dsbev


NAME

dsbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A


SYNOPSIS

  SUBROUTINE DSBEV( JOBZ, UPLO, N, NDIAG, A, LDA, W, Z, LDZ, WORK, 
 *      INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER N, NDIAG, LDA, LDZ, INFO
  DOUBLE PRECISION A(LDA,*), W(*), Z(LDZ,*), WORK(*)
 
  SUBROUTINE DSBEV_64( JOBZ, UPLO, N, NDIAG, A, LDA, W, Z, LDZ, WORK, 
 *      INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 N, NDIAG, LDA, LDZ, INFO
  DOUBLE PRECISION A(LDA,*), W(*), Z(LDZ,*), WORK(*)
 

F95 INTERFACE

  SUBROUTINE SBEV( JOBZ, UPLO, [N], NDIAG, A, [LDA], W, Z, [LDZ], 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: N, NDIAG, LDA, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: A, Z
 
  SUBROUTINE SBEV_64( JOBZ, UPLO, [N], NDIAG, A, [LDA], W, Z, [LDZ], 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: N, NDIAG, LDA, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: A, Z
 

C INTERFACE

#include <sunperf.h>

void dsbev(char jobz, char uplo, int n, int ndiag, double *a, int lda, double *w, double *z, int ldz, int *info);

void dsbev_64(char jobz, char uplo, long n, long ndiag, double *a, long lda, double *w, double *z, long ldz, long *info);


PURPOSE

dsbev computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A.


ARGUMENTS

* JOBZ (input)
* UPLO (input)

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

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

* A (input/output)
On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first NDIAG+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 NDIAG and NDIAG+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 >= NDIAG + 1.

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

* Z (input)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(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 >= max(1,N).

* WORK (workspace)
dimension(MAX(1,3*N-2))

* INFO (output)