|
from __future__ import print_function, division
from sympy.matrices.expressions import MatrixExpr
from sympy import Q
class Factorization(MatrixExpr):
arg = property(lambda self: self.args[0])
shape = property(lambda self: self.arg.shape)
class LofLU(Factorization):
predicates = Q.lower_triangular,
class UofLU(Factorization):
predicates = Q.upper_triangular,
class LofCholesky(LofLU): pass
class UofCholesky(UofLU): pass
class QofQR(Factorization):
predicates = Q.orthogonal,
class RofQR(Factorization):
predicates = Q.upper_triangular,
class EigenVectors(Factorization):
predicates = Q.orthogonal,
class EigenValues(Factorization):
predicates = Q.diagonal,
class UofSVD(Factorization):
predicates = Q.orthogonal,
class SofSVD(Factorization):
predicates = Q.diagonal,
class VofSVD(Factorization):
predicates = 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)
|
