SRC/ssbgst.f(3)            Library Functions Manual            SRC/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.

LAPACK                          Version 3.12.0                 SRC/ssbgst.f(3)