Chebyshev Bounds.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import numpy.random as random\n",
    "import math as math\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.linalg as splin\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import copy as copy\n",
    "import math\n",
    "import pickle\n",
    "import matplotlib.lines as mlines\n",
    "import matplotlib.patches as mpatches\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def saveThing(thing,file):\n",
    "    with open(file,'wb') as fil:\n",
    "        pick = pickle.Pickler(fil,protocol=4)\n",
    "        pick.dump(thing)\n",
    "        pick.clear_memo()\n",
    "def openThing(file):\n",
    "    with open(file,'rb') as fil:\n",
    "        pick = pickle.Unpickler(fil)\n",
    "        thing = pick.load()\n",
    "    return thing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1D Vandermonde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def useParams(thetaList,M=1):\n",
    "    if sum([A for lam,A in thetaList]) < M:\n",
    "        return True\n",
    "    return False\n",
    "\n",
    "def evalPoints(xList,thetaList):\n",
    "    return [sum([A*np.exp(-lam*x) for lam,A in thetaList]) for x in xList]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def trianglePlot(arry,clist,emphPoints = [],dim=2,title=''):\n",
    "    \n",
    "    ranges = [arry[:,idx].max()-arry[:,idx].min() for idx in range(dim+1)]\n",
    "    axesDist = 0.6*max(ranges)\n",
    "    \n",
    "    figs,axs = plt.subplots(nrows=dim,ncols=dim,figsize=(15,15))\n",
    "    plt.suptitle(title)\n",
    "    for row in range(dim-1,-1,-1):\n",
    "        for col in range(dim-1,-1,-1):\n",
    "            if col >= row:\n",
    "                py = arry[:,row]\n",
    "                px = arry[:,col+1]\n",
    "                \n",
    "                centerX = (px.max()+px.min())/2\n",
    "                centerY = (py.max()+py.min())/2\n",
    "                \n",
    "                sc1 = axs[row,col].scatter(px,py,s=5,c=clist,edgecolor='black',linewidth=0.2, cmap='plasma')\n",
    "                for p in emphPoints:\n",
    "                    axs[row,col].scatter([px[0]],[py[0]],s=100,c='C1',edgecolor='black',linewidth=0.2)\n",
    "                \n",
    "                axs[row,col].set_xlim([centerX-axesDist,centerX+axesDist])\n",
    "                axs[row,col].set_ylim([centerY-axesDist,centerY+axesDist])\n",
    "                if row != col:\n",
    "                    axs[row,col].set_xticks([])\n",
    "                    axs[row,col].set_yticks([])\n",
    "                if row == col:\n",
    "                    axs[row,col].set_ylabel('dir '+str(row+1))\n",
    "                    axs[row,col].set_xlabel('dir '+str(col+2))\n",
    "                axs[row,col].ticklabel_format(style='sci',scilimits=(-2,2),axis='both')\n",
    "            else:\n",
    "                axs[row,col].axis('off')\n",
    "    plt.subplots_adjust(wspace=0, hspace=0)\n",
    "    plt.show()\n",
    "    \n",
    "def trianglePlotBound(arry,clist,radii,radius,emphPoints = [],dim=2,title=''):\n",
    "    \n",
    "    axesDist = 1.05*radius*radii[0]\n",
    "    \n",
    "    theta = np.linspace(0, 2 * np.pi, 100)\n",
    "    perim = np.array([radius*np.cos(theta),radius*np.sin(theta)])\n",
    "    \n",
    "    figs,axs = plt.subplots(nrows=dim,ncols=dim,figsize=(15,15))\n",
    "    plt.suptitle(title)\n",
    "    for row in range(dim-1,-1,-1):\n",
    "        for col in range(dim-1,-1,-1):\n",
    "            if col >= row:\n",
    "                py = arry[:,row]\n",
    "                px = arry[:,col+1]\n",
    "                \n",
    "                ellipse = np.dot(np.diag([radii[col+1],radii[row]]),perim)\n",
    "                \n",
    "                centerX = (px.max()+px.min())/2\n",
    "                centerY = (py.max()+py.min())/2\n",
    "                \n",
    "                sc1 = axs[row,col].scatter(px,py,s=1,c=clist,edgecolor='black',linewidth=0.1, cmap='plasma')\n",
    "                sc2 = axs[row,col].plot(ellipse[0],ellipse[1],c='C0')\n",
    "                for p in emphPoints:\n",
    "                    axs[row,col].scatter([px[0]],[py[0]],s=100,c='C1',edgecolor='black',linewidth=0.2)\n",
    "                \n",
    "                axs[row,col].set_xlim([-axesDist,axesDist])\n",
    "                axs[row,col].set_ylim([-axesDist,axesDist])\n",
    "                if row != col:\n",
    "                    axs[row,col].set_xticks([])\n",
    "                    axs[row,col].set_yticks([])\n",
    "                if row == col:\n",
    "                    axs[row,col].set_ylabel('dir '+str(row+1))\n",
    "                    axs[row,col].set_xlabel('dir '+str(col+2))\n",
    "                axs[row,col].ticklabel_format(style='sci',scilimits=(-2,2),axis='both')\n",
    "            else:\n",
    "                axs[row,col].axis('off')\n",
    "    plt.subplots_adjust(wspace=0, hspace=0)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Tn(x,n):\n",
    "    deg = [0.0 for i in range(n+1)]\n",
    "    deg[n] = 1\n",
    "    return np.polynomial.chebyshev.chebval(x,deg)\n",
    "\n",
    "def JCheb(xList,rho,n=0):\n",
    "    if n == 0:\n",
    "        n = len(xList)\n",
    "    return np.array([[rho**(-d)*Tn(x,d) for d in range(n)] for x in xList])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.   0.5  1. ]\n",
