Task: LU decomposition


C++: #include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <limits>
#include <numeric>
#include <sstream>
#include <vector>

template <typename scalar_type> class matrix {
public:
    matrix(size_t rows, size_t columns)
        : rows_(rows), columns_(columns), elements_(rows * columns) {}

    matrix(size_t rows, size_t columns, scalar_type value)
        : rows_(rows), columns_(columns), elements_(rows * columns, value) {}

    matrix(size_t rows, size_t columns,
        const std::initializer_list<std::initializer_list<scalar_type>>& values)
        : rows_(rows), columns_(columns), elements_(rows * columns) {
        assert(values.size() <= rows_);
        size_t i = 0;
        for (const auto& row : values) {
            assert(row.size() <= columns_);
            std::copy(begin(row), end(row), &elements_[i]);
            i += columns_;
        }
    }

    size_t rows() const { return rows_; }
    size_t columns() const { return columns_; }

    const scalar_type& operator()(size_t row, size_t column) const {
        assert(row < rows_);
        assert(column < columns_);
        return elements_[row * columns_ + column];
    }
    scalar_type& operator()(size_t row, size_t column) {
        assert(row < rows_);
        assert(column < columns_);
        return elements_[row * columns_ + column];
    }
private:
    size_t rows_;
    size_t columns_;
    std::vector<scalar_type> elements_;
};

template <typename scalar_type>
void print(std::wostream& out, const matrix<scalar_type>& a) {
    const wchar_t* box_top_left = L"\x23a1";
    const wchar_t* box_top_right = L"\x23a4";
    const wchar_t* box_left = L"\x23a2";
    const wchar_t* box_right = L"\x23a5";
    const wchar_t* box_bottom_left = L"\x23a3";
    const wchar_t* box_bottom_right = L"\x23a6";

    const int precision = 5;
    size_t rows = a.rows(), columns = a.columns();
    std::vector<size_t> width(columns);
    for (size_t column = 0; column < columns; ++column) {
        size_t max_width = 0;
        for (size_t row = 0; row < rows; ++row) {
            std::ostringstream str;
            str << std::fixed << std::setprecision(precision) << a(row, column);
            max_width = std::max(max_width, str.str().length());
        }
        width[column] = max_width;
    }
    out << std::fixed << std::setprecision(precision);
    for (size_t row = 0; row < rows; ++row) {
        const bool top(row == 0), bottom(row + 1 == rows);
        out << (top ? box_top_left : (bottom ? box_bottom_left : box_left));
        for (size_t column = 0; column < columns; ++column) {
            if (column > 0)
                out << L' ';
            out << std::setw(width[column]) << a(row, column);
        }
        out << (top ? box_top_right : (bottom ? box_bottom_right : box_right));
        out << L'\n';
    }
}


template <typename scalar_type>
auto lu_decompose(const matrix<scalar_type>& input) {
    assert(input.rows() == input.columns());
    size_t n = input.rows();
    std::vector<size_t> perm(n);
    std::iota(perm.begin(), perm.end(), 0);
    matrix<scalar_type> lower(n, n);
    matrix<scalar_type> upper(n, n);
    matrix<scalar_type> input1(input);
    for (size_t j = 0; j < n; ++j) {
        size_t max_index = j;
        scalar_type max_value = 0;
        for (size_t i = j; i < n; ++i) {
            scalar_type value = std::abs(input1(perm[i], j));
            if (value > max_value) {
                max_index = i;
                max_value = value;
            }
        }
        if (max_value <= std::numeric_limits<scalar_type>::epsilon())
            throw std::runtime_error("matrix is singular");
        if (j != max_index)
            std::swap(perm[j], perm[max_index]);
        size_t jj = perm[j];
        for (size_t i = j + 1; i < n; ++i) {
            size_t ii = perm[i];
            input1(ii, j) /= input1(jj, j);
            for (size_t k = j + 1; k < n; ++k)
                input1(ii, k) -= input1(ii, j) * input1(jj, k);
        }
    }
    
    for (size_t j = 0; j < n; ++j) {
        lower(j, j) = 1;
        for (size_t i = j + 1; i < n; ++i)
            lower(i, j) = input1(perm[i], j);
        for (size_t i = 0; i <= j; ++i)
            upper(i, j) = input1(perm[i], j);
    }
    
    matrix<scalar_type> pivot(n, n);
    for (size_t i = 0; i < n; ++i)
        pivot(i, perm[i]) = 1;

