SSPGST (3lapack)

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 symmetric 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.

  BP      (input) REAL array, dimension (N*(N+1)/2)
          The triangular factor from the Cholesky factorization 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 illegal value