      "4191  points\n",
      "acceptance ratio of  0.041909161816763664\n",
      "8256  points\n",
      "acceptance ratio of  0.04127958720412796\n",
      "12474  points\n",
      "acceptance ratio of  0.04157972280184799\n",
      "16705  points\n",
      "acceptance ratio of  0.041762291188544055\n",
      "20955  points\n",
      "acceptance ratio of  0.04190983236067056\n",
      "25170  points\n",
      "acceptance ratio of  0.04194986016713278\n",
      "29309  points\n",
      "acceptance ratio of  0.04186988037177037\n",
      "33543  points\n",
      "acceptance ratio of  0.041928645178387056\n",
      "37766  points\n",
      "acceptance ratio of  0.04196212897304673\n"
     ]
    }
   ],
   "source": [
    "nX = 3\n",
    "xList = np.linspace(0,1,nX)\n",
    "nParams = 4\n",
    "ARange = 1\n",
    "lambdaRange = 2\n",
    "M = 1\n",
    "print(xList)\n",
    "\n",
    "sampledPoints0 = []\n",
    "iterations = 10**6\n",
    "for idx in range(iterations):\n",
    "    thetaList = np.array([[lambdaRange*np.random.random(),ARange*np.random.random()] for x in range(nParams)])\n",
    "    if useParams(thetaList,M=M):\n",
    "        pointDict = {'thetaList':thetaList,'xList':xList,'pointVals':evalPoints(xList,thetaList)}\n",
    "        sampledPoints0.append(pointDict)\n",
    "    if (idx > 1) and (idx%(iterations/10) == 1):\n",
    "        print(len(sampledPoints0),' points')\n",
    "        print('acceptance ratio of ',len(sampledPoints0)/(idx+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#sampledPoints0 = openThing('1DexponentialSampling.pckl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#saveThing(sampledPoints0,'1DexponentialSampling_21Points.pckl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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y5iBgZpYxBwEzs4x5ddAY4JVCZjZU7gmYmWXMQcDMLGMeDhpjPDRkZoPhnoCZWcYcBMzM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\nbwaMG0UmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f03b18e5d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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k1RDYmQ7xkP7uSu1jwLxSv7mpbSwNV7ebmVkftRoC64Hz0/D5wM2l9hWSZkhaSHEC+J50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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f03b7dc7b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nBins = 100\n",
    "\n",
    "AList = []\n",
    "lambdaList = []\n",
    "for p in sampledPoints0:\n",
    "    lambdaList.extend(list(p['thetaList'][:,0]))\n",
    "    AList.extend(list(p['thetaList'][:,1]))\n",
    "\n",
    "n, bins, patches = plt.hist(AList,bins=nBins)\n",
    "plt.title('Amplitudes (n='+str(len(AList))+')')\n",
    "plt.show()\n",
    "\n",
    "n, bins, patches = plt.hist(lambdaList,bins=nBins)\n",
    "plt.title('Lambda (n='+str(len(lambdaList))+')')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4/vnn8e1vfzvtsUpKSnDo0CHz+fDhwygpKUH//v3NsgMHDmDjxo34v//7P8+2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\nBEFQ+H/DaM/SOUFogAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0362d71fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xList = np.linspace(min(sampledPoints0[0]['xList']),max(sampledPoints0[0]['xList']),51)\n",
    "xShifted = xList-(max(xList)+min(xList))/2\n",
    "\n",
    "X = JCheb(xShifted,2,n=len(sampledPoints0[0]['xList']))\n",
    "\n",
    "radius = 2*M*np.sqrt(len(sampledPoints0[0]['xList']))\n",
    "upper = [np.dot(row,radius*row/np.linalg.norm(row)) for row in X]\n",
    "lower = [0.0 for x in xList]\n",
    "\n",
    "plotSamples = []\n",
    "for i in range(100):\n",
    "    for sample in sampledPoints0:\n",
    "        thetas = sample['thetaList']\n",
    "        if (sum(thetas[:,1]) > i*nParams/100) and (sum(thetas[:,1]) < (i+1)*nParams/100):\n",
    "            plotSamples.append(sample)\n",
    "            break\n",
    "\n",
    "plt.figure(figsize=(6,5))\n",
    "\n",
    "plt.fill_between(xList,[0.0 for x in xList],upper,color='black',alpha=0.03)\n",
    "\n",
    "plt.plot(xList,upper,label='Polynomial Bound')\n",
    "plt.plot([xList[0],xList[0]],[0,upper[0]],c='C0')\n",
    "plt.plot([xList[-1],xList[-1]],[0,upper[-1]],c='C0')\n",
    "\n",
    "for p in plotSamples:\n",
    "    y = evalPoints(xList,p['thetaList'])\n",
    "    plt.plot(xList,y,c='C1',alpha=0.2)\n",
    "\n",
    "p = plotSamples[math.ceil(len(plotSamples)/2)]\n",
    "y = evalPoints(xList,p['thetaList'])\n",
    "plt.plot(xList,y,c='C1',label='Model Predictions with \\nDifferent Parameters ('+r'$\\theta$'+')')\n",
    "\n",
    "xList = sampledPoints0[0]['xList']\n",
    "plt.xticks(xList,fontsize=14)\n",
    "plt.grid()\n",
    "\n",
    "plt.legend(loc='upper right',fontsize=14)\n",
    "    \n",
    "plt.ylabel(r'$y_{\\theta}(t)$',fontsize=16)\n",
    "plt.xlabel('Time',fontsize=16)\n",
    "\n",
    "#plt.yticks([np.sqrt(3)],[r'$\\sqrt{3}$'])\n",
    "\n",
    "#plt.xlim([0,1])\n",
    "plt.ylim([0,1.5*max(upper)])\n",
    "\n",
    "#plt.savefig('exponential_manifold_C.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0Xb58ObNmzWLgwIHk5+dz1llnsXHjRrUap9FoZM6cOdx8883cddddFBUVcfLJ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BIWNXs99joeaV0hShIsXaWUEnjoes+n2vPRFTFRv1oXCqqpnMFOLyLs+aQtEzmRKGd0bD/EGHBp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9jY2IDH42HevHkKn6DuDXrbpLCwEK2trcwNS5MGo+q0jun8zruriSu6p2FkZKSW81G9Qa80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\niNai4/0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0362e61438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(7,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "### WIREFRAME ###\n",
