "axs[1].set_xlabel(r\"$J_z$\")\n", + "axs[2].hist(samples[:, 2], bins=50, weights=soft_weights)\n", + "axs[2].set_xlabel(r\"$L_z$\")\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/spheroid_sampled_actions.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3fbdb10f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors\n", + "plt.figure(figsize=(12,6))\n", + "plt.subplot(231)\n", + "plt.hist2d(x2, y2, bins=50, cmap=\"viridis\", weights=soft_weights2)#, norm=colors.LogNorm(), cmin=1, weights=soft_weights)\n", + "plt.xlabel('x [kpc]')\n", + "plt.ylabel('y [kpc]')\n", + "plt.axis('equal')\n", + "plt.subplot(232)\n", + "plt.hist2d(x2, z2, bins=50, cmap=\"viridis\", weights=soft_weights2)\n", + "plt.xlabel('x [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.axis('equal')\n", + "plt.subplot(233)\n", + "plt.hist2d(y2, z2, bins=50, cmap=\"viridis\", weights=soft_weights2)\n", + "plt.xlabel('y [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.axis('equal')\n", + "\n", + "\n", + "plt.subplot(234)\n", + "plt.hist(v_x2, bins=50, weights=soft_weights2)#, range=(-2000, 2000))\n", + "plt.xlabel(r\"$v_\\text{x}$ (km/s)\")\n", + "plt.ylabel(\"Number of stars\")\n", + "\n", + "plt.subplot(235)\n", + "plt.hist(v_y2, bins=50, weights=soft_weights2)#, range=(-2000, 2000))\n", + "plt.xlabel(r\"$v_\\text{y}$ (km/s)\")\n", + "plt.ylabel(\"Number of stars\")\n", + "\n", + "plt.subplot(236)\n", + "plt.hist(v_z2, bins=50, weights=soft_weights2)\n", + "plt.xlabel(r\"$v_\\text{z}$ (km/s)\")\n", + "plt.ylabel(\"Number of stars\")\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/spheroid_phasespace.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "fc1be153", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as mcolors\n", + "from scipy.stats import binned_statistic_2d\n", + "\n", + "# Helper function to calculate weighted mean\n", + "def weighted_mean_2d(x_pos, y_pos, values, weights, x_bins, y_bins):\n", + " # Sum of (value * weight) in each bin\n", + " weighted_sum, _, _, _ = binned_statistic_2d(\n", + " x_pos, y_pos, values * weights, statistic='sum', bins=[x_bins, y_bins]\n", + " )\n", + " # Sum of weights in each bin\n", + " sum_of_weights, _, _, _ = binned_statistic_2d(\n", + " x_pos, y_pos, weights, statistic='sum', bins=[x_bins, y_bins]\n", + " )\n", + " \n", + " # Divide, handling division by zero (where sum_of_weights is 0)\n", + " with np.errstate(divide='ignore', invalid='ignore'):\n", + " result = weighted_sum / sum_of_weights\n", + " \n", + " return result\n", + "\n", + "num_bins_x = 40\n", + "num_bins_y = 40\n", + "num_bins_z = 40 \n", + "\n", + "# Example: x, z, v_y are 1D arrays of particle positions and velocities\n", + "# Define bin edges\n", + "x_bins = np.linspace(x2.min(), x2.max(), num_bins_x + 1)\n", + "y_bins = np.linspace(y2.min(), y2.max(), num_bins_y + 1)\n", + "z_bins = np.linspace(z2.min(), z2.max(), num_bins_z + 1)\n", + "\n", + "# Digitize positions to bin indices\n", + "x_idx = np.digitize(x2, x_bins) - 1\n", + "y_idx = np.digitize(y2, y_bins) - 1\n", + "z_idx = np.digitize(z2, z_bins) - 1\n", + "\n", + "# Initialize array for mean v_y\n", + "mean_vx = np.full((num_bins_y, num_bins_z), np.nan)\n", + "mean_vy = np.full((num_bins_x, num_bins_z), np.nan)\n", + "mean_vz = np.full((num_bins_x, num_bins_y), np.nan)\n", + "\n", + "# 1. Mean v_x (y vs z)\n", + "mean_vx = weighted_mean_2d(y2, z2, v_x2, soft_weights2, y_bins, z_bins)\n", + "\n", + "# 2. Mean v_y (x vs z)\n", + "mean_vy = weighted_mean_2d(x2, z2, v_y2, soft_weights2, x_bins, z_bins)\n", + "\n", + "# 3. Mean v_z (x vs y)\n", + "mean_vz = weighted_mean_2d(x2, y2, v_z2, soft_weights2, x_bins, y_bins)\n", + "\n", + " \n", + "# Plot mean velocity maps side-by-side (y vs z, x vs z, x vs y)\n", + "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n", + "# mean_vx: y vs z\n", + "im0 = axs[0].imshow(mean_vx.T, origin='lower', aspect='auto',\n", + " extent=[y_bins[0], y_bins[-1], z_bins[0], z_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[0].set_xlabel('y')\n", + "axs[0].set_ylabel('z')\n", + "axs[0].set_title('Mean $v_x$ (y vs z)')\n", + "axs[0].axis('equal')\n", + "plt.colorbar(im0, ax=axs[0], label='Mean $v_x$')\n", + "# mean_vy: x vs z\n", + "im1 = axs[1].imshow(mean_vy.T, origin='lower', aspect='auto',\n", + " extent=[x_bins[0], x_bins[-1], z_bins[0], z_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[1].set_xlabel('x')\n", + "axs[1].set_ylabel('z')\n", + "axs[1].set_title('Mean $v_y$ (x vs z)')\n", + "axs[1].axis('equal')\n", + "plt.colorbar(im1, ax=axs[1], label='Mean $v_y$')\n", + "# mean_vz: x vs y\n", + "im2 = axs[2].imshow(mean_vz.T, origin='lower', aspect='auto',\n", + " extent=[x_bins[0], x_bins[-1], y_bins[0], y_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[2].set_xlabel('x')\n", + "axs[2].set_ylabel('y')\n", + "axs[2].set_title('Mean $v_z$ (x vs y)')\n", + "plt.colorbar(im2, ax=axs[2], label='Mean $v_z$')\n", + "axs[2].axis('equal')\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/spheroid_velocities.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3c1ffb51", + "metadata": {}, + "source": [ + "# Combine disk and spheroid" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "f7801296", + "metadata": {}, + "outputs": [], + "source": [ + "x_tot = jnp.concatenate([x, x2])\n", + "y_tot = jnp.concatenate([y, y2])\n", + "z_tot = jnp.concatenate([z, z2])\n", + "v_x_tot = jnp.concatenate([v_x, v_x2])\n", + "v_y_tot = jnp.concatenate([v_y, v_y2])\n", + "v_z_tot = jnp.concatenate([v_z, v_z2]) \n", + "soft_weights_tot = jnp.concatenate([soft_weights, soft_weights2])" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "641c002b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as mcolors\n", + "from scipy.stats import binned_statistic_2d\n", + "\n", + "# Helper function to calculate weighted mean\n", + "def weighted_mean_2d(x_pos, y_pos, values, weights, x_bins, y_bins):\n", + " # Sum of (value * weight) in each bin\n", + " weighted_sum, _, _, _ = binned_statistic_2d(\n", + " x_pos, y_pos, values * weights, statistic='sum', bins=[x_bins, y_bins]\n", + " )\n", + " # Sum of weights in each bin\n", + " sum_of_weights, _, _, _ = binned_statistic_2d(\n", + " x_pos, y_pos, weights, statistic='sum', bins=[x_bins, y_bins]\n", + " )\n", + " \n", + " # Divide, handling division by zero (where sum_of_weights is 0)\n", + " with np.errstate(divide='ignore', invalid='ignore'):\n", + " result = weighted_sum / sum_of_weights\n", + " \n", + " return result\n", + "\n", + "num_bins_x = 40\n", + "num_bins_y = 40\n", + "num_bins_z = 40 \n", + "\n", + "# Example: x, z, v_y are 1D arrays of particle positions and velocities\n", + "# Define bin edges\n", + "x_bins = np.linspace(x_tot.min(), x_tot.max(), num_bins_x + 1)\n", + "y_bins = np.linspace(y_tot.min(), y_tot.max(), num_bins_y + 1)\n", + "z_bins = np.linspace(z_tot.min(), z_tot.max(), num_bins_z + 1)\n", + "\n", + "# Digitize positions to bin indices\n", + "x_idx = np.digitize(x_tot, x_bins) - 1\n", + "y_idx = np.digitize(y_tot, y_bins) - 1\n", + "z_idx = np.digitize(z_tot, z_bins) - 1\n", + "\n", + "# Initialize array for mean v_y\n", + "mean_vx = np.full((num_bins_y, num_bins_z), np.nan)\n", + "mean_vy = np.full((num_bins_x, num_bins_z), np.nan)\n", + "mean_vz = np.full((num_bins_x, num_bins_y), np.nan)\n", + "\n", + "# 1. Mean v_x (y vs z)\n", + "mean_vx = weighted_mean_2d(y_tot, z_tot, v_x_tot, soft_weights_tot, y_bins, z_bins)\n", + "\n", + "# 2. Mean v_y (x vs z)\n", + "mean_vy = weighted_mean_2d(x_tot, z_tot, v_y_tot, soft_weights_tot, x_bins, z_bins)\n", + "\n", + "# 3. Mean v_z (x vs y)\n", + "mean_vz = weighted_mean_2d(x_tot, y_tot, v_z_tot, soft_weights_tot, x_bins, y_bins)\n", + "\n", + " \n", + "# Plot mean velocity maps side-by-side (y vs z, x vs z, x vs y)\n", + "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n", + "# mean_vx: y vs z\n", + "im0 = axs[0].imshow(mean_vx.T, origin='lower', aspect='auto',\n", + " extent=[y_bins[0], y_bins[-1], z_bins[0], z_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[0].set_xlabel('y')\n", + "axs[0].set_ylabel('z')\n", + "axs[0].set_title('Mean $v_x$ (y vs z)')\n", + "axs[0].axis('equal')\n", + "plt.colorbar(im0, ax=axs[0], label='Mean $v_x$')\n", + "# mean_vy: x vs z\n", + "im1 = axs[1].imshow(mean_vy.T, origin='lower', aspect='auto',\n", + " extent=[x_bins[0], x_bins[-1], z_bins[0], z_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[1].set_xlabel('x')\n", + "axs[1].set_ylabel('z')\n", + "axs[1].set_title('Mean $v_y$ (x vs z)')\n", + "axs[1].axis('equal')\n", + "plt.colorbar(im1, ax=axs[1], label='Mean $v_y$')\n", + "# mean_vz: x vs y\n", + "im2 = axs[2].imshow(mean_vz.T, origin='lower', aspect='auto',\n", + " extent=[x_bins[0], x_bins[-1], y_bins[0], y_bins[-1]],\n", + " cmap='RdBu')\n", + "axs[2].set_xlabel('x')\n", + "axs[2].set_ylabel('y')\n", + "axs[2].set_title('Mean $v_z$ (x vs y)')\n", + "plt.colorbar(im2, ax=axs[2], label='Mean $v_z$')\n", + "axs[2].axis('equal')\n", + "plt.tight_layout()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "phoenix", + "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": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/selfconsitency_disk.ipynb b/notebooks/selfconsitency_disk.ipynb new file mode 100644 index 0000000..d489656 --- /dev/null +++ b/notebooks/selfconsitency_disk.ipynb @@ -0,0 +1,472 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "34c0bec3", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix import sampling, actions_to_phase_space\n", + "from phoenix.potentials import miyamoto_nagai_potential, plummer_potential\n", + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bfec7291", + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " \"R0\": 8.0, # for actions to phase space\n", + " \"Rinit\": 8.0, # for sampling\n", + " \"Rd\": 2.5,\n", + " \"Sigma0\": 100.0,\n", + " \"RsigR\": 18.0,\n", + " \"RsigZ\": 10.0,\n", + " \"sigmaR0_R0\": 140.0,\n", + " \"sigmaz0_R0\": 50.0,\n", + " \"L0\": 1000.0,\n", + " \"Rinit_for_Rc\": 8.0,\n", + "}\n", + "\n", + "envelope_max = 3.0\n", + "n_candidates = 250_000\n", + "key = jax.random.PRNGKey(42)\n", + "\n", + "Phi_disk = miyamoto_nagai_potential\n", + "theta_disk = jnp.array([1e12, 60.0, 0.01]) # (M, a, b) z.B. für Miyamoto-Nagai" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c0de3432", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:13: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:37: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:62: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:87: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n", + "/home/annalena/phoenix/phoenix/distributionfunctions_disky_Binney.py:115: UserWarning: As of jaxtyping version 0.2.24, jaxtyping now prefers the syntax\n", + "```\n", + "from jaxtyping import jaxtyped\n", + "# Use your favourite typechecker: usually one of the two lines below.\n", + "from typeguard import typechecked as typechecker\n", + "from beartype import beartype as typechecker\n", + "\n", + "@jaxtyped(typechecker=typechecker)\n", + "def foo(...):\n", + "```\n", + "and the old double-decorator syntax\n", + "```\n", + "@jaxtyped\n", + "@typechecker\n", + "def foo(...):\n", + "```\n", + "should no longer be used. (It will continue to work as it did before, but the new approach will produce more readable error messages.)\n", + "In particular note that `typechecker` must be passed via keyword argument; the following is not valid:\n", + "```\n", + "@jaxtyped(typechecker)\n", + "def foo(...):\n", + "```\n", + "\n", + " @jaxtyped\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of candidate actions: 250000\n" + ] + } + ], + "source": [ + "#Generate candidate actions\n", + "from phoenix.distributionfunctions_disky_Binney import f_disc_from_params\n", + "candidates, samples, soft_weights = sampling.sample_df_potential(f_disc_from_params, key, params, Phi_disk, theta_disk, n_candidates, envelope_max, tau=0.01)\n", + "print(\"Number of candidate actions:\", samples.shape[0])\n", + "\n", + "#Map the candidate actions to phase-space coordinates\n", + "phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi_disk, theta_disk)\n", + "x = phase_space_coords[:, 0]\n", + "y = phase_space_coords[:, 1]\n", + "z = phase_space_coords[:, 2]\n", + "v_x = phase_space_coords[:, 3]\n", + "v_y = phase_space_coords[:, 4]\n", + "v_z = phase_space_coords[:, 5]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "94a7a8c2", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "\n", + "def compute_density_jax(x, y, z, weights, r_bins, z_bins):\n", + " # 1. Compute radial distance r\n", + " r = jnp.sqrt(x**2 + y**2)\n", + "\n", + " # 2. Use histogram2d to accumulate weights efficiently\n", + " # This replaces the entire fori_loop and digitize logic\n", + " counts, _, _ = jnp.histogram2d(\n", + " r, z, \n", + " bins=[r_bins, z_bins], \n", + " weights=weights\n", + " )\n", + "\n", + " # 3. Compute the volume of each bin\n", + " # Use midpoint r for volume calculation to be more accurate\n", + " r_mid = (r_bins[:-1] + r_bins[1:]) / 2\n", + " r_widths = jnp.diff(r_bins)\n", + " z_widths = jnp.diff(z_bins)\n", + " \n", + " # Calculate volume of cylindrical shell: V = 2 * pi * r * dr * dz\n", + " bin_volumes = 2 * jnp.pi * jnp.outer(r_mid * r_widths, z_widths)\n", + "\n", + " # 4. Normalize\n", + " density = counts / bin_volumes\n", + " \n", + " return density" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "746e87db", + "metadata": {}, + "outputs": [], + "source": [ + "rbin = jnp.linspace(0, 10, 20)\n", + "zbin = jnp.linspace(-1, 1, 20)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "fc349ff2", + "metadata": {}, + "outputs": [], + "source": [ + "density = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "781d5a2d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(density.T, origin='lower', aspect='auto',\n", + " extent=[0, 10, -1, 1], cmap='viridis', norm=colors.LogNorm())\n", + "plt.colorbar(label='Density')\n", + "plt.xlabel('r [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.title('Density Distribution in r-z Plane')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "501bdeff", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_laplacian_on_grid(potential, theta, r_bins, z_bins):\n", + " \"\"\"\n", + " Computes nabla^2 Phi (Laplacian) on the centers of the R-Z bins.\n", + " \"\"\"\n", + " \n", + " # 1. Define the Laplacian for a SINGLE point (x, y, z)\n", + " def potential_wrapper(x, y, z):\n", + " return potential(x, y, z, *theta)\n", + "\n", + " def laplacian_fn(x, y, z):\n", + " # jax.hessian returns a 3x3 matrix of second derivatives\n", + " # argnums=(0, 1, 2) makes it return a nested tuple structure relative to x,y,z\n", + " # However, it's easier to treat input as a vector for Hessian logic,\n", + " # but since our function takes scalars, we can just sum unmixed 2nd derivatives.\n", + " \n", + " # Method A: Direct curvature calculation (faster/simpler than full Hessian)\n", + " # We use simple nested grad or specific derivative operators\n", + " d2dx2 = jax.grad(lambda x_: jax.grad(potential_wrapper, argnums=0)(x_, y, z))(x)\n", + " d2dy2 = jax.grad(lambda y_: jax.grad(potential_wrapper, argnums=1)(x, y_, z))(y)\n", + " d2dz2 = jax.grad(lambda z_: jax.grad(potential_wrapper, argnums=2)(x, y, z_))(z)\n", + " \n", + " return d2dx2 + d2dy2 + d2dz2\n", + " \n", + " # 2. Vectorize the Laplacian function\n", + " # Maps over inputs x, y, z\n", + " laplacian_vmap = jax.vmap(laplacian_fn, in_axes=(0, 0, 0))\n", + "\n", + " # 3. Setup Grid (Bin Centers)\n", + " r_centers = 0.5 * (r_bins[:-1] + r_bins[1:])\n", + " z_centers = 0.5 * (z_bins[:-1] + z_bins[1:])\n", + " \n", + " # Create Meshgrid (indexing='ij' matches density shape)\n", + " R_grid, Z_grid = jnp.meshgrid(r_centers, z_centers, indexing='ij')\n", + "\n", + " # 4. Convert R-Z to Cartesian X-Y-Z\n", + " # We evaluate at y=0, so x=R\n", + " X_flat = R_grid.flatten()\n", + " Y_flat = jnp.zeros_like(X_flat)\n", + " Z_flat = Z_grid.flatten()\n", + "\n", + " # 5. Compute\n", + " laplacian_flat = laplacian_vmap(X_flat, Y_flat, Z_flat)\n", + " \n", + " # Reshape back to (N_r, N_z)\n", + " laplacian_grid = laplacian_flat.reshape(R_grid.shape)\n", + " \n", + " return laplacian_grid" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "fd192c7f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Laplacian shape: (19, 19)\n" + ] + } + ], + "source": [ + "\n", + "nabla2_Phi = compute_laplacian_on_grid(Phi_disk, theta_disk, rbin, zbin)\n", + "\n", + "print(\"Laplacian shape:\", nabla2_Phi.