We are all a big family.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We all are from the same big family"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>$('.mytoggle').remove();$('.code_cell').prepend(\"<button style='width:32px' class='mytoggle' onclick='f(this)'>&gt;</button>\");function f(e){$(e).parent().find('.input').toggle()}</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display, HTML\n",
    "# Hide/Show input area\n",
    "display(HTML(\n",
    "\"<script>$('.mytoggle').remove();$('.code_cell').prepend(\\\"<button style='width:32px' class='mytoggle' onclick=\\'f(this)\\'>&gt;</button>\\\");\\\n",
    "function f(e){$(e).parent().find('.input').toggle()}</script>\"\n",
    "))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np;\n",
    "import matplotlib.pyplot as plt;\n",
    "\n",
    "import scipy\n",
    "import scipy.cluster.hierarchy as sch\n",
    "from scipy import linalg, stats\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "def rnorm(n,u,s):\n",
    "    return np.random.standard_normal(n)*s+u\n",
    "\n",
    "def imshowcluster(D):\n",
    "    # Based on http://stackoverflow.com/questions/2982929/plotting-results-of-hierarchical-clustering-ontop-of-a-matrix-of-data-in-python\n",
    "    fig = plt.figure()\n",
    "\n",
    "    # Compute and plot dendrogram.\n",
    "    axdendro1 = fig.add_axes([0.0,0.2,0.19,0.8])\n",
    "    Y1 = sch.linkage(D, method='centroid')\n",
    "    Z1 = sch.dendrogram(Y1, orientation='right')\n",
    "    axdendro1.set_xticks([])\n",
    "    axdendro1.set_yticks([])\n",
    "\n",
    "    # Compute and plot dendrogram.\n",
    "    axdendro2 = fig.add_axes([0.2,0.00,0.6,0.19])\n",
    "    Y2 = sch.linkage(D.transpose(), method='centroid')\n",
    "    Z2 = sch.dendrogram(Y2, orientation='bottom')\n",
    "    axdendro2.set_xticks([])\n",
    "    axdendro2.set_yticks([])\n",
    "\n",
    "    # Plot distance matrix.\n",
    "    axmatrix = fig.add_axes([0.2,0.2,0.6,0.8])\n",
    "    idx1 = Z1['leaves']\n",
    "    idx2 = Z2['leaves']\n",
    "    D = D[idx1,:]\n",
    "    D = D[:,idx2]\n",
    "    im = axmatrix.matshow(D, aspect='auto', origin='lower')\n",
    "    axmatrix.set_xticks([])\n",
    "    axmatrix.set_yticks([])\n",
    "\n",
    "    # Plot colorbar.\n",
    "    axcolor = fig.add_axes([0.91,0.1,0.02,0.8])\n",
    "    plt.colorbar(im, cax=axcolor)\n",
    "\n",
    "    # Add axes labels\n",
    "    axmatrix.set_xticks(range(D.shape[0]))\n",
    "    axmatrix.set_xticklabels(idx1, minor=False)\n",
    "    axmatrix.xaxis.set_label_position('bottom')\n",
    "    axmatrix.xaxis.tick_bottom()\n",
    "\n",
    "    plt.xticks(rotation=-90, fontsize=4)\n",
    "\n",
    "    axmatrix.set_yticks(range(D.shape[1]))\n",
    "    axmatrix.set_yticklabels(idx2, minor=False)\n",
    "    axmatrix.yaxis.set_label_position('right')\n",
    "    axmatrix.yaxis.tick_right()\n",
    "    # Display and save figure.\n",
    "    #fig.savefig('dendrogram.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Falconer_h2(pmz1,pmz2,pdz1,pdz2):\n",
    "    # Falconer's method\n",
    "    rmz=np.corrcoef(pmz1,pmz2)[0,1];\n",
    "    rdz=np.corrcoef(pdz1,pdz2)[0,1];\n",
    "    A=2*(rmz-rdz);\n",
    "    C=2*rdz-rmz;\n",
    "    E=1-A-C;\n",
    "    return A,C,E;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def HasemanElstonRegression_h2(K,P,M):\n",
    "    # h2 is computed using a subsample of M pairs out of the total using\n",
    "    # Haseman & Elston regression. In the case of unrelated subjects,\n",
    "    # Schaum & Purcell's weighted Haseman & Elston regression\n",
    "    # is equivalent to cross-product H&E regression.\n",
    "    # In the original formulation the entries Kij are a proportion of\n",
    "    # IBD/IBS -- from 0 to 1, here they are correlations -- from -1 to 1.\n",
    "    N=P.shape[0];\n",
    "    zz=np.zeros(M);\n",
    "    a=np.zeros(M);\n",
    "    k=0;\n",
    "    for k in range(M):\n",
    "        i=int(N*np.random.rand());\n",
    "        j=int(N*np.random.rand());\n",
    "        if(i==j):\n",
    "            j=int(N*np.random.rand());\n",
    "        zz[k]=P[i]*P[j];\n",
    "        a[k]=K[i,j];\n",
