inv.cpp

用矩阵变换法求逆矩阵 C++,已通过测试

// inv.cpp : Defines the entry point for the console application.
//


#include "stdafx.h"
#include "inv.h"

#ifdef _DEBUG
#define new DEBUG_NEW
#undef THIS_FILE
static char THIS_FILE[] = __FILE__;
#endif

/////////////////////////////////////////////////////////////////////////////

 //用矩阵变换法求逆矩阵

#include<iostream>
using namespace std;
class Matrix
{
public:

    void SetSize( void );
    void Initial( void );
    void Assign( void );
    void Display( void );
    void converse( void );
    void Show( void );

private:

    int Row;
    int Column;
    float MatrixA[100] [200];
};

 

//set matrix size

void Matrix::SetSize( void )
{
    int n;
    cout << "Please input a n*n Matrix to be converse:" << endl << "n=";
    cin >> n;
    Row = Column = n;
}

//initilize matrix data

void Matrix::Initial( void )
{
    int i( 0 ), j( 0 );
    for ( i = 0; i < Row; i++ )
    {
        for ( j = 0; j < Column; j++ )
        {
            MatrixA[i] [j] = float( 0.0 );
            MatrixA[i] [Column + j] = float( i == j ? 1.0 : 0.0 );
        }
    }
}

//input matrix data

void Matrix::Assign( void )
{
    int i( 0 ), j( 0 );
    cout << "Please input Matrix data:" << endl;
    for ( i = 0; i < Row; i++ )
    {
        for ( j = 0; j < Column; j++ )
        {
            cout << "Row=" << i << "," << "Column=" << j << endl;
            cin >> MatrixA[i] [j];
        }
    }
}

//show inverse process  

void Matrix::Show( void )
{
    int i( 0 ), j( 0 );
    cout << endl;
    for ( i = 0; i < Row; i++ )
    {
        for ( j = 0; j < 2 * Column; j++ )
        {
            cout << MatrixA[i] [j] << " ";
        }
        cout << endl;
    }
}

//display matrix data

void Matrix::Display()
{
    int i( 0 ), j( 0 );
    cout << "Matrix A:" << endl;
    for ( i = 0; i < Row; i++ )
    {
        for ( j = 0; j < Column; j++ )
        {
            cout << MatrixA[i] [j] << " ";
        }
        cout << endl;
    }
    cout << "converse Matrix:" << endl;
    for ( i = 0; i < Row; i++ )
    {
        for ( j = Column; j < 2 * Column; j++ )
        {
            cout << MatrixA[i] [j] << " ";
        }
        cout << endl;
    }
}

 //converse matrix

void Matrix::converse( void )
{
    int i( 0 ), j( 0 ), n( 0 ), i1( 0 ), i2( 0 ), j1( 0 );
    static int i3( 0 );
    float temp( 0.0 );
    Show();
    for ( i = 0; i < Row; i++ )
    {
        if ( MatrixA[i] [i] == 0 ) //If the number on the cross of
        {
//the current line is zero,swap the line with another one
		    i3++;
            for ( j = 0; j < 2 * Column; j++ )
            {
                temp = MatrixA[i] [j];
                MatrixA[i] [j] = MatrixA[i3] [j];
                MatrixA[i3] [j] = temp;
            }
            Show();
            i--;
            continue;
        }
        Show();
 
        //change the number on the cross to one
        if ( MatrixA[i] [i] != 1 )
        {
            for ( j = 2 * Column - 1; j >= 0; j-- )
            {
                MatrixA[i] [j] /= MatrixA[i] [i];
            }
			Show();

//将矩阵变成上对角阵
            for ( i1 = i + 1; i1 < Row; i1++ )
            {
                for ( j1 = 2 * Column; j1 >= i; j1-- )
                {
                    MatrixA[i1] [j1] -= MatrixA[i] [j1] * MatrixA[i1] [i];
                }
                Show();
            }
        }
}

//将上对角阵变成单位阵

    for ( i = 0; i < Row - 1; i++ )
    {
        for ( i2 = i; i2 < Row - 1; i2++ )
        {
            for ( j = 2 * Column - 1; j >= 0; j-- )
            {
                MatrixA[i] [j] -= MatrixA[i] [i2 + 1] * MatrixA[i2 + 1] [j];
            }
        }
 
        Show();
    }
}

int main( void )
{
    Matrix Matrix1;
    cout << "converse Matrix!" << endl << "Program designed by Yang Yuan." << endl << endl;
    Matrix1.SetSize();
    Matrix1.Initial();
    Matrix1.Assign();
    Matrix1.converse();
    Matrix1.Display();
    return 0;
}