pylops_gpu.LinearOperator

class pylops_gpu.LinearOperator(shape, dtype, Op=None, explicit=False, device='cpu', togpu=(False, False), tocpu=(False, False))[source]

Common interface for performing matrix-vector products.

This class is an overload of the pylops.LinearOperator class. It adds functionalities for operators on GPUs; specifically, it allows users specifying when to move model and data from the host to the device and viceversa.

Compared to its equivalent PyLops class pylops.LinearOperator, it requires input model and data to be torch.Tensor objects.

Note

End users of PyLops should not use this class directly but simply use operators that are already implemented. This class is meant for developers and it has to be used as the parent class of any new operator developed within PyLops-gpu. Find more details regarding implementation of new operators at Implementing new operators.

Parameters:
shape : tuple

Operator shape

dtype : torch.dtype, optional

Type of elements in input array.

Op : pylops.LinearOperator

Operator to wrap in LinearOperator (if None, self must implement _matvec_ and _rmatvec_)

explicit : bool

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

device : str, optional

Device to be used

togpu : tuple, optional

Move model and data from cpu to gpu prior to applying matvec and rmatvec, respectively (only when device='gpu')

tocpu : tuple, optional

Move data and model from gpu to cpu after applying matvec and rmatvec, respectively (only when device='gpu')

Methods

__init__(shape, dtype[, Op, explicit, …]) 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, tol]) 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[, kfirst]) Matrix-matrix multiplication.
matvec(x) Matrix-vector multiplication.
rmatmat(X[, kfirst]) Adjoint 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.
transpose() Transpose this linear operator.
matvec(x)[source]

Matrix-vector multiplication.

Performs the operation y = A * x where A is an \(N \times M\) linear operator and x is a 1-d array.

Parameters:
x : torch.Tensor

An array with shape (M,)
Returns:
y : torch.Tensor

An array with shape (N,)
rmatvec(x)[source]

Adjoint matrix-vector multiplication.

Performs the operation y = A^H * x where A is an \(N imes M\) linear operator and x is a 1-d array.

Parameters:
x : torch.Tensor

An array with shape (N,)
Returns:
y : torch.Tensor

An array with shape (M,)
matmat(X, kfirst=False)[source]

Matrix-matrix multiplication.

Performs the operation Y = A * X where A is an \(N imes M\) linear operator and X is a 2-d array of size \(K imes M\) (kfirst=True) or \(M imes K\) (kfirst=False).

Parameters:
x : torch.Tensor

An array with shape (M, K) or (K, M)

kfirst : bool, optional

Dimension K along which the matrix multiplication is performed is in the first dimension (True) or in the second dimension (False)
Returns:
y : torch.Tensor

An array with shape (N, K) or (K, N)
rmatmat(X, kfirst=False)[source]

Adjoint matrix-matrix multiplication.

Performs the operation Y = A^H * X where A is an \(N imes M\) linear operator and X is a 2-d array of size \(K imes N\) (kfirst=True) or \(N imes K\) (kfirst=False).

Parameters:
x : torch.Tensor

An array with shape (N, K) or (K, N)

kfirst : bool, optional

Dimension K along which the matrix multiplication is performed is in the first dimension (True) or in the second dimension (False)
Returns:
y : torch.Tensor

An array with shape (M, K) or (K, M)
dot(x)[source]

Matrix-vector multiplication.

Parameters:
x : torch.Tensor or pytorch_complex_tensor.ComplexTensor

1-d or 2-d array, representing a vector or matrix.
Returns:
Ax : torch.Tensor or pytorch_complex_tensor.ComplexTensor

1-d or 2-d array (depending on the shape of x) that represents the result of applying this linear operator on x.
adjoint()[source]

Hermitian adjoint.

Returns the Hermitian adjoint. Can be abbreviated self.H instead of self.adjoint().

H

Hermitian adjoint.

Returns the Hermitian adjoint. Can be abbreviated self.H instead of self.adjoint().

div(y, niter=100, tol=0.0001)[source]

Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).

Overloading of operator / to improve expressivity of Pylops_gpu when solving inverse problems.

Parameters:
y : torch.Tensor

Data

niter : int, optional

Number of iterations (to be used only when explicit=False)

tol : int

Residual norm tolerance
Returns:
xest : np.ndarray

Estimated model