    "xList = np.array(sampledPoints0[0]['xList'])\n",
    "xShifted = xList - (max(xList)+min(xList))/2\n",
    "xShifted = xShifted/max(xShifted)\n",
    "rho = 2\n",
    "J = JCheb(xShifted,rho)\n",
    "u,s,vt = np.linalg.svd(J)\n",
    "\n",
    "theta = np.linspace(0, 2 * np.pi, 200)\n",
    "phi = np.linspace(0, np.pi, 200)\n",
    "\n",
    "radius = 2*M*np.sqrt(len(xList))\n",
    "x = radius*np.outer(np.cos(theta), np.sin(phi))\n",
    "y = radius*np.outer(np.sin(theta), np.sin(phi))\n",
    "z = radius*np.outer(np.ones_like(theta), np.cos(phi))\n",
    "\n",
    "x_rot = copy.deepcopy(x)\n",
    "y_rot = copy.deepcopy(y)\n",
    "z_rot = copy.deepcopy(z)\n",
    "\n",
    "Jacob = np.dot(np.dot(u,np.diag(s)),[[0,0,1],[0,1,0],[1,0,0]]) #np.dot(np.diag(s[0:3]),[[0,0,1],[0,1,0],[1,0,0]])\n",
    "for i in range(len(x_rot)):\n",
    "    for j in range(len(x_rot[0])):\n",
    "        vect = [x_rot[i][j],y_rot[i][j],z_rot[i][j]]\n",
    "        vect_rot = np.dot(Jacob,vect)\n",
    "        x_rot[i][j] = vect_rot[0]\n",
    "        y_rot[i][j] = vect_rot[1]\n",
    "        z_rot[i][j] = vect_rot[2]\n",
    "\n",
    "ax.plot_wireframe(x_rot, y_rot, z_rot, rstride=5, cstride=4, alpha=0.2)\n",
    "\n",
    "### MODEL MANIFOLD ###\n",
    "\n",
    "proj = np.array([p['pointVals'] for p in sampledPoints0])\n",
    "\n",
    "pointsX = proj[:,0]\n",
    "pointsY = proj[:,1]\n",
    "pointsZ = proj[:,2]\n",
    "\n",
    "ax.scatter3D(pointsX,pointsY,pointsZ,color='C1',s=2,edgecolor='black',linewidth=0.1)\n",
    "\n",
    "# Adjustment of the axes, so that they all have the same span:\n",
    "max_range = 1.1*max([np.dot(row,radius*row/np.linalg.norm(row)) for row in J])\n",
    "\n",
    "for axis in 'xyz':\n",
    "    getattr(ax, 'set_{}lim'.format(axis))((-max_range, max_range))\n",
    "    \n",
    "#for angle in range(0,360,20):\n",
    "#    ax.view_init(30,angle)\n",
    "#    plt.savefig('rotating/'+str(angle)+'.png')\n",
    "\n",
    "ax.set_xlabel('\\n'+r'$y_{\\theta}(t_1)$',fontsize=16)\n",
    "ax.set_ylabel('\\n'+r'$y_{\\theta}(t_2)$',fontsize=16)\n",
    "ax.set_zlabel('\\n'+r'$y_{\\theta}(t_3)$',fontsize=16)\n",
    "\n",
    "\n",
    "label0 = mlines.Line2D([], [], color='C0', label='Chebyshev Bound')\n",
    "label1 = mlines.Line2D([], [], color='C1',marker='o',linewidth=0, markersize=5, label='Model Predictions with \\nDifferent Parameters ('+r'$\\theta$'+')')\n",
    "plt.legend(handles=[label0,label1],fontsize=14,loc = 'upper left')\n",
    "\n",
    "\n",
    "#fig.savefig('exponential_manifold_B.png')\n",
    "#ax.view_init(48,185)\n",
    "#fig.savefig('exponential_manifold_A.png')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "### WIREFRAME ###\n",
    "xList = np.array(sampledPoints0[0]['xList'])/max(sampledPoints0[0]['xList'])\n",
    "xList = xList - sum(xList)/len(xList)\n",
    "rho = 2\n",
    "J = JCheb(xList,rho)\n",
    "u,s,vt = np.linalg.svd(J)\n",
    "\n",
    "theta = np.linspace(0, 2 * np.pi, 200)\n",
    "phi = np.linspace(0, np.pi, 200)\n",
    "\n",
    "radius = ARange*nParams\n",
    "x = radius*np.outer(np.cos(theta), np.sin(phi))\n",
    "y = radius*np.outer(np.sin(theta), np.sin(phi))\n",
    "z = radius*np.outer(np.ones_like(theta), np.cos(phi))\n",
    "\n",
    "x_rot = copy.deepcopy(x)\n",
    "y_rot = copy.deepcopy(y)\n",
    "z_rot = copy.deepcopy(z)\n",
    "\n",
    "Jacob = np.dot(np.diag(s[0:3]),[[0,0,1],[0,1,0],[1,0,0]])\n",
    "for i in range(len(x_rot)):\n",
    "    for j in range(len(x_rot[0])):\n",
    "        vect = [x_rot[i][j],y_rot[i][j],z_rot[i][j]]\n",
    "        vect_rot = np.dot(Jacob,vect)\n",
    "        x_rot[i][j] = vect_rot[2]\n",
    "        y_rot[i][j] = vect_rot[1]\n",
    "        z_rot[i][j] = vect_rot[0]\n",
    "\n",
    "ax.plot_wireframe(x_rot, y_rot, z_rot, rstride=5, cstride=4, alpha=0.2,label='Bound from Chebychev')\n",
    "\n",
    "### MODEL MANIFOLD ###\n",
    "\n",
    "proj = np.dot([p['pointVals'] for p in sampledPoints0],u)\n",
    "\n",
    "pointsX = proj[:,2]\n",
    "pointsY = proj[:,1]\n",
    "pointsZ = proj[:,0]\n",
    "\n",
    "ax.scatter3D(pointsX,pointsY,pointsZ,color='C1',edgecolors='black',s=1,linewidth=0.1,label='Model Predictions')\n",
    "\n",
    "# Adjustment of the axes, so that they all have the same span:\n",
    "max_radius = radius*s[0]\n",
    "for axis in 'xyz':\n",
    "    getattr(ax, 'set_{}lim'.format(axis))((-max_radius, max_radius))\n",
    "#ax.view_init(0,0)\n",
    "#ax.set_xlabel('first time point')\n",
    "#ax.set_ylabel('second time point')\n",
    "#ax.set_zlabel('third time point')\n",
    "\n",
    "plt.show()\n",
    "#trianglePlotBound(proj,['C1' for p in sampledPoints0],s,len(xList),dim=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lengths = np.array([max(proj[:,i])-min(proj[:,i]) for i in range(proj.shape[1])])\n",
    "polyLengths = 2*radius*s\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot([i for i in range(len(polyLengths))],polyLengths,label='Chebychev Bound',marker='o')\n",
    "plt.plot([i for i in range(len(lengths))],lengths,label='Model Manifold',marker='o')\n",
