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 JOBZ, UPLO

INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N

INTEGER IWORK( ∗ )

DOUBLE PRECISION AB( LDAB, ∗ ), W( ∗ ), WORK( ∗ ), Z( LDZ, ∗ )

#include <sunperf.h>

void dsbevd(char jobz, char uplo, int n, int kd, double ∗dab, int ldab, double ∗w, double ∗dz, int ldz, int ∗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) CHARACTER∗1
= ’N’:  Compute eigenvalues only;
= ’V’:  Compute eigenvalues and eigenvectors.

UPLO (input) CHARACTER∗1
= ’U’:  Upper triangle of A is stored;
= ’L’:  Lower triangle of A is stored.

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

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

AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
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) INTEGER
The leading dimension of the array AB.  LDAB >= KD + 1.

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

Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
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) INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if JOBZ = ’V’, LDZ >= max(1,N).

WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK) On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.

LWORK (input) INTEGER
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 + 4∗N + 2∗N∗lg N + 3∗N∗∗2 ), where lg( N ) = smallest integer k such that 2∗∗k >= N.

IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

LIWORK (input) INTEGER
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 2 + 5∗N.

INFO (output) INTEGER
= 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.

SunOS 5.0  —  Last change: 10 Dec 1998