tensor.slinalg – Linear Algebra Ops Using Scipy

API

class theano.tensor.slinalg.Cholesky(lower=True)

Return a triangular matrix square root of positive semi-definite x

L = cholesky(X, lower=True) implies dot(L, L.T) == X

class theano.tensor.slinalg.CholeskyGrad(lower=True)

perform(node, inputs, outputs)

Implements the “reverse-mode” gradient [1] for the Cholesky factorization of a positive-definite matrix.

[1]	S. P. Smith. “Differentiation of the Cholesky Algorithm”. Journal of Computational and Graphical Statistics, Vol. 4, No. 2 (Jun.,1995), pp. 134-147 http://www.jstor.org/stable/1390762

class theano.tensor.slinalg.Eigvalsh(lower=True)

Generalized eigenvalues of a Hermetian positive definite eigensystem

class theano.tensor.slinalg.EigvalshGrad(lower=True)

Gradient of generalized eigenvalues of a Hermetian positive definite eigensystem

class theano.tensor.slinalg.Solve(A_structure='general', lower=False, overwrite_A=False, overwrite_b=False)

Solve a system of linear equations

theano.tensor.slinalg.kron(a, b)

Kronecker product

Same as scipy.linalg.kron(a, b).

Note:

numpy.kron(a, b) != scipy.linalg.kron(a, b)! They don’t have the same shape and order when a.ndim != b.ndim != 2.

Parameters:

• a – array_like
• b – array_like

Returns:

array_like with a.ndim + b.ndim - 2 dimensions.