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Updated: June 2017
 
 

zhpgvd (3p)

Name

zhpgvd - 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 ZHPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

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

SUBROUTINE ZHPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

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




C INTERFACE
#include <sunperf.h>

void  zhpgvd(int itype, char jobz, char uplo, int n, doublecomplex *ap,
doublecomplex *bp, double *w, doublecomplex *z, int ldz,  int
*info);

void  zhpgvd_64(long itype, char jobz, char uplo, long n, doublecomplex
*ap, doublecomplex *bp, double  *w,  doublecomplex  *z,  long
ldz, long *info);

Description

Oracle Solaris Studio Performance Library                           zhpgvd(3P)



NAME
       zhpgvd  - 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 ZHPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
             LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

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

       SUBROUTINE ZHPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
             LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

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




   C INTERFACE
       #include <sunperf.h>

       void  zhpgvd(int itype, char jobz, char uplo, int n, doublecomplex *ap,
                 doublecomplex *bp, double *w, doublecomplex *z, int ldz,  int
                 *info);

       void  zhpgvd_64(long itype, char jobz, char uplo, long n, doublecomplex
                 *ap, doublecomplex *bp, double  *w,  doublecomplex  *z,  long
                 ldz, long *info);



PURPOSE
       zhpgvd  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*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  fac-
                 torization B = U**H*U or B = L*L**H, in the same storage for-
                 mat as B.


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


       Z (output) COMPLEX*16 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*16 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) DOUBLE PRECISION 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 ZHPEVD returned an error code:
                 <= N:  if INFO = i, ZHPEVD 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




                                  7 Nov 2015                        zhpgvd(3P)