zhpevd (l)  Linux Manuals
zhpevd: computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
NAME
ZHPEVD  computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storageSYNOPSIS
 SUBROUTINE ZHPEVD(
 JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
 CHARACTER JOBZ, UPLO
 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
 INTEGER IWORK( * )
 DOUBLE PRECISION RWORK( * ), W( * )
 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
PURPOSE
ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. 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.
 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
 On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The jth column of A is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j1)*(2*nj)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = aqUaq, the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = aqLaq, the diagonal and first subdiagonal of T overwrite the corresponding elements of A.
 W (output) DOUBLE PRECISION array, dimension (N)
 If INFO = 0, the eigenvalues in ascending order.
 Z (output) COMPLEX*16 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) COMPLEX*16 array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the required LWORK.
 LWORK (input) INTEGER
 The dimension of array WORK. If N <= 1, LWORK must be at least 1. If JOBZ = aqNaq and N > 1, LWORK must be at least N. If JOBZ = aqVaq and N > 1, LWORK must be at least 2*N. If LWORK = 1, then a workspace query is assumed; the routine only calculates the required 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.
 RWORK (workspace/output) DOUBLE PRECISION array,
 dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
 LRWORK (input) INTEGER
 The dimension of array RWORK. If N <= 1, LRWORK must be at least 1. If JOBZ = aqNaq and N > 1, LRWORK must be at least N. If JOBZ = aqVaq 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 required 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.
 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
 LIWORK (input) INTEGER
 The dimension of array IWORK. If JOBZ = aqNaq or N <= 1, LIWORK must be at least 1. If JOBZ = aqVaq 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 required 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.
 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.