• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

ztzrqf - routine is deprecated and has been replaced by routine CTZRZF

SYNOPSIS

  SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO)
  DOUBLE COMPLEX A(LDA,*), TAU(*)
  INTEGER M, N, LDA, INFO

  SUBROUTINE ZTZRQF_64( M, N, A, LDA, TAU, INFO)
  DOUBLE COMPLEX A(LDA,*), TAU(*)
  INTEGER*8 M, N, LDA, INFO

F95 INTERFACE

  SUBROUTINE TZRQF( [M], [N], A, [LDA], TAU, [INFO])
  COMPLEX(8), DIMENSION(:) :: TAU
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: M, N, LDA, INFO

  SUBROUTINE TZRQF_64( [M], [N], A, [LDA], TAU, [INFO])
  COMPLEX(8), DIMENSION(:) :: TAU
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: M, N, LDA, INFO

C INTERFACE

#include <sunperf.h>

void ztzrqf(int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info);

void ztzrqf_64(long m, long n, doublecomplex *a, long lda, doublecomplex *tau, long *info);

PURPOSE

ztzrqf routine is deprecated and has been replaced by routine CTZRZF.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.

ARGUMENTS

• 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 unitary matrix Z as a product of M elementary reflectors.

• 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 illegal value

FURTHER DETAILS

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 ).