Package rdkit :: Package ML :: Package Data :: Module Stats
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Source Code for Module rdkit.ML.Data.Stats

  1  ## Automatically adapted for numpy.oldnumeric Jun 27, 2008 by -c 
  2   
  3  # $Id$ 
  4  # 
  5  #  Copyright (C) 2001-2008  greg Landrum and Rational Discovery LLC 
  6  #  All Rights Reserved 
  7  # 
  8  """ various statistical operations on data 
  9   
 10  """ 
 11  import numpy 
 12   
13 -def StandardizeMatrix(mat):
14 """ 15 16 This is the standard *subtract off the average and divide by the deviation* 17 standardization function. 18 19 **Arguments** 20 21 - mat: a numpy array 22 23 **Notes** 24 25 - in addition to being returned, _mat_ is modified in place, so **beware** 26 27 """ 28 nObjs = len(mat) 29 avgs = sum(mat,0)/float(nObjs) 30 mat -= avgs 31 devs =sqrt(sum(mat*mat,0)/(float(nObjs-1))) 32 try: 33 newMat = mat/devs 34 except OverflowError: 35 newMat = numpy.zeros(mat.shape,'d') 36 for i in range(mat.shape[1]): 37 if devs[i] != 0.0: 38 newMat[:,i] = mat[:,i]/devs[i] 39 return newMat
40
41 -def FormCovarianceMatrix(mat):
42 """ form and return the covariance matrix 43 44 """ 45 nPts = mat.shape[0] 46 sumVect = sum(mat) 47 sumVect /= float(nPts) 48 for row in mat: 49 row -= sumVect 50 return numpy.dot(numpy.transpose(mat),mat)/(nPts-1)
51
52 -def FormCorrelationMatrix(mat):
53 """ form and return the covariance matrix 54 55 """ 56 nVars = len(mat[0]) 57 N = len(mat) 58 59 res = numpy.zeros((nVars,nVars),'d') 60 for i in range(nVars): 61 x = mat[:,i] 62 sumX = sum(x) 63 sumX2 = sum(x*x) 64 for j in range(i,nVars): 65 y = mat[:,j] 66 sumY = sum(y) 67 sumY2 = sum(y*y) 68 numerator = N*sum(x*y) - sumX*sumY 69 denom = numpy.sqrt((N*sumX2-sumX**2)*(N*sumY2-sumY**2)) 70 if denom != 0.0: 71 res[i,j] = numerator/denom 72 res[j,i] = numerator/denom 73 else: 74 res[i,j] = 0 75 res[j,i] = 0 76 return res
77 -def PrincipalComponents(mat,reverseOrder=1):
78 """ do a principal components analysis 79 80 """ 81 covMat = FormCorrelationMatrix(mat) 82 83 eigenVals,eigenVects = numpy.linalg.eig(covMat) 84 # The the 'real' component, if it exists as its own attribute 85 eigenVals = getattr(eigenVals, "real", eigenVals) 86 eigenVects = getattr(eigenVects, "real", eigenVects) 87 88 # and now sort: 89 ptOrder = numpy.argsort(eigenVals).tolist() 90 if reverseOrder: 91 ptOrder.reverse() 92 eigenVals = numpy.array([eigenVals[x] for x in ptOrder]) 93 eigenVects = numpy.array([eigenVects[x] for x in ptOrder]) 94 return eigenVals,eigenVects
95
96 -def TransformPoints(tFormMat,pts):
97 """ transforms a set of points using tFormMat 98 99 **Arguments** 100 101 - tFormMat: a numpy array 102 103 - pts: a list of numpy arrays (or a 2D array) 104 105 **Returns** 106 107 a list of numpy arrays 108 109 """ 110 pts = numpy.array(pts) 111 nPts = len(pts) 112 avgP = sum(pts)/nPts 113 pts = pts - avgP 114 res = [None]*nPts 115 for i in range(nPts): 116 res[i] = numpy.dot(tFormMat,pts[i]) 117 118 return res
119
120 -def MeanAndDev(vect,sampleSD=1):
121 """ returns the mean and standard deviation of a vector """ 122 vect = numpy.array(vect,'d') 123 n = vect.shape[0] 124 if n <= 0: 125 return 0.,0. 126 mean = sum(vect)/n 127 v = vect-mean 128 if n > 1: 129 if sampleSD: 130 dev = numpy.sqrt(sum(v*v)/(n-1)) 131 else: 132 dev = numpy.sqrt(sum(v*v)/(n)) 133 134 else: 135 dev = 0 136 return mean,dev
137
138 -def R2(orig,residSum):
