# 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.

## Examples using pylops.Diagonal¶ Describe Diagonal 01. The LinearOpeator 02. The Dot-Test