---
name: "dgegs.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/dgegs.f"
---

# dgegs.f(3)

## NAME

SRC/DEPRECATED/dgegs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dgegs** (jobvsl, jobvsr, n, a, lda, b, ldb, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, info)\
  **DGEGS computes the eigenvalues, real Schur form, and, optionally, the left and/or right Schur vectors of a real matrix pair (A,B)**

## Function/Subroutine Documentation

### subroutine dgegs (character jobvsl, character jobvsr, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( \* ) alphar, double precision, dimension( \* ) alphai, double precision, dimension( \* ) beta, double precision, dimension( ldvsl, \* ) vsl, integer ldvsl, double precision, dimension( ldvsr, \* ) vsr, integer ldvsr, double precision, dimension( \* ) work, integer lwork, integer info)

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

**Purpose:**

```
!>
!> This routine is deprecated and has been replaced by routine DGGES.
!>
!> DGEGS computes the eigenvalues, real Schur form, and, optionally,
!> left and or/right Schur vectors of a real matrix pair (A,B).
!> Given two square matrices A and B, the generalized real Schur
!> factorization has the form
!>
!>   A = Q*S*Z**T,  B = Q*T*Z**T
!>
!> where Q and Z are orthogonal matrices, T is upper triangular, and S
!> is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
!> blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
!> of eigenvalues of (A,B).  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
!> DGEGV should be used instead.  See DGEGV 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 DOUBLE PRECISION array, dimension (LDA, N)
!>          On entry, the matrix A.
!>          On exit, the upper quasi-triangular matrix S from the
!>          generalized real Schur factorization.
!>
```

*LDA*

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

*B*

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

*LDB*

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

*ALPHAR*

```
!>          ALPHAR is DOUBLE PRECISION array, dimension (N)
!>          The real parts of each scalar alpha defining an eigenvalue
!>          of GNEP.
!>
```

*ALPHAI*

```
!>          ALPHAI is DOUBLE PRECISION array, dimension (N)
!>          The imaginary parts of each scalar alpha defining an
!>          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th
!>          eigenvalue is real; if positive, then the j-th and (j+1)-st
!>          eigenvalues are a complex conjugate pair, with
!>          ALPHAI(j+1) = -ALPHAI(j).
!>
```

*BETA*

```
!>          BETA is DOUBLE PRECISION array, dimension (N)
!>          The scalars beta that define the eigenvalues of GNEP.
!>          Together, the quantities alpha = (ALPHAR(j),ALPHAI(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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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(1,4*N).
!>          For good performance, LWORK must generally be larger.
!>          To compute the optimal value of LWORK, call ILAENV to get
!>          blocksizes (for DGEQRF, DORMQR, and DORGQR.)  Then compute:
!>          NB  -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR
!>          The optimal LWORK is  2*N + 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.
!>
```

*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 ALPHAR(j), ALPHAI(j), and BETA(j) should
!>                be correct for j=INFO+1,...,N.
!>          > N:  errors that usually indicate LAPACK problems:
!>                =N+1: error return from DGGBAL
!>                =N+2: error return from DGEQRF
!>                =N+3: error return from DORMQR
!>                =N+4: error return from DORGQR
!>                =N+5: error return from DGGHRD
!>                =N+6: error return from DHGEQZ (other than failed
!>                                                iteration)
!>                =N+7: error return from DGGBAK (computing VSL)
!>                =N+8: error return from DGGBAK (computing VSR)
!>                =N+9: error return from DLASCL (various places)
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **224** of file **dgegs.f**.

## Author

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