# stzrqf.f man page

stzrqf.f —

## Synopsis

### Functions/Subroutines

subroutine **stzrqf** (M, **N**, A, **LDA**, TAU, INFO)**STZRQF**

## Function/Subroutine Documentation

### subroutine stzrqf (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, integer INFO)

**STZRQF**

**Purpose:**

This routine is deprecated and has been replaced by routine STZRZF. STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal 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 REAL 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 orthogonal 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 REAL 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**Further Details:**

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 )**T, 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 140 of file stzrqf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page stzrqf(3) is an alias of stzrqf.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK