Hide keyboard shortcuts

Hot-keys on this page

r m x p   toggle line displays

j k   next/prev highlighted chunk

0   (zero) top of page

1   (one) first highlighted chunk

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

from builtins import range 

# 

# LSST Data Management System 

# 

# Copyright 2008-2016 AURA/LSST. 

# 

# This product includes software developed by the 

# LSST Project (http://www.lsst.org/). 

# 

# This program is free software: you can redistribute it and/or modify 

# it under the terms of the GNU General Public License as published by 

# the Free Software Foundation, either version 3 of the License, or 

# (at your option) any later version. 

# 

# This program is distributed in the hope that it will be useful, 

# but WITHOUT ANY WARRANTY; without even the implied warranty of 

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

# GNU General Public License for more details. 

# 

# You should have received a copy of the LSST License Statement and 

# the GNU General Public License along with this program. If not, 

# see <https://www.lsstcorp.org/LegalNotices/>. 

# 

import unittest 

import numpy 

try: 

import scipy.integrate 

import scipy.stats 

import scipy.special 

except ImportError: 

scipy = None 

 

import lsst.log 

import lsst.log.utils 

import lsst.utils.tests 

import lsst.meas.modelfit 

 

 

if False: 

lsst.log.utils.traceSetAt("meas.modelfit.integrals", 5) 

lsst.log.utils.traceSetAt("meas.modelfit.TruncatedGaussian", 5) 

 

 

class TruncatedGaussianTestCase(lsst.utils.tests.TestCase): 

 

def setUp(self): 

numpy.random.seed(500) 

 

def check1d(self, mu, hessian, tg): 

evaluator = tg.evaluate() 

logEvaluator = tg.evaluateLog() 

dist = scipy.stats.norm(loc=mu[0], scale=hessian[0, 0]**-0.5) 

self.assertFloatsAlmostEqual(1.0 - dist.cdf(0.0), tg.getUntruncatedFraction()) 

eps = 1E-7 

if numpy.all(mu >= 0.0): 

self.assertFloatsAlmostEqual(logEvaluator(mu), tg.getLogPeakAmplitude()) 

self.assertGreater(logEvaluator(mu+eps), tg.getLogPeakAmplitude()) 

self.assertGreater(logEvaluator(mu-eps), tg.getLogPeakAmplitude()) 

peak = numpy.array([tg.maximize()]) # workaround NumPy automatic-scalarification 

self.assertGreater(evaluator(peak), 0.0) 

self.assertLess(evaluator(peak+eps), evaluator(peak)) 

self.assertLess(evaluator(peak-eps), evaluator(peak)) 

 

def altLogEval(x): 

if numpy.any(x < 0): 

return float("inf") 

return tg.getLogPeakAmplitude() + 0.5*hessian[0, 0]*(x-mu[0])**2 

for alpha in (numpy.random.randn(10, 1) * hessian[0, 0]**-0.5 + mu[0]): 

x1 = logEvaluator(alpha) 

x2 = altLogEval(alpha[0]) 

if numpy.isfinite(x1) and numpy.isfinite(x2): 

self.assertFloatsAlmostEqual(x1, x2, rtol=1E-14) 

else: 

self.assertEqual(x1, x2) 

integral, check = self.integrate1d(tg) 

self.assertLess(check, 1E-7) 

self.assertFloatsAlmostEqual(integral, numpy.exp(-tg.getLogIntegral()), atol=check) 

 

def check2d(self, mu, hessian, tg, isDegenerate=False): 

evaluator = tg.evaluate() 

logEvaluator = tg.evaluateLog() 

unit1 = numpy.array([1.0, 0.0]) 

unit2 = numpy.array([0.0, 1.0]) 

eps = 1E-7 

85 ↛ 91line 85 didn't jump to line 91, because the condition on line 85 was never false if numpy.all(mu >= 0.0): 

self.assertFloatsAlmostEqual(logEvaluator(mu), tg.getLogPeakAmplitude()) 

self.assertGreater(logEvaluator(mu + unit1*eps), tg.getLogPeakAmplitude()) 

self.assertGreater(logEvaluator(mu - unit1*eps), tg.getLogPeakAmplitude()) 

self.assertGreater(logEvaluator(mu + unit2*eps), tg.getLogPeakAmplitude()) 

self.assertGreater(logEvaluator(mu - unit2*eps), tg.getLogPeakAmplitude()) 

peak = tg.maximize() 

self.assertGreater(evaluator(peak), 0.0) 

self.assertLess(evaluator(peak + unit1*eps) / evaluator(peak), 1.0) 

self.assertLess(evaluator(peak - unit1*eps) / evaluator(peak), 1.0) 

self.assertLess(evaluator(peak + unit2*eps) / evaluator(peak), 1.0) 

self.assertLess(evaluator(peak - unit2*eps) / evaluator(peak), 1.0) 

