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@csullivan
Created October 15, 2017 21:08
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Exploring conditioning, floating point errors, and stability of algorithms
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chris Sullivan - 10/16/17\n",
"Conditioning - Floating Point Numbers - Stability\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def random_square_matrix(m):\n",
" return np.random.normal(0,np.power(m,-0.5),size=(m,m))\n",
" #return np.random.randn(m,m)/np.sqrt(m)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def plot_eigenvals_rand_matrix(sizes=[],iterations=1,ax=None):\n",
" if ax is None:\n",
" fig,ax=plt.subplots()\n",
" for size in sizes:\n",
" total = iterations\n",
" while total:\n",
" total-=1\n",
" evals = np.linalg.eigvals(random_square_matrix(size))\n",
" for eval in evals:\n",
" ax.scatter(eval.real,eval.imag)\n",
" ax.set_xlabel(r'Re[Eigenvalue]')\n",
" ax.set_ylabel(r'Im[Eigenvalue]')\n",
" return ax\n",
"\n",
"def plot_abs_eigenvals_rand_matrix(sizes=[],iterations=1,ax=None):\n",
" if ax is None:\n",
" fig,ax=plt.subplots()\n",
" for size in sizes:\n",
" total = iterations\n",
" while total:\n",
" total-= 1\n",
" evals = np.linalg.eigvals(random_square_matrix(size))\n",
" ax.scatter(range(1,size+1),np.absolute(evals),color='black')\n",
" ax.set_ylabel(r'$\\vert\\lambda\\vert$')\n",
" return ax"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def spectral_radius(eigenvals):\n",
" return np.max([np.absolute(eval) for eval in eigenvals])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 12.3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Part (a)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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YUhUWgcudEnKPz693uioJuT92W8Ukb7sSqBguAV0pIBS4lkfnRYF9GeI6/0gK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46lzbzjClki/aXjbFMBfT2PPcCNONSrv6voqT4WZAV8OAg6T9Bl3pUl86uicNdUUG2lKCGxxhTx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\nCyJTWLp3BnlS0CMk611m8n6SDYrByvYAzsITWNFiNE8nVqGOlkOHWgqY1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QWcwIO4+NqV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\nJhpNJ91WwwzPm5wIFXMwsJh0IGQL0Jh1AE/ERZs9QHpbCLtVo4u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ElmIag8wDZgKzReTq\nHi53d+sKuLPbvYuA/4Pp0XkFMDnm9NPAz5RSc4HbgdUx5yYDy6w8/JOIOIBXgDti0txhHQsAK5VS\ns4Brgf/bMW20F2V3AM8Cq5RSs4EXgCd6c63m4kF3BWj6E7fVXzoM0yT7Oev4UuvzqbWfjim0x5Lc\nI2lXQAzzgPVKqToAEfkDMNE6dz0wNUYDM0Uk3dp+RykVBIIiUo1pnfipiORbYp0H1Culjlvi+KQl\n/lGrPEMxLRbPxSRgOqYbGJhm1YNnjrsmJWhh1fQnfqXUTBHxACXALcBrmPO+/0Up9avYxCIyOsXP\ntwELlFKBbs8B0/Ohgwhdv40/AKswLRZfsY7djSm0s5VSIRE5Ari6PStMfIuw47wAe5RSCy+oJJpB\nje4K0PQ7Sqk24CHgCRGxYYrstzpqjyIyzPJ4PR+2AYtFJFtEDMwmfwfvAX/bsSMiZ6v5dvAKpmvU\nKkyRBfAB1ZaoXguMSnLdUczacZqIZAFLrOOfA3kistDKg0MuHfNpjYWusWoGBKuZfQi4Uyn1exGZ\nAnxs1R5bgK9j1hy709Gd0MH/KKU6F9FTpvH2k8BWzKU99gON1umHgF+KSBnmd/9DTMeks+VzjxUW\nVqm6bOleAt4Skd3AdusZ3a87LiKvYlopVmB1cyil2kVkFfCMiPisfPwcq79Zc2mg3a00gxarK+Bt\npdT0L3hdujId8w3gdeAFpdTrfZDFlCMijwMtSqlzhaFpBjG6K0AzmIkAvm411N7wuHVNR23xzynP\nWR8gIk9h1tR1LOtFjq6xajQaTYrRNVaNRqNJMVpYNRqNJsVoYdVoNJoUo4VVo9FoUowWVo1Go0kx\n/x+FyCEoUgpgbgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04d438c9e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axes=plt.subplots(figsize=(5,5))\n",
"axes = plot_eigenvals_rand_matrix(sizes=[128],iterations=100,ax=axes)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The eigenvalues fill out the unit circle in $\\mathbb{C}$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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ZrUYAa4H/qmgbHBFbe36XmdnOqehQwEPAOuAJYFm+vFLSQ5KOqlVxZmaNqGiw3glMjoiR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\n+Xb4EXAmWbj+OG8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"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b63864e0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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wGPiP0jHK9jkL+FdAwCeAZ7L2rWFNnwT2SZfPLNXU1e8xh5o+DTzYk761qqnd\n/lOBn9byferpw2e4PTcNuD1dvh04u8L+U4DlEVHLL150t6Zq9+/Rc0ZEW0Q8ly6/B7wEjK/Cscsd\nC7waESsiYgtwV1pb+1rviMTPgZGSmjL2rUlNEfFURLydrv4cmFCF4/aqphr1rebz/h7wwyoct+oc\nuD23X0S0pctrgP0q7D+d3f8RfDX9c/G2avz53o2aAnhM0kJJM3rQvxY1ASBpEnAU8ExZczXep/HA\n62Xrq9g91DvbJ0vfWtVU7sskZ+Alnf0e86jpk+nv5F8l/WY3+9aqJiR9BDgDuKesuRbvU4/4rr1d\nkPQY0NGtZK8oX4mIkNTp5R6SBgOfAy4va/4e8Nck/xj+Gvg28Mc51XRiRLRKGgs8KmlpRDzZnddU\ng5qQtBfJfygXR8S7aXOP3qdGI+lkksA9say54u+xRp4DJkbE++mY+v3AITkcN4upwM8i4q2ytqLe\np904cLsQEZ/pbJukNyQ1RURb+mfn2i6e6kzguYh4o+y5dy5L+j7wYF41RURr+nOtpPtI/mR7EujO\na6pqTZIGkYTtnRFxb9lz9+h96kArcEDZ+oS0Lcs+gzL0rVVNSJoM3AqcGRFvltq7+D3WtKay/xkS\nEQ9LulnS6KyvpxY1ldntL8kavU894iGFnnsAuCBdvgCY08W+u40ppeFT8nnghTxqkrSnpOGlZeC0\nsmN35zVVsyYBPwBeiojvtNtWrffpWeAQSQemf3FMT2trX+v56dUKnwA2pMMhWfrWpCZJE4F7gfMi\n4pWy9q5+j7WuaVz6O0PSsSQ58maWvrWqKa1lBPApyv6N1fB96pmiP7Xrqw9gX2A+sAx4DBiVtu8P\nPFy2354k/xhHtOv/T8ASYDHJP56mPGoi+aT3P9LHi8AVlfrnUNOJJEMGi4Hn08dZ1X6fSK5CeIXk\nE+8r0ravAF9JlwV8N92+BGjuqm+V/h1VqulW4O2y96Wl0u8xh5ouTI/5HyQf5H2y6PcpXf8ScFe7\nfjV7n3ry8DfNzMxy4iEFM7OcOHDNzHLiwDUzy4kD18wsJw5cM7OcOHCtcOnMTs+nMzrdV7pusov9\nJ0naKOn5Dp6j9JiZtt8q6fBav4ZKJL3fi77XSFoj6dJq1mT58zfNrB5sjIgjASTdDvwpcG2FPstL\nfdo/R7mI+O/VK7MYEXGZpA+KrsN6z2e4Vm+eBg4uraTznD6bTpTy9e4+maR/k9ScLn9Z0iuSfiHp\n+5JuStvpA4eVAAAC1UlEQVTHSLonPc6zkk5I22elE+b8m6QVkr6Wtl8t6c/KjjFL0qWS9pI0X9Jz\n6dn6bjNaKZlL9sGy9ZskfSldPkbSE0omWZnX7lt21gAcuFY3JA0ATiX5RhCSTiOZFOVY4EjgGEn/\npZPuw9oNKXyx3XPvD1xJMs/tCcDHyzbfAFwXEb8DfIHk210lHwdOT2v4q3TOhx8B55btc27atgn4\nfEQcDZwMfLv0FdgMr30Q8A/AORFxDHAb8M0sfa3v8JCC1YNh6XjseJLJom9J209LH4vS9b1IAvg/\nO3iODocUyhwLPBHpLFKSfgx8LN32GeDwsmzcW8nMZQAPRcRmYLOktSTTTS6SNDYN8THA2xHxehqa\nf5v+T2FH+nr2I5mWspJDgSNIZrOCZNLtti57WJ/jwLV6sDEijlQyl+k8kqks7yWZ2+BbEfF/y3dW\nMmduNe0BfCIiNrU7DsDmsqbtfPjfzI+Bc0impfxR2vYHJAF8TERslbQSGNruWNvY9S/L0nYBL0bE\n8b16JVbXPKRgdSMifg18DfimpD1IwvePS2ebksYrmdO0J54FPiVpH0kDSYYOSh4BvlpakdTVmXLJ\nj0hmrTqHJHwBRgBr07A9GfhoB/1eIzmbHiJpJMmdQABeBsZIOj6tYZA+nNjbGoTPcK2upH+uvwp8\nMSJ+KOkw4On0bPN94A9JzjTbKw1LlPwkInbebDCSCaj/FvgF8BawFNiQbv4a8F1Ji0n+m3iSZCaq\nrup8Mb18rTU+vKPFncBcSUuAlvQY7fu9LulukikCf0U6XBIRWySdA9yYTjM4ELiedDzbGoNnC7M+\nJx1SeDAijuhmv70iuUvBQOA+4LaIuK8GJVadpFnA+xFR6XI5q2MeUrC+aDswot0ZbRaz0j6ls8v7\nq15ZDUi6huTM3tfi9nE+wzUzy4nPcM3McuLANTPLiQPXzCwnDlwzs5w4cM3McuLANTPLyf8HragE\n2BsuVf8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04accc0cf8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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HbqF3mnWkv/YDIGkMyRnmUGwFjs9bPi4t60bSPOC7wKKIeD1XHhFb0/ftwH0k/yG8RUQs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\nTpqamsoWuO7DNbN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8Df8EXJi3zYVp2T7gExFxOsmkJn+rAmd1SY/7v0ju1noPcDtwXSH7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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04acbd6b70>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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j3cYhYAWwPnshOedccRst8f4cGG1o18ezFItzrsAc23koL0ZwLjSj1fF+LqpA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\n2P8PUXeeh/zqS+gAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04acb8d7b8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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fX1DX8uSOQxzftI/Tx/qpaqjlvEXTGTs3/YLNoAL733ypx/eyS8mfU8WUfg+B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\nmOgahmGEiImuYRhGiPz/dAKNdyxcpegAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b5fca0f0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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SZZRa3UyiuJoNTc9qiTCohJXvqNqky+YvQx0pTHxQR5o48Mri0Dqy1arrGged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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04adafb8d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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yopVrPecl0TZM0VtpZTSNYoKjjKYBkBBcRRo7zDpusbTNYeLB+4VTEwKr0UQA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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04afe4a668>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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KedSuXMHlry/GE1W3CbSHuPx1NTrUftY4QH6zC6Cqb37qYBmU68oy5J7n93HP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\naXaztrldsQwyBF0Rv9YKpVGldCM7Jd5riWTE4e0uVc9OoawH6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LL+8+P5XybctBublu2l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\n/wd18gjFfJkAqAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b5eb6630>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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b9+N2v55xXqumX6M7rnL6sXaK+sMM7g7qFWsApVPif9wKqISnJ+jIE7EA0FZc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uU4ms0vCq/Xm9HIAnqHmHLARzg+yk2NupgKcU3d386bl/U8dzudSJYYlcO8XOiz8V5uDvOKixAC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RG3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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b5e7ed68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"powers_of_two = [np.power(2,x) for x in range(3,12)]\n",
"for i in powers_of_two:\n",
" fig,axes=plt.subplots(figsize=(5,5))\n",
" plot_eigenvals_rand_matrix(sizes=[i],ax=axes)\n",
" axes.set_title('{}x{}'.format(i,i))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Shown below are the absolute (modulus) values of the eigenvalues for a normally distributed random matrix, as well as the spectral radius as a function of matrix size"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f04b36cb2e8>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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sNmtiTm1PT4/vYFNcy1UzmUzg4Be5xRYpUY2sdTNYyifpixWS8bckagBL3QzW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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3ce2a90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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kKm9n//79ucpbtbbRblUu8SiRSs+LsahyaB0xknnomqhnzpzJVS7xKJFKz4ux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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3a6c6d8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ROHr0KFZXV6GqWF1d3RTRKK9vJex3BrpadLN3knTRlNHR0Z7sWUMhJX1L2FYl\ncUTdra1QLH8YUdpXrVa3+KvV6qbftUeb9MqoO++8syd75kSZSPX9YLCJ9EqUYJFL1D2OYJVLdav5\n+fltASsR2byG61YqSfuTbl9UwKg9Id2Ja9/znV7f8rsKsVWmbv/+/YH+/fv3q6rq0NBQoH9oaEhV\n3YXMykpIOmshKlGFlHs2kb7E2pMp6etbfmtPJ9c9n6w9rVz3rHL1X3HFFYHr4oeGhvDaa69xzyZC\nfCDpYJFrsCrprAFrjrOb2KTV8Uq76IgrFFLSlyS9RNM1WOUqxFYepRV1z/tWJgMDAz3ZnYky/vf9\n4Bwp2QlWMCfp6ycZrLK2MrH81hxqkK91pOF33cokKmCwiZB847qW39qzKsyf9Z5KSfujElVIGWwi\npE9ZWFjAzMwMzpw5g/HxcczOzm7WMk06mJS1PypRg01cIkpIH7KwsIDp6enNBPzl5eXNraqLUBh6\ndHQUFy5cCLQnAYNNhPQhVtGVbj26vKzF79brTGoETiElpA+x0qdc1+JnDbcaIYQkjpU+Za3FTz29\nyHMopIT0Ia55rCsrK4H+bvaiQyElpA+p1+toNBqo1WoQEdRqNTQajc1Ak+97SvkG058IIYGEpUft\n3r07cMvosbExnDt3LvP0Jq61J4R4Qb1ex9LSEtbX17G0tLQlLWpubm7bctFyuYy5ubm0m+kFFFJC\nyI4IEtJ+hUJKSEa4VMjPmpmZmW2BpZWVldg2/8sbXNlESAbkfWVR0pv/5Y3Ue6QicpOIvCAip0Xk\n7gB/XUSeFZHviMiTIvILabeRkKRJejvnpElj8788kaqQikgZwCcB3AxgEsAdIjLZcdpfA/gVVf15\nAB8D0EizjYSkQd57dNbmev1G2j3SdwM4raovquoKgEcA3NJ+gqo+qao/aj78BoC9KbeRkMQpQo+u\nc0uW9sfWdtBFI20hvQrA99sev9S0deODAL4S5BCRaRFZFJHFs2fPxthEQpInju2cs+TIkSPbtitZ\nW1vDkSNHAABTU1OBz+tmzz1RipbGdQC4FcCn2x7fCeC+Lue+D8DzAMas67KwM8kjLhXyswZG4WRr\nl9Skdwm1/D38nf4VdhaR6wHcq6q/2nx8Dzb+sv/Qcd47AfwJgJtV9ZR1Xa5sIkXD2iU0a6yVQ1nv\nQlr0lU3fAnCtiFwtIgMAbgfwWPsJIjIO4IsA7owiooQUEd+DUWNjY6H2Xbt2Bfq72fNOqkKqqqsA\nPgTgq9gkbxOzAAAI+0lEQVQYtj+qqidF5KCIHGye9rsAxgAcFZFnRIRdTdJ3+B6Muu2220LtedtO\n2RUWLSHEQzoT9oGNYFR7haYssaYesh66F31oT0hhsKLqLlF3q8xd1vg+9ZA6USJSvh+M2pO0cd13\nPg+EbddsReWt7Zyt54+Ojgb6R0dHVdW/qH3mIhjHQSElaWMJgeX3nUOHDgW2vyWm+/fvD/Tv379f\nVW0htL5oLCH2TUg5R0rIDrDSeyy/71QqlW0J98BGqbzV1VXTH2WOMqxwNOdICekDrKi671F3iyCR\nbLdb/n6DQkrIDrCWeOZ9z6NuRZpbdstv5Zm2shKWl5ehqptlBFsBudztUhpl/O/7wTlSkgVhSzyj\n+H3GmiO1/PPz81qtVrf4qtXq5j2w5pBLpVKgv1Qqqap/c6SZi2AcB4WUkPgJi9pH8Yd9kRRtrT2H\n9oSQQI4ePYrV1VWoKlZXV3H06NGe/GHkfQ65EwopISR2rDnQa665JvB53ey+QyElJCN8rjfqirWV\nyhNPPBH4vG523+Hmd4RkQN43v7OwlpB2y6WNmmMrIl3zdLOAPVJCMiDvm99ZJD0HGiSiYfakoZAS\nkgFFL/rhmkfbrWeZVY/TgkJKSAYULWrdiWv1qk4RtuxZQyElJAPyvvIpCvV6HUtLS1hfX8fS0tIW\nEbVWPl28eDHQ37JXKsHhnW72pKGQEpIBvtcbTZq5uTlUq9Uttmq1irm5OQAbRWGCaNlXV1cD/d3s\nSUMhJSQjwnpsRSAsvater+Phhx/e8kXy8MMPb94D16h+2rCMHiEkdly3SmEZPUJI35N0epdvUX0K\nKSF9SpIrq4I2xuu0h72+JZSDg4OB/m72xIlS2cT3g9WfCOmNpPeUalWF6jzK5XKk17fK9AX5gOyq\nP2UugnEcFFJCeiPpPaUsIYvy+mFl+nwTUgabCOlDkt5Tytr33vX1R0dHA3NNR0ZGcOHCBQabCCHJ\nE8fKqrA5zqmpqcDntOyurz80NNSTPXGidFt9Pzi0J6Q3XOdIredbQ3fX1w+6NjIc2mcugnEcFFJC\nesdlTylLKK2tRFxf3wpmFV5IAdwE4AUApwHcHeAXAL/f9D8L4Beta1JICUkXSyjHxsYC/WNjY5Ff\nI0xofeuRpjpHKiJlAJ8EcDOASQB3iMhkx2k3A7i2eUwDuD/NNhJCbJKuXmVtVWJtBz052SkrCLW7\nknaw6d0ATqvqi6q6AuARALd0nHMLgD9sfiF8A8CbReStKbeTEBKCVb3q/Pnzgc/rZu/EWhm1trYW\n+LyW/eTJk9tEc3JyEidPnoz0+r2StpBeBeD7bY9fatp6PYcQkiFW9SrXHqtV+LpWqwX62+0nT57c\nMvxOSkSBHKc/ici0iCyKyOLZs2ezbg4hfUdY9SrXequWEPtWzzVtIX0ZwNvaHu9t2no9B6raUNV9\nqrpvz549sTeUELJzXOutWkLpXT3XKBGpuA5s7Fr6IoCrAQwA+DaAn+s45/0AvoKN6P17AHzTui6j\n9oQUD5f0qLhAxKh9qnX5VXVVRD4E4KsAygAeUtWTInKw6f8UgOMAprCR/nQJwG+k2UZCiB/U6/Xc\nFLtOfYMTVT2ODbFst32q7XcF8Ftpt4sQQnZKboNNhBDiCxRSQghxhEJKCCGOUEgJIcQRCikhhDhC\nISWEEEcopIQQ4giFlBBCHKGQEkKII4XYRVREzgLYvmXh37AbwLmUmrMT2D432D432L7u1FTVrIpU\nCCG1EJFFjbClalawfW6wfW6wfe5waE8IIY5QSAkhxJF+EdJG1g0wYPvcYPvcYPsc6Ys5UkIISZJ+\n6ZESQkhiUEgJIcSRQgupiNwkIi+IyGkRuTvr9nQiIksi8h0ReUZEFrNuDwCIyEMi8oqIPNdm2yUi\n/0NE/qr582c8atu9IvJy8x4+IyJTWbSt2Za3icgTIvJdETkpIkeadl/uX7f2eXEPRWRIRL4pIt8W\nkedF5Peadi/uXxiFnSMVkTKAUwD+IYCXAHwLwB2q+t1MG9aGiCwB2Keq3iRDi8jfB3ABwB+q6jua\ntv8I4Lyq/l7zC+lnVPUjnrTtXgAXVPU/pd2eTkTkrQDeqqp/KSJvAvA0gF8D8AH4cf+6te82eHAP\nRUQAjKjqBRGpAvjfAH4HwD+BB/cvjCL3SN8N4LSqvqiqKwAeAXBLxm3yHlX9OoDzHeZbABxr/n4M\nGx++1OnSNm9Q1R+o6l82f/8pgOcBXAV/7l+39nlBc+POC82HVWxskPkjeHL/wiiykF4F4Pttj1+C\nR2+aJgrgf4rI0yIynXVjQniLqv6g+fv/BfCWLBsTwIdF5Nnm0N+LYZ+ITAD4uwD+Dzy8fx3tAzy5\nhyJSFpFnALwC4Guq+hw8vH+dFFlI88B7VfU6ADcD+K3m0NVrmru8+jQfdD+AtwO4DsAPAPznbJsD\niMgogC8A+G1V/X/tPh/uX0D7vLmHqrrW/EzsBfDLIvK+Dn/m9y+IIgvpywDe1vZ4b9PmDar6cvPn\nKwD+BBvTET7yw+b8Wmue7ZWM27OJqv6w+eFbB/AHyPgeNuf2vgBgQVW/2DR7c/+C2ufbPWy26ccA\n/huAffDo/nWjyEL6LQDXisjVIjIA4HYAj2Xcpk1EZKQ54Q8RGQHwjwA8F/6szHgMwIHm7wcA/GmG\nbdlC6wPW5NeR4T1sBkseBPC8qv6XNpcX969b+3y5hyKyR0Te3Pz9CmwEip+BJ/cvjMJG7QGgmcbx\nCWxMWj+kqrMZN2kTEXk7NnqhAFAB8Ec+tE9EPgfgRmyULvshgI8C+BKARwGMY6Nc4W2qmnrQp0vb\nbsTGkFQBLAG4q20+Le32vRfA/wLwHQDrTfO/xsY8pA/3r1v77oAH91BE3omNYFKpecyr6sdFZAwe\n3L8wCi2khBCSBkUe2hNCSCpQSAkhxBEKKSGEOEIhJYQQRyikhBDiCIWU9BUi8mTWbSDFg+lPhBDi\nCHukpK8QkQv2WYT0BoWUEEIcoZASQogjFFJCCHGEQkoIIY5QSAkhxBGmPxFCiCPskRJCiCMUUkII\ncYRCSgghjlBICSHEEQopIYQ4QiElhBBHKKSEEOLI/wfhJExy164GaQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3996cf8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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LqP6xY8cSua4CqYj01W9Uv1qtsnfv3tbo/rDvDdVutP63IjKw9v2ibr311tZz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3867e48>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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FupnZKuAa4lW/3P03wCxgJLCCcGTBWTnv7QgcC3yj1sfeaGZlhCs8rKxjuzRVFMGNN8K0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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3ce2940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"spectral_radii = []\n",
"powers = range(3,7)\n",
"for i in powers:\n",
" fig,axes = plt.subplots(figsize=(5,5))\n",
" m = np.power(2,i)\n",
" evals_x = range(1,m+1)\n",
" spec_radii = []\n",
" for j in range(100):\n",
" evals_mod = np.absolute(np.linalg.eigvals(random_square_matrix(m)))\n",
" spec_radii.append(np.max(evals_mod))\n",
" axes.scatter(evals_x,evals_mod,color='black')\n",
" spectral_radii.append(np.mean(spec_radii))\n",
" axes.set_xlabel('i')\n",
" axes.set_ylabel(r'$\\vert\\lambda_i\\vert$')\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"axes.plot([np.power(2,i) for i in powers],spectral_radii,color='red')\n",
"axes.set_ylabel('Mean spectral radius')\n",
"axes.set_xlabel('Matrix size (m x m)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There appears to be no discernable trend in the spectral radii for a normally distributed random matrix."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Part (b), two-norm"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f04b3530fd0>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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EA7/97W+btN7QoUOJ5FfSkpOTAfj000/5wQ9+ELHtNoXCT8QDdYWfc46Kiopmbbu8vPyE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\nES8p/ETESwo/EfGSwk9EvKTwExEv/X+Td44DBfVmtQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b35c5a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"powers = range(3,7)\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"spectral = []\n",
"two_norms = []\n",
"for i in powers:\n",
" m = np.power(2,i)\n",
" spec = []\n",
" norm = []\n",
" for j in range(100):\n",
" A=random_square_matrix(m)\n",
" norm.append(np.linalg.norm(A,ord=2))\n",
" spec.append(np.max(np.absolute(np.linalg.eigvals(A))))\n",
" two_norms.append(np.mean(norm))\n",
" spectral.append(np.mean(spec))\n",
"axes.plot([np.power(2,i) for i in powers],two_norms,color='black',label='two norm')\n",
"axes.plot([np.power(2,i) for i in powers],spectral,color='red',label='spectral radius')\n",
"axes.set_xlabel('Matrix size (m x m)')\n",
"axes.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The spectral norm is $\\leq$ the two norm, but does not approch equality as m goes to infinity."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Part (c)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f04b34d90b8>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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13QWrpNOAy4EW4NqI+GKXdmXtpwOvAudExP1Z23XAu4HnIuLoXX2Xg9WsyWzc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\nmVWYg9XMrMIcrGZmFfb/AWjRnqDZbY6tAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3539828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"powers = range(3,7)\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"sigma_min = []\n",
"for i in powers:\n",