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "73cbe1fd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(nabla2_Phi.T, origin='lower', aspect='auto',\n", + " extent=[0, 10, -1, 1], cmap='viridis', norm=colors.LogNorm())\n", + "plt.colorbar(label='Density')\n", + "plt.xlabel('r [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.title('Laplacian of Potential in r-z Plane')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "2fea078c", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix.constants import G\n", + "\n", + "def compute_loss(key, params, Phi_disk, theta_disk, n_candidates, envelope_max, rbin, zbin):\n", + " candidates, samples, soft_weights = sampling.sample_df_potential(f_disc_from_params, key, params, Phi_disk, theta_disk, n_candidates, envelope_max, tau=0.01)\n", + " phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi_disk, theta_disk)\n", + " x = phase_space_coords[:, 0]\n", + " y = phase_space_coords[:, 1]\n", + " z = phase_space_coords[:, 2]\n", + " density = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)\n", + " nabla2_Phi = compute_laplacian_on_grid(Phi_disk, theta_disk, r_bins=rbin, z_bins=zbin)\n", + " lossplane = (4*jnp.pi*G*density - nabla2_Phi)*density/density\n", + "\n", + " return lossplane" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "015ad00f", + "metadata": {}, + "outputs": [], + "source": [ + "lossplane = compute_loss(key, params, Phi_disk, theta_disk, n_candidates, envelope_max, rbin, zbin)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "91eef618", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(lossplane.T, origin='lower', aspect='auto',\n", + " extent=[0, 2, -1, 1], cmap='viridis')#, norm=colors.LogNorm())\n", + "plt.colorbar(label='loss')\n", + "plt.xlabel('r [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.title('Loss Distribution in r-z Plane')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "phoenix", + "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": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/selfconsitency_spheroid.ipynb b/notebooks/selfconsitency_spheroid.ipynb new file mode 100644 index 0000000..24fb4ff --- /dev/null +++ b/notebooks/selfconsitency_spheroid.ipynb @@ -0,0 +1,786 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "34c0bec3", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix import sampling, actions_to_phase_space\n", + "from phoenix.potentials import miyamoto_nagai_potential, plummer_potential\n", + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bfec7291", + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " \"R0\": 8.0, # for actions to phase space\n", + " \"N0_spheroid\": 1e6,\n", + " \"J0_spheroid\": 1000.0,\n", + " \"Gamma_spheroid\": 2.5,\n", + " \"Beta_spheroid\": 3.5,\n", + "}\n", + "\n", + "envelope_max = 3.0\n", + "n_candidates = 250_000\n", + "key = jax.random.PRNGKey(42)\n", + "\n", + "Phi_spheroid = plummer_potential\n", + "theta_spheroid = jnp.array([1e12, 10.0]) # (M, a) z.B. für Plummer" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c0de3432", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of candidate actions: 250000\n" + ] + } + ], + "source": [ + "#Generate candidate actions\n", + "from phoenix.distributionfunctions_spheroidal import f_double_power_law\n", + "candidates, samples, soft_weights = sampling.sample_df_potential(f_double_power_law, key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, tau=0.01)\n", + "print(\"Number of candidate actions:\", samples.shape[0])\n", + "\n", + "#Map the candidate actions to phase-space coordinates\n", + "phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi_spheroid, theta_spheroid)\n", + "x = phase_space_coords[:, 0]\n", + "y = phase_space_coords[:, 1]\n", + "z = phase_space_coords[:, 2]\n", + "v_x = phase_space_coords[:, 3]\n", + "v_y = phase_space_coords[:, 4]\n", + "v_z = phase_space_coords[:, 5]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "94a7a8c2", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "\n", + "def compute_density_jax(x, y, z, weights, r_bins, z_bins):\n", + " # 1. Compute radial distance r\n", + " r = jnp.sqrt(x**2 + y**2)\n", + "\n", + " # 2. Use histogram2d to accumulate weights efficiently\n", + " # This replaces the entire fori_loop and digitize logic\n", + " counts, _, _ = jnp.histogram2d(\n", + " r, z, \n", + " bins=[r_bins, z_bins], \n", + " weights=weights\n", + " )\n", + "\n", + " # 3. Compute the volume of each bin\n", + " # Use midpoint r for volume calculation to be more accurate\n", + " r_mid = (r_bins[:-1] + r_bins[1:]) / 2\n", + " r_widths = jnp.diff(r_bins)\n", + " z_widths = jnp.diff(z_bins)\n", + " \n", + " # Calculate volume of cylindrical shell: V = 2 * pi * r * dr * dz\n", + " bin_volumes = 2 * jnp.pi * jnp.outer(r_mid * r_widths, z_widths)\n", + "\n", + " # 4. Normalize\n", + " density = counts / bin_volumes\n", + " valid_mask = (density > 0).astype(jnp.float32)\n", + " \n", + " return density, valid_mask" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "746e87db", + "metadata": {}, + "outputs": [], + "source": [ + "r_min = 0\n", + "r_max = 10\n", + "z_min = -5\n", + "z_max = 5\n", + "rbin = jnp.linspace(r_min, r_max, 20)\n", + "zbin = jnp.linspace(z_min, z_max, 20)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "fc349ff2", + "metadata": {}, + "outputs": [], + "source": [ + "density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "781d5a2d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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/atasqTvuuMP1y7pz585q166dli1bpmuvvVa/+c1vyp1TVlaWa+2h8+fPu1ZaPnjwoO6///5if2H8Ups2bdSrVy916dJFERER2rZtm959991CA4sL8h89erTi4+MVGBio+++/v9w5/lJwcLDWrFmjhIQExcbGavXq1Vq1apWefvppVzdFeHi47rnnHs2aNUs2m02tWrXSypUrix234U5uzz//vNatW6cbb7xRjzzyiGrUqKG5c+cqLy9PU6dOrdDnqWq++eYbTZkyRTfffLNOnDhRZF0qT4vp4lxzzTVq1aqVxo4dq2PHjiksLEz//Oc/PVovp2fPnnrooYeUkpKiXbt26fbbb1fNmjX1/fffa9myZXrttdd09913m/gpgKqDggeSpIkTJ0qSgoKCFBERofbt22vGjBkaPnx4kcG5bdq00bZt2zR58mTNnz9fp0+fVsOGDdW5c2dXHHf07NlTW7du1ZIlS5SZmanw8HB1795dCxcuLPVf0t26ddOUKVM0Z84crVmzRk6nU4cOHSo0C+vBBx/Uk08+6fZg5R9//NF1Tp06ddSoUSNdf/31mj17tm677bYyzx89erRWrFihtWvXKi8vT82bN9fzzz/vWixRuryW0KOPPqolS5bonXfekWEYFS54AgMDtWbNGj388MN64oknFBoaqkmTJhX5esyaNUsXL17UnDlzZLfbde+99+rll18utF6Ru7m1bdtWn3zyicaPH6+UlBQ5nU7FxsbqnXfeKbIGj686ffq0DMPQ5s2btXnz5iLvV0bBU7NmTX344YcaPXq0UlJSFBwcrIEDByopKanEhTXLY86cOerSpYvmzp2rp59+WjVq1FCLFi30+9//Xj169DDxEwBVi82o6EhBwAe89tprevzxx3X48OFiZ/MAAKoHCh74LcMw1LFjR9WvX5/1RQCgmqNLC34nNzdXK1as0KZNm/TNN9/ogw8+sDolAIDFaOGB3zl8+LBiYmJUt25dPfLII3rhhResTgkAYDEKHgAA4PdYhwcAAPg9Ch4AAOD3qtWgZafTqePHjys0NNTUZf0BAP7FMAydO3dOjRs3VkBA5bUNXLhwocgDaisqKCio0CKxKKxaFTzHjx/3qef6AACslZ6eriZNmlRK7AsXLiimeR1lnDDnAb7R0dE6dOgQRU8JqlXBU7BicHp6uk893wcA4F3Z2dlq2rRpkZXmzZSfn6+MEw4d2d5CYaGetSJln3OqeZfDys/Pp+ApQbUqeAq6scLCwih4AABl8sbwhzqhNtUJ9ew6TjFMoyzVquABAKCqcRhOOTxcIMZhOM1Jxo9R8AAAYCGnDDnlWcXj6fnVAdPSAQCA36PgAQDAQk6T/pOkbt26qU2bNkpNTbX4U1U9dGkBAGAhh2HI4eFTngrOT0tLY1JOCWjhAQAAfo8WHgAALMSgZe+g4AEAwEJOGXJQ8FQ6urQAAIDfo4UHAAAL0aXlHbTwAABgoYJZWp5uEtPSS0MLDwAAfoJp6SWj4AEAwELO/26exkDpKHgAALCQw4RZWp6eXx1Q8AAAYCGHIROelm5OLv6MQcsAAMDv0cIDAICFGMPjHRQ8AABYyCmbHLJ5HAOlo0sLAAD4PQoeAAAs5DTM2SQWHiwNXVoAAFjIYUKXVsH5LDxYMlp4AACA36OFBwAAC5nZwoOSUfAAAGAhp2GT0/BwlpaH51cHdGkBAAC/RwsPAAAWokvLOyh4AACwkEMBcnjY4eIwKRd/RsEDAICFDBPG8BiM4SkTY3gAAIDfo+ABAMBCBWN4PN0kVloujc8WPC+++KJsNpvGjBljdSoAAFSYwwgwZZMur7T87bffKjEx0eJPVfX4ZMGTlpamuXPnqkOHDlanAgAAfIDPFTw5OTkaMmSI/vKXv6hevXpWpwMAgEecssmpAA83Bi2XxecKnsTERPXv319xcXFlHpuXl6fs7OxCGwAAVYmZY3hQMp+alr5kyRLt2LFDaWlp5To+JSVFkydPruSsAABAVeczLTzp6el67LHHtHDhQgUHB5frnPHjxysrK8u1paenV3KWAAC4x8xByyiZz7TwbN++XSdOnNBvfvMb1z6Hw6EtW7bo9ddfV15engIDAwudY7fbZbfbvZ0qAADldnkMj4cPD6VLq0w+U/Dceuut+uabbwrtGz58uK655ho99dRTRYodAACAAj5T8ISGhqpdu3aF9tWuXVv169cvsh8AAF/hNOFZWk4ZJmXjv3ym4AEAwB+ZMQbHYVDwlMWnC56PP/7Y6hQAAPBIwVo6nsWg4CkLw7oBAIDf8+kWHgAAfJ3DsMlheDbLytPzqwNaeAAAsJDjv4OWPd0knpZeGlp4AADwE2lpaQoLC7M6jSqJggcAAAs5jQA5PZyl5WSWVpkoeAAAsJDDhHV4HMzSKhNjeAAAgN+jhQcAAAs55fksK6c5qfg1Ch4AACxkzsKDdNiUhTsEAAD8Hi08AABYyJxnadF+URYKHgAALOSUTU55OoaHlZbLQsEDAICFaOHxDu4QAADwe7TwAABgIXMWHqT9oiwUPAAAWMhp2OT0dB0enpZeJkpCAADg92jhAQDAQk4TurRYeLBsFDwAAFjInKelU/CUhTsEAAD8Hi08AABYyCGbHB4uHOjp+dUBLTwAAFiooEvL002SunXrpjZt2ig1NdXiT1X10MIDAICfSEtLU1hYmNVpVEkUPAAAWMghz7ukHOak4tcoeAAAsBCztLyDggcAAAvx8FDv4A4BAAC/RwsPAAAWMmST08MxPAbT0stEwQMAgIXo0vIO7hAAAPB7tPAAAGAhp2GT0/CsS8rT86sDCh4AACzkMOFp6Z6eXx1whwAAgN+jhQcAAAvRpeUdFDwAAFjIqQA5Pexw8fT86oA7BAAA/B4tPAAAWMhh2OTwsEvK0/OrAwoeAAAsxBge76DgAQDAQoYJT0s3WGm5TNwhAADg92jhAQDAQg7Z5PDw4Z+enl8dUPAAAGAhp+H5GBynYVIyfowuLQAA4Pdo4QEAwEJOEwYte3p+dUDBAwCAhZyyyenhGBxPz68OKAkBAIDfo4UHAAALsdKyd9DCAwCAhQrG8Hi6edvAgQNVr1493X333V6/dkVQ8AAAALc99thjWrBggdVplBsFDwAAFnLK5nqeVoU3CwYt9+rVS6GhoV6/bkVR8AAAYCHjv7O0PNkMNwueLVu26I477lDjxo1ls9m0fPnyIsekpqaqRYsWCg4OVmxsrLZu3WrSJ7YGBQ8AABbyuHWnAk9bz83NVceOHZWamlrs+0uXLlVycrImTZqkHTt2qGPHjoqPj9eJEyfM+MiWYJYWAAB+Ijs7u9Bru90uu91e5Li+ffuqb9++JcaZPn26Ro0apeHDh0uS5syZo1WrVumtt97SuHHjzE3aSyh4AFiuT90/mB5zzdm/mR6zMtxuH2JqvLV5C02Nh8pn5krLTZs2LbR/0qRJevbZZ92KlZ+fr+3bt2v8+PGufQEBAYqLi9MXX3zhUZ5WouABAMBCFemSKi6GJKWnpyssLMy1v7jWnbKcOnVKDodDUVFRhfZHRUVp7969rtdxcXHavXu3cnNz1aRJEy1btkzXX399BT9B5aPgAQDAT4SFhRUqeCrT+vXrvXIds1DwAABgoar2LK0GDRooMDBQmZmZhfZnZmYqOjratOt4G7O0AACwkBWztEoTFBSkLl26aMOGDf/L0enUhg0bqnSXVVlo4QEAwE9069ZNgYGBSkxMVGJiYonH5eTk6MCBA67Xhw4d0q5duxQREaFmzZopOTlZCQkJ6tq1q7p3764ZM2YoNzfXNWvLF1HwAABgITMHLaelpZVrDM+2bdvUu3dv1+vk5GRJUkJCgubPn6/77rtPJ0+e1MSJE5WRkaFOnTppzZo1RQYy+xIKHgAALGRmwVNevXr1kmEYpR6TlJSkpKQkT9KqUhjDAwAA/B4tPAAAWMiKFp7qyGdaeFJSUtStWzeFhoaqYcOGGjBggPbt22d1WgAAeMSQTHh4KMriMwXP5s2blZiYqC+//FLr1q3TxYsXdfvttys3N9fq1AAAqDAzp6V369ZNbdq0KfGhoNWZz3RprVmzptDr+fPnq2HDhtq+fbtuvvlmi7ICAKDqKO8srerIZwqeX8vKypIkRURElHhMXl6e8vLyXK9//RRZAACsxhge7/CZLq1fcjqdGjNmjHr06KF27dqVeFxKSorCw8Nd26+fIgsAgNWq2krL/sonC57ExETt2bNHS5YsKfW48ePHKysry7Wlp6d7KUMAAFCV+FyXVlJSklauXKktW7aoSZMmpR5rt9tlt9u9lBkAAO6jS8s7fKaFxzAMJSUl6f3339fGjRsVExNjdUoAAHjMMGymbBKztErjMy08iYmJWrRokT744AOFhoYqIyNDkhQeHq6QkBCLswMAwHrM0iqZz7TwzJ49W1lZWerVq5caNWrk2pYuXWp1agAAVJiniw4WbCidz7TwlPWQMytdNeVV02PaKuHj1vvOaXrM8w1Nrpkr4Wf2Ym3zYwZcND9mZajxs/kxAy6a/83p/H3Jsy0rquuI6abHDLhk/mcP6tfJ1Hi3d3vW1HiSFHjK/CU9Vh8y/+vjqxjD4x0+08IDAABQUT7TwgMAgD/65aBjT2KgdBQ8AABYiC4t76DgAQDAQrTweAdjeAAA8BOsw1MyWngAALCQYUKXVkELD+vwlIyCBwAACxmSPF15peou3FJ10KUFAAD8Hi08AABYyCmbbB6uuspKy2Wj4AEAwELM0vIOurQAAIDfo4UHAAALOQ2bbCw8WOlo4QEAwEKGYc4msQ5PaWjhAQDAT7AOT8koeAAAsBCDlr2DggcAAAtR8HgHBQ8AABZi0LJ3MGgZAAD4vWrZwnPL+kkKrG03Ld6l1uYPEAsIcJoeM6v9JdNj/pxj3n2UpJrB5ufodJhf11+6UAk/OhfN/xdawPlA02MageY/tSfojPl55l0y/37WPmZ6SOVGmfvZbc7apsaTpODt/zY9Jv7nl7OsPImB0lXLggcAgKricsHj6Rgek5LxY3RpAQAAv0cLDwAAFmKWlndQ8AAAYCHjv5unMVA6urQAAPATPFqiZLTwAABgITO7tHi0RMkoeAAAsBJ9Wl5BwQMAgJVMaOERg5bLxBgeAADg92jhAQDAQqy07B0UPAAAWIh1eLyDLi0AAOD3aOEBAMBKhs3zQce08JSJggcAAAsxhsc76NICAAB+jxYeAACsxMKDXkHBAwCAhZil5R10aQEA4Cd4eGjJaOEBAMBqJnVJ8fDQklXLgmdI860KqWPeR/+2YWPTYhUIlNP0mNmXQkyPmXspyNR4P+XVMjWeJF24VNP0mOcvmh/zTFZt02M6gh2mxzR+Nv+vjYvh5n+/18wyvwE7P9T8boOwdHO/RjaH+YM5nDd2Mj0m/ocuLe+olgUPAABVBoOWvYIxPAAAwO/RwgMAgKVs/908jYHSUPAAAGAlurS8gi4tAADg9yh4AACwkmHS5md++OEHU+OVq0vr66+/djtwmzZtVKMGPWYAAJSKp6UXq3Xr1urZs6f+8Ic/6O6771ZwcLBH8cpVkXTq1Ek2m01GOR/HGhAQoP3796tly5YeJQcAAKqnHTt2aN68eUpOTlZSUpLuu+8+/eEPf1D37t0rFK/cTTBfffWVIiMjyzzOMAy1a9euQskAAFDdGMblzdMY/qZTp0567bXXNG3aNK1YsULz58/XjTfeqKuuukojRozQ0KFDy1WXFChXwdOzZ0+1bt1adevWLVfQm2++WSEh5q/qCwCA32GWVqlq1KihQYMGqX///nrjjTc0fvx4jR07Vk8//bTuvfdevfTSS2rUqFGZcco1aHnTpk3lLnYk6aOPPirXxQEAAEqzbds2PfLII2rUqJGmT5+usWPH6uDBg1q3bp2OHz+uu+66q1xxGFUMAICVGLRcrOnTp2vevHnat2+f+vXrpwULFqhfv34KCLjcVhMTE6P58+erRYsW5Yrn9rT0wYMH66WXXiqyf+rUqbrnnnvcDQcAQLVmM8zZ/M3s2bP1u9/9TkeOHNHy5cv129/+1lXsFGjYsKH+9re/lSue2wXPli1b1K9fvyL7+/btqy1btrgbDgCA6o11eIq1bt06PfXUU0WGyBiGoaNHj0qSgoKClJCQUK54bhc8OTk5CgoKKrK/Zs2ays7OdjccAABAEa1atdKpU6eK7P/pp58UExPjdjy3C5727dtr6dKlRfYvWbJEbdq0cTsBAACqtYIxPJ5ufqaktf9ycnIqtAih24OWJ0yYoEGDBungwYO65ZZbJEkbNmzQ4sWLtWzZMrcTAACgWjNxWnq3bt0UGBioxMREJSYmepqZJZKTkyVJNptNEydOVK1atVzvORwOffXVV+rUqZPbcd0ueO644w4tX75cf/7zn/Xuu+8qJCREHTp00Pr169WzZ0+3EwAAAOZIS0tTWFiY1Wl4ZOfOnZIut/B88803hYbRBAUFqWPHjho7dqzbcSs0Lb1///7q379/RU6tEoaHZSgs1Lznpm4PPmxarALf50eZHjP9YoTpMffmmLveUo0Ap6nxJMlZCU29AZUwJcLpND9P46JvPB/YaTf/6x5wyfzPXjPH/K+7I8jcr7uzRqCp8SQp5Mdzpse8LcD8Wb3rnD7ay8DCg4Vs2rRJkjR8+HC99tprphVwFV6HZ9u2bfruu+8kXX5QaJcuXUxJCACAaoWCp1jz5s0zNZ7bBc+PP/6oBx54QJ999plr9eWzZ8/qhhtu0JIlS9SkSRNTEwQAANXDoEGDNH/+fIWFhWnQoEGlHvvee++5FdvtNt+RI0fq4sWL+u677/TTTz/pp59+0nfffSen06mRI0e6Gw4AgOqNWVou4eHhstlsrj+XtrnL7RaezZs36/PPP9fVV1/t2nf11Vdr1qxZuummm9xOAACA6syMlZL9ZaXlX3Zjmd2l5XYLT9OmTXXx4sUi+x0Ohxo3bmxKUgAAoHr7+eefdf78edfrI0eOaMaMGVq7dm2F4rld8Lz88st69NFHtW3bNte+bdu26bHHHtMrr7xSoSTckZqaqhYtWig4OFixsbHaunVrpV8TAIBKw6MlinXXXXdpwYIFki6PFe7evbumTZumu+66S7Nnz3Y7ntsFz7Bhw7Rr1y7FxsbKbrfLbrcrNjZWO3bs0IgRIxQREeHazLZ06VIlJydr0qRJ2rFjhzp27Kj4+HidOHHC9GsBAADr7NixwzVU5t1331V0dLSOHDmiBQsWaObMmW7Hc3sMz6uvvuoaUORt06dP16hRozR8+HBJ0pw5c7Rq1Sq99dZbGjdunCU5AQDgCZtMGMNjSiZVy/nz5xUaGipJWrt2rQYNGqSAgABdd911OnLkiNvx3C54hg0bVuJ7P//8s0JCQtxOojzy8/O1fft2jR8/3rUvICBAcXFx+uKLL4o9Jy8vT3l5ea7XPNwUAADf0Lp1ay1fvlwDBw7Uv/71Lz3++OOSpBMnTlRoMUK3u7RGjx5d7P7c3Fz169fP7QTK69SpU3I4HIqKKrwCcVRUlDIyMoo9JyUlpdAUtqZNm1ZafgAAVAjT0os1ceJEjR07Vi1atFBsbKyuv/56SZdbezp37ux2PLcLnlWrVmnSpEmF9uXm5qpPnz66dOmS2wlUpvHjxysrK8u1paenW50SAACFMWi5WHfffbeOHj2qbdu2ac2aNa79t956q1599VW347ndpbV27VrddNNNqlevnsaMGaNz584pPj5eNWrU0OrVq91OoLwaNGigwMBAZWZmFtqfmZmp6OjoYs8pGFQNAAB8T3R0dJHf8d27d69QLLcLnlatWmnNmjXq3bu3AgICtHjxYtntdq1atUq1a9euUBLlERQUpC5dumjDhg0aMGCAJMnpdGrDhg1KSkqqtOsCAFCpeJZWsXJzc/Xiiy9qw4YNOnHihJzOwg8Z/uGHH9yKV6GHh3bo0EErV67UbbfdptjYWK1cubLSBiv/UnJyshISEtS1a1d1795dM2bMUG5urmvWFgAAvoaVlos3cuRIbd68WUOHDlWjRo08niFeroKnc+fOxV7Ibrfr+PHj6tGjh2vfjh07PEqoNPfdd59OnjypiRMnKiMjQ506ddKaNWuKDGQGAAC+bfXq1Vq1alWhGsMT5Sp4CrqQqoKkpCS6sAAA/oMurWLVq1fP1EWMy1Xw/HpWFgAAMAkFT7GmTJmiiRMn6u2331atWrU8jlehMTwAAACVadq0aTp48KCioqLUokUL1axZs9D77g6hKVfBExERof3796tBgwblCtqsWTN98sknat68uVvJAABQ3TBouXhmD6cpV8Fz9uxZrV69WuHh4eUKevr0aTkcDo8Sq0xvZl2hEId5jVvH8uqZFqtAntP8xrfsS+bPpMt1BJkaL6ASfmprBpr/vZj1c7DpMW0B5n/2ALv5n91ZCSu61jhj/ve74fayqmVz2M3/7LUO5pV9kBucQeZ/cOfXe02Puc65zPSYPsuMlZL9cKVls4fTlPtvmYSEBFMvDAAAxBieUpw9e1bvvvuuDh48qCeeeEIRERHasWOHoqKidMUVV7gVq1wFz68X+wEAAKhMX3/9teLi4hQeHq7Dhw9r1KhRioiI0HvvvaejR49qwYIFbsWrhEZfAABQXgVjeDzd/E1ycrKGDRum77//XsHB/xtG0K9fP23ZssXteMzSAgDASnRpFSstLU1z584tsv+KK65QRkaG2/Fo4QEAAG5buXKlrr76al155ZX661//anp8u92u7OzsIvv379+vyMhIt+NR8AAAYCUzurO83MJz6dIlJScna+PGjdq5c6defvllnT592tRr3HnnnXruued08eJFSZLNZtPRo0f11FNPafDgwW7Ho+ABAMBKhkmbF23dulVt27bVFVdcoTp16qhv375au3atqdeYNm2acnJyFBkZqZ9//lk9e/ZU69atFRoaqhdeeMHteG4XPLfccosmT55cZP+ZM2d0yy23uJ0AAADwri1btuiOO+5Q48aNZbPZtHz58iLHpKamqkWLFgoODlZsbKy2bt3qeu/48eOFpoVfccUVOnbsmKk5hoeHa926dVq1apVmzpyppKQkffTRR9q8ebNq167tdjy3By1//PHH+uabb7Rz504tXLjQddH8/Hxt3rzZ7QQAAKjWLBi0nJubq44dO2rEiBEaNGhQkfeXLl2q5ORkzZkzR7GxsZoxY4bi4+O1b98+NWzY0MNky+Z0OjV//ny99957Onz4sGw2m2JiYhQdHS3DMGSzub/QYoW6tNavX6+MjAxdd911Onz4cEVCAAAAmTstPTs7u9CWl1f8St59+/bV888/r4EDBxb7/vTp0zVq1CgNHz5cbdq00Zw5c1SrVi299dZbkqTGjRsXatE5duyYGjdubMr9MAxDd955p0aOHKljx46pffv2atu2rY4cOaJhw4aVmHNZKlTwNGrUSJs3b1b79u3VrVs3ffzxxxW6OAAAME/Tpk0VHh7u2lJSUtyOkZ+fr+3btysuLs61LyAgQHFxcfriiy8kSd27d9eePXt07Ngx5eTkaPXq1YqPjzflM8yfP19btmzRhg0btHPnTi1evFhLlizR7t27tX79em3cuNHtRQelCnRpFTQj2e12LVq0SM8//7z69Omjp556yu2LAwAA86SnpyssLMz12m63ux3j1KlTcjgcioqKKrQ/KipKe/defq5ajRo1NG3aNPXu3VtOp1NPPvmk6tev71ny/7V48WI9/fTT6t27d5H3brnlFo0bN04LFy7Ugw8+6FZctwsewyjcUfjMM8/o2muv5VlbAABUhIljeMLCwgoVPJXpzjvv1J133ml63K+//lpTp04t8f2+fftq5syZbsd1u+A5dOhQkQV/Bg8erGuuuUbbtm1zOwEAAKozMx4NYeajJRo0aKDAwEBlZmYW2p+Zmano6GjzLlSCn376qUjr0i9FRUXpzJkzbsd1ewxP8+bNix0d3bZtW1p5AADwcUFBQerSpYs2bNjg2ud0OrVhwwZdf/31lX59h8OhGjVKbo8JDAzUpUuX3I7Ls7QAALCaSS003bp1U2BgoBITE5WYmFjicTk5OTpw4IDr9aFDh7Rr1y5FRESoWbNmSk5OVkJCgrp27aru3btrxowZys3N1fDhw81JtBSGYWjYsGEljj8qaeZZWSh4AACwkoljeNLS0so1hmfbtm2FBgUnJydLkhISEjR//nzdd999OnnypCZOnKiMjAx16tRJa9asKbWrySzl6S1yd8CyRMEDAEC106tXryKTkH4tKSlJSUlJXsrof+bNm1cpcatlwfPF2VaqeTHItHjfnjS/4s3PN/9LU6OG0/SYFy8GmhqvRg2HqfEk6edzwabHDKhp/r105Jv/aLuAszVNj1nzgvsrnJYlIN/8mDbzv0RyhJgf80J9c79GQefM/xlC5apqg5b9VbUseAAAqDIseLREdcTT0gEA8BPdunVTmzZtlJqaanUqVQ4tPAAAWMjMLq3yDlqujih4AACwEl1aXkGXFgAA8Hu08AAAYCVaeLyCggcAAAsxLd07KHgAALASLTxewRgeAAD8BNPSS0YLDwAAVrLgWVrVEQUPAAAWYgyPd9ClBQAA/B4tPAAAWIlBy15BwQMAgIXo0vIOurQAAIDfo+ABAMBKhkmbmJZeGrq0AACwEtPSvYIWHgAA4Pdo4QEAwEK2/26exkDpqmXB83b310xt8us2bLppsQoEhJv/7Vsz1/xh/AF1zc3TYTc1nCQp4qT5n9vmMD2k8sMq4a+sSmjDNSohZkC++TGNQPNjBv9k/vfSxdrm3tDwHRmmxpOk1c5lpsfELzAt3SuqZcEDAEBVwbR072AMDwAA8Hu08AAAYCW6tLyCggcAAKtRsFQ6urQAAPATLDxYMlp4AACwkJmDlll4sGQUPAAAWIkxPF5BlxYAAPB7tPAAAGAh1uHxDgoeAACsRJeWV9ClBQAA/B4tPAAAWIguLe+g4AEAwEp0aXkFBQ8AAFai4PEKxvAAAOAnWGm5ZLTwAABgIVZa9g4KHgAArESXllfQpQUAAPweLTwmSJufbHUKQLH6XvGo6TFXH5tleszK0KfuH0yPuebs30yPCdgMQzbDsyYaT8+vDih4AACwEl1aXuETXVqHDx/WH/7wB8XExCgkJEStWrXSpEmTlJ+fb3VqAADAB/hEC8/evXvldDo1d+5ctW7dWnv27NGoUaOUm5urV155xer0AACoMFZa9g6fKHj69OmjPn36uF63bNlS+/bt0+zZsyl4AAC+jS4tr/CJgqc4WVlZioiIKPWYvLw85eXluV5nZ2dXdloAAKAK8okxPL924MABzZo1Sw899FCpx6WkpCg8PNy1NW3a1EsZAgBQPgVdWp5uKJ2lBc+4ceNks9lK3fbu3VvonGPHjqlPnz665557NGrUqFLjjx8/XllZWa4tPT29Mj8OAADuM0zaUCpLu7T+3//7fxo2bFipx7Rs2dL15+PHj6t379664YYb9Oabb5YZ3263y263e5omAACVhkHL3mFpwRMZGanIyMhyHXvs2DH17t1bXbp00bx58xQQ4JO9cQAAwAI+UTUcO3ZMvXr1UrNmzfTKK6/o5MmTysjIUEZGhtWpAQDgGRO7tHhaesl8YpbWunXrdODAAR04cEBNmjQp9J7BctoAAB9nVpcUT0svmU+08AwbNkyGYRS7AQAAlMUnWngAAPBbhnF58zQGSkXBAwCAhZil5R0+0aUFAADgCVp4AACwEs/S8goKHgAALGRzXt48jYHS0aUFAAD8Hi08AABYiS4tr6DgAfzY6mOzrE7BMmvO/s3qFIByYZaWd1DwAABgJdbh8QrG8AAAAL9HCw8AABaiS8s7KHgAALASg5a9gi4tAADg92jhAQDAQnRpeQcFDwAAVmKWllfQpQUAAPweBQ8AABYq6NLydJOkbt26qU2bNkpNTbX2Q1VBdGkBAGAlE2dppaWlKSwszNOM/BItPAAAwO/RwgMAgIWYpeUdFDwAAFjJaVzePI2BUlHwAABgJVZa9grG8AAAAL9HCw8AABayyYQxPKZk4t8oeAAAsBIrLXsFXVoAAMDv0cIDAICFmJbuHRQ8AABYiVlaXkGXFgAA8Hu08AAAYCGbYcjm4aBjT8+vDih4AACwkvO/m6cxUCq6tAAAgN+jhQcAAAvRpeUdFDwAAFiJWVpeQcEDAICVWGnZKxjDAwAA/B4tPAAAWIiVlr2DggcAACvRpeUVdGkBAAC/RwsPAAAWsjkvb57GQOkoeAAAsBJdWl5BlxYAAPB7FDwAAFjJMGmrYgYOHKh69erp7rvvtjoVSRQ8AABYquDREp5uVc1jjz2mBQsWWJ2GCwUPAAAwXa9evRQaGmp1Gi4UPAAAWKlg0LKnmxu2bNmiO+64Q40bN5bNZtPy5cuLHJOamqoWLVooODhYsbGx2rp1q0kf2BoUPAAAWMmQ5PRwc7NHKzc3Vx07dlRqamqx7y9dulTJycmaNGmSduzYoY4dOyo+Pl4nTpxwHdOpUye1a9euyHb8+HH3kvESpqUDAGAhM8bgFJyfnZ1daL/dbpfdbi9yfN++fdW3b98S402fPl2jRo3S8OHDJUlz5szRqlWr9NZbb2ncuHGSpF27dnmUs7fRwgMAgJ9o2rSpwsPDXVtKSorbMfLz87V9+3bFxcW59gUEBCguLk5ffPGFmel6FS08AABYyZAJCw9e/l96errCwsJcu4tr3SnLqVOn5HA4FBUVVWh/VFSU9u7dW+44cXFx2r17t3Jzc9WkSRMtW7ZM119/vdv5mIWCBwAAK5m40nJYWFihgsdK69evtzqFQujSAgAALg0aNFBgYKAyMzML7c/MzFR0dLRFWXmOggcAACt5OkOrYDNJUFCQunTpog0bNvwvRadTGzZssLRLylN0aQEAYCEzZ2l169ZNgYGBSkxMVGJiYonH5+Tk6MCBA67Xhw4d0q5duxQREaFmzZopOTlZCQkJ6tq1q7p3764ZM2YoNzfXNWvLF1HwAADgJ9LS0so1hmfbtm3q3bu363VycrIkKSEhQfPnz9d9992nkydPauLEicrIyFCnTp20Zs2aIgOZfQkFDwAAVjJx0HJ59erVS0YZ5yQlJSkpKcmTrKoUCh4AAKxkQcFTHTFoGQAA+D1aeAAAsBItPF5BCw8AAFYycVp6t27d1KZNmxIfClqd0cIDAICFzJyWXt5ZWtURLTwAAMDv+VzBk5eXp06dOslms/nco+kBACiiYAyPpxtK5XMFz5NPPqnGjRtbnQYAAOZwGuZsKJVPFTyrV6/W2rVr9corr1idCgAA8CE+U/BkZmZq1KhR+vvf/65atWpZnQ4AAOYwsUuLWVol84lZWoZhaNiwYfrTn/6krl276vDhw+U6Ly8vT3l5ea7X2dnZlZQhAAAVZcYYHGZplcXSFp5x48bJZrOVuu3du1ezZs3SuXPnNH78eLfip6SkKDw83LU1bdq0kj4JAACoymxGWU8Pq0QnT57U6dOnSz2mZcuWuvfee/Xhhx/KZrO59jscDgUGBmrIkCF6++23iz23uBaepk2bKisriwoYAFCi7OxshYeHV+rvi4JrxMU8qhoBdo9iXXLmaf2hWfx+K4WlXVqRkZGKjIws87iZM2fq+eefd70+fvy44uPjtXTpUsXGxpZ4nt1ul93u2TcRAACVymmooEvKsxgojU+M4WnWrFmh13Xq1JEktWrVSk2aNLEiJQAA4EN8ouABAMBvGc7Lm6cxUCqfmZb+Sy1atJBhGOrUqZPVqQAA4BmmpXsFLTwAAFjJxDE8TEsvmU+28AAAALiDFh4AAKxkxsM/eXhomSh4AACwkiETCh5TMvFrdGkBAAC/RwsPAABWokvLKyh4AACwktMpycN1dJysw1MWurQAAIDfo+ABAMBKLDzoFXRpAQBgJRPH8LDwYMlo4QEAAH6PFh4AAKxk4qMlUDIKHgAALGQYThkePu3c0/OrAwoeAACsZBiet9CwDk+ZGMMDAAD8Hi08AABYyTBhDA8tPGWi4AEAwEpOp2TzcAwOY3jKRJcWAADwexQ8AABYiZWWvYIuLQAALGQ4nTI87NIqmJbOSsslo4UHAAD4PVp4AACwErO0vIKCBwAAKzkNyUbBU9no0gIAAH6PFh4AAKxkGJI8XYeHFp6yUPAAAGAhw2nI8LBLy6DgKRMFDwAAVjKc8ryFh5WWy8IYHgAA4Pdo4QEAwEJ0aXkHBQ8AAFaiS8srqlXBU1ABZ2dnW5wJAKAqK/g94Y2Wk0u66PG6g5d00Zxk/Fi1KnhOnz4tSWratKnFmQAAfMHp06cVHh5eKbGDgoIUHR2tTzM+MiVedHS0goKCTInlj2xGNer4O3v2rOrVq6ejR49W2jewv8rOzlbTpk2Vnp7Og+ncxL3zDPev4rh3FZeVlaVmzZrpzJkzqlu3bqVd58KFC8rPzzclVlBQkIKDg02J5Y+qVQtPQMDlSWnh4eH88FdQWFgY966CuHee4f5VHPeu4gp+b1SW4OBgihQvYVo6AADwexQ8AADA71Wrgsdut2vSpEmy2+1Wp+JzuHcVx73zDPev4rh3Fce98z/VatAyAAConqpVCw8AAKieKHgAAIDfo+ABAAB+j4IHAAD4vWpT8KSmpqpFixYKDg5WbGystm7danVKPiElJUXdunVTaGioGjZsqAEDBmjfvn1Wp+WTXnzxRdlsNo0ZM8bqVHzCsWPH9Pvf/17169dXSEiI2rdvr23btlmdlk9wOByaMGGCYmJiFBISolatWmnKlCk8UbsYW7Zs0R133KHGjRvLZrNp+fLlhd43DEMTJ05Uo0aNFBISori4OH3//ffWJAuPVIuCZ+nSpUpOTtakSZO0Y8cOdezYUfHx8Tpx4oTVqVV5mzdvVmJior788kutW7dOFy9e1O23367c3FyrU/MpaWlpmjt3rjp06GB1Kj7hzJkz6tGjh2rWrKnVq1fr22+/1bRp01SvXj2rU/MJL730kmbPnq3XX39d3333nV566SVNnTpVs2bNsjq1Kic3N1cdO3ZUampqse9PnTpVM2fO1Jw5c/TVV1+pdu3aio+P14ULF7ycKTxmVAPdu3c3EhMTXa8dDofRuHFjIyUlxcKsfNOJEycMScbmzZutTsVnnDt3zrjyyiuNdevWGT179jQee+wxq1Oq8p566injxhtvtDoNn9W/f39jxIgRhfYNGjTIGDJkiEUZ+QZJxvvvv+967XQ6jejoaOPll1927Tt79qxht9uNxYsXW5AhPOH3LTz5+fnavn274uLiXPsCAgIUFxenL774wsLMfFNWVpYkKSIiwuJMfEdiYqL69+9f6HsQpVuxYoW6du2qe+65Rw0bNlTnzp31l7/8xeq0fMYNN9ygDRs2aP/+/ZKk3bt369NPP1Xfvn0tzsy3HDp0SBkZGYV+dsPDwxUbG8vvDx/k9w8PPXXqlBwOh6Kiogrtj4qK0t69ey3Kyjc5nU6NGTNGPXr0ULt27axOxycsWbJEO3bsUFpamtWp+JQffvhBs2fPVnJysp5++mmlpaVp9OjRCgoKUkJCgtXpVXnjxo1Tdna2rrnmGgUGBsrhcOiFF17QkCFDrE7Np2RkZEhSsb8/Ct6D7/D7ggfmSUxM1J49e/Tpp59anYpPSE9P12OPPaZ169bxNGQ3OZ1Ode3aVX/+858lSZ07d9aePXs0Z84cCp5y+Mc//qGFCxdq0aJFatu2rXbt2qUxY8aocePG3D9UW37fpdWgQQMFBgYqMzOz0P7MzExFR0dblJXvSUpK0sqVK7Vp0yY1adLE6nR8wvbt23XixAn95je/UY0aNVSjRg1t3rxZM2fOVI0aNeRwOKxOscpq1KiR2rRpU2jftddeq6NHj1qUkW954oknNG7cON1///1q3769hg4dqscff1wpKSlWp+ZTCn5H8PvDP/h9wRMUFKQuXbpow4YNrn1Op1MbNmzQ9ddfb2FmvsEwDCUlJen999/Xxo0bFRMTY3VKPuPWW2/VN998o127drm2rl27asiQIdq1a5cCAwOtTrHK6tGjR5HlD/bv36/mzZtblJFvOX/+vAICCv/1HhgYKKfTaVFGvikmJkbR0dGFfn9kZ2frq6++4veHD6oWXVrJyclKSEhQ165d1b17d82YMUO5ubkaPny41alVeYmJiVq0aJE++OADhYaGuvqtw8PDFRISYnF2VVtoaGiRsU61a9dW/fr1GQNVhscff1w33HCD/vznP+vee+/V1q1b9eabb+rNN9+0OjWfcMcdd+iFF15Qs2bN1LZtW+3cuVPTp0/XiBEjrE6tysnJydGBAwdcrw8dOqRdu3YpIiJCzZo105gxY/T888/ryiuvVExMjCZMmKDGjRtrwIAB1iWNirF6mpi3zJo1y2jWrJkRFBRkdO/e3fjyyy+tTsknSCp2mzdvntWp+SSmpZffhx9+aLRr186w2+3GNddcY7z55ptWp+QzsrOzjccee8xo1qyZERwcbLRs2dL4v//7PyMvL8/q1KqcTZs2Fft3XEJCgmEYl6emT5gwwYiKijLsdrtx6623Gvv27bM2aVSIzTBYehMAAPg3vx/DAwAAQMEDAAD8HgUPAADwexQ8AADA71HwAAAAv0fBAwAA/B4FDwAA8HsUPIAfGjZsmGw2m2w2m5YvXy5JOnz4sGw2m3bt2lVp150/f77rumPGjKm06wCAuyh4AD/Vp08f/ec//1Hfvn29ds377rtP//nPf3jOEIAqp1o8SwvwV/n5+QoKCir2Pbvd7vUnOoeEhCgkJKTEnADAKrTwAD6kV69eSkpK0pgxY9SgQQPFx8dXOJbD4dCIESN0zTXX6OjRo5Ikm82m2bNnq2/fvgoJCVHLli317rvvFjrvxx9/1AMPPKCIiAjVrl1bXbt21VdffeXR5wKAykbBA/iYt99+W0FBQfrss880Z86cCsXIy8vTPffco127dumTTz5Rs2bNXO9NmDBBgwcP1u7duzVkyBDdf//9+u677yRdfrJ0z549dezYMa1YsUK7d+/Wk08+KafTacpnA4DKQpcW4GOuvPJKTZ06tcLn5+TkqH///srLy9OmTZsUHh5e6P177rlHI0eOlCRNmTJF69at06xZs/TGG29o0aJFOnnypNLS0hQRESFJat26dcU/DAB4CS08gI/p0qWLR+c/8MADys3N1dq1a4sUO5KKDDi+/vrrXS08u3btUufOnV3FDgD4CgoewMfUrl3bo/P79eunr7/+Wl988YXb54aEhHh0bQCwCgUPUM08/PDDevHFF3XnnXdq8+bNRd7/8ssvi7y+9tprJUkdOnTQrl279NNPP3klVwAwCwUPUA09+uijev755/Xb3/5Wn376aaH3li1bprfeekv79+/XpEmTtHXrViUlJUm63B0WHR2tAQMG6LPPPtMPP/ygf/7znxVqLQIAb6LgAaqpMWPGaPLkyerXr58+//xz1/7JkydryZIl6tChgxYsWKDFixerTZs2kqSgoCCtXbtWDRs2VL9+/dS+fXu9+OKLCgwMtOpjAEC5MEsL8CEff/xxhc9t0aKFDMMotC85OVnJycmF9jVu3Fhr164tMU7z5s2LrM0DAFUdLTyAn1q5cqXq1KmjlStXeu2aCxcuVJ06dfTJJ5947ZoAUB4249f/5APg806cOKHs7GxJUqNGjco9s8tms+n999/XgAEDKnTdc+fOKTMzU5JUt25dNWjQoEJxAMBsFDwAAMDv0aUFAAD8HgUPAADwexQ8AADA71HwAAAAv0fBAwAA/B4FDwAA8HsUPAAAwO9R8AAAAL9HwQMAAPze/wcNl54TtSa2qAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(density.T, origin='lower', aspect='auto',\n", + " extent=[r_min, r_max, z_min, z_max], cmap='viridis', norm=colors.LogNorm())\n", + "plt.colorbar(label='Density')\n", + "plt.xlabel('r [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.title('Density Distribution in r-z Plane')\n", + "plt.savefig('./figures/spheroid_density.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "501bdeff", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_laplacian_on_grid(potential, theta, r_bins, z_bins):\n", + " \"\"\"\n", + " Computes nabla^2 Phi (Laplacian) on the centers of the R-Z bins.\n", + " \"\"\"\n", + " \n", + " # 1. Define the Laplacian for a SINGLE point (x, y, z)\n", + " def potential_wrapper(x, y, z):\n", + " return potential(x, y, z, *theta)\n", + "\n", + " def laplacian_fn(x, y, z):\n", + " # jax.hessian returns a 3x3 matrix of second derivatives\n", + " # argnums=(0, 1, 2) makes it return a nested tuple structure relative to x,y,z\n", + " # However, it's easier to treat input as a vector for Hessian logic,\n", + " # but since our function takes scalars, we can just sum unmixed 2nd derivatives.\n", + " \n", + " # Method A: Direct curvature calculation (faster/simpler than full Hessian)\n", + " # We use simple nested grad or specific derivative operators\n", + " d2dx2 = jax.grad(lambda x_: jax.grad(potential_wrapper, argnums=0)(x_, y, z))(x)\n", + " d2dy2 = jax.grad(lambda y_: jax.grad(potential_wrapper, argnums=1)(x, y_, z))(y)\n", + " d2dz2 = jax.grad(lambda z_: jax.grad(potential_wrapper, argnums=2)(x, y, z_))(z)\n", + " \n", + " return d2dx2 + d2dy2 + d2dz2\n", + " \n", + " # 2. Vectorize the Laplacian function\n", + " # Maps over inputs x, y, z\n", + " laplacian_vmap = jax.vmap(laplacian_fn, in_axes=(0, 0, 0))\n", + "\n", + " # 3. Setup Grid (Bin Centers)\n", + " r_centers = 0.5 * (r_bins[:-1] + r_bins[1:])\n", + " z_centers = 0.5 * (z_bins[:-1] + z_bins[1:])\n", + " \n", + " # Create Meshgrid (indexing='ij' matches density shape)\n", + " R_grid, Z_grid = jnp.meshgrid(r_centers, z_centers, indexing='ij')\n", + "\n", + " # 4. Convert R-Z to Cartesian X-Y-Z\n", + " # We evaluate at y=0, so x=R\n", + " X_flat = R_grid.flatten()\n", + " Y_flat = jnp.zeros_like(X_flat)\n", + " Z_flat = Z_grid.flatten()\n", + "\n", + " # 5. Compute\n", + " laplacian_flat = laplacian_vmap(X_flat, Y_flat, Z_flat)\n", + " \n", + " # Reshape back to (N_r, N_z)\n", + " laplacian_grid = laplacian_flat.reshape(R_grid.shape)\n", + " \n", + " return laplacian_grid" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "fd192c7f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Laplacian shape: (19, 19)\n" + ] + } + ], + "source": [ + "\n", + "nabla2_Phi = compute_laplacian_on_grid(Phi_spheroid, theta_spheroid, rbin, zbin)\n", + "\n", + "print(\"Laplacian shape:\", nabla2_Phi.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "73cbe1fd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(nabla2_Phi.T, origin='lower', aspect='auto',\n", + " extent=[r_min, r_max, z_min, z_max], cmap='viridis', norm=colors.LogNorm())\n", + "plt.colorbar(label='Density')\n", + "plt.xlabel('r [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.title('Laplacian of Potential in r-z Plane')\n", + "plt.savefig('./figures/spheroid_laplacian.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "2fea078c", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix.constants import G\n", + "\n", + "def compute_loss(key, params, Phi, theta, n_candidates, envelope_max, rbin, zbin):\n", + " candidates, samples, soft_weights = sampling.sample_df_potential(f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, tau=0.01)\n", + " phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi, theta)\n", + " x = phase_space_coords[:, 0]\n", + " y = phase_space_coords[:, 1]\n", + " z = phase_space_coords[:, 2]\n", + " density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)\n", + " nabla2_Phi = compute_laplacian_on_grid(Phi, theta, r_bins=rbin, z_bins=zbin)\n", + " lossplane = (4*jnp.pi*G*density - nabla2_Phi)\n", + " lossplane = lossplane * mask\n", + "\n", + " return lossplane" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "015ad00f", + "metadata": {}, + "outputs": [], + "source": [ + "lossplane = compute_loss(key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, rbin, zbin)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "91eef618", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(lossplane.T, origin='lower', aspect='auto',\n", + " extent=[r_min, r_max, z_min, z_max], cmap='viridis')#, norm=colors.LogNorm())\n", + "plt.colorbar(label='loss')\n", + "plt.xlabel('r [kpc]')\n", + "plt.ylabel('z [kpc]')\n", + "plt.title('Loss Distribution in r-z Plane')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "446aaabd", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_lossvalue(key, params, Phi, theta, n_candidates, envelope_max, rbin, zbin):\n", + " candidates, samples, soft_weights = sampling.sample_df_potential(f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, tau=0.01)\n", + " phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi, theta)\n", + " x = phase_space_coords[:, 0]\n", + " y = phase_space_coords[:, 1]\n", + " z = phase_space_coords[:, 2]\n", + " density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)\n", + " nabla2_Phi = compute_laplacian_on_grid(Phi, theta, r_bins=rbin, z_bins=zbin)\n", + " lossplane = (4*jnp.pi*G*density - nabla2_Phi)\n", + " lossplane = lossplane * mask\n", + " loss = jnp.sum(lossplane**2)\n", + "\n", + " return loss" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5d920aa0", + "metadata": {}, + "outputs": [], + "source": [ + "loss = compute_lossvalue(key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, rbin, zbin)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "f36d2e8b", + "metadata": {}, + "outputs": [], + "source": [ + "val_and_grad_fn = jax.value_and_grad(compute_lossvalue, argnums=3)\n", + "loss_val, theta_gradient = val_and_grad_fn(key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, rbin, zbin)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "a6922f57", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.729519e-02 -4.298330e+09]\n" + ] + } + ], + "source": [ + "print(theta_gradient)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "f90f4796", + "metadata": {}, + "outputs": [], + "source": [ + "import optax\n", + "#from tqdm import tqdm\n", + "import jax.numpy as jnp\n", + "import jax\n", + "\n", + "def adam_optimizer(key, params, Phi_spheroid, theta_init, n_candidates, envelope_max, rbin, zbin, learning, num_iterations=2000):\n", + " # 1. Start in Log Space\n", + " current_log_theta = jnp.log(theta_init)\n", + " \n", + " # 2. Initialize the optimizer on the log values\n", + " optimizer = optax.adam(learning)\n", + " opt_state = optimizer.init(current_log_theta)\n", + "\n", + " # 3. Define the compiled update step\n", + " @jax.jit\n", + " def step(log_theta, state, step_key):\n", + " # We define a helper to ensure JAX differentiates through the exp()\n", + " def loss_wrapper(lt):\n", + " t_phys = jnp.exp(lt)\n", + " return compute_lossvalue(step_key, params, Phi_spheroid, t_phys, \n", + " n_candidates, envelope_max, rbin, zbin)\n", + " \n", + " # Now we differentiate w.r.t 'log_theta' directly\n", + " loss_val, grads = jax.value_and_grad(loss_wrapper)(log_theta)\n", + " \n", + " updates, new_state = optimizer.update(grads, state, log_theta)\n", + " new_log_theta = optax.apply_updates(log_theta, updates)\n", + " \n", + " return new_log_theta, new_state, loss_val\n", + "\n", + " loss_history = []\n", + " theta_history = []\n", + " \n", + " # 4. The Training Loop\n", + " #pbar = tqdm(range(num_iterations), desc=\"Optimizing Physics Parameters\")\n", + "\n", + " for i in range(num_iterations):\n", + " key, subkey = jax.random.split(key)\n", + " \n", + " current_log_theta, opt_state, loss_val = step(current_log_theta, opt_state, subkey)\n", + " \n", + " # Convert back to physical space for your records\n", + " phys_theta = jnp.exp(current_log_theta)\n", + " \n", + " loss_history.append(float(loss_val))\n", + " theta_history.append(phys_theta)\n", + " \n", + " if i % 100 == 0:\n", + " print(f\"Iteration {i}, Loss: {loss_val:.4f}, Theta: {phys_theta}\")\n", + " #pbar.set_postfix({\"Loss\": f\"{loss_val:.2e}\", \"Theta\": [f\"{t:.2e}\" for t in phys_theta]})\n", + "\n", + " return jnp.exp(current_log_theta), loss_history, theta_history" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "8d8bbbe9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0, Loss: 8330837504.0000, Theta: [9.5123053e+11 1.0512709e+01]\n", + "Iteration 100, Loss: 24038360.0000, Theta: [4.0904812e+11 2.4823328e+01]\n", + "Iteration 200, Loss: 12412055.0000, Theta: [3.7388101e+11 2.7430676e+01]\n", + "Iteration 300, Loss: 7653841.5000, Theta: [3.5014712e+11 2.9525129e+01]\n", + "Iteration 400, Loss: 4957760.0000, Theta: [3.3295617e+11 3.1253101e+01]\n", + "Iteration 500, Loss: 3471157.7500, Theta: [3.1970102e+11 3.2729240e+01]\n", + "Iteration 600, Loss: 2742568.7500, Theta: [3.0901908e+11 3.4022411e+01]\n", + "Iteration 700, Loss: 2143130.0000, Theta: [3.0013145e+11 3.5178055e+01]\n", + "Iteration 800, Loss: 1720204.3750, Theta: [2.9252036e+11 3.6230270e+01]\n", + "Iteration 900, Loss: 1431017.1250, Theta: [2.8588969e+11 3.7198826e+01]\n", + "Iteration 1000, Loss: 1205846.1250, Theta: [2.8001167e+11 3.8099796e+01]\n", + "Iteration 1100, Loss: 1014931.5625, Theta: [2.7475658e+11 3.8942631e+01]\n", + "Iteration 1200, Loss: 870638.2500, Theta: [2.7000976e+11 3.9735416e+01]\n", + "Iteration 1300, Loss: 765852.0000, Theta: [2.6565334e+11 4.0491352e+01]\n", + "Iteration 1400, Loss: 669573.0000, Theta: [2.6165602e+11 4.1209515e+01]\n", + "Iteration 1500, Loss: 603152.4375, Theta: [2.5794752e+11 4.1897968e+01]\n", + "Iteration 1600, Loss: 533606.7500, Theta: [2.5448808e+11 4.2560738e+01]\n", + "Iteration 1700, Loss: 464136.8750, Theta: [2.5124751e+11 4.3200844e+01]\n", + "Iteration 1800, Loss: 416823.5312, Theta: [2.4819063e+11 4.3821556e+01]\n", + "Iteration 