@node Matrix Factorizations, Ranges, Matrix and Vector Operations, Top
@chapter Matrix Factorizations
@cindex matrix factorizations
@cindex factorizations

@deftypefn  {} {}AEPBALANCE (void)
@deftypefnx  {} {}AEPBALANCE (const Matrix &@var{a}, const char *@var{balance_job})
@deftypefnx  {} {}AEPBALANCE (const AEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} AEPBALANCE& {operator =} (const AEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} Matrix balanced_matrix (void) const
@deftypefnx {} Matrix balancing_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const AEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} ComplexAEPBALANCE (void)
@deftypefnx {} ComplexAEPBALANCE (const ComplexMatrix &@var{a}, const char *@var{balance_job})
@deftypefnx {} ComplexAEPBALANCE (const ComplexAEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} ComplexAEPBALANCE& {operator =} (const ComplexAEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} ComplexMatrix balanced_matrix (void) const
@deftypefnx {} ComplexMatrix balancing_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexAEPBALANCE &@var{a})
@end deftypefn

@deftypefn  {} {}DET (void)
@deftypefnx  {} {}DET (const DET &@var{a})
@end deftypefn

@deftypefn {} DET& {operator =} (const DET &@var{a})
@end deftypefn

@deftypefn {} int value_will_overflow (void) const
@deftypefnx {} int value_will_underflow (void) const
@end deftypefn

@deftypefn {} double coefficient (void) const
@deftypefnx {} int exponent (void) const
@deftypefnx {} double value (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const DET &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexDET (void)
@deftypefnx  {} {}ComplexDET (const ComplexDET &@var{a})
@end deftypefn

@deftypefn {} ComplexDET& {operator =} (const ComplexDET &@var{a})
@end deftypefn

@deftypefn {} int value_will_overflow (void) const
@deftypefnx {} int value_will_underflow (void) const
@end deftypefn

@deftypefn {} Complex coefficient (void) const
@deftypefnx {} int exponent (void) const
@deftypefnx {} Complex value (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexDET &@var{a})
@end deftypefn

@deftypefn  {} {}GEPBALANCE (void)
@deftypefnx  {} {}GEPBALANCE (const Matrix &@var{a}, const Matrix &, const char *@var{balance_job})
@deftypefnx  {} {}GEPBALANCE (const GEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} GEPBALANCE& {operator =} (const GEPBALANCE &@var{a})
@end deftypefn

@deftypefn {} Matrix balanced_a_matrix (void) const
@deftypefnx {} Matrix balanced_b_matrix (void) const
@deftypefnx {} Matrix left_balancing_matrix (void) const
@deftypefnx {} Matrix right_balancing_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const GEPBALANCE &@var{a})
@end deftypefn

@deftypefn  {} {}CHOL (void)
@deftypefnx  {} {}CHOL (const Matrix &@var{a})
@deftypefnx  {} {}CHOL (const Matrix &@var{a}, int &@var{info})
@deftypefnx  {} {}CHOL (const CHOL &@var{a})
@end deftypefn

@deftypefn {} CHOL& {operator =} (const CHOL &@var{a})
@end deftypefn

@deftypefn {} Matrix chol_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CHOL &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexCHOL (void)
@deftypefnx  {} {}ComplexCHOL (const ComplexMatrix &@var{a})
@deftypefnx  {} {}ComplexCHOL (const ComplexMatrix &@var{a}, int &@var{info})
@deftypefnx  {} {}ComplexCHOL (const ComplexCHOL &@var{a})
@end deftypefn

@deftypefn {} ComplexCHOL& {operator =} (const ComplexCHOL &@var{a})
@end deftypefn

@deftypefn {} ComplexMatrix chol_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexCHOL &@var{a})
@end deftypefn

@deftypefn  {} {}HESS (void)
@deftypefnx  {} {}HESS (const Matrix &@var{a})
@deftypefnx  {} {}HESS (const Matrix&a, int &@var{info})
@deftypefnx  {} {}HESS (const HESS &@var{a})
@end deftypefn

@deftypefn {} HESS& {operator =} (const HESS &@var{a})
@end deftypefn

@deftypefn {} Matrix hess_matrix (void) const
@deftypefnx {} Matrix unitary_hess_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const HESS &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexHESS (void)
@deftypefnx  {} {}ComplexHESS (const ComplexMatrix &@var{a})
@deftypefnx  {} {}ComplexHESS (const ComplexMatrix &@var{a}, int &@var{info})
@deftypefnx  {} {}ComplexHESS (const ComplexHESS &@var{a})
@end deftypefn

@deftypefn {} ComplexHESS& {operator =} (const ComplexHESS &@var{a})
@end deftypefn

@deftypefn {} ComplexMatrix hess_matrix (void) const
@deftypefnx {} ComplexMatrix unitary_hess_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexHESS &@var{a})
@end deftypefn

