647 lines
21 KiB
C++
647 lines
21 KiB
C++
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#if !defined(MATRIX_H)
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#define MATRIX_H
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#include <stdio.h>
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#include <iostream>
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#include <tchar.h>
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#include <math.h>
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#include <stdlib.h>
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class CMatrix
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{
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private:
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int m_rows;
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int m_cols;
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char m_name[128];
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CMatrix();
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public:
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double **m_pData;
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CMatrix(const char *name, int rows, int cols) :
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m_rows(rows), m_cols(cols)
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{
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strcpy(m_name, name);
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m_pData = new double*[m_rows];
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for (int i = 0; i < m_rows; i++)
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m_pData[i] = new double[m_cols];
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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m_pData[i][j] = 0.0;
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}
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}
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}
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CMatrix(const CMatrix &other)
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{
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strcpy(m_name, other.m_name);
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m_rows = other.m_rows;
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m_cols = other.m_cols;
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m_pData = new double*[m_rows];
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for (int i = 0; i < m_rows; i++)
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m_pData[i] = new double[m_cols];
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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m_pData[i][j] = other.m_pData[i][j];
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}
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}
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}
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~CMatrix()
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{
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for (int i = 0; i < m_rows; i++)
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delete[] m_pData[i];
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delete[] m_pData;
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m_rows = m_cols = 0;
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}
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void SetName(const char *name)
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{
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strcpy(m_name, name);
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}
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const char* GetName() const
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{
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return m_name;
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}
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void GetInput()
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{
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std::cin >> *this;
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}
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void FillSimulatedInput()
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{
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static int factor1 = 1, factor2 = 2;
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std::cout << "\n\nEnter Input For Matrix : " << m_name << " Rows: "
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<< m_rows << " Cols: " << m_cols << "\n";
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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std::cout << "Input For Row: " << i + 1 << " Col: " << j
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+ 1 << " = ";
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int data = ((i + 1) * factor1) + (j + 1) * factor2;
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m_pData[i][j] = data / 10.2;
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std::cout << m_pData[i][j] << "\n";
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factor1 += (rand() % 4);
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factor2 += (rand() % 3);
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}
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std::cout << "\n";
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}
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std::cout << "\n";
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}
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double Determinant()
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{
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double det = 0;
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double **pd = m_pData;
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switch (m_rows)
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{
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case 2:
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{
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det = pd[0][0] * pd[1][1] - pd[0][1] * pd[1][0];
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return det;
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}
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break;
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case 3:
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{
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/***
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a b c
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d e f
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g h i
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a b c a b c
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d e f d e f
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g h i g h i
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// det (A) = aei + bfg + cdh - afh - bdi - ceg.
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***/
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double a = pd[0][0];
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double b = pd[0][1];
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double c = pd[0][2];
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double d = pd[1][0];
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double e = pd[1][1];
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double f = pd[1][2];
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double g = pd[2][0];
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double h = pd[2][1];
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double i = pd[2][2];
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double det = (a * e * i + b * f * g + c * d * h); // - a*f*h - b*d*i - c*e*g);
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det = det - a * f * h;
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det = det - b * d * i;
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det = det - c * e * g;
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//std::cout << *this;
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//std::cout << "deter: " << det << " \n";
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return det;
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}
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break;
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case 4:
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{
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CMatrix *temp[4];
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for (int i = 0; i < 4; i++)
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temp[i] = new CMatrix("", 3, 3);
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for (int k = 0; k < 4; k++)
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{
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for (int i = 1; i < 4; i++)
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{
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int j1 = 0;