1900, Loss: 383226.2500, Theta: [2.4531363e+11 4.4422390e+01]\n", + "Iteration 2000, Loss: 356422.5938, Theta: [2.425736e+11 4.500790e+01]\n", + "Iteration 2100, Loss: 314047.7500, Theta: [2.3996255e+11 4.5580280e+01]\n", + "Iteration 2200, Loss: 289426.6250, Theta: [2.3747153e+11 4.6139694e+01]\n", + "Iteration 2300, Loss: 261323.8906, Theta: [2.3509828e+11 4.6686432e+01]\n", + "Iteration 2400, Loss: 244785.1094, Theta: [2.3280514e+11 4.7224632e+01]\n", + "Iteration 2500, Loss: 221925.5938, Theta: [2.3061001e+11 4.7751953e+01]\n", + "Iteration 2600, Loss: 205120.9531, Theta: [2.2848699e+11 4.8271751e+01]\n", + "Iteration 2700, Loss: 191965.3750, Theta: [2.2644916e+11 4.8782066e+01]\n", + "Iteration 2800, Loss: 179712.5000, Theta: [2.2446975e+11 4.9286312e+01]\n", + "Iteration 2900, Loss: 163858.3125, Theta: [2.2255305e+11 4.9783997e+01]\n" + ] + } + ], + "source": [ + "learning = 5e-2\n", + "theta_opt, loss_hist, theta_hist = adam_optimizer(key, params, Phi_spheroid, theta_spheroid, n_candidates, envelope_max, rbin, zbin, learning, num_iterations=3000)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "1eb9a7fc", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "def plot_training_results(loss_history, theta_history):\n", + " # Convert lists to numpy arrays\n", + " loss_history = np.array(loss_history)\n", + " theta_history = np.array(theta_history) # Shape: (iterations, 2)\n", + "\n", + " # Create 3 subplots side-by-side\n", + " fig, ax = plt.subplots(1, 3, figsize=(18, 5))\n", + "\n", + " # 1. Loss History (Log Scale)\n", + " ax[0].plot(loss_history, color='black', lw=1.5)\n", + " ax[0].set_yscale('log')\n", + " ax[0].set_title(\"Total Loss Convergence\", fontsize=14)\n", + " ax[0].set_xlabel(\"Iteration\")\n", + " ax[0].set_ylabel(\"Loss\")\n", + " ax[0].grid(True, which=\"both\", ls=\"-\", alpha=0.15)\n", + "\n", + " # 2. Theta 1 Evolution\n", + " ax[1].plot(theta_history[:, 0], color='tab:blue', lw=2)\n", + " ax[1].set_title(r\"Parameter $\\theta_1$: Mass\", fontsize=14)\n", + " ax[1].set_xlabel(\"Iteration\")\n", + " ax[1].set_ylabel(\"Value\")\n", + " ax[1].grid(True, alpha=0.2)\n", + "\n", + " # 3. Theta 2 Evolution\n", + " ax[2].plot(theta_history[:, 1], color='tab:orange', lw=2)\n", + " ax[2].set_title(r\"Parameter $\\theta_2: a$\", fontsize=14)\n", + " ax[2].set_xlabel(\"Iteration\")\n", + " ax[2].set_ylabel(\"Value\")\n", + " ax[2].grid(True, alpha=0.2)\n", + "\n", + " plt.tight_layout()\n", + " plt.savefig('./figures/spheroid_loss_parameter_history.jpeg')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "57edf0f4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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c8jOH/MwhP3PIzxzW9Ct/GOkHAABKyz333KNBgwYpKSlJO3fu1MMPPyyHw6Grr75aLpdLN9xwg1JSUlStWjUlJCTo9ttvV7du3dS1a1erSwcAAJKUlyvtWC1t/ML3Z9dPx9+3djup2d9NvsQukiOy9OoMI5p+J8GafmVXhR5qXArIzxzyM4f8zCE/c8rCVAsovuCmn4WFAACACu+vv/7S1VdfrQMHDqhmzZo677zztGLFCtWsWVOS9MILL8hut2vo0KHyer3q37+/XnnlFYurBgCgkjt6UNq0yNfk27RQyjhY9H4xLqlJL6lpX9//JtQt3TpLCU0/C0RG+jrG/mk+AQAAUDR70PSedP0AAED4zJw584Tvx8TEBJaFAQAAFjEMaffPvibf71/41ukz8oret24HqVk/X6Ov/lmSo+K3xCr+T1gG+Zt+hmEoNzdXERF8DAAAAEWxMb0nAAAAAACVW6Zb+mOxtHGBtHGhlL676P2i4qUmPX2NvmZ9pfg6pVpmWUC36SQMwwj5U+UFm3xZWVlyOBwhPX5l4P9ceOK/ZMjPHPIzh/zMIT9zwp0fn0voFRzpl3ucB/cAAAAAAEAFYhjS/t+l3xf4RvRtXy7l5RS9b82WvgZfs/6+tfkiokq31jKGpt8x/NM05ObmSpI8Hk/Im3JZWVmBrw8fPqy8PO5gnSrDMJSRkSGJ9ZNKgvzMIT9zyM8c8jMn3Pl5PJ6QH7OyszPSDwAAAACAii/rqLT1G1+Tb+MX0uHtRe8XESs1vkBq/ve0nacllW6dZRxNv2MkJycrOTlZbrdbLpdLTqdTTqczpOeIiooK+jrUx68M/CMpnE4nN71LgPzMIT9zyM8c8jMn3Pn5HxpC6BRs+jGSEgAAAACACuTgFmnjl74m39ZvpJzMovc7rZFvJF+zflKjc6XI2FItszyh6XcSNpst5DcF/Wv6SVJOTg43bUvI/9mQX8mQnznkZw75mUN+5oQzPz6T0LPb87/Oo+cHAAAAAED5lZMlbV+W3+jb/3vR+9kjfc29Zv18f6o3lbjnUiw0/Sxgs9kUERGhnJwcZWdnW10OAABAmcX0ngAAAAAAlGPunflNvj8WS1npRe8XX+/vtfn6Sad3l6LjS7XMioKmn0UiIyNp+gEAAJxEcNPPwkIAAAAAAMDJ5eZIO76Xfl/ga/bt+aXo/Wx2KbHL342+/lLtNozmCwGafidhGEZY1o+JjIxURkaGsrKyWJ+mBPyfC9mVDPmZQ37mkJ855GdOuPPjcwk9e4HrffIFAAAAAKAMOnpQ2rRQ+n2+tGmRlHm46P3iqktN+0rN+0lNekmxp5VqmZUBTb9jpKamKjU1Vbm5uZIkj8cjh8MR8vNERPiid7vd8ng8IT9+RWcYhjIyMiSxflJJkJ855GcO+ZlDfuaEOz/+Tg89GyP9AAAAAAAoWwzDtx7f7/OlDfOlP1dIRl7R+9Y7wzeSr1k/39d2e+nWWsnQ9DtGcnKykpOT5Xa75XK55HQ65XQ6Q36eqKgoSb7mXziOX9H5n/R3Op3c9C4B8jOH/MwhP3PIz5xw5+d/aAihU3CkH2v6AQAAAABgkZwsafsy37SdGz6XDm0per9ol9S0l6/J17SPVKVW6dZZydH0OwmbzRaWm4KRkZGSpJycHG7alpD/syG/kiE/c8jPHPIzh/zMCWd+fCahV3BNP4OhfgAAAAAAlJ6jB6WNX+RP2+l1F71f9WZS8/5SiwG+dfockaVbJwJo+lmkYNMPAAAARbMzvScAAAAAAKXDMKR9631Nvt8XSH/+r+hpO20OKekcqfmFvkZf9SalXyuKRNPPIv41/bKzsy2uBAAAVHZHjhzRgw8+qI8//lh79+7VGWecoRdffFFnn3221aXJVmCqf6b3BAAAAAAgxHKypG3fSRs+V/yGz2VL2170fjFVfVN2Nu/vm7YztmppVolioulnEf9IP5p+AADAajfeeKPWrl2rt956S/Xq1dPbb7+tPn366Ndff1X9+vUtrY2RfgAAAAAAhJhnv7TxS+n3z6VNX0lZR2ST5Dh2vxrNfaP5ml/497SdtJTKOj6hkzAMQ0YYnir3N/2ysrLCcvyKzv+5kF3JkJ855GcO+ZlDfuaEO7/y+LlkZGToww8/1CeffKILLrhAkvTII49o7ty5mjJlih5//HFL67MXWCaxPOYLAAAAAIDlDEPa+9vf03bOl/5cKanwv7ENe4SUdI5szQf4RvQxbWe5Q9PvGKmpqUpNTVVubq4kyePxyOEo1N82zW73zVWVnp4uj8cT8uNXdIZhKCMjQ5JkKzACAMVDfuaQnznkZw75mRPu/Mrj3+k5OTnKzc1VTExM0PbY2Fh9++23RX6P1+uV1+sNvHa7fQt5h6OhWvBTyqPhXSI8LGAO+ZlDfuaRoTnkZw4PTAEAUI7leKWt3/rW5vv9c+nwcabtjD1NatZPRvMLlVazk1y1EiXuOZVbNP2OkZycrOTkZLndbrlcLjmdTjmdzpCfx39jzW63h+X4FZ3/HwZOp5Ob3iVAfuaQnznkZw75mRPu/PwPDZUn8fHx6tatmx577DG1atVKtWvX1rvvvqvly5eradOmRX7PpEmTNHHixELb09LSQn7zLisnf8HwrOwcpaWlhfT4lYFhGEpPT5fEwwIlQX7mkJ95ZGgO+ZkT7vz8Dw4BAIAQOXpQ2viFtH6etPkrKSu96P1qtvSN5Gs+QErsLNkdvtGA/Ju73KPpdxI2my0sF7b+6T1zcnL4h0cJ+T8b8isZ8jOH/MwhP3PIz5xw5ldeP5O33npLo0ePVv369eVwOHTmmWfq6quv1urVq4vcf8KECUpJSQm8drvdSkxMlMvlUkJCQkhry87Nb/rZHQ65XK6QHr8y8DdiXS5Xuf0dtRL5mUN+5pGhOeRnTrjz4zMBACAEDm2TNnzma/RtWyYZRTyQbI+UGp379/p8/aVqp5d+nSgVNP0s4m/6ZWdnW1wJAACo7Jo0aaIlS5bI4/HI7Xarbt26uvLKK3X66UX/IyA6OlrR0dGFtoejmer4e0p0yffQITcHS4aHBcwhP3PIzzwyNIf8zOGBKQAAyhjDkHb/7Gvyrf9M2vNL0fvFVvt7NF9/qUlvKSa0D+mibKLpZxGafgAAoKzxT2t+6NAhLViwQM8884zVJcle4F5gHuv+AAAAAAAqo9xsadt3vkbfhs+ltD+L3u+0xlLLi31/Erv4pu1EpULTzyI0/QAAQFmxYMECGYahFi1aaNOmTbr33nvVsmVLjRo1yurSgkYA5NHzAwAAAABUFt4j0qaFvkbfxi+kzOOst1fvzPxGX82WEiPpKzWafhah6QcAAMqKtLQ0TZgwQX/99ZeqVaumoUOH6oknnghcr1jNbvM1/BjpBwAAAACo0I7szl+fb8tSKTer8D72SKnxBb4mX4sBUkK90q8TZRZNP4vQ9AMAAGXFsGHDNGzYMKvLOC67zaY8w5BB0w8AAAAAUJEYhrRvg7Rhnq/Rt2N10ftFu6RmfX2NvqZ9WJ8Px0XTzyI0/QAAAIrHbrNJMpjeEwAAAABQ/uXlSn+u/LvR95l0cHPR+yXUl1pc5Gv0JZ0rRUSVbp0ol2j6nYQRpqfKIyJ80WdnZ/PUegn4PxeyKxnyM4f8zCE/c8jPnHDnx+cSHv7lCJjeEwAAAABQLmVnSJu/9jX6NsyXju4ver/abfMbfXU7sD4fThlNv2OkpqYqNTVVubm5kiSPxyOHwxHy89j+/j+rx+ORx+MJ+fErOsMwlJGRISk/SxQf+ZlDfuaQnznkZ0648+Pv9PCw//1ZMdIPAAAAAFBueA5Iv8/3rdG3+Ssp+2jhfWwOKemcvxt9F0mnNSr1MlGx0PQ7RnJyspKTk+V2u+VyueR0OuV0OkN+ntjYWEm+G47hOH5F5x9J4XQ6ueldAuRnDvmZQ37mkJ854c7P/9AQQsv+90fFSEoAAAAAQJl2aKtvbb7186TtyyUjr/A+kXFS095Si4ul5v2luGqlXiYqLpp+J2Gz2cJyU7Dgmn7ctC0Z/2dDfiVDfuaQnznkZw75mRPO/PhMwoORfgAAAACAMmvfBunXOdJvc6TdPxe9j7Om1GKAr9F3encpMrZ0a0SlQdPPIgWbfgAAADg+1vQDAAAAAJQZhiHt+snX5PttrrT/96L3q97UtzZfi4ulBp0ke+iXEQOORdPPIjT9AAAAiicw0o+hfgAAAAAAK+TlSX+t/HtE31wpbXvR+9U7Q2o1SGo5SKrZvHRrBETTzzI0/QAAAIrH/veifgz0AwAAAACUmtxsaes3vibf+nlS+p4idrJJDbv5Gn2tBkpVG5Z6mUBBNP0sQtMPAACgeJjeEwAAAABQKrIzpc1f+Rp9Gz6TMg8X3sceITW+4O8RfQOlKrVKvUzgeGj6WcTf9MvJybG4EgAAgLItML0nPT8AAAAAQKh5j0gbv/A1+jZ+KWWlF94nIkZq0tvX6GtxoRR7WunXCRQDTT+LMNIPAACgeP6e3VMGI/0AAAAAAKFw9KC04XNfo2/zV1Kut/A+UVWk5v19jb6mfaXoKqVfJ3CK7FYXUFnR9AMAACgeRvoBAAArPPXUU7LZbLrzzjsD23r06CGbzRb05+abb7auSABA8aXvlVZNld68VHq2qfTJrdLvnwc3/GJPkzpeK109S7p3s3T5NKnNZTT8UG4w0s8iNP0AAACKhzX9AABAaVu1apX+/e9/q3379oXeGzNmjB599NHA67i4uNIsDQBwKtL3Sr/NkdbNlrZ9Jxl5hfepUkdqNdA3oi/pPMlB2wTlF7+9FqHpBwAAUDz+kX65NP0AAEApSE9P1zXXXKP//Oc/evzxxwu9HxcXpzp16lhQGQCgWNL3SuvnnrjRV7Wh1OoS358GZ0t2JkVExUDT7yQMwwjL+jEREb7os7KyWJ+mBPyfC9mVDPmZQ37mkJ855GdOuPPjcwkPf9OPeAEAQGlITk7WxRdfrD59+hTZ9HvnnXf09ttvq06dOho0aJAefPBBRvsBgNXS90q/zpHz5w+kHf8rutFX7XSp9WCpzWCpTvv8aWWACoSm3zFSU1OVmpqq3NxcSZLH45HD4Qj5efLyfP/R8Xq98ng8IT9+RWcYhjIyMiRJNv7jfMrIzxzyM4f8zCE/c8KdH3+nh4fdP70ni/oBAIAwmzlzpn744QetWrWqyPeHDx+upKQk1atXTz///LPuu+8+bdiwQR999NFxj+n1euX15q8X5Xa7JYXvQXMeFDSH/MwhP3PI7xSl75V+myv9Olva9p1sRp4ij9nFKNjoq90uuNFHzkH4/TOnrDxoTtPvGMnJyUpOTpbb7ZbL5ZLT6ZTT6Qz5eapU8S38mZeXF5bjV3T+X3Cn08lN7xIgP3PIzxzyM4f8zAl3fv6HhhBa9r+7fqzpBwAAwunPP//UuHHj9OWXXyomJqbIfW666abA1+3atVPdunXVu3dvbd68WU2aNCnyeyZNmqSJEycW2p6Wlha2pl96erokHhQsCfIzh/zMIb+Ts3n2KXLTfEVunKeIHf+TrYgRfbmuRspufrGym12s3Jqt8xt9fz90gaLx+2dOuPNzF/P3l6bfSdhstrB8QFFRUZJ8a/rxf6CS8X825Fcy5GcO+ZlDfuaQnznhzI/PJDyY3hMAAJSG1atXa+/evTrzzDMD23Jzc7V06VK9/PLL8nq9hWaD6tKliyRp06ZNx236TZgwQSkpKYHXbrdbiYmJcrlcSkhICPnP4W8kulwurk9LgPzMIT9zyO84ihjRdyyj2ulSq0t1JKmPqjTppmi7XdGlX2m5xu+fOeHOr7jHpOlnkchI30Dj7OxsiysBAAAo2wLTe9L1AwAAYdS7d2/98ssvQdtGjRqlli1b6r777ity+Zc1a9ZIkurWrXvc40ZHRys6uvCt53A+yMeDguaQnznkZw75/S19r/TbHGndbGnbd8dfo6/NZVLrwbLVaSdDUl5ammx2O/mVEL9/5pSFB81p+lmEph8AAEDx+C9sWdIPAACEU3x8vNq2bRu0zel0qnr16mrbtq02b96sGTNm6KKLLlL16tX1888/66677tIFF1yg9u3bW1Q1AFQg6fuk3z4pdqNPdVijDzgWTT+L0PQDAAAoHkb6AQCAsiAqKkoLFy7U5MmT5fF4lJiYqKFDh+qBBx6wujQAKL8yDkvrP5XWfij9sUQycgvvc6JGH4AgNP0sQtMPAACgeFjTDwAAWGXx4sWBrxMTE7VkyRLrigGAiiLLI2343Nfo27RQys0qvA+NPqBEaPpZhKYfAABA8TDSDwAAAADKuRyvr8H3ywfS7/Ol7KOF96maJLUd6mv20egDSoSmn0Vo+gEAABRP/pp+NP0AAAAAoNzIzZG2LPGN6PvtU8mbVnifKnWktkN8zb76Z9HoA0yi6WcRmn4AAADFYw80/SwuBAAAAABwYnl50p8rfCP6fv1EOrq/8D6x1aTWl/oafUnnSHZH6dcJVFA0/SxC0w8AAKB47AUe9DQMIzDyDwAAAABQBhiGtPMHae1Hvj9HdhbeJypeajXQ1+g7vYfkiCz1MoHKgKafRWj6AQAAFI+9QJMvz5Ac9PwAAAAAwHr7fpd+nuWbvvPQlsLvR8RIzS/0Nfqa9ZMiY0q/RqCSoelnEZp+AAAAxVNwYF+eYcghun4AAAAAYIkje3xNvp9nSbvWFH7fHik17e1r9LUYIEXHl3qJQGVG088i/qZfbm4u01QBAACcQPBIPxb2AwAAAIBS5T0irZ/na/T9sVgy8oLft9mlRuf7Gn2tBklx1SwpEwBNP8v4m36Sb7RfVFSUhdUAAACUXQWbfvT8AAAAAKAU5GZLm7/2NfrWz5NyMgrvU7ej1P5Kqe0QKb5OqZcIoDCafhah6QcAAFA89mOm9wQAAAAAhIFhSDtW/71O30fS0f2F96na0NfoazdMqtm89GsEcEI0/SxybNMPAAAARbMFTe9pYSEAAAAAUBEd2Cz9/J70y3vSwT8Kvx97mtRmiNR+mJTYJXjhdQBlSoVu+v3f//2fpk+fLpvNpvHjx+vaa6+1uqQAmn4AAADFw0g/AAAAAAgxz37faL6fZ0k7vi/8viNaajHAN6qvaR8pgpnqgPKgwjb9fvnlF82YMUOrV6+WYRjq2bOnBg4cqKpVq1pdmiTJbrfLbrcrLy+Pph8AAMAJBK3pl3eCHQEAAAAAx5fjlX6fL615V9r0pZSXc8wONqnx+b5GX6tBUozLkjIBlFyFbfr99ttv6tatm2JiYiRJHTp00Pz583XVVVdZXFm+yMhIeb1emn4AAAAnwEg/AAAAACgh/zp9a2ZIaz+UMg8X3qd2O9/Une0ulxLqlXqJAELHbnUBx7N06VINGjRI9erVk81m0+zZswvtk5qaqkaNGikmJkZdunTRypUrA++1bdtWixcv1uHDh3Xo0CEtXrxYO3bsKMWf4OT8U3zS9AMAADg+m73gmn40/QAAAADgpNL+kr55Tnr5bOn13tL3U4MbfvH1pHPvlG5ZJt3yrXTuHTT8gAqgzI7083g86tChg0aPHq0hQ4YUen/WrFlKSUnRq6++qi5dumjy5Mnq37+/NmzYoFq1aql169a644471KtXL7lcLnXt2lUOh8OCn+T4aPoBAACcXMHpPfPo+QEAAABA0bI80m9zfaP6tiyVdMw/oCJifdN2drxaatxdspet++UAzCuzTb8BAwZowIABx33/+eef15gxYzRq1ChJ0quvvqp58+Zp2rRpGj9+vCRp7NixGjt2rCTpxhtvVLNmzY57PK/XK6/XG3jtdrslSYZhyAjDE+WGYSgiwhd/VlZWWM5Rkfk/F3IrGfIzh/zMIT9zyM+ccOfH5xIeBaf3JGMAAAAAKCAvT9r2nfTTu9Kvn0hZ6YX3STrP1+hrdYkUk1D6NQIoNWW26XciWVlZWr16tSZMmBDYZrfb1adPHy1fvjywbe/evapVq5Y2bNiglStX6tVXXz3uMSdNmqSJEycW2u7xeMIyQrBg08/tdsvj8YT8HBWZYRjKyMiQJNkKPP2P4iE/c8jPHPIzh/zMCXd+/H0eHjZG+gEAAABAsIN/+Eb0/TRLStte+P3TGksdrpY6XCmd1qjUywNgjXLZ9Nu/f79yc3NVu3btoO21a9fW+vXrA68vvfRSpaWlyel0avr06YEmW1EmTJiglJSUwGu3263ExEQ5nU45nc6Q/wyGYSgqKkqSFBEREZZzVGT+p/ydTic3vUuA/MwhP3PIzxzyMyfc+eXm5ob8mKUhNzdXjzzyiN5++23t3r1b9erV08iRI/XAAw+Uid+zgiP9WNMPAAAAQKWVddQ3mu/Ht6Vt3xZ+PzpBanOZ1HG4lNhFKgP/ngNQuspl06+4Co76O5no6GhFR0cX2m6z2cJ2s8vfhMzJySkTN9TKG/9nQ3YlQ37mkJ855GcO+ZkTzvzK62fy9NNPa8qUKfrvf/+rNm3a6Pvvv9eoUaPkcrl0xx13WF3eMWv60fQDAAAAUIkYhrRjtfTjW9IvH0pZR4Lft9mlJr18o/paXixFxlpTJ4AyoVw2/WrUqCGHw6E9e/YEbd+zZ4/q1KkT0nOFc02/yMhISVJ2djbr05wi1rQyh/zMIT9zyM8c8jOHNf2KtmzZMl166aW6+OKLJUmNGjXSu+++q5UrV1pcmU/wmn7W1QEAAAAApcazX/pppm9U377fCr9fvZl0xrVS+yulhLqlXx+AMqlcNv2ioqJ01llnadGiRRo8eLAkKS8vT4sWLdJtt91m6tipqalKTU0NTM8VzjX9/Mc9cuQIawCdIta0Mof8zCE/c8jPHPIzhzX9inbOOefotdde0++//67mzZvrp59+0rfffqvnn3++yP29Xq+8Xm/gtdvtlhS+h6UKfla5eXnltrlqFR4WMIf8zCE/88jQHPIzhwemAKCU5eUoYssi6fePpQ2fS3k5we9HVfFN33nGdVJiZ6bvBFBImW36paena9OmTYHXW7Zs0Zo1a1StWjU1bNhQKSkpGjFihDp16qTOnTtr8uTJ8ng8GjVqlKnzJicnKzk5WW63Wy6Xq1TW9HM4HKzpd4pY08oc8jOH/MwhP3PIzxzW9Cva+PHj5Xa71bJlSzkcDuXm5uqJJ57QNddcU+T+kyZN0sSJEwttT0tLC8vNu5zs7PxzuI8oLSLnBHvjWIZhKD09XRIPC5QE+ZlDfuaRoTnkZ0648/M/OAQAld6Bzb4RfT+9qypHdhV+v2E336i+1oOl6CqlXh6A8qPMNv2+//579ezZM/A6JSVFkjRixAi98cYbuvLKK7Vv3z499NBD2r17tzp27Kj58+erdu3aIa0jnGsm+af3ZE2/kmFNK3PIzxzyM4f8zCE/c1jTr7D33ntP77zzjmbMmKE2bdpozZo1uvPOO1WvXj2NGDGi0P4TJkwIXJtJvht2iYmJcrlcSkhICHl9MdFRga+dVarI5eIfuafC34h1uVzl9nfUSuRnDvmZR4bmkJ854c6PzwRApZblkX79xNfs2/adJCnov4pVavvW6TvjWqlGM0tKBFD+lNmmX48ePU76pPhtt91mejrPkymNNf2ysrKY0uIUMUWLOeRnDvmZQ37mkJ85TFFVtHvvvVfjx4/XVVddJUlq166dtm3bpkmTJhXZ9IuOjlZ0dHSh7eFqptqPOSY3CE8dDwuYQ37mkJ95ZGgO+ZnDA1MAEGI7fpBWvyGt/UjKOhL0lmGPUHbj3oo8e6RszfpJjjJ7+x5AGcV/NY5Rmmv62e12Sb6pTMvrGkBWYU0rc8jPHPIzh/zMIT9zWNOvaEePHg1cl/g5HA7l5eVZVFGwgh9VXvnsqwIAAACozDLd0toPfM2+XT8Vfr9Gc986fe2v1NHcaLlcLtbrA1AiNP2OUZpr+vmfkLfb7azpd4pY08oc8jOH/MwhP3PIzxzW9CvaoEGD9MQTT6hhw4Zq06aNfvzxRz3//PMaPXq01aVJCh7pl0vXDwAAAEB5YBjSzr9H9f3yoZR9zEOiUVWktkN8zb4GZ/uafIYhpaVZUi6AioGm30mwpl/ZxRQt5pCfOeRnDvmZQ37mMEVVYS+99JIefPBB3Xrrrdq7d6/q1aunsWPH6qGHHrK6NEmSvUCsNP0AAAAAlGmZbumX96XV06XdvxR+v96ZUqdRUpshUjTrlQMILZp+J8GafmUTa1qZQ37mkJ855GcO+ZnDmn5Fi4+P1+TJkzV58mSrSymSvUDXr5xGDAAAAKAiM4y/1+qbLq39UMo+Gvx+VLzUfph01gipbgdragRQKdD0O0ZprunnHw3g8XjK7RpAVmFNK3PIzxzyM4f8zCE/c1jTr3xyFJzek64fAAAAgLIi0y398p5vCs+iRvXVP0s6aySj+gCUGpp+xyjNNf1iYmIk+W46sqbfqWFNK3PIzxzyM4f8zCE/c1jTr3xy2FnTDwAAAEAZsnut9P1U6adZhdfqi07wjeo7c4RUt7019QGotGj6nQRr+pVdrGllDvmZQ37mkJ855GcOa/qVPwWn98xjpB8AAAAAK+R4pV/nSKtel/5cUfj9+p18o/raDpGiGOABwBo0/Szkb/plZ2dbXAkAAEDZFTS9JyP9AAAAAJSmQ9t8a/X98JZ0dH/we5FOqcOVUqfRUp121tQHAAXQ9DsJwzACU4GF+rgREb74s7KywnKOisz/uZBbyZCfOeRnDvmZQ37mhDs/PpfwKDi9Zx5NPwAAAADhlpcrbVrkm8Lz9wWSjvl3SM1W0tk3SO2vlGISLCkRAIpC0+8YqampSk1NDazJ4/F45HA4Qn4ewzACU4AdPXpUHo/nJN+BggzDUEZGhiSmUisJ8jOH/MwhP3PIz5xw58ff5+FhLzjSj8YqAAAAgHDxHJB+fEv6fpp0eFvwe/ZIqfUlUqcbpKRzJP5NDqAMoul3jOTkZCUnJ8vtdsvlcsnpdMrpDP0czIZhKDY2NvA6HOeoyPwjKZxOJze9S4D8zCE/c8jPHPIzJ9z5+R8aQmg57PlfM70nAAAAgJDb9bP0v39Lv7wv5XqD30toIHUaKZ1xvRRf25LyAKC4aPqdhM1mC9tNVf+afjk5Ody4LQH/Z0N2JUN+5pCfOeRnDvmZE878+EzCo+BIvzxG+gEAgFLy1FNPacKECRo3bpwmT54sScrMzNTdd9+tmTNnyuv1qn///nrllVdUuzaNAKDcyc2RNszzNfu2fVf4/Sa9pbNvlJr1kxzcRgdQPvBfKwv5m37Z2dkWVwIAAFB2FVzTLzfPwkIAAEClsWrVKv373/9W+/btg7bfddddmjdvnt5//325XC7ddtttGjJkiL77roiGAYCy6ehB6Yc3pVWvS2l/Br8X7ZLOvE7qNFqq3sSa+gDABJp+FqLpBwAAcHJBa/oxvScAAAiz9PR0XXPNNfrPf/6jxx9/PLA9LS1NU6dO1YwZM9SrVy9J0vTp09WqVSutWLFCXbt2tapkAMWx9zfpf69KP82ScjKC36vRXOoyVmp/lRRdxZr6ACAEaPqdhGEYgfV/Qn3ciAhf/NnZ2WE5R0Xm/1zIrWTIzxzyM4f8zCE/c8KdH59LeNgLjPQjYwAAEG7Jycm6+OKL1adPn6Cm3+rVq5Wdna0+ffoEtrVs2VINGzbU8uXLafoBZVFerrTxC2nFFGnLksLvN+vva/Y16SWxXAOACoCm3zFSU1OVmpqq3NxcSZLH45HD4Qj5eQrecMzIyJDH4wn5OSoywzCUkeF7Iof1k04d+ZlDfuaQnznkZ0648+Pv8/BwFPiocmn6AQCAMJo5c6Z++OEHrVq1qtB7u3fvVlRUlKpWrRq0vXbt2tq9e/dxj+n1euX1egOv3W63pPA+aM6DgiVHfuaUmfwy06Q170grX5Pt0Nagt4yoKlLH4VLnscFTeFpds8pQfuUU+ZlDfuaUlQfNafodIzk5WcnJyXK73XK5XHI6nXI6nSE/j2EYiouLC3wdjnNUZP5fcKfTyU3vEiA/c8jPHPIzh/zMCXd+/oeGEFrBa/rxjw8AABAef/75p8aNG6cvv/xSMTExITvupEmTNHHixELb09LSwtb0S09Pl8SDgiVBfuZYnZ89bbuif5ymqHXvyZYd/FBmritJ3o4jldX6Cik63rcxLa3UazwRq/Mr78jPHPIzJ9z5+R8aOhmafidhs9nC9gseFRUlyTe9J/8nOnX+z4bsSob8zCE/c8jPHPIzJ5z58ZmER8E1/fJ44hAAAITJ6tWrtXfvXp155pmBbbm5uVq6dKlefvllLViwQFlZWTp8+HDQaL89e/aoTp06xz3uhAkTlJKSEnjtdruVmJgol8ulhISEkP8c/kaiy+Xi+rQEyM8cy/L763tp+UvSb3NlM/KCazq9p9RlrOzN+inWZlds6VV1yvj9M4f8zCE/c8KdX3GPSdPPQgXX9AMAAEDRgkf6WVgIAACo0Hr37q1ffvklaNuoUaPUsmVL3XfffUpMTFRkZKQWLVqkoUOHSpI2bNig7du3q1u3bsc9bnR0tKKjowttD+eDfDwoaA75mVNq+eXlShs+k5a9LP25Ivi9iFipw1VSl5tlq9UyvHWEGL9/5pCfOeRnTll40Jymn4UiIyMl0fQDAAA4EXuBpl8e03sCAIAwiY+PV9u2bYO2OZ1OVa9ePbD9hhtuUEpKiqpVq6aEhATdfvvt6tatm7p27WpFyUDllOWR1syQVrwiHfwj+D1nLanzTVKn0ZKzujX1AYCFaPpZyD+9Z1ZWlsWVAAAAlF2OAk+z5TK9JwAAsNALL7wgu92uoUOHyuv1qn///nrllVesLguoHI7skVa+Jn0/Vco4FPxezZZSt9ukdldIkaFbkxMAyhuafhbyT+3g9XotrgQAAKDsCp7ek6YfAAAoPYsXLw56HRMTo9TUVKWmplpTEFAZ7flVWp4q/fKelHvM4InG3aVzbpea9pGYjhAAaPqdjGEYgQUYQ31c/0i/zMzMsJyjIvN/LuRWMuRnDvmZQ37mkJ854c6PzyU87AX+8Z5HxgAAAEDFZxjS1m+l7yZLmxYGv2ePkNpeLnVLluq2t6Q8ACiraPodw/+0Vm5uriTJ4/HI4XCE/DyGYQQWXjx69Kg8Hk/Iz1GRGYahjIwMScVfwBL5yM8c8jOH/MwhP3PCnR9/n4eHw57/NSP9AAAAgAosL0/6/XPpm+elHd8HvxftkjqNlDqPlVz1LSkPAMo6mn7HSE5OVnJystxut1wul5xOp5xOZ8jPYxiGEhISJPnW9AvHOSoy/0gKp9PJTe8SID9zyM8c8jOH/MwJd37+h4YQWkzvCQAAAFRwudnSLx/4RvbtWx/8XtWGUtdbpTOulaLjLSkPAMoLmn4nYbPZwnZTNTY2VpJvek9u3J46/2dDdiVDfuaQnznkZw75mRPO/PhMwoPpPQEAAIAKKuuo9OPb0rKXpLTtwe/VaiOdd5fU5jLJwW1sACgO/mtpoejoaEmS1+u1uBIAAICyK3ikn4WFAAAAAAiNjMPSqv9IK16Vju4Pfi+xq3R+itSsn8SDlQBwSmj6WSgmJkaSb6QfAAAAisZIPwAAAKCCOLJbWp4qfT9dyjoS/F6zfr6RfUnnWFMbAFQANP0sVLDpZxgGU4IBAAAUgTX9AAAAgHLu8J/Sty/4pvLMLTDrmc3um77zvLukOu2sqw8AKgiafhbyT++Zl5ennJwcRUZGWlwRAABA2eOw0fQDAAAAyqXD26Vvnvc1+/Ky87c7oqSO10jn3iFVO926+gCggqHpZyF/00/yjfaj6QcAAFCY3Z7/NdN7AgAAAOXAoa3St89La2ZIeTn526OqSJ1GS92Spfg6lpUHABUVTb+TMAxDRhhuLhmGoaioqMDrjIwMValSJeTnqaj8n0s4PpvKgPzMIT9zyM8c8jMn3PnxuYQH03sCAAAA5cShrYpd9KT020fHNPvipS5jfc2+uGrW1QcAFRxNv2OkpqYqNTVVubm5kiSPxyOHwxHy8xiGIa/Xq6ioKGVlZengwYOKi4sL+XkqKsMwlJGRIUmshVgC5GcO+ZlDfuaQnznhzs/j8YT8mJDsBaf3pLEKAAAAlD0HNkvfPCf9NFPRRm7+9ugEqcvNUtdbaPYBQCmg6XeM5ORkJScny+12y+Vyyel0yul0hvw8/pEAMTExysrKkt1uD8t5Kip/fk6nk5veJUB+5pCfOeRnDvmZE+78/A8NIbQKjvTLY6QfAAAAUHbs3yQtfVb65T3JyJP/yt2ITpCt661S15ul2NMsLREAKhOafidhs9nCdlPVZrMpJiZGbrdbXq+Xm7enyP/ZkFvJkJ855GcO+ZlDfuaEMz8+k/BwFBzpl2dhIQAAAAB8DmyWljwt/fK+ZORfpBsxVZV5xmjFXDBOiq1qXX0AUEnR9LNYTEyMJMnr9VpcCQAAQNlkLzjSj+k9AQAAAOuk/SUteUb68W2p4DSesaf51uvrfJO8mYZiYlzW1QgAlRhNP4v5m36ZmZkWVwIAAFA2Fej5KZfpPQEAAIDSl77Xt2bf99Ok3Kz87bGnSefcLnW+SYqOlwxDykyzrk4AqORo+lmMph8AAMCJORjpBwAAAFjj6EHpuxella9J2Ufzt0cnSN1uk7reIsUkWFcfACAITT+LRUdHS6LpBwAAcDx2G00/AAAAoFRluqUVU6TlL0ted/72iFipy1jp3HFSXDXr6gMAFImmn8UY6QcAAHBiBUf6Mb0nAAAAEEY5Xt8UnkuflY4eyN/uiJI6jZbOS5Hia1tXHwDghGj6WYymHwAAwIk5bAWbfhYWAgAAAFRUeXnS2g+krx6TDm/P325zSGdcK11wr1Q10br6AADFQtPPYv6mX0ZGhsWVAAAAlE121vQDAAAAwsMwpM1fSQsflnb/Evxe28ulnvdL1ZtYUxsA4JTR9LNYXFycJJp+AAAAx8P0ngAAAEAY7PxR+vJhacuS4O1Nekl9HpHqdrCkLABAydmtLqCyi42NlSQdPXrU4koAAEBl1ahRI9lstkJ/kpOTrS5NkmQvOL0nI/0AAAAAcw7+IX0wWnqtR3DDr24H6brZ0nUf0/ADgHKKkX4W8zf9GOkHAACssmrVKuXm5gZer127Vn379tUVV1xhYVX5HAUeU8tjpB8AAABQMhmHpCXPSitfk/Ky87ef1kjq9aDUZohkZ4wIAJRnNP1OwjAMGWF4otx/XP/0nh6PJyznqaj8+ZFZyZCfOeRnDvmZQ37mhDu/8vq51KxZM+j1U089pSZNmqh79+4WVRTMYWN6TwAAAKDEcrOlVVOlJU/5Gn9+cTWk7vdJZ42UIqIsKw8AEDo0/Y6Rmpqq1NTUwNPuHo9HDocj5OcxDEMZGRmBYx85ckQejyfk56mo/PlJkq3AjUAUD/mZQ37mkJ855GdOuPOrCH+XZ2Vl6e2331ZKSspxM/J6vfJ6vYHXbrdbUvgelipYRi5N71PGwwLmkJ855GceGZpDfubwwBRQzhmG9Pt86YsHpAOb8rdHxErn3Cadc4cUk2BdfQCAkKPpd4zk5GQlJyfL7XbL5XLJ6XTK6XSG/Dz+C9uqVatK8t1gC8d5Kip/fk6nk5veJUB+5pCfOeRnDvmZE+78Ck6RWV7Nnj1bhw8f1siRI4+7z6RJkzRx4sRC29PS0sJy885zNCvwtTcrW2lpaSE/R0VmGIbS09Ml8bBASZCfOeRnHhmaQ37mhDs//4NDAMJg91ppwf3Ba/ZJUvsrpd4PSa4G1tQFAAgrmn4nYbPZwvYPA5vNFrSmH/8AOTX+z4bcSob8zCE/c8jPHPIzJ5z5VYTPZOrUqRowYIDq1at33H0mTJiglJSUwGu3263ExES5XC4lJIThSeHI/Kaf3e6Qy+UK/TkqMH8j1uVyVYjf0dJGfuaQn3lkaA75mRPu/PhMgDA4skf6+nHpx7clIy9/e8NuUv8npPpnWVcbACDsaPpZzL+mn3+qMQAAAKts27ZNCxcu1EcffXTC/aKjoxUdHV1oe7iaqQ6HPfB1nsENwpLgYQFzyM8c8jOPDM0hP3N4YAooJ3K80vKXpW+el7LS87dXTZL6Piq1vjR43nwAQIVE089i/pF+R48etbgSAABQ2U2fPl21atXSxRdfbHUpQRwFbk7k5rH2DwAAABDk9wXS/PHSwT/yt0UnSBfcI3UeK0XGWFcbAKBU0fSzGCP9AABAWZCXl6fp06drxIgRiogoW5eI9vyBfsoNw5qBAAAAQLl0YLNv3b7f5+dvs9mls0ZKPe6XqtS0rDQAgDXK1h2dSoiRfgAAoCxYuHChtm/frtGjR1tdSiEFR/rlMdIPAAAAlV2WxzeN57J/Sbn561+r4TnSRc9IddpZVxsAwFI0/SzmH+lH0w8AAFipX79+MsroKDqHvcD0nmW0RgAAACDsDEP6dba04AHJ/Vf+9vi6Ur/HpbZDWbcPACo5mn4Wq1KliiTJ4/FYXAkAAEDZZLPZZJNkiJF+AAAAqKT2rpc+u0fa+k3+Nnuk1C1ZuuBeKbqKdbUBAMoMmn4WS0hIkCS53W6LKwEAACi7HHabcvIMRvoBAACgcsnOkJY+K333opSXk7+9aR/pwqelGk2tqw0AUObQ9LNYfHy8JOnIkSPKy8uT3W63uCIAAICyxz/DZ26etXUAAAAApWbTQmne3dKhrfnbqiZJFz4ltRjAVJ4AgELoMFnMP9LPMAym+AQAADgO+99dP6b3BAAA4TJlyhS1b99eCQkJSkhIULdu3fT5558H3u/Ro4dv2vECf26++WYLK0aFdWSP9MFo6e2h+Q0/e6R0wT+k5P9JLS+i4QcAKBIj/SwWGxsrh8Oh3Nxcud3uwMg/AAAA5Iv4u+nH9J4AACBcGjRooKeeekrNmjWTYRj673//q0svvVQ//vij2rRpI0kaM2aMHn300cD3xMXFWVUuKqK8PGn1dGnhRMmblr896Txp4AtSzebW1QYAKBdo+lnMZrMpISFBhw4dktvtVv369a0uCQAAoMxx/P0kcw7zewIAgDAZNGhQ0OsnnnhCU6ZM0YoVKwJNv7i4ONWpU8eK8lDR7V4rfXqn9Neq/G2x1aR+j0sdhzOyDwBQLEzvWQb4p/h0u90WVwIAAFA2Of4e6ZfD9J4AAKAU5ObmaubMmfJ4POrWrVtg+zvvvKMaNWqobdu2mjBhgo4ePWphlagQsjOlRY9K/74guOHX8Rrptu+lM66h4QcAKDZG+pUBNP0AAABOLMLhH+lH0w8AAITPL7/8om7duikzM1NVqlTRxx9/rNatW0uShg8frqSkJNWrV08///yz7rvvPm3YsEEfffTRCY/p9Xrl9XoDr/33fwzDkBGGqcv9xw3HsSuDUs3vz5XSnNtk2/97/vmrN5MGPi81Ot9fUPjrCCF+/8whP3PIzxzyMyfc+RX3uDT9ygCafgAAACcWmN6TkX4AACCMWrRooTVr1igtLU0ffPCBRowYoSVLlqh169a66aabAvu1a9dOdevWVe/evbV582Y1adLkuMecNGmSJk6cWGh7Wlpa2Jp+6enpknzLyuDUlEp+2UcV+92zilozXTb5fgcMe6QyO98mb6dbpIhoKS3tJAcpm/j9M4f8zCE/c8jPnHDnV9z+UYVu+r3wwgt6/fXXZRiG+vTpoxdffLFM/rLS9AMAADgx/0i/3DzW9AMAAOETFRWlpk2bSpLOOussrVq1Si+++KL+/e9/F9q3S5cukqRNmzadsOk3YcIEpaSkBF673W4lJibK5XIF7gmFkr+R6HK5yuR9sLIu7Pn9sUSae4dsh7fln7PemdKlLyumVmvFhP6MpYrfP3PIzxzyM4f8zAl3fsU9ZoVt+u3bt08vv/yy1q1bp8jISF1wwQVasWJF0DzsZQVNPwAAgBOLsDO9JwAAKH15eXlBU3MWtGbNGklS3bp1T3iM6OhoRUdHF9pus9nCdlPVf2xu2pZMWPLLTJO+eED64c38bRExUs9/ytb1VslRcW7T8vtnDvmZQ37mkJ854cyv0jf9JCknJ0eZmZmSpOzsbNWqVcviiopG0w8AAODEAk0/pvcEAABhMmHCBA0YMEANGzbUkSNHNGPGDC1evFgLFizQ5s2bNWPGDF100UWqXr26fv75Z91111264IIL1L59e6tLR1n3+wJp7jjpyK78bUnnSpe8JFU//ihRAABOld3qAo5n6dKlGjRokOrVqyebzabZs2cX2ic1NVWNGjVSTEyMunTpopUrVwbeq1mzpu655x41bNhQ9erVU58+fU441YKVaPoBAACcmCPQ9GN6TwAAEB579+7V9ddfrxYtWqh3795atWqVFixYoL59+yoqKkoLFy5Uv3791LJlS919990aOnSo5s6da3XZKMu8R6Q5t0szhuU3/KKqSBc/J434lIYfACDkyuxIP4/How4dOmj06NEaMmRIofdnzZqllJQUvfrqq+rSpYsmT56s/v37a8OGDapVq5YOHTqkTz/9VFu3blVsbKwGDBigpUuX6oILLrDgpzkxmn4AAAAnxkg/AAAQblOnTj3ue4mJiVqyZEkpVoNyb9sy6eObpQJr96lpH2ngZKlqomVlAQAqtjLb9BswYIAGDBhw3Peff/55jRkzRqNGjZIkvfrqq5o3b56mTZum8ePHa+HChWratKmqVasmSbr44ou1YsWK4zb9vF5v0Bzt/gacYRiBBRhDyX9cwzAUHx8vSUpLSwvLuSqigvnh1JGfOeRnDvmZQ37mhDs/Ppfw8Y/0MwwpN88IvAYAAADKlByv9PUT0nf/kvT3vw8indKFT0pnjpBYJwsAEEZltul3IllZWVq9erUmTJgQ2Ga329WnTx8tX75cku8JrGXLlikzM1ORkZFavHixbrrppuMec9KkSZo4cWKh7R6PRw6HI+Q/g2EYysjIkCTFxcVJkvbv3y+PxxPyc1VEBfNjUdFTR37mkJ855GcO+ZkT7vz4ezx8Igo0+XLy8uSwh/76DAAAADBl9y/SR2OlvevytyV2lS57VarW2Lq6AACVRrls+u3fv1+5ubmqXbt20PbatWtr/fr1kqSuXbvqoosu0hlnnCG73a7evXvrkksuOe4xJ0yYoJSUlMBrt9utxMREOZ1OOZ3OkP8M/pEATqdT9erVkyQdPnw4LOeqiArmx03vU0d+5pCfOeRnDvmZE+78cnNzQ35M+AQ1/XINRZfLq1gAAABUSHm50ncvSl8/KeVl+7bZI6Ve/5TOuUPigTUAQCmp0LdLnnjiCT3xxBPF2jc6OlrR0dGFtttstrDdVPUfu0aNGpKkAwcOcAP3FPjzI7OSIT9zyM8c8jOH/MwJZ358JuHjCBrpxzSqAAAAKCPS/pI+HCNtX5a/rVYbachrUp221tUFAKiUymXTr0aNGnI4HNqzZ0/Q9j179qhOnTohPVdprOnnX3fwwIEDrAVUTKxpZQ75mUN+5pCfOeRnDmv6lV8FR/rl0vQDAABAWfDbXOmT26TMw39vsEnnjpN63i9FFB5cAABAuJXLpl9UVJTOOussLVq0SIMHD5Yk5eXladGiRbrttttMHTs1NVWpqamB6blKY02/mJgYSdKRI0d06NAhRUVFhfx8FQ1rWplDfuaQnznkZw75mcOafuVX0Ei/3DwLKwEAAECll50hLfin9P3U/G0JDaSh/5GSzrGuLgBApVdmm37p6enatGlT4PWWLVu0Zs0aVatWTQ0bNlRKSopGjBihTp06qXPnzpo8ebI8Ho9GjRpl6rzJyclKTk6W2+2Wy+UqlTX9YmNjZbPZZBiGvF6vTjvttJCfr6JhTStzyM8c8jOH/MwhP3NY06/8inAwvScAAADKgL3rpQ9GS3vX5W9rdYl0yb+kWO7pAQCsVWabft9//7169uwZeJ2SkiJJGjFihN544w1deeWV2rdvnx566CHt3r1bHTt21Pz581W7du2Q1lEaa/pFRETotNNO08GDB3Xw4EHVrVs3LOeraFjTyhzyM4f8zCE/c8jPHNb0K5+CR/rR9AMAAEApMwxp9RvS/AlSjm/2EEXESBdOks4aJfFvAQBAGVBmm349evQ46bo4t912m+npPE+mNNb0k6Tq1avr4MGDrOtXTKxpZQ75mUN+5pCfOeRnDmv6lV8F1/TLyWN6TwAAAJSizDRpzu3Sr5/kb6vVWrp8mlSrlXV1AQBwjDLb9LOKFWv62Ww2Va1aVZK0Y8cO1gMqBta0Mof8zCE/c8jPHPIzhzX9yq/gph/NVQAAAJSS3Wul966TDv6Rv63TDVL/J6TIWOvqAgCgCDT9jmHFmn42m021atWS5LtZGI7zVTSsaWUO+ZlDfuaQnznkZw5r+pVfEUzvCQAAgNK2Zob0aUr+dJ4xLumSl6XWl1hbFwAAx0HT7yRKY00/m82mGjVqSJL279/PTdxiYk0rc8jPHPIzh/zMIT9zWNOvfHIwvScAAABKS06mNOdB6cc387fV7SANe1M6rZFlZQEAcDI0/U6itNb0q1u3riTf9J6sB3RyrGllDvmZQ37mkJ855GcOa/qVXw6m9wQAAEBpOLRVVWZdI9u+dfnbzhopXfi0FBljWVkAABQHTb9jWLWmn396z61bt7IeUDGwppU55GcO+ZlDfuaQnzms6Vd+Mb0nAAAAwm7DfOnjmxSRmeZ7HRErDXxB6ni1tXUBAFBMNP2OYdWafqeffrokaffu3azpVwysaWUO+ZlDfuaQnznkZw5r+pVfEUzvCQAAgHDJy5OWPistflL+q06jWhPZrnxLqt3G0tIAADgVNP1OorTW9GvYsKEk6a+//uImbjGxppU55GcO+ZlDfuaQnzms6Vc+FWz65TK9JwAAAELFmy7Nvln6bW5gU1bTAYq8/N9SjMvCwgAAOHU0/cqIBg0aSJL27NmjrKwsRUVFWVwRAABA2eFgek8AAACE2sEt0szh0t5f/95gk9H7YR1tO1Ku6ARLSwMAoCRo+p2EYRiBqcDCcVz/satXr66oqChlZWVpx44datSoUcjPWZEcmx9ODfmZQ37mkJ855GdOuPPjcwmfCIc98HUOI/0AAABg1uavpQ9GSRmHfK+jXdLlU6WmfaS0NGtrAwCghGj6HSM1NVWpqamBNXk8Ho8cDkfIz2MYhjIyMiTlTwVWv359bdmyRRs3blTNmjVDfs6KpKj8UHzkZw75mUN+5pCfOeHOz+PxhPyY8CnQ81NOLmv6AQAAoIQMQ1rxivTFA5Lx93VljebSVe9KNZr63gcAoJyi6XeM5ORkJScny+12y+Vyyel0yul0hvw8/pEATqczcNMxMTFRW7Zs0YEDB8JyzoqkqPxQfORnDvmZQ37mkJ854c7P/9BQacnJydHixYu1efNmDR8+XPHx8dq5c6cSEhJUpUqVUq0l3CLsjPQDAADHV5mui2BCbrb06V3Sj2/lb2t+oTTkNdbvAwBUCDT9TsJms4Xtpqr/2AWbfpK0Y8cObuQWw7H54dSQnznkZw75mUN+5oQzv9L8TLZt26YLL7xQ27dvl9frVd++fRUfH6+nn35aXq9Xr776aqnVUhoiCq7pl8dIPwAAkK+yXRehhDIOS+9dL21Zkr/t/Huknv+UCjxgBgBAecbfaGVIgwYNJEmbNm2yuBIAAFDWjRs3Tp06ddKhQ4cUGxsb2H7ZZZdp0aJFFlYWHsHTezLSDwAA5Kts10UogUNbpan98ht+jmhp6FSp94M0/AAAFQoj/cqQs88+W5K0fPlyiysBAABl3TfffKNly5YpKioqaHujRo20Y8cOi6oKH6b3BAAAx1PZrotwiv76Xnr3Ksmzz/c6rrpv/b6GXaytCwCAMKDpdxKGYQTW/wnHcQseu1OnTpKkX3/9VR6PR3FxcSE/b0VRVH4oPvIzh/zMIT9zyM+ccOdXmp9LXl5ekWsI/vXXX4qPjy+1OkqLI2h6T37/AQBAvsp2XYRTsG629PFYKSfT97p6M+ma96Rqp1taFgAA4VKipt+ff/4pm80WmI5y5cqVmjFjhlq3bq2bbroppAWWttTUVKWmpgYuFj0ejxwOR8jPYxiGMjIyJOWv/1OtWjXVq1dPO3fu1NKlS3X++eeH/LwVRVH5ofjIzxzyM4f8zCE/c8Kdn8fjCfkxj6dfv36aPHmyXnvtNUm+nyc9PV0PP/ywLrroolKro7QEremXy5p+AAAgX2W7LkIxrXhVmn9f/utG50tXviXFnmZdTQAAhFmJmn7Dhw/XTTfdpOuuu067d+9W37591aZNG73zzjvavXu3HnrooVDXWWqSk5OVnJwst9stl8slp9Mpp9MZ8vP4RwI4nc6gm46tWrXSzp07tXfv3rCct6I4Xn4oHvIzh/zMIT9zyM+ccOdX1BPm4fLcc8+pf//+at26tTIzMzV8+HBt3LhRNWrU0LvvvnvKx9uxY4fuu+8+ff755zp69KiaNm2q6dOnB2YisFrBkX65jPQDAAAFhPq6COWcYUhfPSZ981z+to7XSAMnSxFRx/02AAAqghI1/dauXavOnTtLkt577z21bdtW3333nb744gvdfPPN5brpdyybzRa2m6r+Yxc8fsOGDSVJ27dv52buSRSVH4qP/MwhP3PIzxzyMyec+ZXmZ9KgQQP99NNPmjlzpn7++Welp6frhhtu0DXXXKPY2NhTOtahQ4d07rnnqmfPnvr8889Vs2ZNbdy4UaedVnaego4s0PTLzqXpBwAA8oXyugjlXG6O9Omd0o9v5W+74B9Sz/sl/v0EAKgEStT0y87OVnR0tCRp4cKFuuSSSyRJLVu21K5du0JXXSXUvHlzSb7GKgAAwIlERETo2muvNX2cp59+WomJiZo+fXpgW+PGjU0fN5QiHEzvCQAAji9U10Uox7IzpA9GSxs++3uDTRrwjNSlfC9FBADAqShR069NmzZ69dVXdfHFF+vLL7/UY489JknauXOnqlevHtICKxv/CMr//e9/FlcCAADKsjfffPOE719//fXFPtacOXPUv39/XXHFFVqyZInq16+vW2+9VWPGjClyf6/XK6/XG3jtdrsl+aZP9U+hGkqGYQSN9PPm5IXlPBWV/3Mhs5IhP3PIzzwyNIf8zAl3fqE6biivi1BOZRyS3r1a2r7c99oeKQ15TWo7xNq6AAAoZSVq+j399NO67LLL9Oyzz2rEiBHq0KGDJN8NI3/TCiXjXzdn27ZtWrdundq0aWNxRQAAoCwaN25c0Ovs7GwdPXpUUVFRiouLO6WbW3/88YemTJmilJQU3X///Vq1apXuuOMORUVFacSIEYX2nzRpkiZOnFhoe1paWtiafjnZmYHXR45mKC0tLeTnqagMw1B6erqk0p2CtqIgP3PIzzwyNIf8zAl3fv4Hh8wK5XURyqEje6S3Bkt7f/W9jqoiXfWOdHoPK6sCAMASJWr69ejRQ/v375fb7Q5a6+Wmm25SXFxcyIqrjBISEgJft23blqcRAQBAkQ4dOlRo28aNG3XLLbfo3nvvPaVj5eXlqVOnTnryySclSWeccYbWrl2rV199tcim34QJE5SSkhJ47Xa7lZiYKJfLFXQtEyqGYSjBeSTw2u6IlMvlCvl5Kir/9aTL5eKGdwmQnznkZx4ZmkN+5oQ7v1AdM5TXRShn0v6S/nuJdHCz77WzpnTNB1K9jpaWBQCAVUrU9MvIyJBhGIGG37Zt2/Txxx+rVatW6t+/f0gLtFo4p6k63rFbt26tX3/9NbAfCmOKFnPIzxzyM4f8zCE/c8rLFFUl1axZMz311FO69tprtX79+mJ/X926ddW6deugba1atdKHH35Y5P7R0dGB9Z0LstlsYbuhGh1hD3ydlZvHjdtT5P9syK1kyM8c8jOPDM0hP3PCmV84P5OSXhehHDm4RXrzEunwdt9rV6J0/SdS9SbW1gUAgIVK1PS79NJLNWTIEN188806fPiwunTposjISO3fv1/PP/+8brnlllDXWWpSU1OVmpqq3NxcSZLH45HD4Qj5eQzDUEZGhqTCF7mzZs1Su3btJEnffPONzjzzzJCfv7w7UX44OfIzh/zMIT9zyM+ccOfn8XhCfsxTFRERoZ07d57S95x77rnasGFD0Lbff/9dSUlJoSzNlAhHftMvOzfPwkoAAEB5UZLrIpQT+36X3rxUOvL351vtdOn6OVLVRGvrAgDAYiVq+v3www964YUXJEkffPCBateurR9//FEffvihHnrooXLd9EtOTlZycrLcbrdcLpecTqecTmfIz+MfCeB0OgvddCy4jt/777+v888/P+TnL+9OlB9OjvzMIT9zyM8c8jMn3Pn5HxoqDXPmzAl6bRiGdu3apZdfflnnnnvuKR3rrrvu0jnnnKMnn3xSw4YN08qVK/Xaa6/ptddeC2XJpkRF5H9eWTk0/QAAQL5QXhehHNi91reGn2ef73XNlr4RfvF1LC0LAICyoERNv6NHjyo+Pl6S9MUXX2jIkCGy2+3q2rWrtm3bFtICrRbOKUBONEVGjx49tHjxYr388st66aWXwnL+8o4pWswhP3PIzxzyM4f8zCmvU1Qda/DgwYXOXbNmTfXq1UvPPffcKR3r7LPP1scff6wJEybo0UcfVePGjTV58mRdc801IazYnChH8PSeAAAAfqG8LkIZt/NH6a3LpIy/13Gs0066brbkrGFpWQAAlBX2k+9SWNOmTTV79mz9+eefWrBggfr16ydJ2rt3rxISEkJaYGU1fPjwwNdLly61sBIAAFAW5eXlBf3Jzc3V7t27NWPGDNWtW/eUjzdw4ED98ssvyszM1G+//aYxY8aEoeqSi3QUHOnHmpYAACBfqK6LpkyZovbt2yshIUEJCQnq1q2bPv/888D7mZmZSk5OVvXq1VWlShUNHTpUe/bsCcePhKLsXOOb0tPf8KvfSRoxl4YfAAAFlKjp99BDD+mee+5Ro0aN1LlzZ3Xr1k2Sb9TfGWecEdICK6sbb7wx8HX37t0trAQAAMB6kYz0AwAAYdagQQM99dRTWr16tb7//nv16tVLl156qdatWyfJNyX63Llz9f7772vJkiXauXOnhgwZYnHVlcSun30Nv8w03+ukc6XrZ0uxp1laFgAAZU2Jpve8/PLLdd5552nXrl3q0KFDYHvv3r112WWXhay4ysxms6l79+5asmSJJGn16tU666yzLK4KAABYKSUlpdj7Pv/882GspPQVHOmXzZp+AABUeuG4Lho0aFDQ6yeeeEJTpkzRihUr1KBBA02dOlUzZsxQr169JEnTp09Xq1attGLFCnXt2rX4xePU7Fn3d8PvsO91w27S8Pek6CqWlgUAQFlUoqafJNWpU0d16tTRX3/9Jcn3NFTnzp1DVhik999/X7Vq1ZIkderUSYbBVFYAAFRmP/74Y7H2q4jrPbKmHwAAKCjc10W5ubl6//335fF41K1bN61evVrZ2dnq06dPYJ+WLVuqYcOGWr58OU2/cNn7m/TfS6SMg77XDTpL17xPww8AgOMoUdMvLy9Pjz/+uJ577jmlp6dLkuLj43X33Xfrn//8p+z2Es0aimPUrFkz6PXGjRvVrFkzi6oBAABW+/rrr60uwTIOu00Ou025eYayGOkHAEClF67rol9++UXdunVTZmamqlSpoo8//litW7fWmjVrFBUVpapVqwbtX7t2be3evfuEx/R6vfJ6vYHXbrdbkmQYRlge8PYft9w/PL5vg/TfQbId3S9JMup3kq79QIqqIoXxZ6sw+VmE/MwhP3PIzxzyMyfc+RX3uCVq+v3zn//U1KlT9dRTT+ncc8+VJH377bd65JFHlJmZqSeeeKIkhy2TrL4Ae/zxx/XAAw9Ikpo3b668PG5ySfwHyCzyM4f8zCE/c8jPnLJyAYaSiXT4mn7ZjPQDAABh0qJFC61Zs0ZpaWn64IMPNGLEiMDSKyU1adIkTZw4sdD2tLS0sN1z8j+kX15ngLCnbVeV94bK7tknScqp3V6eQdNkZBr56/qFSUXIz0rkZw75mUN+5pCfOeHOz//Q0MmUqOn33//+V6+//rouueSSwLb27durfv36uvXWW8t10y81NVWpqanKzc2VJHk8HjkcjpCfxzAMZWRkSDrxL8C4ceO0Z88evfTSS5J8T7IxjWrx80PRyM8c8jOH/MwhP3PCnZ/H4wn5MU/k+++/13vvvaft27crKysr6L2PPvqoVGspDVEOuzKz8xjpBwAACgnVdVFUVJSaNm0qSTrrrLO0atUqvfjii7ryyiuVlZWlw4cPB43227Nnj+rUqXPCY06YMCFoDUK3263ExES5XC4lJCQUu7bi8jcSXS5X+fw3w5Hd0uzrZPPslSQZddrLcf0cJcRWLZXTl/v8LEZ+5pCfOeRnDvmZE+78invMEjX9Dh48qJYtWxba3rJlSx08eLAkhywzkpOTlZycLLfbLZfLJafTKafTGfLz+H8BnE7nST+sUaNGBZp+vXv3VkZGhqKjo0NeU3lyKvmhMPIzh/zMIT9zyM+ccOfnf2ioNMycOVPXX3+9+vfvry+++EL9+vXT77//rj179uiyyy4rtTpKU2SEbwp51vQDAAAFhfO6KC8vT16vV2eddZYiIyO1aNEiDR06VJK0YcMGbd++Xd26dTvhMaKjo4u8j2Oz2cJ2Te8/drn7N0PGIentodKhrb7XNVrIdt1sKe60Ui2j3OZXRpCfOeRnDvmZQ37mhDO/sDb9OnTooJdffln/+te/gra//PLLat++fUkOWWaVhQuwM844I+j1k08+qUcffTQsNZUn/AfIHPIzh/zMIT9zyM+csnABFgpPPvmkXnjhBSUnJys+Pl4vvviiGjdurLFjx6pu3bqlVkdpinb83fRjpB8AACggVNdFEyZM0IABA9SwYUMdOXJEM2bM0OLFi7VgwQK5XC7dcMMNSklJUbVq1ZSQkKDbb79d3bp1U9euXcP401UiWR7pnWHS3nW+166G0nUfS87q1tYFAEA5UqKm3zPPPKOLL75YCxcuDDzNtHz5cv3555/67LPPQlogfPbs2aPatWtLkh577DFNnDiRm70AAFRimzdv1sUXXyzJNw2Vx+ORzWbTXXfdpV69ehW5bkx5F+lgpB8AACgsVNdFe/fu1fXXX69du3bJ5XKpffv2WrBggfr27StJeuGFF2S32zV06FB5vV71799fr7zySth+rkolxyvNulb6a6XvtbOmdP1syVXf0rIAAChv7CX5pu7du+v333/XZZddpsOHD+vw4cMaMmSI1q1bp7feeivUNUJSrVq1dM011wRef/rppxZWAwAArHbaaafpyJEjkqT69etr7dq1kqTDhw/r6NGjVpYWNlF/T++ZzUg/AABQQKiui6ZOnaqtW7fK6/Vq7969WrhwYaDhJ0kxMTFKTU3VwYMH5fF49NFHH510PT8UQ16u9PFYafNXvtfRLunaj6TqTaytCwCAcqhETT9Jqlevnp544gl9+OGH+vDDD/X444/r0KFDmjp1aijrQwGvv/564OtLLrlEXq/XwmoAAIAV/DexLrjgAn355ZeSpCuuuELjxo3TmDFjdPXVV6t3795Wlhg2UazpBwAACqjM10UVyhcPSus+9n0dESsNnyXVrVjLBwEAUFpK3PRD6YuJidFTTz0V9JrGHwAAlUv79u3VpUsXtWvXTldccYUk6Z///KdSUlK0Z88eDR06tMI+hOWf3jM715BhGBZXAwAArFaZr4sqjBWvSitSfV/bHNKwN6WkbtbWBABAOUbTr5y57777dPnllwdeM80nAACVy5IlS9SmTRtNmjRJrVq10ogRI/Tdd99p/PjxmjNnjp577jmddtppVpcZFv6RfhKj/QAAQOW+LqoQfvtUmj8+//XAF6Tm/ayrBwCACoCmXzk0bdq0wNeXX365cnNzLawGAACUpvPPP1/Tpk3Trl279NJLL2nr1q3q3r27mjdvrqefflq7d++2usSwiXTYAl9nsa4fAACVXmW+Lir3/lotfXijpL9nbzj/HumsEZaWBABARRBxKjsPGTLkhO8fPnzYTC0opvj4eI0aNUrTp0+XJH300UeBaSwAAEDl4HQ6NWrUKI0aNUqbNm3S9OnTlZqaqgcffFAXXnih5syZY3WJIRftyH9eLTuX6T0BAIBPZbwuKtcObpFmDJNyMnyv2w2Tej1gbU0AAFQQpzTSz+VynfBPUlKSrr/++nDVigJef/31wNfDhg3T5MmTrSsGAABYqmnTprr//vv1wAMPKD4+XvPmzbO6pLAImt6TkX4AAKAIleW6qNzKTJNmXCkd3e973eh86dKXJZvtxN8HAACK5ZRG+vlHlsF6drtdc+bM0SWXXCJJuuuuu3TTTTcpLi7O4soAAEBpWrp0qaZNm6YPP/xQdrtdw4YN0w033GB1WWERHeEIfJ2ZzfTmAAAgWGW6LiqX8nKlD8dI+zf4XtdoLl35lhQRbW1dAABUIKzpV44NHDhQLpcr8Pr++++3sBoAAFBadu7cqSeffFLNmzdXjx49tGnTJv3rX//Szp079Z///Eddu3a1usSwiIkq0PTLoekHAAAq73VRufTVY9LGBb6vY6pKw2dJsadZWhIAABXNKY30q4wMw5BhhH7NGP9xzR57x44dqlKliiTpxRdfVOPGjXXHHXeEosQyLVT5VVbkZw75mUN+5pCfOeHOrzQ+lwEDBmjhwoWqUaOGrr/+eo0ePVotWrQI+3nLgpgC03tmZNH0AwCgsqvM10Xlzs/vS9++4Pva5pCG/Veqdrq1NQEAUAHR9DtGamqqUlNTlZvru5Hk8XjkcDhO8l2nzjAMZWT4Fiy2mZy3/Oabb9arr74qSbrzzjs1cuTIsNRcloQyv8qI/MwhP3PIzxzyMyfc+Xk8npAf81iRkZH64IMPNHDgwAr/9/2xYguO9MtmTT8AACq7ynxdVK7s+EGac1v+6wsnSaf3sKwcAAAqMpp+x0hOTlZycrLcbrdcLpecTqecTmfIz+MfCeB0Ok3fdHzllVe0YMECbdmyRZJUtWpVeb1eRUZGmq6zrAplfpUR+ZlDfuaQnznkZ0648/M/NBROc+bMCfs5yqrYSNb0AwAA+SrzdVG5cWSPNPMaKSfT9/rM66XON1lbEwAAFRhNv5Ow2Wxhu6nqP3Yojr9x40ZFROR/nC+88ILuu+8+08cty0KZX2VEfuaQnznkZw75mRPO/PhMwiu6QNMvg6YfAABA2ZabI30wSjqy0/e6YTfpouckrpkBAAgb+8l3QXngcDg0ZsyYwOvx48fr6NGjFlYEAAAQWrGR+ZeujPQDAAAo4xZNlLZ95/s6vp407C0pIsramgAAqOBo+lUgqampQa/DMS0pAACAVWIY6QcAAFA+/DZXWvYv39f2SGnYm1KVmtbWBABAJUDTrwKJjIyUx+MJ2jZ79mxrigEAAAix4DX98iysBAAAAMd1YLM0+9b81/2flBLPtq4eAAAqEZp+FUxcXJzGjx8feH3ZZZfp559/trAiAACA0IgOavox0g8AAKDMyToqzbpO8rp9r9sOlTqPOfH3AACAkKHpVwE9+OCDQa87dOiggwcPWlQNAABAaLCmHwAAQBk3725p7zrf1zVaSIP+Jdls1tYEAEAlQtOvAoqLi9Mff/wRtG3YsGEWVQMAABAaQWv6ZdH0AwAAKFN+min9NMP3daRTuvItKbqKtTUBAFDJ0PSroBo3bqxDhw4FXi9atEizZs2ysCIAAABzgtb0y6HpBwAAUGYc2Owb5ec36EWpZgvr6gEAoJKi6VeBVa1aVR988EHg9VVXXaX169dbWBEAAEDJBY/0y7OwEgAAAATkZEkf3iBlpfted7xGan+FtTUBAFBJ0fSr4IYOHRr0ulWrVsrJybGoGgAAgJIr2PRjTT8AAIAy4qtHpZ0/+r6u1kQa8Iy19QAAUInR9KsE1q1bF/Q6MjJSGRkZFlUDAABQMrGR+ZeuNP0AAADKgE0LpWUv+b62R0qXT2MdPwAALETTrxJo3bq15s6dG7Tt7LPPtqgaAACAkgma3pOmHwAAgLXS90kf35z/uu+jUr2OlpUDAABo+lUaAwcO1LRp0wKv161bp5dfftnCigAAAE5NbIGmnyeLph8AAIBlDEP69E7Js8/3ulk/qestlpYEAABo+lUqo0aN0vr16wOvb7/9dv36668WVgQAAFB8drtNVaIjJEnpmdkWVwMAAFCJ/TxLWv+p7+u46tKlqZLNZm1NAACApl9lc/rppwe9btOmjdLT0y2qBgAA4NQ4o32j/TxeRvoBAABYIu0v6bN/5L8eOFmqUsuycgAAQL4K2/TbsGGDOnbsGPgTGxur2bNnW12W5SIjI7Vx40bdfvvtgW3x8fFBIwABAADKqsBIP2+OxZUAAABUQoYhfXKb5E3zvW5/pdT6EmtrAgAAARW26deiRQutWbNGa9as0bfffiun06m+fftaXVaZ0LRpU73wwgtB21q1aqW8vDyLKgIAACieKjGRkiRPVo7y8gyLqwEAAKhkvp8q/fG17+v4etKAp62tBwAABKmwTb+C5syZo969e8vpdFpdSpnhcDh06NChQtv++usviyoCAABWeeSRR2Sz2YL+tGzZ0uqyilTl7+k9DUM6ms0UnwAAAKXm4B/SFw/mv770JSn2NOvqAQAAhZTZpt/SpUs1aNAg1atXTzabrcipOVNTU9WoUSPFxMSoS5cuWrlyZZHHeu+993TllVeGueLyp2rVqnr99deDtjVs2FBer9eiigAAgFXatGmjXbt2Bf58++23VpdUJP/0npKUnskUnwAAAKUiL0/65HYp+6jv9