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@tobydriscoll
Created September 6, 2016 13:42
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TB Lecture 3 (matlab)
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 3: Norms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Vector norms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The contour lines of the major $p$-norms give some idea of the metric structure created by them."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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++uijH/3oRzt27HjuuefuuuuugYGBBx98UKoSORyONWvWrFmz5uzZswAQFRX1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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ezcontour('sqrt(x.^2+y.^2)',[-1 1],[-1 1])\n",
"axis equal, title('2-norm')\n",
"xlabel('x_1'), ylabel('x_2')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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toPnvSym8L6WwJzMU/tT00sHy5TtLtFqSl4LayyO25Qj6P1BU3/DKmdyVWX8TMbnb7S5z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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ezcontour('abs(x)+abs(y)',[-1 1],[-1 1])\n",
"axis equal, title('1-norm')\n",
"xlabel('x_1'), ylabel('x_2')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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g2LBh15+rHRkZad2nBwC4IY4hAQCkQCEBAKRAIQEApEAhAQCkQCEBAKRAIQEApMBp33Aa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\nLh0EAJACW0gAAClQSAAAKVBIAAAp/H+sCoEYdvEDPAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ezcontour('max(abs(x),abs(y))',[-1 1],[-1 1])\n",
"axis equal, title('\\infty-norm')\n",
"xlabel('x_1'), ylabel('x_2')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Induced matrix norms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A matrix norm is the maximum of $\\|Ax\\|$ over all unit vectors $x$. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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hxBKKk3ElUGztX8vtv8vul2wNsG8uuaaDiCWdUchZRSTYdMPLotUAWVqvE+am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\nY6HpKCMrEMT7FDXrTOeQYTT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E5BhU72d1iLt7KYgnBKszybPc+kpPkM1PUFNJkpO36zjf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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"A = [-2 0; -1 3];\n",
"t = linspace(0,2*pi,300);\n",
"x1 = cos(t); x2 = sin(t);\n",
"Ax = A*[x1;x2];\n",
"subplot(121), scatter(x1,x2,4,t,'.'), axis equal, axis off, title('x')\n",
"subplot(122), scatter(Ax(1,:),Ax(2,:),4,t,'.'), axis equal, axis off, title('Ax')\n",
"colormap(hsv)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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u3cOGDbt06RJfoWzatCkqKsrW1nbz5s1ffvkl5yc2qaGhQavVcgadnJwIIbdu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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(t,sqrt( sum(Ax.^2,1) ))\n",
"xlim([0 2*pi])\n",
"xlabel('angle'), ylabel('||Ax||_2')\n",
"hold on, plot([0 2*pi],[norm(A),norm(A)],':')\n",
"text(6.4,norm(A),'||A||_2')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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sIm8vwKIwiwIqSFkrkE84n4Dzfr07L/FUDY6bTiDOY0dTQwNtzUSAJm4xnUVM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\nSUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = linspace(-1,1,100); o = ones(size(t));\n",
"x1 = [t,o,t,-o]; x2 = [o,t,-o,t];\n",
"Ax = A*[x1;x2];\n",
"subplot(121), scatter(x1,x2,4,1:400,'.'), axis equal, axis off, title('x')\n",
"subplot(122), scatter(Ax(1,:),Ax(2,:),4,1:400,'.'), axis equal, axis off, title('Ax')\n",
"colormap(hsv)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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da/BDN27cmDVr1uuvv+6BvbKnvr7+ypUrvXv39vf3t2wMDAwMCAjw9fU1m80a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\nAJjw/9m8bfZVcxO3AAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(max(abs(Ax),[],1))\n",
"ylabel('||Ax||_\\infty')\n",
"hold on, plot([1 400],[norm(A,inf),norm(A,inf)],':')\n",
"text(402,norm(A,inf),'||A||_\\infty')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `max` and `sum` functions can operate along a specified dimension of a matrix, making the matrix norm easy to compute directly."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"onenorm =\n",
"\n",
" 3\n"
]
}
],
"source": [
"onenorm = max( sum(abs(A),1), [],2)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"infnorm =\n",
"\n",
" 4\n"
]
}
],
"source": [
"infnorm = max( sum(abs(A),2), [],1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unitary matrices"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A unitary (or real orthogonal) matrix preserves the 2-norm---i.e., Euclidean distances. So they represent rotations and reflections. "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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LXdcNLk4hxLe+9a01a9b8/e9/X7JkyWc+85ldGdVACokGznZmV8eNDH3MatXu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7AJAI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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"[Phi,Theta] = ndgrid(linspace(0,1.5*pi,60),linspace(0.25*pi,pi,50));\n",
"x = [ cos(Phi(:)).*sin(Theta(:)) sin(Phi(:)).*sin(Theta(:)) cos(Theta(:)) ];\n",
"[Q,~] = qr(magic(3));\n",
"Qx = (Q*x')';\n",
"\n",
"colr = sum(x,2);\n",
"subplot(121)\n",
"scatter3(x(:,1),x(:,2),x(:,3),40,colr,'.')\n",
"axis equal, title('x')\n",
"subplot(122)\n",
"scatter3(Qx(:,1),Qx(:,2),Qx(:,3),40,colr,'.')\n",
"axis equal, title('Qx')\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Matlab",
"language": "matlab",
"name": "matlab"
},
"language_info": {
"codemirror_mode": "octave",
"file_extension": ".m",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "matlab",
"version": "0.11.0"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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