---
name: "ssbgst.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/ssbgst.f"
---

# ssbgst.f(3)

## NAME

SRC/ssbgst.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ssbgst** (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)\
 **SSBGST**

## Function/Subroutine Documentation

### subroutine ssbgst (character vect, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, \* ) ab, integer ldab, real, dimension( ldbb, \* ) bb, integer ldbb, real, dimension( ldx, \* ) x, integer ldx, real, dimension( \* ) work, integer info)

**SSBGST**

**Purpose:**

```
!>
!> SSBGST reduces a real symmetric-definite banded generalized
!> eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
!> such that C has the same bandwidth as A.
!>
!> B must have been previously factorized as S**T*S by SPBSTF, using a
!> split Cholesky factorization. A is overwritten by C = X**T*A*X, where
!> X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
!> bandwidth of A.
!>
```

**Parameters**

*VECT*

```
!>          VECT is CHARACTER*1
!>          = 'N':  do not form the transformation matrix X;
!>          = 'V':  form X.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*KA*

```
!>          KA is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KA >= 0.
!>
```

*KB*

```
!>          KB is INTEGER
!>          The number of superdiagonals of the matrix B if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
!>
```

*AB*

```
!>          AB is REAL array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first ka+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
!>
!>          On exit, the transformed matrix X**T*A*X, stored in the same
!>          format as A.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KA+1.
!>
```

*BB*

```
!>          BB is REAL array, dimension (LDBB,N)
!>          The banded factor S from the split Cholesky factorization of
!>          B, as returned by SPBSTF, stored in the first KB+1 rows of
!>          the array.
!>
```

*LDBB*

```
!>          LDBB is INTEGER
!>          The leading dimension of the array BB.  LDBB >= KB+1.
!>
```

*X*

```
!>          X is REAL array, dimension (LDX,N)
!>          If VECT = 'V', the n-by-n matrix X.
!>          If VECT = 'N', the array X is not referenced.
!>
```

*LDX*

```
!>          LDX is INTEGER
!>          The leading dimension of the array X.
!>          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
!>
```

*WORK*

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

*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.

Definition at line **157** of file **ssbgst.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.