VmjpKZ9rK0JAAAUUmabfh6PRx06dFBqamqR78+aNUspKSl6+OGH9cMPP6hDhw7q37+/9u7dG7Sf2+3WsmXLdNFFF5VG2eXODTfcELSen2EYatGiBY0/AAAqmYiICNWpUyfwp0aNGlaXVCRnwaYf6/oBAACUjh/flLb9/VBY1YZSv8etrQcAABQp4uS7WGPAgAEaMGDAcd9//vnnNWbMGI0aNUqS9Oqrr2revHmaNm2axo8fH9jvk08+Ub9+/RQTE3PC83m93qBGl9vtluRrghlG6NeL8R83HMc+Vc2bN9djjz2mBx/0TdGwbds2xcTEyOv1KjIy0uLqilaW8iuPyM8c8jOH/MwhP3PCnV95/lw2btyoevXqKSYmRt26ddOkSZPUsGFDq8sqJJ6mHwAAQOly75K+eCj/9cDJUnQVy8oBAADHV2abfieSlZWl1atXa8KECYFtdrtdffr00fLly4P2fe+993TTTTed9JiTJk3SxIkTC233eDxyOBzmiz6GYRjKyMiQJNlstpAf/1Tdeeed8nq9evzx/Ce1Ro4cqddee83Cqo6vrOVX3pCfOeRnDvmZQ37mhDs/j8cT8mOWhi5duuiNN95QixYttGvXLk2cOFHnn3++1q5dq/j4+EL7W/mwVMGRfkcys8t1o7W08LCAOeRnDvmZR4bmkJ85PDAFSdLn90reNN/XHYZLTXtbWw8AADiuctn0279/v3Jzc1W7du2g7bVr1w6aqjItLU0rV67Uhx9+eNJjTpgwQSkpKYHXbrdbiYmJcjqdcjqdoSv+b/4LW6fz/9u78/ioqvv/4+/JJJNlkkwSQhICYV8UhLCIiAuiIItLtfJtkVoFtLgFlWJdcKtYLSqtRf3FtQq2KlotaOtCS5GlUJR9E2VHEEggQDLJZM/c3x8hA0MChNyZzCTzej4ePLhz586dM++5gZP7uedce9CctH3kkUe8in6zZ8/W5Zdfrl/96lcBbFXdgjG/poT8zCE/c8jPHPIzx9/5VVVV+XyfjeHE2RV69eqlAQMGqF27dvrb3/6m2267rdb2p7pYqqCgwG9Fv6KiIklSuHF8dN+hI04VFATnrATB5MT8+Hfj7JGfOeRnHhmaQ37m+Du/mguHEMQ2/0P67p/VyzHJ0vBnAtseAABwWk2y6FdfDodDubm59do2MjJSkZGRtdZbLBa//WJQs+9g+cUjOjpahmHoxRdf1KRJkyRJt99+u4YPHx6U03sFW35NDfmZQ37mkJ855GeOP/NrLt9JQkKCunbtqu3bt9f5/KkulnI4HIqPj/d5e2oKiQ6HQ8mOAs96t9Umh8Ph8/drbk7Mr7kco42J/MwhP/PI0BzyM8ff+fGdBLmSfOmL3xx/fNXzUkxSwJoDAADOrEkW/ZKTk2W1WmsV9HJzc5WWlubT9wqFe/qd7J577vEU/SSpXbt2GjdunN56662g6ZAHc35NAfmZQ37mkJ855GcOU1TVT1FRkXbs2KGbb765zucDebGUI+b4yL6C0sqg6ZsEOy4WMIf8zCE/88jQHPIzJ5QumJo2bZrmzJmj77//XtHR0brooov03HPPqVu3bp5tBg8erMWLF3u97o477tBrr73W2M31v/mPS0XHzr11HSH1uCGw7QEAAGfUJIt+NptN/fr104IFC3T99ddLktxutxYsWKCJEyea2nd2drays7M903OFyj39Tpafn6+EhATP41mzZqlly5Z64oknTv2iRhTs+QU78jOH/MwhP3PIzxzu6Ve33/zmN7r22mvVrl077d+/X7/97W9ltVo1ZsyYQDetloQYm2c5v7g8gC0BAADNzeLFi5WVlaX+/fursrJSjzzyiIYNG6bNmzd73fplwoQJeuqppzyPY2JiAtFc/9rztbTmL9XLtjjp6hckfv8AACDoBW3Rr6ioyGtKqV27dmndunVKSkpS27ZtNXnyZI0dO1bnn3++LrjgAs2YMUMul0vjx4839b5ZWVnKysqS0+mUw+EIqXv6nayoqEixsbGex9OnT9fNN9+s8847L4CtqtYU8gtm5GcO+ZlDfuaQnznc069uP/74o8aMGaPDhw+rZcuWuuSSS/T111+rZcuWgW5aLYknjPQ7StEPAAD40Lx587wez5o1SykpKVq9erUGDRrkWR8TE+PzmaaCSlWl9Pn9xx8PeUJytA5cewAAQL0FbdFv1apVuvzyyz2Pa+4bM3bsWM2aNUujR4/WoUOH9MQTTygnJ0e9e/fWvHnzlJqaGqgmNzsxMTFyOp1e9+bp1auXvv32W5177rkBbBkAAPClDz74INBNqLfEE0b6HS2uCGBLAABAc1dQUH0v4aQk7/vYvffee3r33XeVlpama6+9Vo8//njzGu234g0pd1P1cqveUv/bAtocAABQf0Fb9Bs8ePAZ74szceJE09N5nozpPb1ZLBa9+OKLuu+++zzrevTooe7du2vZsmUKDw/MIdRU8gtW5GcO+ZlDfuaQnzlM79n0JZx4Tz+KfgAAwE/cbrcmTZqkiy++2GvGo1/84hdq166d0tPTtWHDBj300EPasmWL5syZc8p9lZWVqayszPPY6XRKkt/uNW3qPtaFB6SFv5dFkiGLdPUfJUuY1EzuXV0f3EfdHPIzh/zMIT9zyM8cf+dX3/0GbdEvUJjes7asrCyFhYXpnnvu8azbvHmzEhMT5Xa7A9KmppRfMCI/c8jPHPIzh/zMYXrPpi82MlzhYRZVug2m9wQAAH6TlZWlTZs2aenSpV7rb7/9ds9yz5491apVKw0ZMkQ7duxQp06d6tzXtGnTNHXq1FrrCwoK/Fb0KyoqknT2F7rFfPGQbOWFkqTy88aoJLazdGzEY6gwkx/IzyzyM4f8zCE/c/ydX81FQ2dC0e8MLBaL3w7wmn0H+w+Q1WrVxIkT1aVLF40YMcLruYcffljPPfdcQNrVVPILVuRnDvmZQ37mkJ85/syP78T/LBaLEmIilFdUrnxG+gEAAD+YOHGiPvvsMy1ZskRt2rQ57bYDBgyQJG3fvv2URb8pU6Z4blsjVZ+0y8jIkMPh8Lqliq/UFBIdDsfZ9U93LpZl6z+q9xGdJNvIp2WLcfi8fcGuwflBEvmZRX7mkJ855GeOv/Or7z4p+qHehg8frnnz5nkV/p5//nk5HA498sgjAWwZAAAIJQkxNuUVlTPSDwAA+JRhGLrnnns0d+5cLVq0SB06dDjja9atWydJatWq1Sm3iYyMVGRkZK31QXWheWW59OUDx19/5VOSvYVf2tYUcKGlOeRnDvmZQ37mkJ85wXChOUW/MwjK+dUDaNiwYSooKJDDcfxKr0cffVSfffaZ3nvvPbVv375R2tFU8wsW5GcO+ZlDfuaQnznBMr86zEmKsUmSisurVFpRpagI399/GQAAhJ6srCy9//77+vTTTxUXF6ecnBxJ1VfsR0dHa8eOHXr//fd11VVXqUWLFtqwYYN+/etfa9CgQerVq1eAW2/SijekvK3Vy20ukHrfFNj2AACABqHod5Ls7GxlZ2d77snjcrlktfr+RJJhGCopKZHU9KYCCwsL04cffqjRo0d71i1fvlwdO3bUP//5Tw0ePNjvbWjK+QUD8jOH/MwhP3PIzxx/5+dyuXy+T9TWMu74lfIHnWVq2yImgK0BAADNxauvvipJtc5rzJw5U+PGjZPNZtN//vMfzZgxQy6XSxkZGRo1apQee+yxALTWh1yHpcXPH3tgka6aLoWFBbRJAACgYSj6nSQrK0tZWVlyOp1yOByy2+2y2+0+f5+akQB2u71JnrT92c9+pv/7v//Tn/70J/3mN7/xrL/22ms1a9Ys3XLLLX59/6aeX6CRnznkZw75mUN+5vg7v5qLhuBfqfFRnuUcZylFPwAA4BNnmrUhIyNDixcvbqTWNKLFz0plBdXLvW+S0nsHtDkAAKDhKPqdQVDNrx5kLBaL7r//flmtVv3617/2rB83bpw2btyoZ599VuHh/jvEmnp+gUZ+5pCfOeRnDvmZEwzzq8OcNMfxkX45ztIAtgQAAKCJO7RFWvlW9XKEXbqiiY9aBAAgxDFWH6bdd999Wr58ude6P/7xj3r00UcD1CIAANCcnTjS7yBFPwAAgIb79+OScWy2iksmSfGtAtocAABgDiP9zsAwjDNO72Bmv/7YdyAMGDBA3333nc4991zPuueff14JCQm69957FRPj22m3mlt+jY38zCE/c8jPHPIzx9/58b00Dq/pPQso+gEAADTInm+kbf+qXo5vLQ2cGNj2AAAA0yj6nSQ7O1vZ2dmee/K4XC5ZrVafv49hGCopKZHUfKYCa9OmjQoLCxUXF+dZ98gjj+iRRx7RN998o+7du/vsvZpjfo2J/MwhP3PIzxzyM8ff+blcLp/vE7WlnXRPPwAAADTAot8fXx78sGTjPskAADR1FP1OkpWVpaysLDmdTjkcDtntdtntdp+/T81IALvd3uxO2paUlGjkyJFatGiRZ92AAQN05ZVX6t1331XLli1Nv0dzzq8xkJ855GcO+ZlDfub4O7+ai4bgX2mO40W/XIp+AAAAZ2/3MmnnourlxA5S5piANgcAAPgGRb8zsFgsfjupWrPv5nbSNioqSgsXLtTWrVvVrVs3z/r58+crNTVVbrfbJ5+5uebXWMjPHPIzh/zMIT9z/Jkf30njiIqwKjEmQkeLK/Tj0ZJANwcAAKDpWTL9+PJlD0nWiMC1BQAA+ExYoBuA5qtr16769ttva60PCwtTbm5uAFoEAACai/bJ1TMxHCgoVXF5ZYBbAwAA0IQc/F7aubB6ObG91PNnAW0OAADwHYp+8Kvu3bvXeX+jtLQ0LV26NAAtAgAAzUHH5FjP8u684gC2BAAAoIlZ8frx5QF3SlYmAgMAoLngf/UzMAzDc/8ff+zXH/sONtHR0SosLFR6eroKCws96y+99FJJ0s9+9jN9+OGHZ7XPUMrPH8jPHPIzh/zMIT9z/J0f30vj6djy+D2Xd+YVqXt6fABbAwAA0ESUFUnrP6hetsVKvX8R2PYAAACfouh3kuzsbGVnZ6uqqkqS5HK5ZLVaff4+hmGopKT6HjShcv+f/fv3a9myZRoxYoTX+o8++khTpkxRly5d6r2vUMzPl8jPHPIzh/zMIT9z/J1fXaPb4R8dk48X/XYdIncAAIB62fKFVHFsloSeP5OiHIFtDwAA8CmKfifJyspSVlaWnE6nHA6H7Ha77Hb7mV94lmpGAtjt9pA6aTts2DC53W6FhXnPLNu3b1+9+uqrGj9+vGw22xn3E6r5+Qr5mUN+5pCfOeRnjr/zq7loCP7X4YSRftsOFgWwJQAAAE3Ixo+PL3MvPwAAmh2KfmdgsVj8dlK1Zt+heNK2vLxcjz32mJ5//nnPurvuuksrVqzQW2+9JenMIzBCOT9fID9zyM8c8jOH/MzxZ358J42nU8tY2cLDVF7p1sZ9BYFuDgAAQPArOSrtWFC9HN9aajswsO0BAAA+F3bmTQDfi4iI0HPPPadly5Z5jaScOXOmwsLCFBYWphUrVgSwhQAAIJhFWMPUvVX1ffx25blUUFIR4BYBAAAEuZ2LJXdl9XL366QwTgsCANDc8L87Auqiiy5SUVGRbrnlllrPDRgwgGnSAADAKWW2OX4Pmo0/MtoPAADgtHYuPL7caUjg2gEAAPyGoh+CwjvvvKMZM2bUWh8eHq7Jkyd77sEEAABQIzMjwbO8YveRwDUEAACgKdhxrOhntUntLgpsWwAAgF9Q9EPQuO+++1RWVlZr/Z/+9Cd16NBBu3fvpvgHAAA8BnZq4VlesvVQAFsCAAAQ5PL3Svk/VC9nDJBsMYFtDwAA8IvwQDcg2BmG4ZdCU81+KWJ5i4iI0O7du9W+fXuv9T/88IM6dOigBx54QM899xz5mUR+5pCfOeRnDvmZ4+/8+F4aVytHtLqlxmlLbqHW/5ivo65yJdptgW4WAABA8Nm3+vhy24GBawcAAPArin4nyc7OVnZ2tudeci6XS1ar1efvYxiGSkpKJEkWi8Xn+2/KWrRoocLCQi1cuFA/+clPvJ6bPn26pk+frvnz56tXr16SyK8hOP7MIT9zyM8c8jPH3/m5XC6f7xOnN7hbS23JLZRhSIu2HtRP+7QJdJMAAACCz/61x5fT+wSuHQAAwK8o+p0kKytLWVlZcjqdcjgcstvtstvtPn+fmpEAdrudk7ancM011+itt97SbbfdVuu5K6+8Ur/85S/1zjvvkF8DcPyZQ37mkJ855GeOv/OruWgIjWfIual6fclOSdKcNfso+gEAANRl/5rjyxT9AABotij6nYHFYvHbSdWafXPS9tRuvfVW3XrrrVqyZIkuu+wyr+feffddvfvuu7riiiv0ySefKC4uLkCtbJo4/swhP3PIzxzyM8ef+fGdNL7z2yUqIylae4+UaNn2POUUlCrNERXoZgEAAAQPw5AObKhejk2T4lsFtj0AAMBvwgLdAKA+Bg0apMOHD2vSpEm1nvvqq68UHx+vpUuXNn7DAABAQIWFWTyj+9yG9N43PwS4RQAAAEHGlSeV5lcvp5wb0KYAAAD/ouiHJiMpKUl/+tOfdOutt9b5/KWXXiqLxaJt27Y1cssAAEAgjbkgQ+Fh1aMs/7L8B7nKKgPcIgAAgCCSt/X4cnLXwLUDAAD4HUU/NDlvvvmm5s6dqyuuuKLO57t27aq1a9fW+RwAAGh+WjmidV3v1pKkgpIKvfs1o/0AAAA8vIp+XQLXDgAA4HcU/dDkhIWF6brrrtOnn34qt9utzz77rNY2ffv21aWXXqpdu3bpxx9/DEArAQBAY7rjso6quaVi9sLtyi8uD2yDAAAAgsXh7ceXKfoBANCsUfRDk3f11Vdr8eLFtdYvXbpUHTt2VEZGhv73v/8FoGUAAKCxdE2N0//1rb63n7O0Ui8t2H6GVwAAAISIvBNug9KCoh8AAM1ZeKAbEOwMw5BhGH7brz/2HQpOzu/SSy+V2+3WVVddpXnz5tXa/uKLL9aePXvUpk2bxm5qUOL4M4f8zCE/c8jPHH/nx/cSWPcP66Z/btiv0gq33lm+W6P6tVaPdEegmwUAABBYBXur/7bapLhWgW0LAADwK4p+J8nOzlZ2draqqqokSS6XS1ar1efvYxiGSkpKJEmWmrmoUG+nyu+jjz6SJL3//vu64447vF7Ttm1b3XPPPXrooYfkcIT2CUCOP3PIzxzyM4f8zPF3fi6Xy+f7RP2lOaJ09+DOemH+VlW5DU2Zs1Fz775Y1jB+VgAAQAgr2Ff9d3xrKYxJvwAAaM4o+p0kKytLWVlZcjqdcjgcstvtstvtPn+fmpEAdrudk7YNcKb8JkyYoJ/+9Ke666679Pe//92z/uWXX9bLL7/seVxeXq7w8ND7MeD4M4f8zCE/c8jPHH/nV3PREALnzss66Z/r92vbwSJt+LFAM5ft0q8u7RjoZgEAAARGqVMqK6hedjD7EQAAzV3oVTvOksVi8dtJ1Zp9c9K2Yc6UX8uWLfXxxx9r586d6tSpU53bpKena9OmTUpNTfVnU4MSx5855GcO+ZlDfub4Mz++k8CzhYfp2VE99X+vLZdhSH/49xYN7paizimxgW4aAABA43PuO74c3zpw7QAAAI2CMf1o9jp27CjDMLR3795az+Xl5SktLU1z5swJQMsAAIA/9GuXpFsubCdJKq1wa9KHa1Ve6Q5wqwAAAAKg4ISiHyP9AABo9ij6IWS0adNGhmEoMzOz1nOjRo2SxWLRTTfdFICWAQAAX3t45Lnq1LJ6ivZN+5x6Yf7WALcIAAAgAApOuADawUg/AACaO4p+CDlr167V+vXr63zu/fffV3x8vFatWqWFCxdybyYAAJqoaJtVL97YRxHW6ilXX1+yQ//bnhfgVgEAADQy5/7jy/GM9AMAoLmj6IeQY7FY1KtXL5WUlGj37t21ni8sLFT//v11xRVXKDw8XEVFRY3fSAAAAuTZZ5+VxWLRpEmTAt0U085r7dADw7tJkgxDuveDdcp1lga4VQAAAI3IdfD4clxq4NoBAAAaBUU/hKyoqCi1a9dOhmFo69ZTT/kVFxenO+64Q/v37z/lNgAANAcrV67U66+/rl69egW6KT7zq0s66tIuyZKkvKIyZb23RhVV3N8PAACECNcJMx3EJAeuHQAAoFFQ9AMkdenSRYZhnHJU3xtvvKHWrVvLYrHopZdeauTWAQDgf0VFRbrpppv05ptvKjExMdDN8ZmwMItmjO6tdEeUJGnVD0c17YvvA9wqAACARnJi0c9O0Q8AgOaOoh9wArvdrqqqKt19992n3Oa+++7TTTfdpL/+9a91Tg8KAEBTlJWVpauvvlpDhw4NdFN8rkVspLJv6uu5v9/by3bpH+sZwQ8AALxNmzZN/fv3V1xcnFJSUnT99ddry5YtXtuUlpYqKytLLVq0UGxsrEaNGqXc3NwAtbgeXIeq/450SOGRgW0LAADwu/BANwAINmFhYXrppZc0atQorV+/XpMnT661zfvvv6/3339fkrRx40a1b99edrtdFoulsZsLAIBpH3zwgdasWaOVK1fWa/uysjKVlZV5HjudTkmSYRgyDMPn7avZr5l9985I0G+v7a7HPvlWkvTgx+vVLilavdok+KiVwcsX+YUy8jOH/MwjQ3PIzxx/5xds38vixYuVlZWl/v37q7KyUo888oiGDRumzZs3y263S5J+/etf6/PPP9dHH30kh8OhiRMn6oYbbtCyZcsC3PpTKD420s/eIrDtAAAAjYKiH1AHq9WqK664QldccYV+/etfS5JWr16t888/v9a2PXv29CyXlpYqMpIr5wAATcfevXt13333af78+YqKiqrXa6ZNm6apU6fWWl9QUOC3ol/NFNxmLrC5uptDK3qm6B8bD6q0wq3bZq3Uu2MzlRbfvP/v9lV+oYr8zCE/88jQHPIzx9/51Vw4FCzmzZvn9XjWrFlKSUnR6tWrNWjQIBUUFOitt97S+++/ryuuuEKSNHPmTJ177rn6+uuvdeGFFwai2adWVS6VFlQv21sGti0AAKBRUPQD6qlfv35yOp2Kj48/5TZRUVH673//q0suuaQRWwYAQMOtXr1aBw8eVN++fT3rqqqqtGTJEv2///f/VFZWJqvV6vWaKVOmeI2EdzqdysjIkMPhOO3/kw1VU0h0OBymTzg+//M+2l+4Qqt2H1Weq0K/nrtFH90xUPbI5tst9mV+oYj8zCE/88jQHPIzx9/5Bft3UlBQXTBLSkqSVN1vqqio8JoO/ZxzzlHbtm21fPnyUxb9AjZLQtEh1SRs2JOlIBtZGawYIWwO+ZlDfuaQnznkZ06wzJDQfM9u+EgwT1MVygKVX2xsrNxutyRp06ZN6tWrV61tLr30UknSv/71Lw0ePFgRERGN2sb64Pgzh/zMIT9zyM+cYOmABZMhQ4Zo48aNXuvGjx+vc845Rw899FCtgp8kRUZG1jmy3WKx+O3kXc2+ze4/KiJcb9x8vq7PXqY9R4r13YFC3ffBOr1+cz+FW5vv7a59lV+oIj9zyM88MjSH/MzxZ37B/J243W5NmjRJF198sc477zxJUk5Ojmw2mxISEry2TU1NVU5Ozin3FahZEqwlP6jmcqzycIdKjhUxcXqMEDaH/MwhP3PIzxzyMydYZkig6HeS7OxsZWdnq6qqSpLkcrnqPNlllmEYKikpkcQPUEMEQ34dOnRQYWGhduzYod69e9d6fvjw4ZKkBx54QI899pjCwoLnRGIw5NeUkZ855GcO+Znj7/xcLpfP9+lvcXFxnhNZNex2u1q0aFFrfXORZLfp7XH9dcMry+QsrdSC7w/qkbkb9dyoXvxcAQAASVJWVpY2bdqkpUuXmt5XoGZJiC0t9ayzJabL5nD4/L2aI0YIm0N+5pCfOeRnDvmZEywzJFD0O0lWVpaysrLkdDrlcDhkt9s9N2v2pZoDwG638wPUAMGUX69eveR2u7VixYo6p/KYPn26pk+fLknasmWLunTp0thNrCWY8muKyM8c8jOH/Mzxd341Fw0h+HVOidVrv+ynsTNXqKLK0N9W/ShHdIQeuepcfrYAAAhxEydO1GeffaYlS5aoTZs2nvVpaWkqLy9Xfn6+12i/3NxcpaWlnXJ/AZsloeTo8ccxLST6OPXGCGFzyM8c8jOH/MwhP3OCYYYEin5n0BSmqQpVwZbfgAEDZBiG3G63brvtNs2aNavWNt26dZMkPfPMMxo7dqxKS0vVqVOnRm5ptWDLr6khP3PIzxzyMycYOmDBbtGiRYFuQqO4qHOyZozuo4mz18gwpDf/u0sJMTZlXd450E0DAAABYBiG7rnnHs2dO1eLFi1Shw4dvJ7v16+fIiIitGDBAo0aNUpS9cW9e/bs0cCBAwPR5NMrPWE6z+iEgDUDAAA0nuCZbxBoJsLCwjRz5kxVVlZq/PjxdW7z6KOPqk2bNurcubOOHj1a5zYAAMD/ru7VSr//aU/P4+n/2qJZy3YFsEUAACBQsrKy9O677+r9999XXFyccnJylJOT45ke3uFw6LbbbtPkyZO1cOFCrV69WuPHj9fAgQPrnPkn4E4s+kUxtScAAKGAoh/gJ1arVW+//bY2btzoNR3IyZKSktSiRQstWLBAu3ZxkhEAgMY25oK2enjkOZ7HT/5zs95ayv/JAACEmldffVUFBQUaPHiwWrVq5fnz4Ycferb505/+pGuuuUajRo3SoEGDlJaWpjlz5gSw1adB0Q8AgJDD9J6An5133nnau3evysvL9d133+mNN97QK6+84rXNkSNHNHToUM/jtWvXqnfv3o3cUgAAQtedl3WSq6xSL3+1XZL0u882y+02NGFQxwC3DAAANJaa+z+fTlRUlLKzs5Wdnd0ILTKJoh8AACGHkX5AI7HZbMrMzFR2drYMw5BhGIqPj69z2z59+shisejOO+9s5FYCABC6Jl/ZVZOGdvE8fuaL75S9cHu9TgACAAAEnTKKfgAAhBqKfkAAFRQU6I033jjl86+//rosFovuuusuFRUVNWLLAAAIPRaLRZOGdtX9V3b1rJv+ry363Wffye2m8AcAAJoYRvoBABByKPoBATZhwgQZhqEVK1boF7/4RZ3bvPbaa4qLi5PFYpHD4aAACACAH90zpIvXPf7eXrZL936wVmWVVQFsFQAAwFnyFP0ski0uoE0BAACNg6IfECT69++v9957T4Zh6Icffjjldk6n01MA7NGjh8rKyhqxlQAAhIY7L+uk50f1kjXMIkn6bMMBjZ+5UoWlFQFuGQAAQD3VFP2i4qUwTgECABAK+B8fCEJt27aV2+1WeXm5unTpcsrtNm/erKioKCUkJKi0tLQRWwgAQPP38/4ZevOWfoqKqO4y/2/HYf3steXae6Q4wC0DAACoB0/Rj6k9AQAIFRT9gCBlsVgUERGhrVu3qrKy8rTbFhQUKDo6WjExMXr00Uf15ZdfNlIrAQBo3q44J1XvT7hQiTERkqTvcwr1k/+3VP/bkRfglgEAAJyGYVD0AwAgBFH0A5oAq9WqvXv36pVXXtHq1av1xBNP6PXXX6+1XUlJiX7/+9/rqquuUqtWrfTvf/87AK0FAKB56ds2UX+/6yJ1TLZLko4WV+jmt1boL8t3yzCMALcOAACgDlVlslSVVy9HJQS0KQAAoPFQ9AOaiDZt2uiuu+5S3759NXXqVN1+++2qqKhQZmZmndvn5ORo+PDhstlseuGFF/Svf/3rjCMGAQBA3Tq2jNXcrIt1WdeWkqQqt6EnPv1WD368QSXlVQFuHQAAgDdLWcHxB4z0AwAgZFD0A5qw8PBwrVu3ToZhaPv27XVuU1FRofvvv18jRoxQRESErr32Wq1du7aRWwoAQNPniI7Q2+P6645BHT3rPlr9o67LXqptuYUBbBkAAIA3S1nR8Qe22MA1BAAANCqKfkAz0alTJxmGoT//+c+n3e6zzz5Tv379FBcXp7CwML388svKz8+X0+lspJYCANB0WcMsmnLVuZoxureiI6ySpK25RfrJ/1umv6/+McCtAwAAqGapKD7+IJKiHwAAoYKiH9DM3HbbbcrPz5dhGMrLy1NcXNxpt7/33nuVmJio1q1bq7y8vJFaCQBA03Z9n9b65z0Xq1tq9f+zJRVVuv+j9Zr84ToVlFQEuHUAACDkVbiOL9vsgWsHAABoVM266Ldr1y5dfvnl6t69u3r27CmXy3XmFwHNgMNRPV9/ixYt5HQ6tWXLFs2dO1fjxo1T375963xNUVGRIiMj9fvf/17ffPON3n33XRmG0ZjNBgCgSemcEqdPsi7Wjf0zPOvmrN2nETOW6L/bDgWwZQAAINRZvIp+jPQDACBUNOui37hx4/TUU09p8+bNWrx4sSIjIwPdJCAgunbtquuvv14zZ87U6tWrdcstt5xy20cffVQXXnihbr75ZoWFhemaa67R66+/rq+//roRWwwAQNMQbbPq2VG9NGN0b8VFhkuSDhSU6ua3VuixTzbKVVYZ4BYCAIBQZClnpB8AAKGo2Rb9vv32W0VEROjSSy+VJCUlJSk8PDzArQKCw6xZs5Sfn68lS5boxx9/1KhRo0657eeff64777xTAwcO1OrVq1VYWNiILQUAoGm4vk9rzfv1IF3SOdmz7t2v92j4jCVauOVgAFsGAABCESP9AAAITUFb9FuyZImuvfZapaeny2Kx6JNPPqm1TXZ2ttq3b6+oqCgNGDBAK1as8Dy3bds2xcbG6tprr1Xfvn31+9//vhFbDwQ/q9WqSy65RK1bt9bHH38swzA0ffr0077m/PPPV3x8vCwWi/bt26eqqqpGai0AAMGvdUK0/nLrBfrddT0UHWGVJP14tETjZ67U3e+tVq6zNMAtBAAAocJSXnz8ASP9AAAIGUFb9HO5XMrMzFR2dnadz3/44YeaPHmyfvvb32rNmjXKzMzU8OHDdfBg9ZXUlZWV+u9//6tXXnlFy5cv1/z58zV//vzG/AhAk/Ob3/xGhmHIMAwdPXr0tNu2adNG4eHhslgsnvtlVlVVqaysrDGaCgBAUAoLs+jmge315X2X6sKOSZ71X2zM0ZA/LtasZbtU5eaeuQAAwM8Y6QcAQEgK2vkuR44cqZEjR57y+RdeeEETJkzQ+PHjJUmvvfaaPv/8c7399tt6+OGH1bp1a51//vnKyMiQJF111VVat26drrzyyjr3V1ZW5lWscDqdkuQpgPhazX79se9QQH7m1Cc/h8Mht9utI0eO6JNPPtGvfvWrU24bG+v9C8SXX36p4cOH+6y9wYbjzxzyM4f8zPF3fnwvqNE+2a7ZEy7U3LX79PTn3+mIq1xFZZV68p+b9cHKvXr8mu66+ISpQAEAAHzJUsFIPwAAQlHQFv1Op7y8XKtXr9aUKVM868LCwjR06FAtX75cktS/f38dPHhQR48elcPh0JIlS3THHXeccp/Tpk3T1KlTa613uVyyWq0+/wyGYaikpESSZLFYfL7/5o78zDmb/CIjIzV69GiNGjVK27Zt0+uvv6633nrrtK+pKdgnJyfrn//8p9q1a6e4uDjfND4IcPyZQ37mkJ85/s6vZuQzIFUfYzf0baMrzknRc/O+1+wVeyVJ3+cU6qY/f6Oh56bokavOVceWXH0PAAB8y1JedPwBRT8AAEJGkyz65eXlqaqqSqmpqV7rU1NT9f3330uSwsPD9fvf/16DBg2SYRgaNmyYrrnmmlPuc8qUKZo8ebLnsdPpVEZGhux2u+x233eOakYC2O12Tto2APmZ09D8zj//fJ1//vl68803JUlr165Vv379Trl9Xl6eBg4c6Hm8YMECtWzZUj169GjS3xvHnznkZw75mePv/LjXKeqSEGPTtBt66f/6tdGT/9isjfsKJEn/+e6gFm05pJsHttO9V3RRot0W4JYCAIDmwnukHxcYAQAQKoL2nn6+MHLkSG3cuFGbNm3SCy+8cNptIyMjFR8f7/UHwOn16dNHbrdbR48e9Uy1ezpDhgxRr169ZLVa9e9//9tzD04AAEJBv3ZJ+jTrYv3xZ5lKjY+UJFW6Dc1ctluXPr9Qf5q/Vc7SigC3EgAANAsn3tMvkqIfAAChokmO9EtOTpbValVubq7X+tzcXKWlpZnad3Z2trKzsz1X6jO9Z3AiP3N8nV94eLheeuklvfTSS3K73fr1r3+tQ4cO6bvvvtP27dvrfM2IESO8Ho8ZM0ZPPPGE0tPTFRYW3NcjcPyZQ37mkJ85TO+JQAsLs2hUvzYa2TNNbyzZqdcX71RJRZWKyir14oJtemf5bt0xqJPGXtROMbYm2VUHAABBwFLOPf0AAAhFTfJMgs1mU79+/bRgwQJdf/31kiS3260FCxZo4sSJpvadlZWlrKwsOZ1OORwOpvcMUuRnjr/z+/Of/+xZnj17tm666aYzvmb27NmaPXu25/HMmTN1yy23BOX3y/FnDvmZQ37mML0ngkWMLVyThnbVjf3b6uWvtunDlXtV6TaUX1yh5+Z9r7eW7tQdgzrpFwPayh7ZJLvsAAAggCwnjvSLoOgHAECoCNozCEVFRV4jhHbt2qV169YpKSlJbdu21eTJkzV27Fidf/75uuCCCzRjxgy5XK56TTF4NiwWi99Oqtbsm5O2DUN+5jRWfr/4xS80dOhQPfTQQxo1apT+8Ic/aPHixWd83fjx4z0/z2vXrlVmZmZQfdccf+aQnznkZ44/8+M7wdlKc0TpmZ/21B2DOunFBds0d+2PchtSXlG5nvniO2Uv2q6xA9tr3EXtuecfAACoN0/RLzxKsgbt6T8AAOBjQfu//qpVq3T55Zd7Hk+ePFmSNHbsWM2aNUujR4/WoUOH9MQTTygnJ0e9e/fWvHnzlJqa6tN2GIbhGRXgj/36Y9+hgPzMaez8WrZsqbfffluSdPXVV3vWHzlyRF999ZVmzpypL7/88pSv79Onj6Tqn/8uXbpo3LhxSk9P92+jT4PjzxzyM4f8zPF3fnwvaKi2LWL0x59n6q7BnfSn/2zV5xsOSJLyiyv04oJtevO/OzXmgrb61aUd1MoRHeDWAgCAoFd+rOjH1J4AAISUoC36DR48+IwnziZOnGh6Os+TcU+/poH8zAmW/CIjIzVy5EiNHDlSe/bs0fz581VWVqYPPvhAa9eurbX9O++8I0l67LHHJFWPBnzggQeUkZHRqO0OlvyaKvIzh/zM4Z5+CHadU2KV/Yu+mjSkUK8u3qFP1+1XldtQcXmV3lq6S39ZvltX92yl8Rd3UGZGQqCbCwAAgpSl4tg9/Sj6AQAQUoK26Bco3NOvaSA/c4Ixv3PPPVfnnnuuJOmBBx5QVVWVLrzwQq1evfqUr5k5c6ZmzpwpSercubO+/vprJSUl+b2twZhfU0J+5pCfOdzTD01Fl9Q4vfDz3pp8ZVe9uWSnPli5V2WVblVUGfpk3X59sm6/+rZN0K2XdNDwHmmKsIYFuskAACCIWCqrL3RTRExgGwIAABoVRb8z4J5+wYv8zAn2/MLDw7Vq1SpJ0s6dO/WHP/xBc+fOVU5OTp3bb9++XcnJyZ7HkyZN0p/+9Ce/tS/Y8wt25GcO+ZnDPf3QlLRJjNHU687TPUO6aOayXXrvmz3KL66QJK3Zk681769VK0eUfnlhO/2sXxulxEcFuMUAACDgDEOqLK1eDqdvAABAKOGSYABBr2PHjnrllVd04MABPfPMM7rzzjs1dOjQ075mxowZnpP6t956qwYPHqz33nuvkVoMAIBvJcdG6oHh52j5w0M07Yae6poa63nuQEGppv9riwY++5Um/GWVvvo+V1Vu7i8JAEDIclfIYrirlyO4FzAAAKGEkX5nYBjGGe8taGa//th3KCA/c5pyflOmTPF6vHXrVo0ZM6bOewDWqJkCdPHixfrlL38pSVq6dKkGDBjQoHt2NuX8ggH5mUN+5vg7P74X+Fu0zaoxF7TVjf0z9L8dhzVz2S4t+P6gDEOqchuavzlX8zfnqpUjSj87P0M/P7+NWidwsg8AgJBSUXJ8mZF+AACEFIp+J8nOzlZ2drbnnjwul6tBRYEzMQxDJSXVnTCmAjt75GdOc8qvdevWWrJkiYqLizVz5kxlZmbqmWee0dKlS0/7uksuucTr8erVq9W1a9d6vWdzyi8QyM8c8jPH3/m5XC6f7xOoi8Vi0cWdk3Vx52TtPVKsv63aq7+t2qtcZ5mk6tF/Ly3YppcWbNOADkkacU6SbrggRo5oW4BbDgAA/K5mak+JkX4AAIQYin4nycrKUlZWlpxOpxwOh+x2u+x2u8/fp2YkgN1u56RtA5CfOc0xP7vdrgcffFCSNHz4cElSVVWVli1bpnfffVcrV67U+vXrT/n6fv36eT1+7733NGbMmDq3bY75NSbyM4f8zPF3fjUXDQGNKSMpRvcP66b7hnTRoi2HNHvFHi3cclA1M3x+s+uIvtl1RM/O36mh3VN1Q5/WGtS1pSKszPQPAECzdGLRj5F+AACEFIp+Z1BzTzB/7puTtg1DfuaEQn7h4eG67LLLdNlll6miokJr1qzR/Pnz9fjjj5/xtTfddJNuuukmz+ORI0dqzpw5stlsXtk15/z8ifzMIT9z/Jkf3wkCKdwapqHdUzW0e6oOFJTo41U/au7afdqZVz0CtazSrc83HNDnGw4oyW7TNb1a6eqerXR++yRZwzh2AQBoNioo+gEAEKq4vBdASIiIiNCAAQP02