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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import  matplotlib.pyplot as plt\n",
      "%pylab inline\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Equations 22-24 of [Hogg and Lang](http://arxiv.org/pdf/1210.6563.pdf) explicitly write what we want to evaluate, namely, a model that convolves the \"pixel-convolved\" PSF with the intrinsic galaxy profile.  We can copy Hogg and Lang and represent the deVauc profile as a sum of Gaussians.  The PSF we will represent as Gaussian for this project.  The only question is how to get the pixel-convolved PSF represented as a Gaussian (do we need to go through their minimization procedure?)  What exactly does that mean?\n",
      "\n",
      "From pg 8: \"Other definitions for the PSF (the non-pixel-convolved, for example) require that the user do two convolutions, the first with the PSF and the second with the square (or worse) pixel.\"\n",
      "\n",
      "We might not have to worry about speed so much in our case, because we can just do this once and plop it down in the center of random pixels, and then maybe recycle through several positions with respect to the center of the pixel to make sure we're not biasing things by just choosing the center.  Then the model looks very simple, so we can just write slow code to do the square pixel convolution.\n",
      "\n",
      "In summary, we should represent the deVauc profile as 10 Gaussians and the PSF as a single Gaussian and use Eqn. 22-24 as our base model.  Then we should convolve that model with the SDSS pixels.  We should end up with something like Fig 6.\n",
      "\n",
      "The model will just tell us how to weight the noise when we start grabbing real SDSS images."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Doris, can you grab the Gaussian coefficients from the Hogg and Lang paper (download source and grab with python from the tex, or by hand..) and code them up in the deVauc function?\n",
      "\n",
      "def N(xgrid,ygrid,m,Vinv):\n",
      "  \"\"\"\n",
      "  2d normal (Gaussian) distribution.\n",
      "  #http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function\n",
      "  xgrid,ygrid is the output of a meshgrid.\n",
      "  #m is the mean (x_0,y_0)\n",
      "  Vinv is a 2x2 np.array, you already took the inverse!\n",
      "  \"\"\"\n",
      "  assert Vinv[0,1] == Vinv[0,1]\n",
      "  exparg = (xgrid - m[0])*Vinv[0,0]*(xgrid - m[0]) + \\\n",
      "           2*(xgrid - m[0])*Vinv[1,0]*(ygrid -m[1]) + \\\n",
      "           (ygrid - m[1])*Vinv[1,1]*(ygrid - m[1])\n",
      "  \n",
      "  return (np.linalg.det(Vinv))**0.5/(2.*np.pi)*np.exp(-0.5*exparg)\n",
      "\n",
      "def N2diso(r,sig2inv):\n",
      "  exparg = r**2*sig2inv\n",
      "  return (0.5/np.pi)*sig2inv*np.exp(-0.5*exparg)\n",
      "  \n",
      "def deVauc1d(r,Ie,re,aopt=1):\n",
      "  \"\"\"\n",
      "  Input r in units of the half-light radius.\n",
      "  aopt = 0: straight-up deVauc formula.\n",
      "  aopt = 1: SDSS approximation ('luv') Eqn 17-18 of Hogg and Lang.\n",
      "  aopt = 2: Hogg and Lang approximation to luv (sum over 10 2d isotropic Gaussians).\n",
      "  \"\"\"\n",
      "  xi = np.fabs(r/re)\n",
      "  if aopt == 0:\n",
      "    return Ie*np.exp(-7.66924944*((xi)**(0.25)-1))\n",
      "  if aopt == 1:\n",
      "    result = np.zeros(len(r))\n",
      "    result = Ie*np.exp(-7.66925*(((xi)**2 + 0.0004)**(0.125)-1))\n",
      "    xx = np.where(xi > 8.)[0]\n",
      "    if len(xx) > 0:\n",
      "      result[xx] = 0.\n",
      "    xx = np.where((xi >= 7.) & (xi < 8.))[0]\n",
      "    if len(xx) > 0.:\n",
      "      result[xx] = result[xx] * (1.-(xi[xx]-7)**2)**2\n",
      "    return result\n",
      "  if aopt == 2:\n",
      "    ## hard code Hogg/Lang coefficients.\n",
      "    mluv10={0.01468:0.01190**-2, \\\n",
      "            0.09627:0.02210**-2, \\\n",
      "            0.28454:0.03995**-2, \\\n",
      "            0.63005:0.07117**-2, \\\n",
      "            1.19909:0.12586**-2, \\\n",
      "            2.03195:0.22240**-2, \\\n",
