---
name: "zgsvts3.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zgsvts3.f"
---

# zgsvts3.f(3)

## NAME

TESTING/EIG/zgsvts3.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zgsvts3** (m, p, n, a, af, lda, b, bf, ldb, u, ldu, v, ldv, q, ldq, alpha, beta, r, ldr, iwork, work, lwork, rwork, result)\
 **ZGSVTS3**

## Function/Subroutine Documentation

### subroutine zgsvts3 (integer m, integer p, integer n, complex\*16, dimension( lda, \* ) a, complex\*16, dimension( lda, \* ) af, integer lda, complex\*16, dimension( ldb, \* ) b, complex\*16, dimension( ldb, \* ) bf, integer ldb, complex\*16, dimension( ldu, \* ) u, integer ldu, complex\*16, dimension( ldv, \* ) v, integer ldv, complex\*16, dimension( ldq, \* ) q, integer ldq, double precision, dimension( \* ) alpha, double precision, dimension( \* ) beta, complex\*16, dimension( ldr, \* ) r, integer ldr, integer, dimension( \* ) iwork, complex\*16, dimension( lwork ) work, integer lwork, double precision, dimension( \* ) rwork, double precision, dimension( 6 ) result)

**ZGSVTS3**

**Purpose:**

```
!>
!> ZGSVTS3 tests ZGGSVD3, 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 COMPLEX*16 array, dimension (LDA,M)
!>          The M-by-N matrix A.
!>
```

*AF*

```
!>          AF is COMPLEX*16 array, dimension (LDA,N)
!>          Details of the GSVD of A and B, as returned by ZGGSVD3,
!>          see ZGGSVD3 for further details.
!>
```

*LDA*

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

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,P)
!>          On entry, the P-by-N matrix B.
!>
```

*BF*

```
!>          BF is COMPLEX*16 array, dimension (LDB,N)
!>          Details of the GSVD of A and B, as returned by ZGGSVD3,
!>          see ZGGSVD3 for further details.
!>
```

*LDB*

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

*U*

```
!>          U is COMPLEX*16 array, dimension(LDU,M)
!>          The M by M unitary matrix U.
!>
```

*LDU*

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

*V*

```
!>          V is COMPLEX*16 array, dimension(LDV,M)
!>          The P by P unitary matrix V.
!>
```

*LDV*

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

*Q*

```
!>          Q is COMPLEX*16 array, dimension(LDQ,N)
!>          The N by N unitary matrix Q.
!>
```

*LDQ*

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

*ALPHA*

```
!>          ALPHA is DOUBLE PRECISION array, dimension (N)
!>
```

*BETA*

```
!>          BETA is DOUBLE PRECISION 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 ZGGSVD3 for details.
!>
```

*R*

```
!>          R is COMPLEX*16 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 COMPLEX*16 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 DOUBLE PRECISION array, dimension (max(M,P,N))
!>
```

*RESULT*

```
!>          RESULT is DOUBLE PRECISION 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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **206** of file **zgsvts3.f**.

## Author

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