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CentOS 7.0 - man page for chpgvx (centos section 3)

chpgvx.f(3)				      LAPACK				      chpgvx.f(3)

NAME
       chpgvx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chpgvx (ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z,
	   LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
	   CHPGST

Function/Subroutine Documentation
   subroutine chpgvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN,
       complex, dimension( * )AP, complex, dimension( * )BP, realVL, realVU, integerIL,
       integerIU, realABSTOL, integerM, real, dimension( * )W, complex, dimension( ldz, * )Z,
       integerLDZ, complex, dimension( * )WORK, real, dimension( * )RWORK, integer, dimension( *
       )IWORK, integer, dimension( * )IFAIL, integerINFO)
       CHPGST

       Purpose:

	    CHPGVX computes selected eigenvalues and, optionally, eigenvectors
	    of a complex generalized 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.

       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.

	   RANGE

		     RANGE is 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

		     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 COMPLEX 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

		     BP is COMPLEX 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

		     VL is REAL

	   VU

		     VU is REAL

		     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

		     IL is INTEGER

	   IU

		     IU is 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

		     ABSTOL is REAL
		     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*SLAMCH('S'), not zero.
		     If this routine returns with INFO>0, indicating that some
		     eigenvectors did not converge, try setting ABSTOL to
		     2*SLAMCH('S').

	   M

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

	   W

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

	   Z

		     Z is COMPLEX 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
		     corresponding to the selected eigenvalues, with the i-th
		     column of Z holding the eigenvector 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

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

	   WORK

		     WORK is COMPLEX array, dimension (2*N)

	   RWORK

		     RWORK is REAL array, dimension (7*N)

	   IWORK

		     IWORK is INTEGER array, dimension (5*N)

	   IFAIL

		     IFAIL is 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

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  CPPTRF or CHPEVX returned an error code:
			<= N:  if INFO = i, CHPEVX 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 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 267 of file chpgvx.f.

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

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


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