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for (int j = 0; j < 4; j++)
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{
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if (k == j)
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continue;
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temp[k]->m_pData[i - 1][j1++]
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= this->m_pData[i][j];
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}
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}
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}
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double det = this->m_pData[0][0] * temp[0]->Determinant()
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- this->m_pData[0][1] * temp[1]->Determinant()
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+ this->m_pData[0][2] * temp[2]->Determinant()
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- this->m_pData[0][3] * temp[3]->Determinant();
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return det;
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}
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break;
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case 5:
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{
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CMatrix *temp[5];
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for (int i = 0; i < 5; i++)
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temp[i] = new CMatrix("", 4, 4);
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for (int k = 0; k < 5; k++)
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{
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for (int i = 1; i < 5; i++)
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{
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int j1 = 0;
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for (int j = 0; j < 5; j++)
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{
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if (k == j)
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continue;
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temp[k]->m_pData[i - 1][j1++]
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= this->m_pData[i][j];
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}
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}
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}
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double det = this->m_pData[0][0] * temp[0]->Determinant()
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- this->m_pData[0][1] * temp[1]->Determinant()
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+ this->m_pData[0][2] * temp[2]->Determinant()
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- this->m_pData[0][3] * temp[3]->Determinant()
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+ this->m_pData[0][4] * temp[4]->Determinant();
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return det;
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}
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case 6:
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case 7:
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case 8:
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case 9:
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case 10:
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case 11:
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case 12:
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default:
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{
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int DIM = m_rows;
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CMatrix **temp = new CMatrix*[DIM];
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for (int i = 0; i < DIM; i++)
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temp[i] = new CMatrix("", DIM - 1, DIM - 1);
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for (int k = 0; k < DIM; k++)
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{
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for (int i = 1; i < DIM; i++)
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{
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int j1 = 0;
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for (int j = 0; j < DIM; j++)
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{
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if (k == j)
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continue;
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temp[k]->m_pData[i - 1][j1++]
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= this->m_pData[i][j];
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}
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}
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}
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double det = 0;
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for (int k = 0; k < DIM; k++)
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{
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if ((k % 2) == 0)
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det = det + (this->m_pData[0][k]
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* temp[k]->Determinant());
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else
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det = det - (this->m_pData[0][k]
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* temp[k]->Determinant());
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}
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for (int i = 0; i < DIM; i++)
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delete temp[i];
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delete[] temp;
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return det;
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}
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break;
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}
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}
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CMatrix& operator =(const CMatrix &other)
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{
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if (this->m_rows != other.m_rows || this->m_cols != other.m_cols)
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{
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std::cout
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<< "WARNING: Assignment is taking place with by changing the number of rows and columns of the matrix";
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}
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for (int i = 0; i < m_rows; i++)
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delete[] m_pData[i];
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delete[] m_pData;
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m_rows = m_cols = 0;
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strcpy(m_name, other.m_name);
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m_rows = other.m_rows;
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m_cols = other.m_cols;
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m_pData = new double*[m_rows];
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for (int i = 0; i < m_rows; i++)
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m_pData[i] = new double[m_cols];
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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m_pData[i][j] = other.m_pData[i][j];
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}
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}
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return *this;
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}
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CMatrix CoFactor()
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{
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CMatrix cofactor("COF", m_rows, m_cols);
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if (m_rows != m_cols)
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return cofactor;
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if (m_rows < 2)
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return cofactor;
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else if (m_rows == 2)
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{
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cofactor.m_pData[0][0] = m_pData[1][1];
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cofactor.m_pData[0][1] = -m_pData[1][0];
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cofactor.m_pData[1][0] = -m_pData[0][1];
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cofactor.m_pData[1][1] = m_pData[0][0];
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return cofactor;
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}
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else if (m_rows >= 3)
