Task: Gaussian elimination


C++: #include <algorithm>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#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,
        const std::initializer_list<std::initializer_list<scalar_type>>& values)
        : rows_(rows), columns_(columns), elements_(rows * columns) {
        assert(values.size() <= rows_);
        auto i = elements_.begin();
        for (const auto& row : values) {
            assert(row.size() <= columns_);
            std::copy(begin(row), end(row), 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 swap_rows(matrix<scalar_type>& m, size_t i, size_t j) {
    size_t columns = m.columns();
    for (size_t k = 0; k < columns; ++k)
        std::swap(m(i, k), m(j, k));
}

template <typename scalar_type>
std::vector<scalar_type> gauss_partial(const matrix<scalar_type>& a0,
                                       const std::vector<scalar_type>& b0) {
    size_t n = a0.rows();
    assert(a0.columns() == n);
    assert(b0.size() == n);
    
    matrix<scalar_type> a(n, n + 1);
    for (size_t i = 0; i < n; ++i) {
        for (size_t j = 0; j < n; ++j)
            a(i, j) = a0(i, j);
        a(i, n) = b0[i];
    }
    
    
    for (size_t k = 0; k < n; ++k) {
        
        size_t max_index = k;
        scalar_type max_value = 0;
        for (size_t i = k; i < n; ++i) {
            
            scalar_type scale_factor = 0;
            for (size_t j = k; j < n; ++j)
                scale_factor = std::max(std::abs(a(i, j)), scale_factor);
            if (scale_factor == 0)
                continue;
            
            scalar_type abs = std::abs(a(i, k))/scale_factor;
            if (abs > max_value) {
                max_index = i;
                max_value = abs;
            }
        }
        if (a(max_index, k) == 0)
            throw std::runtime_error("matrix is singular");
        if (k != max_index)
            swap_rows(a, k, max_index);
        for (size_t i = k + 1; i < n; ++i) {
            scalar_type f = a(i, k)/a(k, k);
            for (size_t j = k + 1; j <= n; ++j)
                a(i, j) -= a(k, j) * f;
            a(i, k) = 0;
        }
    }
    
    std::vector<scalar_type> x(n);
    for (size_t i = n; i-- > 0; ) {
        x[i] = a(i, n);
        for (size_t j = i + 1; j < n; ++j)
            x[i] -= a(i, j) * x[j];
        x[i] /= a(i, i);
    }
    return x;
}

int main() {
    matrix<double> a(6, 6, {
        {1.00, 0.00, 0.00, 0.00, 0.00, 0.00},
        {1.00, 0.63, 0.39, 0.25, 0.16, 0.10},
        {1.00, 1.26, 1.58, 1.98, 2.49, 3.13},
        {1.00, 1.88, 3.55, 6.70, 12.62, 23.80},
        {1.00, 2.51, 6.32, 15.88, 39.90, 100.28},
        {1.00, 3.14, 9.87, 31.01, 97.41, 306.02}
    });
    std::vector<double> b{-0.01, 0.61, 0.91, 0.99, 0.60, 0.02};
    std::vector<double> x{-0.01, 1.602790394502114, -1.6132030599055613,
            1.2454941213714368, -0.4909897195846576, 0.065760696175232};
    std::vector<double> y(gauss_partial(a, b));
    std::cout << std::setprecision(16);
    const double epsilon = 1e-14;
    for (size_t i = 0; i < y.size(); ++i) {
        assert(std::abs(x[i] - y[i]) <= epsilon);
        std::cout << y[i] << '\n';
    }
    return 0;
}


C#: using System;

namespace Rosetta
{
    internal class Vector
    {
        private double[] b;
        internal readonly int rows;

        internal Vector(int rows)
        {
            this.rows = rows;
            b = new double[rows];
        }

        internal Vector(double[] initArray)
        {
            b = (double[])initArray.Clone();
            rows = b.Length;
        }

        internal Vector Clone()
        {
            Vector v = new Vector(b);
            return v;
        }

        internal double this[int row]
        {
            get { return b[row]; }
            set { b[row] = value; }
        }

        internal void SwapRows(int r1, int r2)
        {
            if (r1 == r2) return;
            double tmp = b[r1];
            b[r1] = b[r2];
            b[r2] = tmp;
        }

        internal double norm(double[] weights)
        {
            double sum = 0;
            for (int i = 0; i < rows; i++)
            {
                double d = b[i] * weights[i];
                sum +=  d*d;
            }
            return Math.Sqrt(sum);
        }

        internal void print()
        {
            for (int i = 0; i < rows; i++)
                Console.WriteLine(b[i]);
            Console.WriteLine();
        }

        public static Vector operator-(Vector lhs, Vector rhs)
        {
            Vector v = new Vector(lhs.rows);
            for (int i = 0; i < lhs.rows; i++)
                v[i] = lhs[i] - rhs[i];
            return v;
        }
    }

    class Matrix
    {
        private double[] b;
        internal readonly int rows, cols;

        internal Matrix(int rows, int cols)
        {
            this.rows = rows;
            this.cols = cols;
            b = new double[rows * cols];            
        }

        internal Matrix(int size)
        {
            this.rows = size;
            this.cols = size;
            b = new double[rows * cols];
            for (int i = 0; i < size; i++)
                this[i, i] = 1;
        }

        internal Matrix(int rows, int cols, double[] initArray)
        {
            this.rows = rows;
            this.cols = cols;
            b = (double[])initArray.Clone();
            if (b.Length != rows * cols) throw new Exception("bad init array");
        }

        internal double this[int row, int col]
        {
            get { return b[row * cols + col]; }
            set { b[row * cols + col] = value; }
        }        
        
        public static Vector operator*(Matrix lhs, Vector rhs)
        {
            if (lhs.cols != rhs.rows) throw new Exception("I can't multiply matrix by vector");
            Vector v = new Vector(lhs.rows);
            for (int i = 0; i < lhs.rows; i++)
            {
                double sum = 0;
                for (int j = 0; j < rhs.rows; j++)
                    sum += lhs[i,j]*rhs[j];
                v[i] = sum;
            }
            return v;
        }

        internal void SwapRows(int r1, int r2)
        {
            if (r1 == r2) return;
            int firstR1 = r1 * cols;
            int firstR2 = r2 * cols;
            for (int i = 0; i < cols; i++)
            {
                double tmp = b[firstR1 + i];
                b[firstR1 + i] = b[firstR2 + i];
                b[firstR2 + i] = tmp;
            }
        }

        
        internal void ElimPartial(Vector B)
        {
            for (int diag = 0; diag < rows; diag++)
            {
                int max_row = diag;
                double max_val = Math.Abs(this[diag, diag]);
                double d;
                for (int row = diag + 1; row < rows; row++)
                    if ((d = Math.Abs(this[row, diag])) > max_val)
                    {
                        max_row = row;
                        max_val = d;
                    }
                SwapRows(diag, max_row);
                B.SwapRows(diag, max_row);
                double invd = 1 / this[diag, diag];
                for (int col = diag; col < cols; col++)
                    this[diag, col] *= invd;
                B[diag] *= invd;
                for (int row = 0; row < rows; row++)
                {
                    d = this[row, diag];
                    if (row != diag)
                    {
                        for (int col = diag; col < cols; col++)
                            this[row, col] -= d * this[diag, col];
                        B[row] -= d * B[diag];
                    }
                }
            }
        }
        
        internal void print()
        {
            for (int i = 0; i < rows; i++)
            {
                for (int j = 0; j < cols; j++)
                    Console.Write(this[i,j].ToString()+"  ");
                Console.WriteLine();
            }
        }
    }
}