• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

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 * 1 JOBZ, UPLO
  INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
  DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)

  SUBROUTINE DSBGV_64( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, 
 *      Z, LDZ, WORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
  DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE SBGV( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W, 
 *       Z, [LDZ], [WORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: AB, BB, Z

  SUBROUTINE SBGV_64( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], 
 *       W, Z, [LDZ], [WORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: AB, BB, Z

C INTERFACE

#include <sunperf.h>

void dsbgv(char jobz, char uplo, int n, int ka, int kb, double *ab, int ldab, double *bb, int ldbb, double *w, double *z, int ldz, int *info);

void dsbgv_64(char jobz, char uplo, long n, long ka, long kb, double *ab, long ldab, double *bb, long ldbb, double *w, double *z, long ldz, long *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)
  

   = '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.

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

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

• AB (input/output)
  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 (input)
  The leading dimension of the array AB. LDAB > = KA+1.

• BB (input/output)
  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 SPBSTF.

• LDBB (input)
  The leading dimension of the array BB. LDBB > = KB+1.

• W (output)
  If INFO = 0, the eigenvalues in ascending order.

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

• WORK (workspace)
  dimension(3*N)

• INFO (output)
  

   = 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 SPBSTF

  returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.