{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from pystencils.session import *\n",
"from pystencils.fd.derivation import *"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2D standard stencils\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"stencil = [(-1, 0), (1, 0), (0, -1), (0, 1), (0, 0)]\n",
"standard_2d_00 = FiniteDifferenceStencilDerivation((0,0), stencil)\n",
"f = ps.fields(\"f: [2D]\")\n",
"standard_2d_00_res = standard_2d_00.get_stencil()\n",
"res = standard_2d_00_res.apply(f.center)\n",
"expected = f[-1, 0] - 2 * f[0, 0] + f[1, 0]\n",
"assert res == expected"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Finite difference stencil of accuracy 2, isotropic error: False"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"assert standard_2d_00_res.accuracy == 2\n",
"assert not standard_2d_00_res.is_isotropic\n",
"standard_2d_00_res"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"ename": "AttributeError",
"evalue": "MutableDenseMatrix has no attribute tomatrix.",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-4-ea41cd8e50a0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mstandard_2d_00\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_stencil\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m~/pystencils/pystencils/pystencils/fd/derivation.py\u001b[0m in \u001b[0;36mas_matrix\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 185\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mdirection\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweight\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstencil\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mweights\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 186\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmax_offset\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mdirection\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_offset\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mdirection\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mweight\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 187\u001b[0;31m \u001b[0mresult\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtomatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtomatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 188\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"test\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 189\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mdim\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/anaconda3/envs/pystencils/lib/python3.7/site-packages/sympy/matrices/matrices.py\u001b[0m in \u001b[0;36m__getattr__\u001b[0;34m(self, attr)\u001b[0m\n\u001b[1;32m 2139\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2140\u001b[0m raise AttributeError(\n\u001b[0;32m-> 2141\u001b[0;31m \"%s has no attribute %s.\" % (self.__class__.__name__, attr))\n\u001b[0m\u001b[1;32m 2142\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2143\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__len__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mAttributeError\u001b[0m: MutableDenseMatrix has no attribute tomatrix."
]
}
],
"source": [
"standard_2d_00.get_stencil().as_matrix()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2D isotropic stencils\n",
"\n",
"## second x-derivative"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"stencil = [(i, j) for i in (-1, 0, 1) for j in (-1, 0, 1)]\n",
"isotropic_2d_00 = FiniteDifferenceStencilDerivation((0,0), stencil)\n",
"isotropic_2d_00_res = isotropic_2d_00.get_stencil(isotropic=True)\n",
"assert isotropic_2d_00_res.is_isotropic\n",
"assert isotropic_2d_00_res.accuracy == 2\n",
"isotropic_2d_00_res"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"isotropic_2d_00_res.as_matrix()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.figure(figsize=(2,2))\n",
"isotropic_2d_00_res.visualize()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"expected_result = sp.Matrix([[1, -2, 1], [10, -20, 10], [1, -2, 1]]) / 12\n",
"assert expected_result == isotropic_2d_00_res.as_matrix()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"type(isotropic_2d_00_res.as_matrix())"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"type(expected_result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Isotropic laplacian"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"isotropic_2d_11 = FiniteDifferenceStencilDerivation((1,1), stencil)\n",
"isotropic_2d_11_res = isotropic_2d_11.get_stencil(isotropic=True)\n",
"iso_laplacian = isotropic_2d_00_res.as_matrix() + isotropic_2d_11_res.as_matrix()\n",
"iso_laplacian"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"expected_result = sp.Matrix([[1, 4, 1], [4, -20, 4], [1, 4, 1]]) / 6\n",
"assert iso_laplacian == expected_result"
]
}
],
"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",
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"nbformat": 4,
"nbformat_minor": 2
}