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dsbgv (3)
  • >> dsbgv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dsbgv - compute all the  eigenvalues,  and  optionally,  the
         eigenvectors of a real generalized symmetric-definite banded
         eigenproblem, of the form A*x=(lambda)*B*x
    
    SYNOPSIS
         SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
                   W, Z, LDZ, WORK, INFO )
    
         CHARACTER JOBZ, UPLO
    
         INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
    
         DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ), WORK(
                   * ), Z( LDZ, * )
    
    
    
         #include <sunperf.h>
    
         void dsbgv(char jobz, char uplo, int n, int ka, int kb, dou-
                   ble  *dab,  int ldab, double *bb, int ldbb, double
                   *w, double *dz, int ldz, int *info) ;
    
    PURPOSE
         DSBGV computes all  the  eigenvalues,  and  optionally,  the
         eigenvectors of a real generalized symmetric-definite banded
         eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are
         assumed  to  be symmetric and banded, and B is also positive
         definite.
    
    
    ARGUMENTS
         JOBZ      (input) CHARACTER*1
                   = 'N':  Compute eigenvalues only;
                   = 'V':  Compute eigenvalues and eigenvectors.
    
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangles of A and B are stored;
                   = 'L':  Lower triangles of A and B are stored.
    
         N         (input) INTEGER
                   The order of the matrices A and B.  N >= 0.
    
         KA        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'. KA >= 0.
    
         KB        (input) INTEGER
                   The number of superdiagonals of the  matrix  B  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'. KB >= 0.
    
         AB        (input/output) DOUBLE PRECISION  array,  dimension
                   (LDAB, N)
                   On entry, the upper or lower triangle of the  sym-
                   metric  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) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KA+1.
    
         BB        (input/output) DOUBLE PRECISION  array,  dimension
                   (LDBB, N)
                   On entry, the upper or lower triangle of the  sym-
                   metric  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 fac-
                   torization B = S**T*S, as returned by DPBSTF.
    
         LDBB      (input) INTEGER
                   The leading dimension of the array  BB.   LDBB  >=
                   KB+1.
    
         W         (output) DOUBLE PRECISION array, dimension (N)
                   If INFO = 0, the eigenvalues 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, with the i-th column of
                   Z holding the eigenvector  associated  with  W(i).
                   The eigenvectors are normalized so that Z**T*B*Z =
                   I.  If JOBZ = 'N', then Z is not referenced.
    
         LDZ       (input) INTEGER
                   The leading dimension of the array Z.  LDZ  >=  1,
                   and if JOBZ = 'V', LDZ >= N.
    
         WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
                   (3*N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   > 0:  if INFO = i, and i is:
                   <= N:  the algorithm 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 DPBSTF
                   returned INFO = i: B  is  not  positive  definite.
                   The  factorization of B could not be completed and
                   no eigenvalues or eigenvectors were computed.
    
    
    
    


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