      "            3.07255:0.39593**-2, \\\n",
      "            4.10682:0.71922**-2, \\\n",
      "            4.83948:1.37549**-2, \\\n",
      "            4.94943:3.13117**-2}\n",
      "            \n",
      "    #mdev10={0.00139:0.00087, \\\n",
      "    #        0.00941:0.00296, \\\n",
      "    #        0.04441:0.00792, \\\n",
      "    #        0.16162:0.01902, \\\n",
      "    #        0.48121:0.04289, \\\n",
      "    #        1.20357:0.09351, \\\n",
      "    #        2.54182:0.20168, \\\n",
      "    #        4.46441:0.44126, \\\n",
      "    #        6.22820:1.01833, \\\n",
      "    #        6.15393:2.74555}\n",
      "            \n",
      "    result = np.zeros(len(r))\n",
      "    xx = np.where(xi > 8.)[0]\n",
      "    for kk, vv in mluv10.iteritems():\n",
      "      result += kk*N2diso(xi,vv)\n",
      "    if len(xx) > 0:\n",
      "      result[xx] = 0.\n",
      "    result = Ie*result\n",
      "    return result\n",
      "    \n",
      "    \n",
      "    \n",
      "\n",
      "def intT1d(r,pofr):\n",
      "  \"\"\"\n",
      "  Trapezoid rule for integration.\n",
      "  \"\"\"\n",
      "  return 0.5*((r[1:]-r[:-1])*(pofr[1:]+pofr[:-1])).sum()\n",
      "\n",
      "## Plot of the deVauc and LUV profiles.  Can you add the plot of the Gaussian approximation?\n",
      "\n",
      "r=10**np.arange(-3,2,0.001)\n",
      "print len(r)\n",
      "\n",
      "print 'this shows that parameter dependence works!'\n",
      "\n",
      "plt.figure()\n",
      "Ieval = 1.; reval = 1.\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,0),'b')\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,1),'g')\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,2),'r')\n",
      "\n",
      "plt.figure()\n",
      "Ieval = 2.; reval = 1.\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,0),'b')\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,1),'g')\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,2),'r')\n",
      "\n",
      "plt.figure()\n",
      "Ieval = 1.; reval = 2.\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,0),'b')\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,1),'g')\n",
      "plt.loglog(r,deVauc1d(r,Ieval,reval,2),'r') \n",
      "    \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5000\n",
        "this shows that parameter dependence works!\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "[<matplotlib.lines.Line2D at 0x104980d10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10492e590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uczGlHe8BHvUzRhGJMZH0tE9pt94KSUn2L/7ua/J/C5PovRUVcO8JtAAuA1oB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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104952a50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kqsXaYyksCu5judOmwcaN8MILQf2YgAqLPn9N7CYiwRJrj+Vs0dmgfka1aqHr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\nAXH6RDx+/t4+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1049258d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r=np.arange(100)\n",
      "r = np.array([float(i) for i in r])\n",
      "print r\n",
      "plt.ylim(0,2)\n",
      "plt.plot(r,deVauc1d(r,0.5,0.5,2)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  0.   1.   2.   3.   4.   5.   6.   7.   8.   9.  10.  11.  12.  13.  14.\n",
        "  15.  16.  17.  18.  19.  20.  21.  22.  23.  24.  25.  26.  27.  28.  29.\n",
        "  30.  31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.\n",
        "  45.  46.  47.  48.  49.  50.  51.  52.  53.  54.  55.  56.  57.  58.  59.\n",
        "  60.  61.  62.  63.  64.  65.  66.  67.  68.  69.  70.  71.  72.  73.  74.\n",
        "  75.  76.  77.  78.  79.  80.  81.  82.  83.  84.  85.  86.  87.  88.  89.\n",
        "  90.  91.  92.  93.  94.  95.  96.  97.  98.  99.]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1052800d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkiRJkiRJkiRJkiRJkiRJGon/AyF0bSV4s7PWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105280350>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = N2diso(np.arange(1000),10)\n",
      "# plt.plot(result)\n",
      "# plt.figure()\n",
      "plt.loglog(result)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0x104bd3d90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10491aa90>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = N2diso(np.arange(100),0.001)\n",
      "# plt.plot(result)\n",
      "# plt.figure()\n",
      "plt.loglog(result)\n",
      "plt.xlim(0,10**2)\n",
      "plt.ylim(10**-8,10**-3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "(1e-08, 0.001)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x104f14f90>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = N2diso(np.arange(1000),0.001)\n",
      "plt.plot(result)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[<matplotlib.lines.Line2D at 0x104febc90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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efn4y+bkO3yCMJf0boddxEz50LkmSJEmSJEmSJEmSJEmSJEmSJEmS8uj/AwFW\nfx30bRiIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104a5b3d0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=r\n",
      "y=deVauc1d(r,1.,1.,0)*2*np.pi*x\n",
      "y2=deVauc1d(r,1.,1.,1)*2*np.pi*x\n",
      "y3=deVauc1d(r,1.,1.,2)*2*np.pi*x\n",
      "ihalf = np.where(r > 1.)[0].min()\n",
      "print 'half light radius correct?', x[ihalf], intT1d(x[:ihalf],y[:ihalf])/intT1d(x,y)\n",
      "print 'half light approx correct for LUV profile?',intT1d(x[:ihalf],y2[:ihalf])/intT1d(x,y2)\n",
      "print 'half light approx correct for Hogg profile?',intT1d(x[:ihalf],y3[:ihalf])/intT1d(x,y3)\n",
      "\n",
      "print 'note that the profiles are not normalized to have unit flux, but to be 1 at the half light radius!'\n",
      "print 'therefore the total integrated flux is ~21, agrees with Hogg Sum over a_luv'\n",
      "intT1d(x,y),intT1d(x,y2),intT1d(x,y3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "half light radius correct? 1.00230523808 0.499975031558\n",
        "half light approx correct for LUV profile? 0.52884049292\n",
        "half light approx correct for Hogg profile? 0.528455293308\n",
        "note that the profiles are not normalized to have unit flux, but to be 1 at the half light radius!\n",
        "therefore the total integrated flux is ~21, agrees with Hogg Sum over a_luv\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(22.662326549606234, 21.019904088683031, 21.036406893930479)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## BR: no edits below this point!!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## Plot of the deVauc and LUV profiles.  Can you add the plot of the Gaussian approximation?\n",
      "\n",
      "r=10**np.arange(-3,2,0.001)\n",
      "print len(r)\n",
      "# plt.loglog(r,deVauc(r,1.,1.,0),'b')\n",
      "plt.loglog(r,deVauc(r,1.,1.,0),'b')\n",
      "plt.loglog(r,deVauc(r,1.,1.,1),'g')\n",
      "# plt.loglog(r,deVauc(r,1.,1.,2),'r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5000\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10ef902d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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N6ce6deHpp8P/earhKyIxxWGL9SYD53DACy+Yyl/hTGeq4SsiManT650Y22Us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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ef9f110>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=r\n",
      "y=deVauc(r,1.,1.,0)*2*np.pi*x\n",
      "y2=deVauc(r,1.,1.,1)*2*np.pi*x\n",
      "ihalf = np.where(r > 1.)[0].min()\n",
      "print 'half light radius correct?', x[ihalf], intT1d(x[:ihalf],y[:ihalf])/intT1d(x,y)\n",
      "print 'half light approx correct for LUV profile?',intT1d(x[:ihalf],y2[:ihalf])/intT1d(x,y2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "half light radius correct? 1.00230523808 0.499975031558\n",
        "half light approx correct for LUV profile? 0.52884049292\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "V = np.array([[80,0],[0,10]])\n",
      "# V = np.array([[80,0],[0,80]]) #circular profile\n",
      "Vinv = np.linalg.inv(V)\n",
      "if 0==1:\n",
      "  print V\n",
