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Updated: June 2017
 
 

chbgv (3p)

Name

chbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

Synopsis

SUBROUTINE CHBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, RWORK, INFO)

CHARACTER*1 JOBZ, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL W(*), RWORK(*)

SUBROUTINE CHBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, RWORK, INFO)

CHARACTER*1 JOBZ, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL W(*), RWORK(*)




F95 INTERFACE
SUBROUTINE HBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
Z, LDZ, WORK, RWORK, INFO)

CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, Z
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL, DIMENSION(:) :: W, RWORK

SUBROUTINE HBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
W, Z, LDZ, WORK, RWORK, INFO)

CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, Z
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL, DIMENSION(:) :: W, RWORK




C INTERFACE
#include <sunperf.h>

void  chbgv(char  jobz,  char uplo, int n, int ka, int kb, complex *ab,
int ldab, complex *bb, int ldbb, float *w,  complex  *z,  int
ldz, int *info);

void  chbgv_64(char  jobz, char uplo, long n, long ka, long kb, complex
*ab, long ldab, complex *bb, long ldbb, float *w, complex *z,
long ldz, long *info);

Description

Oracle Solaris Studio Performance Library                            chbgv(3P)



NAME
       chbgv  -  compute all the eigenvalues, and optionally, the eigenvectors
       of a complex generalized Hermitian-definite banded eigenproblem, of the
       form A*x=(lambda)*B*x


SYNOPSIS
       SUBROUTINE CHBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
             LDZ, WORK, RWORK, INFO)

       CHARACTER*1 JOBZ, UPLO
       COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
       INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
       REAL W(*), RWORK(*)

       SUBROUTINE CHBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
             LDZ, WORK, RWORK, INFO)

       CHARACTER*1 JOBZ, UPLO
       COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
       INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
       REAL W(*), RWORK(*)




   F95 INTERFACE
       SUBROUTINE HBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
              Z, LDZ, WORK, RWORK, INFO)

       CHARACTER(LEN=1) :: JOBZ, UPLO
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: AB, BB, Z
       INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
       REAL, DIMENSION(:) :: W, RWORK

       SUBROUTINE HBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
              W, Z, LDZ, WORK, RWORK, INFO)

       CHARACTER(LEN=1) :: JOBZ, UPLO
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: AB, BB, Z
       INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
       REAL, DIMENSION(:) :: W, RWORK




   C INTERFACE
       #include <sunperf.h>

       void  chbgv(char  jobz,  char uplo, int n, int ka, int kb, complex *ab,
                 int ldab, complex *bb, int ldbb, float *w,  complex  *z,  int
                 ldz, int *info);

       void  chbgv_64(char  jobz, char uplo, long n, long ka, long kb, complex
                 *ab, long ldab, complex *bb, long ldbb, float *w, complex *z,
                 long ldz, long *info);



PURPOSE
       chbgv computes all the eigenvalues, and optionally, the eigenvectors of
       a complex generalized Hermitian-definite banded  eigenproblem,  of  the
       form  A*x=(lambda)*B*x.  Here  A  and B are assumed to be Hermitian and
       banded, and B is also positive definite.


ARGUMENTS
       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.


       KA (input)
                 The number of superdiagonals of the matrix A if UPLO  =  'U',
                 or the number of subdiagonals if UPLO = 'L'. KA >= 0.


       KB (input)
                 The  number  of superdiagonals of the matrix B if UPLO = 'U',
                 or the number of subdiagonals if UPLO = 'L'. KB >= 0.


       AB (input/output)
                 On entry, the upper or lower triangle of the  Hermitian  band
                 matrix A, stored in the first ka+1 rows of the array.  The j-
                 th column of A is stored in the j-th column of the  array  AB
                 as  follows:  if  UPLO  =  'U',  AB(ka+1+i-j,j)  = A(i,j) for
                 max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
                 j<=i<=min(n,j+ka).

                 On exit, the contents of AB are destroyed.


       LDAB (input)
                 The leading dimension of the array AB.  LDAB >= KA+1.


       BB (input/output)
                 On  entry,  the upper or lower triangle of the Hermitian band
                 matrix B, stored in the first kb+1 rows of the array.  The j-
                 th  column  of B is stored in the j-th column of the array BB
                 as follows: if  UPLO  =  'U',  BB(kb+1+i-j,j)  =  B(i,j)  for
                 max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for
                 j<=i<=min(n,j+kb).

                 On exit, the factor S from the split Cholesky factorization B
                 = S**H*S, as returned by CPBSTF.


       LDBB (input)
                 The leading dimension of the array BB.  LDBB >= KB+1.


       W (output)
                 If INFO = 0, the eigenvalues in ascending order.


       Z (output)
                 If  JOBZ  = 'V', then if INFO = 0, Z contains the matrix Z of
                 eigenvectors, with the i-th column of Z holding the eigenvec-
                 tor  associated with W(i). The eigenvectors are normalized so
                 that Z**H*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 >= N.


       WORK (workspace)
                 dimension(N)

       RWORK (workspace)
                 dimension(3*N)

       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value
                 > 0:  if INFO = i, and i is:
                 <= N:  the algorithm failed to converge: i off-diagonal  ele-
                 ments of an intermediate tridiagonal form did not converge to
                 zero; > N:   if INFO = N + i, for 1 <= i <= N, then CPBSTF
                 returned INFO = i: B is not positive definite.   The  factor-
                 ization  of  B  could  not be completed and no eigenvalues or
                 eigenvectors were computed.




                                  7 Nov 2015                         chbgv(3P)