Quick Navigator

 Search Site Miscellaneous Server Agreement Year 2038 Credits
 ztzrqf.f(3) LAPACK ztzrqf.f(3)

ztzrqf.f -

# SYNOPSIS

## Functions/Subroutines

subroutine ztzrqf (M, N, A, LDA, TAU, INFO)

ZTZRQF

# Function/Subroutine Documentation

## subroutine ztzrqf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, integerINFO)

ZTZRQF
Purpose:
``` This routine is deprecated and has been replaced by routine ZTZRZF.

ZTZRQF 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.
```
Parameters:
M
```          M is INTEGER
The number of rows of the matrix A.  M >= 0.
```
N
```          N is INTEGER
The number of columns of the matrix A.  N >= M.
```
A
```          A is COMPLEX*16 array, dimension (LDA,N)
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
```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).
```
TAU
```          TAU is COMPLEX*16 array, dimension (M)
The scalar factors of the elementary reflectors.
```
INFO
```          INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
```
Author:
Univ. of Tennessee
Univ. of California Berkeley
NAG Ltd.
Date:
November 2011
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 )**H,   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 ).
```
Definition at line 139 of file ztzrqf.f.

# Author

Generated automatically by Doxygen for LAPACK from the source code.
 Sat Nov 16 2013 Version 3.4.2

Search for    or go to Top of page |  Section 3 |  Main Index

Visit the GSP FreeBSD Man Page Interface.
Output converted with ManDoc.