def matrix_inverse(M, method='default'):
from .config import matrix_inverse_method, matrix_inverse_fallback_method
if method == 'default':
method = matrix_inverse_method
if method == 'GE':
try:
from sympy.matrices import dotprodsimp
# GE loses it without this assumption. Well with
# sympy-1.6.2 and the master version, GE still loses it
# with a poor pivot.
with dotprodsimp(False):
return M.inv(method='GE')
except:
return M.inv(method='GE')
elif method.startswith('DM-'):
try:
# This is experimental and requires sympy to be built from
# git. It only works for rational function fields but
# fails for polynomial rings. The latter can be handled
# by converting it to a field, however, we just fall back
# on a standard method.
from sympy.polys.domainmatrix import DomainMatrix
dM = DomainMatrix.from_list_sympy(*M.shape, rows=M.tolist())
return dM.inv(method=method[3:]).to_Matrix()
except:
method = matrix_inverse_fallback_method
return M.inv(method=method)
def test_DomainMatrix_from_list_sympy():
ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
A = DomainMatrix.from_list_sympy(2, 2, [[1, 2], [3, 4]])
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == ZZ
K = QQ.algebraic_field(sqrt(2))
ddm = DDM([[
K.convert(1 + sqrt(2)), K.convert(2 + sqrt(2))
], [K.convert(3 + sqrt(2)), K.convert(4 + sqrt(2))]], (2, 2), K)
A = DomainMatrix.from_list_sympy(
2,
2, [[1 + sqrt(2), 2 + sqrt(2)], [3 + sqrt(2), 4 + sqrt(2)]],
extension=True)
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == K
def matrix_inverse(M, method='default'):
from .config import matrix_inverse_method
if method == 'default':
method = matrix_inverse_method
if method == 'new':
try:
from sympy.polys.domainmatrix import DomainMatrix
dM = DomainMatrix.from_list_sympy(*M.shape, rows=M.tolist())
return dM.inv().to_Matrix()
except (ImportError, ValueError):
method = 'ADJ'
return M.inv(method=method)
def test_DomainMatrix_from_list_sympy():
ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
A = DomainMatrix.from_list_sympy(2, 2, [[1, 2], [3, 4]])
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == ZZ
def matrix_inverse(M, method='default'):
from .config import matrix_inverse_method, matrix_inverse_fallback_method
N = M.shape[0]
if N >= 10:
warn("""
This may take a while... A symbolic matrix inversion is O(%d^3) for a matrix
of size %dx%d""" % (N, N, N))
if method == 'default':
method = matrix_inverse_method
if method == 'GE':
try:
from sympy.matrices import dotprodsimp
# GE loses it without this assumption. Well with
# sympy-1.6.2 and the master version, GE still loses it
# with a poor pivot.
with dotprodsimp(False):
return M.inv(method='GE')
except:
return M.inv(method='GE')
elif method.startswith('DM-'):
try:
# This is experimental and requires sympy to be built from
# git. It only works for rational function fields but
# fails for polynomial rings. The latter can be handled
# by converting it to a field, however, we just fall back
# on a standard method.
from sympy.polys.domainmatrix import DomainMatrix
dM = DomainMatrix.from_list_sympy(*M.shape, rows=M.tolist())
return dM.inv(method=method[3:]).to_Matrix()
except:
method = matrix_inverse_fallback_method
return M.inv(method=method)
def canonical(self):
return self.applyfunc(self._typewrap.canonical)
def general(self):
return self.applyfunc(self._typewrap.general)
def mixedfrac(self):
return self.applyfunc(self._typewrap.mixedfrac)
def partfrac(self):
return self.applyfunc(self._typewrap.partfrac)
def timeconst(self):
return self.applyfunc(self._typewrap.timeconst)
def ZPK(self):
return self.applyfunc(self._typewrap.ZPK)