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sspgv

 NAME
      SSPGV - compute all the eigenvalues and, optionally, the
      eigenvectors of a real generalized symmetric-definite eigen-
      problem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
      B*A*x=(lambda)*x

 SYNOPSIS
      SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ,
                        WORK, INFO )

          CHARACTER     JOBZ, UPLO

          INTEGER       INFO, ITYPE, LDZ, N

          REAL          AP( * ), BP( * ), W( * ), WORK( * ), Z(
                        LDZ, * )

 PURPOSE
      SSPGV computes all the eigenvalues and, optionally, the
      eigenvectors of a real generalized symmetric-definite eigen-
      problem, of the form A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or
      B*A*x=(lambda)*x.  Here A and B are assumed to be symmetric,
      stored in packed format, and B is also positive definite.

 ARGUMENTS
      ITYPE   (input) INTEGER
              Specifies the problem type to be solved:
              = 1:  A*x = (lambda)*B*x
              = 2:  A*B*x = (lambda)*x
              = 3:  B*A*x = (lambda)*x

      JOBZ    (input) CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.

      UPLO    (input) CHARACTER*1
              = 'U':  Upper triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

      N       (input) INTEGER
              The order of the matrix A.  N >= 0.

      AP      (input/workspace) 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, the contents of AP are destroyed.

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

              On exit, the triangular factor U or L from the
              Cholesky factorization B = U**T*U or B = L*L**T, in
              the same storage format as B.

      W       (output) REAL array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

      Z       (output) REAL array, dimension (LDZ, N)
              If JOBZ = 'V', then if INFO = 0, Z contains the
              matrix Z of eigenvectors.  The eigenvectors are nor-
              malized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I;
              if ITYPE = 3, Z**T*inv(B)*Z = I.  If JOBZ = 'N',
              then Z is not referenced.

      LDZ     (input) INTEGER
              The leading dimension of the array Z.  LDZ >= 1, and
              if JOBZ = 'V', LDZ >= max(1,N).

      WORK    (workspace) REAL array, dimension (3*N)

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value
              > 0:  SPPTRF or SSPEV returned an error code:
              <= N:  if INFO = i, SSPEV failed to converge; i
              off-diagonal elements of an intermediate tridiagonal
              form did not converge to zero.  > N:   if INFO = n +
              i, for 1 <= i <= n, then the leading minor of order
              i of B is not positive definite.  The factorization
              of B could not be completed and no eigenvalues or
              eigenvectors were computed.