# sgsvts3.f - Man Page

TESTING/EIG/sgsvts3.f

## Synopsis

### Functions/Subroutines

subroutine sgsvts3 (m, p, n, a, af, lda, b, bf, ldb, u, ldu, v, ldv, q, ldq, alpha, beta, r, ldr, iwork, work, lwork, rwork, result)
SGSVTS3

## Function/Subroutine Documentation

### subroutine sgsvts3 (integer m, integer p, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, integer ldb, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) alpha, real, dimension( * ) beta, real, dimension( ldr, * ) r, integer ldr, integer, dimension( * ) iwork, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 6 ) result)

SGSVTS3

Purpose:

``` SGSVTS3 tests SGGSVD3, which computes the GSVD of an M-by-N matrix A
and a P-by-N matrix B:
U'*A*Q = D1*R and V'*B*Q = D2*R.```
Parameters

M

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

P

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

N

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

A

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

AF

```          AF is REAL array, dimension (LDA,N)
Details of the GSVD of A and B, as returned by SGGSVD3,
see SGGSVD3 for further details.```

LDA

```          LDA is INTEGER
The leading dimension of the arrays A and AF.
LDA >= max( 1,M ).```

B

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

BF

```          BF is REAL array, dimension (LDB,N)
Details of the GSVD of A and B, as returned by SGGSVD3,
see SGGSVD3 for further details.```

LDB

```          LDB is INTEGER
The leading dimension of the arrays B and BF.
LDB >= max(1,P).```

U

```          U is REAL array, dimension(LDU,M)
The M by M orthogonal matrix U.```

LDU

```          LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M).```

V

```          V is REAL array, dimension(LDV,M)
The P by P orthogonal matrix V.```

LDV

```          LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P).```

Q

```          Q is REAL array, dimension(LDQ,N)
The N by N orthogonal matrix Q.```

LDQ

```          LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).```

ALPHA

`          ALPHA is REAL array, dimension (N)`

BETA

```          BETA is REAL array, dimension (N)

The generalized singular value pairs of A and B, the
“diagonal” matrices D1 and D2 are constructed from
ALPHA and BETA, see subroutine SGGSVD3 for details.```

R

```          R is REAL array, dimension(LDQ,N)
The upper triangular matrix R.```

LDR

```          LDR is INTEGER
The leading dimension of the array R. LDR >= max(1,N).```

IWORK

`          IWORK is INTEGER array, dimension (N)`

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

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

RWORK

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

RESULT

```          RESULT is REAL array, dimension (6)
The test ratios:
RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - U'*U ) / ( M*ULP )
RESULT(4) = norm( I - V'*V ) / ( P*ULP )
RESULT(5) = norm( I - Q'*Q ) / ( N*ULP )
RESULT(6) = 0        if ALPHA is in decreasing order;
= ULPINV   otherwise.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 207 of file sgsvts3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgsvts3(3) is an alias of sgsvts3.f(3).

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