import numpy as np
from scipy.sparse.linalg.interface import _get_dtype
from pylops import LinearOperator
[docs]class BlockDiag(LinearOperator):
r"""Block-diagonal operator.
Create a block-diagonal operator from N linear operators.
Parameters
----------
ops : :obj:`list`
Linear operators to be stacked
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
-----
A block-diagonal operator composed of N linear operators is created such
as its application in forward mode leads to
.. math::
\begin{bmatrix}
\mathbf{L_1} & \mathbf{0} & ... & \mathbf{0} \\
\mathbf{0} & \mathbf{L_2} & ... & \mathbf{0} \\
... & ... & ... & ... \\
\mathbf{0} & \mathbf{0} & ... & \mathbf{L_N}
\end{bmatrix}
\begin{bmatrix}
\mathbf{x}_{1} \\
\mathbf{x}_{2} \\
... \\
\mathbf{x}_{N}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L_1} \mathbf{x}_{1} \\
\mathbf{L_2} \mathbf{x}_{2} \\
... \\
\mathbf{L_N} \mathbf{x}_{N}
\end{bmatrix}
while its application in adjoint mode leads to
.. math::
\begin{bmatrix}
\mathbf{L_1}^H \quad \mathbf{0} \quad ... \quad \mathbf{0} \\
\mathbf{0} \quad \mathbf{L_2}^H \quad ... \quad \mathbf{0} \\
... \quad ... \quad ... \quad ... \\
\mathbf{0} \quad \mathbf{0} \quad ... \quad \mathbf{L_N}^H
\end{bmatrix}
\begin{bmatrix}
\mathbf{y}_{1} \\
\mathbf{y}_{2} \\
... \\
\mathbf{y}_{N}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L_1}^H \mathbf{y}_{1} \\
\mathbf{L_2}^H \mathbf{y}_{2} \\
... \\
\mathbf{L_N}^H \mathbf{y}_{N}
\end{bmatrix}
"""
def __init__(self, ops, dtype=None):
self.ops = ops
mops = np.zeros(len(ops), dtype=np.int)
nops = np.zeros(len(ops), dtype=np.int)
for iop, oper in enumerate(ops):
nops[iop] = oper.shape[0]
mops[iop] = oper.shape[1]
self.nops = nops.sum()
self.mops = mops.sum()
self.nnops = np.insert(np.cumsum(nops), 0, 0)
self.mmops = np.insert(np.cumsum(mops), 0, 0)
self.shape = (self.nops, self.mops)
if dtype is None:
self.dtype = _get_dtype(ops)
else:
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
y = np.zeros(self.nops, dtype=self.dtype)
for iop, oper in enumerate(self.ops):
y[self.nnops[iop]:self.nnops[iop + 1]] = \
oper.matvec(x[self.mmops[iop]:self.mmops[iop + 1]])
return y
def _rmatvec(self, x):
y = np.zeros(self.mops, dtype=self.dtype)
for iop, oper in enumerate(self.ops):
y[self.mmops[iop]:self.mmops[iop + 1]] = \
oper.rmatvec(x[self.nnops[iop]:self.nnops[iop + 1]])
return y