mm-tensor-visualise.ipynb

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "628ac162",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "327c9bb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def construct_mm_tensor(n):\n",
    "    \"\"\"\n",
    "    Construct the matrix multiplication tensor, M, of a given size, n.\n",
    "    \n",
    "    Matrix multiplication\n",
    "    C = A.B\n",
    "    \n",
    "    Return the MM tensor s.t.\n",
    "    C[i] = sum_ai sum_bi T[i,ai,bi] x A[ai] x B[bi]\n",
    "    (where i, ai, bi are indices to the scalar values of the matrices)\n",
    "    \n",
    "    Assumes:\n",
    "        - A, B are both nxn matrices\n",
    "    \n",
    "    Example\n",
    "    C[0, 0] <- A[0,0]*B[0,0] + A[0,1]*B[1,0]            \n",
    "    C[0, 1] <- A[0,0]*B[0,1] + A[0,1]*B[1,1]            \n",
    "    C[1, 0] <- A[1,0]*B[0,0] + A[1,1]*B[1,0]            \n",
    "    C[1, 1] <- A[1,0]*B[0,1] + A[1,1]*B[1,1]\n",
    "\n",
    "    Args:\n",
    "        n (int): the size\n",
    "    Returns:\n",
    "        M: the matrix multiplication tensor\n",
    "    \"\"\"\n",
    "\n",
    "    MMT = np.zeros((n, n, n, n, n, n))\n",
    "    for i_r in range(n):  # for each row of C\n",
    "        for i_c in range(n):  # for each col of C\n",
    "            for k in range(n):  # inner prod\n",
    "\n",
    "\n",
    "                # C_row x C_col x A_row x A_col x B_row x B_col\n",
    "                MMT[i_r, i_c, i_r, k, k, i_c] += 1\n",
    "    return MMT\n",
    "            \n",
    "    \n",
    "def matmul(MMT, A, B):\n",
    "    \"\"\"\n",
    "    Use the matrix multiplcation tensor to do matrix multiplication.\n",
    "    \n",
    "    Assumes:\n",
    "    - A, B are both nxn matrices\n",
    "    \n",
    "    Args:\n",
    "        MMT (np.ndarray): nxnxnxnxnxn the matrix multiplication tensor\n",
    "        A (np.ndarray): nxn  input matrix to be matmul-ed\n",
    "        B (np.ndarray): nxn input matrix to be matmul-ed\n",
    "    \"\"\"\n",
    "    C = np.zeros((n,n))\n",
    "    for i_r in range(n):  # for each row of C\n",
    "        for i_c in range(n):  # for each col of C\n",
    "            for j_r in range(n):  # for each row of A\n",
    "                for j_c in range(n):  # for each col of A\n",
    "                    for k_r in range(n):  # for each row of B\n",
    "                        for k_c in range(n):  # for each col of B\n",
    "                            C[i_r, i_c] += A[j_r, j_c]*B[k_r, k_c]*MMT[i_r, i_c, j_r, j_c, k_r, k_c]\n",
    "    return C      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8d1361a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# need to test this!\n",
    "n = 6\n",
    "MMT = construct_mm_tensor(n)\n",
    "\n",
    "A = np.random.standard_normal((n,n))\n",
    "B = np.random.standard_normal((n,n))\n",
    "\n",
    "C_true = np.matmul(A, B)\n",
    "C = matmul(MMT, A, B)\n",
    "\n",
    "assert np.isclose(C, C_true).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9ebfa9b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# reshape to 3 dims so we can visualise\n",
    "MMT = MMT.reshape((n**2, n**2, n**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d13a0fb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# split into 0s and 1s\n",
    "x, y, z = np.where(MMT==1)\n",
    "x_, y_, z_ = np.where(MMT==0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6444b8d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.express as px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8f12afc2",
   "metadata": {},
   "outputs": [
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