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zhbgvd() void zhbgvd ( char  jobz, char  uplo, int  n, int  ka, int  kb, int  ldab, doublecomplex  ab[], int  ldbb, doublecomplex  bb[], double  w[], int  ldz, doublecomplex  z[], doublecomplex  work[], int  lwork, double  rwork[], int  lrwork, int  iwork[], int  liwork, int *  info  ) (Divide and conquer driver) Generalized eigenvalue problem of Hermitian band matrices Purpose This routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x = lambda*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. Parameters [in] jobz = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] uplo = 'U': Upper triangles of A and B are stored. = 'L': Lower triangles of A and B are stored. [in] n Order of the matrices A and B. (n >= 0) (If n = 0, returns without computation) [in] ka Number of super-diagonals of the matrix A if uplo = 'U' or the number of sub-diagonals if uplo = 'L'. (ka >= 0) [in] kb Number of super-diagonals of the matrix B if uplo = 'U' or the number of sub-diagonals if uplo = 'L'. (kb >= 0) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= ka + 1) [in,out] ab[][] Array ab[lab][ldab] (lab >= n) [in] The upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 columns of the array. The j-th column of A is stored in the j-th row of the array ab as follows. uplo = 'U': ab[j][ka + i - j] = Aij for max(0, j - ka - 1) <= i <= j <= n - 1. uplo = 'L': ab[j][i - j] = Aij for 0 <= j <= i <= min(n - 1, j + ka - 1). [out] The contents of ab[][] are destroyed. [in] ldbb Leading dimension of the two dimensional array bb[][]. (ldbb >= kb + 1) [in,out] bb[][] Array bb[lbb][ldbb] (lbb >= n) [in] The upper or lower triangle of the Hermitian positive definite band matrix B, stored in the first kb+1 columns of the array. The j-th column of B is stored in the j-th row of the array bb as follows. uplo = 'U': bb[j][kb + i - j] = Bij for max(0, j - kb - 1) <= i <= j <= n - 1. uplo = 'L': bb[j][i - j] = Bij for 0 <= j <= i <= min(n - 1, j + kb - 1). [out] The factor S from the split Cholesky factorization B = S^H*S, as returned by zpbstf. [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 if jobz = 'N', ldz >= max(1, n) if jobz = 'V') [out] z[][] Array z[lz][ldz] (lz >= n) jobz = 'V': If info = 0, z[][] contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with w[i]. The eigenvectors are normalized so that Z^H*B*Z = 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[]. (lwork >= 1 (if n <= 1), n (if jobz = 'N'), 2*n^2 (if jobz = 'V')) If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size 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 size 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 size 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) = -4: The argument ka had an illegal value (ka < 0) = -5: The argument kb had an illegal value (kb < 0 or kb > ka) = -6: The argument ldab had an illegal value (ldab < ka + 1) = -8: The argument ldbb had an illegal value (ldbb < kb + 1) = -11: The argument ldz had an illegal value (ldz too small) = -14: The argument lwork had an illegal value (lwork too small) = -16: The argument lrwork had an illegal value (lrwork too small) = -18: The argument liwork had an illegal value (liwork too small) = i (0 < i <= n): The algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. = i (i > n): zpbstf returned info = i-n. B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Reference LAPACK