LMCAS::anonymous_namespace{matrix_decomposition_cholesky.cpp} 命名空间参考

函数
static bool	cholesky_decomposition_impl (const std::shared_ptr< SymbolicExpr > &A, std::shared_ptr< SymbolicExpr > &L)
Result< void >	prove_exact_spd (const std::shared_ptr< const MatrixNode > &matrix, ComputationContext &context, const std::string &operation)

函数说明

cholesky_decomposition_impl()

bool LMCAS::anonymous_namespace{matrix_decomposition_cholesky.cpp}::cholesky_decomposition_impl ( const std::shared_ptr< SymbolicExpr > & A, std::shared_ptr< SymbolicExpr > & L )

static

在文件 matrix_decomposition_cholesky.cpp 第 52 行定义.

                                    {
    auto mat = std::dynamic_pointer_cast<const MatrixNode>(LMCAS::detail::node(A));
    if (!mat || mat->rows() != mat->cols()) return false;
    size_t n = mat->rows();
    std::vector<std::vector<std::shared_ptr<SymbolicExpr>>> L_grid(n, std::vector<std::shared_ptr<SymbolicExpr>>(n, SymbolicExpr::number(0)));
    for (size_t i = 0; i < n; i++) {
        for (size_t j = 0; j <= i; j++) {
            auto sum = SymbolicExpr::number(0);
            for (size_t k = 0; k < j; k++) sum = SymbolicExpr::add(sum, SymbolicExpr::multiply(L_grid[i][k], L_grid[j][k]));
            auto a_ij = LMCAS::detail::make_expression_ptr(mat->get(i, j));
            auto diff = SymbolicExpr::add(a_ij, SymbolicExpr::multiply(SymbolicExpr::number(-1), sum));
            if (i == j) L_grid[i][j] = SymbolicExpr::sqrt(diff);
            else L_grid[i][j] = SymbolicExpr::divide(diff, L_grid[j][j]);
        }
    }
    L = SymbolicExpr::matrix(L_grid);
    return true;
}

引用了 cholesky_decomposition_impl(), LMCAS::detail::make_expression_ptr() , 以及 LMCAS::detail::node().

被这些函数引用 cholesky_decomposition_impl().

函数调用图:

这是这个函数的调用关系图:

prove_exact_spd()

Result< void > LMCAS::anonymous_namespace{matrix_decomposition_cholesky.cpp}::prove_exact_spd	(	const std::shared_ptr< const MatrixNode > &	matrix,
		ComputationContext &	context,
		const std::string &	operation )

在文件 matrix_decomposition_cholesky.cpp 第 10 行定义.

                                {
    auto values = exact_rational_matrix(matrix, context);
    if (!values) {
        return Result<void>::failure(
            CasErrc::Inconclusive,
            "Cholesky input is outside the exact rational SPD support domain",
            operation);
    }
    const size_t n = values->size();
    for (size_t row = 0; row < n; ++row) {
        for (size_t col = row + 1; col < n; ++col) {
            if ((*values)[row][col] != (*values)[col][row]) {
                return Result<void>::failure(
                    CasErrc::DomainError,
                    "Cholesky input must be symmetric",
                    operation);
            }
        }
    }
    for (size_t order = 1; order <= n; ++order) {
        std::vector<Rational> leading;
        leading.reserve(order * order);
        for (size_t row = 0; row < order; ++row) {
            for (size_t col = 0; col < order; ++col) {
                leading.push_back((*values)[row][col]);
            }
        }
        auto determinant = detail::rational_determinant_exact(
            order, std::move(leading), context, operation);
        if (!determinant) return Result<void>::failure(determinant.error());
        if (determinant.value() <= Rational(0)) {
            return Result<void>::failure(
                CasErrc::DomainError,
                "Cholesky input is not positive definite",
                operation);
        }
    }
    return Result<void>::success();
}

引用了 LMCAS::context, LMCAS::DomainError, LMCAS::detail::matrix_decomposition::exact_rational_matrix(), LMCAS::Result< T >::failure(), LMCAS::Inconclusive, LMCAS::order, prove_exact_spd(), LMCAS::detail::rational_determinant_exact() , 以及 LMCAS::Result< T >::success().

被这些函数引用 prove_exact_spd().

函数调用图:

这是这个函数的调用关系图: