gemseo / core / derivatives

jacobian_operator module¶

Abstraction of Jacobian as linear operators.

class gemseo.core.derivatives.jacobian_operator.JacobianOperator(*args, **kwargs)[source]¶

Bases: LinearOperator

The Jacobian of a discipline as linear operator.

Initialize this LinearOperator.

To be called by subclasses. dtype may be None; shape should be convertible to a length-2 tuple.

Parameters:

dtype (dtype) – The data type of the Jacobian.
shape (tuple[int, ...]) – The shape of the Jacobian.

adjoint()¶

Hermitian adjoint.

Returns the Hermitian adjoint of self, aka the Hermitian conjugate or Hermitian transpose. For a complex matrix, the Hermitian adjoint is equal to the conjugate transpose.

Can be abbreviated self.H instead of self.adjoint().

Returns:: A_H – Hermitian adjoint of self.
Return type:: LinearOperator

copy()[source]¶

Create a shallow copy of the Jacobian operator.

Returns:: A shallow copy of the Jacobian operator.
Return type:: JacobianOperator

dot(x)¶

Matrix-matrix or matrix-vector multiplication.

Parameters:: x (array_like) – 1-d or 2-d array, representing a vector or matrix.
Returns:: Ax – 1-d or 2-d array (depending on the shape of x) that represents the result of applying this linear operator on x.
Return type:: array

get_matrix_representation()[source]¶

Compute the matrix representation of the Jacobian.

Returns:: The matrix representation of the Jacobian.
Return type:: ndarray

matmat(X)¶

Matrix-matrix multiplication.

Performs the operation y=A*X where A is an MxN linear operator and X dense N*K matrix or ndarray.

Parameters:: X ({matrix, ndarray}) – An array with shape (N,K).
Returns:: Y – A matrix or ndarray with shape (M,K) depending on the type of the X argument.
Return type:: {matrix, ndarray}

Notes

This matmat wraps any user-specified matmat routine or overridden _matmat method to ensure that y has the correct type.

matvec(x)¶

Matrix-vector multiplication.

Performs the operation y=A*x where A is an MxN linear operator and x is a column vector or 1-d array.

Parameters:: x ({matrix, ndarray}) – An array with shape (N,) or (N,1).
Returns:: y – A matrix or ndarray with shape (M,) or (M,1) depending on the type and shape of the x argument.
Return type:: {matrix, ndarray}

Notes

This matvec wraps the user-specified matvec routine or overridden _matvec method to ensure that y has the correct shape and type.

rmatmat(X)¶

Adjoint matrix-matrix multiplication.

Performs the operation y = A^H * x where A is an MxN linear operator and x is a column vector or 1-d array, or 2-d array. The default implementation defers to the adjoint.

Parameters:: X ({matrix, ndarray}) – A matrix or 2D array.
Returns:: Y – A matrix or 2D array depending on the type of the input.
Return type:: {matrix, ndarray}

Notes

This rmatmat wraps the user-specified rmatmat routine.

rmatvec(x)¶

Adjoint matrix-vector multiplication.

Performs the operation y = A^H * x where A is an MxN linear operator and x is a column vector or 1-d array.

Parameters:: x ({matrix, ndarray}) – An array with shape (M,) or (M,1).
Returns:: y – A matrix or ndarray with shape (N,) or (N,1) depending on the type and shape of the x argument.
Return type:: {matrix, ndarray}

Notes

This rmatvec wraps the user-specified rmatvec routine or overridden _rmatvec method to ensure that y has the correct shape and type.

shift_identity()[source]¶

Substract the identity to the Jacobian operator.

Returns:: The Jacobian operator shifted by minus the identity.
Return type:: _SubJacobianOperator

transpose()¶

Transpose this linear operator.

Returns a LinearOperator that represents the transpose of this one. Can be abbreviated self.T instead of self.transpose().

property H¶

Hermitian adjoint.

Returns the Hermitian adjoint of self, aka the Hermitian conjugate or Hermitian transpose. For a complex matrix, the Hermitian adjoint is equal to the conjugate transpose.

Can be abbreviated self.H instead of self.adjoint().

Returns:: A_H – Hermitian adjoint of self.
Return type:: LinearOperator

property T: _AdjointJacobianOperator¶

The transpose of the Jacobian operator.

Returns:: The transpose of the Jacobian operator.

ndim = 2¶

property real: _RealJacobianOperator¶: The real casting of the Jacobian operator output.