" m = np.power(2,i)\n",
" smin = []\n",
" for j in range(100):\n",
" A=random_square_matrix(m)\n",
" u,s,v = np.linalg.svd(A)\n",
" smin.append(np.min(s))\n",
" sigma_min.append(np.mean(smin))\n",
"axes.plot([np.power(2,i) for i in powers],sigma_min,color='red')\n",
"axes.set_xlabel('Matrix size (m x m)')\n",
"axes.set_ylabel(r'$\\sigma_{min}$')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The smallest singular value decreases with increasing matrix size."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f04b371d2b0>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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llAcslsYB7buxj5upN3mvojqUN9vlfbBqKAQ/Bn1+VesW2YhNJ2/w9m9H8XRz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\ngxVRY4zxw/8D4n3Q19d1qh0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3449e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"iterations = 100\n",
"powers = range(3,7)\n",
"proportion_with_smin_lt_threshold = []\n",
"thresholds = [1./np.power(2,i) for i in powers]\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"for i in powers:\n",
"\n",
" m = np.power(2,i)\n",
" smin = []\n",
" for j in range(iterations):\n",
" A=random_square_matrix(m)\n",
" u,s,v = np.linalg.svd(A)\n",
" smin.append(np.min(s))\n",
" count_per_threshold = np.zeros(len(thresholds),dtype=np.float)\n",
" for sigma in smin:\n",
" for j,threshold in enumerate(thresholds):\n",
" if sigma <= threshold:\n",
" count_per_threshold[j] += 1\n",
" count_per_threshold /= iterations\n",
" axes.plot(thresholds,count_per_threshold,label='{}x{}'.format(m,m))\n",
"axes.set_ylabel(r'proportion of $\\sigma_{min}\\leq$ threshold')\n",
"axes.set_xlabel('threshold (1/m^i)')\n",
"axes.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The proportion of matrices in $\\mathbb{R}^{mxm}$ with $\\sigma_{min}$ less than or equal to inverse powers of two, increases rapidly with increasing m."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Part (d)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By using an upper triangular matrices the same relationships are observed. Now, the imaginary component of the eigenvalues is always zero, and the trends are all enhanced. However, the specific eigenvalue number and value of the eigenvalues now appear to be uncorrelated which was not the case with the full matrix."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f04b31314e0>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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FVfjBkoZRzKgHxcx/o5SeVShpoKTjyr892x/4ytj2G2kIYDXw/oj4nqTXUEzm\nDfAs8CGKK9TOOoY6OvwoIl6Ywzki1kv6CvAr4GngYWBL2v1p4CpJyyj+vfycYtaurupcnm7BWx8v\nTn15A7BQ0oMUM+Y9XKXf45LmU8z+9RhpCCYidqh48OYVKh6bNYBikvXlXdVh+xfP2mYHlDRMcWtE\nvLaH/Q6NiGfTlfEPgesi4od1KLHmJF0MPBsR3d3yZxnzMIUdaHYDQztdCZdxcerTcVVarwnLa0rS\npRQ/Efhe4/2cr4zNzDLgK2Mzsww4jM3MMuAwNjPLgMPYzCwDDmMzsww4jM3MMvD/ActalesbOs6N\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3642b00>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b36beeb8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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1qTK/KvxsivsZRuEI57MRsam6VVpPSXonhXA+ta9r2Q9XA38TEe2ScnVwOPdQ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\ncjibmSXofwA0Lmy5q8tvqAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3d1f828>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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DhrTU8/KOU3hky6doartQIBVVZZz20cPbBfKGn/yWnUsrUUXVrmXRVM+KF27n2WFbaS5r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\nrDq6IukK4AqAiRM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"text/plain": [
"<matplotlib.figure.Figure at 0x7f04accea780>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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J/9WSLiz2sZiZ9Yb+OjNeACyOiFnA4mQ+h6RS4BbgYmAOcJWkOcnil4A/BZ5s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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3721630>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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PilKRiMgAtN8wdvdvHKpCREQGsv0eMzazG3tbQD5tRERk/3o7TDHXzDbvZ74B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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3db8b70>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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pGElNkp5Obv9+qPbJzKwvBurIeB6wICJmAguS+U4kZYFbgMuB2cAHJM2uoP/K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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04adc08e80>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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M3BeOv5/gq9pxdJqeiEhJFXtE/QGC62k8GN4mhdPi6LcTRURKqtjT87YAn+xm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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04acc9d390>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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cqkLMzIazffYZS7pyoBVU08bMzPZtoG6KqyVt2sd8AR8Crhu8kszMhp+Bwvge\n4KIB2tw5SLWYmQ1bA/UZ/+mhKsTMbDir9jfwZpNctW1W+TK+UJCZ2eCo9uLyPwG+DtyKLyZvZjbo\nqg3jzoi4tqaVmJkNY9WG8bWSrgFuBzp7JkbEw7UoysxsuKk2jI8H/gR4PXu6KQL4g1oUZWY23FQb\nxm8FZkdEVy2LMTMbrqr9QdIngHG1LMTMbDir9sh4HPC0pIfo3WfsU9vMzAZBtWH89zWtwsxsmKsq\njCv9Bp6ZmQ2efYaxpB1U/kUPARERY2pSlZnZMDPQtSma9zXfzMwGR7VnU5iZWQ05jM3MMsBhbGaW\nAQ5jM7MMcBibmWWAw9jMLAMcxmZmGeAwNjPLAIexmVkGOIzNzDLAYWxmlgEOYzOzDBiSMJY0QdKd\nkpalf8f30+58SUslLZd09UDLS5olqV3SI+nta4dqn8zMDsZQHRlfDdwVES3AXel4L5JywJeBC4B5\nwNslzati+WcjYn56u6qWO2FmNliGKowvBm5Ih28A3lShzSnA8ohYkf4Q6o3pctUub2Z22BiqMJ4a\nEWvT4XXA1AptZgCrysZXp9MGWn522kVxj6QzB7NoM7NaqfY38PabpF8C0yrM+nj5SESEpEq/JlKV\nPsuvBY6KiBclnQz8RNJxEbG9Qn1XAlcCHHXUUQe6eTOzQVGzMI6Ic/qbJ2m9pOkRsVbSdGBDhWZr\ngJll40em0wAqLh8RnaS/Xh0RiyQ9C8wFFlao7zrgOoDW1tYDfjEwMxsMQ9VNcQtweTp8OfDTCm0e\nAlokzZbUAFyWLtfv8pImpx/8IWkO0AKsqMkemJkNoqEK408D50paBpyTjiPpCEm3AUREAXg/cDvw\nFHBTRCzZ1/LA64DHJD0C/AC4KiI2H6J9MjM7YIrwO/TW1tZYuHCvngwzs4MiaVFEtFbT1t/AMzPL\nAIexmVkGOIzNzDLAYWxmlgEOYzOzDHAYm5llgMPYzCwDHMZmZhngMDYzywCHsZlZBjiMzcwywGFs\nZpYBDmMzswxwGJuZZYDD2MwsAxzGZmYZ4DA2M8sAh7