zhbev zhbevd zhbevx zheev zheevd zheevr zheevx zhpev zhpevd zhpevx

zhpevd() void zhpevd ( char  jobz, char  uplo, int  n, doublecomplex  ap[], double  w[], int  ldz, doublecomplex  z[], doublecomplex  work[], int  lwork, double  rwork[], int  lrwork, int  iwork[], int  liwork, int *  info  ) (Divide and conquer driver) Eigenvalues and eigenvectors of a Hermitian matrix in packed form Purpose This routine computes all the eigenvalues and, optionally, eigenvectors of a Hermitian matrix A in packed form. If only eigenvalues are desired, it uses a QL or QR method. If eigenvectors are also desired, it uses a divide and conquer algorithm. Parameters [in] jobz = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] uplo = 'U': Upper triangle of A is stored. = 'L': Lower triangle of A is stored. [in] n Order of the matrix A. (n >= 0) (If n = 0, returns without computation) [in,out] ap[] Array ap[lap] (lap >= n(n + 1)/2) [in] The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array ap as follows. uplo = 'U': ap[i + j*(j + 1)/2] = A(i, j) for 0 <= i <= j <= n - 1. uplo = 'L': ap[(i + j*(2*n - j - 1)/2] = A(i, j) for 0 <= j < = i <= n - 1. [out] 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. If uplo = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. [out] w[] Array w[lw] (lw >= n) If info = 0, the eigenvalues in ascending order. [in] ldz Leading dimension of the two dimensional array z[][]. (ldz >= 1 (jobz = 'N'), ldz >= max(1, n) (jobz = 'V')) [out] z[][] Array z[lz][ldz] (lz >= n) jobz = 'V': If info = 0, z[][] contains the orthonormal eigenvectors of the matrix A, with the i-th row of z[][] holding the eigenvector associated with w[i]. jobz = 'N': z[][] is not referenced. [out] work[] Array work[lwork] Complex work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The size of work[]. (lrwork >= 1 (if n <= 1), n (if jobz = 'N'), 2*n (if jobz = 'V')) If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal sizes of the work[], rwork[] and iwork[] arrays, and returns these values in work[0], rwork[0] and iwork[0]. [out] rwork[] Array rwork[lrwork] Work array. On exit, if info = 0, rwork[0] returns the optimal lwork. [in] lrwork The size of rwork[]. (lrwork >= 1 (if n <= 1), n (if jobz = 'N'), 2*n^2 + 5*n + 1 (if jobz = 'V')) If lrwork = -1, then a workspace query is assumed. The routine only calculates the optimal sizes of the work[], rwork[] and iwork[] arrays, and returns these values in work[0], rwork[0] and iwork[0]. [out] iwork[] Array iwork[liwork] Integer work array. On exit, if info = 0, iwork[0] returns the optimal liwork. [in] liwork The size of iwork[]. (liwork >= 1 (if n <= 1), 1 (if jobz = 'N'), 5*n + 3 (if jobz = 'V')) If liwork = -1, then a workspace query is assumed. The routine only calculates the optimal sizes of the work[], rwork[] and iwork[] arrays, and returns these values in work[0], rwork[0] and iwork[0]. [out] info = 0: Successful exit = -1: The argument jobz had an illegal value (jobz != 'V' nor 'N') = -2: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -3: The argument n had an illegal value (n < 0) = -6: The argument ldz had an illegal value (ldz too small) = -9: The argument lwork had an illegal value (lwork too small) = -11: The argument lrwork had an illegal value (lrwork too small) = -13: The argument liwork had an illegal value (liwork too small) = i > 0: The algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero Reference LAPACK