/usr/share/pyshared/linop/blkop.py is in python-linop 0.8.2-2.
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#All rights reserved.
#
#Copyright (c) 2013-2014, Ghislain Vaillant <ghisvail@gmail.com>
#All rights reserved.
#
#Redistribution and use in source and binary forms, with or without
#modification, are permitted provided that the following conditions
#are met:
#1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
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#3. Neither the name of the linop developers nor the names of any contributors
# may be used to endorse or promote products derived from this software
# without specific prior written permission.
#
#THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
#ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
#IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
#ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
#FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
#DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
#OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
#HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
#LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
#OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
#SUCH DAMAGE.
from .linop import BaseLinearOperator, LinearOperator
from .linop import ShapeError, null_log
import numpy as np
import itertools
from functools import reduce
class BlockLinearOperator(LinearOperator):
"""
A linear operator defined by blocks. Each block must be a linear operator.
`blocks` should be a list of lists describing the blocks row-wise.
If there is only one block row, it should be specified as
`[[b1, b2, ..., bn]]`, not as `[b1, b2, ..., bn]`.
If the overall linear operator is symmetric, only its upper triangle
need be specified, e.g., `[[A,B,C], [D,E], [F]]`, and the blocks on the
diagonal must be square and symmetric.
"""
def __init__(self, blocks, symmetric=False, **kwargs):
# If building a symmetric operator, fill in the blanks.
# They're just references to existing objects.
try:
for block_row in blocks:
for block_col in block_row:
op_shape = block_col.shape
except (TypeError, AttributeError):
raise ValueError('blocks should be a nested list of operators')
if symmetric:
nrow = len(blocks)
ncol = len(blocks[0])
if nrow != ncol:
raise ShapeError('Inconsistent shape.')
for block_row in blocks:
if not block_row[0].symmetric:
raise ValueError('Blocks on diagonal must be symmetric.')
self._blocks = blocks[:]
for i in range(1, nrow):
for j in range(i - 1, -1, -1):
self._blocks[i].insert(0, self._blocks[j][i].T)
else:
self._blocks = blocks
log = kwargs.get('logger', null_log)
log.debug('Building new BlockLinearOperator')
nargins = [[blk.shape[-1] for blk in row] for row in self._blocks]
log.debug('nargins = ' + repr(nargins))
nargins_by_row = [nargin[0] for nargin in nargins]
if min(nargins_by_row) != max(nargins_by_row):
raise ShapeError('Inconsistent block shapes')
nargouts = [[blk.shape[0] for blk in row] for row in self._blocks]
log.debug('nargouts = ' + repr(nargouts))
for row in nargouts:
if min(row) != max(row):
raise ShapeError('Inconsistent block shapes')
nargin = sum(nargins[0])
nargout = sum([out[0] for out in nargouts])
# Create blocks of transpose operator.
blocksT = list(map(lambda *row: [blk.T for blk in row], *self._blocks))
def blk_matvec(x, blks):
nargins = [[blk.shape[-1] for blk in blkrow] for blkrow in blks]
nargouts = [[blk.shape[0] for blk in blkrow] for blkrow in blks]
nargin = sum(nargins[0])
nargout = sum([out[0] for out in nargouts])
nx = len(x)
self.logger.debug('Multiplying with a vector of size %d' % nx)
self.logger.debug('nargin=%d, nargout=%d' % (nargin, nargout))
if nx != nargin:
raise ShapeError('Multiplying with vector of wrong shape.')
result_type = np.result_type(self.dtype, x.dtype)
y = np.zeros(nargout, dtype=result_type)
nblk_row = len(blks)
nblk_col = len(blks[0])
row_start = col_start = 0
for row in range(nblk_row):
row_end = row_start + nargouts[row][0]
yout = y[row_start:row_end]
for col in range(nblk_col):
col_end = col_start + nargins[0][col]
xin = x[col_start:col_end]
B = blks[row][col]
yout[:] += B * xin
col_start = col_end
row_start = row_end
col_start = 0
return y
flat_blocks = list(itertools.chain(*blocks))
blk_dtypes = [blk.dtype for blk in flat_blocks]
op_dtype = np.result_type(*blk_dtypes)
super(BlockLinearOperator, self).__init__(
nargin, nargout,
symmetric=symmetric,
matvec=lambda x: blk_matvec(x, self._blocks),
rmatvec=lambda x: blk_matvec(x, blocksT),
dtype=op_dtype,
**kwargs)
self.H._blocks = blocksT
@property
def blocks(self):
"""The list of blocks defining the block operator."""
return self._blocks
def __getitem__(self, indices):
blks = np.matrix(self._blocks, dtype=object)[indices]
# If indexing narrowed it down to a single block, return it.
if isinstance(blks, BaseLinearOperator):
return blks
# Otherwise, we have a matrix of blocks.
return BlockLinearOperator(blks.tolist(), symmetric=False)
def __contains__(self, op):
flat_blocks = list(itertools.chain(*self.blocks))
return op in flat_blocks
def __iter__(self):
for block in self._blocks:
yield block
class BlockDiagonalLinearOperator(LinearOperator):
"""
A block diagonal linear operator.
