---
name: "cggsvp3.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/cggsvp3.f"
---

# cggsvp3.f(3)

## NAME

SRC/cggsvp3.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cggsvp3** (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)\
 **CGGSVP3**

## Function/Subroutine Documentation

### subroutine cggsvp3 (character jobu, character jobv, character jobq, integer m, integer p, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldb, \* ) b, integer ldb, real tola, real tolb, integer k, integer l, complex, dimension( ldu, \* ) u, integer ldu, complex, dimension( ldv, \* ) v, integer ldv, complex, dimension( ldq, \* ) q, integer ldq, integer, dimension( \* ) iwork, real, dimension( \* ) rwork, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer lwork, integer info)

**CGGSVP3**

**Purpose:**

```
!>
!> CGGSVP3 computes unitary matrices U, V and Q such that
!>
!>                    N-K-L  K    L
!>  U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
!>                 L ( 0     0   A23 )
!>             M-K-L ( 0     0    0  )
!>
!>                  N-K-L  K    L
!>         =     K ( 0    A12  A13 )  if M-K-L < 0;
!>             M-K ( 0     0   A23 )
!>
!>                  N-K-L  K    L
!>  V**H*B*Q =   L ( 0     0   B13 )
!>             P-L ( 0     0    0  )
!>
!> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
!> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
!> otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
!> numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
!>
!> This decomposition is the preprocessing step for computing the
!> Generalized Singular Value Decomposition (GSVD), see subroutine
!> CGGSVD3.
!>
```

**Parameters**

*JOBU*

```
!>          JOBU is CHARACTER*1
!>          = 'U':  Unitary matrix U is computed;
!>          = 'N':  U is not computed.
!>
```

*JOBV*

```
!>          JOBV is CHARACTER*1
!>          = 'V':  Unitary matrix V is computed;
!>          = 'N':  V is not computed.
!>
```

*JOBQ*

```
!>          JOBQ is CHARACTER*1
!>          = 'Q':  Unitary matrix Q is computed;
!>          = 'N':  Q is not computed.
!>
```

*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 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit, A contains the triangular (or trapezoidal) matrix
!>          described in the Purpose section.
!>
```

*LDA*

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

*B*

```
!>          B is COMPLEX array, dimension (LDB,N)
!>          On entry, the P-by-N matrix B.
!>          On exit, B contains the triangular matrix described in
!>          the Purpose section.
!>
```

*LDB*

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

*TOLA*

```
!>          TOLA is REAL
!>
```

*TOLB*

```
!>          TOLB is REAL
!>
!>          TOLA and TOLB are the thresholds to determine the effective
!>          numerical rank of matrix B and a subblock of A. Generally,
!>          they are set to
!>             TOLA = MAX(M,N)*norm(A)*MACHEPS,
!>             TOLB = MAX(P,N)*norm(B)*MACHEPS.
!>          The size of TOLA and TOLB may affect the size of backward
!>          errors of the decomposition.
!>
```

*K*

```
!>          K is INTEGER
!>
```

*L*

```
!>          L is INTEGER
!>
!>          On exit, K and L specify the dimension of the subblocks
!>          described in Purpose section.
!>          K + L = effective numerical rank of (A**H,B**H)**H.
!>
```

*U*

```
!>          U is COMPLEX array, dimension (LDU,M)
!>          If JOBU = 'U', U contains the unitary matrix U.
!>          If JOBU = 'N', U is not referenced.
!>
```

*LDU*

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

*V*

```
!>          V is COMPLEX array, dimension (LDV,P)
!>          If JOBV = 'V', V contains the unitary matrix V.
!>          If JOBV = 'N', V is not referenced.
!>
```

*LDV*

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

*Q*

```
!>          Q is COMPLEX array, dimension (LDQ,N)
!>          If JOBQ = 'Q', Q contains the unitary matrix Q.
!>          If JOBQ = 'N', Q is not referenced.
!>
```

*LDQ*

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

*IWORK*

```
!>          IWORK is INTEGER array, dimension (N)
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (2*N)
!>
```

*TAU*

```
!>          TAU is COMPLEX array, dimension (N)
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK >= 1.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>
```

*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.

**Further Details:**

```
!>
!>  The subroutine uses LAPACK subroutine CGEQP3 for the QR factorization
!>  with column pivoting to detect the effective numerical rank of the
!>  a matrix. It may be replaced by a better rank determination strategy.
!>
!>  CGGSVP3 replaces the deprecated subroutine CGGSVP.
!>
!>
```

Definition at line **275** of file **cggsvp3.f**.

## Author

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