docs/demo/tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python tutorial with SeqArray files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.ma as ma\n",
    "import PySeqArray as ps\n",
    "import pandas\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "import types\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Open an existing SeqArray file and display its structure. The dimensions of `sample.id` and `variant.id` tell you the total numbers of samples and variants, i.e., 1092 samples and 19,773 variants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File: /Users/sts/anaconda/lib/python3.6/site-packages/PySeqArray/data/1KG_phase1_release_v3_chr22.gds (1.1M)\n",
      "+    [  ] *\n",
      "|--+ description   [  ] *\n",
      "|--+ sample.id   { Str8 1092 LZMA_ra(10.5%), 914B } *\n",
      "|--+ variant.id   { Int32 19773 LZMA_ra(8.39%), 6.5K } *\n",
      "|--+ position   { Int32 19773 LZMA_ra(52.0%), 40.1K } *\n",
      "|--+ chromosome   { Str8 19773 LZMA_ra(0.28%), 166B } *\n",
      "|--+ allele   { Str8 19773 LZMA_ra(22.7%), 109.2K } *\n",
      "|--+ genotype   [  ] *\n",
      "|  |--+ data   { Bit2 19773x1092x2 LZMA_ra(8.17%), 861.8K } *\n",
      "|  |--+ extra.index   { Int32 0x3 LZMA_ra, 19B } *\n",
      "|  \\--+ extra   { Int16 0 LZMA_ra, 19B }\n",
      "|--+ phase   [  ]\n",
      "|  |--+ data   { Bit1 19773x1092 LZMA_ra(0.02%), 550B } *\n",
      "|  |--+ extra.index   { Int32 0x3 LZMA_ra, 19B } *\n",
      "|  \\--+ extra   { Bit1 0 LZMA_ra, 19B }\n",
      "|--+ annotation   [  ]\n",
      "|  |--+ id   { Str8 19773 LZMA_ra(35.2%), 75.2K } *\n",
      "|  |--+ qual   { Float32 19773 LZMA_ra(3.62%), 2.8K } *\n",
      "|  |--+ filter   { Int32,factor 19773 LZMA_ra(0.21%), 170B } *\n",
      "|  |--+ info   [  ]\n",
      "|  \\--+ format   [  ]\n",
      "\\--+ sample.annotation   [  ]\n",
      "   |--+ Family.ID   { Str8 1092 LZMA_ra(15.3%), 1.1K }\n",
      "   |--+ Population   { Str8 1092 LZMA_ra(5.08%), 222B }\n",
      "   |--+ Gender   { Str8 1092 LZMA_ra(5.85%), 386B }\n",
      "   \\--+ Ancestry   { Str8 1092 LZMA_ra(2.43%), 233B }\n"
     ]
    }
   ],
   "source": [
    "fn = ps.seqExample('1KG_phase1_release_v3_chr22.gds')\n",
    "f = ps.SeqArrayFile()\n",
    "f.open(fn)\n",
    "f.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Genotypic data and annotations are stored in an array-oriented manner, providing efficient data access using the Python programming language. `FilterSet()` and `GetData()` can be used together to retrieve data for a selected set of samples from a defined genomic region. `Apply()` applies a user-defined function to array margins of genotypes and annotations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['HG00096', 'HG00097', 'HG00099', ..., 'NA20819', 'NA20826',\n",
       "       'NA20828'], dtype=object)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampid = f.GetData('sample.id')\n",
    "sampid  # a list of sample IDs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    1,     2,     3, ..., 19771, 19772, 19773], dtype=int32)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "varid = f.GetData('variant.id')\n",
    "varid  # a list of variant IDs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 100.,  100.,  100., ...,  100.,  100.,  100.], dtype=float32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.GetData('annotation/qual')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['PASS', 'PASS', 'PASS', ..., 'PASS', 'PASS', 'PASS'], dtype=object)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.GetData('annotation/filter')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define a subset of samples and variants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f.FilterSet(sample_id = sampid[:4], variant_id = varid[:6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get data from the subset of variant data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['22', '22', '22', '22', '22', '22'], dtype=object)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.GetData('chromosome')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['A,G', 'G,A', 'G,T', 'C,T', 'G,A', 'G,A'], dtype=object)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.GetData('allele')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 4, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geno = f.GetData('genotype')\n",
    "geno.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 0],\n",
       "        [1, 0],\n",
       "        [1, 0],\n",
       "        [0, 1]],\n",
       "\n",
       "       [[0, 0],\n",
       "        [0, 1],\n",
       "        [0, 1],\n",
       "        [0, 0]],\n",
       "\n",
       "       [[0, 0],\n",
       "        [0, 0],\n",
       "        [0, 0],\n",
       "        [0, 0]],\n",
       "\n",
       "       [[0, 0],\n",
       "        [0, 0],\n",
       "        [0, 0],\n",
       "        [0, 0]],\n",
       "\n",
       "       [[0, 0],\n",
       "        [1, 0],\n",
       "        [0, 1],\n",
       "        [0, 0]],\n",
       "\n",
       "       [[0, 0],\n",
       "        [0, 0],\n",
       "        [0, 0],\n",
       "        [0, 0]]], dtype=uint8)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geno  # 0: the reference allele, 1: the first alternative allele, 255: missing value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 4)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dosage = f.GetData('$dosage')\n",
    "dosage.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 1, 1],\n",
       "       [2, 1, 1, 2],\n",
       "       [2, 2, 2, 2],\n",
       "       [2, 2, 2, 2],\n",
       "       [2, 1, 1, 2],\n",
       "       [2, 2, 2, 2]], dtype=uint8)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dosage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculation of Allele Frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f.FilterReset()  # reset the filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.69505495,  0.94322344,  0.99954212, ...,  0.99679487,\n",