      "  print Vinv\n",
      "  print V*Vinv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## set up the model using the geometry of the image files.\n",
      "# https://www.sdss3.org/instruments/camera.php#Filters\n",
      "nx = 2048\n",
      "ny = 1361\n",
      "psize = 0.396 # arcseconds per pixel.\n",
      "\n",
      "# coordinates of center of pixels\n",
      "x = (np.arange(0,nx,1)+0.5)*psize\n",
      "y = (np.arange(0,ny,1)+0.5)*psize\n",
      "\n",
      "xM, yM = np.meshgrid(x,y,indexing='xy')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 2048*1361"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print x[-10:]\n",
      "print y[-10:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 807.246  807.642  808.038  808.434  808.83   809.226  809.622  810.018\n",
        "  810.414  810.81 ]\n",
        "[ 535.194  535.59   535.986  536.382  536.778  537.174  537.57   537.966\n",
        "  538.362  538.758]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = np.array([100,300])\n",
      "## test with a fat Gaussian that spans many pixels.\n",
      "I = N(xM,yM,m,Vinv)\n",
      "# check -- is the Gaussian profile normalized?\n",
      "parea = psize**2\n",
      "print 'should sum to 1.  Error:',(I[:,:].flatten()).sum()*parea-1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "should sum to 1.  Error: -3.46389583683e-14\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.matshow(I,origin='lower',extent = [x.min(),x.max(),y.min(),y.max()],interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.image.AxesImage at 0x10f075d50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10f0361d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mysize=1\n",
      "xx = np.where((np.fabs(xM - m[0]) < V[0,0]**0.5*mysize) & (np.fabs(yM - m[1]) < V[1,1]**0.5*mysize))\n",
      "extent = max(xx[0].max()-xx[0].min(),xx[1].max()-xx[1].min())\n",
      "print extent\n",
      "xcen = int(xx[0].mean())\n",
      "ycen = int(xx[1].mean())\n",
      "\n",
      "## zoom\n",
      "#plt.matshow(I[xx[0].min():xx[0].max()+1,xx[1].min():xx[1].max()+1],origin='lower',extent = [x.min(),x.max(),y.min(),y.max()])\n",
      "## zoom, keeping aspect ratio.\n",
      "#myextent = xM[\n",
      "plt.matshow(I[xcen-extent/2:xcen+extent/2,ycen-extent/2:ycen+extent/2],origin='lower',interpolation='nearest')#extent = [xM[xx[0]].min(),xM[xx[0]].max(),yM[xx[1]].min(),yM[xx[1]].max()])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "44\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<matplotlib.image.AxesImage at 0x10f19d8d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jPM0ZIS97frOLktdPzaCbiH0NYvNSpF3sTraqLUD7WFjS/tSu8Dfw+dGw82Nsb4scLek4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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10efe21d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Repesenting PSF as a single Gaussian K=1, simplify eq 22 to:\n",
      "\n",
      "$$I = \\displaystyle \\sum^{M_{dev}}_{m=1}a_m^{dev} N(x-m,V)$$\n",
      "The m inside the Gaussian (mean) is different from the m-components we are summing over."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mdev6 = {0.01308: 0.00263, 0.12425: 0.01202,0.63551: 0.04031,2.22560: 0.12128,5.63989: 0.36229,9.81523: 1.23604}\n",
      "# check sum as 18.454 as in Table 1 \n",
      "sum(mdev6.keys())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "18.45356"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = np.linspace(0,8)\n",
      "sig = 2\n",
      "mu=0\n",
      "N= 1./(sig*np.sqrt(2*np.pi))*np.exp(-(r-mu)**2/(2*sig**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 157,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1288ea550>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1288e2ad0>"
       ]
      }
     ],
     "prompt_number": 157
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def N_1d(r,mu,sig):\n",
      "    # sig = std_dev = sqrt(v) (just the scalar given in the table, nothing needs to be done to it)\n",
      "    mu=0\n",
      "    return 1./(sig*np.sqrt(2*np.pi))*np.exp(-(r-mu)**2/(2*sig**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def Iconv_1d(r, mdev):\n",
