dsygv man page on IRIX

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DSYGV(3F)							     DSYGV(3F)

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

	 CHARACTER     JOBZ, UPLO

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

	 DOUBLE	       PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )

PURPOSE
     DSYGV 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 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.

     A	     (input/output) DOUBLE PRECISION array, dimension (LDA, N)
	     On entry, the symmetric matrix A.	If UPLO = 'U', the leading N-
	     by-N upper triangular 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

									Page 1

DSYGV(3F)							     DSYGV(3F)

	     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) DOUBLE PRECISION array, dimension (LDB, N)
	     On entry, the symmetric matrix B.	If UPLO = 'U', the leading N-
	     by-N upper triangular 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) DOUBLE PRECISION array, dimension (N)
	     If INFO = 0, the eigenvalues in ascending order.

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

     LWORK   (input) INTEGER
	     The length of the array WORK.  LWORK >= max(1,3*N-1).  For
	     optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize
	     for DSYTRD returned by ILAENV.

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

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