import numpy as np
from pylops_distributed import LinearOperator
from pylops_distributed.signalprocessing import Convolve1D
[docs]class SecondDerivative(LinearOperator):
r"""Second derivative.
Apply second-order centered second derivative.
Parameters
----------
N : :obj:`int`
Number of samples in model.
dims : :obj:`tuple`, optional
Number of samples for each dimension
(``None`` if only one dimension is available)
dir : :obj:`int`, optional
Direction along which smoothing is applied.
sampling : :obj:`float`, optional
Sampling step ``dx``.
compute : :obj:`tuple`, optional
Compute the outcome of forward and adjoint or simply define the graph
and return a :obj:`dask.array.array`
chunks : :obj:`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 : :obj:`tuple`, optional
Apply :func:`dask.array.from_array` to model and data before applying
forward and adjoint respectively
dtype : :obj:`str`, optional
Type of elements in input array.
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly (``True``) or
not (``False``)
Notes
-----
Refer to :class:`pylops.basicoperators.SecondDerivative` for implementation
details.
"""
def __init__(self, N, dims=None, dir=0, sampling=1.,
compute=(False, False), chunks=(None, None),
todask=(False, False), dtype='float64'):
h = np.array([1., -2, 1.], dtype=dtype) / sampling**2
self.compute = compute
self.chunks = chunks
self.todask = todask
self.shape = (N, N)
self.dtype = dtype
self.explicit = False
self.Op = Convolve1D(N, h, offset=1, dims=dims, dir=dir,
compute=compute, chunks=chunks,
todask=todask, dtype='float64')