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from sympy.matrices.expressions import MatrixExpr
from sympy.assumptions.ask import Q
class Factorization(MatrixExpr):
arg = property(lambda self: self.args[0])
shape = property(lambda self: self.arg.shape) # type: ignore
class LofLU(Factorization):
@property
def predicates(self):
return (Q.lower_triangular,)
class UofLU(Factorization):
@property
def predicates(self):
return (Q.upper_triangular,)
class LofCholesky(LofLU): pass
class UofCholesky(UofLU): pass
class QofQR(Factorization):
@property
def predicates(self):
return (Q.orthogonal,)
class RofQR(Factorization):
@property
def predicates(self):
return (Q.upper_triangular,)
class EigenVectors(Factorization):
@property
def predicates(self):
return (Q.orthogonal,)
class EigenValues(Factorization):
@property
def predicates(self):
return (Q.diagonal,)
class UofSVD(Factorization):
@property
def predicates(self):
return (Q.orthogonal,)
class SofSVD(Factorization):
@property
def predicates(self):
return (Q.diagonal,)
class VofSVD(Factorization):
@property
def predicates(self):
return (Q.orthogonal,)
def lu(expr):
return LofLU(expr), UofLU(expr)
def qr(expr):
return QofQR(expr), RofQR(expr)
def eig(expr):
return EigenValues(expr), EigenVectors(expr)
def svd(expr):
return UofSVD(expr), SofSVD(expr), VofSVD(expr)
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