zgsev zgsevs zgsgv zgsgvs znaupd zneupd

zgsgvs() void zgsgvs ( char  jobz, char  uplo2, int  n, const doublecomplex  val[], const int  ptr[], const int  ind[], int  base, const doublecomplex  val2[], const int  ptr2[], const int  ind2[], int  base2, 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  ) Generalized eigenvalue problem of a complex sparse matrix (shift and invert mode) (driver) Purpose This routine computes the eigenvalues, and optionally, the eigenvectors of a generalized eigenproblem, of the form Ax = λBx by Implicitly restarted Arnoldi method (IRAM). Here A is a complex general sparse matrix and B is an Hermitian positive definite sparse matrix. It is assumed that the sparse matrix A is stored in CSC or CSR format, and the upper or lower triangular part or both (whole matrix) of the Hermitian sparse matrix B is stored in CSC or CSR format. The generalized eigenvalue problem is solved by using arpack routines dnaupd and dneupd (shift and invert mode (Mode 3)). In shift and invert mode, the eigenvalues closest to σ (shift) specified by the user can be obtained. Let's consider the other eigenvalue problem OPx = νMx where OP = (A - σ*M)^(-1)*M. M = B 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] uplo2 Specifies whether the upper or lower triangular part of the matrix B is stored. = 'U': Upper triangular part is stored. = 'L': Lower triangular part is stored. = 'B': Whole matrix is stored (both upper and lower parts are stored). The other triangular elements (not including diagonal elements) are ignored. [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 matrix A (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 matrix A. [in] ind[] Array ind[lind] (lind >= nnz) Row indices (if CSC) or column indices (if CSR) of matrix A (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] val2[] Array val2[lval2] (lval2 >= nnz2) Values of nonzero elements of matrix B (where nnz2 is the number of nonzero elements). [in] ptr2[] Array ptr2[lptr2] (lptr2 >= n + 1) Column pointers (if CSC) or row pointers (if CSR) of matrix B. [in] ind2[] Array ind2[lind2] (lind2 >= nnz2) Row indices (if CSC) or column indices (if CSR) of matrix B (where nnz2 is the number of nonzero elements). [in] base2 Indexing of ptr2[] and ind2[]. = 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 of matrix A and B. = 0: CSR format. = 1: CSC format. [in] sigma Shift σ in shift and invert mode (OP = (A - σ*M)^(-1)*M, M = B). [out] d[] Array d[ld] (ld >= nev) Contains the Ritz value approximations to the eigenvalues of A*z = λ*B*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*B*z corresponding to the Ritz value approximations. If jobz = 'N' then z[] is not referenced. [in] which Specifies which eigenvalues are found. This is applied to the eigenvalue ν of the operator OP = (A - σ*M)^(-1)*M (however λ is returned in d). Generally, the closest eigenvalue λ to σ can be obtained by specifying "LM". = "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 >= 3*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. = 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 a 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.