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MatricesCPP.cpp
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MatricesCPP.cpp
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#include <iostream>
using namespace std;
/*This class is only for the diagonal matrix.*/
class Diagonal
{
private:
int *A;
int n;
public:
Diagonal()
{
n = 2;
A = new int[2];
}
Diagonal(int n)
{
this->n = n;
A = new int[n];
}
~Diagonal()
{
delete[]A;
}
void Set(int i, int j, int x);
int Get(int i, int j);
void Display();
};
void Diagonal::Set(int i, int j, int x)
{
if (i == j)
A[i - 1] = x;
}
int Diagonal::Get(int i, int j)
{
if (i == j)
return A[i - 1];
else
return 0;
}
void Diagonal::Display()
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i == j)
cout << A[i] << " ";
else
cout << 0 << " ";
}
cout << endl;
}
}
/*This class is only for Lower Triangular matrix.*/
class LTMatrix
{
private:
int* A;
int n;
public:
LTMatrix()
{
n = 2;
A = new int[3];
}
LTMatrix(int n)
{
this->n = n;
A = new int[n * (n + 1) / 2];
}
~LTMatrix()
{
delete[]A;
}
void Set(int i, int j, int x);
int Get(int i, int j);
void Display();
};
//tex:
// This is using Row Major Formula.
// $$\text{Index}(A[i][j])=\frac{i(i-j)}{2}+j-1$$
// The formula for column major is:
// $$\text{Index}(A[i][j])=n(j-1)-\frac{(j-2)\times(j-1)}{2}+i-j$$
//Now I'm using Row major. We can also use Column major the changes is just in the formulas
void LTMatrix::Set(int i, int j, int x)
{
if (i >= j)
A[i * (i - 1) / 2 + (j - 1)]=x;
}
int LTMatrix::Get(int i, int j)
{
if (i >= j)
return A[i * (i - 1) / 2 + (j - 1)];
else
return 0;
}
void LTMatrix::Display()
{
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= n; j++)
{
if (i >= j)
cout << A[i * (i - 1) / 2 + (j - 1)] << " ";
else
cout << "0 ";
}
cout << endl;
}
}
/*This class is only for upper triangular matrix.*/
class UTMatrix
{
private:
int* A;
int n;
public:
UTMatrix()
{
n = 2;
A = new int[3];
}
UTMatrix(int n)
{
this->n = n;
A = new int[n * (n + 1) / 2];
}
~UTMatrix()
{
delete[]A;
}
void Set(int i, int j, int x);
int Get(int i, int j);
void Display();
};
//tex:
//Formula for Row Major.
//$$\text{Index}(A[i][j])=n(i-1)-\frac{(i-2)(i-1)}{2}+j-1$$
//Formula for Column Major.
//$$\text{Index}(A[i][j])=\frac{j(j-1)}{2}+i-1$$
//Now I'm using column major. We can also use row major the changes is just in the formulas.
void UTMatrix::Set(int i, int j, int x)
{
if (i <= j)
A[j * (j - 1) / 2 + i - 1] = x;
}
int UTMatrix::Get(int i, int j)
{
if (i <= j)
return A[j * (j - 1) / 2 + i - 1];
else
return 0;
}
void UTMatrix::Display()
{
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= n; j++)
{
if (i <= j)
cout << A[j * (j - 1) / 2 + i - 1] << " ";
else
cout << "0 ";
}
cout << endl;
}
}
/*This calss is for symmetric matrix and also use the
row major formula of the lower triangular matrix.
If A[i][j]==A[j][i] then the matrix is symmetric.*/
class SymMatrix
{
private:
int* A;
int n;
public:
SymMatrix() //Non-Parametrize constructor.
{
n = 2;
A = new int[3];
}
SymMatrix(int n) //Parametrize constructor.
{
this->n = n;
A = new int[n * (n + 1) / 2];
}
~SymMatrix() //Destructor
{
delete[]A;
}
void Set(int i, int j, int x);
int Get(int i, int j);
void Display();
void Array();
};
void SymMatrix::Set(int i, int j,int x)
{
if (i >= j)
A[i * (i - 1) / 2 + j - 1] = x; // Here the elements will be only stored in the lower triangular part of the symmetric matrix.
