pylops_distributed.signalprocessing.Fredholm1

class pylops_distributed.signalprocessing.Fredholm1(G, nz=1, saveGt=True, compute=(False, False), chunks=(None, None), todask=(None, None), dtype='float64')

Fredholm integral of first kind.

Implement a multi-dimensional Fredholm integral of first kind. Note that if the integral is two dimensional, this can be directly implemented using pylops.basicoperators.MatrixMult. A multi-dimensional Fredholm integral can be performed as a pylops.basicoperators.BlockDiag operator of a series of pylops.basicoperators.MatrixMult. However, here we take advantage of the structure of the kernel and perform it in a more efficient manner.

Parameters:

G : numpy.ndarray

Multi-dimensional convolution kernel of size \([n_{slice} \times n_x \times n_y]\)

nz : numpy.ndarray, optional

Additional dimension of model

saveGt : bool, optional

Save G and G^H to speed up the computation of adjoint (True) or create G^H on-the-fly (False) Note that saveGt=True will double the amount of required memory

compute : tuple, optional

Compute the outcome of forward and adjoint or simply define the graph and return a dask.array

chunks : tuple, optional

Chunk size for model and data. If provided it will rechunk the model before applying the forward pass and the data before applying the adjoint pass

todask : tuple, optional

Apply dask.array.from_array to model and data before applying forward and adjoint respectively

dtype : str, optional

Type of elements in input array.

Notes

Refer to pylops.signalprocessing.Identity for implementation details.

Attributes:

shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

__init__(G[, nz, saveGt, compute, chunks, …])	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])	Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x)	Matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg])	Most significant eigenvalues of linear operator.
matmat(X)	Matrix-matrix multiplication.
matvec(x)	Matrix-vector multiplication.
rmatmat(X)	Adjoint matrix-matrix multiplication.
rmatvec(x)	Adjoint Matrix-vector multiplication.
todense()	Return dense matrix.
tosparse()	Return sparse matrix.
transpose()	Transpose this linear operator.