SSPGST  -  reduce  a  real  symmetric-definite generalized
       eigenproblem to standard form, using packed storage


SYNOPSIS

       SUBROUTINE SSPGST( ITYPE, UPLO, N, AP, BP, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, ITYPE, N

           REAL           AP( * ), BP( * )


PURPOSE

       SSPGST  reduces  a  real  symmetric-definite   generalized
       eigenproblem  to  standard form, using packed storage.  If
       ITYPE = 1, the problem is A*x = lambda*B*x,
       and   A   is   overwritten   by   inv(U**T)*A*inv(U)    or
       inv(L)*A*inv(L**T)

       If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
       B*A*x  =  lambda*x,  and  A  is overwritten by U*A*U**T or
       L**T*A*L.

       B must have been previously factorized as U**T*U or L*L**T
       by SPPTRF.


ARGUMENTS

       ITYPE   (input) INTEGER
               =     1:     compute     inv(U**T)*A*inv(U)     or
               inv(L)*A*inv(L**T);
               = 2 or 3: compute U*A*U**T or L**T*A*L.

       UPLO    (input) CHARACTER
               = 'U':  Upper triangle of A is  stored  and  B  is
               factored as U**T*U; = 'L':  Lower triangle of A is
               stored and B is factored as L*L**T.

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

       AP      (input/output) REAL array, dimension (N*(N+1)/2)
               On entry, the upper or lower triangle of the  sym­
               metric  matrix  A,  packed  columnwise in a linear
               array.  The j-th column of  A  is  stored  in  the
               array  AP  as  follows:  if  UPLO  =  'U',  AP(i +
               (j-1)*j/2) = A(i,j) for 1<=i<=j; if  UPLO  =  'L',
               AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

               On  exit,  if  INFO  =  0, the transformed matrix,
               stored in the same format as A.

               The triangular factor from the Cholesky factoriza­
               tion  of  B,  stored  in  the same format as A, as
               returned by SPPTRF.

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


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