pylops.Sum

class pylops.Sum(dims, axis=-1, forceflat=None, dtype='float64', name='S')

Sum operator.

Sum along axis of a multi-dimensional array (at least 2 dimensions are required) in forward model, and spread along the same axis in adjoint mode.

Parameters:

dimstuple

Number of samples for each dimension

axisint, optional

Added in version 2.0.0.

Axis along which model is summed.

forceflatbool, optional

Added in version 2.2.0.

Force an array to be flattened after rmatvec. Note that this is only required when len(dims)=2, otherwise pylops will detect whether to return a 1d or nd array.

dtypestr, optional

Type of elements in input array.

namestr, optional

Added in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

Attributes:

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening.

For example, y_reshaped = (Op * x.ravel()).reshape(Op.dimsd).

shapetuple

Operator shape.

Notes

Given a two dimensional array, the Sum operator re-arranges the input model into a multi-dimensional array of size dims and sums values along axis:

\[y_j = \sum_i x_{i, j}\]

In adjoint mode, the data is spread along the same direction:

\[x_{i, j} = y_j \quad \forall i=0, N-1\]

Methods

__init__(dims[, axis, forceflat, 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.
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()

Examples using pylops.Sum

Sum

Sum