---
name: "zgegs.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/zgegs.f"
---

# zgegs.f(3)

## NAME

SRC/DEPRECATED/zgegs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zgegs** (jobvsl, jobvsr, n, a, lda, b, ldb, alpha, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, rwork, info)\
  **ZGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B)**

## Function/Subroutine Documentation

### subroutine zgegs (character jobvsl, character jobvsr, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( \* ) alpha, complex\*16, dimension( \* ) beta, complex\*16, dimension( ldvsl, \* ) vsl, integer ldvsl, complex\*16, dimension( ldvsr, \* ) vsr, integer ldvsr, complex\*16, dimension( \* ) work, integer lwork, double precision, dimension( \* ) rwork, integer info)

 **ZGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B)**

**Purpose:**

```
!>
!> This routine is deprecated and has been replaced by routine ZGGES.
!>
!> ZGEGS computes the eigenvalues, Schur form, and, optionally, the
!> left and or/right Schur vectors of a complex matrix pair (A,B).
!> Given two square matrices A and B, the generalized Schur
!> factorization has the form
!>
!>    A = Q*S*Z**H,  B = Q*T*Z**H
!>
!> where Q and Z are unitary matrices and S and T are upper triangular.
!> The columns of Q are the left Schur vectors
!> and the columns of Z are the right Schur vectors.
!>
!> If only the eigenvalues of (A,B) are needed, the driver routine
!> ZGEGV should be used instead.  See ZGEGV for a description of the
!> eigenvalues of the generalized nonsymmetric eigenvalue problem
!> (GNEP).
!>
```

**Parameters**

*JOBVSL*

```
!>          JOBVSL is CHARACTER*1
!>          = 'N':  do not compute the left Schur vectors;
!>          = 'V':  compute the left Schur vectors (returned in VSL).
!>
```

*JOBVSR*

```
!>          JOBVSR is CHARACTER*1
!>          = 'N':  do not compute the right Schur vectors;
!>          = 'V':  compute the right Schur vectors (returned in VSR).
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA, N)
!>          On entry, the matrix A.
!>          On exit, the upper triangular matrix S from the generalized
!>          Schur factorization.
!>
```

*LDA*

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

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB, N)
!>          On entry, the matrix B.
!>          On exit, the upper triangular matrix T from the generalized
!>          Schur factorization.
!>
```

*LDB*

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

*ALPHA*

```
!>          ALPHA is COMPLEX*16 array, dimension (N)
!>          The complex scalars alpha that define the eigenvalues of
!>          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
!>          form of A.
!>
```

*BETA*

```
!>          BETA is COMPLEX*16 array, dimension (N)
!>          The non-negative real scalars beta that define the
!>          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
!>          of the triangular factor T.
!>
!>          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
!>          represent the j-th eigenvalue of the matrix pair (A,B), in
!>          one of the forms lambda = alpha/beta or mu = beta/alpha.
!>          Since either lambda or mu may overflow, they should not,
!>          in general, be computed.
!>
```

*VSL*

```
!>          VSL is COMPLEX*16 array, dimension (LDVSL,N)
!>          If JOBVSL = 'V', the matrix of left Schur vectors Q.
!>          Not referenced if JOBVSL = 'N'.
!>
```

*LDVSL*

```
!>          LDVSL is INTEGER
!>          The leading dimension of the matrix VSL. LDVSL >= 1, and
!>          if JOBVSL = 'V', LDVSL >= N.
!>
```

*VSR*

```
!>          VSR is COMPLEX*16 array, dimension (LDVSR,N)
!>          If JOBVSR = 'V', the matrix of right Schur vectors Z.
!>          Not referenced if JOBVSR = 'N'.
!>
```

*LDVSR*

```
!>          LDVSR is INTEGER
!>          The leading dimension of the matrix VSR. LDVSR >= 1, and
!>          if JOBVSR = 'V', LDVSR >= N.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 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 >= max(1,2*N).
!>          For good performance, LWORK must generally be larger.
!>          To compute the optimal value of LWORK, call ILAENV to get
!>          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:
!>          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
!>          the optimal LWORK is N*(NB+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.
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (3*N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          =1,...,N:
!>                The QZ iteration failed.  (A,B) are not in Schur
!>                form, but ALPHA(j) and BETA(j) should be correct for
!>                j=INFO+1,...,N.
!>          > N:  errors that usually indicate LAPACK problems:
!>                =N+1: error return from ZGGBAL
!>                =N+2: error return from ZGEQRF
!>                =N+3: error return from ZUNMQR
!>                =N+4: error return from ZUNGQR
!>                =N+5: error return from ZGGHRD
!>                =N+6: error return from ZHGEQZ (other than failed
!>                                               iteration)
!>                =N+7: error return from ZGGBAK (computing VSL)
!>                =N+8: error return from ZGGBAK (computing VSR)
!>                =N+9: error return from ZLASCL (various places)
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **222** of file **zgegs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.