endas.CovarianceOperator¶

class endas.CovarianceOperator¶

Bases: object

Abstract representation of a covariance matrix.

The base class defines interface required by covariance matrix implementations. See the endas.cov module for concrete implementations.

shape¶: Returns the shape of the covariance matrix represented by this operator. Since this is a covariance matrix, the shape is always square

is_diagonal¶

Returns True if the covariance is represented by a diagonal matrix.

The default implementation returns False.

Note

If True, calling to_matrix(False) must return an instance of scipy.sparse.dia_matrix, i.e. a sparse matrix in diagonal format.

mc_only¶

Returns True if this covariance operator only supports Monte-Carlo sampling via the random_multivariate_normal().

The default implementation returns True as this is the minimal functionality a covariance operator must support. Implementations that return False will throw NotImplementedError from any method other than random_multivariate_normal().

to_matrix(force_dense=False, out=None)¶

Returns the covariance matrix.

Parameters:	force_dense – If True, the returned matrix is always dense. Otherwise a sparse matrix may be returned, if suitable for the covariance operator. out – If specified, the array is used as the output buffer instead of allocating new array. The provided array must have the correct shape.

The default implementation raises NotImplementedError.

Raises:	`NotImplementedError` – if the operation is not supported `MemoryError` – if the covariance matrix array cannot be allocated

Note

Please note that this should only be used on special cases such as diagonal covariance matrices (see is_diagonal()) or for visualization and debugging. The call is likely to run out of memory when use on a large covariance operator.

random_multivariate_normal(N=1)¶

Implements generation of a random sample from multivariate Normal distribution with zero mean and covariance given by this CovarianceMatrix instance.

Parameters:	N – The number of independent samples to draw.
Returns:	nxN array where n is the state space size (i.e. self.shape[0]).

solve(b, overwrite_b=False)¶

Solves the system \(\mathbf{C}x = b\), where \(\mathbf{C}\) is the covariance matrix represented by this CovarianceOperator instance.

Parameters:	b (n x m array) – Data for the right hand side, where n is the size of the covariance matrix and \(m \geq 1\)
Returns:	The solution x. The shape of the array is equivalent to the shape of b.

add_to(x)¶

Sums this covariance matrix and x and stores the result in x. Please note that this may not be supported by all covariance matrix implementations.

Generally, only covariance matrices that can afford to be represented explicitly (small matrices, diagonal matrices) implement this. In other cases NotImplementedError is raised.

localize(selected, taper)¶

Returns new CovarianceOperator for a subset of the original operator.

The default implementation raises NotImplementedError.

Parameters:	selected – Array of indexes of observations to select
Returns:	An instance of `ObservationOperator` of shape (s, n), where `s = len(selected)`.
Raises:	`NotImplementedError` – if the operation is not supported by this operator