ssbevx (3p)

Name

ssbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

Synopsis

SUBROUTINE SSBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)

CHARACTER*1 JOBZ, RANGE, UPLO
INTEGER N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK2(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)

SUBROUTINE SSBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)

CHARACTER*1 JOBZ, RANGE, UPLO
INTEGER*8 N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK2(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)




F95 INTERFACE
SUBROUTINE SBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ,
VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2,
IFAIL, INFO)

CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK2, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: A, Q, Z

SUBROUTINE SBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ,
VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2,
IFAIL, INFO)

CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: A, Q, Z




C INTERFACE
#include <sunperf.h>

void ssbevx(char jobz, char range, char uplo, int n, int kd, float  *a,
int  lda,  float *q, int ldq, float vl, float vu, int il, int
iu, float abtol, int *nfound, float *w, float  *z,  int  ldz,
int *ifail, int *info);

void ssbevx_64(char jobz, char range, char uplo, long n, long kd, float
*a, long lda, float *q, long ldq, float vl,  float  vu,  long
il,  long  iu, float abtol, long *nfound, float *w, float *z,
long ldz, long *ifail, long *info);

Description

Oracle Solaris Studio Performance Library                           ssbevx(3P)



NAME
       ssbevx  - compute selected eigenvalues and, optionally, eigenvectors of
       a real symmetric band matrix A


SYNOPSIS
       SUBROUTINE SSBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
             VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)

       CHARACTER*1 JOBZ, RANGE, UPLO
       INTEGER N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
       INTEGER IWORK2(*), IFAIL(*)
       REAL VL, VU, ABTOL
       REAL A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)

       SUBROUTINE SSBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
             VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)

       CHARACTER*1 JOBZ, RANGE, UPLO
       INTEGER*8 N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
       INTEGER*8 IWORK2(*), IFAIL(*)
       REAL VL, VU, ABTOL
       REAL A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)




   F95 INTERFACE
       SUBROUTINE SBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ,
              VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2,
              IFAIL, INFO)

       CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
       INTEGER :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
       INTEGER, DIMENSION(:) :: IWORK2, IFAIL
       REAL :: VL, VU, ABTOL
       REAL, DIMENSION(:) :: W, WORK
       REAL, DIMENSION(:,:) :: A, Q, Z

       SUBROUTINE SBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ,
              VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2,
              IFAIL, INFO)

       CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
       INTEGER(8) :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
       INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
       REAL :: VL, VU, ABTOL
       REAL, DIMENSION(:) :: W, WORK
       REAL, DIMENSION(:,:) :: A, Q, Z




   C INTERFACE
       #include <sunperf.h>

       void ssbevx(char jobz, char range, char uplo, int n, int kd, float  *a,
                 int  lda,  float *q, int ldq, float vl, float vu, int il, int
                 iu, float abtol, int *nfound, float *w, float  *z,  int  ldz,
                 int *ifail, int *info);

       void ssbevx_64(char jobz, char range, char uplo, long n, long kd, float
                 *a, long lda, float *q, long ldq, float vl,  float  vu,  long
                 il,  long  iu, float abtol, long *nfound, float *w, float *z,
                 long ldz, long *ifail, long *info);



PURPOSE
       ssbevx computes selected eigenvalues and, optionally, eigenvectors of a
       real  symmetric  band  matrix  A.   Eigenvalues and eigenvectors can be
       selected by specifying either a range of values or a range  of  indices
       for the desired eigenvalues.


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


       RANGE (input)
                 = 'A': all eigenvalues will be found;
                 = 'V': all eigenvalues in the half-open interval (VL,VU] will
                 be found; = 'I': the IL-th through IU-th eigenvalues will  be
                 found.


       UPLO (input)
                 = 'U':  Upper triangle of A is stored;
                 = 'L':  Lower triangle of A is stored.


       N (input) The order of the matrix A.  N >= 0.


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


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

                 On  exit,  A  is  overwritten  by values generated during the
                 reduction to tridiagonal form.  If  UPLO  =  'U',  the  first
                 superdiagonal  and  the  diagonal of the tridiagonal matrix T
                 are returned in rows KD and KD+1 of A, and if UPLO = 'L', the
                 diagonal and first subdiagonal of T are returned in the first
                 two rows of A.


