Github user MechCoder commented on a diff in the pull request:
https://github.com/apache/spark/pull/13248#discussion_r65794427
--- Diff: python/pyspark/ml/stat/distribution.py ---
@@ -0,0 +1,267 @@
+#
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements. See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+
+from pyspark.ml.linalg import DenseVector, DenseMatrix, Vector
+import numpy as np
+
+__all__ = ['MultivariateGaussian']
+
+
+
+class MultivariateGaussian():
+ """
+ This class provides basic functionality for a Multivariate Gaussian
(Normal) Distribution. In
+ the event that the covariance matrix is singular, the density will be
computed in a
+ reduced dimensional subspace under which the distribution is supported.
+ (see
[[http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case]])
+
+ mu The mean vector of the distribution
+ sigma The covariance matrix of the distribution
+
+
+ >>> mu = Vectors.dense([0.0, 0.0])
+ >>> sigma= DenseMatrix(2, 2, [1.0, 1.0, 1.0, 1.0])
+ >>> x = Vectors.dense([1.0, 1.0])
+ >>> m = MultivariateGaussian(mu, sigma)
+ >>> m.pdf(x)
+ 0.0682586811486
+
+ """
+
+ def __init__(self, mu, sigma):
+ """
+ __init__(self, mu, sigma)
+
+ mu The mean vector of the distribution
+ sigma The covariance matrix of the distribution
+
+ mu and sigma must be instances of DenseVector and DenseMatrix
respectively.
+
+ """
+
+
+ assert (isinstance(mu, DenseVector)), "mu must be a DenseVector
Object"
+ assert (isinstance(sigma, DenseMatrix)), "sigma must be a
DenseMatrix Object"
+
+ sigma_shape=sigma.toArray().shape
+ assert (sigma_shape[0]==sigma_shape[1]) , "Covariance matrix must
be square"
+ assert (sigma_shape[0]==mu.size) , "Mean vector length must match
covariance matrix size"
+
+ # initialize eagerly precomputed attributes
+
+ self.mu=mu
+
+ # storing sigma as numpy.ndarray
+ # furthur calculations are done ndarray only
+ self.sigma=sigma.toArray()
+
+
+ # initialize attributes to be computed later
+
+ self.prec_U = None
+ self.log_det_cov = None
+
+ # compute distribution dependent constants
+ self.__calculateCovarianceConstants()
+
+
+ def pdf(self,x):
+ """
+ Returns density of this multivariate Gaussian at a point given by
Vector x
+ """
+ assert (isinstance(x, Vector)), "x must be of Vector Type"
+ return float(self.__pdf(x))
+
+ def logpdf(self,x):
+ """
+ Returns the log-density of this multivariate Gaussian at a point
given by Vector x
+ """
+ assert (isinstance(x, Vector)), "x must be of Vector Type"
+ return float(self.__logpdf(x))
+
+ def __calculateCovarianceConstants(self):
+ """
+ Calculates distribution dependent components used for the density
function
+ based on scipy multivariate library
+ refer
https://github.com/scipy/scipy/blob/master/scipy/stats/_multivariate.py
+ tested with precision of 9 significant digits(refer testcase)
+
+
+ """
+
+ try :
+ # pre-processing input parameters
+ # throws ValueError with invalid inputs
+ self.dim, self.mu, self.sigma =
self.__process_parameters(None, self.mu, self.sigma)
+
+ # return the eigenvalues and eigenvectors
+ # of a Hermitian or symmetric matrix.
+ # s = eigen values
+ # u = eigen vectors
+ s, u = np.linalg.eigh(self.sigma)
+
+ #Singular values are considered to be non-zero only if
+ #they exceed a tolerance based on machine precision, matrix
size, and
+ #relation to the maximum singular value (same tolerance used
by, e.g., Octave).
+
+ # calculation for machine precision
+ t = u.dtype.char.lower()
+ factor = {'f': 1E3, 'd': 1E6}
+ cond = factor[t] * np.finfo(t).eps
+
+ eps = cond * np.max(abs(s))
+
+ # checkng whether covariance matrix has any non-zero singular
values
+ if np.min(s) < -eps:
+ raise ValueError
+
+ #computing the pseudoinverse
+ s_pinv = self.__pinv_1d(s, eps)
+
+ # prec_U ndarray
+ # A decomposition such that np.dot(prec_U, prec_U.T)
+ # is the precision matrix, i.e. inverse of the covariance
matrix.
