Task: Cramer's rule


C++: #include <algorithm>
#include <iostream>
#include <vector>

class SubMatrix {
    const std::vector<std::vector<double>> *source;
    std::vector<double> replaceColumn;
    const SubMatrix *prev;
    size_t sz;
    int colIndex = -1;

public:
    SubMatrix(const std::vector<std::vector<double>> &src, const std::vector<double> &rc) : source(&src), replaceColumn(rc), prev(nullptr), colIndex(-1) {
        sz = replaceColumn.size();
    }

    SubMatrix(const SubMatrix &p) : source(nullptr), prev(&p), colIndex(-1) {
        sz = p.size() - 1;
    }

    SubMatrix(const SubMatrix &p, int deletedColumnIndex) : source(nullptr), prev(&p), colIndex(deletedColumnIndex) {
        sz = p.size() - 1;
    }

    int columnIndex() const {
        return colIndex;
    }
    void columnIndex(int index) {
        colIndex = index;
    }

    size_t size() const {
        return sz;
    }

    double index(int row, int col) const {
        if (source != nullptr) {
            if (col == colIndex) {
                return replaceColumn[row];
            } else {
                return (*source)[row][col];
            }
        } else {
            if (col < colIndex) {
                return prev->index(row + 1, col);
            } else {
                return prev->index(row + 1, col + 1);
            }
        }
    }

    double det() const {
        if (sz == 1) {
            return index(0, 0);
        }
        if (sz == 2) {
            return index(0, 0) * index(1, 1) - index(0, 1) * index(1, 0);
        }
        SubMatrix m(*this);
        double det = 0.0;
        int sign = 1;
        for (size_t c = 0; c < sz; ++c) {
            m.columnIndex(c);
            double d = m.det();
            det += index(0, c) * d * sign;
            sign = -sign;
        }
        return det;
    }
};

std::vector<double> solve(SubMatrix &matrix) {
    double det = matrix.det();
    if (det == 0.0) {
        throw std::runtime_error("The determinant is zero.");
    }

    std::vector<double> answer(matrix.size());
    for (int i = 0; i < matrix.size(); ++i) {
        matrix.columnIndex(i);
        answer[i] = matrix.det() / det;
    }
    return answer;
}

std::vector<double> solveCramer(const std::vector<std::vector<double>> &equations) {
    int size = equations.size();
    if (std::any_of(
        equations.cbegin(), equations.cend(),
        [size](const std::vector<double> &a) { return a.size() != size + 1; }
    )) {
        throw std::runtime_error("Each equation must have the expected size.");
    }

    std::vector<std::vector<double>> matrix(size);
    std::vector<double> column(size);
    for (int r = 0; r < size; ++r) {
        column[r] = equations[r][size];
        matrix[r].resize(size);
        for (int c = 0; c < size; ++c) {
            matrix[r][c] = equations[r][c];
        }
    }

    SubMatrix sm(matrix, column);
    return solve(sm);
}

template<typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    auto it = v.cbegin();
    auto end = v.cend();

    os << '[';
    if (it != end) {
        os << *it++;
    }
    while (it != end) {
        os << ", " << *it++;
    }

    return os << ']';
}

int main() {
    std::vector<std::vector<double>> equations = {
        { 2, -1,  5,  1,  -3},
        { 3,  2,  2, -6, -32},
        { 1,  3,  3, -1, -47},
        { 5, -2, -3,  3,  49},
    };

    auto solution = solveCramer(equations);
    std::cout << solution << '\n';

    return 0;
}










Ada: with Ada.Text_IO;
with Ada.Numerics.Generic_Real_Arrays;

procedure Cramers_Rules is

   type Real is new Float;
   

   package Real_Arrays is
      new Ada.Numerics.Generic_Real_Arrays (Real);

   use Real_Arrays;

   function Solve_Cramer (M : in Real_Matrix;
                          V : in Real_Vector)
                         return Real_Vector
   is
      Denominator : Real;
      Nom_Matrix  : Real_Matrix (M'Range (1),
                                 M'Range (2));
      Numerator   : Real;
      Result      : Real_Vector (M'Range (1));
   begin
      if
        M'Length (2) /= V'Length or
        M'Length (1) /= M'Length (2)
      then
         raise Constraint_Error with "Dimensions does not match";
      end if;

      Denominator := Determinant (M);

      for Col in V'Range loop
         Nom_Matrix := M;

         
         for Row in V'Range loop
            Nom_Matrix (Row, Col) := V (Row);
         end loop;

         Numerator    := Determinant (Nom_Matrix);
         Result (Col) := Numerator / Denominator;
      end loop;

      return Result;
   end Solve_Cramer;

   procedure Put (V : Real_Vector) is
      use Ada.Text_IO;
      package Real_IO is
         new Ada.Text_IO.Float_IO (Real);
   begin
      Put ("[");
      for E of V loop
         Real_IO.Put (E, Exp => 0, Aft => 2);
         Put (" ");
      end loop;
      Put ("]");
      New_Line;
   end Put;

   M : constant Real_Matrix := ((2.0, -1.0,  5.0,  1.0),
                                (3.0,  2.0,  2.0, -6.0),
                                (1.0,  3.0,  3.0, -1.0),
                                (5.0, -2.0, -3.0,  3.0));
   V : constant Real_Vector := (-3.0, -32.0, -47.0, 49.0);
   R : constant Real_Vector := Solve_Cramer (M, V);
begin
   Put (R);
end Cramers_Rules;