       LDA (input)
                 The leading dimension of the array A.  LDA >= KD + 1.


       Q (output) REAL array, dimension (LDQ, N)
                 If JOBZ = 'V', the  N-by-N  orthogonal  matrix  used  in  the
                 reduction to tridiagonal form.  If JOBZ = 'N', the array Q is
                 not referenced.


       LDQ (input)
                 The leading dimension of the array Q.  If JOBZ  =  'V',  then
                 LDQ >= max(1,N).


       VL (input)
                 If  RANGE='V',  the lower and upper bounds of the interval to
                 be searched for eigenvalues. VL  <  VU.   Not  referenced  if
                 RANGE = 'A' or 'I'.


       VU (input)
                 See the description of VL.


       IL (input)
                 If  RANGE='I', the indices (in ascending order) of the small-
                 est and largest eigenvalues to be returned.  1 <= IL <= IU <=
                 N,  if  N > 0; IL = 1 and IU = 0 if N = 0.  Not referenced if
                 RANGE = 'A' or 'V'.


       IU (input)
                 See the description of IL.


       ABTOL (input)
                 The absolute error tolerance for the eigenvalues.  An approx-
                 imate  eigenvalue  is accepted as converged when it is deter-
                 mined to lie in an interval [a,b] of width less than or equal
                 to

                 ABTOL + EPS *   max( |a|,|b| ) ,

                 where EPS is the machine precision.  If ABTOL is less than or
                 equal to zero, then  EPS*|T|  will  be  used  in  its  place,
                 where |T| is the 1-norm of the tridiagonal matrix obtained by
                 reducing A to tridiagonal form.

                 Eigenvalues will be computed most accurately  when  ABTOL  is
                 set to twice the underflow threshold 2*SLAMCH('S'), not zero.
                 If this routine returns with  INFO>0,  indicating  that  some
                 eigenvectors   did   not   converge,  try  setting  ABTOL  to
                 2*SLAMCH('S').

                 See "Computing Small Singular Values of  Bidiagonal  Matrices
                 with Guaranteed High Relative Accuracy," by Demmel and Kahan,
                 LAPACK Working Note #3.


       NFOUND (output)
                 The total number of eigenvalues found.  0 <= NFOUND <= N.  If
                 RANGE  =  'A',  NFOUND  = N, and if RANGE = 'I', NFOUND = IU-
                 IL+1.


       W (output)  REAL array, dimension (N)
                 The first NFOUND elements contain the selected eigenvalues in
                 ascending order.


       Z (output) REAL array, dimension (LDZ, max(1,M))
                 If  JOBZ = 'V', then if INFO = 0, the first NFOUND columns of
                 Z contain the orthonormal eigenvectors of the matrix A corre-
                 sponding to the selected eigenvalues, with the i-th column of
                 Z holding the eigenvector associated with W(i).  If an eigen-
                 vector  fails to converge, then that column of Z contains the
                 latest approximation to the eigenvector, and the index of the
                 eigenvector  is  returned in IFAIL.  If JOBZ = 'N', then Z is
                 not referenced.  Note: the user must  ensure  that  at  least
                 max(1,NFOUND) columns are supplied in the array Z; if RANGE =
                 'V', the exact value of NFOUND is not known in advance and an
                 upper bound must be used.


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


       WORK (workspace) REAL array, dimension (7*N)


       IWORK2 (workspace) INTEGER array, dimension (5*N)


       IFAIL (output) INTEGER array, dimension (N)
                 If JOBZ = 'V', then if INFO = 0, the first NFOUND elements of
                 IFAIL are zero.  If INFO > 0, then IFAIL contains the indices
                 of the eigenvectors that failed to converge.  If JOBZ =  'N',
                 then IFAIL is not referenced.


       INFO (output)
                 = 0:  successful exit.
                 < 0:  if INFO = -i, the i-th argument had an illegal value.
                 >  0:   if  INFO = i, then i eigenvectors failed to converge.
                 Their indices are stored in array IFAIL.




                                  7 Nov 2015                        ssbevx(3P)