# slatrz.f (3) - Linux Man Pages

slatrz.f -

## SYNOPSIS

### Functions/Subroutines

subroutine slatrz (M, N, L, A, LDA, TAU, WORK)
SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

## Function/Subroutine Documentation

### subroutine slatrz (integerM, integerN, integerL, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK)

SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

Purpose:

``` SLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
[ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
matrix and, R and A1 are M-by-M upper triangular matrices.
```

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 >= 0.
```

L

```          L is INTEGER
The number of columns of the matrix A containing the
meaningful part of the Householder vectors. N-M >= L >= 0.
```

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 N-L+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.
```

WORK

```          WORK is REAL array, dimension (M)
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

September 2012

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

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 l element vector. tau and z( k )
are chosen to annihilate the elements of the kth row of A2.

The scalar tau is returned in the kth element of TAU and the vector
u( k ) in the kth row of A2, such that the elements of z( k ) are
in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
the upper triangular part of A1.

Z is given by

Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
```

Definition at line 141 of file slatrz.f.

## Author

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