DSBGST(3)      LAPACK routine of NEC Numeric Library Collection      DSBGST(3)



NAME
       DSBGST

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



PURPOSE
            DSBGST 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 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)
                     VECT is CHARACTER*1
                     = 'N':  do not form the transformation matrix X;
                     = 'V':  form X.

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

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

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

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

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

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

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (2*N)

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



LAPACK routine                  31 October 2017                      DSBGST(3)