csc_ilu csc_ilu0 csc_ilu_solve csc_ssor_solve csr_ilu csr_ilu0 csr_ilu_solve csr_ssor_solve csx_ds csx_ds_solve csx_ssor

csc_ilu() void csc_ilu ( int  n, const double  val[], const int  colptr[], const int  rowind[], int  base, int  p, int  nnz2, double  val2[], int  colptr2[], int  rowind2[], int  base2, double  d[], double  work[], int  iwork[], int *  info  ) Incomplete LU decomposition with level (ILU(p)) (CSC) Purpose This routine computes the incomplete LU decomposition of the coefficient matrix A of the sparse linear equations. A = L * U + R where R is the difference from the complete LU decomposition. Assuming that R is small, the following preconditioner matrix is obtained by solving the equations using this decomposition. M = L * U In order to suppress fill-ins, new non-zero elements generated during decomposition with level values larger than the specified value p are dropped. This is called as ILU(p). Level values are initialized as follows. lev(a(i,j)) = 0 (if a(i,j) != 0 or i = j), = ∞ (if a(i,j) = 0) In the elimination process of LU decomposition, the operation a(i,j) = a(i,j) - a(i,k)*a(k,j) is required. At the time, the level value of a(i,j) is updated as follows. lev(a(i,j)) = min{ lev(a(i,j)), lev(a(i,k)) + lev(a(k,j)) + 1 } Due to this algorithm, the level of the position of the non-zero element of A before decomposition remains 0 until the last. When decomposition is completed, elements with level values greater than p are dropped. This routine outputs the lower triangular matrix L and the upper triangular matrix U in val2[], rowind2[] and colptr2[]. The diagonal elements of U are copied to d[]. val2[], rowind2[], colptr2[] and d[] will be used by csc_ilu_solve(). Parameters [in] n Dimension of matrix A. (n >= 0) (If n = 0, returns without computation) [in] val[] Array val[lval] (lval >= nnz) (nnz is number of non-zero elements of matrix A) Values of non-zero elements of matrix A. [in] colptr[] Array colptr[lcolptr] (lcolptr >= n + 1) Column pointers of matrix A. [in] rowind[] Array rowind[lrowind] (lrowind >= nnz) Row indices of matrix A. [in] base Indexing of colptr[] and rowind[]. = 0: Zero-based (C style) indexing: Starting index is 0. = 1: One-based (Fortran style) indexing: Starting index is 1. [in] p The value of level p of ILU(p) algorithm. (p >= 0) Note: it is possible to set p = 0. However, it is recommended to use csc_ilu0() since it is faster. [in] nnz2 Maximum number of non-zero elements of matrix L*U. If the number of non-zero elements exceeds this during the factorization, the routine will terminate with error (info = -7). [out] val2[] Array val2[lval2] (lval2 >= nnz2) Values of non-zero elements of the lower triangular matrix L and the upper triangular matrix U. [out] colptr2[] Array colptr2[lcolptr2] (lcolptr2 >= n + 1) Column pointers of matrix L*U. [out] rowind2[] Array rowind2[lrowind2] (lrowind2 >= nnz2) Row indices of matrix L*U. (nnz is number of non-zero elements) [in] base2 Indexing of colptr2[] and rowind2[]. = 0: Zero-based (C style) indexing: Starting index is 0. = 1: One-based (Fortran style) indexing: Starting index is 1. [out] d[] Array d[ld] (ld >= n) The diagonal elements of upper triangular matrix U. [out] work[] Array work[lwork] (lwork >= n) Work array. [out] iwork[] Array iwork[liwork] (liwork >= nnz2 + 2*n) Integer work array. [out] info = 0: Successful exit. = i < 0: The (-i)-th argument is invalid. = j > 0: Matrix is singular (j-th diagonal element is zero).