      "#     I_conv = numpy.zeros((50,))\n",
      "    I_conv = np.zeros_like(r)\n",
      "    for a in mdev.keys():\n",
      "        sig =mdev[a]\n",
      "#         r = np.linspace(0,8)\n",
      "        I_conv += a*N_1d(r,0,sig)\n",
      "    return I_conv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plt.plot(Iconv_1d(mdev6))\n",
      "r = np.linspace(0,8)\n",
      "print len(r)\n",
      "# plt.plot(r,Iconv_1d(r,mdev6))\n",
      "plt.loglog(r,Iconv_1d(r,mdev6))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "50\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 137,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1258c9bd0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x126b1e850>"
       ]
      }
     ],
     "prompt_number": 137
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plt.plot(Iconv_1d(mdev6))\n",
      "r = np.linspace(0,10,100000)\n",
      "print len(r)\n",
      "# plt.plot(r,Iconv_1d(r,mdev6))\n",
      "plt.loglog(r,Iconv_1d(r,mdev6))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 140,
       "text": [
        "[<matplotlib.lines.Line2D at 0x127711a50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12775c2d0>"
       ]
      }
     ],
     "prompt_number": 140
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r=10**np.arange(0,1.676,0.001)\n",
      "plt.loglog(r,Iconv_1d(r,mdev6))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 132,
       "text": [
        "[<matplotlib.lines.Line2D at 0x12690d6d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x126bc5890>"
       ]
      }
     ],
     "prompt_number": 132
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mdev8 = {0.00262:0.00113, 0.02500:0.00475,0.13413:0.01462,0.51326:0.03930,1.52005:0.09926,3.56204:0.24699,6.44845:0.63883,8.10105:1.92560}\n",
      "mdev10={0.00139:0.00087, 0.00941:0.00296,0.04441:0.00792,0.16162:0.01902,0.48121:0.04289,1.20357:0.09351,2.54182:0.20168,4.46441:0.44126,6.22820:1.01833,6.15393:2.74555}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 165
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# r=10**np.arange(-3,2,0.001)\n",
      "r=10**np.linspace(-3,1,5000)\n",
      "plt.loglog(r,deVauc(r,1.,1.,0),'b')\n",
      "plt.loglog(r,deVauc(r,1.,1.,1),'g')\n",
      "plt.loglog(r,Iconv_1d(r,mdev6),'r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 181,
       "text": [
        "[<matplotlib.lines.Line2D at 0x129a38650>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tYvlq1CoQEbHOyJGwcWPId6O+jEREIt3Ike3SQtCIaSIika66Grp3hxMnICmp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\niESY/w/uvALXDZF1SgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1297e3490>"
       ]
      }
     ],
     "prompt_number": 181
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# r=10**np.arange(-3,2,0.001)\n",
      "r=10**np.linspace(-3,1,5000)\n",
      "# print len(r)\n",
      "# plt.loglog(r,deVauc(r,1.,1.,0),'b')\n",
      "plt.loglog(r,deVauc(r,1.,1.,0),'b')\n",
      "plt.loglog(r,deVauc(r,1.,1.,1),'g')\n",
      "# plt.loglog(r,Iconv_1d(r,mdev6),'r')\n",
      "# plt.loglog(r,Iconv_1d(r,mdev8),'c')\n",
      "plt.loglog(r,Iconv_1d(r,mdev10),'m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 182,
       "text": [
        "[<matplotlib.lines.Line2D at 0x129b04c50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wjPscfqPg7z0K/t7VEYNVQ+kK/i3bHyj/r7emm1Aq8D6Q7t6eBowF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x129a626d0>"
       ]
      }
     ],
     "prompt_number": 182
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r=10**np.linspace(-3,1,5000)\n",
      "plt.loglog(r,Iconv_1d(r,mdev6),'r')\n",
      "plt.loglog(r,Iconv_1d(r,mdev8),'c')\n",
      "plt.loglog(r,Iconv_1d(r,mdev10),'m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 186,
       "text": [
        "[<matplotlib.lines.Line2D at 0x129e5ea50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RXDBzpgKCiIgAM2bAnj0prUIBQUQkF0yfroAgIiLYI4T3309pFQoIIiK5QCME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\nfPbCpdq+BZUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x129da9e50>"