    "    slope, intercept, r_value, p_value, std_err = stats.linregress(a,zz);\n",
    "    h2=slope/np.var(P);\n",
    "\n",
    "    return intercept,slope,h2,p_value;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plotHasemanElstonRegression(K,P,M):\n",
    "    N=P.shape[0];\n",
    "    zz=np.zeros(M);\n",
    "    a=np.zeros(M);\n",
    "    k=0;\n",
    "    for k in range(M):\n",
    "        i=int(N*np.random.rand());\n",
    "        j=int(N*np.random.rand());\n",
    "        if(i==j):\n",
    "            j=int(N*np.random.rand());\n",
    "        zz[k]=P[i]*P[j];\n",
    "        a[k]=K[i,j];\n",
    "    plt.scatter(a,zz,alpha=0.01);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#First approach\n",
    "##Mixing ancestral genomes\n",
    "\n",
    "###Production of a population of related subjects and their phenotype\n",
    "\n",
    "Suppose there are $Ne$ independent ancestors. Each ancestor $i$ has a genome that produces a phenotypic value $Pe_i$ with a certain heritability $h^2$.\n",
    "\n",
    "The observed population consists of $N$ subjects. The genome of each of these subjects is a random mix of the ancestral genomes. The phenotype $P_i$ of each subject is then a weighted mix of the ancestor's phenotypes.\n",
    "\n",
    "The degree of genetic relatedness of a pair of subjects reflects how much their proportions of ancestral genome are similar. All degrees of genetic relatedness among subjects are stored in the kinship matrix $K$.\n",
    "\n",
    "We compute the genotypes of the subjects in the population by mixing the ancestral genomes with random proportions. We draw the proportion of ancestral genome $i$ from a uniform distribution, and the total proportions are normalised so that they add to 1.\n",
    "\n",
    "Based on these genomes we compute the kinship matrix by comparing the similarity of the ancestral genome proportions of each pair of subjects. We compute the absolute difference in the proportions of ancestral genomes. The minimum value of the difference is 0 when both subjects have exactly the same proportions, and 2 in the case where both both proportions are completely different. We transform these difference so that they go from 0 for completely different genomes, to 1 in the case of identical genomes. The degree of relatedness is then:\n",
    "\n",
    "$K_{ij}=1-\\frac {\\sum |G_i-Gj|} 2$.\n",
    "\n",
    "Using each subject's genome proportions, compute their phenotype as\n",
    "\n",
    "$P=G \\cdot P_e$.\n",
    "\n",
    "Each row $i$ of $G$ represent the ancestral genome proportions of subject $i$, and $P_e$ is the phenotype associated to each of the ancestral genomes.\n",
    "\n",
    "###Estimation of $h^2$ from a population of related subjects\n",
    "\n",
    "Now we aim at recovering $h^2$ from the observed phenotypes and kinship matrix generated before. From Visscher et al (2014): For unrelated individuals, where the phenotypic correlation between individuals is small, mixed linear model analysis using the REML approach is asymptotically equivalent to simple regression analysis of pairwise phenotypic similarity/difference on pairwise genetic similarity, as measured by identity-by-descent (IBD) or identity-by-state (IBS) at genome-wide markers (Haseman-Elston regression papers: 17–20). Under such circumstance, a regression of the cross-product of the phenotypes is equivalent to using both the squared difference and squared sum of the pairwise phenotypes, and using the cross- product is equivalent to using maximum likelihood [19]. The model for the regression-based analysis can be written as:\n",
    "\n",
    "$z_{ij}=\\mu+b A_{ij} + \\epsilon_{ij}$.\n",
    "\n",
    "Here $z_{ij}=y_i y_j$, the product of the phenotypes each with mean 0 and variance 1, $A_{ij}$ is the $ij$-th element of the genetic relationship matrix, and $\\epsilon_{ij}$ is the residual of the regression. The coefficient $b$ is equivalent to $\\sigma_G^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: 5797.75585728\n",
      "slope: 5115.83145161\n",
      "h2: 2.60393182451\n",
      "p_value: 0.000518256666994\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEACAYAAACd2SCPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEmSgv8HhT1Zm01kUDsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c00b40d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=1000; # observed subjects\n",
