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RedHat 9 (Linux i386) - man page for dspgvd (redhat section l)

DSPGVD(l)					)					DSPGVD(l)

NAME
       DSPGVD  - compute all the eigenvalues, and optionally, the eigenvectors of a real general-
       ized 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  general-
       ized  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 arith-
       metic. 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.

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 factorization 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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