Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  reduces  a  real  symmetric-definite  banded  generalized  eigenproblem A*x =
lambda*B*x to standard form C*y = lambda*y,

```

#### SYNOPSIS

```       SUBROUTINE SSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO )

CHARACTER      UPLO, VECT

INTEGER        INFO, KA, KB, LDAB, LDBB, LDX, N

REAL           AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )

```

#### 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.

```

#### ARGUMENTS

```        VECT    (input) CHARACTER*1
= 'N':  do not form the transformation matrix X;
= 'V':  form X.

UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

KA      (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KA >= 0.

KB      (input) INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.

AB      (input/output) 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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KA+1.

BB      (input) 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    (input) INTEGER
The leading dimension of the array BB.  LDBB >= KB+1.

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

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

WORK    (workspace) REAL array, dimension (2*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

LAPACK routine (version 3.2)               April 2011                            SSBGST(3lapack)
```