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dspgvd.f(3)				      LAPACK				      dspgvd.f(3)

NAME
       dspgvd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dspgvd (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
	   INFO)
	   DSPGST

Function/Subroutine Documentation
   subroutine dspgvd (integerITYPE, characterJOBZ, characterUPLO, integerN, double precision,
       dimension( * )AP, double precision, dimension( * )BP, double precision, dimension( * )W,
       double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK,
       integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
       DSPGST

       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 digits, but we know of none.

       Parameters:
	   ITYPE

		     ITYPE is 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

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

	   UPLO

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

	   N

		     N is INTEGER
		     The order of the matrices A and B.  N >= 0.

	   AP

		     AP is 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

		     BP is 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
		     factorization B = U**T*U or B = L*L**T, in the same storage
		     format as B.

	   W

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

	   Z

		     Z is 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

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

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the required LWORK.

	   LWORK

		     LWORK is 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 required sizes of the WORK and IWORK
		     arrays, returns these values as the first entries of the WORK
		     and IWORK arrays, and no error message related to LWORK or
		     LIWORK is issued by XERBLA.

	   IWORK

		     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
		     On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

	   LIWORK

		     LIWORK is 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 required sizes of the WORK and
		     IWORK arrays, returns these values as the first entries of
		     the WORK and IWORK arrays, and no error message related to
		     LWORK or LIWORK is issued by XERBLA.

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

       Definition at line 210 of file dspgvd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dspgvd.f(3)
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