# sgqrts.f - Man Page

TESTING/EIG/sgqrts.f

## Synopsis

### Functions/Subroutines

subroutine sgqrts (n, m, p, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)
SGQRTS

## Function/Subroutine Documentation

### subroutine sgqrts (integer n, integer m, integer p, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) taua, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, real, dimension( ldb, * ) z, real, dimension( ldb, * ) t, real, dimension( ldb, * ) bwk, integer ldb, real, dimension( * ) taub, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 4 ) result)

SGQRTS

Purpose:

``` SGQRTS tests SGGQRF, which computes the GQR factorization of an
N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.```
Parameters

N

```          N is INTEGER
The number of rows of the matrices A and B.  N >= 0.```

M

```          M is INTEGER
The number of columns of the matrix A.  M >= 0.```

P

```          P is INTEGER
The number of columns of the matrix B.  P >= 0.```

A

```          A is REAL array, dimension (LDA,M)
The N-by-M matrix A.```

AF

```          AF is REAL array, dimension (LDA,N)
Details of the GQR factorization of A and B, as returned
by SGGQRF, see SGGQRF for further details.```

Q

```          Q is REAL array, dimension (LDA,N)
The M-by-M orthogonal matrix Q.```

R

`          R is REAL array, dimension (LDA,MAX(M,N))`

LDA

```          LDA is INTEGER
The leading dimension of the arrays A, AF, R and Q.
LDA >= max(M,N).```

TAUA

```          TAUA is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by SGGQRF.```

B

```          B is REAL array, dimension (LDB,P)
On entry, the N-by-P matrix A.```

BF

```          BF is REAL array, dimension (LDB,N)
Details of the GQR factorization of A and B, as returned
by SGGQRF, see SGGQRF for further details.```

Z

```          Z is REAL array, dimension (LDB,P)
The P-by-P orthogonal matrix Z.```

T

`          T is REAL array, dimension (LDB,max(P,N))`

BWK

`          BWK is REAL array, dimension (LDB,N)`

LDB

```          LDB is INTEGER
The leading dimension of the arrays B, BF, Z and T.
LDB >= max(P,N).```

TAUB

```          TAUB is REAL array, dimension (min(P,N))
The scalar factors of the elementary reflectors, as returned
by SGGRQF.```

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The dimension of the array WORK, LWORK >= max(N,M,P)**2.```

RWORK

`          RWORK is REAL array, dimension (max(N,M,P))`

RESULT

```          RESULT is REAL array, dimension (4)
The test ratios:
RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 174 of file sgqrts.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK