def _eigenvals_list(M, error_when_incomplete=True, simplify=False, **flags):
iblocks = M.strongly_connected_components()
all_eigs = []
for b in iblocks:
block = M[b, b]
if isinstance(simplify, FunctionType):
charpoly = block.charpoly(simplify=simplify)
else:
charpoly = block.charpoly()
eigs = roots(charpoly, multiple=True, **flags)
if len(eigs) != block.rows:
degree = int(charpoly.degree())
f = charpoly.as_expr()
x = charpoly.gen
try:
eigs = [CRootOf(f, x, idx) for idx in range(degree)]
except NotImplementedError:
if error_when_incomplete:
raise MatrixError(eigenvals_error_message)
else:
eigs = []
all_eigs += eigs
if not simplify:
return all_eigs
if not isinstance(simplify, FunctionType):
simplify = _simplify
return [simplify(value) for value in all_eigs]
def _eigenvals_dict(
M, error_when_incomplete=True, simplify=False, **flags):
iblocks = M.strongly_connected_components()
all_eigs = {}
is_dom = M._rep.domain in (ZZ, QQ)
for b in iblocks:
# Fast path for a 1x1 block:
if is_dom and len(b) == 1:
index = b[0]
val = M[index, index]
all_eigs[val] = all_eigs.get(val, 0) + 1
continue
block = M[b, b]
if isinstance(simplify, FunctionType):
charpoly = block.charpoly(simplify=simplify)
else:
charpoly = block.charpoly()
eigs = roots(charpoly, multiple=False, **flags)
if sum(eigs.values()) != block.rows:
degree = int(charpoly.degree())
f = charpoly.as_expr()
x = charpoly.gen
try:
eigs = {CRootOf(f, x, idx): 1 for idx in range(degree)}
except NotImplementedError:
if error_when_incomplete:
raise MatrixError(eigenvals_error_message)
else:
eigs = {}
for k, v in eigs.items():
if k in all_eigs:
all_eigs[k] += v
else:
all_eigs[k] = v
if not simplify:
return all_eigs
if not isinstance(simplify, FunctionType):
simplify = _simplify
return {simplify(key): value for key, value in all_eigs.items()}
def _eigenvals_list(
M, error_when_incomplete=True, simplify=False, **flags):
iblocks = M.strongly_connected_components()
all_eigs = []
is_dom = M._rep.domain in (ZZ, QQ)
for b in iblocks:
# Fast path for a 1x1 block:
if is_dom and len(b) == 1:
index = b[0]
val = M[index, index]
all_eigs.append(val)
continue
block = M[b, b]
if isinstance(simplify, FunctionType):
charpoly = block.charpoly(simplify=simplify)
else:
charpoly = block.charpoly()
eigs = roots(charpoly, multiple=True, **flags)
if len(eigs) != block.rows:
degree = int(charpoly.degree())
f = charpoly.as_expr()
x = charpoly.gen
try:
eigs = [CRootOf(f, x, idx) for idx in range(degree)]
except NotImplementedError:
if error_when_incomplete:
raise MatrixError(eigenvals_error_message)
else:
eigs = []
all_eigs += eigs
if not simplify:
return all_eigs
if not isinstance(simplify, FunctionType):
simplify = _simplify
return [simplify(value) for value in all_eigs]
def _eigenvals_dict(
M, error_when_incomplete=True, simplify=False, **flags):
iblocks = M.connected_components()
all_eigs = {}
for b in iblocks:
block = M[b, b]
if isinstance(simplify, FunctionType):
charpoly = block.charpoly(simplify=simplify)
else:
charpoly = block.charpoly()
eigs = roots(charpoly, multiple=False, **flags)
if sum(eigs.values()) != block.rows:
degree = int(charpoly.degree())
f = charpoly.as_expr()
x = charpoly.gen
try:
eigs = {CRootOf(f, x, idx): 1 for idx in range(degree)}
except NotImplementedError:
if error_when_incomplete:
raise MatrixError(eigenvals_error_message)
else:
eigs = {}
for k, v in eigs.items():
if k in all_eigs:
all_eigs[k] += v
else:
all_eigs[k] = v
if not simplify:
return all_eigs
if not isinstance(simplify, FunctionType):
simplify = _simplify
return {simplify(key): value for key, value in all_eigs.items()}