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

make_node
(x)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inputs, outputs)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
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 is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.

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

grad
(inputs, g_outputs)[source]¶ Construct a graph for the gradient with respect to each input variable.
Each returned Variable represents the gradient with respect to that input computed based on the symbolic gradients with respect to each output. If the output is not differentiable with respect to an input, then this method should return an instance of type NullType for that input.
Parameters:  inputs (list of Variable) – The input variables.
 output_grads (list of Variable) – The gradients of the output variables.
Returns: grads – The gradients with respect to each Variable in inputs.
Return type: list of Variable

make_node
(a, b)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inputs, outputs)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
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 is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.


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

make_node
(a, b, gw)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inputs, outputs)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
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 is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.


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

grad
(inputs, outputs)[source]¶ Construct a graph for the gradient with respect to each input variable.
Each returned Variable represents the gradient with respect to that input computed based on the symbolic gradients with respect to each output. If the output is not differentiable with respect to an input, then this method should return an instance of type NullType for that input.
Parameters:  inputs (list of Variable) – The input variables.
 output_grads (list of Variable) – The gradients of the output variables.
Returns: grads – The gradients with respect to each Variable in inputs.
Return type: list of Variable

make_node
(A)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inputs, outputs)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
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 is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.


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

make_node
(A, gw)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inputs, outputs)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
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 is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.


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/

make_node
(A, b)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inputs, output_storage)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
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 is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.


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.