Software & Finance





C++ - Matrix Cofactor





Finding determinant is one difficult task for large (5 X 5 and above) square matrices. Another head ache would be finding the cofactor of a matrix.

 

I have written a C++ program to solve the cofactor problem that can accept any square matrix even 24 X 24 is possible.

 

I have used recursion and dynamic memory allocation a lot to solve this problem.

 


Source Code


#if !defined(MATRIX_H)

#define MATRIX_H

 

#include <stdio.h>

#include <iostream>

#include <tchar.h>

#include <math.h>

 

class CMatrix

{

private:

    int m_rows;

    int m_cols;

    char m_name[128];

 

    CMatrix();

public:

    double **m_pData;

 

    CMatrix(const char *name, int rows, int cols) : m_rows(rows), m_cols(cols)

    {

        strcpy(m_name, name);

        m_pData = new double*[m_rows];

        for(int i = 0; i < m_rows; i++)

            m_pData[i] = new double[m_cols];

 

        for(int i = 0; i < m_rows; i++)

        {

            for(int j = 0; j < m_cols; j++)

            {

                m_pData[i][j] = 0.0;

            }

        }

    }

 

    CMatrix(const CMatrix &other)

    {

        strcpy(m_name, other.m_name);

        m_rows = other.m_rows;

        m_cols = other.m_cols;

 

        m_pData = new double*[m_rows];

        for(int i = 0; i < m_rows; i++)

            m_pData[i] = new double[m_cols];

 

        for(int i = 0; i < m_rows; i++)

        {

            for(int j = 0; j < m_cols; j++)

            {

                m_pData[i][j] = other.m_pData[i][j];

            }

        }

    }

 

    ~CMatrix()

    {

        for(int i = 0; i < m_rows; i++)

            delete [] m_pData[i];

        delete [] m_pData;

        m_rows = m_cols = 0;

    }

 

    void SetName(const char *name) { strcpy(m_name, name); }

    const char* GetName() const { return m_name; }

 

    void GetInput()

    {

        std::cin >> *this;

    }

 

    void FillSimulatedInput()

    {

        static int factor1 = 1, factor2 = 2;

        std::cout << "\n\nEnter Input For Matrix : " << m_name << " Rows: " << m_rows << " Cols: " << m_cols << "\n";

        for(int i = 0; i < m_rows; i++)

        {

            for(int j = 0; j < m_cols; j++)

            {

                std::cout << "Input For Row: " << i + 1 << " Col: " << j + 1 << " = ";

                int data = ((i + 1) * factor1) + (j + 1) * factor2;

                m_pData[i][j] = data / 10.2;

                std::cout << m_pData[i][j] << "\n";

 

                factor1 += (rand() % 4);

                factor2 += (rand() % 3);

            }

            std::cout << "\n";

        }

 

        std::cout << "\n";

    }   

 

    double Determinant()

    {

        double det = 0;

        double **pd = m_pData;

        switch(m_rows)

        {

       

        case 2:

        {

            det = pd[0][0] * pd[1][1] - pd[0][1] * pd[1][0];

            return det;

        }

        break;

 

        case 3:

        {

            /***

            a b c

            d e f

            g h i

 

            a b c a b c

            d e f d e f

            g h i g h i

 

            // det (A) = aei + bfg + cdh - afh - bdi - ceg.

            ***/

 

            double a = pd[0][0];

            double b = pd[0][1];

            double c = pd[0][2];

 

            double d = pd[1][0];

            double e = pd[1][1];

            double f = pd[1][2];

 

            double g = pd[2][0];

            double h = pd[2][1];

            double i = pd[2][2];

 

            double det = (a*e*i + b*f*g + c*d*h);

            det = det - a*f*h;

            det = det - b*d*i;

            det = det - c*e*g;

           

            return det;

        }

        break;

 

        case 4:

        {

            CMatrix *temp[4];

            for(int i = 0; i < 4; i++)

                temp[i] = new CMatrix("", 3,3);

