sspgv (3p)

Name

sspgv - 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 SSPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)

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

SUBROUTINE SSPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO)

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




C INTERFACE
#include <sunperf.h>

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

void sspgv_64(long itype, char jobz, char  uplo,  long  n,  float  *ap,
float *bp, float *w, float *z, long ldz, long *info);

Description

Oracle Solaris Studio Performance Library                            sspgv(3P)



NAME
       sspgv  -  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 SSPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)

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

       SUBROUTINE SSPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
             INFO)

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




   C INTERFACE
       #include <sunperf.h>

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

       void sspgv_64(long itype, char jobz, char  uplo,  long  n,  float  *ap,
                 float *bp, float *w, float *z, long ldz, long *info);



PURPOSE
       sspgv 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)
                 Real  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 AP are destroyed.


       BP (input/output)
                 Real 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)
                 Real  array,  dimension  (N)  If INFO = 0, the eigenvalues in
                 ascending order.


       Z (output)
                 Real 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)
                 Real array, dimension(3*N)

       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value
                 > 0:  SPPTRF or SSPEV returned an error code:
                 <=  N:  if INFO = i, SSPEV 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                         sspgv(3P)