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

dssevs() void dssevs ( char  jobz, char  uplo, int  n, const double  val[], const int  ptr[], const int  ind[], int  base, int  format, double  sigma, double  d[], 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, int  iwork[], int *  info  ) Eigenvalues and eigenvectors of a symmetric sparse matrix (shift and invert mode) (driver) Purpose The eigenvalues and eigenvectors of a real symmetric sparse matrix are computed by Implicitly restarted Lanczos method (IRLM). It is assumed that the upper or lower triangular part of the sparse matrix is stored in CSC or CSR format. The eigenvalue problem is solved by using arpack routines dsaupd and dseupd (shift and invert mode (Mode 3)). 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] uplo Specifies whether the upper or lower triangular part of the matrix is stored. = 'U': Upper triangular part is stored. = 'L': Lower triangular part is 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 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 σ represents the shift 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. The values are returned in ascending order. [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 Specifies which eigenvalues are found. This is applied to the eigenvalue ν of the operator OP = (A - σ*I)^(-1) (however λ is returned in d). Generally, the closest eigenvalue λ to σ can be obtained by specifying "LM". = "LA": Compute the nev largest (algebraic) eigenvalues. = "SA": Compute the nev smallest (algebraic) eigenvalues. = "LM": Compute the nev largest (in magnitude) eigenvalues. = "SM": Compute the nev smallest (in magnitude) eigenvalues. = "BE": Compute nev eigenvalues, half from each end of the spectrum. When nev is odd, compute one more from the high end than from the low end. [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 Lanczos 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 Lanczos basis vectors. [in] maxiter Maximum number of Lanczos 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 >= ncv^2 + 8*ncv) [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 Lanczos 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 Lanczos 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 Lanczos factorization. = 13: Error return from LAPACK eigenvalue calculation. = 14: dsaupd did not find any eigenvalues to sufficient accuracy. = 15 to 19: Internal code error.