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DSPGVD(l)			       )			     DSPGVD(l)

NAME
       DSPGVD  - 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

SYNOPSIS
       SUBROUTINE DSPGVD( ITYPE,  JOBZ,	 UPLO,	N,  AP,	 BP,  W, Z, LDZ, WORK,
			  LWORK, IWORK, LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

	   INTEGER	  INFO, ITYPE, LDZ, LIWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION AP( * ), BP( * ), W( * ), WORK(  *	),  Z(
			  LDZ, * )

PURPOSE
       DSPGVD  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.
       If eigenvectors are desired, it uses a divide and conquer algorithm.

       The  divide  and	 conquer  algorithm  makes very mild assumptions about
       floating point arithmetic. It will work on machines with a guard	 digit
       in add/subtract, or on those binary machines without guard digits which
       subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It	 could
       conceivably  fail on hexadecimal or decimal machines without guard dig‐
       its, but we know of none.

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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 factor‐
	       ization B = U**T*U or B = L*L**T, in the same storage format as
	       B.

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

       Z       (output) DOUBLE PRECISION 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/output) DOUBLE PRECISION array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The   dimension	 of   the   array   WORK.    If	  N   <=    1,
	       LWORK  >= 1.  If JOBZ = 'N' and N > 1, LWORK >= 2*N.  If JOBZ =
	       'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.

	       If LWORK = -1, then a workspace query is assumed;  the  routine
	       only  calculates	 the  optimal  size of the WORK array, returns
	       this value as the first entry of the WORK array, and  no	 error
	       message related to LWORK is issued by XERBLA.

       IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
	       On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

       LIWORK  (input) INTEGER
	       The  dimension  of  the array IWORK.  If JOBZ  = 'N' or N <= 1,
	       LIWORK >= 1.  If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.

	       If LIWORK = -1, then a workspace query is assumed; the  routine
	       only  calculates	 the  optimal size of the IWORK array, returns
	       this value as the first entry of the IWORK array, and no	 error
	       message related to LIWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  DPPTRF or DSPEVD returned an error code:
	       <=  N:	if INFO = i, DSPEVD 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.

FURTHER DETAILS
       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

LAPACK version 3.0		 15 June 2000			     DSPGVD(l)
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