 

            for(int k = 0; k < 4; k++)

            {

               

                for(int i = 1; i < 4; i++)

                {

                    int j1 = 0;

                    for(int j = 0; j < 4; j++)

                    {

                        if(k == j)

                            continue;

                        temp[k]->m_pData[i-1][j1++] = this->m_pData[i][j];

                    }

                }

            }

            double det = this->m_pData[0][0] * temp[0]->Determinant() -

            this->m_pData[0][1] * temp[1]->Determinant() +

            this->m_pData[0][2] * temp[2]->Determinant() -

            this->m_pData[0][3] * temp[3]->Determinant();

            return det;

        }

        break;

 

        case 5:

        {

            CMatrix *temp[5];

            for(int i = 0; i < 5; i++)

                temp[i] = new CMatrix("", 4,4);

 

            for(int k = 0; k < 5; k++)

            {

               

                for(int i = 1; i < 5; i++)

                {

                    int j1 = 0;

                    for(int j = 0; j < 5; j++)

                    {

                        if(k == j)

                            continue;

                        temp[k]->m_pData[i-1][j1++] = this->m_pData[i][j];

                    }

                }

            }

            double det = this->m_pData[0][0] * temp[0]->Determinant() -

            this->m_pData[0][1] * temp[1]->Determinant() +

            this->m_pData[0][2] * temp[2]->Determinant() -

            this->m_pData[0][3] * temp[3]->Determinant() +

            this->m_pData[0][4] * temp[4]->Determinant();

            return det;

        }

        case 6:

        case 7:

        case 8:

        case 9:

        case 10:

        case 11:

        case 12:

        default:

        {

            int DIM = m_rows;

            CMatrix **temp = new CMatrix*[DIM];

            for(int i = 0; i < DIM; i++)

                temp[i] = new CMatrix("", DIM - 1,DIM - 1);

 

            for(int k = 0; k < DIM; k++)

            {

               

                for(int i = 1; i < DIM; i++)

                {

                    int j1 = 0;

                    for(int j = 0; j < DIM; j++)

                    {

                        if(k == j)

                            continue;

                        temp[k]->m_pData[i-1][j1++] = this->m_pData[i][j];

                    }

                }

            }

 

            double det = 0;

            for(int k = 0; k < DIM; k++)

            {

                if( (k %2) == 0)

                    det = det + (this->m_pData[0][k] * temp[k]->Determinant());

                else

                    det = det - (this->m_pData[0][k] * temp[k]->Determinant());

            }

 

            for(int i = 0; i < DIM; i++)

                delete temp[i];

            delete [] temp;

 

            return det;

        }

        break;

        }

    }

 

    CMatrix& operator = (const CMatrix &other)

    {

        if( this->m_rows != other.m_rows ||

            this->m_cols != other.m_cols)

        {

            std::cout << "WARNING: Assignment is taking place with by changing the number of rows and columns of the matrix";

        }

        for(int i = 0; i < m_rows; i++)

            delete [] m_pData[i];

        delete [] m_pData;

        m_rows = m_cols = 0;

 

        strcpy(m_name, other.m_name);

        m_rows = other.m_rows;

        m_cols = other.m_cols;

 

        m_pData = new double*[m_rows];

        for(int i = 0; i < m_rows; i++)

            m_pData[i] = new double[m_cols];

 

        for(int i = 0; i < m_rows; i++)

        {

            for(int j = 0; j < m_cols; j++)

            {

                m_pData[i][j] = other.m_pData[i][j];

            }

        }

 

        return *this;

    }

 

    CMatrix CoFactor()

    {

        CMatrix cofactor("COF", m_rows, m_cols);

        if(m_rows != m_cols)

            return cofactor;

 

        if(m_rows < 2)

            return cofactor;

        else if(m_rows == 2)

        {

            cofactor.m_pData[0][0] = m_pData[1][1];

            cofactor.m_pData[0][1] = -m_pData[1][0];

            cofactor.m_pData[1][0] = -m_pData[0][1];

            cofactor.m_pData[1][1] = m_pData[0][0];

            return cofactor;

