{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Timing matrix-vector multiplication"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"using FundamentalsNumericalComputation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's repeat the experiment of the previous figure for more, and larger, values of $n$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"randn(4,4)*randn(4); # throwaway to force compilation\n",
"\n",
"n = 400:200:6000\n",
"t = zeros(size(n))\n",
"for (i,n) in enumerate(n) \n",
" A = randn(n,n) \n",
" x = randn(n)\n",
" t[i] = @elapsed for j = 1:10; A*x; end\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting the time as a function of $n$ on log-log scales is equivalent to plotting the logs of the variables, but is formatted more neatly."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": "\n\n",
"image/svg+xml": "\n\n"
},
"metadata": {},
"execution_count": 4
}
],
"source": [
"plot(n,t, m=:o,\n",
" xaxis=(:log10,\"\\$n\\$\"), yaxis=(:log10,\"elapsed time (sec)\"),\n",
" title=\"Timing of matrix-vector multiplications\", label=\"data\", leg=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see that while the full story is complicated, the graph is trending to a straight line of positive slope. For comparison, we can plot a line that represents $O(n^2)$ growth exactly. (All such lines have slope equal to 2.)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=2}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot!(n,(n/n[1]).^2*t[1], l=:dash,\n",
" label=\"\\$O(n^3)\\$\", legend=:topleft)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia (faststart)",
"language": "julia",
"name": "julia-fast"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "3.7.3-final"
}
},
"nbformat": 4,
"nbformat_minor": 4
}