GOPqaqqSoZhqLS0VC+88EK9Xv/ll18qOjpaVqtVmZmZ+vTTT/3cYgAAGq6VI1r3DOmiBfdfprl3X6Qx/VopyX58as8jrnL9ZfkPGv3G17pw2gI98ekmLd9xWFVu7ksJAECTV3nCPf0iKPoBABBKGOl3BoZheKYC88d+/bHvUEB+5oR6fhaLRYZhyGazadKkSZo0aZL+8pe/aM2aNRo0aJA+/fRT/fWvfz3l6zdu3Khf/vKX+uUvf6nIyEiVlZVp27Zt6tChg0pLSxUTE9OIn6bpCfXjzyzyM8ff+fG9INhYLBb1zkhQh/iOmvrTTP13W57mrN2n+ZtzVV7pliQdKizTX5b/oL8s/0HJsTYN75Gmq3u20gUdkhTOFKAAADQ9XiP9uKcfAAChhKLfSbKzs5Wdne25J4/L5ZLVavX5+xiGoZKS6iuvmArs7JGfOeRX26hRozRq1ChJ1fcEfOWVV7R9+3b16dPntK8rKyuTJHXp0qXWc08//bTuvPNORUZG+r7BTRjHnznkZ46/83O5XD7fJ+ArEdYwDTk3VUPOTZWztEJffXdQn288oMVbD3kKgHlF5Xrvmz1675s9io8K1+XnpGjIuam6rGtLOaIjAvwJAABAvZx4Tz9G+gEAEFIo+p0kKytLWVlZcjqdcjgcstvtstvtPn+fmpEAdrudk7YNQH7mkF/9ZGZmyu12ex7n5OQoPT293q9/7LHH9Nhjj0mSZs+erdGjR/u8jU0Rx5855GeOv/OruWgICHbxURG6vk9rXd+ntYrKKrXgu1x9uTFHC7ccVNmxAqCztFKfrtuvT9ftV3iYRf3bJ1XfM/DcFLVr4fv+MQAAwWDJkiWaPn26Vq9erQMHDmju3Lm6/vrrPc+PGzdO77zzjtdrhg8frnnz5jVyS0+j4oTpPRnpBwBASKHodwYWi8VvJ1Vr9s1J24YhP3PI7+y1atXKMy2gy+XS1q1bNWjQoHqN7BkzZozGjBnjefzvf/9bXbp0UXJysmJjY/3Z7KDE8WcO+Znjz/ya6nfy6quv6tVXX9Xu3bslST169NATTzyhkSNHBrZhaBSxkeG6rndrXde7tVxllVq45aDmbcrR4q2HVFhaKUmqdBtavvOwlu88rN99tlmdU2J1WdeWurRLsgZ0aKFom+9nxgAAIBBcLpcyMzN166236oYbbqhzmxEjRmjmzJmex0E3u0tl2fFlRvoBABBSKPoBQAP16dNHRUVFkqS1a9dq+fLlysrKqtdrhw0b5vW4R48eWr16tf7whz9o1KhROuecc3zeXgA4lTZt2ujZZ59Vly5dZBiG3nnnHV133XVau3atevToEejmoRHZI8N1Ta90XdMrXRVVbq3cdUTzv8vVgu8Oas+RYs922w8WafvBIr21dJds4WG6oH2SBnVN1qVdWuqctLgmWwAHAGDkyJFnvPApMjJSaWlpjdSiBqg8caQfRT8AAEIJRT8A8IE+ffqoT58+6t69u2JiYvTee+/prrvuUnFxsW688UZt27bttK//9ttvFRVV/ctYzZSgkyZN0tChQ3XVVVdx8hSAX1177bVej5955hm9+uqr+vrrryn6hbAIa5gu6pysizon64lrumv7wSJPAXDtnqNyV8+Wq/JKt5Zuz9PS7XmSvlfLuEhd2iVZl3ZJ1sCOyUpzcLIRANC8LFq0SCkpKUpMTNQVV1yhp59+Wi1atDjl9mVlZZ77wUuS0+mUJM9MMr5mVJSo5jdIIzxS8sN7NGc134s/vptQQH7mkJ855GcO+Znj7/zqu1+Kfmfgtw4YP0CmkJ855GfO6fK77LLLJEn9+/f3rNuyZYvKy8u1atUqTZ48WStWrKjX+8yYMUMzZszwWrdlyxZ17ty5SRcBOf7MIT9zgqUDFsyqqqr00UcfyeVyaeDAgYFuDoKExWJRl9Q4dUmN092DOyu/uFzLth/Wf7cd0pKth7S/oNSz7aHCMs1Zs09z1uyTJHVItuvCji10YcckDezYQinxFAEBAE3XiBEjdMMNN6hDhw7asWOHHnnkEY0cOVLLly+X1Vr3dNfTpk3T1KlTa60vKCjwS//RVnhUMceWi8sNVRQU+Pw9mjPDMDyz+jTl370DhfzMIT9zyM8c8jPH3/nVXDR0JhT9TpKdna3s7GxVVVVJqp7L/VSdNjMMw1BJSfV0C/wAnT3yM4f8zGlofpmZmVqwYIEKCgq0aNEiJSYm6ptvvtHdd9+tn//851qyZMkZ99GtWzfPssVi0aOPPqr7779f4eHh2r9/v1JSUhQeHtz/tHP8mUN+5vg7v/rc4zNYbdy4UQMHDlRpaaliY2M1d+5cde/evc5tG/1qdYrdpvgjP0d0hK7qmaareqbJMAztPOTSkm15WrrtkJbvPKKSiirPtrvyXNqV59LsFXskSR1b2jXwWBFwQIcWahkXZPdBOgnHnznkZx4ZmkN+5nDBVG033nijZ7lnz57q1auXOnXqpEWLFmnIkCF1vmbKlCmaPHmy57HT6VRGRoYcDofi4+N93kbjhF8JYxxJksPh8/dozmqOS4fDwe9cDUB+5pCfOeRnDvmZ4+/86rvP4D4zHABZWVnKysqS0+mUw+GQ3W6X3W73+fvUHAB2u50foAYgP3PIzxyz+dntdv3iF7+QJM+9IhYtWqS5c+dq6dKl+ulPf6rFixfr8ccfP2M7nn76aT399NNe67/99lu5XC516NDhtFPMBArHnznkZ46/86u5aKgp6tatm9atW6eCggJ9/PHHGjt2rBYvXlxn4a+xr1bnakNzGiO/5EjphvMSdcN5iSqvdGv9PqdW/FCglXsKtGl/kSrdx4+LnYdc2nnIpfe+qS4Ctk+KVmbrOPVuE6/ebeLUPik6qL5njj9zyM88MjSH/MwJlivWg1nHjh2VnJys7du3n7LoFxkZqcjI2he5WCwW/xyXlcdH4FsioiWO/bNW893w70bDkJ855GcO+ZlDfub4Mz+Kfj7izwOcHyBzyM8c8jPHH/ndcMMNuuGGGyRJl1xyiebMmaOjR49qxIgReu211+q9nxPvv/XEE0/o8OHDeuyxx4LqRvMcf+aQnznB0AELRjabTZ07d5Yk9evXTytXrtSLL76o119/vda2jX61OlcbmhKI/Ia2SNTQXtXLxeWVWv3DUX2984i+3nlYG34s8CoC7j5Sot1HSvTpxoOSpIToCPVtl6jz2yWqb7tEZbZxKCrC9zNv1BfHnznkZx4ZmkN+5gTLFevB7Mcff9Thw4fVqlWrQDfluMrjMzIoPDpw7QAAAI2Ooh8ABCGLxaKVK1fK7XYrIiJCr776qgzDkMVi0Zo1a9SvXz9ZrVYlJCTo8OHDp9zPU089Jal66mJJGjZsmKKjo9WvXz/deuutat26daN8HgBNj9vt9prC80SNfrW6KHabFcj87JERGtQ1RYO6pkiSXGWVWvXDUX2987C+3nlYm/YVqKLqeBEwv6RCX31/UF99X10EjLBa1CPdob5tE9W7bYIy2zjUNimmUT8Lx5855GceGZpDfuaE2gVTRUVF2r59u+fxrl27tG7dOiUlJSkpKUlTp07VqFGjlJaWph07dujBBx9U586dNXz48AC2+iQVJceXw7mXLgAAoYSiHwAEKavV6nVP0ZpfiPv27Vtr+rz169dr3rx5evjhh0+7z3//+9+SpE8//VRPPPGEJOniiy/W4sWL/XL/UgBNw5QpUzRy5Ei1bdtWhYWFev/997Vo0SL961//CnTT0AzZI8N1WdeWuqxrS0lSaUWVNu4r0KrdR7X6hyNa/cNRHS2u8GxfUWVo3d58rdubLy2rXpcQE6FebRLUu41DmRkJ6tUmIejvDQgAaBpWrVqlyy+/3PO4ZnaDsWPH6tVXX9WGDRv0zjvvKD8/X+np6Ro2bJh+97vf1XlBVMCcML2nIij6AQAQSij6AUAzkJmZqczMTD300EPauXOn1q9fr1/+8pcqLi4+42uXLVum8HDv/w7S09N11VVX6Y9//KNfpuoDEFwOHjyoW265RQcOHJDD4VCvXr30r3/9S1deeWWgm4YQEBVhVf/2SerfPklSJxmGoZ15Lq3efVSrjhUBdxxyeb0mv7hCS7Ye0pKthzzrWidEq5enCOjQea0dio+KaORPAwBo6gYPHnzaexQ3iYuiTiz6MdIPAICQQtHvDAzDOG1nz+x+/bHvUEB+5pCfOcGeX4cOHdShQwcVFRVJklauXKkNGzZozJgx6tatm/bt23fGfezfv19//vOf9ec//1mS1L17d7377rvq0KGDtm3bpn79+jV4Kp5gzy/YkZ85/s6vqX4vb731VqCbAHhYLBZ1ahmrTi1j9fP+GZKkI65yrf8xX+v35mvDjwVavzdfh13lXq/bl1+iffkl+nJTjmdd26QY9UiPV4/0eHVPj1ePdIdS4iKDcjo5AAB85sTpPSO4px8AAKGEot9JsrOzlZ2draqqKkmSy+Xyy5R3hmGopKS6E8ZJh7NHfuaQnzlNLb/u3bure/fuMgxD33//vSQpLy9P33//vQ4cOKBbb731jPvYvHmz+vbt67Xugw8+0PDhw7V9+3aVl5erV69e9WpPU8sv2JCfOf7Oz+VynXkjAGctyW7T5d1SdHm36vsCGoahH4+WVBcAjxUDN+4rUHF5ldfr9hwp1p4jxV6FwORYm7qnO44XA1vFq30Lu8LC+DcVANBMMNIPAICQRdHvJFlZWcrKypLT6ZTD4ZDdbpfdbvf5+9SMBLDb7Zy0bQDyM4f8zGkO+dntdrVr106SNG7cOFVVVemrr77Sxx9/rHbt2umxxx474z5uvPHGOtf/8Y9/1FdffaWLL764znsMNof8Aon8zPF3fjUXDQHwL4vFooykGGUkxejqXq0kSVVuQzsOFWnd3nxt+DFf3+536vsDhSqp8P65zCsqrzU1qN1m1Tmt4tU1NU7npMV5/k602xr1cwEA4BNe9/RjpB8AAKGEot8ZWCwWv51Urdk3J20bhvzMIT9zmlt+4eHhGjZsmIYNGyZJuueee/Tmm29q5syZ+vbbb89qX/fff78k6fPPP9cjjzwiSRoxYoSmTJmiLl26KCUlpdnl19jIzxx/5sd3AgSONcyirqnVBbufn189LWiV29CuvCJ9u9+pzfud+na/U9/uL9DR4gqv17rKq7T6h6Na/cNRr/Ut4yLVLTVO7RNt6tm2hc5Ji1eX1FjF2Pg1CgAQxCpOKPpZIwPXDgAA0Oj4bRUAUEt8fLzuv/9+3X///dq2bZssFovat2+vr7/+Wi1bttR7772npUuXauHChfXa37x58zRv3jyvdStXrlRCQoI6d+7sj48AAICsYRZ1TolT55Q4Xde7taTqEb8HCko9BcCaYuC+/JJarz9UWKZDhWVaKkkr90uSLJbqewV2TY1Tt9Q4dUmN9dyDMNrm+9sCAABw1iqr/08zrJGyhIUFuDEAAKAxUfQDAJxWly5dPMuXXHKJJOmpp57yrHO73froo4/0ySef6IMPPqj3fvv371/n+jlz5ig9PV0XXHABo6YAAD5nsViUnhCt9IRoXdk91bPeWVqhbbmF2pJTpC05Tm3JLdSWnMJaowINQ/rhcLF+OFys+ZtzvZ5rnRCtTimx6twyVp1S7Mf+jlULu43/0wAAjadmpF8E9/MDACDUUPQDAJgSFham0aNHa/To0Zo9e7ZnfWVlpV544QU99NBDZ7W/G264wevxJ598oksvvVRxcXHasGGDEhIS1KlTJ5+0HQCAGvFREerXLkn92iV51hmGoUOFZVq9I0f7itzaeqwQuDW3qNa9AiVpX36J9uWXeN0vUJIc0RHqnBKrTi3tx/6u/tMmMVrhVkZgAAB8rOaefuHczw8AgFBD0Q8A4Bfh4eF68MEH9eCDD2r9+vWaP3++UlJS9OSTT2rPnj2qqqp9srQu119/fa11q1evVq9evWS1Whk5AQDwG4vFopZxkRrYIUEOh8Pzf47bbWjv0WJtySnUjkMubT9YpB2HirTjYJEKyypr7aegpKLOewaGh1mUkRSjdi1i1L6FXR2S7WrXIkYdku1qnUBBEADQQBXHpqxmpB8AACGHoh8AwO8yMzOVmZkpSbr55pvlcrlkt9tlsVh05MgRjRo1SmvWrJHT6azX/vr16+f1uFu3btqyZYsiIyP1t7/9TRdeeKFSUlJUVVUlq5X7KwEAfCsszKJ2Lexq18Lutb5mZOD2YwXAHYdc2nGoSNsPFulAQWmt/VS6De3Kc2lXnkuS9+jAmoJg+xYxap9sV/sWdrVPtqtDC7vSE6IoCAIATq2yrPpvRvoBABByKPoBAAIqKSlJCxculFQ9gq9NmzbKzs7W7373u3rvY8uWLZKksrIyXXfddbWev/322zVx4kT17NnTN40GAKAOFotFKfFRSomP0kWdkr2eKyqr1K5DLm0/VKgdB13amVekXXnF+uGwS8XltUe/exUEt3gXBCOsFmUkVhcD27WIUdukGGUkxigjKUYZSdGKsfFrHgCELMOQKhnpBwBAqOK3wTMwDEOGYfhtv/7YdyggP3PIzxzyM+d0+fXt21eSNHXqVE2dOtWz/a5du5SRkSGn06mePXsqJyfnrN7zjTfe0BtvvKF27drp9ttv13fffafbb79dF198sSQ1qSlCOf7M8Xd+fC8ATiU2Mlw92zjUs43Da33N6MBdeS7tPuzS7sPF2n2s2PfD4eI67x1YUWVoZ55LO/Ncdb5XcqytugCYeKwgmBTtKQq2cjBKEACataoKWQx39XI4RT8AAEINRb+TZGdnKzs723OvKZfL5Zep4QzDUElJ9ZVXTelkc7AgP3PIzxzyM6ch+aWmpqq8vFxRUVHatm2bZ/3s2bM1ceJE9e7dWytWrDjjfn744Qc9+uijkqR333231vOTJk3SPffco/j4eEVFBecvyBx/5vg7P5er7hPwAHAqJ44OHNCxhddzhmHoYE1BMO94QbC6OOhSaYW7zn3mFZUrr6hca/fk13ouPMyi9IRor0JgRlKMWidEq3VCtFrGRcoaxv8vANBk1Yzykyj6AQAQgij6nSQrK0tZWVlyOp1yOByy2+2y2+1nfuFZqhkJUHNPK5wd8jOH/MwhP3N8md+vfvUr/epXv5Ik5eTkKCcnR4sXL9aVV16pf/zjH3rkkUfOan8zZszQjBkzPI8vueQSPffccxowYIDCwqpHRRw5ckQOhyNg9wrk+DPH3/nVXDQEAL5gsViUGh+l1PgoXVhHQTDXWabdh13ae6RYe4+WVP99pFh7jxYr11lW5z4r3Yb2HCnWniPFkg7Xej7CalGaI0rpjmi1TqwuBKYneP8dbeN+uQAQtCpOuIcs03sCABByKPqdgcVi8dtJ1Zp9c9K2YcjPHPIzh/zM8Ud+rVq1UqtWrdSnTx9JUo8ePfTwww9rx44d6tixo8LCwvTyyy/r3nvvrfc+ly5d6pkC9GSXXXaZXnzxRfXq1avRjwOOP3P8mR/fCYDGYrFUF+fSHLULgpJUWlGlH2sKgUeLtedw9d97j1SvKyyrrHO/FVXGsW1KpF11v3eS3ab0hCivQmDNcnpCtJJjbfx7CACB4jXSLzpw7QAAAAFB0Q8A0GxZLBZ17tzZ8/iee+7RyJEjZbfbNXnyZIWFhalt27ay2Wx66qmnzmrfixcvVu/evb3WpaSkaO3atUpPT/dF8wEAaLCoCKs6p8Sqc0psrecMw1BBSYX2HDlWBDxarAP5JdqXX6J9+aXan1+igpKKU+77iKtcR1zl2rTPWefztvAwtU6IVlp8dVEyMcqidi3j1coRrVaOaKU6IpVsj1QY04gCgO8x0g8AgJBG0Q8AEFJqioCzZ8/2Wj916lRJ0pdffqmrrrqqQfs+ePCgWrduXWv9xRdfrAkTJugnP/mJEhMTG7RvAAB8xWKxKCHGpoQYm3q1Sahzm8LSCh0oKK0uBB4t0f786j/78ku0P79UOc5SVbmNOl9bXunWrjyXduWd+j6nEVaLUuKi1MoRpVRHlFodKxCmOarXpTmilRIXqQhrmC8+MgCEjsoTin6M9AMAIORQ9AMA4AQjR45UZWWl1z379uzZo6efflq9evVSbm6uXnvtNeXl5dV7n8uWLdOyZcs8j2fOnKkxY8ZIkl577TUNHTpUPXr08N2HAADApLioCMVFRahralydz1dWuZVbWOYpBv5YR2Gw6BRTiErV04juO7btqVgsUnJsZHVhMD5KqfGRSo2LUkp8pFLiotQyLlKp8VFqYbcxahAAangV/SID1w4AABAQFP0AADjJiQU/SWrbtq3eeOMNz+Pf/e53nuXt27dr0aJF+vLLLzVnzpx67X/8+PEaP358rfWZmZn6/PPPlZeXp169emnt2rU655xzFBMT08BPAgCAf4Rbwzz38juVwtIK5RSUavv+wyqqsiqnoFQHnKXKKTj2x1mqI67yU77eMKRDhWU6VFgmqeCU21nDLEqOtSk1PkopcZFqGVf9d83jlPjjxcFwRg4CaO4quKcfAAChjKIfAAAmdO7cWZ07d9avfvUrSVJVVZUeeugh/fGPf9SkSZPUqVMn3XPPPfXa1/r169WmTZta619//XWtWbNGbrdbEydOVHp6uqKiohQezn/jAIDgFRcVodjIcLWMrJLD4ZDFUns0XmlFlQ46y3SgoEQ5zlIdKDheFKwuEJboUGGZTjGTqCSpym0o11mmXGfZadtjsUgt7JHHCoLVowWrRw1GKsVTIIxSy9hI2cIpDgJooiq5px8AAKGMs4UAAPiQ1WrVH/7wB02fPt1zcvPuu+/Wpk2b1K1bN7344ov6+9//rhUrVtR7n3fccYdn+c033/QsP/DAAyooKND//d//6cILL1RcXN1TsAEAEKyiIqxq2yJGbVucelR7ZZVbh4rKdNBZplxnqQ4WlulgYZkOFZYq11mmg4WlOugsU17R6YuDhiHlFVVvt/nA6duVEBOh5NhItbDblBwXqZaxkUqOtSk5NrL6T9zxx1ER1tPvDAAak9dIP4p+AACEGop+AAD4wYmjGcLCwtSrVy9J0oMPPqgHH3xQkvTtt98qLi5OW7dulcVi0dChQ8/qPaZPny5JXlOP1ujbt6++/vprVVVVyTAMRUZGat26derZs6ciIiIa+rEAAGh04dYwtXJEq5Xj9NPUVbkNHS6qLgh6ioPHioK5zuoi4cFj04VWnq46KCm/uEL5xRXaXo/2xUaGn1QQrF5uERuplicVCu02a50jHgHAZ7xG+jG9JwAAoYaiHwAAAdKjRw9J1fcMlCTDqD4BWVFRoWeeeUZut1vbt2/X7Nmzz3rfa9askc1mq7X+oosu0rJly0y0GgCA4GQNs1RP0xkfpfNaO065ndtt6Ehxuacg6Pn7hGLh4aJy5RWVqbi86ozvW1RWqaKySu0+XHzGbaMiwuosCCbZbWoRa1OSvfpPC3ukEu0RigxnFCGAs3Ri0Y+RfgAAhByKfgAABJmIiAg9+eSTnsfvv/++JKmoqEiFhYXasGGDOnbsqKuuukrbt9dnDMJx//vf/zwjDKxWq6qqqtS7d2/97Gc/08iRI9W1a1dFR0crLIx7GQEAmqewMIun2NZd8afdtri8UnmF5Tp0bFrQvKLjBcG8ojLlFVYvHyoqU2Fp5Rnfu7TCrR+PlujHoyVn3FaqHkWYZLfJERWmlvExamG3KSnWVv23PfLY3zZP0TDGxq/4QMiroOgHAEAo4zcCAACaiNjYWNntdsXFxclut2vbtm1ez2/btk0ffPCBFi1apK+++uqM+6uqqh69sG7dOq1bt06PPvqo57nExESdf/75cjgcmjp1qjp37iybzaYdO3aobdu2TBEKAAgJMbZwtW0Rftp7DtYorajSEZd3QfBQXYXConIdLS6XcfoZRiUdH0UoSdpfdMbtoyLCPKMEaxUFTygOJtkjlRgTofioCIWFMd0o0KxUnnBRQQRFPwAAQg1FvzMwDMMz3Zo/9uuPfYcC8jOH/MwhP3PIz5zT5de5c2c99thjeuyxx1RZWSmLxaLFixeruLhYP/nJT87qfY4ePar58+dLkj7++ONazy9atEiDBg2SJOXk5CgpKanO6USDjb+PP45rAAhdURFWpSdEKz3hzPfQqqxyHysQVhcDj7jKddhVriOuY8tF5TriOv4nv6SiXm0orXBrX36J9uXXbyRhmEVKiLEpISZCiTE2JcZEKCGmujh48rrEGJsS7RFKiLbJFs6MAEDQ8hrpxz39AAAINRT9TpKdna3s7GzP6AeXyyWr1ff3UTAMQyUl1b+IcSP3s0d+5pCfOeRnDvmZc7b5DRgwQJK0fft2ffTRR+rWrZuio6OVnZ2tBQsWePZ1tgYPHnzK93vyySfVr18/Wa1W5efnKyUlpUHv4Q/+Pv5cLpfP9wkAaH7CrWGe+w+eiWEYOnw0X+7waB0trtDhY4XBk4uDJ64/4iqXux7XobgNebaX6v9/WGxkuKcoWPP3iYXC4wXD6kJhYoxNMTYrfT+gMTDSDwCAkEbR7yRZWVnKysqS0+mUw+GQ3W6X3W73+fvUjASw2+384tMA5GcO+ZlDfuaQnzkNza9jx4566KGHPI+HDx8uSVq7dq2++OILxcfHa9y4cerZs6f27NnT4PZ98803GjlypNe6tm3bym636/XXX9cll1zS4H37gr+Pv5qLhgAA8KXwMIsccZHHioRxZ9ze7TZUUFJxbPRg9QjCw65yHfWMKCzX0eIKHXVVTzWaX1xxfBrReqiZdrS+9yaUJJs1rFZRMCEmQo6Y6tGDjugIJcREKCE6QvE1yzE22SkWAmeHkX4AAIQ0in5nYLFY/PYLRs2++QWmYcjPHPIzh/zMIT9zfJlf37591bdvX8/jH374QZK0Zs0adezYUQkJCTp48KC++OILjR8/vkHvUVNErJkOtEZ8fLycTqemTZumu+++W3a73S+j60/mz+OPYxoAEAzCwixKtNuUaK//1NvllW7ll1QXAGuKgUeLKzxFwaOu449r1uUX129EoSSVV7l1sLBMBwvLzuqzhIdZ5IiuLg46oquLggkx1UXCmkLh8b9tXusirExDihBUeULRj5F+AACEHIp+AACglhMLgSkpKRo3bpzGjRunwsJCxcTEKDs7W08++aQefvhhrxGEZ8PpdEqSpkyZoilTpng9N336dA0dOlRHjx6Vy+XSNddc0/APAwAAzsgWHqaUuCilxNW/SOB2GyosrfQUAo8Wl+uo64RC4Ql/H3EdXy6rdNf7PSrdhg4fG6F4tuw2qxwxEYqzWZUUG3Vs9OCxkYTRNsVHh8sRHaH4qOp11cvhiqdgiKaskpF+AACEMop+AACg3uLiqqcUu/fee3XvvfdKkh588EHP8wcPHtQtt9yiAQMGaP78+YqNjdX8+fPP+n0eeOCBWutSUlLkdrs1bdo03XbbbSotLVVpaakSExMb+GkAAIAZYWGW6hF4MRFqr/rfFqOkvEpHi8tVUFKh/OIKFZRUqODYKMOCkgrll1SowLN8fH1haf2nIJUkV3mVXOXHpt4+eHb33Y2xWY8VA09dGIw/tt4RXb1dfFR1FrG2cIWFMfofAVJxwrS74ZGBawcAAAgIin4AAMBnUlJSNG/ePEnS1KlTJUllZWX69a9/rSuvvFJ5eXnq1KmT1qxZo3379mnGjBn13vfBgwclSRMmTNCECRPq3OYnP/mJXn/9daWlpZn7IAAAwG+ibVZF26KVnnB2o5Aqq9xyllYeKxaWK7+kQs5jhcP8E4qEBScUD/OPjTasrO88pMcUl1epuLxKOc6zepkkyWKR4iLD5Yg5Viw8uTBYUzA8oaAYFxWhuKhwxUWFy07REGZ4Te/JSD8AAEINRT8AAOBXkZGReuWVV7zWXXHFFZKk5557Tjt37lTbtm21atUqXXbZZabe6x//+If+8Y9/eB5brVZlZ2ersrJSd999t6l9AwCAwAq3hinJblOS3SbVc2ShYRjKz8+XLSZWBSWVJ4wuLJezpFLO0urCYUFJhZyllScsV8h5bPuSiqqzaqdhqHpfpZWSSs64/cksFik2MvxYMfD439V/jq2LjvB+fGy5ZtsYm5V7DYeqihOn9+SefgAAhBqKfgAAIGBsNpvOOeccSdKgQYNUWFioFStWaMuWLbr88ss9z0nSF198oauvvvqs9l9VVaU777xTkjRx4kRJ0nXXXac5c+ZwIgwAgBBhsVgUYwuXPTLirEcXSlJ5pVuFpacvDJ5cPCwsqZm29OxHGRqGVFhaedbTmZ7IGmZRbORJhcKoiGPFwfATRhZ6FxHjT1gXHWFt8PsjgCpPnN6Toh8AAKGGoh8AAAgasbGxuuKKKzwjAU901VVXyTAMHTx4UCtWrJAkffvtt/rwww+VkZHhNcLvdD799FNt2LBBvXv39mXTAQBAM2ULD1OL2Ei1iD37+6MZhqHSCncdhcETCobH7ldYWFa9rrC0+rGztHq5rNJ91u9b5TY8RceGjDaUpPBjhcPYSKv+M/kyRdk4hdQkVJZJkgxrZPWwUQAAEFLosQEAgCYlJSVF11xzjSTpmmuu0UMPPeR5buvWrUpMTNTs2bN13333nXIfe/bsoegHAAD8zmKxHLuHoVVpjoaNuiqrrPKM/KspCBYeKxo6PY9PLBZWnLRtpcqrzr5wWOk2lF9SocLSCtnCwxrUdgRARXWR1wiPEiU/AABCD0U/AADQbHTt2lWSdO+99yorK0urVq1Samqq2rdvrx9//FGvvPKKRo0apb59+wa4pQAAAPUTGW5VZKxVyQ0YaVijtKKqzgJhTfG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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors\n", + "import numpy as np\n", + "\n", + "initial_lp = compute_loss(key, params, Phi_spheroid, theta_hist[0], n_candidates, envelope_max, rbin, zbin)\n", + "final_lp = compute_loss(key, params, Phi_spheroid, theta_hist[-1], n_candidates, envelope_max, rbin, zbin)\n", + "\n", + "vmin = min(np.nanmin(initial_lp), np.nanmin(final_lp))\n", + "vmax = max(np.nanmax(initial_lp), np.nanmax(final_lp))\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(15, 6), sharey=True)\n", + "\n", + "# Common settings for imshow\n", + "im_kwargs = {\n", + " 'origin': 'lower',\n", + " 'aspect': 'auto',\n", + " 'extent': [r_min, r_max, z_min, z_max],\n", + " 'cmap': 'viridis',\n", + " 'vmin': vmin,\n", + " 'vmax': vmax\n", + "}\n", + "\n", + "# Left Plot: Initial\n", + "im0 = axes[0].imshow(initial_lp.T, **im_kwargs)\n", + "axes[0].set_title(f'Initial Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[0]]}')\n", + "axes[0].set_xlabel('r [kpc]')\n", + "axes[0].set_ylabel('z [kpc]')\n", + "\n", + "# Right Plot: Optimized\n", + "im1 = axes[1].imshow(final_lp.T, **im_kwargs)\n", + "axes[1].set_title(f'Optimized Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[-1]]}')\n", + "axes[1].set_xlabel('r [kpc]')\n", + "\n", + "# Add one shared colorbar\n", + "fig.subplots_adjust(right=0.85)\n", + "cbar_ax = fig.add_axes([0.88, 0.15, 0.02, 0.7])\n", + "fig.colorbar(im1, cax=cbar_ax, label='Loss Residual')\n", + "\n", + "plt.savefig('./figures/spheroid_loss_plane.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "b9269967", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", + "\n", + "# Create the figure with two subplots\n", + "fig, axes = plt.subplots(1, 2, figsize=(14, 6), sharey=True)\n", + "\n", + "# Define common imshow parameters\n", + "im_kwargs = {\n", + " 'origin': 'lower',\n", + " 'aspect': 'auto',\n", + " 'extent': [r_min, r_max, z_min, z_max],\n", + " 'cmap': 'viridis'\n", + "}\n", + "\n", + "# --- Left Plot: Initial ---\n", + "im0 = axes[0].imshow(initial_lp.T, **im_kwargs)\n", + "axes[0].set_title(f'Initial Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[0]]}')\n", + "axes[0].set_xlabel('r [kpc]')\n", + "axes[0].set_ylabel('z [kpc]')\n", + "\n", + "# Create individual colorbar for the left plot\n", + "divider0 = make_axes_locatable(axes[0])\n", + "cax0 = divider0.append_axes(\"right\", size=\"5%\", pad=0.1)\n", + "fig.colorbar(im0, cax=cax0, label='loss')\n", + "\n", + "# --- Right Plot: Final ---\n", + "im1 = axes[1].imshow(final_lp.T, **im_kwargs)\n", + "axes[1].set_title(f'Final Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[-1]]}')\n", + "axes[1].set_xlabel('r [kpc]')\n", + "\n", + "# Create individual colorbar for the right plot\n", + "divider1 = make_axes_locatable(axes[1])\n", + "cax1 = divider1.append_axes(\"right\", size=\"5%\", pad=0.1)\n", + "fig.colorbar(im1, cax=cax1, label='loss')\n", + "\n", + "plt.tight_layout()\n", + "plt.savefig('./figures/spheroid_loss_plane2.