pylops.Diagonal

class pylops.Diagonal(diag, dims=None, dir=0, dtype='float64')[source]

Diagonal operator.

Applies element-wise multiplication of the input vector with the vector diag in forward and with its complex conjugate in adjoint mode.

This operator can also broadcast; in this case the input vector is reshaped into its dimensions dims and the element-wise multiplication with diag is perfomed on the direction dir. Note that the vector diag will need to have size equal to dims[dir].

Parameters:
diag : numpy.ndarray

Vector to be used for element-wise multiplication.

dims : list, optional

Number of samples for each dimension (None if only one dimension is available)

dir : int, optional

Direction along which multiplication is applied.

dtype : str, optional

Type of elements in input array.

Notes

Element-wise multiplication between the model \(\mathbf{x}\) and/or data \(\mathbf{y}\) vectors and the array \(\mathbf{d}\) can be expressed as

\[y_i = d_i x_i \quad \forall i=1,2,...,N\]

This is equivalent to a matrix-vector multiplication with a matrix containing the vector \(\mathbf{d}\) along its main diagonal.

For real-valued diag, the Diagonal operator is self-adjoint as the adjoint of a diagonal matrix is the diagonal matrix itself. For complex-valued diag, the adjoint is equivalent to the element-wise multiplication with the complex conjugate elements of diag.

Attributes:
shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

__init__(self, diag[, dims, dir, dtype]) Initialize this LinearOperator.
adjoint(self) Hermitian adjoint.
apply_columns(self, cols) Apply subset of columns of operator
cond(self, **kwargs_eig) Condition number of linear operator.
conj(self) Complex conjugate operator
div(self, y[, niter]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(self, x) Matrix-matrix or matrix-vector multiplication.
eigs(self[, neigs, symmetric, niter]) Most significant eigenvalues of linear operator.
matmat(self, X) Matrix-matrix multiplication.
matrix(self) Return diagonal matrix as dense numpy.ndarray
matvec(self, x) Matrix-vector multiplication.
rmatmat(self, X) Adjoint matrix-matrix multiplication.
rmatvec(self, x) Adjoint matrix-vector multiplication.
todense(self) Return dense matrix.
transpose(self) Transpose this linear operator.
matrix(self)[source]

Return diagonal matrix as dense numpy.ndarray

Returns:
densemat : numpy.ndarray

Dense matrix.

Examples using pylops.Diagonal