chpgvd man page on OpenIndiana

Man page or keyword search:  
man Server   20441 pages
apropos Keyword Search (all sections)
Output format
OpenIndiana logo
[printable version]

chpgvd(3P)		    Sun Performance Library		    chpgvd(3P)

NAME
       chpgvd  - compute all the eigenvalues and, optionally, the 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

SYNOPSIS
       SUBROUTINE CHPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
	     LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

       CHARACTER * 1 JOBZ, UPLO
       COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*)
       INTEGER ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
       INTEGER IWORK(*)
       REAL W(*), RWORK(*)

       SUBROUTINE CHPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
	     LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

       CHARACTER * 1 JOBZ, UPLO
       COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*)
       INTEGER*8 ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
       INTEGER*8 IWORK(*)
       REAL W(*), RWORK(*)

   F95 INTERFACE
       SUBROUTINE HPGVD(ITYPE, JOBZ, UPLO, [N], AP, BP, W, Z, [LDZ], [WORK],
	      [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])

       CHARACTER(LEN=1) :: JOBZ, UPLO
       COMPLEX, DIMENSION(:) :: AP, BP, WORK
       COMPLEX, DIMENSION(:,:) :: Z
       INTEGER :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
       INTEGER, DIMENSION(:) :: IWORK
       REAL, DIMENSION(:) :: W, RWORK

       SUBROUTINE HPGVD_64(ITYPE, JOBZ, UPLO, [N], AP, BP, W, Z, [LDZ],
	      [WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])

       CHARACTER(LEN=1) :: JOBZ, UPLO
       COMPLEX, DIMENSION(:) :: AP, BP, WORK
       COMPLEX, DIMENSION(:,:) :: Z
       INTEGER(8) :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
       INTEGER(8), DIMENSION(:) :: IWORK
       REAL, DIMENSION(:) :: W, RWORK

   C INTERFACE
       #include <sunperf.h>

       void  chpgvd(int	 itype, char jobz, char uplo, int n, complex *ap, com‐
		 plex *bp, float *w, complex *z, int ldz, int *info);

       void chpgvd_64(long itype, char jobz, char uplo, long n,	 complex  *ap,
		 complex *bp, float *w, complex *z, long ldz, long *info);

PURPOSE
       chpgvd  computes	 all the eigenvalues and, optionally, the 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.
       If eigenvectors are desired, it uses a divide and conquer algorithm.

       The  divide  and	 conquer  algorithm  makes very mild assumptions about
       floating point arithmetic. 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 dig‐
       its, but we know of none.

ARGUMENTS
       ITYPE (input)
		 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)
		 = 'N':	 Compute eigenvalues only;
		 = 'V':	 Compute eigenvalues and eigenvectors.

       UPLO (input)
		 = 'U':	 Upper triangles of A and B are stored;
		 = 'L':	 Lower triangles of A and B are stored.

       N (input) The order of the matrices A and B.  N >= 0.

       AP (input/output) 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 (input/output) 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  fac‐
		 torization B = U**H*U or B = L*L**H, in the same storage for‐
		 mat as B.

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

       Z (output) COMPLEX 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**H*B*Z = I; if ITYPE = 3,  Z**H*inv(B)*Z  =
		 I.  If JOBZ = 'N', then Z is not referenced.

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

       WORK (workspace) COMPLEX array, dimension (LWORK)
		 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK (input)
		 The dimension of array WORK.  If N <= 1,		 LWORK
		 >=  1.	  If  JOBZ = 'N' and N > 1, LWORK >= N.	 If JOBZ = 'V'
		 and N > 1, LWORK >= 2*N.

		 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.

       RWORK (workspace) REAL array, dimension (LRWORK)
		 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

       LRWORK (input)
		 The	dimension    of	   array    RWORK.    If   N   <=   1,
		 LRWORK >= 1.  If JOBZ = 'N' and N > 1, LRWORK >= N.  If  JOBZ
		 = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

		 If  LRWORK  = -1, then a workspace query is assumed; the rou‐
		 tine only calculates the optimal size	of  the	 RWORK	array,
		 returns this value as the first entry of the RWORK array, and
		 no error message related to LRWORK is issued by XERBLA.

       IWORK (workspace/output) INTEGER array, dimension (LIWORK)
		 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

       LIWORK (input)
		 The dimension of 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 rou‐
		 tine 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)
		 = 0:  successful exit
		 < 0:  if INFO = -i, the i-th argument had an illegal value
		 > 0:  CPPTRF or CHPEVD returned an error code:
		 <= N:	if INFO = i, CHPEVD failed to converge; i off-diagonal
		 elements  of  an  intermediate	 tridiagonal form did not con‐
		 vergeto 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	eigen‐
		 values or eigenvectors were computed.

FURTHER DETAILS
       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

				  6 Mar 2009			    chpgvd(3P)
[top]

List of man pages available for OpenIndiana

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net