    "plt.yscale('log')\n",
    "#limits = np.array([min([min(x) for x in [lengths, polyLengths]]),max([max(x) for x in [lengths, polyLengths]])])\n",
    "#plt.ylim(limits)\n",
    "#plt.xticks([0,1,2],['Longest\\nEllipsoid Axis','Middle\\n Ellipsoid Axis','Shortest\\nEllipsoid Axis'],fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "#plt.xlabel('Ordered Principal Components',fontsize=16)\n",
    "plt.ylabel('Prediction Space Distance',fontsize=16)\n",
    "plt.title('Manifold Lengths\\nAlong Different Directions',fontsize=20)\n",
    "plt.legend(fontsize=14,loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(7,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "### WIREFRAME ###\n",
    "xList = np.array(sampledPoints0[0]['xList'])/max(sampledPoints0[0]['xList'])\n",
    "xList = xList - (max(xList)+min(xList))/2\n",
    "V = np.array([[x**n for n in range(len(xList))] for x in xList])\n",
    "u,s,vt = np.linalg.svd(V)\n",
    "\n",
    "theta = np.linspace(0, 2 * np.pi, 200)\n",
    "phi = np.linspace(0, np.pi, 200)\n",
    "\n",
    "radius = np.sqrt(len(xList))\n",
    "x = radius*np.outer(np.cos(theta), np.sin(phi))\n",
    "y = radius*np.outer(np.sin(theta), np.sin(phi))\n",
    "z = radius*np.outer(np.ones_like(theta), np.cos(phi))\n",
    "\n",
    "x_rot = copy.deepcopy(x)\n",
    "y_rot = copy.deepcopy(y)\n",
    "z_rot = copy.deepcopy(z)\n",
    "\n",
    "Jacob = np.dot(np.dot(u,np.diag(s)),[[0,0,1],[0,1,0],[1,0,0]])#np.dot(np.diag(s[0:3]),[[0,0,1],[0,1,0],[1,0,0]])\n",
    "for i in range(len(x_rot)):\n",
    "    for j in range(len(x_rot[0])):\n",
    "        vect = [x_rot[i][j],y_rot[i][j],z_rot[i][j]]\n",
    "        vect_rot = np.dot(Jacob,vect)\n",
    "        x_rot[i][j] = vect_rot[0]\n",
    "        y_rot[i][j] = vect_rot[1]\n",
    "        z_rot[i][j] = vect_rot[2]\n",
    "\n",
    "ax.plot_wireframe(x_rot, y_rot, z_rot, rstride=5, cstride=4, alpha=0.2)\n",
    "\n",
    "### MODEL MANIFOLD ###\n",
    "\n",
    "proj = np.array([p['pointVals'] for p in sampledPoints0])\n",
    "\n",
    "pointsX = proj[:,0]\n",
    "pointsY = proj[:,1]\n",
    "pointsZ = proj[:,2]\n",
    "\n",
    "ax.scatter3D(pointsX,pointsY,pointsZ,color='C1',edgecolor='black',linewidth=0.1)\n",
    "\n",
    "# Adjustment of the axes, so that they all have the same span:\n",
    "max_range = 1.1*max([max(pointsX),max(pointsY),max(pointsZ)])\n",
    "for axis in 'xyz':\n",
    "    getattr(ax, 'set_{}lim'.format(axis))((-max_range, max_range))\n",
    "    \n",
    "#for angle in range(0,360,20):\n",
    "#    ax.view_init(30,angle)\n",
    "#    plt.savefig('rotating/'+str(angle)+'.png')\n",
    "\n",
    "ax.set_xlabel('\\n'+r'$y_{\\theta}(t_1)$',fontsize=16)\n",
    "ax.set_ylabel('\\n'+r'$y_{\\theta}(t_2)$',fontsize=16)\n",
    "ax.set_zlabel('\\n'+r'$y_{\\theta}(t_3)$',fontsize=16)\n",
    "\n",
    "\n",
    "label0 = mlines.Line2D([], [], color='C0', label='Polynomial Bound')\n",
    "label1 = mlines.Line2D([], [], color='C1',marker='o',linewidth=0, markersize=5, label='Model Predictions with \\nDifferent Parameters ('+r'$\\theta$'+')')\n",
    "plt.legend(handles=[label0,label1],fontsize=14)\n",
    "\n",
    "\n",
    "#fig.savefig('exponential_manifold_B.png')\n",
    "#ax.view_init(48,185)\n",
    "#fig.savefig('exponential_manifold_A.png')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "### WIREFRAME ###\n",
    "xList = np.array(sampledPoints0[0]['xList'])/max(sampledPoints0[0]['xList'])\n",
    "xList = xList - sum(xList)/len(xList)\n",
    "V = np.array([[x**n for n in range(len(xList))] for x in xList])\n",
    "u,s,vt = np.linalg.svd(V)\n",
    "\n",
    "theta = np.linspace(0, 2 * np.pi, 200)\n",
    "phi = np.linspace(0, np.pi, 200)\n",
    "\n",
    "radius = np.sqrt(len(xList))\n",
    "x = radius*np.outer(np.cos(theta), np.sin(phi))\n",
    "y = radius*np.outer(np.sin(theta), np.sin(phi))\n",
    "z = radius*np.outer(np.ones_like(theta), np.cos(phi))\n",
    "\n",
    "x_rot = copy.deepcopy(x)\n",
    "y_rot = copy.deepcopy(y)\n",
    "z_rot = copy.deepcopy(z)\n",
    "\n",
    "Jacob = np.dot(np.diag(s[0:3]),[[0,0,1],[0,1,0],[1,0,0]])\n",
    "for i in range(len(x_rot)):\n",
    "    for j in range(len(x_rot[0])):\n",
    "        vect = [x_rot[i][j],y_rot[i][j],z_rot[i][j]]\n",
    "        vect_rot = np.dot(Jacob,vect)\n",
    "        x_rot[i][j] = vect_rot[2]\n",
    "        y_rot[i][j] = vect_rot[1]\n",
    "        z_rot[i][j] = vect_rot[0]\n",
    "\n",
    "ax.plot_wireframe(x_rot, y_rot, z_rot, rstride=5, cstride=4, alpha=0.2,label='Bound from Polynomial Fits')\n",
    "\n",
    "### MODEL MANIFOLD ###\n",
    "\n",
    "proj = np.dot([p['pointVals'] for p in sampledPoints0],u)\n",
    "\n",
    "pointsX = proj[:,2]\n",
    "pointsY = -proj[:,1]\n",
    "pointsZ = -proj[:,0]\n",
    "\n",
    "ax.scatter3D(pointsX,pointsY,pointsZ,color='C1',edgecolors='black',linewidth=0.1,label='Model Predictions')\n",
    "\n",
    "# Adjustment of the axes, so that they all have the same span:\n",
    "max_radius = np.sqrt(len(xList))*s[0]\n",
    "for axis in 'xyz':\n",
    "    getattr(ax, 'set_{}lim'.format(axis))((-max_radius, max_radius))\n",
    "ax.view_init(0,0)\n",
    "#ax.set_xlabel('first time point')\n",
    "#ax.set_ylabel('second time point')\n",
    "#ax.set_zlabel('third time point')\n",
    "\n",
    "plt.show()\n",
