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Chapter 1 and Chapter 4 #1

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chapter 1 files
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Created using Colaboratory
ManvithaPonnapati Apr 14, 2020
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207 changes: 127 additions & 80 deletions notebooks/SemiCircleLaw.ipynb
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@@ -1,85 +1,132 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"using RandomMatrices"
]
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"kernelspec": {
"display_name": "Julia 0.6.0",
"language": "julia",
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"colab": {
"name": "SemiCircleLaw.ipynb",
"provenance": []
}
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
"cells": [
{
"cell_type": "code",
"metadata": {
"id": "9nKXerOM9_p_",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 130
},
"outputId": "fb35f8b0-f49b-4979-a8b3-2530cd1b7504"
},
"source": [
"using RandomMatrices"
],
"execution_count": 0,
"outputs": [
{
"output_type": "error",
"ename": "SyntaxError",
"evalue": "ignored",
"traceback": [
"\u001b[0;36m File \u001b[0;32m\"<ipython-input-1-efe7167b7012>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m using RandomMatrices\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
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}
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" </script>\n"
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},
"source": [
"#semicircle.jl\n",
"#Algorithm 1.2 of Random Eigenvalues by Alan Edelman\n",
"\n",
"#Experiment: Sample random symmetric Gaussian matrices\n",
"#Plot: Histogram of the eigenvalues\n",
"#Theory: Semicircle as n->infinity\n",
"\n",
"using Plots\n",
"plotly()\n",
"\n",
"## Parameters\n",
"n = 1000\n",
"t = 1\n",
"\n",
"## Experiment\n",
"vals = Float64[] # initialize result vector\n",
"for i = 1:t\n",
" A = randn(n, n) # draw n by n matrix with idependent gaussians\n",
" S = (A + A')/2 # symmetrize matrix\n",
" vals = append!(vals, eigvals(S)) # calculate eigenvalues and append to result vector\n",
"end\n",
"vals /= √(n/2) # scale eigenvalues\n",
"\n",
" # set limits for x axis in plot\n",
"histogram(vals, xlim=(-2,2), nbins=50, normed=true ) # make histogram\n",
"xvals = -2:.1:2\n",
"plot!(xvals, sqrt.(4 - xvals.^2)/(2*π),color=:red) # plot semi circle"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" </script>\n"
]
},
"metadata": {
"tags": []
},
"execution_count": 32
}
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"cell_type": "code",
"metadata": {
"id": "X4f5pRnA-DF5",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "MTgZpHZ49_qj",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy"
],
"execution_count": 0,
"outputs": []
}
],
"source": [
"#semicircle.jl\n",
"#Algorithm 1.2 of Random Eigenvalues by Alan Edelman\n",
"\n",
"#Experiment: Sample random symmetric Gaussian matrices\n",
"#Plot: Histogram of the eigenvalues\n",
"#Theory: Semicircle as n->infinity\n",
"\n",
"using Plots\n",
"plotly()\n",
"\n",
"## Parameters\n",
"n = 1000\n",
"t = 1\n",
"\n",
"## Experiment\n",
"vals = Float64[] # initialize result vector\n",
"for i = 1:t\n",
" A = randn(n, n) # draw n by n matrix with idependent gaussians\n",
" S = (A + A')/2 # symmetrize matrix\n",
" vals = append!(vals, eigvals(S)) # calculate eigenvalues and append to result vector\n",
"end\n",
"vals /= √(n/2) # scale eigenvalues\n",
"\n",
" # set limits for x axis in plot\n",
"histogram(vals, xlim=(-2,2), nbins=50, normed=true ) # make histogram\n",
"xvals = -2:.1:2\n",
"plot!(xvals, sqrt.(4 - xvals.^2)/(2*π),color=:red) # plot semi circle"
]
},
{
"cell_type": "code",
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