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "4dec562d", + "metadata": {}, + "outputs": [], + "source": [ + "def get_density_and_mask(f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, rbin, zbin):\n", + "\n", + " candidates, samples, soft_weights = sampling.sample_df_potential(\n", + " f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, tau=0.01\n", + " )\n", + "\n", + " phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(\n", + " samples, params, key, Phi, theta\n", + " )\n", + "\n", + " x = phase_space_coords[:, 0]\n", + " y = phase_space_coords[:, 1]\n", + " z = phase_space_coords[:, 2]\n", + "\n", + " density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)\n", + " \n", + " return density, mask" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "35a09156", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "initial_density, mask_initial = get_density_and_mask(f_double_power_law, key, params, Phi_spheroid, theta_hist[0], n_candidates, envelope_max, rbin, zbin)\n", + "final_density, mask_final = get_density_and_mask(f_double_power_law, key, params, Phi_spheroid, theta_hist[-1], n_candidates, envelope_max, rbin, zbin)\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(16, 6), sharey=True)\n", + "extent = [r_min, r_max, z_min, z_max]\n", + "\n", + "combined_vals = np.concatenate([initial_density.flatten(), final_density.flatten()])\n", + "vmin = np.nanmin(combined_vals[combined_vals > 0])\n", + "vmax = np.nanmax(combined_vals)\n", + "shared_norm = colors.LogNorm(vmin=vmin, vmax=vmax)\n", + "\n", + "# Initial Plot\n", + "im0 = axes[0].imshow(initial_density.T, origin='lower', aspect='auto',\n", + " extent=extent, cmap='viridis', norm=shared_norm)\n", + "axes[0].set_title(f'Initial Density Distribution\\n$\\\\theta$: {[f\"{t:.2e}\" for t in theta_hist[0]]}')\n", + "axes[0].set_xlabel('r [kpc]')\n", + "axes[0].set_ylabel('z [kpc]')\n", + "\n", + "# Optimized Plot\n", + "im1 = axes[1].imshow(final_density.T, origin='lower', aspect='auto',\n", + " extent=extent, cmap='viridis', norm=shared_norm)\n", + "axes[1].set_title(f'Optimized Density Distribution\\n$\\\\theta$: {[f\"{t:.2e}\" for t in theta_hist[-1]]}')\n", + "axes[1].set_xlabel('r [kpc]')\n", + "\n", + "fig.subplots_adjust(right=0.9) # Make room for the colorbar\n", + "cbar_ax = fig.add_axes([0.92, 0.15, 0.02, 0.7]) # [left, bottom, width, height]\n", + "fig.colorbar(im1, cax=cbar_ax, label='Density')\n", + "plt.savefig('./figures/spheroid_density_optimization.jpeg')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "abac9028", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "phoenix", + "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": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/selfconsitency_spheroid_short.ipynb b/notebooks/selfconsitency_spheroid_short.ipynb new file mode 100644 index 0000000..43d649e --- /dev/null +++ b/notebooks/selfconsitency_spheroid_short.ipynb @@ -0,0 +1,369 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "34c0bec3", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix.selfconsistency import adam_optimizer_spheroid\n", + "from phoenix.potentials import plummer_potential\n", + "\n", + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bfec7291", + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " \"R0\": 8.0, # for actions to phase space\n", + " \"N0_spheroid\": 1e6,\n", + " \"J0_spheroid\": 1000.0,\n", + " \"Gamma_spheroid\": 2.5,\n", + " \"Beta_spheroid\": 3.5,\n", + "}\n", + "\n", + "envelope_max = 3.0\n", + "n_candidates = 250_000\n", + "key = jax.random.PRNGKey(42)\n", + "\n", + "Phi_spheroid = plummer_potential\n", + "theta_spheroid = jnp.array([1e12, 10.0]) # (M, a) z.B. für Plummer" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "426c8942", + "metadata": {}, + "outputs": [], + "source": [ + "r_min = 0\n", + "r_max = 10\n", + "z_min = -5\n", + "z_max = 5\n", + "rbin = jnp.linspace(r_min, r_max, 20)\n", + "zbin = jnp.linspace(z_min, z_max, 20)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8d8bbbe9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0, Loss: 8330837504.0000, Theta: [9.5123053e+11 1.0512709e+01]\n", + "Iteration 100, Loss: 24038360.0000, Theta: [4.0904812e+11 2.4823328e+01]\n" + ] + } + ], + "source": [ + "learning = 5e-2\n", + "theta_opt, loss_hist, theta_hist = adam_optimizer_spheroid(key, params, Phi_spheroid, theta_spheroid, n_candidates, \n", + " envelope_max, rbin, zbin, learning, num_iterations=3000)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "1eb9a7fc", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "def plot_training_results(loss_history, theta_history):\n", + " # Convert lists to numpy arrays\n", + " loss_history = np.array(loss_history)\n", + " theta_history = np.array(theta_history) # Shape: (iterations, 2)\n", + "\n", + " # Create 3 subplots side-by-side\n", + " fig, ax = plt.subplots(1, 3, figsize=(18, 5))\n", + "\n", + " # 1. Loss History (Log Scale)\n", + " ax[0].plot(loss_history, color='black', lw=1.5)\n", + " ax[0].set_yscale('log')\n", + " ax[0].set_title(\"Total Loss Convergence\", fontsize=14)\n", + " ax[0].set_xlabel(\"Iteration\")\n", + " ax[0].set_ylabel(\"Loss\")\n", + " ax[0].grid(True, which=\"both\", ls=\"-\", alpha=0.15)\n", + "\n", + " # 2. Theta 1 Evolution\n", + " ax[1].plot(theta_history[:, 0], color='tab:blue', lw=2)\n", + " ax[1].set_title(r\"Parameter $\\theta_1$: Mass\", fontsize=14)\n", + " ax[1].set_xlabel(\"Iteration\")\n", + " ax[1].set_ylabel(\"Value\")\n", + " ax[1].grid(True, alpha=0.2)\n", + "\n", + " # 3. Theta 2 Evolution\n", + " ax[2].plot(theta_history[:, 1], color='tab:orange', lw=2)\n", + " ax[2].set_title(r\"Parameter $\\theta_2: a$\", fontsize=14)\n", + " ax[2].set_xlabel(\"Iteration\")\n", + " ax[2].set_ylabel(\"Value\")\n", + " ax[2].grid(True, alpha=0.2)\n", + "\n", + " plt.tight_layout()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "57edf0f4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.colors as colors\n", + "import numpy as np\n", + "from phoenix.selfconsistency import compute_loss\n", + "\n", + "initial_lp = compute_loss(key, params, Phi_spheroid, theta_hist[0], n_candidates, envelope_max, rbin, zbin)\n", + "final_lp = compute_loss(key, params, Phi_spheroid, theta_hist[-1], n_candidates, envelope_max, rbin, zbin)\n", + "\n", + "vmin = min(np.nanmin(initial_lp), np.nanmin(final_lp))\n", + "vmax = max(np.nanmax(initial_lp), np.nanmax(final_lp))\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(15, 6), sharey=True)\n", + "\n", + "# Common settings for imshow\n", + "im_kwargs = {\n", + " 'origin': 'lower',\n", + " 'aspect': 'auto',\n", + " 'extent': [r_min, r_max, z_min, z_max],\n", + " 'cmap': 'viridis',\n", + " 'vmin': vmin,\n", + " 'vmax': vmax\n", + "}\n", + "\n", + "# Left Plot: Initial\n", + "im0 = axes[0].imshow(initial_lp.T, **im_kwargs)\n", + "axes[0].set_title(f'Initial Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[0]]}')\n", + "axes[0].set_xlabel('r [kpc]')\n", + "axes[0].set_ylabel('z [kpc]')\n", + "\n", + "# Right Plot: Optimized\n", + "im1 = axes[1].imshow(final_lp.T, **im_kwargs)\n", + "axes[1].set_title(f'Optimized Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[-1]]}')\n", + "axes[1].set_xlabel('r [kpc]')\n", + "\n", + "# Add one shared colorbar\n", + "fig.subplots_adjust(right=0.85)\n", + "cbar_ax = fig.add_axes([0.88, 0.15, 0.02, 0.7])\n", + "fig.colorbar(im1, cax=cbar_ax, label='Loss Residual')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b9269967", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", + "\n", + "# Create the figure with two subplots\n", + "fig, axes = plt.subplots(1, 2, figsize=(14, 6), sharey=True)\n", + "\n", + "# Define common imshow parameters\n", + "im_kwargs = {\n", + " 'origin': 'lower',\n", + " 'aspect': 'auto',\n", + " 'extent': [r_min, r_max, z_min, z_max],\n", + " 'cmap': 'viridis'\n", + "}\n", + "\n", + "# --- Left Plot: Initial ---\n", + "im0 = axes[0].imshow(initial_lp.T, **im_kwargs)\n", + "axes[0].set_title(f'Initial Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[0]]}')\n", + "axes[0].set_xlabel('r [kpc]')\n", + "axes[0].set_ylabel('z [kpc]')\n", + "\n", + "# Create individual colorbar for the left plot\n", + "divider0 = make_axes_locatable(axes[0])\n", + "cax0 = divider0.append_axes(\"right\", size=\"5%\", pad=0.1)\n", + "fig.colorbar(im0, cax=cax0, label='loss')\n", + "\n", + "# --- Right Plot: Final ---\n", + "im1 = axes[1].imshow(final_lp.T, **im_kwargs)\n", + "axes[1].set_title(f'Final Loss Distribution\\n' + r'$\\theta$: ' + f'{[f\"{t:.2e}\" for t in theta_hist[-1]]}')\n", + "axes[1].set_xlabel('r [kpc]')\n", + "\n", + "# Create individual colorbar for the right plot\n", + "divider1 = make_axes_locatable(axes[1])\n", + "cax1 = divider1.append_axes(\"right\", size=\"5%\", pad=0.1)\n", + "fig.colorbar(im1, cax=cax1, label='loss')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "4dec562d", + "metadata": {}, + "outputs": [], + "source": [ + "from phoenix.distributionfunctions_spheroidal import f_double_power_law\n", + "from phoenix.selfconsistency import compute_density_jax\n", + "from phoenix import sampling, actions_to_phase_space\n", + "\n", + "def get_density_and_mask(f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, rbin, zbin):\n", + "\n", + " candidates, samples, soft_weights = sampling.sample_df_potential(\n", + " f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, tau=0.01\n", + " )\n", + "\n", + " phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(\n", + " samples, params, key, Phi, theta\n", + " )\n", + "\n", + " x = phase_space_coords[:, 0]\n", + " y = phase_space_coords[:, 1]\n", + " z = phase_space_coords[:, 2]\n", + "\n", + " density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin)\n", + " \n", + " return density, mask" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "35a09156", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "initial_density, mask_initial = get_density_and_mask(f_double_power_law, key, params, Phi_spheroid, theta_hist[0], n_candidates, envelope_max, rbin, zbin)\n", + "final_density, mask_final = get_density_and_mask(f_double_power_law, key, params, Phi_spheroid, theta_hist[-1], n_candidates, envelope_max, rbin, zbin)\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(16, 6), sharey=True)\n", + "extent = [r_min, r_max, z_min, z_max]\n", + "\n", + "combined_vals = np.concatenate([initial_density.flatten(), final_density.flatten()])\n", + "vmin = np.nanmin(combined_vals[combined_vals > 0])\n", + "vmax = np.nanmax(combined_vals)\n", + "shared_norm = colors.LogNorm(vmin=vmin, vmax=vmax)\n", + "\n", + "# Initial Plot\n", + "im0 = axes[0].imshow(initial_density.T, origin='lower', aspect='auto',\n", + " extent=extent, cmap='viridis', norm=shared_norm)\n", + "axes[0].set_title(f'Initial Density Distribution\\n$\\\\theta$: {[f\"{t:.2e}\" for t in theta_hist[0]]}')\n", + "axes[0].set_xlabel('r [kpc]')\n", + "axes[0].set_ylabel('z [kpc]')\n", + "\n", + "# Optimized Plot\n", + "im1 = axes[1].imshow(final_density.T, origin='lower', aspect='auto',\n", + " extent=extent, cmap='viridis', norm=shared_norm)\n", + "axes[1].set_title(f'Optimized Density Distribution\\n$\\\\theta$: {[f\"{t:.2e}\" for t in theta_hist[-1]]}')\n", + "axes[1].set_xlabel('r [kpc]')\n", + "\n", + "fig.subplots_adjust(right=0.9) # Make room for the colorbar\n", + "cbar_ax = fig.add_axes([0.92, 0.15, 0.02, 0.7]) # [left, bottom, width, height]\n", + "fig.colorbar(im1, cax=cbar_ax, label='Density')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "abac9028", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "phoenix", + "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": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/phoenix/selfconsistency.py b/phoenix/selfconsistency.py new file mode 100644 index 0000000..0f7cd11 --- /dev/null +++ b/phoenix/selfconsistency.py @@ -0,0 +1,150 @@ +import jax +import jax.numpy as jnp +import optax + +from phoenix.constants import G +from phoenix import sampling, actions_to_phase_space +from phoenix.potentials import miyamoto_nagai_potential, plummer_potential +from phoenix.distributionfunctions_spheroidal import f_double_power_law + +def compute_density_jax(x, y, z, weights, r_bins, z_bins): + # 1. Compute radial distance r + r = jnp.sqrt(x**2 + y**2) + + # 2. Use histogram2d to accumulate weights efficiently + # This replaces the entire fori_loop and digitize logic + counts, _, _ = jnp.histogram2d( + r, z, + bins=[r_bins, z_bins], + weights=weights + ) + + # 3. Compute the volume of each bin + # Use midpoint r for volume calculation to be more accurate + r_mid = (r_bins[:-1] + r_bins[1:]) / 2 + r_widths = jnp.diff(r_bins) + z_widths = jnp.diff(z_bins) + + # Calculate volume of cylindrical shell: V = 2 * pi * r * dr * dz + bin_volumes = 2 * jnp.pi * jnp.outer(r_mid * r_widths, z_widths) + + # 4. Normalize + density = counts / bin_volumes + valid_mask = (density > 0).astype(jnp.float32) + + return density, valid_mask + +def compute_laplacian_on_grid(potential, theta, r_bins, z_bins): + """ + Computes nabla^2 Phi (Laplacian) on the centers of the R-Z bins. + """ + + # 1. Define the Laplacian for a SINGLE point (x, y, z) + def potential_wrapper(x, y, z): + return potential(x, y, z, *theta) + + def laplacian_fn(x, y, z): + # jax.hessian returns a 3x3 matrix of second derivatives + # argnums=(0, 1, 2) makes it return a nested tuple structure relative to x,y,z + # However, it's easier to treat input as a vector for Hessian logic, + # but since our function takes scalars, we can just sum unmixed 2nd derivatives. + + # Method A: Direct curvature calculation (faster/simpler than full Hessian) + # We use simple nested grad or specific derivative operators + d2dx2 = jax.grad(lambda x_: jax.grad(potential_wrapper, argnums=0)(x_, y, z))(x) + d2dy2 = jax.grad(lambda y_: jax.grad(potential_wrapper, argnums=1)(x, y_, z))(y) + d2dz2 = jax.grad(lambda z_: jax.grad(potential_wrapper, argnums=2)(x, y, z_))(z) + + return d2dx2 + d2dy2 + d2dz2 + + # 2. Vectorize the Laplacian function + # Maps over inputs x, y, z + laplacian_vmap = jax.vmap(laplacian_fn, in_axes=(0, 0, 0)) + + # 3. Setup Grid (Bin Centers) + r_centers = 0.5 * (r_bins[:-1] + r_bins[1:]) + z_centers = 0.5 * (z_bins[:-1] + z_bins[1:]) + + # Create Meshgrid (indexing='ij' matches density shape) + R_grid, Z_grid = jnp.meshgrid(r_centers, z_centers, indexing='ij') + + # 4. Convert R-Z to Cartesian X-Y-Z + # We evaluate at y=0, so x=R + X_flat = R_grid.flatten() + Y_flat = jnp.zeros_like(X_flat) + Z_flat = Z_grid.flatten() + + # 5. Compute + laplacian_flat = laplacian_vmap(X_flat, Y_flat, Z_flat) + + # Reshape back to (N_r, N_z) + laplacian_grid = laplacian_flat.reshape(R_grid.shape) + + return laplacian_grid + +def compute_loss(key, params, Phi, theta, n_candidates, envelope_max, rbin, zbin): + candidates, samples, soft_weights = sampling.sample_df_potential(f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, tau=0.01) + phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi, theta) + x = phase_space_coords[:, 0] + y = phase_space_coords[:, 1] + z = phase_space_coords[:, 2] + density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin) + nabla2_Phi = compute_laplacian_on_grid(Phi, theta, r_bins=rbin, z_bins=zbin) + lossplane = (4*jnp.pi*G*density - nabla2_Phi) + lossplane = lossplane * mask + + return lossplane + +def compute_lossvalue(key, params, Phi, theta, n_candidates, envelope_max, rbin, zbin): + candidates, samples, soft_weights = sampling.sample_df_potential(f_double_power_law, key, params, Phi, theta, n_candidates, envelope_max, tau=0.01) + phase_space_coords = actions_to_phase_space.map_actions_to_phase_space(samples, params, key, Phi, theta) + x = phase_space_coords[:, 0] + y = phase_space_coords[:, 1] + z = phase_space_coords[:, 2] + density, mask = compute_density_jax(x, y, z, soft_weights, r_bins=rbin, z_bins=zbin) + nabla2_Phi = compute_laplacian_on_grid(Phi, theta, r_bins=rbin, z_bins=zbin) + lossplane = (4*jnp.pi*G*density - nabla2_Phi) + lossplane = lossplane * mask + loss = jnp.sum(lossplane**2) + + return loss + +def adam_optimizer_spheroid(key, params, Phi_spheroid, theta_init, n_candidates, envelope_max, rbin, zbin, learning, num_iterations=2000): + current_log_theta = jnp.log(theta_init) + + optimizer = optax.adam(learning) + opt_state = optimizer.init(current_log_theta) + + @jax.jit + def step(log_theta, state, step_key): + def loss_wrapper(lt): + t_phys = jnp.exp(lt) + return compute_lossvalue(step_key, params, Phi_spheroid, t_phys, + n_candidates, envelope_max, rbin, zbin) + + # Now we differentiate w.r.t 'log_theta' directly + loss_val, grads = jax.value_and_grad(loss_wrapper)(log_theta) + + updates, new_state = optimizer.update(grads, state, log_theta) + new_log_theta = optax.apply_updates(log_theta, updates) + + return new_log_theta, new_state, loss_val + loss_history = [] + theta_history = [] + + for i in range(num_iterations): + key, subkey = jax.random.split(key) + + current_log_theta, opt_state, loss_val = step(current_log_theta, opt_state, subkey) + + # Convert back to physical space for your records + phys_theta = jnp.exp(current_log_theta) + + loss_history.append(float(loss_val)) + theta_history.append(phys_theta) + + if i % 100 == 0: + print(f"Iteration {i}, Loss: {loss_val:.4f}, Theta: {phys_theta}") + #pbar.set_postfix({"Loss": f"{loss_val:.2e}", "Theta": [f"{t:.2e}" for t in phys_theta]}) + + return jnp.exp(current_log_theta), loss_history, theta_history \ No newline at end of file