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Scientific Computing Examples
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "id": "3fdf98b3", | |
| "metadata": {}, | |
| "source": [ | |
| "### 2D Jacobi Iteration as Stencil\n", | |
| "\n", | |
| "Index set `I` contains the possible indices for both dimensions\n", | |
| "\n", | |
| "Set of States `S` contains the possible values for cells in the array\n", | |
| "\n", | |
| "Initial State `S0` defines the initial state for each cell of the array (boundary conditions)\n", | |
| "\n", | |
| "Stencil `s` defines the neighbor for each point as offsets from the current cell\n", | |
| "\n", | |
| "Transition `T` defines, for each neighbor, the new state of the current cell\n", | |
| "\n", | |
| "Output - `Jacobi-Heat-Distribution.gif`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "id": "be18e9e0", | |
| "metadata": { | |
| "scrolled": true | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
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| |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "I = range(0,100)\n", | |
| "S = float\n", | |
| "S0 = lambda x,y: ((0,1)[x>=len(I)],1)[x<0] # 0 if 0 <= x <= 100; 1 otherwise\n", | |
| "s = [(1,0), (0,1), (-1,0), (0,-1)]\n", | |
| "T = lambda t: sum(t) * 0.25\n", | |
| "\n", | |
| "import numpy as np\n", | |
| "A = np.zeros((100,100))\n", | |
| "B = np.zeros((100,100))\n", | |
| "curr = A\n", | |
| "other = B\n", | |
| "\n", | |
| "def getValue(idx):\n", | |
| " x,y = idx\n", | |
| " # In-Bounds - Return the value in the array\n", | |
| " # Out-of-Bounds - Return boundary condition defined in S0\n", | |
| " if x < len(I) and y < len(I) and x >= 0 and y >= 0:\n", | |
| " return other[idx]\n", | |
| " else:\n", | |
| " return S0(*idx)\n", | |
| " \n", | |
| "for i in I:\n", | |
| " for j in I:\n", | |
| " A[i,j] = S0(i,j)\n", | |
| " B[i,j] = A[i,j]\n", | |
| " \n", | |
| "import matplotlib.pyplot as plt\n", | |
| "import imageio\n", | |
| "import tempfile\n", | |
| "\n", | |
| "# Create an animated gif...\n", | |
| "files = []\n", | |
| "\n", | |
| "with tempfile.TemporaryDirectory() as tmpdir: \n", | |
| " for iterations in range(0,100):\n", | |
| " for i in I:\n", | |
| " for j in I:\n", | |
| " n = [(x + i, y + j) for x,y in s]\n", | |
| " other[i,j] = T(map(getValue, n))\n", | |
| " \n", | |
| " plt.imshow(curr, cmap='hot', interpolation='none')\n", | |
| " tmpfile = tmpdir + '/' + str(iterations) + '.png'\n", | |
| " plt.title(\"Iteration: \" + str(iterations + 1))\n", | |
| " plt.savefig(tmpfile)\n", | |
| " files.append(tmpfile)\n", | |
| " \n", | |
| " # Show every 25\n", | |
| " if iterations == 0 or (iterations+1) % 25 == 0:\n", | |
| " plt.show()\n", | |
| " tmp = curr\n", | |
| " curr = other\n", | |
| " other = tmp\n", | |
| " \n", | |
| " with imageio.get_writer('Jacobi-Heat-Distribution.gif', mode='I') as writer:\n", | |
| " for filename in files:\n", | |
| " image = imageio.imread(filename)\n", | |
| " writer.append_data(image)\n", | |
| " \n", | |
| " # If this is the last file, append it multiple times to simulate having a pause\n", | |
| " if filename == files[-1]:\n", | |
| " for i in range(0,10):\n", | |
| " writer.append_data(image)\n" | |
| ] | |
| } | |
| ], | |
| "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": "3.8.8" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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Note: Stencils are a no-go for persistent memory adoption. Only way it would be used is in Memory Mode (DRAM Cache, NVRAM memory), not App Direct Mode (allocate NVRAM as byte-addressable memory).