# 矩阵求逆（JAVA）初等行变换

```package gaodai.matrix;

import gaodai.determinant.DeterminantCalculation;

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

/**
* 矩阵求逆(初等行变换)
* @author 邱万迟
*
*/
public class InverseOfMatrix {

private List<List<Double>> matrix;
private int lineNum;
private int columnNum;

public InverseOfMatrix(List<List<Double>> data){
matrix = data;
lineNum = data.size();
columnNum = data.get(0).size();
}

public void caculate() throws Exception{

//1.非方正不能求逆
//2.方正的行列式值为零不能求逆
if( lineNum != columnNum){
throw new Exception("此矩阵不能求逆>>>>>>>>>>>>>>>>>");
}
List<List<Double>> tempList = new ArrayList<List<Double>>();
for(List<Double> l : matrix){
List<Double> newList = new ArrayList<Double>();
}

DeterminantCalculation d = new DeterminantCalculation(tempList);
d.chang2UpperTriangle();
double result = d.getValue();
if(result == 0){
throw new Exception("此矩阵不能求逆>>>>>>>>>>>>>>>>>");
}

//增加单位矩阵
for(int i = 0; i < lineNum; i++){
List<Double> list = matrix.get(i);
for(int j = 0; j < columnNum; j++){
if(i == j){
}else{
}
}
}
print();
chang2UpperTriangle();//化为上三角
changeReducedMatrix();//化为约化矩阵
print();
}

public void getValue(){
boolean flag = true;
for(int i = 0; i < lineNum; i++){
if(matrix.get(i).get(i) == 0){
flag = false;
}
if(!flag){
break;
}
}

if(!flag){
System.out.println("此矩阵不可逆>>>>>>>>>>>>>>");
}else{

for(int i = 0; i < lineNum; i++){
List<Double> list = matrix.get(i);
for(int j = 0; j < columnNum; j++){
list.remove(0);
}
}
System.out.println("逆矩阵为>>>>>>>>>>>>>>>>>");
print();
}
}

/**
* 打印
*/
public void print() {
int i = 0, j = 0;
for (List<Double> line : matrix) {
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 < matrix.size(); i++) {
for (int j = 0; j < i; j++) {
if (matrix.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 = lineNum;
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 * matrix.get(j).get(i) / matrix.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 < lineNum; i++){//行
if(i == 0){
//continue;
}
List<Double> temp = matrix.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 <= columnNum; 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 < lineNum; t++){//行
if(t == i || matrix.get(t).get(j) == 0){//本列的其他行
continue;
}

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

/**
* 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 > matrix.size() || b < 1 || b > matrix.size()) {
throw new Exception("输入的行号不合法");
}
List<Double> aLine = matrix.get(a - 1);
List<Double> bLine = matrix.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:");
}

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

System.out.println("请输入矩阵的行数与列数,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>> matrix = new ArrayList<List<Double>>();
for(int i = 0; i < lineNum; i++){
System.out.println("请输入第" + (i + 1) + "行的数,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++){
}
}

InverseOfMatrix m = new InverseOfMatrix(matrix);
m.print();
try {
m.caculate();
m.getValue();
} catch (Exception e) {
e.printStackTrace();
}
}
}
```