Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.8/site-packages/tensorflow/python/ops/distributions/normal.py: 53%

1# Copyright 2016 The TensorFlow Authors. All Rights Reserved. 

2# 

3# Licensed under the Apache License, Version 2.0 (the "License"); 

4# you may not use this file except in compliance with the License. 

5# You may obtain a copy of the License at 

6# 

7# http://www.apache.org/licenses/LICENSE-2.0 

8# 

9# Unless required by applicable law or agreed to in writing, software 

10# distributed under the License is distributed on an "AS IS" BASIS, 

11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 

12# See the License for the specific language governing permissions and 

13# limitations under the License. 

14# ============================================================================== 

15"""The Normal (Gaussian) distribution class.""" 

16 

17import math 

18 

19from tensorflow.python.framework import constant_op 

20from tensorflow.python.framework import dtypes 

21from tensorflow.python.framework import ops 

22from tensorflow.python.framework import tensor_shape 

23from tensorflow.python.ops import array_ops 

24from tensorflow.python.ops import check_ops 

25from tensorflow.python.ops import math_ops 

26from tensorflow.python.ops import nn 

27from tensorflow.python.ops import random_ops 

28from tensorflow.python.ops.distributions import distribution 

29from tensorflow.python.ops.distributions import kullback_leibler 

30from tensorflow.python.ops.distributions import special_math 

31from tensorflow.python.util import deprecation 

32from tensorflow.python.util.tf_export import tf_export 

33 

34 

35__all__ = [ 

36 "Normal", 

37 "NormalWithSoftplusScale", 

38] 

39 

40 

41@tf_export(v1=["distributions.Normal"]) 

42class Normal(distribution.Distribution): 

43 """The Normal distribution with location `loc` and `scale` parameters. 

44 

45 #### Mathematical details 

46 

47 The probability density function (pdf) is, 

48 

49 ```none 

50 pdf(x; mu, sigma) = exp(-0.5 (x - mu)**2 / sigma**2) / Z 

51 Z = (2 pi sigma**2)**0.5 

52 ``` 

53 

54 where `loc = mu` is the mean, `scale = sigma` is the std. deviation, and, `Z` 

55 is the normalization constant. 

56 

57 The Normal distribution is a member of the [location-scale family]( 

58 https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be 

59 constructed as, 

60 

61 ```none 

62 X ~ Normal(loc=0, scale=1) 

63 Y = loc + scale * X 

64 ``` 

65 

66 #### Examples 

67 

68 Examples of initialization of one or a batch of distributions. 

69 

70 ```python 

71 import tensorflow_probability as tfp 

72 tfd = tfp.distributions 

73 

74 # Define a single scalar Normal distribution. 

75 dist = tfd.Normal(loc=0., scale=3.) 

76 

77 # Evaluate the cdf at 1, returning a scalar. 

78 dist.cdf(1.) 

79 

80 # Define a batch of two scalar valued Normals. 

81 # The first has mean 1 and standard deviation 11, the second 2 and 22. 

82 dist = tfd.Normal(loc=[1, 2.], scale=[11, 22.]) 

83 

84 # Evaluate the pdf of the first distribution on 0, and the second on 1.5, 

85 # returning a length two tensor. 

86 dist.prob([0, 1.5]) 

87 

88 # Get 3 samples, returning a 3 x 2 tensor. 

89 dist.sample([3]) 

90 ``` 

91 

92 Arguments are broadcast when possible. 

93 

94 ```python 

95 # Define a batch of two scalar valued Normals. 

96 # Both have mean 1, but different standard deviations. 

97 dist = tfd.Normal(loc=1., scale=[11, 22.]) 

98 

99 # Evaluate the pdf of both distributions on the same point, 3.0, 

100 # returning a length 2 tensor. 

101 dist.prob(3.0) 

102 ``` 

103 

104 """ 

105 

106 @deprecation.deprecated( 

107 "2019-01-01", 

108 "The TensorFlow Distributions library has moved to " 

109 "TensorFlow Probability " 

110 "(https://github.com/tensorflow/probability). You " 

111 "should update all references to use `tfp.distributions` " 

112 "instead of `tf.distributions`.", 

113 warn_once=True) 

114 def __init__(self, 

115 loc, 

116 scale, 

117 validate_args=False, 

118 allow_nan_stats=True, 

119 name="Normal"): 

120 """Construct Normal distributions with mean and stddev `loc` and `scale`. 

121 

122 The parameters `loc` and `scale` must be shaped in a way that supports 

123 broadcasting (e.g. `loc + scale` is a valid operation). 

124 

125 Args: 

126 loc: Floating point tensor; the means of the distribution(s). 

127 scale: Floating point tensor; the stddevs of the distribution(s). 

128 Must contain only positive values. 

129 validate_args: Python `bool`, default `False`. When `True` distribution 

130 parameters are checked for validity despite possibly degrading runtime 

131 performance. When `False` invalid inputs may silently render incorrect 

132 outputs. 

133 allow_nan_stats: Python `bool`, default `True`. When `True`, 

134 statistics (e.g., mean, mode, variance) use the value "`NaN`" to 

135 indicate the result is undefined. When `False`, an exception is raised 

136 if one or more of the statistic's batch members are undefined. 

137 name: Python `str` name prefixed to Ops created by this class. 

