D ddratio L m_D m_L m_max_system_size m_prefix m_rhs m_U m_work norm1 prefix reset RHS save_matrix save_system save_system_with_solution save_vector solve solve TridiagonalSystem U

ddratio() double pism::TridiagonalSystem::ddratio ( unsigned int  system_size ) const Compute diagonal-dominance ratio. If this is less than one then the matrix is strictly diagonally-dominant. Let \(A = (a_{ij})\) be the tridiagonal matrix described by L, D, U for row indices 0 through n. The computed ratio is \[ \max_{j=1, \dots, n} \frac{|a_{j, j-1}|+|a_{j, j+1}|}{|a_{jj}|}, \] where \(a_{1, 0}\) and \(a_{n, n+1}\) are interpreted as zero. If this is smaller than one then it is a theorem that the tridiagonal solve will succeed. We return -1.0 if the absolute value of any diagonal element is less than 1e-12 of the 1-norm of the matrix. Definition at line 102 of file ColumnSystem.cc. References pism::k, m_D, m_L, m_max_system_size, m_U, pism::array::max(), and norm1(). Referenced by pism::columnSystemCtx::reportColumnZeroPivotErrorMFile(), and save_system_with_solution().