Initial commit

.gitignore

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+.idea/

Task 1/convolutions.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import itertools"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c = 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Generate some data\n",
+    "np.random.seed(42)\n",
+    "lambda1 = np.random.normal(size=(c, c))\n",
+    "lambda2 = np.random.normal(size=(c, c))\n",
+    "lambda3 = np.random.normal(size=(c, c))\n",
+    "G1 = np.random.normal(size=(c, c, c))\n",
+    "G2 = np.random.normal(size=(c, c, c))\n",
+    "U = np.random.normal(size=(c, c, c, c))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def Z_naive(lambda1, lambda2, lambda3, G1, G2, U):\n",
+    "    c = lambda1.shape[0]\n",
+    "    Z = np.zeros(shape=(c, c, c, c))\n",
+    "    for a, b, c, d, e, f, g, h, i, j in itertools.product(*([range(c)]*10)):\n",
+    "        Z[a, h, i, j] += lambda1[a, b]*lambda2[d, e]*lambda3[g, h]*G1[c, b, d]*G2[f, e, g]*U[i, j, c, f]\n",
+    "    return Z"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "198 ms ± 30.6 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "Z = Z_naive(lambda1, lambda2, lambda3, G1, G2, U)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(3, 3, 3, 3)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Z = Z_naive(lambda1, lambda2, lambda3, G1, G2, U)\n",
+    "Z.shape"
+   ]
+  }
+ ],
+ "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}