zhbev zhbevd zhbevx zheev zheevd zheevr zheevx zhpev zhpevd zhpevx

zhbevx() void zhbevx ( char  jobz, char  range, char  uplo, int  n, int  kd, int  ldab, doublecomplex  ab[], int  ldq, doublecomplex  q[], double  vl, double  vu, int  il, int  iu, double  abstol, int *  m, double  w[], int  ldz, doublecomplex  z[], doublecomplex  work[], double  rwork[], int  iwork[], int  ifail[], int *  info  ) (Expert driver) Eigenvalues and eigenvectors of a Hermitian band matrix Purpose This routine computes all or selected eigenvalues and, optionally, eigenvectors of a Hermitian band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. If all eigenvalues and eigenvectors are desired, it uses a QL or QR method. If selected eigenvalues and eigenvectors are desired, it uses a bisection and inverse iteration method. Parameters [in] jobz = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] range = 'A': All eigenvalues will be found. = 'V': All eigenvalues in the half-open interval (vl, vu] will be found. = 'I': The il-th through iu-th eigenvalues will be found. [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] kd Number of super-diagonals of the matrix A if uplo = 'U' or number of sub-diagonals if uplo = 'L'. (kd >= 0) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= kd + 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 kd+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][kd + i - j] = A(i, j) for max(0, j - kd - 1) <= i <= j <= n - 1. uplo = 'L': ab[j][i - j] = A(i, j) for 0 <= j <= i <= min(n - 1, j + kd - 1). [out] ab[][] is overwritten by values generated during the reduction to tridiagonal form. [in] ldq Leading dimension of the two dimensional array q[][]. (ldq >= max(1, n) if jobz = 'V')) [out] q[][] Array q[lq][ldq] (lq >= n) jobz = 'V': n x n unitary matrix used in the reduction to tridiagonal form. jobz = 'N': Array q[] is not referenced. [in] vl range = 'V': The lower bound of the interval to be searched for eigenvalues. (vl < vu) range = 'A' or 'I': Not referenced. [in] vu range = 'V': The upper bound of the interval to be searched for eigenvalues. (vl < vu) range = 'A' or 'I': Not referenced. [in] il range = 'I': The index of the smallest eigenvalue to be returned. (1 <= il <= iu <= n, if n > 0; il = 1 and iu = 0 if n = 0) range = 'A' or 'V': Not referenced. [in] iu range = 'I': The index of the largest eigenvalues to be returned. (1 <= il <= iu <= n, if n > 0; il = 1 and iu = 0 if n = 0) range = 'A' or 'V': Not referenced. [in] abstol The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a, b] of width less than or equal to abstol + eps * max(|a|, |b|), where eps is the machine precision. If abstol is less than or equal to zero, then eps*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when abstol is set to twice the underflow threshold 2*dlamch('S'), not zero. If this routine returns with info > 0, indicating that some eigenvectors did not converge, try setting abstol to 2*dlamch('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. [out] m The total number of eigenvalues found. (0 <= m <= n) If range = 'A', m = n, and if range = 'I', m = iu - il + 1. [out] w[] Array w[lw] (lw >= n) The first m elements contain the selected 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 >= max(1, m)) jobz = 'V': If info = 0, the first m columns of z[][] contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of z[][] holding the eigenvector associated with w[i]. If an eigenvector fails to converge, then that column of z[][] contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in ifail[]. jobz = 'N': z[][] is not referenced. Note: The user must ensure that at least max(1,m) columns are supplied in the array z[][]; if range = 'V', the exact value of m is not known in advance and an upper bound must be used. [out] work[] Array work[lwork] (lwork >= n) Work array. [out] rwork[] Array rwork[lrwork] (lrwork >= 7*n) Work array. [out] iwork[] Array iwork[liwork] (liwork >= 5*n) Work array. [out] ifail[] Array ifail[lifail] (lifail >= n) jobz = 'V': If info = 0, the first m elements of ifail[] are zero. If info > 0, then ifail[] contains the indices of the eigenvectors that failed to converge. jobz = 'N': ifail[] is not referenced. [out] info = 0: Successful exit = -1: The argument jobz had an illegal value (jobz != 'V' nor 'N') = -2: The argument range had an illegal value (range != 'A', 'V' nor 'I') = -3: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -4: The argument n had an illegal value (n < 0) = -5: The argument kd had an illegal value (kd < 0) = -6: The argument ldab had an illegal value (ldab < kd + 1) = -8: The argument ldq had an illegal value (ldq < max(1, n)) = -11: The argument vu had an illegal value (vu <= vl) = -12: The argument il had an illegal value (il < 1 or il > n) = -13: The argument iu had an illegal value (iu < min(n, il) or iu > n) = -17: The argument ldz had an illegal value (ldz too small) = i > 0: i eigenvectors failed to converge. Their indices are stored in array ifail[] Reference LAPACK