GZWQY4jM3MMsBhbGaWAQ5jM7MMcBibmWWA\nw9jMLAMcxmZmGeAwNjPLAIexmVkGOIzNzDLAYWxmlgEOYzOzDHAYm5llgMPYzCwDHMZmZhngMDYz\nywCHsZlZBjiMzcwywGFsZpYBDmMzswxwGJuZZYDD2MwsAxzGZmYZ4DA2M8sAh7GZWQY4jM3MMsBh\nbGaWAQ4V2zxvAAAKE0lEQVRjM7MMcBibmWWAw9jMLAOGJIwlTZB0p6Rl6d/x/bQ7X9JSScslXV02\n/X9JWiKpJKm1zzIfTdsvlXRerffFzGwwDNWR8dXAXRHRAtyVjvciKQd8GbgAmAe8XdK8dPYTwFuA\nX/dZZh5wGXAccD7wlXQ9ZmaZNlRhfDFwQzp8A/CmCm1OAZZHxIqI6AJuTJcjIp6KiKX9rPfGiOiM\niOeA5el6zMwybajCeGpErE2H1wFTK7SZAawqG1+dTtuXA1nGzGzI5Wu1Ykm/BKZVmPXx8pGICElR\nqzr6I+lK4EqAo4466lBv3sysl5qFcUSc0988SeslTY+ItZKmAxsqNFsDzCwbPzKdti9VLxMR1wHX\nAbS2th7yFwMzs3JD1U1xC3B5Onw58NMKbR4CWiTNltRA8sHcLVWs9zJJjZJmAy3Ag4NUs5lZzQxV\nGH8aOFfSMuCcdBxJR0i6DSAiCsD7gduBp4CbImJJ2u7NklYDpwM/l3R7uswS4CbgSeAXwF9ERPGQ\n7pmZ2QFQhN+ht7a2xsKFC4e6DDN7iZG0KCJaB27pb+CZmWWCw9jMLAMcxmZmGeAwNjPLAIexmVkG\nOIzNzDLAYWxmlgEOYzOzDHAYm5llgMPYzCwDHMZmZhngMDYzywCHsZlZBjiMzcwywGFsZpYBDmMz\nswxwGJuZZYDD2MwsAxzGZmYZ4N/AAyRtBJ4fpNVNAjYN0roOx+27hmxs3zVkY/tHR8Tkaho6jAeZ\npIXV/gDhS3H7riEb23cN2dj+/nA3hZlZBjiMzcwywGE8+K4b5tsH15CF7YNryML2q+Y+YzOzDPCR\nsZlZBjiM95OkCZLulLQs/Tu+n3bnS1oqabmkq8umnyLpIUmPSFoo6ZRDXUM67wOSnpa0RNJnh6KG\ndP5fSQpJkw7l9iV9Lt3/xyT9WNK4/dj2QPskSdem8x+TdFK1y9Zy+5JmSvqVpCfT//uHDmT7B1ND\n2fycpMWSfjYUNUgaJ+kH6WPgKUmnH2gdgyYifNuPG/BZ4Op0+GrgMxXa5IBngTlAA/AoMC+ddzdw\nQTp8IXD3ENTweuCXQGM6PuVQ15DOnwncTnKO96RDfB+8Acinw5+ptHw/293nPpX9X/8bEHAa8EC1\ny9Z4+9OBk9LhZuCZ/d3+wdZQNv8vgf8CfnaAz8ODqgG4AXhvOtwAjDuQOgbz5iPj/XcxyT+S9O+b\nKrQ5BVgeESsiogu4MV0OYB0wJh0eC/x+CGr4M+DTEdEJEBEbhqAGgC8CfwMcyAcXB7X9iLgjIgpp\nu/uBI6vc7kD71FPbtyNxPzBO0vQql63Z9iNibUQ8DBARO4CngBn7uf2DqgFA0pHAHwL/cQDbPuga\nJI0FXgd8HSAiuiJi60HUMigcxvtvakSsTYfXAVMrtJkBrCobX82eB/3fAl+QtAr4PPDRIahhLnCm\npAck3SPp1Ye6BkkXA2si4tED2PZBb7+PK0iOoKpRzTr7a1NtPbXa/m6SZgEnAg/s5/YHo4YvkbwI\nlw5g24NRw2xgI/DNtKvkPySNOohaBkV+qAvIIkm/BKZVmPXx8pGICEn7e1T3deBDEfFDSZem4+cc\n4hrywASSt26vBm6SNCfS92y1rkHSSOBjJF0F+2pXy/ugZxsfBwrAdw9k+cORpNHAD4EPR8T2Q7zt\nPwI2RMQiSWcfym2XyQMnAR+IiAck/StJV9cnhqie3UVZHxGxVzj2kLS+5y1f+rar0lv8NST9oT2O\nTKcBnAqcmw7fTD9v1Wpcw2rgR2n4PiipRPId/o2HqIaXkRydPCqpZ/rDkk6JiHWHYPs963g38EfA\ngr4vRPuwz3UO0Ka+imVruX0k1ZME8Xcj4kf7ue3BqOES4I2SLgSagDGS/jMi3nkIawhgdUT0vCv4\nAUkYD62h7rQ+3G7A5+j9wdFnK7TJAytIAqfnw4Xj0nmLgbPT4QXAoiGo4SrgH9PhuSRv5XQoa+jT\nbiX7/wHewd4H5wNPApP3c7sD7hNJf2j5B0cP7s/9UcPtC/g28KWDfA4ccA192pzNgX+Ad1A1APcC\nx6TD1wCfO5j7ZDBuQ7rxw/EGTATuApaRnJEwIZ1+BHBbWbsLST6tfhb4eNn0VwMPpg+eB4CTh6CG\nBuA/gSeAh4E/ONQ19FnXSvY/jA/2PlhO8iL0SHr72n5se691krzAXZUOC/hyOv9xoHV/7o9abR94\nLclR4WNl+33hoayhzzrO5gDDeBD+D/OBhel98RNg/IHWMVg3fwPPzCwDfDaFmVkGOIzNzDLAYWxm\nlgEOYzOzDHAYm5llgMPYMk1SUckV7h5Pr67WPED7WZLaJT1SYR09t6vT6f8haV6t92EgknYexLKf\nk7RO0kcGsyY79PwNPMu69oiYDyDpBuB9JNf02Jdne5bpu45yEfHewStzaETEX0vaNdR12MHzkbEd\nTn5H8lVqACT9tZJrQz8m6R/2d2WS7pbUmg6/R9Izkh6UdL2kf0unT5b0w3Q7D0k6I51+jaRvpOtY\nIemD6fRPS/qLsm1cI+kjkkZLukvSw+lR/l5Xa5N0dvn1fSX9W/qVbSSdnF7UaZGk23uugGYvHQ5j\nOyxIypFc02NJOv4GoIXkUorzgZMlva6fxUf06aZ4W591H0FykZjTgDOAY8tm/yvwxYh4Ncl1Fcqv\nJXIscF5aw9+n1334PnBpWZtL02kdwJsj4iSS60l/QemFOarY93rg/wFvjYiTgW8A/1zNsnb4cDeF\nZd2ItP93BsnXpr+WTn9Delucjo8mCecXKqyjYjdFmVOAeyJiM4Ckm0mu2QHJFfXmleXmmPSqZwA/\nj+Sa0J2SNpBc1nOxpClpwE8GtkTEqjRQP5m+YJTS/ZlKcvnPgRwDHA/cmdaRA9bucwk77DiMLeva\nI2J+etnN24E3Aj8iue7ApyLi38sbp9fpHUx1wGkR0dFnOwCdZZOK7Hk+3Qy8leTyn99Pp/0xSTif\nHBHdklaSXLWsXIHe71Z75gtYEhFD/9NAVjPuprDDQkS0AR8E/llSHUkwX9FzlCpphqQpB7j6h4Cz\nJI2XlCfpjuhxB/CBnhFJ+zrC7vF94DKSQL45nTaW5Dq+3ZJeDxxdYbnnSY7CG5X8Jt+CdPpSYLLS\n32mTVC/puOp3zw4HPjK2w0baBbAceFtEfE/SK4DfpUepO4F3khyh9tXT1dHjFxGx+/q1EbFG0idJ\nrqa3GXga2JbO/iDwZUmPkTxffk1yZbB91bkkPQVvTez5NZLvArdKepzkamFPV1hulaSbSK6m9xxp\nF0xEdEl6K3Ctkp8MypP8WsaSfdVhhxdftc1eUtJuip9FxPH7udzoiNiZHhn/GPhGRPy4BiUOOknX\nADsjYqBT/izD3E1hLzVFYGyfI+FqXJMu03NU+pNBr6wGJH2O5B2BzzU+zPnI2MwsA3xkbGaWAQ5j\nM7MMcBibmWWAw9jMLAMcxmZmGeAwNjPLgP8PCaDzefqbPh8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04acbb1b00>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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kdIdp0ERqZhGATwF4H4ArAXzQzK5c87S/BvBP3P0fAPgPAGZDxihcmIapsSV1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\n0iYlUhGRNimRioi06f8DOXCId0k/gq0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b5881550>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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RxiQzD+XKQxnmoPBaR3s9HGsfXVIQXS+9E+uzyJu1T+6WLVtSpZcFA2mBleWh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\nRv8fj/yEdWLfWUcAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b4021c88>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3b49b38>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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Bm+5jEzMK8oW2bnpUyAquE0PTCleWXPCNtdmEKXw9Vl/qyrxtvq6vr19yv/1+v9Jel+dp\nU8ZMzzkRK5sATI2E8Xq8M9h0Y+GYv4Z3Bps+BOCHuvPG8Eh9u7NtTtGJ0e0JdT+mIm+bXDxIU3uq\n8sZ2Ck+M1XRlNrmEDmyF1NbRcG0gTRsZl6XIJiQppLt24ZPY7a4/B+Dw6LtDAA6N/v+bAJ7G7vSn\nbwL4Bd05Y0zI9+nyNTXHTWdDvtDlPU7f9ettD9KZCl1Ie8ryRidA/X5fraysBMv3zF7XnoNLjLRq\nNoRto2AaI606n8m96VZxTUyMNFaKMWrvIobZ+UK1hrHw8YxCNBIusa0ykQrl7buOnPvOJbbNO9fG\nP59X+ZHz/Np+2/m5Lo5GcV8Bm0bGJSzis3F0BoU0ADael6ln43Lu0Ph42z5/a3O+rPJXDYLkBzVC\n5qWNZ2banQzVCLiGo0yF3Le8h+4ZmG5+E7MOUUgNCFkBTWJt2dSQNrr++Xv1eR1HiDifjS068Qid\nlyaLEzLbXT1S15io6wCpLrk2gqE9QJf4buw6RCHVUFYBfTbPMK1USjX/jqayey1ualK816pC7Wu7\nrS1Nz66ou16o+K7rKiyXRiWmsBfzNKZzYHpvfGdTw0IauoUzOZ+uCxZr9NZ2kKNO7DI7Q+dTVaxL\nZ7ttl89nkNHV4/MRUtuehEneVd1fjB5ZSOfANrYeQsgppBpMH4aPp2VbWUO1pqatd5VwmwhGln9l\nXbqqAY26fK8bnXXJSxehVKp+onmIwaW6fDd5jrqeRPHvTfYjDSE8MZwDl8Gp0EJOIdVg6l3kC4Iu\nplr0HqoKvK1YxLq3vGeUL7SmKbsvE9HOxFQnZLaNjO30pbpjdPbpbLPJN5/nWOW9l+VNcZVYv9+P\nsmeur61FXKdLVdVhV+eEQqrBtgLaxlRtRDf0e4lMC1gmpD5z/ExFOxto0y0tdPFsTLt8SunXiNvG\nSE038ig7XofvktM6cQvtQeqeq20M1XZJqcnxnEcaQUiVutSDrFvjbfOgbAtN6EJtWgiz8/usOrHx\nxJQK75Ga3nsmlL721TWQurzWNajF313zKvu9rlyZeJBF6mx13X+06nqmZcomJKS7vwo7KKS26ITV\nVFxsC41Loa7Dxlbd8bpBDluPVNdomHjHdY2S7l5c3maZjwfXibhuj84iZV3vbKOburww9d7rypVJ\nY28z0FWX7ya2FnGJgZr0TGydE1BI/TAViLIHZVtoQk8dqarQVec32RKtyhuxjZHOz8+X/j4/P2+V\n77aNkmle5O81L6Imz0UnJkV8vTgT79l1Q+6Qsee6Bqyqp7GysmL07Kp2mwrlnIBC6ofrCK2LR6qU\nXUxV97uuUBf/3nZLNJ3tPqP2pvlu0yjZVOA8sXsWOuHVeVYmG0nbvu5Zdy9Vz8F1lVeV7S4Nqu1U\nMRMopJ5UPci6fTNdY6Q6dANdNmGIKooewMrKimvW1aKzzdcjVSpcF8+lZ1HXVTe1zSYvdAOerh6p\n7fRA26lWuvPZNqi+U8WqoJB6YlspygpxnQdpg2uYoZiqJoKb3GsodGEEE4/SpoL49A5sRbxMTPIb\nf5Tlc91zMj2+yruuu3edrSZlri6m6lpGdfHdqmcRqitfJJiQAlgwTSYXjJFiCWmbb6sMUShNhdF2\nCzXbRiJ/fFWMtG4TkuLrm226bLa9A52Qu6wkyiqzafd3bm5u715tZ1SY7n/q8sJDm2XFrjNB8j0+\nm23xYq0WDCmkfwjgsdG/dekxkwvGSE127X1buIwQgX7TQqkTu7pzlNltK0xFryo/IFcWt/OZEmSb\n18Xf6wSgaKvpc8oqs+/zNE0mXprJM7dpMEOV2XwqCnfdpijJe6TjkJoebDIZVKlDJ0YhuvKhXtNQ\nxKTA5itgVT7Websu26m5eh62AuAzIBJDNOvyoi4vbZ65CaHCT65CGHpcIgOxhBTAvwDwrwD8fQDv\ns/37GCml6U9VYmrTBfSNMela76I9dW9ALeKy2samwuqEOrTn4fKcbZ5TvjKHGNm2FZ8qr9L2uegI\nFYKqKlcm1IWETEJQZSCmRwrgGgB/C7uvBfmPLucImWJNyHcZhcwPmuTPZTOq7iriWQUyGa3ViV1V\nPNhV6EwrrO+yyGLe6ypQDAHwnRvpk0y9MJ142QqPzXO3iaG6bjkYykMFu/Z26ILrNoXZNV5kM3Jd\nV4GqCrVuXbJJTNW1621aQWxDB0VbbYXW562ltkLmeq0sROLz3IqYeMe9Xs9qpynT+bshyomOUD0X\nxBBSAAcA3Arg8wC+anqR2MlVSE12PLL1tPr9vle8KMOksldVIFcvy7Qb5TIYVEx1IRCdENZNMtdV\noBiDIlne6cRG9/e65+ISH656Vq7zPrMwkG6QUHevtvtBmGBy/daWiAK4G8C3ALwG4C8AfB3APwfw\n9zDGMVLTHY+yjDc9vuodQyapqrWs6hJWTZr3DQ34YJpPddeqE+pY689tdhEqSybo5tDqGgGXaWqm\nE/Jdy6ztEs1YZdK0gWzNIwWwBeAXAPxVAL8D4Btocc5oWXIRUpP16PmM1xWMXq9nfM6y5LICJr8W\nPo9vaKB4fZsuo2kFCu1pYCRmOrHReSsuz67qORRt182hLfMSp6am9rrXdY2Ey5Qglz1o6+7ddVyg\nKhVXbRUHj0xeMV5Xxk1AQCH9ucLn2wA8CeCfAOiZXCR2chFSW3HRVWDfFri4Asa021WFT2jAZzGC\n7dJCne02FdJkulUoTymfbMIURfvyvYqyObe2KR/XrMunkBsnV93r1NSUU+MUSojz57MdPMtA5FH7\ndwH4lwD+yOXvQ6fQQlqW8bqCFGL0V9eFcy0ktiOYtl3IPCZC5bOyyKcyxTj/0tKSV7zYds/bEMll\nALUq6cISrs+p6dBAFWhoiej7MKZLROsy3+X4EA/eZwWMrtti01W3zZvidXRCVbchSgyPEbi4EQgR\nG6xKec891tzKEHkR6lzz8/PB79O1DpQl00UyNXUh+hLRxwrfj9USUZNNeG3ilCE8Hdt3/xSTTetb\nFNb8Ki1dIbc5d9XgW1UBjyU+c3NzpderC3u4inqv14vqYfqWE5u/nZmZKS0jIqKmpqai3F/IMpCM\nRzoOKUbX3nRCfrbBhI0YuaaZmRkj2126+ibJZU6fyabReWJ5pIB9TyNEzDJ0yg9Kug5uDofDyoGv\nuucUc/5trOS6dDhXPiikdfhW2MzraLugVKW6rr7LvWeNS9XgVFXYoO6cZZgOtLmEQWztW19fj+Z1\n1aX8DkhFsZyamjIaAK07t23XPvTgT5OJHmlkIXX1yrIK3NS66RiFKEQDYLqJdYj3GNXdm0ujYDob\no61nnIU9dIN+41AG20xJb1qSYoq5sqmYsgrcdiExTRkxumXDof61KlUx0nzM0sW2/J6dLit0Un6O\nmVDqnmsXhDTzzm0WuvhMdyoCCmk9Lh5pfqpK2wXMNLneq2mB1a0k0uWV70IG4OI9EUzFxWeGRFPP\nTff7OJVDl+Syc5br2vwqQCGtx6ZLmFXQUJ5cr9e75FyxRNr2Xm2SiUcac/Aon2w9l8w+3WKFJmwv\nSz6ruMY15VdxFVcu2ZwnJKCQ1mPzcESq9+wMVWhMB0Bsk+29mqZ8jLQY08yvrnHtesdOWRyybh+D\nUNeKIcqhymRmV+jy7ZpClJsM12XOeUAhrSeF1ryqGxLyGkq5eYVFoa96G8D6+rrWU3fZjjC2R6jb\npCSUJ52NkqfYDS8+xxRtdElVMx5cXugICmk9KQgpgFLbTOf46VLWfTVdV121RVqIGKvt4E52/bYr\nY9vlI3bKehYh197XpbZDJrYxVFBI60ml9S0jRFfY9x1Qod8hld2rbYGv83ZjhFyyNC4Tzscttd1A\nAuV1rgpQSOtpytuo69blV134rv/OdyGL8SDXc2ZeZIhGJ1shY5PvStVXuCafY4wUalFH3eyJ1FIK\n085sAIW0nqYqoMnoq+tu5flUt82dT6hAqbAeqe3OVjFfFDgpKWuQUxkwCm1ryJ4Hu/aBhbSpgjM3\nN9fYCpXQK5kyLzJU/CyU6OUbjaamV6WemizTPqlNj9R0T92CThgJaQ8NIyK3isizInJSRO4t+X1V\nRJ4Ske+KyLdE5AMx7Oj3+8bHiojzdc6cOYO33nqr9Lfs+9OnTzufP8/29jZEBFNTU/jsZz+79/1u\nebDnwoULAICvfe1rQexztaPuPEeOHMHs7GyQ844rNmU5Bqb1Y3Z2FkeOHAEADIfDmCYBAPbv37+X\nN/1+H5/5zGewuroa52ImahsqAegDeA7AewHMYHen/aXCMR8BcOXo/7cB+LbuvDE90mwpY6xRTRNb\nXGNpuvcYAWbd5xj37Zvy3nd+qe84dG9Dp2x/V9/z5AcYbebRmnS9Y8wE8bk/C51Ir2sP4BYAj+Q+\n3wfgvprjrwTwsu68LkLq8hbDEO+4KTu/7nefa/p0p1MYYdU9lzYqZOiU7Rvg2giEmFJUNmE95KIE\noP4dTE3NkrDdDQqJCukdAI7nPn8awBdqjv98/vjCbwcBbALYXFhYsMqcUQZ5ZbzNwxvXAZGsglbZ\nPxgMggyUuaSY72BqOuk2eGkiKVW/EijGM84v+mhymz5LnRhvIQXwMQDfBzDQnTfWWvticDpf0MZV\nHEOntlbtZCGXSXgOKWygotsOsQkb8h5rrEal7o2vZSBRITXq2gN4P3Zjqe8zOW/M99qnvmacyb1C\npSLCbceie71epWPRdD7ZrsZzSTYgUSGdAvA8gOvxzmDTjYVjFgCcBPAR0/OmPI+UKc3UpBeYDRbq\n3l/V1kDZ2tpaMo1K9mx8fq9LsTzSRqc/KaXOA/gcgEew223/mlLqaRE5JCKHRof9FoABgP8gIidE\nZDOGLaGmHJF0sJmmtrCwAAAYDAaxzNljZ2cHSimcOXOm9PeHH35477im6ff7+OhHP7qXHykwcqhq\nmZqacjp3NqUvOKZeX8op5Qn5XU5Nezk2z1X3Oo8upWxgyTR0lZL3aptirWwSZaD+qbO8vKw2N+0c\nV59J9kTPYDDAq6++iqmpKWMvQEQgIqWeWa/Xy4d/SGAGgwF+8pOfGHnFIpLMc5ifn8cbb7yxVz50\nZOXSFBF5Qim1rDuu8ZVNqUAhjUev17voX1N2dnbwwAMPYHp6+qLvp6en8cADD7TS9c0zTmXG1tbT\np08b528qIgoAb775ppWw//jHP45iR2eFNKXCMGns7Ozg9OnTUEoZe6NZrHJ1dRX3338/hsMhRATD\n4RD3339/vKV9FtSVmdREdmdnx7oh6wJXXXVVlPN2NqebWOs7TrRd6d54441Wr+9Dv99v3VvOkzVK\nTdlEpwRofaAoRGryvfaTmFIZPKh6Lk1PDHfNw1TW+b/rXe+qfab9fj/oirCUn0vZc7IBKc4jjZVc\n32ufX6lU9o4XpmaTUtUrzlKaQD/uqcv5OD8/b6URSHEeaWqsrq5ia2sLOzs7OHr0qPPcNOJPFlrY\n3t4u/f3ChQtGXchsG0FSjUk+TipvvvlmlPN2Wkg3NjawuLiIXq+HO++8E+fOnWvbpM5y+eWXe8dp\nRQQLCwt497vfHcgqQszobNO9sbGBu+66C+fPnwcQccUDqaXX60FEKlf92KCUqvRoSXdoY55rZz3S\nQ4cO7YkoaQelFA4cOMBGLBC9Xq/13fK7SmeFNFashJiRdeNfeOGFli0Jz/z8/N4qrSbo9/sQERw4\ncAAHDx7cm4PbVdqIAXdWSOsQEQwGA6OYXdY1JXZkE8YnMe/OnDnzzrSYBsgG4ra3t3H8+HEcOXIk\nqXmtKRGrvFFIS1BKGS+Zu/LKK1loHVFKTWTetTkq/vbbb+Oee+4BAFx22WWt2ZEqsZ5NZ4V0bm4u\nyHlird0lxJVsi8iqt9d2mVjbJnZWSM+ePRvkPF1/FTBJly7PF63i9ddfj3LezgppqM0Lzpw50/o6\ndTIZ9Hq9YGWJZbKcWDN1OpvbIbs9bPlJCHZ2djA1NYXBYOA9KMIy2SydFVJOfyIpcu7cObz22mtt\nm0Es6ezKJkJShQsU4rGyshLlvJ31SCdx/iIhpJqVlRU8+uijUc7dWY+UMSTSFvn3C7EcxqXqHWCh\n6axHSkhbZBWbIhofpRR6vR4WFxexsbER7ToUUnIRDHk0A0W0ObLls3fddVc0MaWQltBVMVlfXw/a\nDepqPpI/M9OyAAAKCElEQVQ0OX/+PA4dOhTl3BTSEiZx/bcJ3/zmN4Oej14XSQ3ukE+i86UvfYle\nJCEOdFZIq+aTzczMcHkdIcSKzk5/OnHiROn3fG8TIcSWzrpe2VZjhBDiS2eFlBBCQtFZIY21wSsh\npHt0VkiPHj2KqanOhogJIQHprJACnDBOCAlDZ4X08OHDePvtt9s2gxAyAXRWSLe3t9s2gRAyIXRW\nSAkhJBQU0jGHcV5C2odCSgghnlBIxxzusERI+zQupCJyq4g8KyInReTekt9/VkT+SETeEpHPN20f\nIYTY0uiMdBHpA/gigE8AeAnA4yLykFLqmdxhPwbwjwH8WpO2EUKIK017pDcDOKmUel4pdQ7AgwBu\nzx+glHpFKfU4AE7yJISMBU0L6bUAXsx9fmn0HSGEjC1jO9gkIgdFZFNENk+dOtW2OYSQDtO0kL4M\n4EDu83Wj76xRSh1TSi0rpZb37dsXxDhCCHGhaSF9HMANInK9iMwA+BSAhxq2gRBCgtLoqL1S6ryI\nfA7AIwD6AL6ilHpaRA6Nfv+yiPwMgE0AfxnAjoj8BoAlpdRPm7SVkHFGRDjHuEEa35BTKfUwgIcL\n33059/8fYbfLTwhxhCJaztzcXJTzju1gky/cIZ+Q7nHZZZdFOW9nhfSaa65p2wRCSMPEeullZ4X0\nmWee0R9ECCEGdFZICSEkFBRSQgjxpLNCGivoTAjpHp0V0uPHj6PX6+ztE0IC0lklWV1dxd13341+\nv9+2KYSQMaezQrqxsYGvfvWruHDhQtumEELGnM4K6eHDh3H27Nm2zSCETACdFVK+154QEorOCilf\nY0wICUVnhZSbOhBCQtFZISWEkFBQSAkhxBMKKSGEeEIhJYR0hliDzBRSQkhniDXITCElhBBPKKSE\nEOIJhZQQQjyhkBJCiCcUUkII8YRCSgjpDJz+RAghnnD6EyGEJAqFlBBCPKGQEkKIJxRSQgjxhEJK\nCCGeUEgJIcQTCikhhHhCISWEEE8opIQQ4gmFlBBCPKGQEkKIJxRSQgjxhEJKCCGeUEgJIcSTxoVU\nRG4VkWdF5KSI3Fvyu4jIvxv9/pSIfKhpGwkhxIZGhVRE+gC+COA2AEsAfl1ElgqH3QbghlE6COBL\nTdpICCG2NO2R3gzgpFLqeaXUOQAPAri9cMztAB5Qu/xfAFeIyHsatpMQQoxpWkivBfBi7vNLo+9s\njyGEkGQY28EmETkoIpsisnnq1Cnrv+/1xvbWCSGODAaDKOdtWk1eBnAg9/m60Xe2x0ApdUwptayU\nWt63b5+1IXfffbf13wDAcDiEUgrr6+uYnZ01/pulpWIoWE8m9iFe2LV//34Mh0OICAaDAaamprzP\nmToiguFwiPX1dSil9p7bzMxM26ZZkT3/ssa/1+thMBhARDA/P9+0aWPFzMwMjh49GufkWQFrIgGY\nAvA8gOsBzAB4EsCNhWP+NoDfByAAPgzgO7rz3nTTTcqFtbU11e/3FQDV6/UUgNo0Ozur1tfX9/5+\nfX1dDYdDJSJqMBio6enp2uOrrt3v99XKysreuYbD4SV/Vzx+//79tbb2er3KaxdtHw6Ham1t7aJ7\nKTtndr7ifZcdOxgMKs89MzNz0bEzMzN7x2f/lt1PWV6VXd/23peWlrTPHkDpvWTPpCpdfvnlF31e\nWlqqvfb+/fsves5ra2u1tteVk9Ap/3zKbF9ZWamtX0W7pqam9p51v99XV1xxxSV5kd3r3NyckX11\neV1XJqoAsKlMtM3koJAJwCcB/ADAcwAOj747BODQ6P+C3ZH95wB8F8Cy7pyuQlqkTlxMHoSukMck\n9LVtzmd7bd3xoc9nS8x7b5q6BnswGFQ2eC7lX4dvXtk6HyEwFVJRkV5P2iTLy8tqc3OzbTMIIROG\niDyhlFrWHccRF0II8YRCSgghnlBICSHEEwopIYR4QiElhBBPKKSEEOIJhZQQQjyhkBJCiCcUUkII\n8YRCSgghnlBICSHEk4lYay8ipwBsW/zJ1QBejWSOLynbBqRtH21zI2XbgHbtGyqltPt0ToSQ2iIi\nmyYbEbRByrYBadtH29xI2TYgffsAdu0JIcQbCikhhHjSVSE91rYBNaRsG5C2fbTNjZRtA9K3r5sx\nUkIICUlXPVJCCAkGhZQQQjzplJCKyK0i8qyInBSRexOw5ysi8oqIfC/33VUi8j9F5M9G/17Zkm0H\nROQPReQZEXlaRO5JxT4RuUxEviMiT4rI90XkX6diW87Gvoj8iYh8I0HbtkTkuyJyQkQ2U7JPRK4Q\nka+LyJ+Onu0tqdhWR2eEVET62H076W0AlgD8uojYv2w+LL8N4NbCd/cC+AOl1A0A/mD0uQ3OA/in\nSqkl7L4W+x+O8isF+94C8HGl1AcAvB/Ax0TklxKxLeMeAN/PfU7JNgD4mFLqg7n5manYdxTA/1BK\n/SyAD2A3D1OxrRqTV41OQgJwC4BHcp/vA3BfAnYtAvhe7vOzAN4z+v97ADzbto0jW/4bgE+kZh+A\nWQCbAH4uFdsAXIfdCv9xAN9I7bkC2AJwdeG71u0D8FcA/BCjQfCUbNOlznikAK4F8GLu80uj71Lj\nGqXUn4/+/yMA17RpDACIyCKAnwfwbSRi36jrfALAKwD+l1Lqe6nYBuDfAvhnAHZy36ViGwAoAI+K\nyBMicnD0XQr2XQ/gFID7R2GR4yIyl4httXRJSMcOtdsEtzo/TUTmAfwugN9QSv00/1ub9imlLiil\nPohd7++XRORjKdgmIr8K4BWl1BNVxyTwXH9xlHe3YTdk88v5H1u0bwrAhwB8SSn18wDOoNCNTyDv\nSumSkL4M4EDu83Wj71Lj/4nIewBg9O8rbRkiItPYFdENpdR/Sc0+AFBKvQbgvwNYTsS2jwL4OyKy\nBeBBAB8XkfVEbAMAKKVeHv37CoD/CuDmROx7CcBLSqlvjz5/HbvCmoJttXRJSB8HcIOIXC8iMwA+\nBeChlm0q4yEAd47+fyd2Y5ONIyIC4D8B+L5S6t/kfmrdPhHZJyJXjP5/OXZjtydSsE0pdZ9S6jql\n1CJ2y9hjSql/kIJtACAicyLyl7L/A/ibAL6Xgn1KqR8BeFFE/vroqxUAz6Rgm5a2g7RNJgCfBPAD\nAM8BOJyAPf8ZwJ8DeBu7rfFnAAywO1DxZwAeBXBVS7b9Ina7UE9hV6ROjPKvdfuwO1L/JwCeBPBd\nAL85+r512wp2/greGWxKwjYA7x3l25MAns7qQUL2fRC7g4dPAfg9AFemYltd4hJRQgjxpEtde0II\niQKFlBBCPKGQEkKIJxRSQgjxhEJKCCGeUEhJpxCRb7VtA5k8OP2JEEI8oUdKOoWIvNm2DWTyoJAS\nQognFFJCCPGEQkoIIZ5QSAkhxBMKKSGEeMLpT4QQ4gk9UkII8YRCSgghnlBICSHEEwopIYR4QiEl\nhBBPKKSEEOIJhZQQQjz5/yMtF1Ncr/rLAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b339de48>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ZZyMtmm31z3/CEUfApElp1avhw+HKK70oSxu5oJp1ZgMGpNlWc+bAueemYVb7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\nujo3dGJnAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3642a90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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uuaHnHz3qdasJDsX8x4IF8NZb3jLBEhOL361u1co7Bqkz0RJCuK5jGgs85JzL\nsxL+0JxzE4AJ4B3zC9O2papISPCOEbZuHXp+Xp43jFfRYMzK8sY5nDXLa10Gq1On+N3qVq28e6bo\nhlG+VJbw2wQEj5nePDAtWAYwNRB8jYGrzCzXOZcZlipFwAupZs28x4UXnjjfOdix48RgzH89f753\nc/lg1at7XXVC7VInJ3vb0rXOVVJZfqsLgLZm1hov9G4GBgUv4Jwr+K/azCYD7yr45JQz8y7Ba9zY\nG+Y/lL17veOOoXatZ8zw7pcSLC7OC8DidqtbttQd9mJUqeHnnMs1s3uBWXhdXSY655ab2V2B+eMr\nuUaR8KlXD1JTvUcoOTmFT8oEtyDnzPFOyhw7VvgzTZqUvGtdr15lfyupAHVyFimP3FwvAEPtVq9f\n7wXn4cOFP9OgQehQzJ+WmKiTMmEUtn5+IhIkPv54eIWSlwdbt4berV6zBj76yBtBJ1itWsXvVrdq\nBWeeqZMylUDhJxJO1ap5fRPPOAO6dz9xvnPeSZdQu9X5XXp27Cj8mYQEr8N3cf0dW7TQ9dQVoPAT\nOZXMvBtJNWrkjYYTyv79xXcGnzXL6+5TtDN40ZMywa3Ili01KG0ICj+RaFOnDrRr5z1COXy4+M7g\n8+fDtGnesclgSUkl71o3aFDZ3yrqKPxEYk316t6N6s86K/T8Y8e8O/aF2rVetszr0pOTU/gz9eoV\nf7a6VSs4/fQqd1JG4SdS1cTFeccBW7TwRt8uyjlvkIlQZ6vXr/e69OzZU/gzNWuG7gwewyP0KPxE\n/MbMa8mdfjp0KeZS/N27TwzF/EcVGaFH4SciJ2rQwHu0bx96ftEReoJbkR9/7O125+UdXz4KR+hR\n+IlI+ZV1hJ5Qu9blHaHnoosq5c6BCj8RCb+KjtCzfv2JI/R8+CFcemnYS1T4icipV54Res4+u1JK\nUPiJSPQJHqGnkuiCQRHxJYWfiPiSwk9EfEnhJyK+pPATEV9S+ImILyn8RMSXFH4i4ksKPxHxJYWf\niPhSxG5daWbbgPWVsOrGwPZKWG9lisWaITbrVs2nRiRrbuWcSyptoYiFX2Uxs4VluWdnNInFmiE2\n61bNp0Ys1KzdXhHxJYWfiPhSVQy/CZEuoAJisWaIzbpV86kR9TVXuWN+IiJlURVbfiIipVL4iYgv\nxXT4mdlEM9tqZsuCpjUysw/NbFXguWEkayzKzFqY2SdmtsLMlpvZ8MD0qK3bzGqY2Vdm9q2ZrTSz\nMYHpUVu1v32uAAAGjElEQVRzPjOLM7NvzOzdwPtYqDnLzJaa2WIzWxiYFtV1m1kDM3vTzP4b+Bu5\nINprjunwAyYDfYtMexj4yDnXFvgo8D6a5AL/45xrB3QH7jGzdkR33YeBS5xz7YF04Cdm1pPorjnf\ncGBl0PtYqBngJ865DkF95aK97qeBmc65c4H2eD/z6K7ZORfTDyAZWBb0/jvgzMDrM4HvIl1jKfVP\nBy6LlbqBWsBCIDXaawaa4/2juwR4N1b+PoAsoHGRaVFbN1AfWEfgBGos1Oyci/mWXyhNnHM/BF7/\nCDSJZDElMbNkoCPwJVFed2D3cTGwFfjUObeMKK8ZGAs8COQFTYv2mgEcMNvMFpnZ0MC0aK67NbAN\nmBQ4xPCSmdUmumuukuFXwHn/5URlXx4zqwO8BdznnNsbPC8a63bOHXPOdcBrTfU0s58UmR9VNZtZ\nP2Crc25RcctEW81BLgr8rK/EOyzSK3hmFNYdD3QCxjnnOgIHKLKLG4U1V8nw22JmZwIEnrdGuJ4T\nmFkCXvC95px7OzA56usGcM7tBmYAGUR3zT2A/maWBUwFLjGz/0d01wyAc25T4Hkr8C+gK9FddzaQ\n7Zz7MvD+TbwwjOaaq2T4vQMMDrwejHdMLWqYmQEvAyudc08GzYraus0sycwaBF7XxDtGuZgortk5\n9zvnXHPnXDJwM/Cxc+7nRHHNAGZW28zq5r8GLgeWEcV1O+d+BDaa2TmBSX2AFURxzUBsn/AApgA/\nAEfx/vf5BZCId5B7FTAbaBTpOovUfBFe838JXoAsBq6K5rrxzvB+A3wLLAUeCkyP2pqL1N+b4yc8\norpmoE3g5/wtsBz4Q4zU3QHvRNgSIBNoGO016/I2EfGlqrjbKyJSKoWfiPiSwk9EfEnhJyK+pPAT\nEV9S+PmImblAR9/89/Fmti1/xJMSPtfBzK4qYX6GmT1zkrU1NbM3T2YdQev6yMzqh2NdJ1nHU0Wv\nzpDoofDzlwNAaqCjMnidlTeV4XMd8PoinsDM4p1zC51zvzmZwpxzm51zN5zMOgL1XAJ875zbc7Lr\nCoNxwAORLkJCU/j5z3vA1YHXt+B1FAfAzLqa2fzAxemfm9k5ZnYaMBK4KTC+3E1m9icze9XM5gGv\nmlnvoPHynjazPwZeX2Fmc8ys0N+ZmV0cWNfiwLbqmlmyBcZlDFwYnz9/m5k9Gpj+gJktMLMlZvbn\nYr7fIAJXEgTW+V8zm2xm35vZ/5nZ5YHvtsrMuhb9sJndb2YTA6/TzGyZmdUqsswQM8sMjFGXZWbD\nzOy3ge/yhZk1AnDOfQ8kR9s4dhIQ6V7Wepy6B7Af72qNN4EaeFeX9Ob41Q/1gPjA60uBtwKvhwDP\nBa3nT8AioGbgffA6auFdmfATvCGNzgpRx7+BHoHXdfAujE8maGiywLxWeOPCtcK7zGsCYHj/ab8L\n9Aqx7v8SGA4qsM5cIC3wmUXApMA6rgUyQ3y+GjAHGIh3xUKPEMsMAVYDdYEkYC9wV2DeU3iDVeQv\n+wpwVaR/93qc+IgvR05KFeCcWxIYSusWvFZgsPrAP82sLd4leAklrOod59yhEOs/aGa/xAuQ+51z\na0J8dh7wpJm9BrztnMv2Lnk+zsxqAG8Aw5xz681sGF4AfhNYpA7QNrCdYE2dc9uD3q9zzi0NrHM5\nMNs558xsKV44Fq0/z8yG4F2m9b/OuXnFfP9PnHP7gH1mthsv0MG7/C89aLnNobYjkafw86d3gMfx\nWmyJQdNH4f2jHhgIyE9LWMeBEualATuApqFmOufGmNkMvOOI88zsCiCnyGLj8YJxduC9AX9zzv1v\nCdsN5XDQ67yg93kU//ffFq+VHLL+cq7XiLKhnMSjY37+NBH4c36LKEh9jp8AGRI0fR/eLl6pzKwV\n8D94g7ReaWbdQixzlnNuqXPu78AC4Nwi8+8B6jrnxgRNngXcERgHETNrZmanhyhhs5k1LkutxdRf\nH3gG6AUkmtnJnoQ5E1h/kuuQSqDw8yHnXLZzLlTXlH8AfzOzbyjcevkEaJd/wqO49QYN1/Vb59xm\nvFF2Xgrswga7L3AiYQneiDzvF5n/WyAt6KTHXc65D4D/A+YHdlnfJHQgf4Y31mBFPQU877yTFb8A\nxhQTsmXVEZh/Ep+XSqJRXaRKMW+E6Zucc3dFQS1nA084566JdC1yIrX8pEpxzn0CtI2GTs7A3cBj\nkS5CQlPLT0R8SS0/EfElhZ+I+JLCT0R8SeEnIr6k8BMRX/r/JUOU3GPWhWUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3243898>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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+SuBP6vbzUWAzcEy2XL+PY4GtwEWk0/OdOUkd/xt4U/b+eNJvVA1TN81mtu10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\n85kAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3197630>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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RgBw4Wsy63fn8+OLeXkcxxngsoGYv1ougev/dloeq3b1ljLFeBEGXmpFLh5Yx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\nY4xL/j9xefq7ciWXQwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b3171b70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# redefine random_square_matrix so that it is upper triangular and rerun all scripts\n",
"def random_square_matrix(m):\n",
" return np.triu(np.random.normal(0,np.power(m,-0.5),size=(m,m)))\n",
"\n",
"powers_of_two = [np.power(2,x) for x in range(3,12)]\n",
"for i in powers_of_two:\n",
" fig,axes=plt.subplots(figsize=(5,5))\n",
" plot_eigenvals_rand_matrix(sizes=[i],ax=axes)\n",
" axes.set_title('{}x{}'.format(i,i))\n",
" \n",
"spectral_radii = []\n",
"powers = range(3,7)\n",
"for i in powers:\n",
" fig,axes = plt.subplots(figsize=(5,5))\n",
" m = np.power(2,i)\n",
" evals_x = range(1,m+1)\n",
" spec_radii = []\n",
" for j in range(100):\n",
" evals_mod = np.absolute(np.linalg.eigvals(random_square_matrix(m)))\n",
" spec_radii.append(np.max(evals_mod))\n",
" axes.scatter(evals_x,evals_mod,color='black')\n",
" spectral_radii.append(np.mean(spec_radii))\n",
" axes.set_xlabel('i')\n",
" axes.set_ylabel(r'$\\vert\\lambda_i\\vert$')\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"axes.plot([np.power(2,i) for i in powers],spectral_radii,color='red')\n",
"axes.set_ylabel('Mean spectral radius')\n",
"axes.set_xlabel('Matrix size (m x m)')\n",
"\n",
"powers = range(3,7)\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"spectral = []\n",
"two_norms = []\n",
"for i in powers:\n",
" m = np.power(2,i)\n",
" spec = []\n",
" norm = []\n",
" for j in range(100):\n",
" A=random_square_matrix(m)\n",
" norm.append(np.linalg.norm(A,ord=2))\n",
" spec.append(np.max(np.absolute(np.linalg.eigvals(A))))\n",
" two_norms.append(np.mean(norm))\n",
" spectral.append(np.mean(spec))\n",
"axes.plot([np.power(2,i) for i in powers],two_norms,color='black',label='two norm')\n",
"axes.plot([np.power(2,i) for i in powers],spectral,color='red',label='spectral radius')\n",
"axes.set_xlabel('Matrix size (m x m)')\n",
"axes.legend()\n",
"\n",
"powers = range(3,7)\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"sigma_min = []\n",
"for i in powers:\n",
" m = np.power(2,i)\n",
" smin = []\n",
" for j in range(100):\n",
" A=random_square_matrix(m)\n",
" u,s,v = np.linalg.svd(A)\n",
" smin.append(np.min(s))\n",
" sigma_min.append(np.mean(smin))\n",
"axes.plot([np.power(2,i) for i in powers],sigma_min,color='red')\n",
"axes.set_xlabel('Matrix size (m x m)')\n",
"axes.set_ylabel(r'$\\sigma_{min}$')\n",
"\n",
"\n",
"iterations = 100\n",
"powers = range(3,7)\n",
"proportion_with_smin_lt_threshold = []\n",
"thresholds = [1./np.power(2,i) for i in powers]\n",
"fig,axes = plt.subplots(figsize=(5,5))\n",
"for i in powers:\n",
"\n",
" m = np.power(2,i)\n",
" smin = []\n",
" for j in range(iterations):\n",
" A=random_square_matrix(m)\n",
" u,s,v = np.linalg.svd(A)\n",
" smin.append(np.min(s))\n",
" count_per_threshold = np.zeros(len(thresholds),dtype=np.float)\n",
" for sigma in smin:\n",
" for j,threshold in enumerate(thresholds):\n",
" if sigma <= threshold:\n",
" count_per_threshold[j] += 1\n",
" count_per_threshold /= iterations\n",
" axes.plot(thresholds,count_per_threshold,label='{}x{}'.format(m,m))\n",
"axes.set_ylabel(r'proportion of $\\sigma_{min}\\leq$ threshold')\n",
"axes.set_xlabel('threshold (1/m^i)')\n",
"axes.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 13.3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Parts (a) & (b)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f04b2df96a0>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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1872+AjCzVsDlQGtgIPCymUX7jn8FuAlo5nsN9LX/AdjtnGsKPAM84btWNeAh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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f04b322a7f0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAmMAAAERCAYAAAA3yqAqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm8lGX9//HXRzYBEZRF3BBXTAkUD7lQWu5fNci00iyV\nTFxy+1UuaGZapn7ta2laaWplWeau5JbkbgoeEFQUtHABN1AUUFnP+fz+uGacOXNmuQ9n7rlneT8f\nj3nM3Mvc9+c+95y5P3Nd131d5u6IiIiISDLWSjoAERERkUamZExEREQkQUrGRERERBKkZExEREQk\nQUrGRERERBKkZExEREQkQTWXjJnZ9Wa2wMxeKNP27jezD83sHznzTzKz/5iZm9mAcuxLREREJFfN\nJWPAH4H9y7i9S4Fv55n/JLA38HoZ9yUiIiLSRs0lY+7+GLAoe56ZbZkq4ZpmZo+b2bYd2N6/gKV5\n5j/r7q91OmARERGRIromHUCZXAMc7+6vmNnOwG+APROOSURERKSkmk/GzGwdYDfgFjNLz+6RWvZV\n4II8b3vT3ferTIQiIiIihdV8Mkaoav3Q3XfIXeDutwO3Vz4kERERkWhqrs1YLndfArxqZl8DsGBk\nwmGJiIiIRFJzyZiZ/Q14ChhmZvPN7BjgCOAYM5sJzALGdWB7jwO3AHultrdfav4pZjYf2AR4zsyu\nLfexiIiIiJi7Jx2DiIiISMOquZIxERERkXpSUw34BwwY4EOHDk06DBEREZGSpk2b9p67Dyy1Xk0l\nY0OHDqW5uTnpMERERERKMrNIo/iomlJEREQkQUrGRERERBKUaDJmZv3M7FYzm21mL5nZrknGIyIi\nIlJpSbcZuxy4390PNbPuQK+E4xERERGpqMSSMTPrC+wOHA3g7iuBlUnFIyIiIpKEJKspNwcWAn8w\ns2fN7Foz6527kplNMLNmM2teuHBh5aMUERERiVGSyVhXYBTwW3ffEfgYOCt3JXe/xt2b3L1p4MCS\nXXWIiIiI1JQkk7H5wHx3n5KavpWQnNW25cvhj38EDTMlIiIiESSWjLn7O8A8MxuWmrUX8GJS8ZTN\nuefC+PEwaVLSkYiIiEgNSPpuypOBG1N3Us4FxiccT+e98054Xrw42ThERESkJiSajLn7DKApyRhE\nREREkqQe+EVEREQSpGRMREREJEFKxkREREQSpGRMREREJEFKxkREREQSpGRMREREJEFKxkREREQS
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