142 lines
3.1 KiB
Python
142 lines
3.1 KiB
Python
from sympy.core.basic import Basic
|
|
from sympy.core.expr import Expr
|
|
from sympy.core.singleton import S
|
|
from sympy.core.sympify import sympify
|
|
from sympy.matrices.common import NonSquareMatrixError
|
|
|
|
|
|
class Determinant(Expr):
|
|
"""Matrix Determinant
|
|
|
|
Represents the determinant of a matrix expression.
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import MatrixSymbol, Determinant, eye
|
|
>>> A = MatrixSymbol('A', 3, 3)
|
|
>>> Determinant(A)
|
|
Determinant(A)
|
|
>>> Determinant(eye(3)).doit()
|
|
1
|
|
"""
|
|
is_commutative = True
|
|
|
|
def __new__(cls, mat):
|
|
mat = sympify(mat)
|
|
if not mat.is_Matrix:
|
|
raise TypeError("Input to Determinant, %s, not a matrix" % str(mat))
|
|
|
|
if mat.is_square is False:
|
|
raise NonSquareMatrixError("Det of a non-square matrix")
|
|
|
|
return Basic.__new__(cls, mat)
|
|
|
|
@property
|
|
def arg(self):
|
|
return self.args[0]
|
|
|
|
@property
|
|
def kind(self):
|
|
return self.arg.kind.element_kind
|
|
|
|
def doit(self, expand=False, **hints):
|
|
try:
|
|
return self.arg._eval_determinant()
|
|
except (AttributeError, NotImplementedError):
|
|
return self
|
|
|
|
def det(matexpr):
|
|
""" Matrix Determinant
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import MatrixSymbol, det, eye
|
|
>>> A = MatrixSymbol('A', 3, 3)
|
|
>>> det(A)
|
|
Determinant(A)
|
|
>>> det(eye(3))
|
|
1
|
|
"""
|
|
|
|
return Determinant(matexpr).doit()
|
|
|
|
class Permanent(Expr):
|
|
"""Matrix Permanent
|
|
|
|
Represents the permanent of a matrix expression.
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import MatrixSymbol, Permanent, ones
|
|
>>> A = MatrixSymbol('A', 3, 3)
|
|
>>> Permanent(A)
|
|
Permanent(A)
|
|
>>> Permanent(ones(3, 3)).doit()
|
|
6
|
|
"""
|
|
|
|
def __new__(cls, mat):
|
|
mat = sympify(mat)
|
|
if not mat.is_Matrix:
|
|
raise TypeError("Input to Permanent, %s, not a matrix" % str(mat))
|
|
|
|
return Basic.__new__(cls, mat)
|
|
|
|
@property
|
|
def arg(self):
|
|
return self.args[0]
|
|
|
|
def doit(self, expand=False, **hints):
|
|
try:
|
|
return self.arg.per()
|
|
except (AttributeError, NotImplementedError):
|
|
return self
|
|
|
|
def per(matexpr):
|
|
""" Matrix Permanent
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import MatrixSymbol, Matrix, per, ones
|
|
>>> A = MatrixSymbol('A', 3, 3)
|
|
>>> per(A)
|
|
Permanent(A)
|
|
>>> per(ones(5, 5))
|
|
120
|
|
>>> M = Matrix([1, 2, 5])
|
|
>>> per(M)
|
|
8
|
|
"""
|
|
|
|
return Permanent(matexpr).doit()
|
|
|
|
from sympy.assumptions.ask import ask, Q
|
|
from sympy.assumptions.refine import handlers_dict
|
|
|
|
|
|
def refine_Determinant(expr, assumptions):
|
|
"""
|
|
>>> from sympy import MatrixSymbol, Q, assuming, refine, det
|
|
>>> X = MatrixSymbol('X', 2, 2)
|
|
>>> det(X)
|
|
Determinant(X)
|
|
>>> with assuming(Q.orthogonal(X)):
|
|
... print(refine(det(X)))
|
|
1
|
|
"""
|
|
if ask(Q.orthogonal(expr.arg), assumptions):
|
|
return S.One
|
|
elif ask(Q.singular(expr.arg), assumptions):
|
|
return S.Zero
|
|
elif ask(Q.unit_triangular(expr.arg), assumptions):
|
|
return S.One
|
|
|
|
return expr
|
|
|
|
|
|
handlers_dict['Determinant'] = refine_Determinant
|