import numpy as np
from pylops import LinearOperator
class Diagonal(LinearOperator):
r"""Diagonal operator.
Applies element-wise multiplication of the input vector with the vector
``diag`` in forward and with its complex conjugate in adjoint mode.
This operator can also broadcast; in this case the input vector is
reshaped into its dimensions ``dims`` and the element-wise multiplication
with ``diag`` is perfomed on the direction ``dir``. Note that the
vector ``diag`` will need to have size equal to ``dims[dir]``.
Parameters
----------
diag : :obj:`numpy.ndarray`
Vector to be used for element-wise multiplication.
dims : :obj:`list`, optional
Number of samples for each dimension
(``None`` if only one dimension is available)
dir : :obj:`int`, optional
Direction along which multiplication is applied.
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
-----
Element-wise multiplication between the model :math:`\mathbf{x}` and/or
data :math:`\mathbf{y}` vectors and the array :math:`\mathbf{d}`
can be expressed as
.. math::
y_i = d_i x_i \quad \forall i=1,2,...,N
This is equivalent to a matrix-vector multiplication with a matrix
containing the vector :math:`\mathbf{d}` along its main diagonal.
For real-valued ``diag``, the Diagonal operator is self-adjoint as the
adjoint of a diagonal matrix is the diagonal matrix itself. For
complex-valued ``diag``, the adjoint is equivalent to the element-wise
multiplication with the complex conjugate elements of ``diag``.
"""
def __init__(self, diag, dims=None, dir=0, dtype='float64'):
self.diag = diag.flatten()
self.complex = True if np.iscomplexobj(self.diag) else False
if dims is None:
self.shape = (len(self.diag), len(self.diag))
self.dims = None
self.reshape = False
else:
diagdims = [1] * len(dims)
diagdims[dir] = dims[dir]
self.diag = self.diag.reshape(diagdims)
self.shape = (np.prod(dims), np.prod(dims))
self.dims = dims
self.reshape = True
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
if not self.reshape:
y = self.diag * x.ravel()
else:
x = x.reshape(self.dims)
y = self.diag * x
return y.ravel()
def _rmatvec(self, x):
if self.complex:
diagadj = self.diag.conj()
else:
diagadj = self.diag
if not self.reshape:
y = diagadj * x.ravel()
else:
x = x.reshape(self.dims)
y = diagadj * x
return y.ravel()
def matrix(self):
"""Return diagonal matrix as dense :obj:`numpy.ndarray`
Returns
----------
densemat : :obj:`numpy.ndarray`
Dense matrix.
"""
densemat = np.diag(self.diag.squeeze())
return densemat