+ self.prec_U = np.multiply(u, np.sqrt(s_pinv))
+
+ #log_det_cov : float
+ #Logarithm of the determinant of the covariance matrix
+ self.log_det_cov = np.sum(np.log(s[s > eps]))
+
+ except ValueError :
+ raise ValueError("Covariance matrix has no non-zero singular
values")
+
+ def __pdf(self,x):
+ """
+ Calculates density at point x using precomputed Constants
+ """
+ return np.exp(self.__logpdf(x))
+
+ def __logpdf(self,x) :
+ """
+ Calculates log-density at point x using precomputed Constants
+
+ x Points at which to evaluate the log of the probability
+ density function
+ log_det_cov : float
+ Logarithm of the determinant of the covariance matrix
+
+ prec_U ndarray
+ A decomposition such that np.dot(prec_U, prec_U.T)
+ is the precision matrix, i.e. inverse of the covariance matrix.
+
+ """
+ x = self.__process_quantiles(x, self.dim)
+ dim = x.shape[-1]
+ delta = x - self.mu
+ maha = np.sum(np.square(np.dot(delta, self.prec_U)), axis=-1)
+ return -0.5 * (dim * np.log(2 * np.pi) + self.log_det_cov + maha)
+
+
+
+
+ def __process_parameters(self, dim, mean, cov):
+ """
+ Helper funtion to process input values, based on scipy multivariate
+
+ Infer dimensionality from mean or covariance matrix, ensure that
+ mean and covariance are full vector resp. matrix.
+
+ """
+
+ # Try to infer dimensionality
+ if dim is None:
+ if mean is None:
+ if cov is None:
+ dim = 1
+ else:
+ cov = np.asarray(cov, dtype=float)
+ if cov.ndim < 2:
+ dim = 1
+ else:
+ dim = cov.shape[0]
+ else:
+ mean = np.asarray(mean, dtype=float)
+ dim = mean.size
+ else:
+ if not np.isscalar(dim):
+ raise ValueError("Dimension of random variable must be a
scalar.")
+
+ # Check input sizes and return full arrays for mean and cov if
necessary
+ if mean is None:
+ mean = np.zeros(dim)
+ mean = np.asarray(mean, dtype=float)
+
+ if cov is None:
+ cov = 1.0
+ cov = np.asarray(cov, dtype=float)
+
+ if dim == 1:
+ mean.shape = (1,)
+ cov.shape = (1, 1)
+
+ if mean.ndim != 1 or mean.shape[0] != dim:
+ raise ValueError("Array 'mean' must be vector of length %d." %
dim)
+ if cov.ndim == 0:
+ cov = cov * np.eye(dim)
+ elif cov.ndim == 1:
+ cov = np.diag(cov)
+ else:
+ if cov.shape != (dim, dim):
+ raise ValueError("Array 'cov' must be at most
two-dimensional,"
+ " but cov.ndim = %d" % cov.ndim)
+
+ return dim, mean, cov
+
+ def __process_quantiles(self, x, dim):
+ """
+ Helper funtion to process quantiles, based on scipy multivariate
+
+ Adjust quantiles array so that last axis labels the components of
+ each data point.
+
+ """
+ x = np.asarray(x, dtype=float)
+
+ if x.ndim == 0:
+ x = x[np.newaxis]
+ elif x.ndim == 1:
+ if dim == 1:
+ x = x[:, np.newaxis]
+ else:
+ x = x[np.newaxis, :]
+
+ return x
+
+
+ def __pinv_1d(self, v, eps=1e-5):
+ """
+ A helper function for computing the pseudoinverse, based on scipy
multivariate
+
+ v : iterable of numbers
+ This may be thought of as a vector of eigenvalues or singular
values.
+ eps : float
+ Elements of v smaller than eps are considered negligible.
+ returns 1d float ndarray
+ A vector of pseudo-inverted numbers.
+ """
+ return np.array([0 if abs(x) < eps else 1/x for x in v],
dtype=float)
--- End diff --
This can be easily vectorized. You are creating a copy anyway.
v_c = v.copy()
mask = v_c <= eps
v_c[mask] = 0.0
v_c[~mask] = 1. / v_c[~mask]
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