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.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016