---
name: "gsvj0"
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/gsvj0"
---

# gsvj0(3)

gsvj0: step in gesvj

## NAME

gsvj0 - gsvj0: step in gesvj

## SYNOPSIS

### Functions

subroutine **cgsvj0** (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)\
 **CGSVJ0** pre-processor for the routine cgesvj.  subroutine **dgsvj0** (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)\
 **DGSVJ0** pre-processor for the routine dgesvj.  subroutine **sgsvj0** (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)\
 **SGSVJ0** pre-processor for the routine sgesvj.  subroutine **zgsvj0** (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)\
  **ZGSVJ0 pre-processor for the routine zgesvj.**

## Detailed Description

## Function Documentation

### subroutine cgsvj0 (character\*1 jobv, integer m, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( n ) d, real, dimension( n ) sva, integer mv, complex, dimension( ldv, \* ) v, integer ldv, real eps, real sfmin, real tol, integer nsweep, complex, dimension( lwork ) work, integer lwork, integer info)

**CGSVJ0** pre-processor for the routine cgesvj.

**Purpose:**

```
!>
!> CGSVJ0 is called from CGESVJ as a pre-processor and that is its main
!> purpose. It applies Jacobi rotations in the same way as CGESVJ does, but
!> it does not check convergence (stopping criterion). Few tuning
!> parameters (marked by [TP]) are available for the implementer.
!>
```

**Parameters**

*JOBV*

```
!>          JOBV is CHARACTER*1
!>          Specifies whether the output from this procedure is used
!>          to compute the matrix V:
!>          = 'V': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the N-by-N array V.
!>                (See the description of V.)
!>          = 'A': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the MV-by-N array V.
!>                (See the descriptions of MV and V.)
!>          = 'N': the Jacobi rotations are not accumulated.
!>
```

*M*

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

*N*

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

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, M-by-N matrix A, such that A*diag(D) represents
!>          the input matrix.
!>          On exit,
!>          A_onexit * diag(D_onexit) represents the input matrix A*diag(D)
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of D, TOL and NSWEEP.)
!>
```

*LDA*

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

*D*

```
!>          D is COMPLEX array, dimension (N)
!>          The array D accumulates the scaling factors from the complex scaled
!>          Jacobi rotations.
!>          On entry, A*diag(D) represents the input matrix.
!>          On exit, A_onexit*diag(D_onexit) represents the input matrix
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of A, TOL and NSWEEP.)
!>
```

*SVA*

```
!>          SVA is REAL array, dimension (N)
!>          On entry, SVA contains the Euclidean norms of the columns of
!>          the matrix A*diag(D).
!>          On exit, SVA contains the Euclidean norms of the columns of
!>          the matrix A_onexit*diag(D_onexit).
!>
```

*MV*

```
!>          MV is INTEGER
!>          If JOBV = 'A', then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then MV is not referenced.
!>
```

*V*

```
!>          V is COMPLEX array, dimension (LDV,N)
!>          If JOBV = 'V' then N rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'A' then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then V is not referenced.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of the array V,  LDV >= 1.
!>          If JOBV = 'V', LDV >= N.
!>          If JOBV = 'A', LDV >= MV.
!>
```

*EPS*

```
!>          EPS is REAL
!>          EPS = SLAMCH('Epsilon')
!>
```

*SFMIN*

```
!>          SFMIN is REAL
!>          SFMIN = SLAMCH('Safe Minimum')
!>
```

*TOL*

```
!>          TOL is REAL
!>          TOL is the threshold for Jacobi rotations. For a pair
!>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
!>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
!>
```

*NSWEEP*

```
!>          NSWEEP is INTEGER
!>          NSWEEP is the number of sweeps of Jacobi rotations to be
!>          performed.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          LWORK is the dimension of WORK. LWORK >= M.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, then the i-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

CGSVJ0 is used just to enable CGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

**Contributor:**

Zlatko Drmac (Zagreb, Croatia)

**Bugs, Examples and Comments:**

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line **216** of file **cgsvj0.f**.

### subroutine dgsvj0 (character\*1 jobv, integer m, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( n ) d, double precision, dimension( n ) sva, integer mv, double precision, dimension( ldv, \* ) v, integer ldv, double precision eps, double precision sfmin, double precision tol, integer nsweep, double precision, dimension( lwork ) work, integer lwork, integer info)

**DGSVJ0** pre-processor for the routine dgesvj.

**Purpose:**

```
!>
!> DGSVJ0 is called from DGESVJ as a pre-processor and that is its main
!> purpose. It applies Jacobi rotations in the same way as DGESVJ does, but
!> it does not check convergence (stopping criterion). Few tuning
!> parameters (marked by [TP]) are available for the implementer.
!>
```

