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

ZHPGVX(l)					)					ZHPGVX(l)

NAME
       ZHPGVX  - compute selected eigenvalues and, optionally, eigenvectors of a complex general-
       ized Hermitian-definite eigenproblem, of the form  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or
       B*A*x=(lambda)*x

SYNOPSIS
       SUBROUTINE ZHPGVX( ITYPE,  JOBZ,  RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z,
			  LDZ, WORK, RWORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

	   INTEGER	  IL, INFO, ITYPE, IU, LDZ, M, N

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION RWORK( * ), W( * )

	   COMPLEX*16	  AP( * ), BP( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       ZHPGVX computes selected eigenvalues and, optionally, eigenvectors of a	complex  general-
       ized  Hermitian-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 Hermitian, stored in packed format, and B
       is  also  positive  definite.   Eigenvalues and eigenvectors can be selected by specifying
       either a range of values or a range of indices for the desired eigenvalues.

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.

       RANGE   (input) CHARACTER*1
	       = 'A': all eigenvalues will be found;
	       = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the
	       IL-th through IU-th eigenvalues will be found.

       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) COMPLEX*16 array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian 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) COMPLEX*16 array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian 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**H*U
	       or B = L*L**H, in the same storage format as B.

       VL      (input) DOUBLE PRECISION
	       VU      (input) DOUBLE PRECISION If RANGE='V', the lower and upper bounds  of  the
	       interval  to  be searched for eigenvalues. VL < VU.  Not referenced if RANGE = 'A'
	       or 'I'.

       IL      (input) INTEGER
	       IU      (input) INTEGER If RANGE='I', the indices  (in  ascending  order)  of  the
	       smallest and largest eigenvalues to be returned.  1 <= IL <= IU <= N, if N > 0; IL
	       = 1 and IU = 0 if N = 0.  Not referenced if RANGE = 'A' or 'V'.

       ABSTOL  (input) DOUBLE PRECISION
	       The absolute error tolerance for the eigenvalues.  An  approximate  eigenvalue  is
	       accepted  as  converged when it is determined to lie in an interval [a,b] of width
	       less than or equal to

	       ABSTOL + EPS *	max( |a|,|b| ) ,

	       where EPS is the machine precision.  If ABSTOL is less than or equal to zero, then
	       EPS*|T|	 will  be  used  in its place, where |T| is the 1-norm of the tridiagonal
	       matrix obtained by reducing AP to tridiagonal form.

	       Eigenvalues will be computed most accurately when  ABSTOL  is  set  to  twice  the
	       underflow threshold 2*DLAMCH('S'), not zero.  If this routine returns with INFO>0,
	       indicating that	some  eigenvectors  did  not  converge,  try  setting  ABSTOL  to
	       2*DLAMCH('S').

       M       (output) INTEGER
	       The  total  number of eigenvalues found.  0 <= M <= N.  If RANGE = 'A', M = N, and
	       if RANGE = 'I', M = IU-IL+1.

       W       (output) DOUBLE PRECISION array, dimension (N)
	       On normal exit, the first M elements contain the selected eigenvalues in ascending
	       order.

       Z       (output) COMPLEX*16 array, dimension (LDZ, N)
	       If  JOBZ  =  'N',  then Z is not referenced.  If JOBZ = 'V', then if INFO = 0, the
	       first M columns of Z contain the orthonormal eigenvectors of the matrix	A  corre-
	       sponding to the selected eigenvalues, with the i-th column of Z holding the eigen-
	       vector associated with W(i).  The eigenvectors are normalized as follows: if ITYPE
	       = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.

	       If  an  eigenvector  fails  to converge, then that column of Z contains the latest
	       approximation to the eigenvector, and the index of the eigenvector is returned  in
	       IFAIL.	Note: the user must ensure that at least max(1,M) columns are supplied in
	       the array Z; if RANGE = 'V', the exact value of M is not known in advance  and  an
	       upper bound must be used.

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

       WORK    (workspace) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION array, dimension (7*N)

       IWORK   (workspace) INTEGER array, dimension (5*N)

       IFAIL   (output) INTEGER array, dimension (N)
	       If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero.  If  INFO
	       >  0, then IFAIL contains the indices of the eigenvectors that failed to converge.
	       If JOBZ = 'N', then IFAIL is not referenced.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  ZPPTRF or ZHPEVX returned an error code:
	       <= N:  if INFO = i, ZHPEVX failed to converge; i eigenvectors failed to	converge.
	       Their indices are stored in array IFAIL.  > N:	if INFO = N + i, for 1 <= i <= n,
	       then the leading minor of order i of B is not positive definite.   The  factoriza-
	       tion 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 				ZHPGVX(l)


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