ztzrzf - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO) DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER M, N, LDA, LWORK, INFO
SUBROUTINE ZTZRZF_64( M, N, A, LDA, TAU, WORK, LWORK, INFO) DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 M, N, LDA, LWORK, INFO
SUBROUTINE TZRZF( [M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO]) COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: M, N, LDA, LWORK, INFO
SUBROUTINE TZRZF_64( [M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO]) COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, LWORK, INFO
#include <sunperf.h>
void ztzrzf(int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info);
void ztzrzf_64(long m, long n, doublecomplex *a, long lda, doublecomplex *tau, long *info);
ztzrzf reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations.
The upper trapezoidal matrix A is factored as
A = ( R 0 ) * Z,
where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.
WORK(1)
returns the optimal LWORK.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
The factorization is obtained by Householder's method. The kth transformation matrix, Z( k ), which is used to introduce zeros into the ( m - k + 1 )th row of A, is given in the form
Z( k ) = ( I 0 ),
( 0 T( k ) )
where
T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), ( 0 ) ( z( k ) )
tau is a scalar and z( k ) is an ( n - m ) element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of X.
The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A, such that the elements of z( k ) are in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A.
Z is given by
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).