139 """ returns the R2 value for a set of predictions """ 140 141 142 # FIX: this just is not right 143 # 144 # A correct formulation of this (from Excel) for 2 variables is: 145 # r2 = [n*(Sxy) - (Sx)(Sy)]^2 / ([n*(Sx2) - (Sx)^2]*[n*(Sy2) - (Sy)^2]) 146 # 147 # 148 149 vect = numpy.array(orig) 150 n = vect.shape[0] 151 if n <= 0: 152 return 0.,0. 153 oMean = sum(vect)/n 154 v = vect-oMean 155 oVar = sum(v*v) 156 return 1. - residSum/oVar
157 158 159 # One Tail 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 160 tConfs = {80:1,90:2,95:3,98:4,99:5,99.8:6,99.9:7} 161 tTable=[ 162 [ 1, 3.078, 6.314, 12.71, 31.82, 63.66, 318.30, 637], 163 [ 2, 1.886, 2.920, 4.303, 6.965, 9.925, 22.330, 31.6], 164 [ 3, 1.638, 2.353, 3.182, 4.541, 5.841, 10.210, 12.92], 165 [ 4, 1.533, 2.132, 2.776, 3.747, 4.604, 7.173, 8.610], 166 [ 5, 1.476, 2.015, 2.571, 3.365, 4.032, 5.893, 6.869], 167 [ 6, 1.440, 1.943, 2.447, 3.143, 3.707, 5.208, 5.959], 168 [ 7, 1.415, 1.895, 2.365, 2.998, 3.499, 4.785, 5.408], 169 [ 8, 1.397, 1.860, 2.306, 2.896, 3.355, 4.501, 5.041], 170 [ 9, 1.383, 1.833, 2.262, 2.821, 3.250, 4.297, 4.781], 171 [ 10, 1.372, 1.812, 2.228, 2.764, 3.169, 4.144, 4.587], 172 [ 11, 1.363, 1.796, 2.201, 2.718, 3.106, 4.025, 4.437], 173 [ 12, 1.356, 1.782, 2.179, 2.681, 3.055, 3.930, 4.318], 174 [ 13, 1.350, 1.771, 2.160, 2.650, 3.012, 3.852, 4.221], 175 [ 14, 1.345, 1.761, 2.145, 2.624, 2.977, 3.787, 4.140], 176 [ 15, 1.341, 1.753, 2.131, 2.602, 2.947, 3.733, 4.073], 177 [ 16, 1.337, 1.746, 2.120, 2.583, 2.921, 3.686, 4.015], 178 [ 17, 1.333, 1.740, 2.110, 2.567, 2.898, 3.646, 3.965], 179 [ 18, 1.330, 1.734, 2.101, 2.552, 2.878, 3.610, 3.922], 180 [ 19, 1.328, 1.729, 2.093, 2.539, 2.861, 3.579, 3.883], 181 [ 20, 1.325, 1.725, 2.086, 2.528, 2.845, 3.552, 3.850], 182 [ 21, 1.323, 1.721, 2.080, 2.518, 2.831, 3.527, 3.819], 183 [ 22, 1.321, 1.717, 2.074, 2.508, 2.819, 3.505, 3.792], 184 [ 23, 1.319, 1.714, 2.069, 2.500, 2.807, 3.485, 3.768], 185 [ 24, 1.318, 1.711, 2.064, 2.492, 2.797, 3.467, 3.745], 186 [ 25, 1.316, 1.708, 2.060, 2.485, 2.787, 3.450, 3.725], 187 [ 26, 1.315, 1.706, 2.056, 2.479, 2.779, 3.435, 3.707], 188 [ 27, 1.314, 1.703, 2.052, 2.473, 2.771, 3.421, 3.690], 189 [ 28, 1.313, 1.701, 2.048, 2.467, 2.763, 3.408, 3.674], 190 [ 29, 1.311, 1.699, 2.045, 2.462, 2.756, 3.396, 3.659], 191 [ 30, 1.310, 1.697, 2.042, 2.457, 2.750, 3.385, 3.646], 192 [ 32, 1.309, 1.694, 2.037, 2.449, 2.738, 3.365, 3.622], 193 [ 34, 1.307, 1.691, 2.032, 2.441, 2.728, 3.348, 3.601], 194 [ 36, 1.306, 1.688, 2.028, 2.434, 2.719, 3.333, 3.582], 195 [ 38, 1.304, 1.686, 2.024, 2.429, 2.712, 3.319, 3.566], 196 [ 40, 1.303, 1.684, 2.021, 2.423, 2.704, 3.307, 3.551], 197 [ 42, 1.302, 1.682, 2.018, 2.418, 2.698, 3.296, 3.538], 198 [ 44, 1.301, 1.680, 2.015, 2.414, 2.692, 3.286, 3.526], 199 [ 46, 1.300, 1.679, 2.013, 2.410, 2.687, 3.277, 3.515], 200 [ 48, 1.299, 1.677, 2.011, 2.407, 2.682, 3.269, 3.505], 201 [ 50, 1.299, 1.676, 2.009, 2.403, 2.678, 3.261, 3.496], 202 [ 55, 1.297, 1.673, 2.004, 2.396, 2.668, 3.245, 3.476], 203 [ 60, 1.296, 1.671, 2.000, 2.390, 2.660, 3.232, 3.460], 204 [ 65, 1.295, 1.669, 1.997, 2.385, 2.654, 3.220, 3.447], 205 [ 70, 1.294, 1.667, 1.994, 2.381, 2.648, 3.211, 3.435], 206 [ 80, 1.292, 1.664, 1.990, 2.374, 2.639, 3.195, 3.416], 207 [100, 1.290, 1.660, 1.984, 2.364, 2.626, 3.174, 3.390], 208 [150, 1.287, 1.655, 1.976, 2.351, 2.609, 3.145, 3.357], 209 [200, 1.286, 1.653, 1.972, 2.345, 2.601, 3.131, 3.340] 210 ]
211 -def GetConfidenceInterval(sd,n,level=95):
212 col = tConfs[level] 213 dofs = n-1 214 sem = sd/numpy.sqrt(n) 215 idx = 0 216 while idx<len(tTable) and tTable[idx][0]<dofs: 217 idx+=1 218 if idx<len(tTable): 219 t = tTable[idx][col] 220 else: 221 t = tTable[-1][col] 222 return t*sem
223