    "#trianglePlotBound(proj,['C1' for p in sampledPoints0],s,len(xList),dim=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lengths = np.array([max(proj[:,i])-min(proj[:,i]) for i in range(proj.shape[1])])\n",
    "polyLengths = 2*np.sqrt(len(xList))*s\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot([i for i in range(len(polyLengths))],polyLengths,label='Polynomial Bound\\n'+r'($2\\sqrt{3}\\sigma_i$)',marker='o')\n",
    "plt.plot([i for i in range(len(lengths))],lengths,label='Model Manifold',marker='o')\n",
    "plt.yscale('log')\n",
    "#limits = np.array([min([min(x) for x in [lengths, polyLengths]]),max([max(x) for x in [lengths, polyLengths]])])\n",
    "#plt.ylim(limits)\n",
    "plt.xticks([0,1,2],['Longest\\nEllipsoid Axis','Middle\\n Ellipsoid Axis','Shortest\\nEllipsoid Axis'],fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "#plt.xlabel('Ordered Principal Components',fontsize=16)\n",
    "plt.ylabel('Prediction Space Distance',fontsize=16)\n",
    "plt.title('Manifold Lengths\\nAlong Different Directions',fontsize=20)\n",
    "plt.legend(fontsize=14,loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(4,8))\n",
    "for e in s:\n",
    "    plt.plot([0,1],[e**2,e**2],c='C0')\n",
    "plt.yscale('log')\n",
    "plt.title('Vandermonde Singular Values')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2D Vandermonde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def singularVals2D(xList,thetaList):\n",
    "    J = []\n",
    "    for lam,A,B in thetaList:\n",
    "        J.append([np.exp(-lam*x*np.exp(-B*beta)) for x,beta in xList])\n",
    "        J.append([-A*x*np.exp(-B*beta-lam*x*np.exp(-B*beta)) for x,beta in xList])\n",
    "        J.append([A*lam*x*beta * np.exp(-B*beta-lam*x*np.exp(-B*beta)) for x,beta in xList])\n",
    "    J = np.array(J).T\n",
    "    u,s,vt = np.linalg.svd(J)\n",
    "    return J,s\n",
    "\n",
    "def evalPoints2D(xList,thetaList):\n",
    "    return [sum([A*np.exp(-lam*x*np.exp(-B*beta)) for lam,A,B in thetaList]) for x,beta in xList]\n",
    "\n",
    "def cMat(n,m,mMax):\n",
    "    c = np.diag([1.0 for i in range(mMax)])\n",
    "    for i in range(1,mMax):\n",
    "        c[i][0] = (-1)**i * n**i\n",
    "    for i in range(2,mMax):\n",
    "        for j in range(1,i):\n",
    "            c[i][j] = c[i-1][j-1]-(n+j)*c[i-1][j]\n",
    "    return c\n",
    "\n",
    "def Vandermonde2D(xList,deg=0):\n",
    "    \"\"\"\n",
    "    Returns a 2D vandermonde for polynomials up to degree P\n",
    "    \"\"\"\n",
    "    if deg > 0:\n",
    "        P = deg\n",
    "    else:\n",
    "        P = polyDeg(xList)\n",
    "    polyList = []\n",
    "    for p in range(P+1):\n",
    "        for n in range(p+1):\n",
    "            polyList.append([n,p-n])\n",
    "    return [[x**n * beta**m for n,m in polyList] for x,beta in xList]\n",
    "\n",
    "def polyDeg(xList):\n",
    "    return math.ceil(np.sqrt(1/4+2*len(xList))-3/2)\n",
    "\n",
    "def useParams2D(xList,thetaList):\n",
    "    P = polyDeg(xList)\n",
    "    \n",
    "    termSum = 0.0\n",
    "    for p in range(P+1):\n",
    "        for n in range(p+1):\n",
    "            termSum += (1/(math.factorial(n)*math.factorial(p-n))*sum([A * B**(p-n) * lam**n * n**(p-n) for lam,A,B in thetaList]))**2\n",
    "    if termSum < (P+2)*(P+1)/2:\n",
    "        return True\n",
    "    return False\n",
    "    \n",
    "    return P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nX = 3\n",
    "nBeta = 5\n",
    "xRange = np.linspace(0,2,nX)\n",
    "betaRange = np.linspace(0,2,nBeta)\n",
    "xList = [[x,beta] for x in xRange for beta in betaRange]\n",
    "\n",
    "nParams = 4\n",
    "ARange = 3\n",
    "lambdaRange = 3\n",
    "BRange = 5.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sampledPoints2D = []\n",
    "time1 = datetime.datetime.now()\n",
    "iterations = 2*10**8\n",
    "for idx in range(iterations):\n",
    "    thetaList = np.array([[lambdaRange*np.random.random(),ARange*np.random.random(),BRange*np.random.random()] for x in range(nParams)])\n",
    "    if useParams2D(xList,thetaList):\n",
    "        pointDict = {'thetaList':thetaList,'xList':xList,'pointVals':evalPoints2D(xList,thetaList)}\n",
    "        sampledPoints2D.append(pointDict)\n",
    "    if idx%(iterations/10) == 1:\n",
    "        print(len(sampledPoints2D),' points')\n",
    "        print('acceptance ratio of ',len(sampledPoints2D)/(idx+1))\n",
    "time2 = datetime.datetime.now()\n",
    "print(time2-time1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#saveThing(sampledPoints2D,'2DexponentialSampling_15Points.pckl')\n",
    "sampledPoints2D = openThing('2DexponentialSampling.pckl')\n",
    "len(sampledPoints2D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#xRange = np.linspace(0,1,nX)\n",
    "#betaRange = np.linspace(0,1,nBeta)\n",
    "#xList = [[x,beta] for x in xRange for beta in betaRange]\n",
    "#eigList2D = []\n",
    "for p in sampledPoints2D:\n",
    "    #p.update({'xList':xList})\n",
    "    p.update({'pointVals':evalPoints2D(p['xList'],p['thetaList'])})\n",
    "    #p.update({'R':RMat(p['thetaList'],100)})\n",
    "    #J,s = singularVals2D(p['xList'],p['thetaList'])\n",
    "    #p.update({'J':J,'s':s})\n",
    "    #eigList2D.extend(list(s**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plotSamples = []\n",
    "for i in range(10):\n",
    "    for sample in sampledPoints2D:\n",
