sparse_performance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook marks the performance of the clifford package with the sparse/numba product implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import clifford as cf\n",
    "import numpy as np\n",
    "import timeit\n",
    "layout,blades = cf.Cl(5)\n",
    "n_dims = len(layout.blades)+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.7 µs ± 103 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "cf.MultiVector(layout,value=np.random.rand(n_dims))*cf.MultiVector(layout,value=np.random.rand(n_dims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.7 µs ± 166 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "cf.MultiVector(layout,value=np.random.rand(n_dims))|cf.MultiVector(layout,value=np.random.rand(n_dims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.2 µs ± 92.5 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "cf.MultiVector(layout,value=np.random.rand(n_dims))^cf.MultiVector(layout,value=np.random.rand(n_dims))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets see how it performs with 5d conformal ga"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "layout,blades = cf.Cl(4,1)\n",
    "n_dims = len(layout.blades)+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.9 µs ± 142 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "cf.MultiVector(layout,value=np.random.rand(n_dims))*cf.MultiVector(layout,value=np.random.rand(n_dims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.4 µs ± 89.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "cf.MultiVector(layout,value=np.random.rand(n_dims))|cf.MultiVector(layout,value=np.random.rand(n_dims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.2 µs ± 127 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "cf.MultiVector(layout,value=np.random.rand(n_dims))^cf.MultiVector(layout,value=np.random.rand(n_dims))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This makes the sparse/numba implementation 65.9/14.7 = 4.48 ~= 4.5 times faster than the existing matrix multiplication. This is obviously not a panacea but it is a significant saving."
   ]
  }
 ],
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