/ipython_notebooks/2015_10/2015_10_26_Distance_effects.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Author**: J W Debelius<br>\n",
    "**Date**: 26 October 2015<br>\n",
    "**Virtualenv**: power\\_play"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import pandas as pd\n",
    "import skbio\n",
    "\n",
    "import absloute_power.distance as dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm going to simulate distances between locations which should be significantly different when the two categories are compared, apply a PERMANOVA and ANOSIM (cites needed), and then determine how to better evaluate effect size on microbiome data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def simulate_distance(num_samps, within1=[0.01, 0.25], within2, between, var):\n",
    "    # Simulates the mapping file\n",
    "    grouping = np.random.binomial(1, 0.5, (num_samps))\n",
    "    \n",
    "    # Determines the number of observations in each group\n",
    "    num1 = grouping.sum()\n",
    "    num0 = num_samps - num1\n",
    "    \n",
    "    # Simulates the "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def simulate_poisson_distance(length, scale, param):\n",
    "    return np.random.poisson(param, length) * scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 3, 2, 4])"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.poisson(3, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "locations = np.random.binomial(1, 0.5, (30))\n",
    "locations.sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "within0 = 0.15\n",
    "within1 = 0.2\n",
    "between = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "locations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# num0 = np.sum(locations == 0)\n",
    "# num1 = np.sum(locations == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "in0 = np.random.uniform(0, 1, np.square(num0 - 1)/2)*within0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num0 = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vec [1]\n",
      "pos1 [1]\n",
      "pos2 [0]\n",
      "[[ 0.  1.]\n",
      " [ 1.  0.]]\n"
     ]
    }
   ],
   "source": [
    "num0 = 2\n",
    "vec = np.arange((np.square(num0)-1)/2) + 1\n",
    "dm0 = np.zeros((num0, num0))\n",
    "print 'vec', vec\n",
    "\n",
    "pos_count = 0\n",
    "dm0 = np.zeros((num0, num0))\n",
    "for i in xrange(num0-1):\n",
    "    pos1 = np.arange(i+1, num0)\n",
    "    print 'pos1', pos1\n",
    "    pos2 = np.arange(i, num0-1) + pos_count\n",
    "    print 'pos2', pos2\n",
    "    pos_count = pos_count + len(pos2) - 1\n",
    "    dm0[i, pos1] = vec[pos2]\n",
    "    dm0[pos1, i] = vec[pos2]\n",
    "print dm0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vec [1 2 3 4]\n",
      "pos1 [1 2]\n",
      "pos2 [0 1]\n",
      "pos1 [2]\n",
      "pos2 [2]\n",
      "[[ 0.  1.  2.]\n",
      " [ 1.  0.  3.]\n",
      " [ 2.  3.  0.]]\n"
     ]
    }
   ],
   "source": [
    "num0 = 3\n",
    "vec = np.arange((np.square(num0)-1)/2) + 1\n",
    "dm0 = np.zeros((num0, num0))\n",
    "print 'vec', vec\n",
    "\n",
    "pos_count = 0\n",
    "dm0 = np.zeros((num0, num0))\n",
    "for i in xrange(num0-1):\n",
    "    pos1 = np.arange(i+1, num0)\n",
    "    print 'pos1', pos1\n",
    "    pos2 = np.arange(i, num0-1) + pos_count\n",
    "    print 'pos2', pos2\n",
    "    pos_count = pos_count + len(pos2) - 1\n",
    "    dm0[i, pos1] = vec[pos2]\n",
    "    dm0[pos1, i] = vec[pos2]\n",
    "print dm0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vec [1 2 3 4 5 6 7]\n",
      "[[ 0.  1.  2.  3.]\n",
      " [ 1.  0.  4.  5.]\n",
      " [ 2.  4.  0.  6.]\n",
      " [ 3.  5.  6.  0.]]\n"
     ]
    }
   ],
   "source": [
    "num0 = 4\n",
    "vec = np.arange((np.square(num0)-1)/2) + 1\n",
    "dm0 = np.zeros((num0, num0))\n",
    "print 'vec', vec\n",
    "\n",
    "pos_count = 0\n",
    "dm0 = np.zeros((num0, num0))\n",
    "for i in xrange(num0-1):\n",
    "    pos1 = np.arange(i+1, num0)\n",
    "    pos2 = np.arange(i, num0-1) + pos_count\n",
    "    pos_count = pos_count + len(pos2) - 1\n",
    "    dm0[i, pos1] = vec[pos2]\n",
    "    dm0[pos1, i] = vec[pos2]\n",
    "print dm0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def convert_to_dm(length, vec):\n",
    "    \"\"\"Converts a condensed distance matrix to a table format\"\"\"\n",
    "    # Stacks the data\n",
    "    vec = np.hstack(vec)\n",
    "    # Creates the output matrix\n",
    "    dm = np.zeros((length, length))\n",
    "    # Adds a counter to watch the positon\n",
    "    pos_count = 0\n",
    "    \n",
    "    # Populates the distance matrix\n",
    "    for idx in xrange(length-1):\n",
    "        pos1 = np.arange(idx+1, length)\n",
    "        pos2 = np.arange(idx, length-1) + pos_count\n",
    "        pos_count = pos_count + len(pos2) - 1\n",
    "        dm[idx, pos1] = vec[pos2]\n",
    "        dm[pos1, idx] = vec[pos2]\n",
    "    \n",
    "    return dm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, I need to be able to simulate distance matrix vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num0 = 4\n",
    "num1 = 4\n",
    "num_d = num0 * num1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11 12 13 14 15 16]\n",
      "[21 22 23 24 25 26]\n",
      "[101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116]\n"
     ]
    }
   ],
   "source": [
    "vec0 = np.arange(0, (num0/2)*(num0-1)) + 11\n",
    "vec1 = np.arange(0, (num1/2)*(num1-1)) + 21\n",
    "veci = np.arange(0, num0 * num1) + 101\n",
    "print vec0\n",
    "print vec1\n",
    "print veci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vec0 = np.array([1, 2, 3])\n",
    "vec1 = np.array([10, 20, 30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dm0 = convert_to_dm(3, vec0)\n",
    "dm1 = convert_to_dm(3, vec1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  1.  2.]\n",
      " [ 1.  0.  3.]\n",
      " [ 2.  3.  0.]]\n",
      "[[  0.  10.  20.]\n",
      " [ 10.   0.  30.]\n",
      " [ 20.  30.   0.]]\n"
     ]
    }
   ],
   "source": [
    "print dm0\n",
    "print dm1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11, 21, 31],\n",
       "       [12, 22, 32],\n",
       "       [13, 23, 33]])"
      ]
     },
     "execution_count": 331,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dmi = np.array([[11, 21, 31],\n",
    "                [12, 22, 32],\n",
    "                [13, 23, 33],\n",
    "                ])\n",
    "\n",
    "dmi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[13, 23, 33],\n",
       "       [12, 22, 32],\n",
       "       [11, 21, 31]])"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dmi[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   1.,   2.,  11.,  21.,  31.],\n",
       "       [  1.,   0.,   3.,  12.,  22.,  32.],\n",
       "       [  2.,   3.,   0.,  13.,  23.,  33.]])"
      ]
     },
     "execution_count": 332,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack([np.hstack([dm0, dmi]),\n",
    "          [np.hstack([])]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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