Each block must be a linear operator.
The blocks may be specified as one list, e.g., `[A, B, C]`.
"""
def __init__(self, blocks, **kwargs):
try:
for block in blocks:
op_shape = block.shape
except (TypeError, AttributeError):
raise ValueError('blocks should be a flattened list of operators')
symmetric = reduce(
lambda x, y: x and y, [blk.symmetric for blk in blocks])
self._blocks = blocks
log = kwargs.get('logger', null_log)
log.debug('Building new BlockDiagonalLinearOperator')
nargins = [blk.shape[-1] for blk in blocks]
log.debug('nargins = ' + repr(nargins))
nargouts = [blk.shape[0] for blk in blocks]
log.debug('nargouts = ' + repr(nargouts))
nargin = sum(nargins)
nargout = sum(nargouts)
# Create blocks of transpose operator.
blocksT = [blk.T for blk in blocks]
def blk_matvec(x, blks):
nx = len(x)
nargins = [blk.shape[-1] for blk in blocks]
nargin = sum(nargins)
nargouts = [blk.shape[0] for blk in blocks]
nargout = sum(nargouts)
self.logger.debug('Multiplying with a vector of size %d' % nx)
self.logger.debug('nargin=%d, nargout=%d' % (nargin, nargout))
if nx != nargin:
raise ShapeError('Multiplying with vector of wrong shape.')
result_type = np.result_type(self.dtype, x.dtype)
y = np.empty(nargout, dtype=result_type)
nblks = len(blks)
row_start = col_start = 0
for blk in range(nblks):
row_end = row_start + nargouts[blk]
yout = y[row_start:row_end]
col_end = col_start + nargins[blk]
xin = x[col_start:col_end]
B = blks[blk]
yout[:] = B * xin
col_start = col_end
row_start = row_end
return y
blk_dtypes = [blk.dtype for blk in blocks]
op_dtype = np.result_type(*blk_dtypes)
super(BlockDiagonalLinearOperator, self).__init__(
nargin, nargout,
symmetric=symmetric,
matvec=lambda x: blk_matvec(x, self._blocks),
rmatvec=lambda x: blk_matvec(x, blocksT),
dtype=op_dtype,
**kwargs)
self.H._blocks = blocksT
@property
def blocks(self):
"""The list of blocks defining the block diagonal operator."""
return self._blocks
def __getitem__(self, idx):
blks = self._blocks[idx]
if isinstance(idx, slice):
return BlockDiagonalLinearOperator(blks, symmetric=self.symmetric)
return blks
def __setitem__(self, idx, ops):
if not isinstance(ops, BaseLinearOperator):
if isinstance(ops, list) or isinstance(ops, tuple):
for op in ops:
if not isinstance(op, BaseLinearOperator):
msg = 'Block operators can only contain'
msg += ' linear operators'
raise ValueError(msg)
self._blocks[idx] = ops
class BlockPreconditioner(BlockLinearOperator):
"""An alias for ``BlockLinearOperator``.
Holds an additional ``solve`` method equivalent to ``__mul__``.
"""
def solve(self, x):
"""An alias to __call__."""
return self.__call__(x)
class BlockDiagonalPreconditioner(BlockDiagonalLinearOperator):
"""
An alias for ``BlockDiagonalLinearOperator``.
Holds an additional ``solve`` method equivalent to ``__mul__``.
"""
def solve(self, x):
"""An alias to __call__."""
return self.__call__(x)
class BlockHorizontalLinearOperator(BlockLinearOperator):
"""
A block horizontal linear operator.
Each block must be a linear operator.
The blocks must be specified as one list, e.g., `[A, B, C]`.
"""
def __init__(self, blocks, **kwargs):
try:
for block in blocks:
op_shape = block.shape
except (TypeError, AttributeError):
raise ValueError('blocks should be a flattened list of operators')
blocks=[[blk for blk in blocks]]
super(BlockHorizontalLinearOperator, self).__init__(
blocks=blocks, symmetric=False, **kwargs)
class BlockVerticalLinearOperator(BlockLinearOperator):
"""
A block vertical linear operator.
Each block must be a linear operator.
The blocks must be specified as one list, e.g., `[A, B, C]`.
"""
def __init__(self, blocks, **kwargs):
try:
for block in blocks:
op_shape = block.shape
except (TypeError, AttributeError):
raise ValueError('blocks should be a flattened list of operators')
blocks=[[blk] for blk in blocks]
super(BlockVerticalLinearOperator, self).__init__(
blocks=blocks, symmetric=False, **kwargs)
# some shorter aliases
BlockOperator = BlockLinearOperator
BlockDiagonalOperator = BlockDiagonalLinearOperator
BlockHorizontalOperator = BlockHorizontalLinearOperator
BlockVerticalOperator = BlockVerticalLinearOperator
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