       "        0.65842491,  0.91346154])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def CalcAF(geno):\n",
    "    gm = ma.masked_array(geno==0, mask=geno==255)  # create a masked array with missing genotypes\n",
    "    v = np.mean(gm, axis=(1,2))                    # gm is a 3D array\n",
    "    v.data[v.mask] = np.nan\n",
    "    return(v.data)\n",
    "\n",
    "af = f.Apply('genotype', CalcAF, asis='unlist')\n",
    "af"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f.FilterReset()  # reset the filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sts/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:5: RuntimeWarning: invalid value encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 39.60517218,  16.51956609,   5.18983317, ...,   0.52165852,\n",
       "         0.51818269,   0.55006929])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pca(val, geno):\n",
    "    gm = ma.masked_array(geno, geno==255)    # create a masked array with missing genotypes\n",
    "    p = np.mean(gm, axis=1).data * 0.5       # allele frequencies (a vector)\n",
    "    g = np.array(geno, 'double')\n",
    "    g = (g.transpose() - 2*p) / np.sqrt(p * (1 - p))  # normalized by allele frequency\n",
    "    g[np.isnan(g)] = 0                                # correct missing values\n",
    "    g[gm.mask.transpose()] = 0\n",
    "    val.cov = val.cov + np.matmul(g, g.transpose())   # update the cov matrix\n",
    "\n",
    "\n",
    "s = types.SimpleNamespace(cov=0)\n",
    "f.Apply('$dosage', pca, s)\n",
    "\n",
    "s.cov = s.cov * (s.cov.shape[0] / sum(np.diag(s.cov)))\n",
    "\n",
    "w, v = np.linalg.eig(s.cov)\n",
    "\n",
    "w  # eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.01471236, -0.01546884, -0.01359907, ..., -0.01394235,\n",
       "       -0.01273124, -0.01216276])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[:,0]  # the first eigenvector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11afccf28>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4lktmlU1lH9RCvv6TnTz6XD93r32R7p4BViyZN6YLenDHXuriN9r+QsGdejNT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\niYQCioiIROL/A2P8Ld9mMTL8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11af96cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(v[:,0], v[:,1], s=10)\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['GBR', 'GBR', 'GBR', ..., 'TSI', 'TSI', 'TSI'], dtype=object)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get population information\n",
    "pop = f.GetData('sample.annotation/Population')\n",
    "pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Europe', 'Europe', 'Europe', ..., 'Europe', 'Europe', 'Europe'], dtype=object)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get ancestry information\n",
    "ancestry = f.GetData('sample.annotation/Ancestry')\n",
    "ancestry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>col_0</th>\n",
       "      <th>ASW</th>\n",
       "      <th>CEU</th>\n",
       "      <th>CHB</th>\n",
       "      <th>CHS</th>\n",
       "      <th>CLM</th>\n",
       "      <th>FIN</th>\n",
       "      <th>GBR</th>\n",
       "      <th>IBS</th>\n",
       "      <th>JPT</th>\n",
       "      <th>LWK</th>\n",
       "      <th>MXL</th>\n",
       "      <th>PUR</th>\n",
       "      <th>TSI</th>\n",
       "      <th>YRI</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>row_0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Africa</th>\n",
       "      <td>61</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>97</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EastAsia</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>97</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Europe</th>\n",
       "      <td>0</td>\n",
       "      <td>85</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>93</td>\n",
       "      <td>89</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>98</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SouthAmerica</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>66</td>\n",
       "      <td>55</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "col_0         ASW  CEU  CHB  CHS  CLM  FIN  GBR  IBS  JPT  LWK  MXL  PUR  TSI  \\\n",
       "row_0                                                                           \n",
       "Africa         61    0    0    0    0    0    0    0    0   97    0    0    0   \n",
       "EastAsia        0    0   97  100    0    0    0    0   89    0    0    0    0   \n",
       "Europe          0   85    0    0    0   93   89   14    0    0    0    0   98   \n",
       "SouthAmerica    0    0    0    0   60    0    0    0    0    0   66   55    0   \n",
       "\n",
       "col_0         YRI  \n",
       "row_0              \n",
       "Africa         88  \n",
       "EastAsia        0  \n",
       "Europe          0  \n",
       "SouthAmerica    0  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pandas.crosstab(ancestry, pop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dict = {'Africa': 'black', 'EastAsia': 'red', 'Europe': 'green', 'SouthAmerica': 'blue'}\n",
    "col = [ dict[i] for i in ancestry ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11ffc4ac8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pp+DVV32TaRh0XrDAQK2kjDIxGAxVEH+avJoABQ8IScit87bNa8DjgA8cExXAd98VVSaB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\nB6mxPG0hv9HEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cfe0208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.scatter(v[:,0], v[:,1], color=col, s=10)\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "\n",
    "patch = [ mpatches.Patch(color=col, label=key) for key, col in dict.items() ]\n",
    "plt.legend(handles=patch, loc='upper right')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}