From 25e11a9862011b0a3da3861671d280f52683a9c1 Mon Sep 17 00:00:00 2001
From: Isuru Fernando <isuruf@gmail.com>
Date: Mon, 7 May 2018 12:23:10 -0500
Subject: [PATCH] Symbolic reduction notebook

---
 .../translations/PDE-reduction-symbolic.ipynb | 133 ++++++++++++++++++
 1 file changed, 133 insertions(+)
 create mode 100644 contrib/translations/PDE-reduction-symbolic.ipynb

diff --git a/contrib/translations/PDE-reduction-symbolic.ipynb b/contrib/translations/PDE-reduction-symbolic.ipynb
new file mode 100644
index 00000000..bffcdf9e
--- /dev/null
+++ b/contrib/translations/PDE-reduction-symbolic.ipynb
@@ -0,0 +1,133 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pyopencl as cl\n",
+    "import sumpy.toys as t\n",
+    "import numpy as np\n",
+    "import numpy.linalg as la\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sumpy.visualization import FieldPlotter\n",
+    "from pytools import add_tuples\n",
+    "\n",
+    "from sumpy.expansion.local import VolumeTaylorLocalExpansion\n",
+    "from sumpy.expansion.multipole import (VolumeTaylorMultipoleExpansion,\n",
+    "    LaplaceConformingVolumeTaylorMultipoleExpansion,\n",
+    "    HelmholtzConformingVolumeTaylorMultipoleExpansion)\n",
+    "                                           \n",
+    "from sumpy.kernel import (YukawaKernel, HelmholtzKernel, LaplaceKernel)\n",
+    "\n",
+    "from sumpy.symbolic import make_sym_vector\n",
+    "\n",
+    "order = 2\n",
+    "dim = 2\n",
+    "\n",
+    "if 0:\n",
+    "    knl = LaplaceKernel(dim)\n",
+    "    extra_kernel_kwargs = {}\n",
+    "    mpole_expn_reduced_class = LaplaceConformingVolumeTaylorMultipoleExpansion\n",
+    "    \n",
+    "else:\n",
+    "    helm_k = 1.2\n",
+    "    knl = HelmholtzKernel(dim)\n",
+    "    extra_kernel_kwargs={\"k\": helm_k}\n",
+    "    mpole_expn_reduced_class = HelmholtzConformingVolumeTaylorMultipoleExpansion\n",
+    "\n",
+    "mpole_expn_reduced = mpole_expn_reduced_class(knl, order)\n",
+    "mpole_expn = VolumeTaylorMultipoleExpansion(knl, order)\n",
+    "local_expn = VolumeTaylorLocalExpansion(knl, order)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pytools import factorial\n",
+    "\n",
+    "def mi_factorial(n):\n",
+    "    return np.prod([factorial(n1) for n1 in n])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reduced_wrangler = mpole_expn_reduced.derivative_wrangler\n",
+    "full_wrangler = mpole_expn.derivative_wrangler\n",
+    "\n",
+    "reduced_derivatives = list(make_sym_vector(\"deriv\", len(reduced_wrangler.stored_identifiers)))\n",
+    "full_derivatives = reduced_wrangler.get_full_kernel_derivatives_from_stored(reduced_derivatives, 1)\n",
+    "\n",
+    "print(reduced_derivatives)\n",
+    "print(full_derivatives)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "full_coeffs = list(make_sym_vector(\"coeff\", len(reduced_wrangler.get_full_coefficient_identifiers())))\n",
+    "\n",
+    "reduced_coeffs = reduced_wrangler.get_stored_mpole_coefficients_from_full(full_mpole_coefficients=full_coeffs, rscale=1)\n",
+    "\n",
+    "print(full_coeffs)\n",
+    "print(reduced_coeffs)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dvec = make_sym_vector(\"d\", dim)\n",
+    "translated_reduce_coeffs = mpole_expn_reduced.translate_from(mpole_expn_reduced, reduced_coeffs, 1, dvec, 1)\n",
+    "translated_full_coeffs = mpole_expn.translate_from(mpole_expn, full_coeffs, 1, dvec, 1)\n",
+    "translated_full_coeffs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eval_reduced = sum(a*b for a, b in zip(translated_reduce_coeffs, reduced_derivatives))\n",
+    "eval_full = sum(a*b for a, b in zip(translated_full_coeffs, full_derivatives))\n",
+    "\n",
+    "(eval_full-eval_reduced).simplify()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.6.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
-- 
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