# Software & Finance

To find out the adjoint of a matrix, you need to follow the follwing steps:

1. Find the cofactor of matrix. It involves lots of determinant calculation.
2. Do the transpose of cofactor of the matrix.

## 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;

}

{

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

if(m_rows != m_cols)

cofactor = this->CoFactor();

// adjoint is transpose of a cofactor of a matrix

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

{

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

{

}

}

}

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", 5,5);

a.FillSimulatedInput();

//CMatrix a("A", 3,3);

//std::cin >> a;

std::cout << a;

## Output

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

Input For Row: 1 Col: 1 = 2

Input For Row: 1 Col: 2 = 3

Input For Row: 1 Col: 3 = -1

Input For Row: 2 Col: 1 = 4

Input For Row: 2 Col: 2 = -3

Input For Row: 2 Col: 3 = 2

Input For Row: 3 Col: 1 = 7

Input For Row: 3 Col: 2 = 5

Input For Row: 3 Col: 3 = 6

Matrix : A Rows: 3 Cols: 3

|       2.00       3.00      -1.00 |

|       4.00      -3.00       2.00 |

|       7.00       5.00       6.00 |

Matrix : ADJ Rows: 3 Cols: 3

|     -28.00     -23.00       3.00 |

|     -10.00      19.00      -8.00 |

|      41.00      11.00     -18.00 |

Press any key to continue . . .

Enter Input For Matrix : A Rows: 5 Cols: 5

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: 2 Col: 1 = 2.54902

Input For Row: 2 Col: 2 = 3.92157

Input For Row: 2 Col: 3 = 5.09804

Input For Row: 2 Col: 4 = 7.05882

Input For Row: 2 Col: 5 = 9.80392

Input For Row: 3 Col: 1 = 6.66667

Input For Row: 3 Col: 2 = 8.92157

Input For Row: 3 Col: 3 = 10.8824

Input For Row: 3 Col: 4 = 12.6471

Input For Row: 3 Col: 5 = 15.3922

Input For Row: 4 Col: 1 = 12.0588

Input For Row: 4 Col: 2 = 15.098

Input For Row: 4 Col: 3 = 18.1373

Input For Row: 4 Col: 4 = 20.7843

Input For Row: 4 Col: 5 = 24.4118

Input For Row: 5 Col: 1 = 21.1765

Input For Row: 5 Col: 2 = 24.7059

Input For Row: 5 Col: 3 = 27.7451

Input For Row: 5 Col: 4 = 31.0784

Input For Row: 5 Col: 5 = 34.3137

Matrix : A Rows: 5 Cols: 5

|       0.29       0.98       1.86       2.84       3.63 |

|       2.55       3.92       5.10       7.06       9.80 |

|       6.67       8.92      10.88      12.65      15.39 |

|      12.06      15.10      18.14      20.78      24.41 |

|      21.18      24.71      27.75      31.08      34.31 |

Matrix : ADJ Rows: 5 Cols: 5

|      -7.39       6.31     -29.55      22.64      -3.87 |

|       2.90      -2.50      42.29     -38.80       9.04 |

|      -6.13      -7.32     -11.57      23.39      -8.71 |

|      18.73      -0.78       1.94     -13.03       6.64 |

|      -9.54       4.54      -4.61       6.85      -2.86 |

Press any key to continue . . .