原文链接: C# 实数矩阵行列式计算
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace MatrixHandler {
class Num {
int numerator = 0;
int denominator = 1;
public static Num operator *(Num n1, Num n2) {
return new Num(n1.Numerator * n2.Numerator, n1.Denominator * n2.Denominator);
}
public static Num operator /(Num n1, Num n2) {
if (n1.Numerator < 0 && n2.Numerator < 0)
return new Num(-n1.Numerator * n2.Denominator, n1.Denominator * -n2.Numerator);
return new Num(n1.Numerator * n2.Denominator, n1.Denominator * n2.Numerator);
}
public static Num operator +(Num n1, Num n2) {
return new Num(n1.Numerator * n2.Denominator + n2.Numerator * n1.Denominator, n1.Denominator * n2.Denominator);
}
public static Num operator -(Num n1, Num n2) {
return new Num(n1.Numerator * n2.Denominator - n2.Numerator * n1.Denominator, n1.Denominator * n2.Denominator);
}
public static Num operator -(Num n) {
return new Num(-n.Numerator, n.Denominator);
}
public Num getCopy() {
return new Num(Numerator, Denominator);
}
public int Numerator {
get {
return numerator;
}
set {
numerator = value;
}
}
public int Denominator {
get {
return denominator;
}
set {
denominator = value;
}
}
public Num(int numerator, int denominator) {
this.Numerator = numerator;
this.Denominator = denominator;
reduce();
}
public Num() { }
public Num(string s) {
if (s.IndexOf('.') != -1) {
string[] str = s.Split('.');
Numerator = Convert.ToInt32(str[0] + str[1]);
Denominator = tenPow(str[1].Length);
} else if (s.IndexOf('/') != -1) {
string[] str = s.Split('/');
Numerator = Convert.ToInt32(str[0]);
Denominator = Convert.ToInt32(str[1]);
} else {
Numerator = Convert.ToInt32(s);
}
reduce();
}
public Num(int val) {
Denominator = 1;
Numerator = val;
}
public override string ToString() {
return denominator == 1 ? Numerator + "" : Numerator + "/" + Denominator;
}
public int gcd(int a, int b) {
int m = Math.Abs(a);
int n = Math.Abs(b);
int t;
while (m != 0) {
t = n % m;
n = m;
m = t;
}
return n;
}
private void reduce() {
int t = gcd(Numerator, Denominator);
Denominator /= t;
Numerator /= t;
if (Numerator == 0)
Denominator = 1;
if (Numerator > 0 != Denominator > 0) {
Numerator = -Math.Abs(Numerator);
Denominator = Math.Abs(Denominator);
}
}
private int tenPow(int n) {
int res = 1;
while (n != 0) {
res *= 10;
--n;
}
return res;
}
}
}
矩阵类
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace MatrixHandler {
class Matrix {
Num[,] nums;
int n;
internal Num[,] Nums {
get {
return nums;
}
set {
nums = value;
}
}
public int N {
get {
return n;
}
set {
n = value;
}
}
public Matrix(Num[,] nums,int n) {
this.Nums = nums;
this.N = n;
}
//余子式
public Matrix getM(int x,int y) {
if (N < 2) return null;
Num[,] temp = new Num[N - 1, N - 1];
for(int i = 0; i < N; ++i) {
for(int j = 0; j < N; ++j) {
if (i < x && j < y) { temp[i, j] = Nums[i, j].getCopy(); }
if(i<x && j > y) { temp[i, j-1] = Nums[i, j].getCopy(); }
if(i>x && j < y) { temp[i - 1, j] = Nums[i, j].getCopy(); }
if(i>x && j > y) { temp[i - 1, j - 1] = Nums[i, j].getCopy(); }
}
}
return new Matrix(temp, N - 1);
}
public Num getVal() {
if (N == 1)
return Nums[0, 0];
if (N == 2)
return Nums[0, 0] * Nums[1, 1] - Nums[0, 1] * Nums[1, 0];
Num res = new Num(0);
int t = 1;
for(int i = 0; i < N; ++i) {
res = res + nums[0,i] * (new Num(t)) * (getM(0, i).getVal().getCopy());
t *= -1;
}
return res;
}
public Matrix getInverse() {
Num val = getVal().getCopy();
Num[,] temp = new Num[N, N];
Num[,] com = getCompany().Nums;
for (int i = 0; i < N; ++i) {
for(int j = 0; j < N; ++j) {
temp[i,j] = (com[i, j]/val).getCopy();
}
}
Matrix res = new Matrix(temp,n);
return res;
}
public Matrix getCompany() {
Num[,] temp = new Num[N,N];
for(int i = 0; i < N; ++i) {
for(int j = 0; j < N; ++j) {
int t = (i + j) % 2 == 0 ? 1 : -1;
temp[j, i] = ( this.getM(i,j).getVal() * (new Num(t))).getCopy();
}
}
Matrix res=new Matrix(temp,N);
return res;
}
public override string ToString() {
string res="";
int x=0, y=0;
for (x = 0; x < N; ++x) {
for (y = 0; y < N; ++y) {
res += Nums[x, y];
if (y == N - 1) res += "\n";
else res += "\t";
}
}
return res;
}
}
}
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace MatrixHandler {
class Program {
delegate void Handler();
static void Main(string[] args) {
while (true) {
mainView();
}
}
public static void mainView(){
Console.WriteLine("实矩阵行列式计算,请选择功能:\n1,行列式求值\t2,矩阵求逆\t3,矩阵求伴随");
try {
int flag = Convert.ToInt32(Console.ReadLine());
Handler[] h = new Handler[3];
h[0] = new Handler(getVal);
h[1] = new Handler(getInverse);
h[2] = new Handler(getCompany);
Console.WriteLine("请输入矩阵");
h[flag - 1].Invoke();
} catch (Exception) {
Console.WriteLine("格式错误!数字之间只能输入一个空格!且本程序只能处理方阵.");
}
}
public static void getVal() {
Matrix m = getMatrix();
Console.WriteLine("输入的行列式为:\n"+m+"该行列式的值为:"+m.getVal());
}
public static void getInverse() {
Matrix m = getMatrix();
if (m.getVal().Numerator == 0)
Console.WriteLine("该矩阵不可逆!");
else
Console.WriteLine("输入的矩阵为:\n" + m + "该矩阵的逆矩阵为:\n" + m.getInverse());
}
public static void getCompany() {
Matrix m = getMatrix();
Console.WriteLine("输入的矩阵为:\n" + m + "该矩阵的伴随矩阵为:\n" + m.getCompany());
}
public static Matrix getMatrix() {
string s = Console.ReadLine();
string[] row = s.Split(' ');
int n = row.Length;
Num[,] nums = new Num[n,n];
for (int i = 0; i < n; ++i)
nums[0,i] = new Num(row[i]).getCopy();
for(int i = 1; i < n; ++i) {
string st = Console.ReadLine();
string[] rowt = st.Split(' ');
for(int j=0;j<n;++j)
nums[i, j] = new Num(rowt[j]).getCopy();
}
return new Matrix(nums, n);
}
}
}
