def sp_expm(A, sparse=False):
"""
Sparse matrix exponential.
"""
if _isdiag(A.indices, A.indptr, A.shape[0]):
A.data = np.exp(A.data)
return A
if sparse:
E = spla.expm(A.tocsc())
else:
E = spla.expm(A.toarray())
return sp.csr_matrix(E)
def sp_expm(A, sparse=False):
"""
Sparse matrix exponential.
"""
if _isdiag(A.indices, A.indptr, A.shape[0]):
A = sp.diags(np.exp(A.diagonal()), shape=A.shape,
format='csr', dtype=complex)
return A
if sparse:
E = spla.expm(A.tocsc())
else:
E = spla.expm(A.toarray())
return sp.csr_matrix(E)
def sp_expm(A, sparse=False):
"""
Sparse matrix exponential.
"""
if _isdiag(A.indices, A.indptr, A.shape[0]):
A = sp.diags(np.exp(A.diagonal()), shape=A.shape,
format='csr', dtype=complex)
return A
if sparse:
E = spla.expm(A.tocsc())
else:
E = spla.expm(A.toarray())
return sp.csr_matrix(E)
def sp_isdiag(A):
"""Determine if sparse CSR matrix is diagonal.
Parameters
----------
A : csr_matrix, csc_matrix
Input matrix
Returns
-------
isdiag : int
True if matix is diagonal, False otherwise.
"""
if not sp.isspmatrix_csr(A):
raise TypeError('Input sparse matrix must be in CSR format.')
return _isdiag(A.indices, A.indptr, A.shape[0])
def sp_isdiag(A):
"""Determine if sparse CSR matrix is diagonal.
Parameters
----------
A : csr_matrix, csc_matrix
Input matrix
Returns
-------
isdiag : int
True if matix is diagonal, False otherwise.
"""
if not sp.isspmatrix_csr(A):
raise TypeError('Input sparse matrix must be in CSR format.')
return _isdiag(A.indices, A.indptr, A.shape[0])
def sp_expm(A, p=13, sparse=False):
"""
Sparse matrix exponential.
Reference
---------
Expokit, ACM-Transactions on Mathematical Software, 24(1):130-156, 1998
"""
if _isdiag(A.indices, A.indptr, A.shape[0]):
A.data = np.exp(A.data)
return A
N = A.shape[0]
c = np.zeros(p + 1, dtype=float)
# Pade coefficients
c[0] = 1
for k in range(p):
c[k + 1] = c[k] * ((p - k) / ((k + 1.0) * (2.0 * p - k)))
# Scaling
if sparse:
A = A.tocsc()
nrm = spla.norm(A, np.inf)
else:
A = A.toarray()
nrm = la.norm(A, np.inf)
if nrm > 0.5:
nrm = max(0, np.fix(np.log(nrm) / np.log(2)) + 2)
A = 2.0**(-nrm) * A
# Horner evaluation of the irreducible fraction
if sparse:
I = sp.identity(N, dtype=complex, format='csc')
else:
I = np.identity(N, dtype=complex)
A2 = A.dot(A)
Q = c[-1] * I
P = c[p] * I
odd = 1
for k in range(p - 2, -1, -1):
if odd == 1:
Q = Q.dot(A2) + c[k] * I
else:
P = P.dot(A2) + c[k] * I
odd = 1 - odd
if odd == 1:
Q = Q.dot(A)
Q = Q - P
if sparse:
E = -(I + 2.0 * spla.spsolve(Q, P))
else:
E = -(I + 2.0 * la.solve(Q, P))
else:
P = P.dot(A)
Q = Q - P
if sparse:
E = I + 2.0 * spla.spsolve(Q, P)
else:
E = I + 2.0 * la.solve(Q, P)
# Squaring
for k in range(int(nrm)):
E = E.dot(E)
return sp.csr_matrix(E)
def sp_expm(A, p=13, sparse=False):
"""
Sparse matrix exponential.
Reference
---------
Expokit, ACM-Transactions on Mathematical Software, 24(1):130-156, 1998
"""
if _isdiag(A.indices, A.indptr, A.shape[0]):
A.data = np.exp(A.data)
return A
N = A.shape[0]
c = np.zeros(p+1,dtype=float)
# Pade coefficients
c[0] = 1
for k in range(p):
c[k+1] = c[k]*((p-k)/((k+1.0)*(2.0*p-k)))
# Scaling
if sparse:
A = A.tocsc()
nrm = spla.norm(A, np.inf)
else:
A = A.toarray()
nrm = la.norm(A, np.inf)
if nrm > 0.5:
nrm = max(0, np.fix(np.log(nrm)/np.log(2))+2)
A = 2.0**(-nrm)*A
# Horner evaluation of the irreducible fraction
if sparse:
I = sp.identity(N, dtype=complex, format='csc')
else:
I = np.identity(N, dtype=complex)
A2 = A.dot(A)
Q = c[-1]*I
P = c[p]*I
odd = 1
for k in range(p-2,-1,-1):
if odd == 1:
Q = Q.dot(A2) +c[k]*I
else:
P = P.dot(A2) +c[k]*I
odd = 1-odd
if odd == 1:
Q = Q.dot(A)
Q = Q-P
if sparse:
E = -(I+2.0*spla.spsolve(Q,P))
else:
E = -(I+2.0*la.solve(Q,P))
else:
P = P.dot(A)
Q = Q-P
if sparse:
E = I+2.0*spla.spsolve(Q,P)
else:
E = I+2.0*la.solve(Q,P)
# Squaring
for k in range(int(nrm)):
E = E.dot(E)
return sp.csr_matrix(E)