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C#中矩陣運(yùn)算方法實(shí)例分析

這篇文章主要介紹了C#中矩陣運(yùn)算方法,實(shí)例分析了通過C#實(shí)現(xiàn)矩陣的初始化、轉(zhuǎn)置矩陣、求逆矩陣等各種常用的操作技巧,具有一定參考借鑒價(jià)值,需要的朋友可以參考下

本文實(shí)例講述了C#中矩陣運(yùn)算方法。分享給大家供大家參考。具體分析如下：

一、測試環(huán)境：

主機(jī):XP

開發(fā)環(huán)境:VS2008

二、功能:

在C#中實(shí)現(xiàn)矩陣運(yùn)算

三、源代碼：

using System;

using System.Collections.Generic;

using System.ComponentModel;

using System.Data;

using System.Drawing;

using System.Linq;

using System.Text;

using System.Windows.Forms;

//矩陣數(shù)據(jù)結(jié)構(gòu)

//二維矩陣

class _Matrix

{

public int m;

public int n;

public float[] arr;

//初始化

public _Matrix()

{

m = 0;

n = 0;

}

public _Matrix(int mm,int nn)

{

m = mm;

n = nn;

}

//設(shè)置m

public void set_mn(int mm,int nn)

{

m = mm;

n = nn;

}

//設(shè)置m

public void set_m(int mm)

{

m = mm;

}

//設(shè)置n

public void set_n(int nn)

{

n = nn;

}

//初始化

public void init_matrix()

{

arr = new float[m * n];

}

//釋放

public void free_matrix()

{

//delete [] arr;

}

//讀取i,j坐標(biāo)的數(shù)據(jù)

//失敗返回-31415,成功返回值

public float read(int i,int j)

{

if (i >= m || j >= n)

{

return -31415;

}

//return *(arr + i * n + j);

return arr[i * n + j];

}

//寫入i,j坐標(biāo)的數(shù)據(jù)

//失敗返回-1,成功返回1

public int write(int i,int j,float val)

{

if (i >= m || j >= n)

{

return -1;

}

arr[i * n + j] = val;

return 1;

}

};

//二維運(yùn)算類

class _Matrix_Calc

{

//初始化

public _Matrix_Calc()

{

}

//C = A + B

//成功返回1,失敗返回-1

public int add(ref _Matrix A,ref _Matrix B,ref _Matrix C)

{

int i = 0;

int j = 0;

//判斷是否可以運(yùn)算

if (A.m != B.m || A.n != B.n ||

A.m != C.m || A.n != C.n)

{

return -1;

}

//運(yùn)算

for (i = 0;i < C.m;i++)

{

for (j = 0;j < C.n;j++)

{

C.write(i,j,A.read(i,j) + B.read(i,j));

}

}

return 1;

}

//C = A - B

//成功返回1,失敗返回-1

public int subtract(ref _Matrix A,ref _Matrix B, ref _Matrix C)

{

int i = 0;

int j = 0;

//判斷是否可以運(yùn)算

if (A.m != B.m || A.n != B.n ||

A.m != C.m || A.n != C.n)

{

return -1;

}

//運(yùn)算

for (i = 0;i < C.m;i++)

{

for (j = 0;j < C.n;j++)

{

C.write(i,j,A.read(i,j) - B.read(i,j));

}

}

return 1;

}

//C = A * B

//成功返回1,失敗返回-1

public int multiply(ref _Matrix A, ref _Matrix B, ref _Matrix C)

{

int i = 0;

int j = 0;

int k = 0;

float temp = 0;

//判斷是否可以運(yùn)算

if (A.m != C.m || B.n != C.n ||

A.n != B.m)

{

return -1;

}

//運(yùn)算

for (i = 0;i < C.m;i++)

{

for (j = 0;j < C.n;j++)

{

temp = 0;

for (k = 0;k < A.n;k++)

{

temp += A.read(i,k) * B.read(k,j);

}

C.write(i,j,temp);

}

}

return 1;

}

//行列式的值,只能計(jì)算2 * 2,3 * 3

//失敗返回-31415,成功返回值

public float det(ref _Matrix A)

{

float value = 0;

//判斷是否可以運(yùn)算

if (A.m != A.n || (A.m != 2 && A.m != 3))

{

return -31415;

}

//運(yùn)算

if (A.m == 2)

{

value = A.read(0,0) * A.read(1,1) - A.read(0,1) * A.read(1,0);

}

else

{

value = A.read(0,0) * A.read(1,1) * A.read(2,2) +

A.read(0,1) * A.read(1,2) * A.read(2,0) +

A.read(0,2) * A.read(1,0) * A.read(2,1) -

A.read(0,0) * A.read(1,2) * A.read(2,1) -

A.read(0,1) * A.read(1,0) * A.read(2,2) -

A.read(0,2) * A.read(1,1) * A.read(2,0);

}

return value;

}

//求轉(zhuǎn)置矩陣,B = AT

//成功返回1,失敗返回-1

public int transpos(ref _Matrix A,ref _Matrix B)

{

int i = 0;

int j = 0;

//判斷是否可以運(yùn)算

if (A.m != B.n || A.n != B.m)

{

return -1;

}

//運(yùn)算

for (i = 0;i < B.m;i++)

{

for (j = 0;j < B.n;j++)

