dsbevd (l)  Linux Manuals
dsbevd: computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
NAME
DSBEVD  computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix ASYNOPSIS
 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 XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
ARGUMENTS
 JOBZ (input) CHARACTER*1

= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.  UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, or the number of subdiagonals if UPLO = aqLaq. 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 jth column of A is stored in the jth column of the array AB as follows: if UPLO = aqUaq, AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = aqLaq, AB(1+ij,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 = aqUaq, the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = aqLaq, 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 = aqVaq, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the ith column of Z holding the eigenvector associated with W(i). If JOBZ = aqNaq, then Z is not referenced.
 LDZ (input) INTEGER
 The leading dimension of the array Z. LDZ >= 1, and if JOBZ = aqVaq, LDZ >= max(1,N).
 WORK (workspace/output) DOUBLE PRECISION array,
 dimension (LWORK) On exit, if INFO = 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 = aqNaq and N > 2, LWORK must be at least 2*N. If JOBZ = aqVaq 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 sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
 LIWORK (input) INTEGER
 The dimension of the array LIWORK. If JOBZ = aqNaq or N <= 1, LIWORK must be at least 1. If JOBZ = aqVaq 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 sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i offdiagonal elements of an intermediate tridiagonal form did not converge to zero.