Start tracking codegen notebook

1 files changed, 1771 insertions, 0 deletions

diff --git a/lbm_codegen.ipynb b/lbm_codegen.ipynb
new file mode 100644
index 0000000..efc1200
--- /dev/null
+++ b/lbm_codegen.ipynb
@@ -0,0 +1,1771 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sympy import *\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "init_printing()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c = [Matrix((x,)) for x in [(-1, 1), ( 0, 1), ( 1, 1), (-1, 0), ( 0, 0), ( 1, 0), (-1, 0), ( 0, -1), ( 1, -1)]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$1$$"
+      ],
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c[1][1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "w = [Rational(*x) for x in [(1,36), (1,9), (1,36), (1,9), (4,9), (1,9), (1,36), (1,9), (1,36)]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$$\\left [ \\frac{1}{36}, \\quad \\frac{1}{9}, \\quad \\frac{1}{36}, \\quad \\frac{1}{9}, \\quad \\frac{4}{9}, \\quad \\frac{1}{9}, \\quad \\frac{1}{36}, \\quad \\frac{1}{9}, \\quad \\frac{1}{36}\\right ]$$"
+      ],
+      "text/plain": [
+       "[1/36, 1/9, 1/36, 1/9, 4/9, 1/9, 1/36, 1/9, 1/36]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "w"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$1$$"
+      ],
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(w)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$$\\frac{\\sqrt{3}}{3}$$"
+      ],
+      "text/plain": [
+       "√3\n",
+       "──\n",
+       "3 "
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c_s = sqrt(Rational(1,3))\n",
+    "c_s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "u_x, u_y, rho, tau = symbols('u_x u_y rho tau')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([f_next_0, f_next_1, f_next_2, f_next_3, f_next_4, f_next_5,\n",
+       "       f_next_6, f_next_7, f_next_8], dtype=object)"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "f_next = symarray('f_next', 9)\n",
+    "f_next"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([f_curr_0, f_curr_1, f_curr_2, f_curr_3, f_curr_4, f_curr_5,\n",
+       "       f_curr_6, f_curr_7, f_curr_8], dtype=object)"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "f_curr = symarray('f_curr', 9)\n",
+    "f_curr"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$$f_{curr 0} + f_{curr 1} + f_{curr 2} + f_{curr 3} + f_{curr 4} + f_{curr 5} + f_{curr 6} + f_{curr 7} + f_{curr 8}$$"
+      ],
+      "text/plain": [
+       "f_curr_0 + f_curr_1 + f_curr_2 + f_curr_3 + f_curr_4 + f_curr_5 + f_curr_6 + f\n",
+       "_curr_7 + f_curr_8"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rho = sum(f_curr)\n",
+    "rho"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$$\\frac{- f_{curr 0} + f_{curr 2} - f_{curr 3} + f_{curr 5} - f_{curr 6} + f_{curr 8}}{f_{curr 0} + f_{curr 1} + f_{curr 2} + f_{curr 3} + f_{curr 4} + f_{curr 5} + f_{curr 6} + f_{curr 7} + f_{curr 8}}$$"
+      ],
+      "text/plain": [
+       "                -f_curr_0 + f_curr_2 - f_curr_3 + f_curr_5 - f_curr_6 + f_curr\n",
+       "──────────────────────────────────────────────────────────────────────────────\n",
+       "f_curr_0 + f_curr_1 + f_curr_2 + f_curr_3 + f_curr_4 + f_curr_5 + f_curr_6 + f\n",
+       "\n",
+       "_8                \n",
+       "──────────────────\n",
+       "_curr_7 + f_curr_8"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "u_x = sum([ (c_i*f_curr[i])[0] for i, c_i in enumerate(c) ]) / rho\n",
+    "u_x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$$\\frac{f_{curr 0} + f_{curr 1} + f_{curr 2} - f_{curr 7} - f_{curr 8}}{f_{curr 0} + f_{curr 1} + f_{curr 2} + f_{curr 3} + f_{curr 4} + f_{curr 5} + f_{curr 6} + f_{curr 7} + f_{curr 8}}$$"
+      ],
+      "text/plain": [
+       "                      f_curr_0 + f_curr_1 + f_curr_2 - f_curr_7 - f_curr_8    \n",
+       "──────────────────────────────────────────────────────────────────────────────\n",
+       "f_curr_0 + f_curr_1 + f_curr_2 + f_curr_3 + f_curr_4 + f_curr_5 + f_curr_6 + f\n",
+       "\n",
+       "                  \n",
+       "──────────────────\n",
+       "_curr_7 + f_curr_8"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "u_y = sum([ (c_i*f_curr[i])[1] for i, c_i in enumerate(c) ]) / rho\n",
+    "u_y"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\left[\\begin{matrix}\\frac{- f_{curr 0} + f_{curr 2} - f_{curr 3} + f_{curr 5} - f_{curr 6} + f_{curr 8}}{f_{curr 0} + f_{curr 1} + f_{curr 2} + f_{curr 3} + f_{curr 4} + f_{curr 5} + f_{curr 6} + f_{curr 7} + f_{curr 8}}\\\\\\frac{f_{curr 0} + f_{curr 1} + f_{curr 2} - f_{curr 7} - f_{curr 8}}{f_{curr 0} + f_{curr 1} + f_{curr 2} + f_{curr 3} + f_{curr 4} + f_{curr 5} + f_{curr 6} + f_{curr 7} + f_{curr 8}}\\end{matrix}\\right]$$"
+      ],
+      "text/plain": [
+       "⎡                -f_curr_0 + f_curr_2 - f_curr_3 + f_curr_5 - f_curr_6 + f_cur\n",
+       "⎢─────────────────────────────────────────────────────────────────────────────\n",
+       "⎢f_curr_0 + f_curr_1 + f_curr_2 + f_curr_3 + f_curr_4 + f_curr_5 + f_curr_6 + \n",
+       "⎢                                                                             \n",
+       "⎢                      f_curr_0 + f_curr_1 + f_curr_2 - f_curr_7 - f_curr_8   \n",
+       "⎢─────────────────────────────────────────────────────────────────────────────\n",
+       "⎣f_curr_0 + f_curr_1 + f_curr_2 + f_curr_3 + f_curr_4 + f_curr_5 + f_curr_6 + \n",
+       "\n",
+       "r_8                ⎤\n",
+       "───────────────────⎥\n",
+       "f_curr_7 + f_curr_8⎥\n",
+       "                   ⎥\n",
+       "                   ⎥\n",
+       "───────────────────⎥\n",
+       "f_curr_7 + f_curr_8⎦"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "u = Matrix([u_x, u_y])\n",
+    "u"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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