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MatBlock.py
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MatBlock.py
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#!/usr/bin/env python
from __future__ import division, print_function, absolute_import
__docformat__ = "restructuredtext en"
#__all__ = ['lil_matrix','isspmatrix_lil']
from bisect import bisect_left
import numpy as np
from scipy.sparse.sputils import getdtype
from scipy.sparse import lil_matrix
# support for the last version of LinearOperator
# from interface import *
def isshape(x):
try:
(m, n) = x
except:
return False
else:
if isinstance(m, int) and isinstance(n, int):
return True
else:
return False
class Block:
"""
A block is an object with at least two attributes
-- shape : (M,N) tuple of integer
-- matvec or dot : a function
that returns a vector of length M
when applies a vector of length N
the initial object with all its attributes is referenced in .orig
Block owns attributes:
-- shape
-- matvec
-- type
-- orig
"""
def __init__(self, block):
if hasattr(block, 'shape'):
self.shape = block.shape
else:
raise TypeError('a block needs a shape.')
if hasattr(block, 'dot'):
self.matvec = block.dot
elif hasattr(block, 'matvec'):
self.matvec = block.matvec
else:
raise TypeError('a block needs a matvec/dot.')
self.type = type(block)
self.orig = block
if hasattr(block, 'dtype'):
self.dtype= block.dtype
else:
self.dtype = float
class MatBlock:
""" class which manages a linear operator by blocks, e.g.,
\t[ A B ]
\t[ C D ]
with A, B, C and D are:
numpy.ndarray OR scipy.sparse.linalg.LinearOperator
It is compatible with scipy.sparse.linalg.LinearOperator,
i.e., all the linear solvers from scipy are usable.
Moreover, the classical operations scalar*, + and - are available.
\n
Row-based linked list sparse matrix
"""
def __init__(self, shape=(0, 0), dtype=int):
if not isshape(shape):
raise ValueError('not an acceptable tuple.')
try:
self.dtype = dtype
r, c = shape
self.Shape = (r, c)
if c>0:
# see if array+concatenate is not better?
##
# this part slows down addBlock()
# because the current update of the offsets needs more loops
# FIXME: remove unnecessary loops (those of empty value)
self.cols = [ list([]) for i in range(c) ]
self.data = [ list([]) for i in range(c) ]
else:
self.cols = [[]]
self.data = [[]]
self.shape = (0, 0)
self._shapes_row = np.array([ -1 for i in range(r) ], dtype=int)
self._shapes_col = np.array([ -1 for i in range(c) ], dtype=int)
self._offsets_row = np.array([ 0 for i in range(r) ], dtype=int)
self._offsets_col = np.array([ 0 for i in range(c) ], dtype=int)
except:
raise TypeError('MatBlock constructor fails. Hum?')
def addBlock(self, pos, b, expert=False):
if not isshape(pos):
raise ValueError('not an acceptable tuple.')
block = Block(b)
if block.dtype == float and self.dtype == int:
self.dtype = float
elif block.dtype == complex and self.dtype == float:
self.dtype = complex
elif block.dtype == complex and self.dtype == int:
self.dtype = complex
R, C = self.shape
rr, cc = self.Shape
r, c = pos
if r+1>=rr:
rr = r+1
if c+1>=cc:
cc = c+1
self.Shape = (rr, cc)
le = len(self._shapes_row)
if le < rr:
t = np.array([ 0 for i in range(le, rr) ], dtype=int)
s = self._shapes_row
self._shapes_row = np.concatenate((s,t))
s = self._offsets_row
self._offsets_row = np.concatenate((s,t))
le = len(self._shapes_col)
if le < cc:
t = np.array([ 0 for i in range(le, cc) ], dtype=int)
s = self._shapes_col
self._shapes_col = np.concatenate((s,t))
s = self._offsets_col
self._offsets_col = np.concatenate((s,t))
le = len(self.cols)
if le < cc:
t = [ [] for i in range(le, cc) ]
self.cols.extend(t)
# warning: reference, pointer and memory
t = [ [] for i in range(le, cc) ]
self.data.extend(t)
if self._shapes_row[r] == 0:
self._shapes_row[r] = block.shape[0]
R += block.shape[0]
elif self._shapes_row[r] != block.shape[0]:
raise ValueError('invalid block size.')
if self._shapes_col[c] == 0:
self._shapes_col[c] = block.shape[1]
C += block.shape[1]
elif self._shapes_col[c] != block.shape[1]:
raise ValueError('invalid block size.')
self.shape = (R, C)
###
# the blocks are stored row-sorted
###
# if the blocks are added in a natural order
# ie (i,j) added before (I,J) ; i<I j<J
# then the insertion is replaced by an append
# because it is faster
# (more or less, memory allocation/reallocation)
#
# the sort is time consuming
# FIXME(for large matrix, expert=True+_expert())
##
# it is assumed that:
# add an already existing block is a rare case
##
N, append = len(self.cols[c]), False
if N == 0:
append = True
else:
if r > self.cols[c][N-1]:
append = True
else:
# this is a naive insertion-sort
## make time if not almost sorted
if expert:
for ii in range(N-1, -2, -1):
if r > self.cols[c][ii]:
self.cols[c].insert(ii+1, r)
self.data[c].insert(ii+1, block)
break
elif r == self.cols[c][ii]:
print('Warning: a block already exists here. Now, overwritten.')
self.data[c][ii] = block
ii = N # ugly hack!
break
if ii == -1:
self.cols[c].insert(0, r)
self.data[c].insert(0, block)
else:
append = True
if append:
self.cols[c].append(r)
self.data[c].append(block)
if not expert:
# these should make time
self._expert()
def _expert(self):
tot = 0
for ii, s in enumerate(self._shapes_col[0:-1]):
tot += s
self._offsets_col[ii+1] = tot
tot = 0
for ii, s in enumerate(self._shapes_row[0:-1]):
tot += s
self._offsets_row[ii+1] = tot
def getBlock(self, pos):
if not isshape(pos):
raise ValueError('not an acceptable tuple.')
r, c = pos
R, C = self.Shape
if r > R-1:
raise ValueError('inexisting block. [row]')
if c > C-1:
raise ValueError('inexisting block. [col]')
try:
i = self.cols[c].index(r)
except:
i = -1
if i >= 0:
return self.data[c][i].orig
else:
return 0
def diag(self):
M = MatBlock()
R, C = self.Shape
I = max(R, C)
for i in range(I):
b = self.getBlock((i, i))
if not isinstance(b, int):
M.addBlock((i, i), b)
return M
def rmBlock(self, pos):
if isinstance(pos, tuple):
raise NotImplementedError
else:
raise NotImplementedError
def matvec(self, x):
x = np.asanyarray(x)
M, N = self.shape
if x.shape != (N,) and x.shape != (N,1):
raise ValueError('dimension mismatch.')
y = np.zeros(x.shape, dtype=self.dtype)
for c, blocks in enumerate(self.data):
beg = self._offsets_col[c]
end = beg + self._shapes_col[c]
xi = x[beg:end]
for i, block in enumerate(blocks):
r = self.cols[c][i]
begg = self._offsets_row[r]
endd = begg + self._shapes_row[r]
y[begg:endd] += block.matvec(xi)
return y
def concatenate(self, M, overwrite=False):
pass
def toLinOp(self):
return LinearOperator(shape=self.shape, matvec=self.matvec)
def tolil(self):
lil = lil_matrix(self.shape, dtype=self.dtype)
for c, blocks in enumerate(self.data):
beg = self._offsets_col[c]
end = beg + self._shapes_col[c]
for i, block in enumerate(blocks):
r = self.cols[c][i]
begg = self._offsets_row[r]
endd = begg + self._shapes_row[r]
if isinstance(block.orig, np.ndarray) \
or isinstance(block.orig, np.matrix):
b = block.orig
else:
try:
b = block.orig.todense()
except:
n, m = block.shape
b = np.empty((n, m), dtype=self.dtype)
for i in range(m):
ei = np.zeros((m,))
ei[i] = 1.0
b[:,i] = block.matvec(ei)
lil[begg:endd,beg:end] = b
return lil
def todense(self):
return self.tolil().todense()
def spy(self):
pass
def view(self):
print(self.todense().view())
def isBlock(x):
return isinstance(x, Block)
def isMatBlock(x):
return isinstance(x, MatBlock)
class Myeye:
def __init__(self,shape=(0,0)):
self.shape=shape
self.dtype=float
def matvec(self,x):
return 2.2*x
if __name__ == "__main__":
print("test")
M1 = MatBlock(dtype=float)
# M2 = MatBlock((2,3))
# # M1.addBlock((1,1),2)
from scipy.sparse import eye
f = Myeye((4,4))
M1.addBlock((0,0),np.ones((2,2)))
M1.addBlock((1,1),2*eye(3,3))
M1.addBlock((2,0),2*np.ones((4,2)))
M1.addBlock((0,2),3*np.ones((2,4)))
M1.addBlock((2,2),f)
u = np.ones(M1.shape[0])
for i in range(M1.shape[0]):
u[i] = i+1
v = M1.matvec(u)
print('----New')
a = M1.toLinOp()
M2 = MatBlock()
M2.addBlock((0,0),M1)
M2.addBlock((1,1),a)
uu = np.ones(M2.shape[0])
# for i in range(M2.shape[0]):
# uu[i] = i+1
vv = M2.matvec(uu)
# a = np.eye(3)
# b = np.eye(4)
# M = MatBlock()
# M.addBlock((7,0), 7*a)
# M.addBlock((4,0), 4*a)
# M.addBlock((2,0), 2*a)
# M.addBlock((6,0), 6*a)
# # M.addBlock((1,0), a)
# M.addBlock((5,0), 5*a)
# M.addBlock((3,0), 3*a)
# M.addBlock((0,0), 0.5*a)
# M.addBlock((1,1), a)
# u = np.ones(M.shape[1])
# v = M.matvec(u)
# a = np.eye(3)
# b = np.eye(4)
# Mb = MatBlock((2,8))
# Mb.addBlock((0,7), 7*a)
# Mb.addBlock((0,4), 4*a)
# Mb.addBlock((0,2), 2*a)
# Mb.addBlock((0,6), 6*a)
# # Mb.addBlock((0,1), a)
# Mb.addBlock((0,5), 5*a)
# Mb.addBlock((0,3), 3*a)
# Mb.addBlock((0,0), 0.5*a)
# # Mb.addBlock((1,0), 2*a)
# Mb.addBlock((1,1), a)
# u = np.ones(Mb.shape[1])
# v = Mb.matvec(u)
# N, coef = 5, 3
# a = np.eye(N)
# # M = MatBlock()
# M = MatBlock((N,N**coef))
# # for j in range(N):
# # for i in range(N**coef):
# # M.addBlock((i,j), j*i*a, expert=True)
# from numpy.random import randint
# for j in randint(N, size=(N,)):
# for i in randint(N**coef, size=(N**coef,)):
# M.addBlock((i,j), j*i*a, expert=True)
# def test1(N,coef):
# a = np.eye(N)
# M = MatBlock()
# for j in xrange(N**coef):
# for i in xrange(N**coef):
# M.addBlock((j,i), j*i*a)
# def test2(N,coef):
# a = np.eye(N)
# M = MatBlock()
# for j in xrange(N**coef,-1,-1):
# for i in xrange(N**coef,-1,-1):
# M.addBlock((j,i), j*i*a)
# def test3(N,coef):
# a = np.eye(N)
# M = MatBlock( (N**coef, N**coef) )
# for j in xrange(N**coef):
# for i in xrange(N**coef):
# M.addBlock((j,i), j*i*a)
# def test(M,r,c,N=2):
# a = np.eye(N)
# for j in xrange(r):
# for i in xrange(c):
# M.addBlock((j,i), j*i*a)
# return M