SYNOPSIS
 SUBROUTINE DSBGST(
 VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO )
 CHARACTER UPLO, VECT
 INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N
 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )
PURPOSE
DSBGST reduces a real symmetricdefinite 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 DPBSTF, 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) DOUBLE PRECISION 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 jth column of A is stored in the jth column of the array AB as follows: if UPLO = 'U', AB(ka+1+ij,j) = A(i,j) for max(1,jka)<=i<=j; if UPLO = 'L', AB(1+ij,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) DOUBLE PRECISION array, dimension (LDBB,N)
 The banded factor S from the split Cholesky factorization of B, as returned by DPBSTF, 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) DOUBLE PRECISION array, dimension (LDX,N)
 If VECT = 'V', the nbyn 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) DOUBLE PRECISION array, dimension (2*N)
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.