Today we are going to write a program to find the inverse of matrix C++, so let’s start with the what is the inverse of a matrix.
Inverse of a Matrix:
For a square matrix A, the inverse is written A-1. When A is multiplied by A-1 the result is the identity matrix I. Non-square matrices do not have inverses.
Note: Not all square matrices have inverses. A square matrix which has an inverse is called invertible or nonsingular, and a square matrix without an inverse is called non-invertible or singular.
AA-1 = A-1A = I
| Example: | For matrix  , its inverse is  since |
AA-1 =  and A-1A =  . |
Program to find Inverse of a Matrix C++:
#if !defined(MATRIX_H)
#define MATRIX_H
#include <stdio.h>
#include <iostream>
#include <tchar.h>
#include <math.h>
#include <stdlib.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 Adjoint()
{
CMatrix cofactor("COF", m_rows, m_cols);
CMatrix adj("ADJ", m_rows, m_cols);
if (m_rows != m_cols)
return adj;
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++)
{
adj.m_pData[j][i] = cofactor.m_pData[i][j];
}
}
return adj;
}
CMatrix Transpose()
{
CMatrix trans("TR", m_cols, m_rows);
for (int i = 0; i < m_rows; i++)
{
for (int j = 0; j < m_cols; j++)
{
trans.m_pData[j][i] = m_pData[i][j];
}
}
return trans;
}
CMatrix Inverse()
{
CMatrix cofactor("COF", m_rows, m_cols);
CMatrix inv("INV", m_rows, m_cols);
if (m_rows != m_cols)
return inv;
// to find out Determinant
double det = Determinant();
cofactor = this->CoFactor();
// inv = transpose of cofactor / Determinant
for (int i = 0; i < m_rows; i++)
{
for (int j = 0; j < m_cols; j++)
{
inv.m_pData[j][i] = cofactor.m_pData[i][j] / det;
}
}
return inv;
}
CMatrix operator +(const CMatrix &other)
{
if (this->m_rows != other.m_rows || this->m_cols != other.m_cols)
{
std::cout
<< "Addition could not take place because number of rows and columns are different between the two matrices";
return *this;
}
CMatrix result("", m_rows, m_cols);
for (int i = 0; i < m_rows; i++)
{
for (int j = 0; j < m_cols; j++)
{
result.m_pData[i][j] = this->m_pData[i][j]
+ other.m_pData[i][j];
}
}
return result;
}
CMatrix operator -(const CMatrix &other)
{
if (this->m_rows != other.m_rows || this->m_cols != other.m_cols)
{
std::cout
<< "Subtraction could not take place because number of rows and columns are different between the two matrices";
return *this;
}
CMatrix result("", m_rows, m_cols);
for (int i = 0; i < m_rows; i++)
{
for (int j = 0; j < m_cols; j++)
{
result.m_pData[i][j] = this->m_pData[i][j]
- other.m_pData[i][j];
}
}
return result;
}
CMatrix operator *(const CMatrix &other)
{
if (this->m_cols != other.m_rows)
{
std::cout
<< "Multiplication could not take place because number of columns of 1st Matrix and number of rows in 2nd Matrix are different";
return *this;
}
CMatrix result("", this->m_rows, other.m_cols);
for (int i = 0; i < this->m_rows; i++)
{
for (int j = 0; j < other.m_cols; j++)
{
for (int k = 0; k < this->m_cols; k++)
{
result.m_pData[i][j] += this->m_pData[i][k]
* other.m_pData[k][j];
}
}
}
return result;
}
bool operator ==(const CMatrix &other)
{
if (this->m_rows != other.m_rows || this->m_cols != other.m_cols)
{
std::cout
<< "Comparision could not take place because number of rows and columns are different between the two matrices";
return false;
}
CMatrix result("", m_rows, m_cols);
bool bEqual = true;
for (int i = 0; i < m_rows; i++)
{
for (int j = 0; j < m_cols; j++)
{
if (this->m_pData[i][j] != other.m_pData[i][j])
bEqual = false;
}
}
return bEqual;
}
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);
//std::cin >> a;
a.FillSimulatedInput();
CMatrix aadj = a.Inverse();
std::cout << a;
std::cout << aadj;
CMatrix unit = (a * aadj);
unit.SetName("A * A-Inv");
std::cout << unit;
}
OUTPUT:
$ g++ InverseOfMatrix.cpp $ a.out 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 : INV Rows: 5 Cols: 5 | -0.93 0.80 -3.74 2.86 -0.49 | | 0.37 -0.32 5.35 -4.91 1.14 | | -0.78 -0.93 -1.46 2.96 -1.10 | | 2.37 -0.10 0.25 -1.65 0.84 | | -1.21 0.57 -0.58 0.87 -0.36 | Matrix : A * A-Inv Rows: 5 Cols: 5 | 1.00 0.00 0.00 0.00 0.00 | | 0.00 1.00 0.00 0.00 0.00 | | 0.00 0.00 1.00 0.00 0.00 | | 0.00 0.00 0.00 1.00 0.00 | | 0.00 0.00 0.00 0.00 1.00 |