       ]
      }
     ],
     "prompt_number": 186
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "--------2D stuff:\n",
      "Doing a 1D plot above to check instead------------\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# V = np.array([[0.,0.],[0.,0.]])\n",
      "def Iconv(mdev):\n",
      "    I_conv = numpy.zeros((1361, 2048))\n",
      "    for a in mdev.keys():\n",
      "        v=mdev[a]\n",
      "        m = np.array([100,300])\n",
      "        v_inv = np.linalg.inv(np.array([[v**2,0],[0,v**2]]))\n",
      "        I_conv += a*N(xM,yM,m,v_inv)\n",
      "    return I_conv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plotI(data):\n",
      "    mysize=1\n",
      "    V = np.array([[5.,0.],[0., 5.]]) \n",
      "    xx = np.where((np.fabs(xM - m[0]) < V[0,0]**0.5*mysize) & (np.fabs(yM - m[1]) < V[1,1]**0.5*mysize))\n",
      "    extent = max(xx[0].max()-xx[0].min(),xx[1].max()-xx[1].min())\n",
      "    xcen = int(xx[0].mean())\n",
      "    ycen = int(xx[1].mean())\n",
      "    plt.matshow(data[xcen-extent/2:xcen+extent/2,ycen-extent/2:ycen+extent/2],origin='lower',interpolation='nearest')#extent = [xM[xx[0]].min(),xM[xx[0]].max(),yM[xx[1]].min(),yM[xx[1]].max()])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I_conv= Iconv(mdev6)\n",
      "plotI(I_conv)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAPYAAAD7CAYAAABZjGkWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nh+1I6twePPVTkiRJkiRJkrSo/RdjuhCXxm5KNQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cdb3210>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mdev8 = {0.00262:0.00113, 0.02500:0.00475,0.13413:0.01462,0.51326:0.03930,1.52005:0.09926,3.56204:0.24699,6.44845:0.63883,8.10105:1.92560}\n",
      "I_conv8= Iconv(mdev8)\n",
      "plotI(I_conv8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAPYAAAD7CAYAAABZjGkWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cf07d90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mdev10={0.00139:0.00087, 0.00941:0.00296,0.04441:0.00792,0.16162:0.01902,0.48121:0.04289,1.20357:0.09351,2.54182:0.20168,4.46441:0.44126,6.22820:1.01833,6.15393:2.74555}\n",
      "I_conv10= Iconv(mdev10)\n",
      "plotI(I_conv10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAPYAAAD7CAYAAABZjGkWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x121788790>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Look very simmilar but not identical by element-wise comparison\n",
      "print np.array_equal(I_conv,I_conv8) \n",
      "print np.array_equal(I_conv8,I_conv10) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "False\n",
        "False\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I_conv.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "(1361, 2048)"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = np.array([100,300])\n",
      "m[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "100"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "See devPlot.py for I-r plot (linear and log scaled)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n=0\n",
      "rlist = []\n",
      "Iconvlst = []\n",
      "m = np.array([100,300]) #center\n",
      "# too large can not run on ipynb\n",
      "for i in arange(I_conv.shape[0]-1):\n",
      "    for j in arange(I_conv.shape[1]-1):\n",
      "#         print(i,j)\n",
      "        r = np.sqrt(abs(i-m[0])**2+abs(j-m[1])**2) #treating center as origin\n",
      "#         print I_conv[i][j]\n",
      "        rlist.append(r)\n",
      "        Iconvlst.append(I_conv[i][j])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# print rlist\n",
      "# print Iconvlst"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(rlist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "2783920"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(Iconvlst)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "2783920"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r=10**np.arange(-3,2,0.001)\n",
      "print len(r)\n",
      "plt.figure()\n",
      "# plt.loglog(I_conv,'b')\n",
