tensor.slinalg
– Linear Algebra Ops Using Scipy¶
Note
This module is not imported by default. You need to import it to use it.
API¶

class
theano.tensor.slinalg.
Cholesky
(lower=True, on_error='raise')[source]¶ Return a triangular matrix square root of positive semidefinite x.
L = cholesky(X, lower=True) implies dot(L, L.T) == X.
 Parameters
lower (bool, default=True) – Whether to return the lower or upper cholesky factor
on_error (['raise', 'nan']) – If on_error is set to ‘raise’, this Op will raise a scipy.linalg.LinAlgError if the matrix is not positive definite. If on_error is set to ‘nan’, it will return a matrix containing nans instead.

L_op
(inputs, outputs, gradients)[source]¶ Cholesky decomposition reversemode gradient update.
Symbolic expression for reversemode Cholesky gradient taken from 1
References
 1
I. Murray, “Differentiation of the Cholesky decomposition”, http://arxiv.org/abs/1602.07527

perform
(node, inputs, outputs)[source]¶ Required: Calculate the function on the inputs and put the variables in the output storage. Return None.
 Parameters
node (Apply instance) – Contains the symbolic inputs and outputs.
inputs (list) – Sequence of inputs (immutable).
output_storage (list) – List of mutable 1element lists (do not change the length of these lists)
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.
 Raises
MethodNotDefined – The subclass does not override this method.

class
theano.tensor.slinalg.
Eigvalsh
(lower=True)[source]¶ Generalized eigenvalues of a Hermitian positive definite eigensystem.

perform
(node, inputs, outputs)[source]¶ Required: Calculate the function on the inputs and put the variables in the output storage. Return None.
 Parameters
node (Apply instance) – Contains the symbolic inputs and outputs.
inputs (list) – Sequence of inputs (immutable).
output_storage (list) – List of mutable 1element lists (do not change the length of these lists)
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.
 Raises
MethodNotDefined – The subclass does not override this method.


class
theano.tensor.slinalg.
EigvalshGrad
(lower=True)[source]¶ Gradient of generalized eigenvalues of a Hermitian positive definite eigensystem.

perform
(node, inputs, outputs)[source]¶ Required: Calculate the function on the inputs and put the variables in the output storage. Return None.
 Parameters
node (Apply instance) – Contains the symbolic inputs and outputs.
inputs (list) – Sequence of inputs (immutable).
output_storage (list) – List of mutable 1element lists (do not change the length of these lists)
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.
 Raises
MethodNotDefined – The subclass does not override this method.


class
theano.tensor.slinalg.
Expm
[source]¶ Compute the matrix exponential of a square array.

perform
(node, inputs, outputs)[source]¶ Required: Calculate the function on the inputs and put the variables in the output storage. Return None.
 Parameters
node (Apply instance) – Contains the symbolic inputs and outputs.
inputs (list) – Sequence of inputs (immutable).
output_storage (list) – List of mutable 1element lists (do not change the length of these lists)
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.
 Raises
MethodNotDefined – The subclass does not override this method.


class
theano.tensor.slinalg.
ExpmGrad
[source]¶ Gradient of the matrix exponential of a square array.

perform
(node, inputs, outputs)[source]¶ Required: Calculate the function on the inputs and put the variables in the output storage. Return None.
 Parameters
node (Apply instance) – Contains the symbolic inputs and outputs.
inputs (list) – Sequence of inputs (immutable).
output_storage (list) – List of mutable 1element lists (do not change the length of these lists)
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.
 Raises
MethodNotDefined – The subclass does not override this method.


class
theano.tensor.slinalg.
Solve
(A_structure='general', lower=False, overwrite_A=False, overwrite_b=False)[source]¶ Solve a system of linear equations.
For on CPU and GPU.

L_op
(inputs, outputs, output_gradients)[source]¶ Reversemode gradient updates for matrix solve operation c = A \b.
Symbolic expression for updates taken from 2.
References
 2
M. B. Giles, “An extended collection of matrix derivative results for forward and reverse mode automatic differentiation”, http://eprints.maths.ox.ac.uk/1079/

perform
(node, inputs, output_storage)[source]¶ Required: Calculate the function on the inputs and put the variables in the output storage. Return None.
 Parameters
node (Apply instance) – Contains the symbolic inputs and outputs.
inputs (list) – Sequence of inputs (immutable).
output_storage (list) – List of mutable 1element lists (do not change the length of these lists)
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.
 Raises
MethodNotDefined – The subclass does not override this method.


theano.tensor.slinalg.
kron
(a, b)[source]¶ Kronecker product.
Same as scipy.linalg.kron(a, b).
 Parameters
a (array_like) –
b (array_like) –
 Returns
 Return type
array_like with a.ndim + b.ndim  2 dimensions
Notes
numpy.kron(a, b) != scipy.linalg.kron(a, b)! They don’t have the same shape and order when a.ndim != b.ndim != 2.

theano.tensor.slinalg.
solve_symmetric
= Solve{('symmetric', False, False, False)}[source]¶ Optimized implementation of
theano.tensor.slinalg.solve()
when A is symmetric.

theano.tensor.slinalg.
solve
(a, b)[source]¶ Solves the equation
a x = b
for x, wherea
is a matrix andb
can be either a vector or a matrix. Parameters
a ((M, M) symbolix matrix) – A square matrix
b ((M,) or (M, N) symbolic vector or matrix) – Right hand side matrix in
a x = b
 Returns
x – x will have the same shape as b
 Return type
(M, ) or (M, N) symbolic vector or matrix

theano.tensor.slinalg.
solve_lower_triangular
(a, b)[source]¶ Optimized implementation of
theano.tensor.slinalg.solve()
when A is lower triangular.

theano.tensor.slinalg.
solve_upper_triangular
(a, b)[source]¶ Optimized implementation of
theano.tensor.slinalg.solve()
when A is upper triangular.