1
2
3
4
5
6 """ various statistical operations on data
7
8 """
9 import numpy
10 import math
11
12
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 = math.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
52
53
79
80
82 """ do a principal components analysis
83
84 """
85 covMat = FormCorrelationMatrix(mat)
86
87 eigenVals, eigenVects = numpy.linalg.eig(covMat)
88
89 eigenVals = getattr(eigenVals, "real", eigenVals)
90 eigenVects = getattr(eigenVects, "real", eigenVects)
91
92
93 ptOrder = numpy.argsort(eigenVals).tolist()
94 if reverseOrder:
95 ptOrder.reverse()
96 eigenVals = numpy.array([eigenVals[x] for x in ptOrder])
97 eigenVects = numpy.array([eigenVects[x] for x in ptOrder])
98 return eigenVals, eigenVects
99
100
124
125
127 """ returns the mean and standard deviation of a vector """
128 vect = numpy.array(vect, 'd')
129 n = vect.shape[0]
130 if n <= 0:
131 return 0., 0.
132 mean = sum(vect) / n
133 v = vect - mean
134 if n > 1:
135 if sampleSD:
136 dev = numpy.sqrt(sum(v * v) / (n - 1))
137 else:
138 dev = numpy.sqrt(sum(v * v) / (n))
139
140 else:
141 dev = 0
142 return mean, dev
143
144
145 -def R2(orig, residSum):
146 """ returns the R2 value for a set of predictions """
147
148
149
150
151
152
153
154
155 vect = numpy.array(orig)
156 n = vect.shape[0]
157 if n <= 0:
158 return 0., 0.
159 oMean = sum(vect) / n
160 v = vect - oMean
161 oVar = sum(v * v)
162 return 1. - residSum / oVar
163
164
165 tConfs = {80: 1, 90: 2, 95: 3, 98: 4, 99: 5, 99.8: 6, 99.9: 7}
166 tTable = [
167 [1, 3.078, 6.314, 12.71, 31.82, 63.66, 318.30, 637],
168 [2, 1.886, 2.920, 4.303, 6.965, 9.925, 22.330, 31.6],
169 [3, 1.638, 2.353, 3.182, 4.541, 5.841, 10.210, 12.92],
170 [4, 1.533, 2.132, 2.776, 3.747, 4.604, 7.173, 8.610],
171 [5, 1.476, 2.015, 2.571, 3.365, 4.032, 5.893, 6.869],
172 [6, 1.440, 1.943, 2.447, 3.143, 3.707, 5.208, 5.959],
173 [7, 1.415, 1.895, 2.365, 2.998, 3.499, 4.785, 5.408],
174 [8, 1.397, 1.860, 2.306, 2.896, 3.355, 4.501, 5.041],
175 [9, 1.383, 1.833, 2.262, 2.821, 3.250, 4.297, 4.781],
176 [10, 1.372, 1.812, 2.228, 2.764, 3.169, 4.144, 4.587],
177 [11, 1.363, 1.796, 2.201, 2.718, 3.106, 4.025, 4.437],
178 [12, 1.356, 1.782, 2.179, 2.681, 3.055, 3.930, 4.318],
179 [13, 1.350, 1.771, 2.160, 2.650, 3.012, 3.852, 4.221],
180 [14, 1.345, 1.761, 2.145, 2.624, 2.977, 3.787, 4.140],
181 [15, 1.341, 1.753, 2.131, 2.602, 2.947, 3.733, 4.073],
182 [16, 1.337, 1.746, 2.120, 2.583, 2.921, 3.686, 4.015],
183 [17, 1.333, 1.740, 2.110, 2.567, 2.898, 3.646, 3.965],
184 [18, 1.330, 1.734, 2.101, 2.552, 2.878, 3.610, 3.922],
185 [19, 1.328, 1.729, 2.093, 2.539, 2.861, 3.579, 3.883],
186 [20, 1.325, 1.725, 2.086, 2.528, 2.845, 3.552, 3.850],
187 [21, 1.323, 1.721, 2.080, 2.518, 2.831, 3.527, 3.819],
188 [22, 1.321, 1.717, 2.074, 2.508, 2.819, 3.505, 3.792],
189 [23, 1.319, 1.714, 2.069, 2.500, 2.807, 3.485, 3.768],
190 [24, 1.318, 1.711, 2.064, 2.492, 2.797, 3.467, 3.745],
191 [25, 1.316, 1.708, 2.060, 2.485, 2.787, 3.450, 3.725],
192 [26, 1.315, 1.706, 2.056, 2.479, 2.779, 3.435, 3.707],
193 [27, 1.314, 1.703, 2.052, 2.473, 2.771, 3.421, 3.690],
194 [28, 1.313, 1.701, 2.048, 2.467, 2.763, 3.408, 3.674],
195 [29, 1.311, 1.699, 2.045, 2.462, 2.756, 3.396, 3.659],
196 [30, 1.310, 1.697, 2.042, 2.457, 2.750, 3.385, 3.646],
197 [32, 1.309, 1.694, 2.037, 2.449, 2.738, 3.365, 3.622],
198 [34, 1.307, 1.691, 2.032, 2.441, 2.728, 3.348, 3.601],
199 [36, 1.306, 1.688, 2.028, 2.434, 2.719, 3.333, 3.582],
200 [38, 1.304, 1.686, 2.024, 2.429, 2.712, 3.319, 3.566],
201 [40, 1.303, 1.684, 2.021, 2.423, 2.704, 3.307, 3.551],
202 [42, 1.302, 1.682, 2.018, 2.418, 2.698, 3.296, 3.538],
203 [44, 1.301, 1.680, 2.015, 2.414, 2.692, 3.286, 3.526],
204 [46, 1.300, 1.679, 2.013, 2.410, 2.687, 3.277, 3.515],
205 [48, 1.299, 1.677, 2.011, 2.407, 2.682, 3.269, 3.505],
206 [50, 1.299, 1.676, 2.009, 2.403, 2.678, 3.261, 3.496],
207 [55, 1.297, 1.673, 2.004, 2.396, 2.668, 3.245, 3.476],
208 [60, 1.296, 1.671, 2.000, 2.390, 2.660, 3.232, 3.460],
209 [65, 1.295, 1.669, 1.997, 2.385, 2.654, 3.220, 3.447],
210 [70, 1.294, 1.667, 1.994, 2.381, 2.648, 3.211, 3.435],
211 [80, 1.292, 1.664, 1.990, 2.374, 2.639, 3.195, 3.416],
212 [100, 1.290, 1.660, 1.984, 2.364, 2.626, 3.174, 3.390],
213 [150, 1.287, 1.655, 1.976, 2.351, 2.609, 3.145, 3.357],
214 [200, 1.286, 1.653, 1.972, 2.345, 2.601, 3.131, 3.340]
215 ]
216
217
219 col = tConfs[level]
220 dofs = n - 1
221 sem = sd / numpy.sqrt(n)
222 idx = 0
223 while idx < len(tTable) and tTable[idx][0] < dofs:
224 idx += 1
225 if idx < len(tTable):
226 t = tTable[idx][col]
227 else:
228 t = tTable[-1][col]
229 return t * sem
230