@deftypefn  {} {}SCHUR (void)
@deftypefnx  {} {}SCHUR (const Matrix &@var{a}, const char *@var{ord})
@deftypefnx  {} {}SCHUR (const Matrix &@var{a}, const char *@var{ord}, int &@var{info})
@deftypefnx  {} {}SCHUR (const SCHUR &@var{a}, const char *@var{ord})
@end deftypefn

@deftypefn {} SCHUR& {operator =} (const SCHUR &@var{a})
@end deftypefn

@deftypefn {} Matrix schur_matrix (void) const
@deftypefnx {} Matrix unitary_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SCHUR &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexSCHUR (void)
@deftypefnx  {} {}ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord})
@deftypefnx  {} {}ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}, int &@var{info})
@deftypefnx  {} {}ComplexSCHUR (const ComplexSCHUR &@var{a}, const char *@var{ord})
@end deftypefn

@deftypefn {} ComplexSCHUR& {operator =} (const ComplexSCHUR &@var{a})
@end deftypefn

@deftypefn {} ComplexMatrix schur_matrix (void) const
@deftypefnx {} ComplexMatrix unitary_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSCHUR &@var{a})
@end deftypefn

@deftypefn  {} {}SVD (void)
@deftypefnx  {} {}SVD (const Matrix &@var{a})
@deftypefnx  {} {}SVD (const Matrix &@var{a}, int &@var{info})
@deftypefnx  {} {}SVD (const SVD &@var{a})
@end deftypefn

@deftypefn {} SVD& {operator =} (const SVD &@var{a})
@end deftypefn

@deftypefn {} DiagMatrix singular_values (void) const
@deftypefnx {} Matrix left_singular_matrix (void) const
@deftypefnx {} Matrix right_singular_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SVD &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexSVD (void)
@deftypefnx  {} {}ComplexSVD (const ComplexMatrix &@var{a})
@deftypefnx  {} {}ComplexSVD (const ComplexMatrix &@var{a}, int &@var{info})
@deftypefnx  {} {}ComplexSVD (const ComplexSVD &@var{a})
@end deftypefn

@deftypefn {} ComplexSVD& {operator =} (const ComplexSVD &@var{a})
@end deftypefn

@deftypefn {} DiagMatrix singular_values (void) const
@deftypefnx {} ComplexMatrix left_singular_matrix (void) const
@deftypefnx {} ComplexMatrix right_singular_matrix (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSVD &@var{a})
@end deftypefn

@deftypefn  {} {}EIG (void)
@deftypefnx  {} {}EIG (const Matrix &@var{a})
@deftypefnx  {} {}EIG (const Matrix &@var{a}, int &@var{info})
@deftypefnx  {} {}EIG (const ComplexMatrix &@var{a})
@deftypefnx  {} {}EIG (const ComplexMatrix &@var{a}, int &@var{info})
@deftypefnx  {} {}EIG (const EIG &@var{a})
@end deftypefn

@deftypefn {} EIG& {operator =} (const EIG &@var{a})
@end deftypefn

@deftypefn {} ComplexColumnVector eigenvalues (void) const
@end deftypefn

@deftypefn {} ComplexMatrix eigenvectors (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const EIG &@var{a})
@end deftypefn

@deftypefn  {} {}LU (void)
@deftypefnx  {} {}LU (const Matrix &@var{a})
@deftypefnx  {} {}LU (const LU &@var{a})
@end deftypefn

@deftypefn {} LU& {operator =} (const LU &@var{a})
@end deftypefn

@deftypefn {} Matrix L (void) const
@deftypefnx {} Matrix U (void) const
@deftypefnx {} Matrix P (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const LU &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexLU (void)
@deftypefnx  {} {}ComplexLU (const ComplexMatrix &@var{a})
@deftypefnx  {} {}ComplexLU (const ComplexLU &@var{a})
@end deftypefn

@deftypefn {} ComplexLU& {operator =} (const ComplexLU &@var{a})
@end deftypefn

@deftypefn {} ComplexMatrix L (void) const
@deftypefnx {} ComplexMatrix U (void) const
@deftypefnx {} Matrix P (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexLU &@var{a})
@end deftypefn

@deftypefn  {} {}QR (void)
@deftypefnx  {} {}QR (const Matrix &@var{A})
@deftypefnx  {} {}QR (const QR &@var{a})
@end deftypefn

@deftypefn {} QR& {operator =} (const QR &@var{a})
@end deftypefn

@deftypefn {} Matrix Q (void) const
@deftypefnx {} Matrix R (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const QR &@var{a})
@end deftypefn

@deftypefn  {} {}ComplexQR (void)
@deftypefnx  {} {}ComplexQR (const ComplexMatrix &@var{A})
@deftypefnx  {} {}ComplexQR (const ComplexQR &@var{a})
@end deftypefn

@deftypefn {} ComplexQR& {operator =} (const ComplexQR &@var{a})
@end deftypefn

@deftypefn {} ComplexMatrix Q (void) const
@deftypefnx {} ComplexMatrix R (void) const
@end deftypefn

@deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexQR &@var{a})
@end deftypefn