zgsev zgsevs zgsgv zgsgvs znaupd zneupd

zgsevs() void zgsevs ( char  jobz, int  n, const doublecomplex  val[], const int  ptr[], const int  ind[], int  base, int  format, doublecomplex  sigma, doublecomplex  d[], int  ldz, doublecomplex  z[], const char *  which, int  nev, double  tol, doublecomplex  resid[], int  ncv, int  ldv, doublecomplex  v[], int  maxiter, doublecomplex  workd[], doublecomplex  workl[], int  lworkl, doublecomplex  workev[], double  rwork[], int  iwork[], int *  info  ) Eigenvalues and eigenvectors of a complex sparse matrix (shift and invert mode) (driver) Purpose The eigenvalues and eigenvectors of a complex sparse matrix are computed by Implicitly restarted Arnoldi method (IRAM). The spaese matrix is stored in CSC or CSR format. arpack routines znaupd and zneupd (shift and invert mode (Mode 3)) are used to find eigenvalues. In shift and invert mode, the eigenvalues closest to σ (shift) specified by the user can be obtained. Assume that the original eigenvalue problem is as below. A*x = λ*x Let's consider the other eigenvalue problem OP*x = ν*x where OP = (A - σ*I)^(-1) and ν is the eigenvalue of this problem. If the eigenvalue ν is found, the eigenvalue λ of the original problem can be computed by ν = 1/(λ - σ). Therefore, the eigenvalue λ closest to σ can be computed if the largest ν is obtained. Parameters [in] jobz = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] n Number of rows and columns of the matrix. (n >= 0) (If n = 0, returns without computation) [in] val[] Array val[lval] (lval >= nnz) Values of nonzero elements of input matrix (where nnz is the number of nonzero elements). [in] ptr[] Array ptr[lptr] (lptr >= n + 1) Column pointers (if CSC) or row pointers (if CSR) of input matrix. [in] ind[] Array ind[lind] (lind >= nnz) Row indices (if CSC) or column indices (if CSR) of input matrix (where nnz is the number of nonzero elements). [in] base Indexing of ptr[] and ind[]. = 0: Zero-based (C style) indexing: Starting index is 0. = 1: One-based (Fortran style) indexing: Starting index is 1. [in] format Sparse matrix format. = 0: CSR format. = 1: CSC format. [in] sigma Shift σ in shift and invert mode (OP = (A - σ*I)^(-1), B = I). [out] d[] Array d[ld] (ld >= nev) Contains the Ritz value approximations to the eigenvalues of A*z = λ*z. [in] ldz Leading dimension of the array z. (ldz >= n if Ritz vectors are desired, ldz >= 1 otherwise) [out] z[] Array z[ldz * lz] (lz >= nev) Contains the Ritz vectors (approximations to the eigenvectors) of the eigensystem A*z = λ*z corresponding to the Ritz value approximations. If jobz = 'N' then z[] is not referenced. [in] which The eigenvalues of OP = (A - σ*I)^(-1) are found as follows. = "LM": Compute the nev eigenvalues of largest magnitude. = "SM": Compute the nev eigenvalues of smallest magnitude. = "LR": Compute the nev eigenvalues of largest real part. = "SR": Compute the nev eigenvalues of smallest real part. = "LI": Compute the nev eigenvalues of largest imaginary part. = "SI": Compute the nev eigenvalues of smallest imaginary part. [in] nev Number of eigenvalues to be computed. (0 < nev < n) [in] tol Stopping criterion: the acceptable relative accuracy of the Ritz value. If tol <= 0, machine precision is assumed. [out] resid[] Array resid[lresid] (lresid >= n) The residual vector. [in] ncv Number of columns of the matrix V. (nev < ncv <= n) This will indicate how many Arnoldi vectors are generated at each iteration (ncv >= 2*nev is recommended). [in] ldv Leading dimension of the array v. (ldv >= n) [out] v[] Array v[ldv * lv] (lv >= ncv) Matrix V containing ncv Arnoldi basis vectors. [in] maxiter Maximum number of Arnoldi update iterations allowed. [out] workd[] Array workd[lworkd] (lworkd >= 3*n) Distributed work array used for reverse communication. [out] workl[] Array workl[lworkl] Local work array. [in] lworkl Size of array workl[]. (lworkl >= 3*ncv^2 + 5*ncv) [out] workev[] Array workev[lworkev] (lworkev >= 2*ncv) Double work array. [out] rwork[] Array rwork[lrwork] (lrwork >= ncv) Private (replicated) work array. [out] iwork[] Array iwork[liwork] (liwork >= max(ncv, 3)) Integer work array. The following values are returned in iwork[0], ..., iwork[2]. iwork[0]: Number of Arnoldi update iterations taken. iwork[1]: Number of Ritz values that satisfy the convergence criterion (nconv). iwork[2]: Total number of OP*x operations (numop). [out] info Return code. = 0: Successful exit. < 0: The (-info)-th argument is invalid. = 1: Maximum number of iterations taken. iparam[4] returns the number of converged Ritz values. = 3: No shifts could be applied during a cycle of the implicitly restarted Arnoldi iteration. A possible remedy is to increase ncv relative to nev (ncv >= 2*nev is recommended). = 11: Initial residual vector is zero. = 12: Failed to build an Arnoldi factorization. = 13: Error return from LAPACK eigenvalue calculation. = 14: znaupd did not find any eigenvalues to sufficient accuracy. = 15 to 19: Internal code error.