**Parameters**

*JOBV*

```
!>          JOBV is CHARACTER*1
!>          Specifies whether the output from this procedure is used
!>          to compute the matrix V:
!>          = 'V': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the N-by-N array V.
!>                (See the description of V.)
!>          = 'A': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the MV-by-N array V.
!>                (See the descriptions of MV and V.)
!>          = 'N': the Jacobi rotations are not accumulated.
!>
```

*M*

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

*N*

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

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, M-by-N matrix A, such that A*diag(D) represents
!>          the input matrix.
!>          On exit,
!>          A_onexit * D_onexit represents the input matrix A*diag(D)
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of D, TOL and NSWEEP.)
!>
```

*LDA*

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

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The array D accumulates the scaling factors from the fast scaled
!>          Jacobi rotations.
!>          On entry, A*diag(D) represents the input matrix.
!>          On exit, A_onexit*diag(D_onexit) represents the input matrix
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of A, TOL and NSWEEP.)
!>
```

*SVA*

```
!>          SVA is DOUBLE PRECISION array, dimension (N)
!>          On entry, SVA contains the Euclidean norms of the columns of
!>          the matrix A*diag(D).
!>          On exit, SVA contains the Euclidean norms of the columns of
!>          the matrix onexit*diag(D_onexit).
!>
```

*MV*

```
!>          MV is INTEGER
!>          If JOBV = 'A', then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then MV is not referenced.
!>
```

*V*

```
!>          V is DOUBLE PRECISION array, dimension (LDV,N)
!>          If JOBV = 'V' then N rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'A' then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then V is not referenced.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of the array V,  LDV >= 1.
!>          If JOBV = 'V', LDV >= N.
!>          If JOBV = 'A', LDV >= MV.
!>
```

*EPS*

```
!>          EPS is DOUBLE PRECISION
!>          EPS = DLAMCH('Epsilon')
!>
```

*SFMIN*

```
!>          SFMIN is DOUBLE PRECISION
!>          SFMIN = DLAMCH('Safe Minimum')
!>
```

*TOL*

```
!>          TOL is DOUBLE PRECISION
!>          TOL is the threshold for Jacobi rotations. For a pair
!>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
!>          applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
!>
```

*NSWEEP*

```
!>          NSWEEP is INTEGER
!>          NSWEEP is the number of sweeps of Jacobi rotations to be
!>          performed.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          LWORK is the dimension of WORK. LWORK >= M.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, then the i-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

DGSVJ0 is used just to enable DGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

**Contributors:**

Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

**Bugs, Examples and Comments:**

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line **216** of file **dgsvj0.f**.

### subroutine sgsvj0 (character\*1 jobv, integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( n ) d, real, dimension( n ) sva, integer mv, real, dimension( ldv, \* ) v, integer ldv, real eps, real sfmin, real tol, integer nsweep, real, dimension( lwork ) work, integer lwork, integer info)

**SGSVJ0** pre-processor for the routine sgesvj.

**Purpose:**

```
!>
!> SGSVJ0 is called from SGESVJ as a pre-processor and that is its main
!> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
!> it does not check convergence (stopping criterion). Few tuning
!> parameters (marked by [TP]) are available for the implementer.
!>
```

**Parameters**

*JOBV*

```
!>          JOBV is CHARACTER*1
!>          Specifies whether the output from this procedure is used
!>          to compute the matrix V:
!>          = 'V': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the N-by-N array V.
!>                (See the description of V.)
!>          = 'A': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the MV-by-N array V.
!>                (See the descriptions of MV and V.)
!>          = 'N': the Jacobi rotations are not accumulated.
!>
```

*M*

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

*N*

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

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          On entry, M-by-N matrix A, such that A*diag(D) represents
!>          the input matrix.
!>          On exit,
!>          A_onexit * D_onexit represents the input matrix A*diag(D)
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of D, TOL and NSWEEP.)
!>
```

*LDA*

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

*D*

```
!>          D is REAL array, dimension (N)
!>          The array D accumulates the scaling factors from the fast scaled
!>          Jacobi rotations.
!>          On entry, A*diag(D) represents the input matrix.
!>          On exit, A_onexit*diag(D_onexit) represents the input matrix
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of A, TOL and NSWEEP.)
!>
```

*SVA*

```
!>          SVA is REAL array, dimension (N)
!>          On entry, SVA contains the Euclidean norms of the columns of
!>          the matrix A*diag(D).
!>          On exit, SVA contains the Euclidean norms of the columns of
!>          the matrix onexit*diag(D_onexit).
!>
```

*MV*

```
!>          MV is INTEGER
!>          If JOBV = 'A', then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then MV is not referenced.
!>
```

