{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Ambient Fisher Gnomonic Interpolant" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "by Kyle Cranmer, Jan 12, 2014, BSD license\n", "based on notes and discussion with Jeff Streets at UCI.\n", "\n", "\"Gnome\"Gnome\n", "" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import numpy.linalg as linalg\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "from sklearn import manifold\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from scipy.optimize import minimize\n", "import scipy.optimize \n", "from scipy.spatial import Delaunay" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Create pairs of (parameter, distribution)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# parameter points\n", "alphas = np.array([[0,0],[1,0],[0,1]])\n", "\n", "# dim = 1+#dim parameters = dim of embedding\n", "dim = 3 \n", "\n", "# for starters, define a parametrized family of functions explicitly and draw from it\n", "f = lambda alpha: lambda x : np.exp(-0.5*(x-alpha[0])**2 / (0.5*alpha[1]+1)**2)/np.sqrt(2*np.pi) / (0.5*alpha[1]+1)\n", "dists = []\n", "for alpha in alphas:\n", " dists.append( f(alpha) )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Calculate pair-wise chord distances, embed on n-sphere, & rotate first to south pole" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's going to be easier to work in the space of the sqrt of distributions, so let's define a simple transformation q " ] }, { "cell_type": "code", "collapsed": false, "input": [ "q = lambda h: (lambda x: np.sqrt(h(x)))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "def inner_product(q1,q2, xmin=-7, xmax=7):\n", " # this is a simple numeric integration\n", " num = 10000.\n", " xarray = np.linspace(xmin,xmax,num)\n", " return np.sum(q1(xarray) * q2(xarray))*(xmax-xmin)/num" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "(inner_product(q(dists[0]),q(dists[0])), inner_product(q(dists[1]),q(dists[1])),inner_product(q(dists[2]),q(dists[2])))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "(0.99989999999745338, 0.99989999901776028, 0.99989694599725443)" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Create pairs of (parameter simplex, Gnomonic simplex)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def getChordDistance(q1,q2):\n", " return 2.*np.sin( np.arccos( inner_product(q1, q2) ) /2. )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "tempSim=[]\n", "for f1 in dists:\n", " temp = []\n", " for f2 in dists:\n", " temp.append(getChordDistance(q(f1),q(f2)))\n", " tempSim.append(temp)\n", "chordDistMatrix=np.array(tempSim)\n", "chordDistMatrix #diagonals should be close to 0" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "array([[ 0.01414214, 0.48495638, 0.28045376],\n", " [ 0.48495638, 0.01414221, 0.4700093 ],\n", " [ 0.28045376, 0.4700093 , 0.01435646]])" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "seed = np.random.RandomState(seed=3)\n", "mds = manifold.MDS(n_components=dim, metric=True, max_iter=3000, eps=1e-9, random_state=seed,dissimilarity=\"precomputed\", n_jobs=1)\n", "embeded = mds.fit(chordDistMatrix).embedding_\n", "mds.fit(chordDistMatrix).stress_" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "0.00030305513607825206" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "def minimizeMe(x):\n", " ret = 0.\n", " for point in embeded:\n", " ret += (linalg.norm( point-x)-1.)**2\n", " return ret" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "center = [0,0,0]\n", "result = minimize(minimizeMe,center, method='nelder-mead',\n", " options={'xtol': 1e-8, 'disp': True})\n", "center = result.x\n", "for point in embeded:\n", " point -= center" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.000000\n", " Iterations: 269\n", " Function evaluations: 486\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Need to translate points so that they are around center of sphere" ] }, { "cell_type": "code", "collapsed": false, "input": [ "u = np.zeros(dim)\n", "u[-1]=-1\n", "v = embeded[0] - embeded[0].dot(u)*u\n", "v/=linalg.norm(v)\n", "v.dot(u)\n", "theta = -np.arccos(embeded[0].dot(u))\n", "vuT=np.outer(v,u.T)\n", "uvT=np.outer(u,v.T)\n", "uuT=np.outer(u,u.T)\n", "vvT=np.outer(v,v.T)\n", "I = np.identity(dim)\n", "A=I + np.sin(theta)*(vuT-uvT) + (np.cos(theta)-1.)*(uuT+vvT)\n", "A.dot(embeded[0])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "array([ 8.40647702e-10, 2.82505769e-10, -1.00000000e+00])" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "pointsOnSphere = embeded.copy()\n", "for i, point in enumerate(embeded):\n", " #if i==0: continue\n", " pointsOnSphere[i] = A.dot(point)\n", " if pointsOnSphere[i,2]>0:\n", " print \"error, shouldn't have points up there\"\n", "pointsOnSphere[0] = np.zeros(dim) #just to get rid of roundoff for this first point\n", "pointsOnSphere[0,-1] = -1.\n", "pointsOnSphere[:3]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 32, "text": [ "array([[ 0. , 0. , -1. ],\n", " [ 0.33008693, 0.33526584, -0.88240548],\n", " [ 0.24984741, -0.12117549, -0.96067308]])" ] } ], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "gnomonicProjection = pointsOnSphere.copy()\n", "for i, point in enumerate(pointsOnSphere):\n", " gnomonicProjection[i] = -1.*point/point[-1]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "nSamples = 15 #samples along ray for visualization\n", "rays = np.zeros((3*nSamples,dim))\n", "for i, point in enumerate(gnomonicProjection):\n", " for j, c in enumerate(np.linspace(0,1,nSamples)):\n", " rays[i*nSamples+j] = c * point" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(5,5))\n", "subpl = fig.add_subplot(111,projection='3d')\n", "subpl.scatter(rays[:, 0], rays[:, 1], rays[:, 2],marker='.',c=pointsOnSphere[:,0]*0+.01)\n", "subpl.scatter(pointsOnSphere[:, 0], pointsOnSphere[:, 1],pointsOnSphere[:, 2],\n", " marker='o',c=-pointsOnSphere[:,2])#,cmap=mpl.cm.gray)\n", "subpl.scatter(gnomonicProjection[:, 0], gnomonicProjection[:, 1], gnomonicProjection[:, 2],\n", " c=-pointsOnSphere[:,2])#,cmap=mpl.cm.gray)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAASUAAAElCAYAAACiZ/R3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "code", "collapsed": false, "input": [ "alphaSimplex = Delaunay(alphas)\n", "gnomonicSimplex = Delaunay(gnomonicProjection[:3,:2])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "normedVertices = gnomonicProjection[:3,:2].copy()\n", "normedVertices[1] /= linalg.norm(normedVertices[1])\n", "normedVertices[2] /= linalg.norm(normedVertices[2])\n", "normedSimplex = Delaunay(normedVertices)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "inner_product(q(dists[0]),q(dists[1])),inner_product(q(dists[0]),q(dists[2])),inner_product(q(dists[1]),q(dists[2]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "(0.88240865285903869, 0.96067284335362202, 0.88954562783004798)" ] } ], "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [ "pointsOnSphere[0].dot(pointsOnSphere[1]),pointsOnSphere[0].dot(pointsOnSphere[2]),pointsOnSphere[1].dot(pointsOnSphere[2])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 38, "text": [ "(0.8824054820506424, 0.96067308353377612, 0.8895485561775559)" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Create Interpolant" ] }, { "cell_type": "code", "collapsed": false, "input": [ "alpha1 = np.array([0.9,0.0]) #for testing\n", "alpha2 = np.array([0.0,.9]) #for testing\n", "alpha = alpha2 #switch for testing\n", "alpha = np.array([0.5,0.3])\n", "baryCoords = alphaSimplex.transform[0,:dim-1,:].dot(alpha)\n", "gnomonicTarget = linalg.inv(gnomonicSimplex.transform[0,:dim-1,:]).dot(baryCoords)\n", "normedBaryCoords = normedSimplex.transform[0,:dim-1,:].dot(gnomonicTarget)\n", "t = np.arctan(linalg.norm(gnomonicTarget))\n", "t, normedBaryCoords, linalg.norm(gnomonicTarget), linalg.norm(gnomonicProjection[1,:2]), linalg.norm(gnomonicProjection[2,:2])\n", "gnomonicProjection[1:], gnomonicTarget" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 332, "text": [ "(array([[ 0.37407624, 0.37994533, -1. ],\n", " [ 0.26007537, -0.12613603, -1. ]]),\n", " array([ 0.26506073, 0.15213185]))" ] } ], "prompt_number": 332 }, { "cell_type": "code", "collapsed": false, "input": [ "dot01 = inner_product(q(dists[0]),q(dists[1]))\n", "dot02 = inner_product(q(dists[0]),q(dists[2]))\n", "t1 = lambda x: q(dists[1])(x) - dot01*q(dists[0])(x)\n", "t2 = lambda x: q(dists[2])(x) - dot02*q(dists[0])(x)\n", "norm1 = inner_product(t1,t1)\n", "norm2 = inner_product(t2,t2)\n", "u1 = lambda x: t1(x)/np.sqrt(norm1)\n", "u2 = lambda x: t2(x)/np.sqrt(norm2)\n", "#unnorm_tan = lambda x: u1(x)*normedBaryCoords[1] + u2(x)*normedBaryCoords[0]\n", "unnorm_tan = lambda x: u1(x)*normedBaryCoords[0]+u2(x)*normedBaryCoords[1]\n", "norm_tan = inner_product(unnorm_tan,unnorm_tan)\n", "tangent = lambda x: unnorm_tan(x) / np.sqrt(norm_tan)\n", "#tangent = lambda x: (u1(x)*normedBaryCoords[1] + u2(x)*normedBaryCoords[0])/np.sqrt(norm_tan)\n", "#tangent = lambda x: (u1(x)*normedBaryCoords[0] + u2(x)*normedBaryCoords[1])/np.sqrt(norm_tan)\n", "print inner_product(q(dists[0]),tangent), inner_product(tangent,tangent)\n", "q_interpolant = lambda x: np.cos(t)*q(dists[0])(x) + np.sin(t)*tangent(x) \n", "interpolant = lambda x: ( np.cos(t)*q(dists[0])(x) + np.sin(t)*tangent(x) )**2\n", "#interpolant = lambda x: (q_interpolant(x)*q_interpolant(x))\n", "#interpolant = lambda x: ( np.cos(t)*q(dists[0])(x) + np.sin(t)*u1(x) )**2\n", "np.arccos(inner_product(q(interpolant),q(dists[0]))),inner_product(q(interpolant),q(interpolant))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.000261968966744 1.0\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 333, "text": [ "(0.29666655331638392, 1.0000549879950498)" ] } ], "prompt_number": 333 }, { "cell_type": "code", "collapsed": false, "input": [ "np.arccos(dot02), t, np.arccos(dot01)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 334, "text": [ "(0.28138111338199134, 0.29660132150652252, 0.48983892578549054)" ] } ], "prompt_number": 334 }, { "cell_type": "code", "collapsed": false, "input": [ "xarray = np.linspace(-5,5,100)\n", "plt.plot(xarray,dists[0](xarray),c='black')\n", "plt.plot(xarray,dists[1](xarray),c='r')\n", "plt.plot(xarray,dists[2](xarray),c='g')\n", "plt.plot(xarray,interpolant(xarray),c='b',ls='dashed')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 335, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIilCzwkiRJEUoWeEmSpAj1P5SLTburVR8RAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 335 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(xarray,u1(xarray),c='r')\n", "plt.plot(xarray,u2(xarray),c='g')\n", "#plt.plot(xarray,unnorm_tan(xarray),c='black')\n", "plt.plot(xarray,tangent(xarray),c='b',ls='dashed')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 336, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncZzoGWPMxHGiZ4wxE/f/kNTbFc2YMiQAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 336 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "check if original points + interpolant work on embeded 2-sphere" ] }, { "cell_type": "code", "collapsed": false, "input": [ "targetOnSphere = gnomonicTarget3d/linalg.norm(gnomonicTarget3d)\n", "targetOnSphere.dot(pointsOnSphere[0]), targetOnSphere.dot(pointsOnSphere[1]), targetOnSphere.dot(pointsOnSphere[2])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 337, "text": [ "(0.95633534781479035, 0.97632579736539182, 0.96442897466420452)" ] } ], "prompt_number": 337 }, { "cell_type": "code", "collapsed": false, "input": [ "inner_product( q(dists[0]),q(interpolant)), inner_product( q(dists[1]),q(interpolant)), inner_product( q(dists[2]),q(interpolant) )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 338, "text": [ "(0.95631628037306926, 0.97634052470453503, 0.96443526233902066)" ] } ], "prompt_number": 338 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize ray pointing to the target" ] }, { "cell_type": "code", "collapsed": false, "input": [ "targetRays = np.zeros(15*3).reshape(15,3)\n", "gnomonicTarget3d = np.zeros(3)\n", "gnomonicTarget3d[:2] = gnomonicTarget\n", "gnomonicTarget3d[2]=-1\n", "for i,l in enumerate(np.linspace(0,1,15)):\n", " targetRays[i] = l*gnomonicTarget3d" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 339 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(5,5))\n", "subpl = fig.add_subplot(111,projection='3d')\n", "subpl.scatter(rays[:, 0], rays[:, 1], rays[:, 2],marker='.',c=pointsOnSphere[:,0]*0+.01)\n", "subpl.scatter(targetRays[:, 0], targetRays[:, 1], targetRays[:, 2],marker='*',c=pointsOnSphere[:,0]*0+.01)\n", "subpl.scatter(gnomonicTarget3d[0], gnomonicTarget3d[1], gnomonicTarget3d[2],marker='o',c=pointsOnSphere[:,0]*0+.01)\n", "subpl.scatter(targetOnSphere[0], targetOnSphere[1], targetOnSphere[2],marker='o',c=pointsOnSphere[:,0]*0+.01)\n", "subpl.scatter(pointsOnSphere[:, 0], pointsOnSphere[:, 1],pointsOnSphere[:, 2],\n", " marker='o',c=-pointsOnSphere[:,2])#,cmap=mpl.cm.gray)\n", "subpl.scatter(gnomonicProjection[:, 0], gnomonicProjection[:, 1], gnomonicProjection[:, 2],\n", " c=-pointsOnSphere[:,2])#,cmap=mpl.cm.gray)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAASUAAAElCAYAAACiZ/R3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDg4OteL/AaX+qMI8GsByAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 340 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }