def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = _PysparseMatrixFromShape(rows=3, cols=3)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _PysparseIdentityMatrix(size=3)
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).numpyArray, tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
N = self.matrix.shape[1]
if isinstance(other, _PysparseMatrix):
return _PysparseMatrix(
matrix=spmatrix.matrixmultiply(self.matrix, other.matrix))
else:
shape = numerix.shape(other)
if shape == ():
L = spmatrix.ll_mat(N, N, N)
L.put(other * numerix.ones(N, 'l'))
return _PysparseMatrix(
matrix=spmatrix.matrixmultiply(self.matrix, L))
elif shape == (N, ):
y = numerix.empty((self.matrix.shape[0], ))
self.matrix.matvec(other, y)
return y
else:
raise TypeError
def jac(self, x, *args, **kwargs):
"""
Evaluate sparse Jacobian of constraints at x.
Returns a sparse matrix in format self.mformat
(0 = compressed sparse row, 1 = linked list).
The constraints appear in the following order:
1. equalities
2. lower bound only
3. upper bound only
4. range constraints.
"""
store_zeros = kwargs.get('store_zeros', False)
store_zeros = 1 if store_zeros else 0
if len(args) > 0:
if type(args[0]).__name__ == 'll_mat':
J = self.model.eval_J(x, self.mformat, store_zeros, args[0])
else:
return None
else:
J = self.model.eval_J(x, self.mformat, store_zeros)
self.Jeval += 1
# Warning!! This next line doesn't work for the coordinate format option.
if self.scale_con is not None:
J = spmatrix.matrixmultiply(self.scale_con_diag, J)
return J #[self.permC,:]
def jac(self, x, *args, **kwargs):
"""
Evaluate sparse Jacobian of constraints at x.
Returns a sparse matrix in format self.mformat
(0 = compressed sparse row, 1 = linked list).
The constraints appear in the following order:
1. equalities
2. lower bound only
3. upper bound only
4. range constraints.
"""
store_zeros = kwargs.get('store_zeros', False)
store_zeros = 1 if store_zeros else 0
if len(args) > 0:
if type(args[0]).__name__ == 'll_mat':
J = self.model.eval_J(x, self.mformat, store_zeros, args[0])
else:
return None
else:
J = self.model.eval_J(x, self.mformat, store_zeros)
self.Jeval += 1
# Warning!! This next line doesn't work for the coordinate format option.
if self.scale_con is not None:
J = spmatrix.matrixmultiply(self.scale_con_diag, J)
return J #[self.permC,:]
def __mul__(self, other):
if isinstance(other, _PysparseMeshMatrix):
return _PysparseMeshMatrix(mesh=self.mesh,
matrix=spmatrix.matrixmultiply(
self.matrix, other.matrix))
else:
return _PysparseMatrixFromShape.__mul__(self, other)
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = _PysparseMatrix(size = 3)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _PysparseIdentityMatrix(size = 3)
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).getNumpyArray(), tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
N = self.matrix.shape[0]
if isinstance(other, _PysparseMatrix):
return _PysparseMatrix(matrix = spmatrix.matrixmultiply(self.matrix, other._getMatrix()))
else:
shape = numerix.shape(other)
if shape == ():
L = spmatrix.ll_mat(N, N, N)
L.put(other * numerix.ones(N))
return _PysparseMatrix(matrix = spmatrix.matrixmultiply(self.matrix, L))
elif shape == (N,):
y = other.copy()
self.matrix.matvec(other, y)
return y
else:
raise TypeError
def outDegreeSequence(self):
"""
Return a vector of the (out)degree for each vertex.
"""
A = self.nativeAdjacencyMatrix()
j = spmatrix.ll_mat(self.vList.getNumVertices(), 1)
j[:, 0] = 1
degrees = spmatrix.matrixmultiply(A, j)
degrees = PysparseMatrix(matrix=degrees)
degrees = numpy.array(degrees.getNumpyArray().ravel(), numpy.int)
return degrees
def outDegreeSequence(self):
"""
Return a vector of the (out)degree for each vertex.
"""
A = self.nativeAdjacencyMatrix()
j = spmatrix.ll_mat(self.vList.getNumVertices(), 1)
j[:, 0] = 1
degrees = spmatrix.matrixmultiply(A, j)
degrees = PysparseMatrix(matrix=degrees)
degrees = numpy.array(degrees.getNumpyArray().ravel(), numpy.int)
return degrees
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = PysparseMatrix(size = 3)
>>> L1.put([3.,10.,numpy.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = PysparseMatrix(size = 3)
>>> L2.put(numpy.ones(3), numpy.arange(3), numpy.arange(3))
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numpy.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numpy.allclose((L1 * L2).getNumpyArray(), tmp)
1
or a sparse matrix by a vector
>>> tmp = numpy.array((29., 6.28318531, 2.5))
>>> numpy.allclose(L1 * numpy.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numpy.array((7.5, 16.28318531, 3.))