      "# plt.show()\n",
      "plt.loglog(rlist,Iconvlst)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5000\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1272ca590>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x127088610>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.nonzero(I_conv.flatten())\n",
      "#truncating all the zero values so that this can be plotted on loglog scale, otherwise -inf error\n",
      "I_conv = [I_conv.flatten()[i] for i in np.nonzero(I_conv.flatten())] \n",
      "# np.where(I_conv>0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(I_conv)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[array([  4.94065646e-323,   4.94065646e-323,   1.43279037e-322, ...,\n",
        "         2.42092166e-322,   9.88131292e-323,   4.94065646e-323])]\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=plt.plot(I_conv,'o'); #semicolon supress matplotlib output (direct output to vars)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ArBKvIUkHoh5gdrNefBzwU2AGMAZ4GDipWcVIkqrz68AG4CngyibXIkmSJGl/pgBrgfXA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\nJEmSJEmSJO3X/wPQGPWShoPEVAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c594150>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plt.loglog(I_conv,'o') # can not loglog since negative exp\n",
      "# a = plt.plot(log(I_conv),'o')#Stilll a delta function"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Now generate a model image and do the fitting exercise.  Eventually the model should be deVauc convolved with Gaussian, but we'll skip that step for now and just use a Gaussian as the model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## work in progress -- want to finish Doris?  We want to evaluate the model (deVauc convolved with Gaussian PSF) on a fine grid, and then sum up the fine pixels that contribute to \n",
      "## the pixels of SDSS camera size.  Given some reasonable parameters for galaxy size (re = 1.0, 1.5, 2.0) and PSF values (take some percentiles from the galaxy files I give you), figure out\n",
      "## how fine the fine grid needs to be.\n",
      "\n",
      "## truncate the fit 5*sigma away from the center.\n",
      "fitsigma = 5.\n",
      "tgal = 1.5 ## rough typical size of a galaxy, in arcseconds.\n",
      "nsub = 10 ## how fine should we subsample the model?  Let's test this empirically for realistic values of p.\n",
      "pfine = psize/float(nsub)\n",
      "\n",
      "nbig = fitsigma*tgal/psize # number of native size pixels.\n",
      "nsmall = nbig*nsub # number of small pixels we sum over to get model in the big pixel.\n",
      "\n",
      "## make mbig the location of the center of the source within the central pixel.\n",
      "mbig = np.array([0.2,0.3])\n",
      "assert (np.fabs(mbig) < 0.99).all()\n",
      "xbig = \n",
      "\n",
      "xf = np.arange(0,nsmall+0.5,1)\n",
      "yf = np.arange(0,nsmall+0.5,1)\n",
      "assert len(xf) == nsmall\n",
      "xbig = np.arange(\n",
      "\n",
      "## width of Gaussian is tg\n",
      "mg = np.array([0.,0.])\n",
      "Vg = np.array([[tgal**2,0],[0,tgal**2]])\n",
      "Vginv = np.linalg.inv(Vg)\n",
      "\n",
      "# coordinates of center of pixels\n",
      "xf = (np.arange(-fitsigma*tgal/pfine+mg[0]+0.5,fitsigma*tgal/pfine+mg[0]-0.4,1))*pfine\n",
      "yf = (np.arange(-fitsigma*tgal/pfine+mg[1]+0.5,fitsigma*tgal/pfine+mg[1]-0.4,1))*pfine\n",
      "\n",
      "xMf, yMf = np.meshgrid(xf,yf,indexing='xy')\n",
      "If = N(xMf,yMf,mg,Vginv)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "SyntaxError",
       "evalue": "invalid syntax (<ipython-input-20-ca0387d0fc62>, line 17)",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-20-ca0387d0fc62>\"\u001b[0;36m, line \u001b[0;32m17\u001b[0m\n\u001b[0;31m    xbig =\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(If,origin='lower',interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## What's next??\n",
      "\n",
      "I wrote some notes here: \n",
      "\n",
      "/home/bareid/imagingsys/notes1 on riemann.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}