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{
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int DIM = m_rows;
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CMatrix ***temp = new CMatrix**[DIM];
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for (int i = 0; i < DIM; i++)
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temp[i] = new CMatrix*[DIM];
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for (int i = 0; i < DIM; i++)
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for (int j = 0; j < DIM; j++)
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temp[i][j] = new CMatrix("", DIM - 1, DIM - 1);
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for (int k1 = 0; k1 < DIM; k1++)
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{
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for (int k2 = 0; k2 < DIM; k2++)
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{
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int i1 = 0;
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for (int i = 0; i < DIM; i++)
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{
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int j1 = 0;
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for (int j = 0; j < DIM; j++)
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{
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if (k1 == i || k2 == j)
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continue;
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temp[k1][k2]->m_pData[i1][j1++]
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= this->m_pData[i][j];
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}
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if (k1 != i)
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i1++;
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}
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}
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}
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bool flagPositive = true;
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for (int k1 = 0; k1 < DIM; k1++)
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{
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flagPositive = ((k1 % 2) == 0);
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for (int k2 = 0; k2 < DIM; k2++)
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{
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if (flagPositive == true)
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{
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cofactor.m_pData[k1][k2]
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= temp[k1][k2]->Determinant();
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flagPositive = false;
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}
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else
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{
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cofactor.m_pData[k1][k2]
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= -temp[k1][k2]->Determinant();
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flagPositive = true;
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}
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}
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}
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for (int i = 0; i < DIM; i++)
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for (int j = 0; j < DIM; j++)
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delete temp[i][j];
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for (int i = 0; i < DIM; i++)
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delete[] temp[i];
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delete[] temp;
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}
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return cofactor;
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}
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CMatrix Adjoint()
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{
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CMatrix cofactor("COF", m_rows, m_cols);
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CMatrix adj("ADJ", m_rows, m_cols);
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if (m_rows != m_cols)
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return adj;
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cofactor = this->CoFactor();
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// adjoint is transpose of a cofactor of a matrix
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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adj.m_pData[j][i] = cofactor.m_pData[i][j];
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}
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}
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return adj;
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}
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CMatrix Transpose()
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{
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CMatrix trans("TR", m_cols, m_rows);
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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trans.m_pData[j][i] = m_pData[i][j];
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}
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}
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return trans;
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}
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CMatrix Inverse()
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{
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CMatrix cofactor("COF", m_rows, m_cols);
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CMatrix inv("INV", m_rows, m_cols);
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if (m_rows != m_cols)
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return inv;
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// to find out Determinant
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double det = Determinant();
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cofactor = this->CoFactor();
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// inv = transpose of cofactor / Determinant
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for (int i = 0; i < m_rows; i++)
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{
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for (int j = 0; j < m_cols; j++)
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{
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inv.m_pData[j][i] = cofactor.m_pData[i][j] / det;
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}
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}
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return inv;
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}
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||
|
|
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", 6, 6);
|
||
|
|
CMatrix b("B", 6, 1);
|
||
|
|
a.FillSimulatedInput();
|
||
|
|
b.FillSimulatedInput();
|
||
|
|
std::cout << a << "\n Determinant : ";
|
||
|
|
std::cout << a.Determinant() << "\n";
|
||
|
|
std::cout << b << "\n Determinant : ";
|
||
|
|
std::cout << b.Determinant() << "\n";
|
||
|
|
CMatrix ainv = a.Inverse();
|
||
|
|
CMatrix q = a * ainv;
|
||
|
|
q.SetName("A * A'");
|
||
|
|
std::cout << q << "\n";
|
||
|
|
CMatrix x = ainv * b;
|
||
|
|
x.SetName("X");
|
||
|
|
std::cout << x << "\n";
|
||
|
|
CMatrix y = a * x; // we will get B
|
||
|
|
y.SetName("Y");
|
||
|
|
std::cout << y << "\n";
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
Enter Input For Matrix : B Rows: 6 Cols: 1
|
||
|
|
Input For Row: 1 Col: 1 = 9.41176
|
||
|
|
|
||
|
|
Input For Row: 2 Col: 1 = 15.7843
|
||
|
|
|
||
|
|
Input For Row: 3 Col: 1 = 22.7451
|
||
|
|
|
||
|
|
Input For Row: 4 Col: 1 = 29.902
|
||
|
|
|
||
|
|
Input For Row: 5 Col: 1 = 37.1569
|
||
|
|
|
||
|
|
Input For Row: 6 Col: 1 = 44.6078
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
|
||
|
|
Matrix : B Rows: 6 Cols: 1
|
||
|
|
|
||
|
|
| 9.41 |
|
||
|
|
| 15.78 |
|
||
|
|
| 22.75 |
|
||
|
|
| 29.90 |
|
||
|
|
| 37.16 |
|
||
|
|
| 44.61 |
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
Determinant : -1.#IND
|
||
|
|
|
||
|
|
|
||
|
|
Matrix : A * A' Rows: 6 Cols: 6
|
||
|
|
|
||
|
|
| 1.00 0.00 0.00 0.00 0.00 0.00 |
|
||
|
|
| 0.00 1.00 0.00 0.00 0.00 0.00 |
|
||
|
|
| 0.00 0.00 1.00 0.00 0.00 0.00 |
|
||
|
|
| 0.00 0.00 0.00 1.00 0.00 0.00 |
|
||
|
|
| 0.00 0.00 0.00 0.00 1.00 0.00 |
|
||
|
|
| 0.00 0.00 0.00 0.00 0.00 1.00 |
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
Matrix : X Rows: 6 Cols: 1
|
||
|
|
|
||
|
|
| 0.82 |
|
||
|
|
| 3.47 |
|
||
|
|
| -9.38 |
|
||
|
|
| 7.71 |
|
||
|
|
| -5.76 |
|
||
|
|
| 3.98 |
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
Matrix : Y Rows: 6 Cols: 1
|
||
|
|
|
||
|
|
| 9.41 |
|
||
|
|
| 15.78 |
|
||
|
|
| 22.75 |
|
||
|
|
| 29.90 |
|
||
|
|
| 37.16 |
|
||
|
|
| 44.61 |
|