    "        thetas = sample['thetaList']\n",
    "        if (sum(thetas[:,1]) > i*4/10) and (sum(thetas[:,1]) < (i+1)*4/10):\n",
    "            plotSamples.append(sample)\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "XRange = np.linspace(0,1,31)\n",
    "YRange = np.linspace(0,1,31)\n",
    "\n",
    "xList = sampledPoints2D[0]['xList']\n",
    "\n",
    "X,Y = np.meshgrid(XRange,YRange)\n",
    "\n",
    "plotPoints = np.array([[x,y] for x in XRange for y in YRange])\n",
    "\n",
    "shiftedPoints = [[plotPoints[i][0]-sum(XRange)/len(XRange),plotPoints[i][1]-sum(YRange)/len(YRange)] for i in range(len(plotPoints))]\n",
    "V = np.array(Vandermonde2D(shiftedPoints,deg=polyDeg(xList)))\n",
    "\n",
    "DOF = len(xList)\n",
    "\n",
    "upper = np.array([np.dot(row,np.sqrt(DOF)*row/np.linalg.norm(row)) for row in V])\n",
    "upper = np.array([np.sqrt(DOF)*np.linalg.norm(row) for row in V])\n",
    "\n",
    "ZSphere = np.array([[upper[i*len(XRange)+j] for i in range(len(XRange))] for j in range(len(YRange))])\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(10,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "fact = 1\n",
    "\n",
    "XRange = fact*XRange\n",
    "YRange = fact*YRange\n",
    "plotPoints = fact*plotPoints\n",
    "\n",
    "X,Y = np.meshgrid(XRange,YRange)\n",
    "\n",
    "X1 = [[fact,fact] for x in range(X.shape[1])]\n",
    "Y1 = [[y,y] for y in Y[:,-1]]\n",
    "Z1 = [[z,0.0] for z in ZSphere[:,-1]]\n",
    "    \n",
    "X2 = [[0.0,0.0] for x in range(X.shape[1])]\n",
    "Y2 = [[y,y] for y in Y[:,0]]\n",
    "Z2 = [[z,0.0] for z in ZSphere[:,0]]\n",
    "    \n",
    "X3 = [[x,x] for x in X[0]]\n",
    "Y3 = [[fact,fact] for y in range(Y.shape[0])]\n",
    "Z3 = [[z,0.0] for z in ZSphere[-1]]\n",
    "    \n",
    "X4 = [[x,x] for x in X[0]]\n",
    "Y4 = [[0.0,0.0] for y in range(Y.shape[0])]\n",
    "Z4 = [[z,0.0] for z in ZSphere[0]]\n",
    "\n",
    "ax.plot_surface(X1,Y1,Z1,color='black',alpha=0.1)\n",
    "ax.plot_wireframe(X1,Y1,Z1,color='C0',rstride=len(X1))\n",
    "ax.plot_surface(X2,Y2,Z2,color='black',alpha=0.1)\n",
    "ax.plot_wireframe(X2,Y2,Z2,color='C0',rstride=len(X2))\n",
    "ax.plot_surface(X3,Y3,Z3,color='black',alpha=0.1)\n",
    "ax.plot_wireframe(X3,Y3,Z3,color='C0',rstride=len(X3))\n",
    "ax.plot_surface(X4,Y4,Z4,color='black',alpha=0.1)\n",
    "ax.plot_wireframe(X4,Y4,Z4,color='C0',rstride=len(X4))\n",
    "\n",
    "for p in plotSamples:\n",
    "    pointVals = evalPoints2D(plotPoints,p['thetaList'])\n",
    "    Z = np.array([[pointVals[i*len(XRange)+j] for i in range(len(XRange))] for j in range(len(YRange))])\n",
    "\n",
    "    ax.plot_surface(X,Y,Z,color='C1',alpha=0.4)\n",
    "    \n",
    "thetaList = np.array([[np.sqrt(15)*0.02,np.sqrt(15),np.sqrt(15)*0.02]])\n",
    "pointVals = evalPoints2D(plotPoints,thetaList)\n",
    "Z = np.array([[pointVals[i*len(XRange)+j] for i in range(len(XRange))] for j in range(len(YRange))])\n",
    "ax.plot_surface(X,Y,Z,color='C1',alpha=0.4)\n",
    "    \n",
    "p = plotSamples[math.ceil(len(plotSamples)/2)]\n",
    "pointVals = evalPoints2D(plotPoints,p['thetaList'])\n",
    "Z = np.array([[pointVals[i*len(XRange)+j] for i in range(len(XRange))] for j in range(len(YRange))])\n",
    "ax.plot_surface(X,Y,Z,color='C1')\n",
    "\n",
    "ax.plot_surface(X,Y,ZSphere,color='C0')\n",
    "\n",
    "#ax.set_xlim([0,1])\n",
    "#ax.set_ylim([0,1])\n",
    "\n",
    "ax.set_xticks([0,0.5,1])\n",
    "ax.set_xticklabels([r'$t_1=0$',r'$t_2=0.5$',r'$t_3=1$'])\n",
    "ax.set_yticks([0,0.25,0.5,0.75,1])\n",
    "ax.set_yticklabels([r'$\\beta_1=0$',r'$\\beta_2=0.25$',r'$\\beta_3=0.5$',r'$\\beta_4=0.75$',r'$\\beta_5=1$'])\n",
    "\n",
    "\"\"\"ax.set_xticks([0,1,2])\n",
    "ax.set_xticklabels([r'$t_1=0$',r'$t_2=1$',r'$t_3=2$'])\n",
    "ax.set_yticks([0,0.5,1,1.5,2])\n",
    "ax.set_yticklabels([r'$\\beta_1=0$',r'$\\beta_2=0.5$',r'$\\beta_3=1$',r'$\\beta_4=1.5$',r'$\\beta_5=2$'])\"\"\"\n",
    "\n",
    "ax.set_zticks([np.sqrt(len(xList))])\n",
    "ax.set_zticklabels([r'$\\sqrt{15}$'])\n",
    "    \n",
    "ax.set_xlabel('\\nTime',fontsize=14)\n",
    "ax.set_ylabel('\\nInverse Temperature',fontsize=14)\n",
    "ax.set_zlabel('\\n'+r'$y_{\\theta}(t,\\beta)$',fontsize=14)\n",
    "\n",
    "ax.set_xlim([0,1])\n",
    "ax.set_ylim([0,1])\n",
    "ax.set_zlim([0,5])\n",
    "\n",
    "#ax.view_init(30,-130)\n",
    "\n",
    "label0 = mpatches.Patch(color='C0', label='Polynomial Bound')\n",
    "label1 = mpatches.Patch(color='C1', label='Model Predictions with \\nDifferent Parameters ('+r'$\\theta$'+')')\n",
    "plt.legend(handles=[label0,label1],fontsize=14)\n",
    "\n",
    "#plt.savefig('exponential2D_manifold_C.png')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nBins = 100\n",
    "\n",
    "AList = []\n",
    "lambdaList = []\n",
    "BList = []\n",
    "for p in sampledPoints2D:\n",
    "    lambdaList.extend(list(p['thetaList'][:,0]))\n",
    "    AList.extend(list(p['thetaList'][:,1]))\n",
    "    BList.extend(list(p['thetaList'][:,2]))\n",
    "\n",
    "n, bins, patches = plt.hist(AList,bins=nBins)\n",
    "plt.title('Amplitudes (n='+str(len(AList))+')')\n",
    "plt.show()\n",
    "\n",
    "n, bins, patches = plt.hist(lambdaList,bins=nBins)\n",
    "plt.title('Lambda (n='+str(len(lambdaList))+')')\n",
    "plt.show()\n",
    "\n",
    "n, bins, patches = plt.hist(BList,bins=nBins)\n",
