scipy.stats.Covariance#
- class scipy.stats.Covariance[source]#
Representation of a covariance matrix
Calculations involving covariance matrices (e.g. data whitening, multivariate normal function evaluation) are often performed more efficiently using a decomposition of the covariance matrix instead of the covariance matrix itself. This class allows the user to construct an object representing a covariance matrix using any of several decompositions and perform calculations using a common interface.
Note
The
Covariance
class cannot be instantiated directly. Instead, use one of the factory methods (e.g.Covariance.from_diagonal
).Examples
The
Covariance
class is is used by calling one of its factory methods to create aCovariance
object, then pass that representation of theCovariance
matrix as a shape parameter of a multivariate distribution.For instance, the multivariate normal distribution can accept an array representing a covariance matrix:
>>> from scipy import stats >>> import numpy as np >>> d = [1, 2, 3] >>> A = np.diag(d) # a diagonal covariance matrix >>> x = [4, -2, 5] # a point of interest >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=A) >>> dist.pdf(x) 4.9595685102808205e-08
but the calculations are performed in a very generic way that does not take advantage of any special properties of the covariance matrix. Because our covariance matrix is diagonal, we can use
Covariance.from_diagonal
to create an object representing the covariance matrix, andmultivariate_normal
can use this to compute the probability density function more efficiently.>>> cov = stats.Covariance.from_diagonal(d) >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=cov) >>> dist.pdf(x) 4.9595685102808205e-08
- Attributes:
covariance
Explicit representation of the covariance matrix
log_pdet
Log of the pseudo-determinant of the covariance matrix
rank
Rank of the covariance matrix
shape
Shape of the covariance array
Methods
colorize
(x)Perform a colorizing transformation on data.
from_cholesky
(cholesky)Representation of a covariance provided via the (lower) Cholesky factor
from_diagonal
(diagonal)Return a representation of a covariance matrix from its diagonal.
from_eigendecomposition
(eigendecomposition)Representation of a covariance provided via eigendecomposition
from_precision
(precision[, covariance])Return a representation of a covariance from its precision matrix.
whiten
(x)Perform a whitening transformation on data.