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

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

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, dir, dtype])	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.
`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.