test_fd_derivation.ipynb

{
 "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": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\1 & -2 & 1\\\\0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  0   0⎤\n",
       "⎢        ⎥\n",
       "⎢1  -2  1⎥\n",
       "⎢        ⎥\n",
       "⎣0  0   0⎦"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "standard_2d_00.get_stencil().as_array()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2D isotropic stencils\n",
    "\n",
    "## second x-derivative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Finite difference stencil of accuracy 2, isotropic error: True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{12} & - \\frac{1}{6} & \\frac{1}{12}\\\\\\frac{5}{6} & - \\frac{5}{3} & \\frac{5}{6}\\\\\\frac{1}{12} & - \\frac{1}{6} & \\frac{1}{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1/12  -1/6  1/12⎤\n",
       "⎢                ⎥\n",
       "⎢5/6   -5/3  5/6 ⎥\n",
       "⎢                ⎥\n",
       "⎣1/12  -1/6  1/12⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isotropic_2d_00_res.as_array()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(2,2))\n",
    "isotropic_2d_00_res.visualize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "expected_result = sp.Array([[1, -2, 1], [10, -20, 10], [1, -2, 1]]) / 12\n",
    "assert expected_result == isotropic_2d_00_res.as_array()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Isotropic laplacian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6}\\\\\\frac{2}{3} & - \\frac{10}{3} & \\frac{2}{3}\\\\\\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1/6   2/3   1/6⎤\n",
       "⎢               ⎥\n",
       "⎢2/3  -10/3  2/3⎥\n",
       "⎢               ⎥\n",
       "⎣1/6   2/3   1/6⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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_array() + isotropic_2d_11_res.as_array()\n",
    "iso_laplacian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "expected_result = sp.Array([[1, 4, 1], [4, -20, 4], [1, 4, 1]]) / 6\n",
    "assert iso_laplacian == expected_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# stencils for staggered fields\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "half = sp.Rational(1, 2)\n",
    "\n",
    "fd_points_ex = (\n",
    "    (half, 0),\n",
    "    (-half, 0),\n",
    "    (half, 1),\n",
    "    (half, -1),\n",
    "    (-half, 1),\n",
    "    (-half, -1)\n",
    ")\n",
    "assert set(fd_points_ex) == set(FiniteDifferenceStaggeredStencilDerivation(\"E\", 2).stencil)\n",
    "\n",
    "fd_points_ey = (\n",
    "    (0, half),\n",
    "    (0, -half),\n",
    "    (-1,-half),\n",
    "    (-1, half),\n",
    "    (1, -half),\n",
    "    (1, half)\n",
    ")\n",
    "assert set(fd_points_ey) == set(FiniteDifferenceStaggeredStencilDerivation(\"N\",2).stencil)\n",
    "\n",
    "fd_points_c = (\n",
    "    (half, half),\n",
    "    (-half, -half),\n",
    "    (half, -half),\n",
    "    (-half, half)\n",
    ")\n",
    "assert set(fd_points_c) ==  set(FiniteDifferenceStaggeredStencilDerivation(\"NE\",2).stencil)\n",
    "\n",
    "assert len(FiniteDifferenceStaggeredStencilDerivation(\"E\",3).points) == 10\n",
    "assert len(FiniteDifferenceStaggeredStencilDerivation(\"NE\",3).points) == 12\n",
    "assert len(FiniteDifferenceStaggeredStencilDerivation(\"TNE\",3).points) == 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = ps.fields(\"c: [2D]\")\n",
    "c3 = ps.fields(\"c3: [3D]\")\n",
    "\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"E\", 2, (0,)).apply(c.center) == c[1, 0] - c[0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"W\", 2, (0,)).apply(c.center) == c[0, 0] - c[-1, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"N\", 2, (1,)).apply(c.center) == c[0, 1] - c[0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"S\", 2, (1,)).apply(c.center) == c[0, 0] - c[0, -1]\n",
    "\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"E\", 3, (0,)).apply(c3.center) == c3[1, 0, 0] - c3[0, 0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"W\", 3, (0,)).apply(c3.center) == c3[0, 0, 0] - c3[-1, 0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"N\", 3, (1,)).apply(c3.center) == c3[0, 1, 0] - c3[0, 0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"S\", 3, (1,)).apply(c3.center) == c3[0, 0, 0] - c3[0, -1, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"T\", 3, (2,)).apply(c3.center) == c3[0, 0, 1] - c3[0, 0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"B\", 3, (2,)).apply(c3.center) == c3[0, 0, 0] - c3[0, 0, -1]\n",
    "\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"S\", 2, (0,)).apply(c.center) == \\\n",
    "       (c[1, 0] + c[1, -1] - c[-1, 0] - c[-1, -1])/4\n",
    "\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"NE\", 2, (0,)).apply(c.center) + \\\n",
    "       FiniteDifferenceStaggeredStencilDerivation(\"NE\", 2, (1,)).apply(c.center) == c[1, 1] - c[0, 0]\n",
    "assert FiniteDifferenceStaggeredStencilDerivation(\"NE\", 3, (0,)).apply(c3.center) + \\\n",
    "       FiniteDifferenceStaggeredStencilDerivation(\"NE\", 3, (1,)).apply(c3.center) == c3[1, 1, 0] - c3[0, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = FiniteDifferenceStaggeredStencilDerivation(\"NE\", 2, (0, 1))\n",
    "assert d.apply(c.center) == c[0,0] + c[1,1] - c[1,0] - c[0,1]\n",
    "d.visualize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "v3 = ps.fields(\"v(3): [3D]\")\n",
    "for i in range(*v3.index_shape):\n",
    "    assert FiniteDifferenceStaggeredStencilDerivation(\"E\", 3, (0,)).apply(v3.center_vector[i]) == \\\n",
    "           v3[1,0,0](i) - v3[0,0,0](i)"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}