用矩阵变换法求逆矩阵

王朝other·作者佚名  2006-01-09
窄屏简体版  字體: |||超大  

//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 Zang Junheng." << endl << endl;

Matrix1.SetSize();

Matrix1.Initial();

Matrix1.Assign();

Matrix1.converse();

Matrix1.Display();

return 0;

}

 
 
 
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