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

NAME

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

SYNOPSIS

  SUBROUTINE DSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, 
 *      LWORK, IWORK, LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
  INTEGER IWORK(*)
  DOUBLE PRECISION AB(LDAB,*), W(*), Z(LDZ,*), WORK(*)

  SUBROUTINE DSBEVD_64( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, 
 *      LWORK, IWORK, LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
  INTEGER*8 IWORK(*)
  DOUBLE PRECISION AB(LDAB,*), W(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE SBEVD( JOBZ, UPLO, [N], KD, AB, [LDAB], W, Z, [LDZ], 
 *       WORK, [LWORK], [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
  INTEGER, DIMENSION(:) :: IWORK
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: AB, Z

  SUBROUTINE SBEVD_64( JOBZ, UPLO, [N], KD, AB, [LDAB], W, Z, [LDZ], 
 *       WORK, [LWORK], [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: N, KD, LDAB, LDZ, LWORK, LIWORK, INFO
  INTEGER(8), DIMENSION(:) :: IWORK
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: AB, Z

C INTERFACE

#include <sunperf.h>

void dsbevd(char jobz, char uplo, int n, int kd, double *ab, int ldab, double *w, double *z, int ldz, double *work, int lwork, int *info);

void dsbevd_64(char jobz, char uplo, long n, long kd, double *ab, long ldab, double *w, double *z, long ldz, double *work, long lwork, long *info);

PURPOSE

dsbevd computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

ARGUMENTS

• JOBZ (input)
  

   = 'N':  Compute eigenvalues only;

   = 'V':  Compute eigenvalues and eigenvectors.

• UPLO (input)
  

   = 'U':  Upper triangle of A is stored;

   = 'L':  Lower triangle of A is stored.

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

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

• AB (input/output)
  On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd) < =i < =j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j < =i < =min(n,j+kd).

  On exit, AB 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 KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB.

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

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

• Z (output)
  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 (output)
  dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

• LWORK (input)
  The dimension of the array WORK. If N < = 1, LWORK must be at least 1. If JOBZ = 'N' and N > 2, LWORK must be at least 2*N. If JOBZ = 'V' and N > 2, LWORK must be at least ( 1 + 5*N + 2*N**2 ).

  If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• IWORK (workspace)
  On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

• LIWORK (input)
  The dimension of the array LIWORK. If JOBZ = 'N' or N < = 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.

  If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

   > 0:  if INFO  = i, the algorithm failed to converge; i
  off-diagonal elements of an intermediate tridiagonal
  form did not converge to zero.