138 

139 Raises: 

140 TypeError: if `loc` and `scale` have different `dtype`. 

141 """ 

142 parameters = dict(locals()) 

143 with ops.name_scope(name, values=[loc, scale]) as name: 

144 with ops.control_dependencies([check_ops.assert_positive(scale)] if 

145 validate_args else []): 

146 self._loc = array_ops.identity(loc, name="loc") 

147 self._scale = array_ops.identity(scale, name="scale") 

148 check_ops.assert_same_float_dtype([self._loc, self._scale]) 

149 super(Normal, self).__init__( 

150 dtype=self._scale.dtype, 

151 reparameterization_type=distribution.FULLY_REPARAMETERIZED, 

152 validate_args=validate_args, 

153 allow_nan_stats=allow_nan_stats, 

154 parameters=parameters, 

155 graph_parents=[self._loc, self._scale], 

156 name=name) 

157 

158 @staticmethod 

159 def _param_shapes(sample_shape): 

160 return dict( 

161 zip(("loc", "scale"), ([ops.convert_to_tensor( 

162 sample_shape, dtype=dtypes.int32)] * 2))) 

163 

164 @property 

165 def loc(self): 

166 """Distribution parameter for the mean.""" 

167 return self._loc 

168 

169 @property 

170 def scale(self): 

171 """Distribution parameter for standard deviation.""" 

172 return self._scale 

173 

174 def _batch_shape_tensor(self): 

175 return array_ops.broadcast_dynamic_shape( 

176 array_ops.shape(self.loc), 

177 array_ops.shape(self.scale)) 

178 

179 def _batch_shape(self): 

180 return array_ops.broadcast_static_shape( 

181 self.loc.get_shape(), 

182 self.scale.get_shape()) 

183 

184 def _event_shape_tensor(self): 

185 return constant_op.constant([], dtype=dtypes.int32) 

186 

187 def _event_shape(self): 

188 return tensor_shape.TensorShape([]) 

189 

190 def _sample_n(self, n, seed=None): 

191 shape = array_ops.concat([[n], self.batch_shape_tensor()], 0) 

192 sampled = random_ops.random_normal( 

193 shape=shape, mean=0., stddev=1., dtype=self.loc.dtype, seed=seed) 

194 return sampled * self.scale + self.loc 

195 

196 def _log_prob(self, x): 

197 return self._log_unnormalized_prob(x) - self._log_normalization() 

198 

199 def _log_cdf(self, x): 

200 return special_math.log_ndtr(self._z(x)) 

201 

202 def _cdf(self, x): 

203 return special_math.ndtr(self._z(x)) 

204 

205 def _log_survival_function(self, x): 

206 return special_math.log_ndtr(-self._z(x)) 

207 

208 def _survival_function(self, x): 

209 return special_math.ndtr(-self._z(x)) 

210 

211 def _log_unnormalized_prob(self, x): 

212 return -0.5 * math_ops.square(self._z(x)) 

213 

214 def _log_normalization(self): 

215 return 0.5 * math.log(2. * math.pi) + math_ops.log(self.scale) 

216 

217 def _entropy(self): 

218 # Use broadcasting rules to calculate the full broadcast scale. 

219 scale = self.scale * array_ops.ones_like(self.loc) 

220 return 0.5 * math.log(2. * math.pi * math.e) + math_ops.log(scale) 

221 

222 def _mean(self): 

223 return self.loc * array_ops.ones_like(self.scale) 

224 

225 def _quantile(self, p): 

226 return self._inv_z(special_math.ndtri(p)) 

227 

228 def _stddev(self): 

229 return self.scale * array_ops.ones_like(self.loc) 

230 

231 def _mode(self): 

232 return self._mean() 

233 

234 def _z(self, x): 

235 """Standardize input `x` to a unit normal.""" 

236 with ops.name_scope("standardize", values=[x]): 

237 return (x - self.loc) / self.scale 

238 

239 def _inv_z(self, z): 

240 """Reconstruct input `x` from a its normalized version.""" 

241 with ops.name_scope("reconstruct", values=[z]): 

242 return z * self.scale + self.loc 

243 

244 

245class NormalWithSoftplusScale(Normal): 

246 """Normal with softplus applied to `scale`.""" 

247 

248 @deprecation.deprecated( 

249 "2019-01-01", 

250 "Use `tfd.Normal(loc, tf.nn.softplus(scale)) " 

251 "instead.", 

252 warn_once=True) 

253 def __init__(self, 

254 loc, 

255 scale, 

256 validate_args=False, 

257 allow_nan_stats=True, 

258 name="NormalWithSoftplusScale"): 

259 parameters = dict(locals()) 

260 with ops.name_scope(name, values=[scale]) as name: 

261 super(NormalWithSoftplusScale, self).__init__( 

262 loc=loc, 

263 scale=nn.softplus(scale, name="softplus_scale"), 

264 validate_args=validate_args, 

265 allow_nan_stats=allow_nan_stats, 

266 name=name) 

267 self._parameters = parameters 

268 

269 

270@kullback_leibler.RegisterKL(Normal, Normal) 

271def _kl_normal_normal(n_a, n_b, name=None): 

272 """Calculate the batched KL divergence KL(n_a || n_b) with n_a and n_b Normal. 

273 

274 Args: 

275 n_a: instance of a Normal distribution object. 

276 n_b: instance of a Normal distribution object. 

277 name: (optional) Name to use for created operations. 

278 default is "kl_normal_normal". 

279 

280 Returns: 

281 Batchwise KL(n_a || n_b) 

282 """ 

283 with ops.name_scope(name, "kl_normal_normal", [n_a.loc, n_b.loc]): 

284 one = constant_op.constant(1, dtype=n_a.dtype) 

285 two = constant_op.constant(2, dtype=n_a.dtype) 

286 half = constant_op.constant(0.5, dtype=n_a.dtype) 

287 s_a_squared = math_ops.square(n_a.scale) 

288 s_b_squared = math_ops.square(n_b.scale) 

289 ratio = s_a_squared / s_b_squared 

290 return (math_ops.squared_difference(n_a.loc, n_b.loc) / (two * s_b_squared) 

291 + half * (ratio - one - math_ops.log(ratio)))