LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  zhbevd (JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) 
ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 
subroutine zhbevd  (  character  JOBZ, 
character  UPLO,  
integer  N,  
integer  KD,  
complex*16, dimension( ldab, * )  AB,  
integer  LDAB,  
double precision, dimension( * )  W,  
complex*16, dimension( ldz, * )  Z,  
integer  LDZ,  
complex*16, dimension( * )  WORK,  
integer  LWORK,  
double precision, dimension( * )  RWORK,  
integer  LRWORK,  
integer, dimension( * )  IWORK,  
integer  LIWORK,  
integer  INFO  
) 
ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Download ZHBEVD + dependencies [TGZ] [ZIP] [TXT]ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian 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.
[in]  JOBZ  JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. 
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  KD  KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. 
[in,out]  AB  AB is COMPLEX*16 array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian 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 = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = 'L', 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 = '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. 
[in]  LDAB  LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1. 
[out]  W  W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[out]  Z  Z is COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'V', 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 = 'N', then Z is not referenced. 
[in]  LDZ  LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). 
[out]  WORK  WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  LWORK  LWORK is INTEGER The dimension of the array WORK. If N <= 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. 
[out]  RWORK  RWORK is DOUBLE PRECISION array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. 
[in]  LRWORK  LRWORK is INTEGER The dimension of array RWORK. If N <= 1, LRWORK must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2. If LRWORK = 1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. 
[out]  IWORK  IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 
[in]  LIWORK  LIWORK is INTEGER The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, 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, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. 
[out]  INFO  INFO is 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. 
Definition at line 215 of file zhbevd.f.