# 解线性方程组

```package gaodai.matrix;

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Test {

public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

System.out.println("请输入方程的个数与未知量的个数,用逗号分隔:");

String sn = scanner.next();
String[] snArr = sn.split(",");
int lineNum = Integer.valueOf(snArr[0]);
int columnNum = Integer.valueOf(snArr[1]);
List<List<Double>> result = new ArrayList<List<Double>>();
for(int i = 0; i < lineNum; i++){
System.out.println("请输入第" + (i + 1) + "个方程的全部系数(未知量的系数跟常数项系数),用逗号分隔:");
String lineData = scanner.next();
String[] lineDataArr = lineData.split(",");
List<Double> line = new ArrayList<Double>();
for(int j = 0; j <= columnNum; j++){
}
}

Matrix m = new Matrix(result);
m.print();
try {
m.chang2UpperTriangle();//化为上三角
m.changeReducedMatrix();//化为约化矩阵
m.clearZeroLine();//去除零行
m.getValue();//判断是否有解
} catch (Exception e) {
e.printStackTrace();
}
}
}
```

```package gaodai.matrix;

import java.util.List;

/**
* 矩阵
* @author 邱万迟
*
*/
public class Matrix {

private int s;//方程的未知个数 + 1(即包括常数项)
private int r;//方程的个数

public Matrix(List<List<Double>> data){
result = data;
this.r = data.size();
this.s = data.get(0).size();
}

private List<List<Double>> result;

/**
* a行与b行互换(两行互换)
* @param a 行号
* @param b 行号
* @throws Exception
*/
public void changeLine(int a, int b) throws Exception {
if (a < 1 || a > result.size() || b < 1 || b > result.size()) {
throw new Exception("输入的行号不合法");
}
List<Double> aLine = result.get(a - 1);
List<Double> bLine = result.get(b - 1);

result.set(a - 1, bLine);
result.set(b - 1, aLine);
System.out.println("第" + a + "行与" + b + "行互换");
}

/**
* 第a行乘以number 加到第b行上
* @param number 乘以的数
* @param a行号
* @param b行号
* @throws Exception
*/
public void lineMultiplyNumAdd2OtherLine(double number, int a, int b) throws Exception {
if (a < 1 || a > result.size() || b < 1 || b > result.size()) {
throw new Exception("输入的行号不合法");
}
List<Double> aLine = result.get(a - 1);
List<Double> bLine = result.get(b - 1);

for (int i = 0; i < bLine.size(); i++) {
double temp = bLine.get(i) + aLine.get(i) * number;
bLine.set(i, temp);
}
System.out.println("第" + a + "行乘以" + number + "加到第" + b + "行:");
}

/**
* 打印
*/
public void print() {
int i = 0, j = 0;
for (List<Double> line : result) {
for (double element : line) {
System.out.print(element);
System.out.print("(" + i + "," + j + ")  ");
System.out.print("  ");
j++;
}
System.out.println();
i++;
j = 0;
}
System.out.println();
}

/**
* 校验是否是上三角，不是就的继续计算
*
* @return
*/
public boolean isCaculate() {
boolean hasCaculate = false;
for (int i = 0; i < result.size(); i++) {
for (int j = 0; j < i; j++) {
if (result.get(i).get(j) != 0.0) {
System.out.println("(" + (i + 1) + "," + (j + 1) + ")元素值不为零");
hasCaculate = true;
break;
}
}
if (hasCaculate) {
break;
}
}
return hasCaculate;
}

private int caculateTimes;

/**
* 化为上三角
* @throws Exception
*/
public void chang2UpperTriangle() throws Exception {

if (!isCaculate()) {
return;
}

int min = r < s ? r : s;

caculateTimes++;
System.out.println("--------------第" + caculateTimes + "次计算--------------");
for (int i = 0; i < min; i++) {
for (int j = i + 1; j < min; j++) {
double multiplyNum = -1 * result.get(j).get(i) / result.get(i).get(i);
if (multiplyNum == 0) {
continue;
}
this.lineMultiplyNumAdd2OtherLine(multiplyNum, (i + 1), (j + 1));
print();
}
}
print();
chang2UpperTriangle();
}

/**
* 变为约化矩阵
*/
public void changeReducedMatrix() throws Exception{
for(int i = 0; i < r; i++){//行
if(i == 0){
continue;
}
List<Double> temp = result.get(i);

for(Double d : temp){
if(d == 0){
continue;
}
double multiplyNum = 1.0 / d;

for(int a = 0; a < temp.size(); a++){
temp.set(a, temp.get(a) * multiplyNum);
}
break;
}
print();
for(int j = 0; j <= s; j++){//列

if(temp.get(j) != 0){//这个数不为零 ，此数为第 i行第j列
for(int t = 0; t < r; t++){//行
if(t == i || result.get(t).get(j) == 0){//本列的其他行
continue;
}

double multiplyNum = -1 * result.get(t).get(j) / temp.get(j);
this.lineMultiplyNumAdd2OtherLine(multiplyNum, (i + 1), (t + 1));
print();
}
break;
}
}
}
}

/**
* 去除零行
*/
public void clearZeroLine(){
for(int i = 0; i < result.size(); i++){
boolean flag = true;
List<Double> temp = result.get(i);
for(Double d : temp){
if(d != 0){
flag = false;
}
}
if(flag){
result.remove(i);
}
}

this.r = result.size();
}

public void getValue(){

if(result.get(r - 1).get(s - 2) == 0 && result.get(r - 1).get(s - 1) != 0){
System.out.println("此方程组无解!!!!!!!!!!!!!!!!!!!!!!!!");
return;
}

if(r < (s - 1)){
System.out.println("此方程组有无数解!!!!!!!!!!!!");
return;
}

System.out.println("此方程组有唯一解!!!!!!!!!!!!!");
for(int i = 0; i < result.size(); i++){
List<Double> temp = result.get(i);
System.out.println("x" + (i + 1) + "=" + temp.get(temp.size() - 1));
}
}
}
```

JAVA实现的解线性方程组

1.无解

2.有唯一解，解为。。。

3.有无穷解

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