dgssv dgssvx

dgssv() void dgssv ( char  col_perm, double  thresh, char  sym_mode, int  n, const double  val[], const int  ptr[], const int  ind[], int  format, int  base, int  perm_c[], int  perm_r[], int  nrhs, int  ldb, double  b[], double *  rcond, int *  info  ) Solves the system of linear equations A*X = B (sparse matrix, direct method (SuperLU)) (simple driver) Purpose This routine solves the system of linear equations A*X = B, using the LU factorization, where A is a general N x N sparse matrix. It performs the following steps: If A is stored column-wise (CSC): 1.1. Permute the columns of A, forming A*Pc, where Pc is a permutation matrix. 1.2. Factor A as Pr*A*Pc = L*U with the permutation Pr determined by Gaussian elimination with partial pivoting. L is unit lower triangular with offdiagonal entries bounded by 1 in magnitude, and U is upper triangular. 1.3. Solve the system of equations A*X = B using the factored form of A. If A is stored row-wise (CSR), apply the above algorithm to the transpose of A: 2.1. Permute columns of transpose(A) (rows of A), forming transpose(A)*Pc, where Pc is a permutation matrix. 2.2. Factor A as Pr*transpose(A)*Pc = L*U with the permutation Pr determined by Gaussian elimination with partial pivoting. L is unit lower triangular with offdiagonal entries bounded by 1 in magnitude, and U is upper triangular. 2.3. Solve the system of equations A*X = B using the factored form of A. Parameters [in] col_perm Specifies the type of column ordering to reduce fill-in. = 'A': Approximate minimum degree (AMD) ordering. = 'N': Natural ordering (No ordering) (Pc = I). = 'M': Multiple minimum degree (MMD) ordering on A^T*A. = 'P': Multiple minimum degree (MMD) ordering on A^T + A. = 'U': User specified ordering. [in] thresh Specifies the threshold used for a diagonal entry to be an acceptable pivot. (0 <= thresh <= 1) [in] sym_mode Specifies whether to use symmetric mode. Symmetric mode gives preference to diagonal pivots, and uses an (A^T + A)-based column permutation algorithm. = 'N': Do not use symmetric mode. = 'S': Use symmetric mode. [in] n Dimension of the matrix A. (n >= 0) (If n = 0, returns without computation) [in] val[] Array val[lval] (lval >= nnz) Values of nonzero elements of the matrix A in CSC/CSR format (where nnz is the number of nonzero elements). [in] ptr[] Array ptr[lptr] (lptr >= n + 1) Column/row pointers of the matrix A in CSC/CSR format. [in] ind[] Array ind[lind] (lind >= nnz) Row/column indices of the matrix A in CSC/CSR format (where nnz is the number of nonzero elements). [in] format Sparse matrix format. = 0: CSR format. = 1: CSC format. [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,out] perm_c[] Array perm_c[lperm_c] (lperm_c >= n) [in] Input permutation vector if option col_perm = 'U'. Otherwise, an output argument. [out] In the case of CSC format, column permutation vector which defines the permutation matrix Pc. perm_c[i] = j means column i of A is in position j in A*Pc. Similarly, in the case of CSR, column permutation vector which describes permutation of columns of A^T (rows of A). Input permutation vector may be overwritten by the product of the input perm_c[] and a permutation that postorders the elimination tree of Pc^T*A^T*A*Pc. perm_c[] is not changed if the elimination tree is already in postorder. [out] perm_r[] Array perm_r[lperm_r] (lperm_r >= n) In the case of CSC format, row permutation vector which defines the permutation matrix Pr, and is determined by partial pivoting. perm_r[i] = j means row i of A is in position j in Pr*A. In the case of CSR format, permutation vector which determines permutation of rows of A^T (columns of A) as described above. [in] nrhs Number of right hand sides, i.e., number of columns of the matrix B. (nrhs >= 0) (If nrhs = 0, returns without computation) [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(0, n)) [in,out] b[][] Array b[lb][ldb] (lb >= nrhs) [in] Right hand side matrix B. [out] Solution matrix X. [out] rcond Estimated reciprocal of the condition number of the matrix A. [out] info = 0: Successful exit. < 0: The (-info)-th argument is invalid. = -10000: Unrecoverble error occured in SuperLU routine. = i > 0 and <= n: U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. = i > n: Memory allocation failure occurred. i - n is the number of bytes allocated. Reference SuperLU