
NAMEzhpevd.f SYNOPSISFunctions/Subroutinessubroutine zhpevd (JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) Function/Subroutine Documentationsubroutine zhpevd (characterJOBZ, characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 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. JOBZ
Author:
JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.N N is INTEGER The order of the matrix A. N >= 0.AP AP is 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 = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', 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 = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A.W W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.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.LDZ LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the required LWORK.LWORK LWORK is INTEGER The dimension of 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. 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 RWORK is DOUBLE PRECISION array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the required LRWORK.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 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 IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the required LIWORK.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 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 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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 201 of file zhpevd.f.
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