    "Ne=1000; # unobserved independent ancestors\n",
    "rng=np.random.RandomState(123); # init random seed\n",
    "\n",
    "# Draw random phenotypic values for each ancestor\n",
    "Pe=rng.randn(Ne);\n",
    "\n",
    "# First part: Make N subjects by randomly mixing the Ne independent genomes\n",
    "# 1. make a vector with the mixing proportions: the genomes\n",
    "G=np.zeros((N,Ne)); # their non-observed relative proportion of each of the ancestors\n",
    "for i in range(0,N):\n",
    "    prop=np.random.uniform(0,1,Ne);\n",
    "    G[i,:]=prop/np.sum(prop);\n",
    "\n",
    "# 2. compute the kinship matrix K\n",
    "K=np.zeros((N,N)); # the real kinship matrix, based on the non-observed proportions of independent ancestral genome\n",
    "for i in range(0,N):\n",
    "    for j in range(i,N):\n",
    "        K[i,j]=1-np.sum(np.abs(G[i]-G[j]))/2.0;\n",
    "        K[j,i]=K[i,j];\n",
    "mu=0;#np.mean(K.flatten());\n",
    "sigma=1;#np.std(K.flatten());\n",
    "K=(K-mu)/sigma;\n",
    "\n",
    "plt.figure();\n",
    "plt.hist(K.flatten(),50);\n",
    "\n",
    "# 3. compute the genomic influence on the phenotype\n",
    "Pg=G.dot(Pe);\n",
    "\n",
    "# 4. add individual randomness to produce the observed phenotype with heritability h2\n",
    "h2t=0.8;\n",
    "P=h2t*Pg/np.var(Pg)+(1-h2t)*rng.randn(N);\n",
    "\n",
    "M=100000;\n",
    "a,b,h2,p_value=HasemanElstonRegression_h2(K,P,M);\n",
    "print \"intercept:\",a;\n",
    "print \"slope:\",b;\n",
    "print \"h2:\",h2;\n",
    "print \"p_value:\",p_value;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEACAYAAAByG0uxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110db67d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotHasemanElstonRegression(K,P,M);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEACAYAAACd2SCPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSRqU/wPd9BapqqHZrAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c03ba410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(G.flatten(),50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#Second approach\n",
    "##A phenotype in a population of unrelated individuals\n",
    "The observed subjects result from a combination of a smaller number of uncorrelated ancestors\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: -0.000171856628687\n",
      "slope: 0.635920530648\n",
      "h2: 0.953246695457\n",
      "p_value: 0.0\n"
     ]
    }
   ],
   "source": [
    "N=10000; # observed subjects\n",
    "Ne=500; # unobserved independent ancestors\n",
    "rng=np.random.RandomState(123); # init random seed\n",
    "\n",
    "# Draw random phenotypic values for each ancestor\n",
    "Pe=rng.randn(Ne);\n",
    "\n",
    "# Create N observed subjects as random combinations of Ne uncorrelated ancestors\n",
    "G=rng.randn(N,Ne);\n",
    "for i in range(N):\n",
    "    G[i,:]/=linalg.norm(G[i,:]);\n",
    "\n",
    "# Compute genetic part of the N observed phenotypes\n",
    "# and add noise to produce a target heritability h2t\n",
    "Pg=G.dot(Pe);\n",
    "h2t=0.8;\n",
    "P=h2t*Pg/np.var(Pg)+(1-h2t)*rng.randn(N);\n",
    "\n",
    "# Kinship matrix\n",
    "K=np.corrcoef(G);\n",
    "\n",
    "M=10000000;\n",
    "a,b,h2,p_value=HasemanElstonRegression_h2(K,P,M);\n",
    "print \"intercept:\",a;\n",
    "print \"slope:\",b;\n",
    "print \"h2:\",h2;\n",
    "print \"p_value:\",p_value;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c44c4e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(K[np.triu_indices(100)],100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Monozygotic and dizygotic twins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: 3.33321608358e-05\n",
      "slope: 0.63906394837\n",
      "h2: 0.898342513078\n",
      "p_value: 0.0\n",
      "A: 0.919888345426\n",
      "C: 0.0217870569628\n",
      "E: 0.0583245976116\n"
     ]
    }
   ],
   "source": [
    "N=10000; # observed subjects\n",
    "Ne=1000; # unobserved independent ancestors\n",
    "rng=np.random.RandomState(123); # init random seed\n",
    "\n",
    "# Draw random phenotypic values for each ancestor\n",
