CXML
        	    
LAPACK version 3.0
sspgv(3)

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

SYNTAX
  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, * )

DESCRIPTION
  SSPGV computes all the eigenvalues and, optionally, the eigenvectors of a
  real generalized symmetric-definite eigenproblem, 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 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)*(2*n-
	  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 symmetric 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)*(2*n-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 normalized 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.