        }

        else if(m_rows >= 3)

        {

            int DIM = m_rows;

            CMatrix ***temp = new CMatrix**[DIM];

            for(int i = 0; i < DIM; i++)

                temp[i] = new CMatrix*[DIM];

            for(int i = 0; i < DIM; i++)

                for(int j = 0; j < DIM; j++)

                    temp[i][j] = new CMatrix("", DIM - 1,DIM - 1);

 

            for(int k1 = 0; k1 < DIM; k1++)

            {  

                for(int k2 = 0; k2 < DIM; k2++)

                {

                    int i1 = 0;

                    for(int i = 0; i < DIM; i++)

                    {

                        int j1 = 0;

                        for(int j = 0; j < DIM; j++)

                        {

                            if(k1 == i || k2 == j)

                                continue;

                            temp[k1][k2]->m_pData[i1][j1++] = this->m_pData[i][j];

                        }

                        if(k1 != i)

                            i1++;

                    }

                }

            }

 

            bool flagPositive = true;

            for(int k1 = 0; k1 < DIM; k1++)

            {  

                flagPositive = ( (k1 % 2) == 0);

                for(int k2 = 0; k2 < DIM; k2++)

                {

                    if(flagPositive == true)

                    {

                        cofactor.m_pData[k1][k2] = temp[k1][k2]->Determinant();

                        flagPositive = false;

                    }

                    else

                    {

                        cofactor.m_pData[k1][k2] = -temp[k1][k2]->Determinant();

                        flagPositive = true;

                    }

                }

               

            }

 

            for(int i = 0; i < DIM; i++)

                for(int j = 0; j < DIM; j++)

                    delete temp[i][j];

 

            for(int i = 0; i < DIM; i++)

                delete [] temp[i];

 

            delete [] temp;

        }

        return cofactor;

    }

 

    friend std::istream& operator >> (std::istream &is, CMatrix &m);

    friend std::ostream& operator << (std::ostream &os, const CMatrix &m);   

};

 

std::istream& operator >> (std::istream &is, CMatrix &m)

{

    std::cout << "\n\nEnter Input For Matrix : " << m.m_name << " Rows: " << m.m_rows << " Cols: " << m.m_cols << "\n";

    for(int i = 0; i < m.m_rows; i++)

    {

        for(int j = 0; j < m.m_cols; j++)

        {

            std::cout << "Input For Row: " << i + 1 << " Col: " << j + 1 << " = ";

            is >> m.m_pData[i][j];

        }

        std::cout << "\n";

    }

    std::cout << "\n";

    return is;

}

 

std::ostream& operator << (std::ostream &os,const CMatrix &m)

{

    os << "\n\nMatrix : " << m.m_name << " Rows: " << m.m_rows << " Cols: " << m.m_cols << "\n\n";

    for(int i = 0; i < m.m_rows; i++)

    {

        os << " | ";

        for(int j = 0; j < m.m_cols; j++)

        {

            char buf[32];

            double data = m.m_pData[i][j];

            if( m.m_pData[i][j] > -0.00001 &&

                m.m_pData[i][j] < 0.00001)

                data = 0;

            sprintf(buf, "%10.2lf ", data);

            os <<  buf;

        }

        os << "|\n";

    }

    os << "\n\n";

    return os;

}

 

 

#endif

 

 

int main()

{  

    CMatrix a("A", 6,6);

   

    a.FillSimulatedInput();

/***

    CMatrix a("A", 3,3);   

    std::cin >> a;

***/   

 

    CMatrix acof = a.CoFactor();

 

    std::cout << a;

    std::cout << acof;

 

    return 0;

}

Output


Enter Input For Matrix : A Rows: 3 Cols: 3

Input For Row: 1 Col: 1 = 1

Input For Row: 1 Col: 2 = 3

Input For Row: 1 Col: 3 = 5

 