    "plt.title('Activation Energy (n='+str(len(BList))+')')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max(AList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(14,8))\n",
    "\n",
    "nBins = 500\n",
    "bins = np.linspace(np.log(min(eigList2D)),np.log(max(eigList2D)),nBins)\n",
    "bins = np.exp(bins)\n",
    "n, bins, patches = plt.hist(eigList2D,bins=bins,normed=1,alpha=0.7,label='Jacobians time and Temp (n = '+str(len(eigList2D))+')')\n",
    "\n",
    "plt.title('Eigvalues with '+str(len(xList))+' points and '+str(3*nParams)+' parameters')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(7,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "### WIREFRAME ###\n",
    "xList = np.array(sampledPoints2D[0]['xList'])\n",
    "\n",
    "xListShifted = xList - np.array([(max(row)+min(row))/2 for row in xList.T])\n",
    "\n",
    "V = Vandermonde2D(xListShifted)\n",
    "u,s,vt = np.linalg.svd(V)\n",
    "\n",
    "xListRand = np.random.rand(len(xList),2)\n",
    "xListRand = xListRand - np.array([(max(row)-min(row))/2 for row in xListRand.T])\n",
    "\n",
    "uRand,sRand,vRandt = np.linalg.svd(Vandermonde2D(xListRand))\n",
    "\n",
    "theta = np.linspace(0, 2 * np.pi, 100)\n",
    "phi = np.linspace(0, np.pi, 100)\n",
    "\n",
    "P = polyDeg(xList)\n",
    "radius = np.sqrt((P+2)*(P+1)/2)\n",
    "x = radius*np.outer(np.cos(theta), np.sin(phi))\n",
    "y = radius*np.outer(np.sin(theta), np.sin(phi))\n",
    "z = radius*np.outer(np.ones_like(theta), np.cos(phi))\n",
    "\n",
    "x_rot = copy.deepcopy(x)\n",
    "y_rot = copy.deepcopy(y)\n",
    "z_rot = copy.deepcopy(z)\n",
    "\n",
    "Jacob = np.dot(np.diag(sRand[0:3]),[[0,0,1],[0,1,0],[1,0,0]])\n",
    "for i in range(len(x_rot)):\n",
    "    for j in range(len(x_rot[0])):\n",
    "        vect = [x_rot[i][j],y_rot[i][j],z_rot[i][j]]\n",
    "        vect_rot = np.dot(Jacob,vect)\n",
    "        x_rot[i][j] = vect_rot[2]\n",
    "        y_rot[i][j] = vect_rot[1]\n",
    "        z_rot[i][j] = vect_rot[0]\n",
    "\n",
    "ax.plot_wireframe(x_rot, y_rot, z_rot, rstride=3, cstride=3, alpha=0.2,label='Bound from Polynomial Fits')\n",
    "\n",
    "### MODEL MANIFOLD ###\n",
    "\n",
    "proj = np.dot([p['pointVals'] for p in sampledPoints2D],u)\n",
    "\n",
    "pointsX = proj[:,2]\n",
    "pointsY = proj[:,1]\n",
    "pointsZ = -proj[:,0]\n",
    "\n",
    "ax.scatter3D(pointsX,pointsY,pointsZ,color='C1',edgecolor='black',linewidth=0.1)\n",
    "\n",
    "#Adjustment of the axes, so that they all have the same span:\n",
    "max_radius = radius*s[0]\n",
    "for axis in 'xyz':\n",
    "    getattr(ax, 'set_{}lim'.format(axis))((-max_radius, max_radius))\n",
    "\n",
    "ax.set_xlabel('\\nThird Largest\\nPrincipal Component',fontsize=14)\n",
    "ax.set_ylabel('\\nSecond Largest\\nPrincipal Component',fontsize=14)\n",
    "ax.set_zlabel('\\nLarges Principal\\nComponent',fontsize=14)\n",
    "\n",
    "label0 = mlines.Line2D([], [], color='C0', label='Polynomial Bound')\n",
    "label1 = mlines.Line2D([], [], color='C1',marker='o',linewidth=0, markersize=5, label='Model Predictions with \\nDifferent Parameters ('+r'$\\theta$'+')')\n",
    "#plt.legend(handles=[label0,label1],fontsize=14)\n",
    "\n",
    "#ax.view_init(0,0)\n",
    "#fig.savefig('exponential2D_manifold_A.png')\n",
    "#fig.savefig('exponential2D_manifold_B.png')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(s)\n",
    "\n",
    "lengths = np.array([max(proj[:,i])-min(proj[:,i]) for i in range(proj.shape[1])])\n",
    "polyLengths = 2*np.sqrt(len(xList))*s\n",
    "polyLengthsRand = 2*np.sqrt(len(xListRand))*sRand\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot([i for i in range(len(polyLengths))],polyLengths,label='Polynomial Bound\\n'+r'($\\sqrt{45}\\sigma_i$)',marker='o')\n",
    "plt.plot([i for i in range(len(lengths))],lengths,label='Model Manifold Length',marker='o')\n",
    "plt.plot([i for i in range(len(polyLengthsRand))],polyLengthsRand,label='Random Poly Bound',marker='o')\n",
    "plt.yscale('log')\n",
    "#limits = np.array([min([min(x) for x in [lengths, polyLengths]]),max([max(x) for x in [lengths, polyLengths]])])\n",
    "#plt.ylim(limits)\n",
    "plt.xticks([i for i in range(len(lengths))],fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.xlabel('Principal Component Direction',fontsize=16)\n",
    "plt.ylabel('Length',fontsize=16)\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()\n",
    "\n",
    "#trianglePlotBound(proj,['C1' for p in sampledPoints2D],s,radius,dim=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### WIREFRAME ###\n",
    "xList = np.array(sampledPoints2D[0]['xList'])\n",
    "\n",
    "xListShifted = xList - np.array([(max(row)+min(row))/2 for row in xList.T])\n",
    "\n",
    "V = Vandermonde2D(xListShifted)\n",
    "u,s,vt = np.linalg.svd(V)\n",
    "\n",
    "\n",
    "\"\"\"xListRand = np.random.rand(len(xList),2)\n",
    "xListRandShifted = xListRand - np.array([(max(row)+min(row))/2 for row in xListRand.T])\n",
    "tDist = max(xListRandShifted[:,0])-min(xListRandShifted[:,0])\n",
    "betaDist = max(xListRandShifted[:,1])-min(xListRandShifted[:,1])\n",
    "xListRandShifted = np.array([[t/tDist,beta/betaDist] for t,beta in xListRandShifted])\n",
    "xListRand = xListRandShifted - np.array([min(row) for row in xListRandShifted.T])\n",
    "\n",
