test-5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Try to use DPP construct polynomial and reconstruct DPP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "K(x,y) = \\frac{1}{\\pi} \\sqrt{\\frac{\\partial^2 }{\\partial x \\partial y}\\log\\boldsymbol{E}(f(x)f(y))}.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra, Distributions, StatsBase, Plots, Polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 6\n",
    "try_GUE = []\n",
    "for i = 1:100000\n",
    "    A = randn(n,n) + im*randn(n,n)\n",
    "    append!(try_GUE, eigvals(Hermitian((A+A')/2)))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histogram(try_GUE, size = (400,300) ,normalize=:pdf, label=false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "grids from -6 to 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5.98:0.02:5.98"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ogrids = -6:0.02:6\n",
    "grids = ogrids[2:end-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "partialxy (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function partialx(M)\n",
    "    return (M[3:end, 2:end-1] - M[1:end-2, 2:end-1])/2/(ogrids[2] - ogrids[1]) ./ M[2:end-1, 2:end-1]\n",
    "end\n",
    "function partialy(M)\n",
    "    return (M[2:end-1, 3:end] - M[2:end-1, 1:end-2])/2/(ogrids[2] - ogrids[1]) ./ M[2:end-1, 2:end-1]\n",
    "end\n",
    "function partialxy(M)\n",
    "    return (M[3:end, 3:end] + M[1:end-2, 1:end-2] - M[1:end-2, 3:end] - M[3:end, 1:end-2]) /4 /(ogrids[2] - ogrids[1])^2 ./ M[2:end-1, 2:end-1]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "copy_num = 5000\n",
    "Eff = zeros(length(ogrids), length(ogrids))\n",
    "Ef = zeros(length(ogrids))\n",
    "for i = 1:copy_num\n",
    "    A = randn(n,n) + im*randn(n,n)\n",
    "    get_p = fromroots(eigvals(Hermitian((A+A')/2)))\n",
    "    f = rand([-1,1]) * get_p.(ogrids)\n",
    "    Ef = (Ef*(i-1) + f) / i\n",
    "    ff = f .* (f)'\n",
    "    Eff = (Eff*(i-1) + ff) / i\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "601-element Vector{Float64}:\n",
       " -977.1627253591784\n",
       " -957.7983690218459\n",
       " -938.7453790030053\n",
       " -919.9998565488075\n",
       " -901.5579385045506\n",
       " -883.4157971043272\n",
       " -865.5696397613643\n",
       " -848.0157088588383\n",
       " -830.7502815414061\n",
       " -813.7696695072718\n",
       "    ⋮\n",
       "   63.71717580623823\n",
       "   63.32883848764498\n",
       "   62.899717791788454\n",
       "   62.4287458767146\n",
       "   61.91483863528265\n",
       "   61.35689554955126\n",
       "   60.75379954457637\n",
       "   60.10441684161355\n",
       "   59.40759681068364"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "Eff = Eff - Ef .* Ef' # with this or without"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "599×599 Matrix{ComplexF64}:\n",
       " 0.000814692+0.0im  0.000819395+0.0im  …  0.000657952+0.0im\n",
       " 0.000819395+0.0im  0.000824124+0.0im     0.000661413+0.0im\n",
       " 0.000824159+0.0im  0.000828913+0.0im     0.000664921+0.0im\n",
       " 0.000828984+0.0im  0.000833764+0.0im     0.000668477+0.0im\n",
       " 0.000833871+0.0im  0.000838678+0.0im     0.000672083+0.0im\n",
       " 0.000838823+0.0im  0.000843656+0.0im  …  0.000675738+0.0im\n",
       " 0.000843841+0.0im  0.000848701+0.0im     0.000679446+0.0im\n",
       " 0.000848925+0.0im  0.000853812+0.0im     0.000683207+0.0im\n",
       " 0.000854078+0.0im  0.000858993+0.0im     0.000687022+0.0im\n",
       "   0.0008593+0.0im  0.000864243+0.0im     0.000690892+0.0im\n",
       "            ⋮                          ⋱  \n",
       " 0.000687812+0.0im  0.000691419+0.0im  …  0.000843877+0.0im\n",
       " 0.000683891+0.0im  0.000687478+0.0im     0.000838904+0.0im\n",
