pylops.Laplacian#
- class pylops.Laplacian(dims, axes=(-2, -1), weights=(1, 1), sampling=(1, 1), edge=False, kind='centered', dtype='float64', name='L')[source]#
Laplacian.
Apply second-order centered Laplacian operator to a multi-dimensional array.
Note
At least 2 dimensions are required, use
pylops.SecondDerivative
for 1d arrays.- Parameters
- dims
tuple
Number of samples for each dimension.
- axes
int
, optional New in version 2.0.0.
Axes along which the Laplacian is applied.
- weights
tuple
, optional Weight to apply to each direction (real laplacian operator if
weights=(1, 1)
)- sampling
tuple
, optional Sampling steps for each direction
- edge
bool
, optional Use reduced order derivative at edges (
True
) or ignore them (False
) for centered derivative- kind
str
, optional Derivative kind (
forward
,centered
, orbackward
)- dtype
str
, optional Type of elements in input array.
- dims
- Raises
- ValueError
If
axes
.weights
, andsampling
do not have the same size
Notes
The Laplacian operator applies a second derivative along two directions of a multi-dimensional array.
For simplicity, given a two dimensional array, the Laplacian is:
\[y[i, j] = (x[i+1, j] + x[i-1, j] + x[i, j-1] +x[i, j+1] - 4x[i, j]) / (\Delta x \Delta y)\]Methods
__init__
(dims[, axes, weights, sampling, ...])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.
matvec
(x)Matrix-vector multiplication.
reset_count
()Reset counters
rmatmat
(X)Matrix-matrix multiplication.
rmatvec
(x)Adjoint matrix-vector multiplication.
todense
([backend])Return dense matrix.
toimag
([forw, adj])Imag operator
toreal
([forw, adj])Real operator
tosparse
()Return sparse matrix.
trace
([neval, method, backend])Trace of linear operator.
transpose
()