    "uRand,sRand,vRandt = np.linalg.svd(Vandermonde2D(xListRandShifted))\n",
    "\"\"\"\n",
    "theta = np.linspace(0, 2 * np.pi, 100)\n",
    "phi = np.linspace(0, np.pi, 100)\n",
    "\n",
    "P = polyDeg(xList)\n",
    "radius = np.sqrt((P+2)*(P+1)/2)\n",
    "x = radius*np.outer(np.cos(theta), np.sin(phi))\n",
    "y = radius*np.outer(np.sin(theta), np.sin(phi))\n",
    "z = radius*np.outer(np.ones_like(theta), np.cos(phi))\n",
    "\n",
    "x_rot = copy.deepcopy(x)\n",
    "y_rot = copy.deepcopy(y)\n",
    "z_rot = copy.deepcopy(z)\n",
    "\n",
    "Jacob = np.dot(np.diag(s[0:3]),[[0,0,1],[0,1,0],[1,0,0]])\n",
    "for i in range(len(x_rot)):\n",
    "    for j in range(len(x_rot[0])):\n",
    "        vect = [x_rot[i][j],y_rot[i][j],z_rot[i][j]]\n",
    "        vect_rot = np.dot(Jacob,vect)\n",
    "        x_rot[i][j] = vect_rot[0]\n",
    "        y_rot[i][j] = vect_rot[2]\n",
    "        z_rot[i][j] = vect_rot[1]\n",
    "        \n",
    "\n",
    "### MODEL MANIFOLD ###\n",
    "\n",
    "xListNew = fact*np.array(xList)\n",
    "proj = np.dot([evalPoints2D(xListNew,p['thetaList']) for p in sampledPoints2D],u)\n",
    "#proj = np.dot([p['pointVals'] for p in sampledPoints2D],u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(7,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.plot_wireframe(x_rot, y_rot, z_rot, rstride=3, cstride=3, alpha=0.2,label='Bound from Polynomial Fits')\n",
    "\n",
    "pointsX = -proj[:,0]\n",
    "pointsY = proj[:,2]\n",
    "pointsZ = proj[:,1]\n",
    "\n",
    "ax.scatter3D(pointsX,pointsY,pointsZ,color='C1',edgecolor='black',linewidth=0.1)\n",
    "\n",
    "#Adjustment of the axes, so that they all have the same span:\n",
    "max_radius = 0.7*max([max(abs(row)) for row in [pointsX,pointsY,pointsZ]])\n",
    "for axis in 'xyz':\n",
    "    getattr(ax, 'set_{}lim'.format(axis))((-max_radius, max_radius))\n",
    "\n",
    "ax.set_xlabel('\\n\\nLargest\\nPrincipal Component',fontsize=14)\n",
    "ax.set_ylabel('\\n\\nThird Largest\\nPrincipal Component',fontsize=14)\n",
    "ax.set_zlabel('\\n\\nSecond Largest\\nPrincipal Component',fontsize=14)\n",
    "\n",
    "label0 = mlines.Line2D([], [], color='C0', label='Polynomial Bound')\n",
    "label1 = mlines.Line2D([], [], color='C1',marker='o',linewidth=0, markersize=5, label='Model Predictions with \\nDifferent Parameters ('+r'$\\theta$'+')')\n",
    "plt.legend(handles=[label0,label1],fontsize=14,loc='upper right')\n",
    "\n",
    "#ax.view_init(0,0)\n",
    "#fig.savefig('exponential2D_manifold_A.png')\n",
    "fig.savefig('exponential2D_manifold_B.png')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "lengths = np.array([max(proj[:,i])-min(proj[:,i]) for i in range(proj.shape[1])])[0:12]\n",
    "polyLengths = 2*np.sqrt(len(xList))*s[0:12]\n",
    "#polyLengthsRand = 2*np.sqrt(len(xListRand))*sRand[0:12]\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot([i for i in range(len(polyLengths))],polyLengths,label='Polynomial Bound\\n'+r'($2\\sqrt{15}\\sigma_i$)',marker='o')\n",
    "#plt.plot([i for i in range(len(polyLengthsRand))],polyLengthsRand,label='Random Poly Bound',marker='o')\n",
    "plt.plot([i for i in range(len(lengths))],lengths,label='Model Manifold',marker='o')\n",
    "plt.yscale('log')\n",
    "#limits = np.array([min([min(x) for x in [lengths, polyLengths]]),max([max(x) for x in [lengths, polyLengths]])])\n",
    "#plt.ylim(limits)\n",
    "plt.xticks([0,len(lengths)-1],['Largest\\n(Longest\\nEllipsoid Axis)','Smallest\\n(Shortest\\nElllipsoid Axis)'],fontsize=14)\n",
    "#plt.xticks([])\n",
    "plt.yticks(fontsize=14)\n",
    "plt.xlabel('Ordered Principal Components',fontsize=16)\n",
    "plt.ylabel('Prediction Space Distance',fontsize=16)\n",
    "plt.title('Manifold Lengths\\nAlong Different Directions',fontsize=20)\n",
    "plt.legend(fontsize=14)\n",
    "plt.savefig('exponential2D_manifold_D.png')\n",
    "plt.show()\n",
    "#trianglePlotBound(proj,['C1' for p in sampledPoints2D],s,radius,dim=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xListNew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xListRand = np.random.rand(len(xList),2)\n",
    "xListRand = xListRand - np.array([(max(row)-min(row))/2 for row in xListRand.T])\n",
    "\n",
    "u,sRand,vt = np.linalg.svd(Vandermonde2D(xListRand))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lengths = np.array([max(proj[:,i])-min(proj[:,i]) for i in range(proj.shape[1])])\n",
    "polyLengths = 2*np.sqrt(len(xList))*s\n",
    "polyLengthsRand = 2*np.sqrt(len(xListRand))*sRand\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot([i for i in range(len(polyLengths))],polyLengths,label='Polynomial Bound\\n'+r'($\\sqrt{15}\\sigma_i$)',marker='o')\n",
    "plt.plot([i for i in range(len(lengths))],lengths,label='Model Manifold Length',marker='o')\n",
    "plt.plot([i for i in range(len(polyLengthsRand))],polyLengthsRand,label='Random Poly Bound',marker='o')\n",
    "plt.yscale('log')\n",
    "#limits = np.array([min([min(x) for x in [lengths, polyLengths]]),max([max(x) for x in [lengths, polyLengths]])])\n",
    "#plt.ylim(limits)\n",
    "plt.xticks([i for i in range(len(lengths))],fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.xlabel('Principal Component Direction',fontsize=16)\n",
    "plt.ylabel('Length',fontsize=16)\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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