pylops.Diagonal

class pylops.Diagonal(diag, dims=None, axis=-1, dtype='float64', name='D')[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 along axis. Note that the vector diag will need to have size equal to dims[axis].

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)

axis : int, optional

New in version 2.0.0.

Axis along which multiplication is applied.

dtype : str, optional

Type of elements in input array.

name : str, optional

New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

Notes

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

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

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__(diag[, dims, axis, dtype, name]) Initialize this LinearOperator.
adjoint() Hermitian adjoint.
apply_columns(cols) Apply subset of columns of operator
cond([uselobpcg]) Condition number of linear operator.
conj() Complex conjugate operator
div(y[, niter, densesolver]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x) Matrix-matrix or matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg]) Most significant eigenvalues of linear operator.
matmat(X) Matrix-matrix multiplication.
matrix() Return diagonal matrix as dense numpy.ndarray
matvec(x) Matrix-vector multiplication.
reset_count() Reset counters
rmatmat(X) Matrix-matrix multiplication.
rmatvec(x) Adjoint matrix-vector multiplication.
todense() Fast implementation of todense based on known structure of the operator
toimag([forw, adj]) Imag operator
toreal([forw, adj]) Real operator
tosparse() Return sparse matrix.
trace([neval, method, backend]) Trace of linear operator.
transpose() Transpose this linear operator.
matrix()[source]

Return diagonal matrix as dense numpy.ndarray

Returns:
densemat : numpy.ndarray

Dense matrix.

todense()[source]

Fast implementation of todense based on known structure of the operator

Returns:
densemat : numpy.ndarray

Dense matrix.