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 withdiag
is perfomed alongaxis
. Note that the vectordiag
will need to have size equal todims[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
)
- diag
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-valueddiag
, the adjoint is equivalent to the element-wise multiplication with the complex conjugate elements ofdiag
.- Attributes
- shape
tuple
Operator shape
- explicit
bool
Operator contains a matrix that can be solved explicitly (
True
) or not (False
)
- shape
Methods
__init__
(diag[, dims, axis, dtype, name])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
()