dsbevd(3F)
DSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
As shipped in IRIX 6.5.15. Unchanged since IRIX 6.5.
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, * ) 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.