       " 0.000680026+0.0im  0.000683595+0.0im     0.000833994+0.0im\n",
       " 0.000676217+0.0im  0.000679767+0.0im     0.000829149+0.0im\n",
       " 0.000672461+0.0im  0.000675993+0.0im     0.000824365+0.0im\n",
       " 0.000668758+0.0im  0.000672272+0.0im  …  0.000819643+0.0im\n",
       " 0.000665106+0.0im  0.000668602+0.0im      0.00081498+0.0im\n",
       " 0.000661505+0.0im  0.000664983+0.0im     0.000810375+0.0im\n",
       " 0.000657952+0.0im  0.000661413+0.0im     0.000805829+0.0im"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logEff = log.((Complex.(Eff)))\n",
    "logEff = Hermitian(logEff)\n",
    "K = .√((logEff[3:end, 3:end] + logEff[1:end-2, 1:end-2] - logEff[1:end-2, 3:end] - logEff[3:end, 1:end-2]) /4 /(ogrids[2] - ogrids[1])^2) *\n",
    "   (grids[2] - grids[1]) / π # correct normalization\n",
    "#K = .√(partialxy(Eff) .- partialx(Eff) .* partialy(Eff)) / π * (grids[2] - grids[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8022272149988545 + 0.0im"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Λ, Q = eigen(K)\n",
    "tr(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "#0.8955044955055671, 1\n",
    "#1.5283230507288368, 2\n",
    "#2.1102178359823873, 3\n",
    "#2.7213506349113645, 4\n",
    "#3.2389773015114853, 5\n",
    "#3.7749715242911313, 6\n",
    "#4.382451985280821, 7\n",
    "#4.966556137020364, 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "<circle clip-path=\"url(#clip272)\" cx=\"2072.68\" cy=\"435.241\" r=\"14.4\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"3.2\"/>\n",
       "<circle clip-path=\"url(#clip272)\" cx=\"2352.76\" cy=\"295.133\" r=\"14.4\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"3.2\"/>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter([i for i in 1:8], [.8955044955055671,1.5283230507288,2.11021783,2.7213506,3.238977301,3.77497152,4.38245198,4.96655613],\n",
    "    xlims = (0.0,8.0),\n",
    "    ylims = (0, 6.0),\n",
    "    label = false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Vector{Float64}:\n",
       " 0.8955044955055671\n",
       " 0.7641615253644\n",
       " 0.7034059433333333\n",
       " 0.68033765\n",
       " 0.6477954602\n",
       " 0.6291619199999999\n",
       " 0.6260645685714286\n",
       " 0.62081951625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[.8955044955055671,1.5283230507288,2.11021783,2.7213506,3.238977301,3.77497152,4.38245198,4.96655613] ./[i for i in 1:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "599-element Vector{ComplexF64}:\n",
       "   -2.88068714035982 - 0.5529079104444294im\n",
       "  -2.829399951595903 + 0.3224266244071893im\n",
       " -2.7370323202268327 - 0.4757817528515083im\n",
       " -2.6596870871046194 - 0.2366874546612425im\n",
       "  -2.573413150105675 - 0.4219885792261867im\n",
       "  -2.427934361158088 - 0.8543363713985355im\n",
       " -2.4033010036080666 + 0.25207233860654876im\n",
       "   -2.38974730564041 + 0.22651178060890664im\n",
       " -2.3637914827472617 + 0.43121426006184677im\n",
       "  -2.343722106385033 - 0.4636715406412483im\n",
       "                     ⋮\n",
       "  2.4596075061342764 - 0.4650276594743604im\n",
       "   2.490053356775069 - 0.293364444354615im\n",
       "  2.6062624642180316 + 1.0856121488817112im\n",
       "    2.90955505314296 + 0.9990794825874854im\n",
       "  4.1563198094312215 + 1.3869979513346213im\n",
       "   4.422303404655029 + 1.259672636274317im\n",
       "   7.040522176070626 + 1.0665812335435856im\n",
       "   7.474997132850346 + 2.055525060706972im\n",
       "  15.413991730585316 + 1.637233736685329im"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Λ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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