*V*

```
!>          V is REAL array, dimension (LDV,N)
!>          If JOBV = 'V' then N rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'A' then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then V is not referenced.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of the array V,  LDV >= 1.
!>          If JOBV = 'V', LDV >= N.
!>          If JOBV = 'A', LDV >= MV.
!>
```

*EPS*

```
!>          EPS is REAL
!>          EPS = SLAMCH('Epsilon')
!>
```

*SFMIN*

```
!>          SFMIN is REAL
!>          SFMIN = SLAMCH('Safe Minimum')
!>
```

*TOL*

```
!>          TOL is REAL
!>          TOL is the threshold for Jacobi rotations. For a pair
!>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
!>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
!>
```

*NSWEEP*

```
!>          NSWEEP is INTEGER
!>          NSWEEP is the number of sweeps of Jacobi rotations to be
!>          performed.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          LWORK is the dimension of WORK. LWORK >= M.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, then the i-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

SGSVJ0 is used just to enable SGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

**Contributors:**

Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

**Bugs, Examples and Comments:**

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line **216** of file **sgsvj0.f**.

### subroutine zgsvj0 (character\*1 jobv, integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( n ) d, double precision, dimension( n ) sva, integer mv, complex\*16, dimension( ldv, \* ) v, integer ldv, double precision eps, double precision sfmin, double precision tol, integer nsweep, complex\*16, dimension( lwork ) work, integer lwork, integer info)

 **ZGSVJ0 pre-processor for the routine zgesvj.**

**Purpose:**

```
!>
!> ZGSVJ0 is called from ZGESVJ as a pre-processor and that is its main
!> purpose. It applies Jacobi rotations in the same way as ZGESVJ does, but
!> it does not check convergence (stopping criterion). Few tuning
!> parameters (marked by [TP]) are available for the implementer.
!>
```

**Parameters**

*JOBV*

```
!>          JOBV is CHARACTER*1
!>          Specifies whether the output from this procedure is used
!>          to compute the matrix V:
!>          = 'V': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the N-by-N array V.
!>                (See the description of V.)
!>          = 'A': the product of the Jacobi rotations is accumulated
!>                 by postmultiplying the MV-by-N array V.
!>                (See the descriptions of MV and V.)
!>          = 'N': the Jacobi rotations are not accumulated.
!>
```

*M*

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

*N*

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

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, M-by-N matrix A, such that A*diag(D) represents
!>          the input matrix.
!>          On exit,
!>          A_onexit * diag(D_onexit) represents the input matrix A*diag(D)
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of D, TOL and NSWEEP.)
!>
```

*LDA*

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

*D*

```
!>          D is COMPLEX*16 array, dimension (N)
!>          The array D accumulates the scaling factors from the complex scaled
!>          Jacobi rotations.
!>          On entry, A*diag(D) represents the input matrix.
!>          On exit, A_onexit*diag(D_onexit) represents the input matrix
!>          post-multiplied by a sequence of Jacobi rotations, where the
!>          rotation threshold and the total number of sweeps are given in
!>          TOL and NSWEEP, respectively.
!>          (See the descriptions of A, TOL and NSWEEP.)
!>
```

*SVA*

```
!>          SVA is DOUBLE PRECISION array, dimension (N)
!>          On entry, SVA contains the Euclidean norms of the columns of
!>          the matrix A*diag(D).
!>          On exit, SVA contains the Euclidean norms of the columns of
!>          the matrix A_onexit*diag(D_onexit).
!>
```

*MV*

```
!>          MV is INTEGER
!>          If JOBV = 'A', then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then MV is not referenced.
!>
```

*V*

```
!>          V is COMPLEX*16 array, dimension (LDV,N)
!>          If JOBV = 'V' then N rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'A' then MV rows of V are post-multiplied by a
!>                           sequence of Jacobi rotations.
!>          If JOBV = 'N',   then V is not referenced.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of the array V,  LDV >= 1.
!>          If JOBV = 'V', LDV >= N.
!>          If JOBV = 'A', LDV >= MV.
!>
```

*EPS*

```
!>          EPS is DOUBLE PRECISION
!>          EPS = DLAMCH('Epsilon')
!>
```

*SFMIN*

```
!>          SFMIN is DOUBLE PRECISION
!>          SFMIN = DLAMCH('Safe Minimum')
!>
```

*TOL*

```
!>          TOL is DOUBLE PRECISION
!>          TOL is the threshold for Jacobi rotations. For a pair
!>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
!>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
!>
```

*NSWEEP*

```
!>          NSWEEP is INTEGER
!>          NSWEEP is the number of sweeps of Jacobi rotations to be
!>          performed.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          LWORK is the dimension of WORK. LWORK >= M.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, then the i-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

Contributor: Zlatko Drmac (Zagreb, Croatia)

**Bugs, Examples and Comments:**

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line **216** of file **zgsvj0.f**.

## Author

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