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Update testing_pde_to_ode.ipynb
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‎test/testing_pde_to_ode.ipynb‎

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"cells": [
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{
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"cell_type": "code",
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"execution_count": 8,
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"LinearPDESystemOperator(2, immutabledict({DerivativeIdentifier(mi=(2, 0), vec_idx=0): 1, DerivativeIdentifier(mi=(0, 2), vec_idx=0): 1}))"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"from collections import namedtuple\n",
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"DerivativeIdentifier = namedtuple(\"DerivativeIdentifier\", [\"mi\", \"vec_idx\"])\n",
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"partial_1 = DerivativeIdentifier((2,0), 0)\n",
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"partial_2 = DerivativeIdentifier((0,2), 0)\n",
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"list_pde = {partial_1: 1, partial_2: 1}\n",
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"list_pde = immutabledict(list_pde)\n",
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"pde_op = LinearPDESystemOperator(2,(list_pde))\n",
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"pde_op"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"LinearPDESystemOperator(2, (immutabledict({DerivativeIdentifier(mi=(2, 0), vec_idx=0): 1, DerivativeIdentifier(mi=(0, 2), vec_idx=0): 1}),))"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"w = make_identity_diff_op(2)\n",
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"laplace2d = laplacian(w)\n",
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"laplace2d"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 67,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"LinearPDESystemOperator(2, immutabledict({DerivativeIdentifier(mi=(2, 0), vec_idx=0): 1, DerivativeIdentifier(mi=(0, 2), vec_idx=0): 1}))"
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]
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},
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"execution_count": 67,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"pde_op"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 62,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\frac{f_{r1}}{\\sqrt{x_{0}^{2} + x_{1}^{2}}} + f_{r2}$"
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],
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"text/plain": [
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"f_r1/sqrt(x0**2 + x1**2) + f_r2"
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"LinearPDESystemOperator(2, (immutabledict({DerivativeIdentifier(mi=(2, 0), vec_idx=0): 1, DerivativeIdentifier(mi=(0, 2), vec_idx=0): 1}),))"
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]
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},
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"execution_count": 13,
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"execution_count": 62,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"ode_in_r, var, ode_order = pde_to_ode_in_r(laplace2d)\n",
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"ode_in_x = ode_in_r_to_x(ode_in_r, var, ode_order).simplify()\n",
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"ode_in_x_cleared = (ode_in_x * var[0]**(ode_order+1)).simplify()\n",
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"ode_in_r.simplify()"
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"laplace2d"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 63,
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"metadata": {},
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"outputs": [
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{
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"ename": "ValueError",
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"evalue": "PDE must be scalar",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"Cell \u001b[0;32mIn[63], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m ode_in_r, var, ode_order \u001b[38;5;241m=\u001b[39m \u001b[43mpde_to_ode_in_r\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpde_op\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 2\u001b[0m ode_in_r\n",
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"File \u001b[0;32m~/Desktop/sumpy/sumpy/recurrence.py:98\u001b[0m, in \u001b[0;36mpde_to_ode_in_r\u001b[0;34m(pde)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124mr\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 84\u001b[0m \u001b[38;5;124;03mReturns an ODE satisfied by the radial derivatives of a function\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;124;03m:math:`f:\\mathbb R^n \\to \\mathbb R` satisfying\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 95\u001b[0m \u001b[38;5;124;03m- *ode_order* the order of ODE that is returned\u001b[39;00m\n\u001b[1;32m 96\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 97\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(pde\u001b[38;5;241m.\u001b[39meqs) \u001b[38;5;241m!=\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[0;32m---> 98\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mPDE must be scalar\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m 100\u001b[0m dim \u001b[38;5;241m=\u001b[39m pde\u001b[38;5;241m.\u001b[39mdim\n\u001b[1;32m 101\u001b[0m ode_order \u001b[38;5;241m=\u001b[39m pde\u001b[38;5;241m.\u001b[39morder\n",
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"\u001b[0;31mValueError\u001b[0m: PDE must be scalar"
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]
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}
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],
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"source": [
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"ode_in_r, var, ode_order = pde_to_ode_in_r(pde_op)\n",
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"ode_in_r"
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]
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},
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{

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