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genkuroki/random orthogonal matrix.ipynb

Last active February 16, 2021 08:27
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random orthogonal matrix
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random orthogonal matrix.ipynb
{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using LinearAlgebra, Plots\n\nfunction rand_orthogonal(n)\n Q, R = qr(randn(n, n))\n Q * diagm(sign.(diag(R)))\nend\n\nn = 2000\nX = rand_orthogonal(n)\nhistogram(angle.(eigvals(X)), bins=range(-π, π, length=51), legend=false)",
"execution_count": 1,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 1,
"data": {
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]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "histogram(rand(10^4), bins=50, legend=false)",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
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"source": "histogram(rand(10^5), bins=50, legend=false)",
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{
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},
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"source": "histogram(rand(10^6), bins=50, legend=false)",
"execution_count": 5,
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{
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"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n, ms = 200, 1.4\nX = rand_orthogonal(n)\nP = scatter(eigvals(X); ms, msc=:auto, size=(520, 500), legend=false)\nH = histogram(angle.(eigvals(X)), bins=range(-π, π, length=51), legend=false)\nY = diagm(exp.(2π*im*rand(n)))\nQ = scatter(eigvals(Y); ms, msc=:auto, size=(520, 500), legend=false)\nK = histogram(angle.(diag(Y)), bins=range(-π, π, length=51), legend=false)\nplot(P, Q, H, K; size=(800, 760))",
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 6,
"data": {
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"source": "using RandomMatrices\n\nn, ms = 200, 1.4\nX = rand(Haar(1), n)\nP = scatter(eigvals(X); ms, msc=:auto, size=(520, 500), legend=false)\nH = histogram(angle.(eigvals(X)), bins=range(-π, π, length=51), legend=false)\nY = diagm(exp.(2π*im*rand(n)))\nQ = scatter(eigvals(Y); ms, msc=:auto, size=(520, 500), legend=false)\nK = histogram(angle.(diag(Y)), bins=range(-π, π, length=51), legend=false)\nplot(P, Q, H, K; size=(800, 760))",
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
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