    "Pe=rng.randn(Ne);\n",
    "\n",
    "# Allocate memory for the genomes\n",
    "G=np.zeros((N,Ne));\n",
    "\n",
    "# Create N/4 pairs of monozygotic twins\n",
    "# MZ twins share the same combination of ancestral genome\n",
    "Gmz=rng.randn(N/4,Ne);\n",
    "for i in range(N/4):\n",
    "    G[2*i,:]=Gmz[i,:];\n",
    "    G[2*i+1,:]=Gmz[i,:];\n",
    "\n",
    "# Create N/4 pairs of dizygotic twins\n",
    "# DZ twins share half of the combination of ancestral genome\n",
    "Gdz=rng.randn(N/2,Ne);\n",
    "for i in range(0,N/2,2):\n",
    "    Gdz[i,:(Ne/2)]=Gdz[i+1,:(Ne/2)]\n",
    "G[N/2:,:]=Gdz;\n",
    "    \n",
    "# Normalize\n",
    "for i in range(N):\n",
    "    G[i,:]/=linalg.norm(G[i,:]);\n",
    "\n",
    "# Compute genetic part of the N observed phenotypes\n",
    "# and add noise to produce a target heritability h2t\n",
    "Pg=G.dot(Pe);\n",
    "h2t=0.8;\n",
    "P=h2t*Pg/np.var(Pg)+(1-h2t)*rng.randn(N);\n",
    "\n",
    "# Kinship matrix\n",
    "K=np.corrcoef(G);\n",
    "\n",
    "# Linear regression method using a subsample of all pairs of subjects\n",
    "M=10000000;\n",
    "a,b,h2,p_value=HasemanElstonRegression_h2(K,P,M);\n",
    "print \"intercept:\",intercept;\n",
    "print \"slope:\",slope;\n",
    "print \"h2:\",h2;\n",
    "print \"p_value:\",p_value;\n",
    "\n",
    "pmz1=P[range(0,N/2,2)]\n",
    "pmz2=P[range(1,N/2+1,2)]\n",
    "pdz1=P[range(N/2,N,2)];\n",
    "pdz2=P[range(N/2+1,N,2)];\n",
    "A,C,E=Falconer_h2(pmz1,pmz2,pdz1,pdz2);\n",
    "print \"A:\",A;\n",
    "print \"C:\",C;\n",
    "print \"E:\",E;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Correlated phenotypes in a population of unrelated individuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110403650>,\n",
       " <matplotlib.lines.Line2D at 0x1104038d0>,\n",
       " <matplotlib.lines.Line2D at 0x110403b10>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fde69d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAboAAAEuCAYAAAD4ANfQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSZIkSTn7fz86KOFrt7+8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105b767d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASEAAAD7CAYAAAAlzyLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fde6e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMA1bJQROLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10feee690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=1000; # number of subjects in the observed population\n",
    "Nr=9; # number of (correlated) phenotypes\n",
    "Ni=3; # number of independent effects\n",
    "rng = np.random.RandomState(123); # init random seed\n",
    "\n",
    "# 1. Create (correlated) phenotypes\n",
    "# Linear combination of Ni uncorrelated variables that produce the Nr correlated variables.\n",
    "# (combination vectors are of unitary norm)\n",
    "M=rng.randn(Nr,Ni);\n",
    "for i in range(Nr):\n",
    "    M[i,:]/=linalg.norm(M[i,:]);\n",
    "\n",
    "# Scale with random eigenvalues\n",
    "W=-np.sort(-np.abs(rng.randn(Ni)));\n",
    "M=M.dot(np.diag(W));\n",
    "\n",
    "# Random Ni values\n",
    "Pi=rng.randn(N,Ni);\n",
    "\n",
    "# Random Nr values produced by combining the independent Ni values\n",
    "# The Nr regions are correlated among them\n",
    "P=Pi.dot(M.T);\n",
    "m=np.corrcoef(P.T);\n",
    "plt.figure();\n",
    "#plt.imshow(m,interpolation=\"nearest\");\n",
    "imshowcluster(m);\n",
    "\n",
    "# 2. Try to guess M from P\n",
    "U,S,VT=linalg.svd(P,full_matrices=False)\n",
    "S=np.diag(S);\n",
    "SVT=S.dot(VT);\n",
    "M1=SVT[:Ni,:].T;\n",
    "\n",
    "plt.figure();\n",
    "plt.subplot(1,2,1);\n",
    "plt.imshow(M,interpolation=\"nearest\");\n",
    "plt.subplot(1,2,2);\n",
    "plt.imshow(M1,interpolation=\"nearest\");\n",
    "\n",
    "plt.figure();\n",
    "plt.subplot(1,2,1);\n",
    "plt.plot(M)\n",
    "plt.subplot(1,2,2);\n",
    "plt.plot(M1)\n",
    "\n",
    "#X_homo = X + sigma * rng.randn(N, Nr); # Adding homoscedastic noise\n",
    "#sigmas = sigma * rng.rand(Nr) + sigma / 2.0; # Adding heteroscedastic noise\n",
    "#X_hetero = X + rng.randn(N, Nr) * sigmas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}