>>> numpy.allclose(numpy.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
M, N = self.getShape()
if isinstance(other, PysparseMatrix):
if N != other.getShape()[0]:
raise TypeError, 'Matrices dimensions do not match for product'
p = spmatrix.matrixmultiply(self.matrix, other.getMatrix())
return PysparseMatrix(matrix=p)
else:
shape = numpy.shape(other)
if shape == (): # other is a scalar
p = self.matrix.copy()
p.scale(other)
return PysparseMatrix(matrix=p)
elif shape == (N,):
y = numpy.empty(M)
self.matrix.matvec(other, y)
return y
else:
raise TypeError, 'Cannot multiply objects'
def testRandomMat(self):
eps = 2.2204460492503131E-16
n = 30; m = 60; k = 30
for i in range(100):
A = spmatrix_util.ll_mat_rand(n, k, 0.9)
B = spmatrix_util.ll_mat_rand(k, m, 0.4)
C = spmatrix.matrixmultiply(A, B)
t = numpy.zeros(k, 'd')
y1 = numpy.zeros(n, 'd')
y2 = numpy.zeros(n, 'd')
for s in range(10):
x = RandomArray.random((m, ))
C.matvec(x, y1)
B.matvec(x, t)
A.matvec(t, y2)
self.failUnless(math.sqrt(numpy.dot(y1 - y2, y1 - y2)) < eps * n*m*k)
def normalizeA(self):
'''
Normalize matrix A on rows
'''
# compute sum of rows in sum vector
v = np.ones(self.n)
sum = np.zeros(self.n)
self.A.matvec(v, sum) # sum = A*v
D = spmatrix.ll_mat(self.n, self.n)
for i in range(self.n):
if sum[i] != 0:
D[i,i] = 1.0/sum[i]
else:
D[i,i] = 1
self.A = spmatrix.matrixmultiply(self.A, D)
def A(self, *args, **kwargs):
"""
Evaluate sparse Jacobian of the linear part of the
constraints. Useful to obtain constraint matrix
when problem is a linear programming problem.
"""
store_zeros = kwargs.get('store_zeros', False)
store_zeros = 1 if store_zeros else 0
if len(args) == 1:
if type(args[0]).__name__ == 'll_mat':
Amat = self.model.eval_A(store_zeros, args[0])
else:
return None
else:
Amat = self.model.eval_A(store_zeros)
if self.scale_con is not None:
Amat = spmatrix.matrixmultiply(Amat, self.scale_con_diag)
return Amat
def A(self, *args, **kwargs):
"""
Evaluate sparse Jacobian of the linear part of the
constraints. Useful to obtain constraint matrix
when problem is a linear programming problem.
"""
store_zeros = kwargs.get('store_zeros', False)
store_zeros = 1 if store_zeros else 0
if len(args) == 1:
if type(args[0]).__name__ == 'll_mat':
Amat = self.model.eval_A(store_zeros,args[0])
else:
return None
else:
Amat = self.model.eval_A(store_zeros)
if self.scale_con is not None:
Amat = spmatrix.matrixmultiply(Amat, self.scale_con_diag)
return Amat
def spmatrixmul(matrix_a, matrix_b):
"""
Sparse Matrix Multiplication using pysparse matrix
Objective:
----------
To multiply two sparse matrices - relatively dense
Reason:
-------
Scipy.sparse unfortunately has matrix indices with datatype
int32. While pysparse is more robust and more efficient.
Process:
--------
It saves the scipy matrices to disk in the standard matrix market
format to the disk. Then reads it to a pysparse format and uses
Pysparse's inbuilt matrixmultipy operation. The result is
converted back to a scipy csr matrix.
This function takes two scipy matrices as input.
"""
sp_matrix_a = spmatrix.ll_mat(matrix_a.shape[0], matrix_a.shape[1])
sp_matrix_b = spmatrix.ll_mat(matrix_b.shape[0], matrix_b.shape[1])
# read it to form a pysparse spmatrix.
sp_matrix_a.update_add_at(matrix_a.tocoo().data,
matrix_a.tocoo().row,
matrix_a.tocoo().col)
sp_matrix_b.update_add_at(matrix_b.tocoo().data,
matrix_b.tocoo().row,
matrix_b.tocoo().col)
# multiply the matrices.
sp_result = spmatrix.matrixmultiply(sp_matrix_a, sp_matrix_b)
#conversion to scipy sparse matrix
data, row, col = sp_result.find()
result = ss.csr_matrix((data, (row, col)), shape=sp_result.shape)
#deleting files and refreshing memory
del sp_result, sp_matrix_a, sp_matrix_b, matrix_a, matrix_b
return result
def spmatrixmul(matrix_a, matrix_b):
"""
Sparse Matrix Multiplication using pysparse matrix
Objective:
----------
To multiply two sparse matrices - relatively dense
Reason:
-------
Scipy.sparse unfortunately has matrix indices with datatype
int32. While pysparse is more robust and more efficient.
