Contents
ztzrzf - reduce the M-by-N ( M<=N ) complex upper tra-
pezoidal matrix A to upper triangular form by means of uni-
tary 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
F95 INTERFACE
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
C INTERFACE
#include <sunperf.h>
void ztzrzf(int m, int n, doublecomplex *a, int lda, doub-
lecomplex *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.
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
A (input/output)
On entry, the leading M-by-N upper trapezoidal
part of the array A must contain the matrix to be
factorized. On exit, the leading M-by-M upper
triangular part of A contains the upper triangular
matrix R, and elements M+1 to N of the first M
rows of A, with the array TAU, represent the uni-
tary matrix Z as a product of M elementary reflec-
tors.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
TAU (output)
The scalar factors of the elementary reflectors.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >=
max(1,M). For optimum performance LWORK >= M*NB,
where NB is the optimal blocksize.
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.
INFO (output)
= 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., Knox-
ville, USA
The factorization is obtained by Householder's method. The
kth transformation matrix, Z( k ), which is used to intro-
duce 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 ).