{

B.write(i,j,A.read(j,i));

}

}

return 1;

}

//求逆矩陣,B = A^(-1)

//成功返回1,失敗返回-1

public int inverse(ref _Matrix A, ref _Matrix B)

{

int i = 0;

int j = 0;

int k = 0;

_Matrix m = new _Matrix(A.m,2 * A.m);

float temp = 0;

float b = 0;

//判斷是否可以運(yùn)算

if (A.m != A.n || B.m != B.n || A.m != B.m)

{

return -1;

}

/*

//如果是2維或者3維求行列式判斷是否可逆

if (A.m == 2 || A.m == 3)

{

if (det(A) == 0)

{

return -1;

}

}

*/

//增廣矩陣m = A | B初始化

m.init_matrix();

for (i = 0;i < m.m;i++)

{

for (j = 0;j < m.n;j++)

{

if (j <= A.n - 1)

{

m.write(i,j,A.read(i,j));

}

else

{

if (i == j - A.n)

{

m.write(i,j,1);

}

else

{

m.write(i,j,0);

}

}

}

}

//高斯消元

//變換下三角

for (k = 0;k < m.m - 1;k++)

{

//如果坐標(biāo)為k,k的數(shù)為0,則行變換

if (m.read(k,k) == 0)

{

for (i = k + 1;i < m.m;i++)

{

if (m.read(i,k) != 0)

{

break;

}

}

if (i >= m.m)

{

return -1;

}

else

{

//交換行

for (j = 0;j < m.n;j++)

{

temp = m.read(k,j);

m.write(k,j,m.read(k + 1,j));

m.write(k + 1,j,temp);

}

}

}

//消元

for (i = k + 1;i < m.m;i++)

{

//獲得倍數(shù)

b = m.read(i,k) / m.read(k,k);

//行變換

for (j = 0;j < m.n;j++)

{

temp = m.read(i,j) - b * m.read(k,j);

m.write(i,j,temp);

}

}

}

//變換上三角

for (k = m.m - 1;k > 0;k--)

{

//如果坐標(biāo)為k,k的數(shù)為0,則行變換

if (m.read(k,k) == 0)

{

for (i = k + 1;i < m.m;i++)

{

if (m.read(i,k) != 0)

{

break;

}

}

if (i >= m.m)

{

return -1;

}

else

{

//交換行

for (j = 0;j < m.n;j++)

{

temp = m.read(k,j);

m.write(k,j,m.read(k + 1,j));

m.write(k + 1,j,temp);

}

}

}

//消元

for (i = k - 1;i >= 0;i--)

{

//獲得倍數(shù)

b = m.read(i,k) / m.read(k,k);

//行變換

for (j = 0;j < m.n;j++)

{

temp = m.read(i,j) - b * m.read(k,j);

m.write(i,j,temp);

}

}

}

//將左邊方陣化為單位矩陣

for (i = 0;i < m.m;i++)

{

if (m.read(i,i) != 1)

{

//獲得倍數(shù)

b = 1 / m.read(i,i);

//行變換

for (j = 0;j < m.n;j++)

{

temp = m.read(i,j) * b;

m.write(i,j,temp);

}

}

}

//求得逆矩陣

for (i = 0;i < B.m;i++)

{

for (j = 0;j < B.m;j++)

{

B.write(i,j,m.read(i,j + m.m));

}

}

//釋放增廣矩陣

m.free_matrix();

return 1;

}

};

namespace test

{

public partial class Form1 : Form

{

double zk;

double xkg, pkg, kk, xk, pk, q, r;

public Form1()

{

InitializeComponent();

xk = 0;

pk = 0;

q = 0.00001;

r = 0.0001;

int i = 0;

int j = 0;

int k = 0;

_Matrix_Calc m_c = new _Matrix_Calc();

//_Matrix m1 = new _Matrix(3,3);

//_Matrix m2 = new _Matrix(3,3);

//_Matrix m3 = new _Matrix(3,3);

_Matrix m1 = new _Matrix(2, 2);

_Matrix m2 = new _Matrix(2, 2);

_Matrix m3 = new _Matrix(2, 2);

//初始化內(nèi)存

m1.init_matrix();

m2.init_matrix();

m3.init_matrix();

//初始化數(shù)據(jù)

k = 1;

for (i = 0;i < m1.m;i++)

{

for (j = 0;j < m1.n;j++)

{

m1.write(i,j,k++);

}

}

for (i = 0;i < m2.m;i++)

{

for (j = 0;j < m2.n;j++)

{

m2.write(i,j,k++);

}

}

m_c.multiply(ref m1,ref m2, ref m3);

//output.Text = Convert.ToString(m3.read(1,1));

output.Text = Convert.ToString(m_c.det(ref m1));

}

/*

private void button1_Click(object sender, EventArgs e)

{

zk = Convert.ToDouble(input.Text);

//時(shí)間方程

xkg = xk;

pkg = pk + q;

//狀態(tài)方程

kk = pkg / (pkg + r);

xk = xkg + kk * (zk - xkg);

pk = (1 - kk) * pkg;

//輸出

output.Text = Convert.ToString(xk);

}

private void textBox1_TextChanged(object sender, EventArgs e)

{

}

* */

}

}

希望本文所述對(duì)大家的C#程序設(shè)計(jì)有所幫助。

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