Contents
ctzrqf - routine is deprecated and has been replaced by rou-
tine CTZRZF
SUBROUTINE CTZRQF(M, N, A, LDA, TAU, INFO)
COMPLEX A(LDA,*), TAU(*)
INTEGER M, N, LDA, INFO
SUBROUTINE CTZRQF_64(M, N, A, LDA, TAU, INFO)
COMPLEX A(LDA,*), TAU(*)
INTEGER*8 M, N, LDA, INFO
F95 INTERFACE
SUBROUTINE TZRQF([M], [N], A, [LDA], TAU, [INFO])
COMPLEX, DIMENSION(:) :: TAU
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, INFO
SUBROUTINE TZRQF_64([M], [N], A, [LDA], TAU, [INFO])
COMPLEX, DIMENSION(:) :: TAU
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, INFO
C INTERFACE
#include <sunperf.h>
void ctzrqf(int m, int n, complex *a, int lda, complex *tau,
int *info);
void ctzrqf_64(long m, long n, complex *a, long lda, complex
*tau, long *info);
ctzrqf routine is deprecated and has been replaced by rou-
tine CTZRZF.
CTZRQF 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 >= M.
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.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
The factorization is obtained by Householder's method. The
kth transformation matrix, Z( k ), whose conjugate transpose
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 ).