}
int SymMatrix::Get(int i, int j)
{
if (i >= j)
return A[i * (i - 1) / 2 + j - 1];
else
return A[j * (j - 1) / 2 + i - 1]; // The elements from the lower part is shown in the uppert by just changing i and j in the formula.
}
void SymMatrix::Display()
{
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= n; j++)
{
if(i>=j)
cout << A[i * (i - 1) / 2 + j - 1] << " ";
else
cout << A[j * (j - 1) / 2 + i - 1] << " ";
}
cout << endl;
}
}
void SymMatrix::Array()
{
for (int i = 0; i < n * (n + 1) / 2; i++)
{
cout << A[i] << " ";
}
}
/*This class is for Tridiagonal matrix.
A tridiagonal matrix has nonzero elements only on the main diagonal,
the diagonal above the main diagonal, and the diagonal below the main diagonal.*/
class TrMatrix
{
private:
int* A;
int n;
public:
TrMatrix() //Non-Parametrize constructor.
{
n = 3;
A = new int[7];
}
TrMatrix(int n) //Parametrize constructor.
{
this->n = n;
A = new int[3 * n - 2];
}
~TrMatrix()
{
delete[]A;
}
void Set(int i, int j, int x);
int Get(int i, int j);
void Display();
void Array();
};
void TrMatrix::Set(int i, int j, int x)
{
if (i - j == 1)
A[i - 2] = x;
else if (i - j == 0)
A[n + i - 2] = x;
else if (i - j == -1)
A[2 * n + i - 2] = x;
}
int TrMatrix::Get(int i, int j)
{
if (i - j == 1)
return A[i - 2];
else if (i - j == 0)
return A[n + i - 2];
else if (i - j == -1)
return A[2 * n + i - 2];
else
return 0;
}
void TrMatrix::Display()
{
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= n; j++)
{
if (i - j == 1)
cout<<A[i - 2]<<" ";
else if (i - j == 0)
cout<<A[n + i - 2]<<" ";
else if (i - j == -1)
cout<<A[2 * n + i - 2]<<" ";
else
cout<<"0 ";
}
cout << endl;
}
cout << endl;
}
void TrMatrix::Array()
{
for (int i = 0; i < 3*n-2; i++)
cout << A[i] << " ";
cout << endl;
}
/*This class is for Toeplitz Matrix.
Toeplitz, is a matrix in which each descending diagonal from left to right is constant.*/
//tex:
//Example is:
//$$\begin{bmatrix}a&b&d&e&f\\c&a&b&d&e\\g&c&a&b&d\\h&g&c&a&b\\i&h&g&c&a\end{bmatrix}$$
class ToeplitzMatrix
{
private:
int* A;
int n;
public:
ToeplitzMatrix()
{
n = 3;
A = new int[2 * 3 - 1];
}
ToeplitzMatrix(int n)
{
this->n = n;
A = new int[2 * n - 1];
}
~ToeplitzMatrix()
{
delete[]A;
}
void Set(int i, int j, int x);
int Get(int i, int j);
void Display();
};
void ToeplitzMatrix::Set(int i, int j, int x)
{
if (i <= j)
A[j - i] = x;
else
A[n + i - j - 1] = x;
}
int ToeplitzMatrix::Get(int i, int j)
{
if (i <= j)
return A[j - i];
else
return A[n + i - j - 1];
}
void ToeplitzMatrix::Display()
{
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= n; j++)
{
if (i <= j)
cout << A[j - i] << " ";
else
cout << A[n + i - j - 1] << " ";
}
cout << endl;
}
}
int main()
{
int d;
cout << "Enter the Dimensions:";
cin >> d;
ToeplitzMatrix Tpm(d);
int x;
cout << "Enter All the Elements:"<<endl;
for (int i = 1; i <= d; i++)
{
for (int j = 1; j <= d; j++)
{
cin >> x;
Tpm.Set(i, j, x);
}
}
cout << endl;
Tpm.Display();
cout << Tpm.Get(2, 3) << endl;
return 0;
}