 

def altLogEval(a): 

if numpy.any(a < 0): 

return float("inf") 

return tg.getLogPeakAmplitude() + 0.5*numpy.dot(numpy.dot(hessian, a - mu).transpose(), a - mu) 

for alpha in (numpy.random.randn(10, 2) * hessian.diagonal()**-0.5 + mu): 

x1 = logEvaluator(alpha) 

x2 = altLogEval(alpha) 

if numpy.isfinite(x1) and numpy.isfinite(x2): 

self.assertFloatsAlmostEqual(x1, x2, rtol=1E-14) 

else: 

self.assertEqual(x1, x2) 

integral, check = self.integrate2d(tg) 

self.assertLess(check, 1E-7) 

self.assertFloatsAlmostEqual(integral, numpy.exp(-tg.getLogIntegral()), atol=check) 

 

def integrate1d(self, tg): 

evaluator = tg.evaluate() 

 

def func(x): 

return evaluator(numpy.array([x])) 

return scipy.integrate.quad(func, 0.0, numpy.Inf) 

 

def integrate2d(self, tg): 

evaluator = tg.evaluate() 

 

def func(x, y): 

return evaluator(numpy.array([x, y])) 

return scipy.integrate.dblquad(func, 0.0, numpy.Inf, lambda x: 0.0, lambda x: numpy.Inf) 

 

def test1d(self): 

128 ↛ 129line 128 didn't jump to line 129, because the condition on line 128 was never true if scipy is None: 

return 

for i in range(5): 

sigma = (numpy.random.randn(1, 1)**2 + 1)*5 

mu = (numpy.random.randn(1))*3 

q0 = float(numpy.random.randn()) 

hessian = numpy.linalg.inv(sigma) 

gradient = -numpy.dot(hessian, mu) 

tg1 = lsst.meas.modelfit.TruncatedGaussian.fromStandardParameters(mu, sigma) 

tg2 = lsst.meas.modelfit.TruncatedGaussian.fromSeriesParameters(q0, gradient, hessian) 

self.assertEqual(tg1.getLogIntegral(), 0.0) 

self.assertFloatsAlmostEqual(tg1.getLogPeakAmplitude(), 

(0.5*numpy.log(numpy.linalg.det(2.0*numpy.pi*sigma)) + 

numpy.log(tg1.getUntruncatedFraction())), 

rtol=1E-13) 

self.assertFloatsAlmostEqual(tg2.getLogPeakAmplitude(), 

q0 + 0.5*numpy.dot(mu, gradient), 

rtol=1E-13) 

self.check1d(mu, hessian, tg1) 

self.check1d(mu, hessian, tg2) 

 

def test2d(self): 

150 ↛ 151line 150 didn't jump to line 151, because the condition on line 150 was never true if scipy is None: 

return 

for i in range(5): 

x = numpy.linspace(-1, 1, 5) 

model = numpy.zeros((x.size, 2), dtype=float) 

model[:, 0] = x 

model[:, 1] = x**2 + x 

data = numpy.random.randn(x.size) + model[:, 0]*0.9 + model[:, 1]*1.1 

q0 = 0.5*float(numpy.dot(data, data)) 

gradient = -numpy.dot(model.transpose(), data) 

hessian = numpy.dot(model.transpose(), model) 

sigma = numpy.linalg.inv(hessian) 

self.assertFloatsAlmostEqual(numpy.linalg.inv(sigma), hessian) 

mu = -numpy.dot(sigma, gradient) 

tg1 = lsst.meas.modelfit.TruncatedGaussian.fromStandardParameters(mu, sigma) 

self.assertFloatsAlmostEqual(tg1.getLogPeakAmplitude(), 

(numpy.log(tg1.getUntruncatedFraction()) + 

0.5*numpy.log(numpy.linalg.det(2.0*numpy.pi*sigma))), 

rtol=1E-13) 

self.assertEqual(tg1.getLogIntegral(), 0.0) 

self.check2d(mu, hessian, tg1) 

tg2 = lsst.meas.modelfit.TruncatedGaussian.fromSeriesParameters(q0, gradient, hessian) 

self.assertFloatsAlmostEqual(tg2.getLogPeakAmplitude(), 

q0+0.5*numpy.dot(mu, gradient), 

rtol=1E-13) 

self.check2d(mu, hessian, tg2) 

 

def testDegenerate(self): 

178 ↛ 179line 178 didn't jump to line 179, because the condition on line 178 was never true if scipy is None: 

return 

for i in range(5): 

x = numpy.linspace(-1, 1, 5) 

model = numpy.zeros((x.size, 2), dtype=float) 

model[:, 0] = x 

model[:, 1] = 2*x 

data = numpy.random.randn(x.size) + model[:, 0]*0.9 + model[:, 1]*1.1 

q0 = 0.5*float(numpy.dot(data, data)) 

gradient = -numpy.dot(model.transpose(), data) 

hessian = numpy.dot(model.transpose(), model) 

mu, _, _, _ = numpy.linalg.lstsq(model, data) 

tg = lsst.meas.modelfit.TruncatedGaussian.fromSeriesParameters(q0, gradient, hessian) 

self.assertFloatsAlmostEqual(tg.getLogPeakAmplitude(), 

q0+0.5*numpy.dot(mu, gradient), 

rtol=1E-13) 

self.check2d(mu, hessian, tg, isDegenerate=True) 

 

 

class TestMemory(lsst.utils.tests.MemoryTestCase): 

pass 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

205 ↛ 206line 205 didn't jump to line 206, because the condition on line 205 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()