Input For Row: 2 Col: 1 = 2

Input For Row: 2 Col: 2 = 4

Input For Row: 2 Col: 3 = 6

 

Input For Row: 3 Col: 1 = 3

Input For Row: 3 Col: 2 = 6

Input For Row: 3 Col: 3 = 9

 

 

 

 

Matrix : A Rows: 3 Cols: 3

 

 |       1.00       3.00       5.00 |

 |       2.00       4.00       6.00 |

 |       3.00       6.00       9.00 |

 

 

 

 

Matrix : COF Rows: 3 Cols: 3

 

 |       0.00       0.00       0.00 |

 |       3.00      -6.00       3.00 |

 |      -2.00       4.00      -2.00 |

 

 

Press any key to continue . . .

 

 

 

 

 

Enter Input For Matrix : A Rows: 6 Cols: 6

Input For Row: 1 Col: 1 = 0.294118

Input For Row: 1 Col: 2 = 0.980392

Input For Row: 1 Col: 3 = 1.86275

Input For Row: 1 Col: 4 = 2.84314

Input For Row: 1 Col: 5 = 3.62745

Input For Row: 1 Col: 6 = 5.58824

 

Input For Row: 2 Col: 1 = 2.94118

Input For Row: 2 Col: 2 = 4.11765

Input For Row: 2 Col: 3 = 5.88235

Input For Row: 2 Col: 4 = 8.43137

Input For Row: 2 Col: 5 = 10.3922

Input For Row: 2 Col: 6 = 12.3529

 

Input For Row: 3 Col: 1 = 8.13725

Input For Row: 3 Col: 2 = 9.70588

Input For Row: 3 Col: 3 = 12.0588

Input For Row: 3 Col: 4 = 15.098

Input For Row: 3 Col: 5 = 17.8431

Input For Row: 3 Col: 6 = 20.5882

 

Input For Row: 4 Col: 1 = 14.902

Input For Row: 4 Col: 2 = 18.2353

Input For Row: 4 Col: 3 = 21.4706

Input For Row: 4 Col: 4 = 24.7059

Input For Row: 4 Col: 5 = 27.549

Input For Row: 4 Col: 6 = 31.1765

 

Input For Row: 5 Col: 1 = 24.902

Input For Row: 5 Col: 2 = 27.9412

Input For Row: 5 Col: 3 = 32.451

Input For Row: 5 Col: 4 = 36.0784

Input For Row: 5 Col: 5 = 39.7059

Input For Row: 5 Col: 6 = 43.9216

 

Input For Row: 6 Col: 1 = 36.3725

Input For Row: 6 Col: 2 = 39.6078

Input For Row: 6 Col: 3 = 43.8235

Input For Row: 6 Col: 4 = 47.2549

Input For Row: 6 Col: 5 = 51.3725

Input For Row: 6 Col: 6 = 55.2941

 

 

 

 

Matrix : A Rows: 6 Cols: 6

 

 |     0.29       0.98      1.86      2.84      3.63     5.59 |

 |     2.94       4.12      5.88      8.43     10.39    12.35 |

 |     8.14       9.71     12.06     15.10     17.84    20.59 |

 |    14.90      18.24     21.47     24.71     27.55    31.18 |

 |    24.90      27.94     32.45     36.08     39.71    43.92 |

 |    36.37      39.61     43.82     47.25     51.37    55.29 |

 

 

 

 

Matrix : COF Rows: 6 Cols: 6

 

 |    -8.71     -3.12    23.91   -33.36     34.48    -14.51 |

 |   -20.30     -1.67    89.31  -147.84     83.23     -7.22 |

 |    15.04      1.99   -72.77   136.12    -85.15      9.14 |

 |    13.08    -13.86    -5.78    14.87    -10.39      2.85 |

 |    -2.01     21.59   -29.61    15.07     -7.42      3.33 |

 |    -5.97     -9.39    31.50   -34.64     21.37     -4.79 |

 

Press any key to continue . . .