ssc_ic0 ssc_ic_solve ssc_ssor_solve ssr_ic0 ssr_ic_solve ssr_ssor_solve

ssc_ic0() void ssc_ic0 ( char  uplo, int  n, const double  val[], const int  colptr[], const int  rowind[], int  base, double  val2[], int  idiag[], double  work[], int *  info  ) Incomplete Cholesky decomposition without fill-in (IC0) (symmetric positive definite matrix) (CSC) Purpose This routine computes the incomplete Cholesky decomposition, without fill-in, of the symmetric positive definite coefficient matrix of the sparse linear equations. A = L * D * L^T + R or A = U^T * D * U + R It is called that fill-in occurs when a position that is zero in coefficient matrix A but it becomes non-zero after Cholesky decomposition is performed. To avoid this, such positions in L or U in the above equation are forcibly set to zeros. R shows the differences from the complete Cholesky decomposition arising from this modification. Assuming that R is not large, it is expected that this incomplete decomposition can be used to obtain a good approximate solution of linear equations. This decomposition is used as the preconditioner matrix M. M = L * D * L^T or M = U^T * D * U This routine outputs L or U and D in val2[], and indices of diagonal elements in idiag[]. val2[] and idiag[] will be used by ssc_ic_solve(). Parameters [in] uplo Specifies whether the upper or lower triangular part of input matrix A is stored. = "U": Upper triangular part (to be factorized to U^T*D*U). = "L": Lower triangular part (to be factorized to L*D*L^T). [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. (only the diagonal and lower triangular elements are referenced) [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. [out] val2[] Array val2[lval2] (lval2 >= nnz) Values of non-zero elements of the lower triangular matrix L and the diagonal matrix D. (nnz is same with the number of non-zero elements of A. The values are stored in the same location of diagonal and lower triangular elements of A.) [out] idiag[] Array idiag[lidiag] (lidiag >= n) Indices of diagonal elements. [out] work[] Array work[lwork] (lwork >= n) Work array. (Not references when uplo = 'L'.) [out] info = 0: Successful exit. = i < 0: The (-i)-th argument is invalid. = i > 0: Matrix is singular (i-th diagonal element is zero).