Source code for pylops.basicoperators.Gradient

import numpy as np

from pylops.basicoperators import FirstDerivative, VStack

[docs]def Gradient(dims, sampling=1, edge=False, dtype="float64", kind="centered"): r"""Gradient. Apply gradient operator to a multi-dimensional array. .. note:: At least 2 dimensions are required, use :py:func:`pylops.FirstDerivative` for 1d arrays. Parameters ---------- dims : :obj:`tuple` Number of samples for each dimension. sampling : :obj:`tuple`, optional Sampling steps for each direction. edge : :obj:`bool`, optional Use reduced order derivative at edges (``True``) or ignore them (``False``). dtype : :obj:`str`, optional Type of elements in input array. kind : :obj:`str`, optional Derivative kind (``forward``, ``centered``, or ``backward``). Returns ------- l2op : :obj:`pylops.LinearOperator` Gradient linear operator Notes ----- The Gradient operator applies a first-order derivative to each dimension of a multi-dimensional array in forward mode. For simplicity, given a three dimensional array, the Gradient in forward mode using a centered stencil can be expressed as: .. math:: \mathbf{g}_{i, j, k} = (f_{i+1, j, k} - f_{i-1, j, k}) / d_1 \mathbf{i_1} + (f_{i, j+1, k} - f_{i, j-1, k}) / d_2 \mathbf{i_2} + (f_{i, j, k+1} - f_{i, j, k-1}) / d_3 \mathbf{i_3} which is discretized as follows: .. math:: \mathbf{g} = \begin{bmatrix} \mathbf{df_1} \\ \mathbf{df_2} \\ \mathbf{df_3} \end{bmatrix} In adjoint mode, the adjoints of the first derivatives along different axes are instead summed together. """ ndims = len(dims) if isinstance(sampling, (int, float)): sampling = [sampling] * ndims gop = VStack( [ FirstDerivative(, dims=dims, dir=idir, sampling=sampling[idir], edge=edge, kind=kind, dtype=dtype, ) for idir in range(ndims) ] ) return gop