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 withdiag
is perfomed on the directiondir
. Note that the vectordiag
will need to have size equal todims[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-valueddiag
, the adjoint is equivalent to the element-wise multiplication with the complex conjugate elements ofdiag
.Attributes: 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. rmatvec
(self, x)Adjoint matrix-vector multiplication. transpose
(self)Transpose this linear operator. -
matrix
(self)[source]¶ Return diagonal matrix as dense
numpy.ndarray
Returns: - densemat :
numpy.ndarray
Dense matrix.
- densemat :
- diag :