    return std::make_tuple(lower, upper, pivot);
}

template <typename scalar_type>
void show_lu_decomposition(const matrix<scalar_type>& input) {
    try {
        std::wcout << L"A\n";
        print(std::wcout, input);
        auto result(lu_decompose(input));
        std::wcout << L"\nL\n";
        print(std::wcout, std::get<0>(result));
        std::wcout << L"\nU\n";
        print(std::wcout, std::get<1>(result));
        std::wcout << L"\nP\n";
        print(std::wcout, std::get<2>(result));
    } catch (const std::exception& ex) {
        std::cerr << ex.what() << '\n';
    }
}

int main() {
    std::wcout.imbue(std::locale(""));
    std::wcout << L"Example 1:\n";
    matrix<double> matrix1(3, 3,
       {{1, 3, 5},
        {2, 4, 7},
        {1, 1, 0}});
    show_lu_decomposition(matrix1);
    std::wcout << '\n';

    std::wcout << L"Example 2:\n";
    matrix<double> matrix2(4, 4,
      {{11, 9, 24, 2},
        {1, 5, 2, 6},
        {3, 17, 18, 1},
        {2, 5, 7, 1}});
    show_lu_decomposition(matrix2);
    std::wcout << '\n';
    
    std::wcout << L"Example 3:\n";
    matrix<double> matrix3(3, 3,
      {{-5, -6, -3},
       {-1,  0, -2},
       {-3, -4, -7}});
    show_lu_decomposition(matrix3);
    std::wcout << '\n';
    
    std::wcout << L"Example 4:\n";
    matrix<double> matrix4(3, 3,
      {{1, 2, 3},
       {4, 5, 6},
       {7, 8, 9}});
    show_lu_decomposition(matrix4);

    return 0;
}




Java: import static java.util.Arrays.stream;
import java.util.Locale;
import static java.util.stream.IntStream.range;

public class Test {

    static double dotProduct(double[] a, double[] b) {
        return range(0, a.length).mapToDouble(i -> a[i] * b[i]).sum();
    }

    static double[][] matrixMul(double[][] A, double[][] B) {
        double[][] result = new double[A.length][B[0].length];
        double[] aux = new double[B.length];

        for (int j = 0; j < B[0].length; j++) {

            for (int k = 0; k < B.length; k++)
                aux[k] = B[k][j];

            for (int i = 0; i < A.length; i++)
                result[i][j] = dotProduct(A[i], aux);
        }
        return result;
    }

    static double[][] pivotize(double[][] m) {
        int n = m.length;
        double[][] id = range(0, n).mapToObj(j -> range(0, n)
                .mapToDouble(i -> i == j ? 1 : 0).toArray())
                .toArray(double[][]::new);

        for (int i = 0; i < n; i++) {
            double maxm = m[i][i];
            int row = i;
            for (int j = i; j < n; j++)
                if (m[j][i] > maxm) {
                    maxm = m[j][i];
                    row = j;
                }

            if (i != row) {
                double[] tmp = id[i];
                id[i] = id[row];
                id[row] = tmp;
            }
        }
        return id;
    }

    static double[][][] lu(double[][] A) {
        int n = A.length;
        double[][] L = new double[n][n];
        double[][] U = new double[n][n];
        double[][] P = pivotize(A);
        double[][] A2 = matrixMul(P, A);

        for (int j = 0; j < n; j++) {
            L[j][j] = 1;
            for (int i = 0; i < j + 1; i++) {
                double s1 = 0;
                for (int k = 0; k < i; k++)
                    s1 += U[k][j] * L[i][k];
                U[i][j] = A2[i][j] - s1;
            }
            for (int i = j; i < n; i++) {
                double s2 = 0;
                for (int k = 0; k < j; k++)
                    s2 += U[k][j] * L[i][k];
                L[i][j] = (A2[i][j] - s2) / U[j][j];
            }
        }
        return new double[][][]{L, U, P};
    }

    static void print(double[][] m) {
        stream(m).forEach(a -> {
            stream(a).forEach(n -> System.out.printf(Locale.US, "%5.1f ", n));
            System.out.println();
        });
        System.out.println();
    }

    public static void main(String[] args) {
        double[][] a = {{1.0, 3, 5}, {2.0, 4, 7}, {1.0, 1, 0}};

        double[][] b = {{11.0, 9, 24, 2}, {1.0, 5, 2, 6}, {3.0, 17, 18, 1},
        {2.0, 5, 7, 1}};

        for (double[][] m : lu(a))
            print(m);

        System.out.println();

        for (double[][] m : lu(b))
            print(m);
    }
}