C++ - Matrix Determinant
Determinant is applicable for only square matrix. If we have up to 2 X 2 or 3 X 3 or 4 X 4 square matrix, then it is OK to calculate it manually. But if we have 6 X 6 matrix or 12 X 12 matrix, then definitely we need calculator or computer program to solve this problem.
I have written a C++ program to solve the determinant 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;
}
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();
double det = a.Determinant();
std::cout << a << "\n Determinant : ";
std::cout << det << "\n";
}
Output
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 |
Determinant : -11.9339
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