dsbgv.f - Man Page

subroutine dsbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info)
DSBGV

DSBGV  

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.

Parameters

JOBZ

          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored.

N

          N is INTEGER
          The order of the matrices A and B.  N >= 0.

KA

          KA is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'. KA >= 0.

KB

          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'. KB >= 0.

AB

          AB is DOUBLE PRECISION array, dimension (LDAB, N)
          On entry, the upper or lower triangle of the symmetric 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

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KA+1.

BB

          BB is DOUBLE PRECISION array, dimension (LDBB, N)
          On entry, the upper or lower triangle of the symmetric 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 factorization
          B = S**T*S, as returned by DPBSTF.

LDBB

          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.

W

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

Z

          Z is 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

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= N.

WORK

          WORK is DOUBLE PRECISION array, dimension (3*N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 175 of file dsbgv.f.