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

SSYGVD(l)					)					SSYGVD(l)

NAME
       SSYGVD  - 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 SSYGVD( ITYPE,  JOBZ,  UPLO,	N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK,
			  INFO )

	   CHARACTER	  JOBZ, UPLO

	   INTEGER	  INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   REAL 	  A( LDA, * ), B( LDB, * ), W( * ), WORK( * )

PURPOSE
       SSYGVD 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 and B is  also  positive  defi-
       nite.  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.

       A       (input/output) REAL array, dimension (LDA, N)
	       On  entry, the symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper trian-
	       gular part of A contains the upper triangular part of the matrix  A.   If  UPLO	=
	       'L',  the  leading N-by-N lower triangular part of A contains the lower triangular
	       part of the matrix A.

	       On exit, if JOBZ = 'V', then if INFO = 0, A 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 on exit the upper triangle  (if
	       UPLO='U')  or  the  lower  triangle (if UPLO='L') of A, including the diagonal, is
	       destroyed.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       B       (input/output) REAL array, dimension (LDB, N)
	       On entry, the symmetric matrix B.  If UPLO = 'U', the leading N-by-N upper  trian-
	       gular  part  of	B  contains the upper triangular part of the matrix B.	If UPLO =
	       'L', the leading N-by-N lower triangular part of B contains the	lower  triangular
	       part of the matrix B.

	       On  exit,  if INFO <= N, the part of B containing the matrix is overwritten by the
	       triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

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

       WORK    (workspace/output) REAL 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+1.  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 N <= 1,		    LIWORK >= 1.  If JOBZ
	       = 'N' and 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:  SPOTRF or SSYEVD returned an error code:
	       <=  N:	if  INFO  =  i,  SSYEVD 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 				SSYGVD(l)


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