class pylops.Sum(dims, dir, dtype='float64')[source]

Sum operator.

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

dims : tuple

Number of samples for each dimension

dir : int

Direction along which summation is performed.

dtype : str, optional

Type of elements in input array.


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 direction dir:

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

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

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

Operator shape

explicit : bool

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


__init__(dims, dir[, dtype]) 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, 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.
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() Transpose this linear operator.

Examples using pylops.Sum