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Updated: June 2017
 
 

dspgv (3p)

Name

dspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

Synopsis

SUBROUTINE DSPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)

CHARACTER*1 JOBZ, UPLO
INTEGER ITYPE, N, LDZ, INFO
DOUBLE PRECISION AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)

SUBROUTINE DSPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO)

CHARACTER*1 JOBZ, UPLO
INTEGER*8 ITYPE, N, LDZ, INFO
DOUBLE PRECISION AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)




F95 INTERFACE
SUBROUTINE SPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO)

CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: ITYPE, N, LDZ, INFO
REAL(8), DIMENSION(:) :: AP, BP, W, WORK
REAL(8), DIMENSION(:,:) :: Z

SUBROUTINE SPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO)

CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: ITYPE, N, LDZ, INFO
REAL(8), DIMENSION(:) :: AP, BP, W, WORK
REAL(8), DIMENSION(:,:) :: Z




C INTERFACE
#include <sunperf.h>

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

void dspgv_64(long itype, char jobz, char uplo,  long  n,  double  *ap,
double *bp, double *w, double *z, long ldz, long *info);

Description

Oracle Solaris Studio Performance Library                            dspgv(3P)



NAME
       dspgv  -  compute all the eigenvalues and, optionally, the eigenvectors
       of a real generalized  symmetric-definite  eigenproblem,  of  the  form
       A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x


SYNOPSIS
       SUBROUTINE DSPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)

       CHARACTER*1 JOBZ, UPLO
       INTEGER ITYPE, N, LDZ, INFO
       DOUBLE PRECISION AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)

       SUBROUTINE DSPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
             INFO)

       CHARACTER*1 JOBZ, UPLO
       INTEGER*8 ITYPE, N, LDZ, INFO
       DOUBLE PRECISION AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)




   F95 INTERFACE
       SUBROUTINE SPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
              INFO)

       CHARACTER(LEN=1) :: JOBZ, UPLO
       INTEGER :: ITYPE, N, LDZ, INFO
       REAL(8), DIMENSION(:) :: AP, BP, W, WORK
       REAL(8), DIMENSION(:,:) :: Z

       SUBROUTINE SPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
              INFO)

       CHARACTER(LEN=1) :: JOBZ, UPLO
       INTEGER(8) :: ITYPE, N, LDZ, INFO
       REAL(8), DIMENSION(:) :: AP, BP, W, WORK
       REAL(8), DIMENSION(:,:) :: Z




   C INTERFACE
       #include <sunperf.h>

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

       void dspgv_64(long itype, char jobz, char uplo,  long  n,  double  *ap,
                 double *bp, double *w, double *z, long ldz, long *info);



PURPOSE
       dspgv computes all the eigenvalues and, optionally, the eigenvectors of
       a  real  generalized  symmetric-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 symmetric, stored in packed format,  and  B  is  also
       positive definite.


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)
                 Double  precision  array, dimension (N*(N+1)/2) On entry, the
                 upper or lower triangle of the  symmetric  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 A are destroyed.


       BP (input/output)
                 Double precision array, dimension (N*(N+1)/2) On  entry,  the
                 upper  or  lower  triangle  of the symmetric 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**T*U or B = L*L**T, in the same storage for-
                 mat as B.


       W (output)
                 Double precision array, dimension (N) If INFO = 0, the eigen-
                 values in ascending order.


       Z (output)
                 Double precision 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**T*B*Z = I; if ITYPE = 3, Z**T*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)
                 Double precision array, dimension(3*N)

       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value
                 > 0:  DPPTRF or DSPEV returned an error code:
                 <=  N:  if INFO = i, DSPEV failed to converge; i off-diagonal
                 elements of an intermediate tridiagonal form did not converge
                 to  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 eigenvalues
                 or eigenvectors were computed.




                                  7 Nov 2015                         dspgv(3P)