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dspgst

 NAME
      DSPGST - reduce a real symmetric-definite generalized eigen-
      problem to standard form, using packed storage

 SYNOPSIS
      SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, INFO )

          CHARACTER      UPLO

          INTEGER        INFO, ITYPE, N

          DOUBLE         PRECISION AP( * ), BP( * )

 PURPOSE
      DSPGST reduces a real symmetric-definite generalized eigen-
      problem 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 DPPTRF.

 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 fac-
              tored 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.

 (N*(N+1)/2)
      AP      (input/output) DOUBLE PRECISION array, dimension
              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.

      BP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
              The triangular factor from the Cholesky factoriza-
              tion of B, stored in the same format as A, as
              returned by DPPTRF.

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