dgsev dgsevs dgsgv dgsgvs dnaupd dneupd dsaupd dseupd dssev dssevs dssgv dssgvs

dgsgv() void dgsgv ( char  jobz, char  uplo2, int  n, const double  val[], const int  ptr[], const int  ind[], int  base, const double  val2[], const int  ptr2[], const int  ind2[], int  base2, int  format, double  dr[], double  di[], int  ldz, double  z[], const char *  which, int  nev, double  tol, double  resid[], int  ncv, int  ldv, double  v[], int  maxiter, double  workd[], double  workl[], int  lworkl, double  workev[], int  iwork[], int *  info  ) Generalized eigenvalue problem of a general sparse matrix (simple 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 general sparse matrix and B is a symmetric 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 sparse matrix B is stored in CSC or CSR format. The generalized eigenvalue problem is solved by using arpack routines dnaupd and dneupd (inverse mode (Mode 2)). 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. [out] dr[] Array dr[ldr] (ldr >= nev + 1) Contains the real part of the Ritz value approximations to the eigenvalues of A*z = λ*B*z. [out] di[] Array di[ldi] (ldi >= nev + 1) Contains the imaginary part of the Ritz value approximations to the eigenvalues of A*z = λ*B*z associated with dr[]. [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 = "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 - 1) [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 + 1 < 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 + 6*ncv) [out] workev[] Array workev[lworkev] (lworkev >= 3*ncv) Double 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: dnaupd did not find any eigenvalues to sufficient accuracy. = 15 to 19: Internal code error.