Process:
--------
It saves the scipy matrices to disk in the standard matrix market
format to the disk. Then reads it to a pysparse format and uses
Pysparse's inbuilt matrixmultipy operation. The result is
converted back to a scipy csr matrix.
This function takes two scipy matrices as input.
"""
sp_matrix_a = spmatrix.ll_mat(matrix_a.shape[0], matrix_a.shape[1])
sp_matrix_b = spmatrix.ll_mat(matrix_b.shape[0], matrix_b.shape[1])
# read it to form a pysparse spmatrix.
sp_matrix_a.update_add_at(matrix_a.tocoo().data, matrix_a.tocoo().row,
matrix_a.tocoo().col)
sp_matrix_b.update_add_at(matrix_b.tocoo().data, matrix_b.tocoo().row,
matrix_b.tocoo().col)
# multiply the matrices.
sp_result = spmatrix.matrixmultiply(sp_matrix_a, sp_matrix_b)
#conversion to scipy sparse matrix
data, row, col = sp_result.find()
result = ss.csr_matrix((data, (row, col)), shape=sp_result.shape)
#deleting files and refreshing memory
del sp_result, sp_matrix_a, sp_matrix_b, matrix_a, matrix_b
return result
T[4:8,1:3] = As[4:8,1:3]
printMatrix(T)
print 'this should raise execptions...\n'
try:
T[6:9,6:9] = A[6:9,6:9]
except:
traceback.print_exc()
try:
T[5:9, 4:10] = A[5:9, 4:10]
except:
traceback.print_exc()
print 'Matrix multiplications'
printMatrix(spmatrix.matrixmultiply(I, A))
printMatrix(spmatrix.matrixmultiply(Is, A))
printMatrix(spmatrix.matrixmultiply(O, O))
printMatrix(spmatrix.matrixmultiply(Os, O))
print 'Dot product'
printMatrix(spmatrix.dot(I, A))
print 'Matrix export'
A[:4,:4].export_mtx('A.mtx', 3)
As[:4,:4].export_mtx('As.mtx', 3)
print open('A.mtx').read()
print open('As.mtx').read()
import time
from pysparse import spmatrix
n = 1000000
# create 2 nxn tridiag matrices
A = spmatrix.ll_mat(n, n)
B = spmatrix.ll_mat(n, n)
for i in xrange(n):
A[i, i] = i
B[i, i] = i
if i > 0:
A[i, i - 1] = 1
B[i, i - 1] = 1
if i < n - 1:
A[i, i + 1] = 1
B[i, i - 1] = 1
t1 = time.clock()
C = spmatrix.matrixmultiply(A, B)
t_mult = time.clock() - t1
print 'time for multiplying %dx%d matrices: %.2f sec' % (n, n, t_mult)
print C[:10, :10]
def __mul__(self, other):
if isinstance(other, _PysparseMeshMatrix):
return _PysparseMeshMatrix(mesh=self.mesh,
matrix=spmatrix.matrixmultiply(self.matrix, other.matrix))
else:
return _PysparseMatrixFromShape.__mul__(self, other)
T[4:8, 1:3] = As[4:8, 1:3]
printMatrix(T)
print 'this should raise execptions...\n'
try:
T[6:9, 6:9] = A[6:9, 6:9]
except:
traceback.print_exc()
try:
T[5:9, 4:10] = A[5:9, 4:10]
except:
traceback.print_exc()
print 'Matrix multiplications'
printMatrix(spmatrix.matrixmultiply(I, A))
printMatrix(spmatrix.matrixmultiply(Is, A))
printMatrix(spmatrix.matrixmultiply(O, O))
printMatrix(spmatrix.matrixmultiply(Os, O))
print 'Dot product'
printMatrix(spmatrix.dot(I, A))
print 'Matrix export'
A[:4, :4].export_mtx('A.mtx', 3)
As[:4, :4].export_mtx('As.mtx', 3)
print open('A.mtx').read()
print open('As.mtx').read()
import time
from pysparse import spmatrix
n = 1000000
# create 2 nxn tridiag matrices
A = spmatrix.ll_mat(n, n)
B = spmatrix.ll_mat(n, n)
for i in xrange(n):
A[i,i] = i
B[i,i] = i
if i > 0:
A[i,i-1] = 1
B[i,i-1] = 1
if i < n-1:
A[i,i+1] = 1
B[i,i-1] = 1
t1 = time.clock()
C = spmatrix.matrixmultiply(A, B)
t_mult = time.clock() - t1
print 'time for multiplying %dx%d matrices: %.2f sec' % (n, n, t_mult)
print C[:10,:10]