dubfi.linalg.dense

Dense numpy array implementation of generic linear algebra types.

Added in version 0.1.0: (initial release)

Classes

DenseMatrix	Operator represented by a dense matrix.
LinParamVector	Linear parametrized simple dense vector.
DenseEnsLinPostRNoloc	Dense operator constructed based on a flux ensemble without localization.
DenseEnsLinPostR	Dense operator constructed based on a flux ensemble with localization.
DiagonalEnsLinPostR	Diagonal operator constructed based on a flux ensemble.

Module Contents

class dubfi.linalg.dense.DenseMatrix(array)

Bases: dubfi.linalg.types.AbstractOperator

Operator represented by a dense matrix.

Parameters:

array (numpy.ndarray)

property shape: tuple[int, Ellipsis]

Shape of array (matrix) representation of self.

Return type:

tuple[int, Ellipsis]

property data: numpy.ndarray

Numpy array (matrix) representation of self.

Return type:

numpy.ndarray

tonumpy()

Numpy array (matrix) representation of self.

Return type:

numpy.ndarray

diagonal()

Return copy of the diagonal of self.

__mul__(other)

Multiply element-wise.

__imul__(other)

Multiply element-wise in-place.

Return type:

Self

__add__(other)

Add two linear operators.

__iadd__(other)

Add two linear operators in-place.

__sub__(other)

Subtract other operator.

__isub__(other)

Subtract other operator in-place.

apply(vec)

Apply operator on vector: self @ vec.

rapply(vec)

Apply transpose operator on vector: self.T @ vec.

inv()

Compute (multiplicative) inverse operator.

solve(vec)

Solve linear equation self @ x = vec for x.

chain(other)

Combine operators: self @ other.

trace()

Compute trace of self.

trace_product(other)

Compute trace of (self @ other).

logdet()

Compute log(det(self)) assuming that self is a positive definite, real-symmetric matrix.

dot(other)

Inner product along non-vector dimensions.

class dubfi.linalg.dense.LinParamVector(array)

Bases: dubfi.linalg.generic.ParametrizedVector

Linear parametrized simple dense vector.

__call__(s)

Vector at given parameter array.

grad(s)

Gradient w.r.t. parameters s.

hess(s)

Hesse matrix w.r.t. parameters s.

class dubfi.linalg.dense.DenseEnsLinPostRNoloc(h_ensemble)

Bases: dubfi.linalg.generic.ParametrizedOperator

Dense operator constructed based on a flux ensemble without localization.

__call__(s)

Operator at given parameter array.

grad(s)

Gradient w.r.t. parameters s.

grad_vec(s, vec)

Equivalent to self.grad(s) @ vec.

hess(s)

Hesse matrix w.r.t. parameters s.

hess_vec(s, vec)

Equivalent to self.hess(s) @ vec.

vec_hess_vec(s, left, right)

Equivalent to left @ (self.hess(s) @ right).

class dubfi.linalg.dense.DenseEnsLinPostR(h_ensemble, loc, regularization=0.0, bg_ens=None, bc_ens=None)

Bases: dubfi.linalg.generic.ParametrizedOperator

Dense operator constructed based on a flux ensemble with localization.

Ensemble-based parametrized linear operator with localization.

Parameters:

• h_ensemble (np.ndarray) – shape (ensemble, state, observations) array representing the observation operator in the different ensemble members.

• loc (np.ndarray) – shape (observations, observations) array for suppressing correlations in the ensemble estimate

• regularization (float | np.ndarray, optional) – regularization term added to the diagonal of self.

• bg_ens (np.ndarray, optional) – ensemble of background concentrations, must be the same ensemble as used for h_ensemble.

• bc_ens (np.ndarray, optional) – ensemble to estimate the boundary condition uncertainty, must be an independent ensemble from bg_ens and h_ensemble.

set_bg_ens(bg_ens)

Set the background (or total concentration) meteorological ensemble.

Parameters:

bg_ens (numpy.ndarray)

Return type:

None

set_bc_ens(bc_ens)

Set boundary condition ensemble.

Parameters:

bc_ens (numpy.ndarray)

Return type:

None

__call__(s)

Compute operator at given parameter vector s.

grad(s)

Gradient at given parameter vector s.

hess(s)

Hesse matrix at given parameter vector s.

class dubfi.linalg.dense.DiagonalEnsLinPostR(h_ensemble, regularization=0.0, bg_ens=None)

Bases: dubfi.linalg.generic.ParametrizedOperator

Diagonal operator constructed based on a flux ensemble.

Parameters:

• h_ensemble (numpy.ndarray)

• regularization (float | numpy.ndarray)

• bg_ens (None | numpy.ndarray)

set_bg_ens(bg_ens)

Set the background (or total concentration) meteorological ensemble.

Parameters:

bg_ens (numpy.ndarray)

Return type:

None

__call__(s)

Compute operator at given parameter vector s.

grad(s)

Gradient at given parameter vector s.

hess(s)

Hesse matrix at given parameter vector s.