package gaodai;
import java.util.List;
/**
* N阶行列式计算
* @author 邱万迟
*
*/
public class DeterminantCalculation {
public DeterminantCalculation(List<List<Double>> determinant){
this.determinant = determinant;
this.sign = 1;
}
private List<List<Double>> determinant;
private int sign;
private int caculateTimes;
/**
* 转置
*/
public void transpose(){
int lineNum = determinant.size();
int columnNum = determinant.get(0).size();
for(int i = 0; i < lineNum; i++){
for(int j = i; j < columnNum; j++){
double t = determinant.get(i).get(j);
determinant.get(i).set(j,determinant.get(j).get(i));
determinant.get(j).set(i,t);
}
}
}
/**
* 获取行列式的值
* @return
*/
public double getValue(){
double temp = 1.0;
for(int i = 0; i < determinant.size(); i++){
temp *= determinant.get(i).get(i);
}
return Math.round((temp * getSign()) * 100)/100.0;
}
/**
* a行与b行互换(两行互换)
* @param determinant 行列式
* @param a 行号
* @param b 行号
* @throws Exception
*/
public void changeLine(int a,int b) throws Exception{
if(a < 1 || a > determinant.size() || b < 1 || b > determinant.size()){
throw new Exception("输入的行号不合法");
}
List<Double> aLine = determinant.get(a - 1);
List<Double> bLine = determinant.get(b - 1);
determinant.set(a - 1, bLine);
determinant.set(b - 1, aLine);
changeSign();
System.out.println("第" + a + "行与" + b + "行互换");
}
/**
* 两列互换
* @param a
* @param b
* @throws Exception
*/
public void changeColumn(int a,int b) throws Exception{
if(a < 1 || a > determinant.get(0).size() || b < 1 || b > determinant.get(0).size()){
throw new Exception("输入的列号不合法");
}
for(int i = 0; i < determinant.size(); i++){
double temp = determinant.get(i).get(a - 1);
determinant.get(i).set(a - 1,determinant.get(i).get(b - 1));
determinant.get(i).set(b - 1,formateDouble(temp));
}
changeSign();
}
/**
* a行加到b行上
* @param a
* @param b
* @throws Exception
*/
public void lineAdd2OtherLine(int a, int b) throws Exception{
lineMultiplyNumAdd2OtherLine(1, a, b);
}
/**
* 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 > determinant.size() || b < 1 || b > determinant.size()){
throw new Exception("输入的行号不合法");
}
List<Double> aLine = determinant.get(a - 1);
List<Double> bLine = determinant.get(b - 1);
for(int i = 0; i < bLine.size(); i++){
double temp = bLine.get(i) + aLine.get(i) * number;
bLine.set(i, formateDouble(temp));
}
System.out.println("第" + a + "行乘以" + number + "加到第" + b + "行:");
print();
}
public double formateDouble(double data){
return Math.round(data * 10000000000L)/10000000000.0;
}
/**
* a列加到b列
* @param a
* @param b
*/
public void columnAdd2OtherColumn(int a, int b){
columnMultiplyNumAdd2OtherColumn(1, a, b);
}
/**
* 第a列乘以number 加到第b列上
* @param number 乘以的数
* @param a行号
* @param b行号
*/
public void columnMultiplyNumAdd2OtherColumn(double number,int a, int b){
for(int i = 0; i < determinant.size(); i++){
double temp = determinant.get(i).get(b - 1) + determinant.get(i).get(a - 1) * number;
determinant.get(i).set(b - 1, temp);
}
}
/**
* 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 < determinant.size(); i++){
for(int j = 0; j < i; j++){
if(determinant.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;
}
}
//System.out.println("isUpperTriangle?>>>>>>>>>>>" + hasCaculate);
return hasCaculate;
}
/**
* @throws Exception
* 变为上三角
* @throws
*/
public void chang2UpperTriangle() throws Exception{
if(!isCaculate()){
return;
}
caculateTimes++;
System.out.println("----------------------------------第" + caculateTimes + "次计算----------------------------------");
for(int i = 0; i < determinant.size(); i++){
for(int j = i + 1; j < determinant.size(); j++){
if(determinant.get(i).get(i) == 0){//每一行在对角线上元素是零就互换行
changeLine(i + 1, j + 1);
print();
continue;
}
double multiplyNum = -1 * determinant.get(j).get(i) / determinant.get(i).get(i);
if(multiplyNum == 0){
continue;
}
this.lineMultiplyNumAdd2OtherLine(multiplyNum, (i + 1), (j + 1));
}
}
print();
chang2UpperTriangle();
}
/**
* 获取a行b列元素所在的下一个非零元素所在的行
* @param a
* @param b
*/
public int getNotZeroLineByColumn(int a,int b){
for(int i = a + 1; i < determinant.size(); i++){
if(determinant.get(i).get(b) != 0){
return i;
}
}
return 0;
}
/**
* 改变符号
*/
private void changeSign(){
this.sign = this.sign * -1;
}
public void print(){
int i = 0,j = 0;
for(List<Double> line : determinant){
for(double element : line){
System.out.print(element);
//System.out.print(Math.round(element*100)/100.0);
System.out.print("(" + i + "," + j + ") ");
System.out.print(" ");
j++;
}
System.out.println();
i++;
j = 0;
}
System.out.println();
}
public List<List<Double>> getDeterminant() {
return determinant;
}
public void setDeterminant(List<List<Double>> determinant) {
this.determinant = determinant;
}
public int getSign() {
return sign;
}
}
package gaodai;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import org.apache.commons.lang.StringUtils;
public class Test {
public static void main(String[] args) {
int lineNum = 0;
Scanner scanner = new Scanner(System.in);
boolean flag = true;
System.out.println("请输入行列式的阶数,系统会随机生成行列式里的数：");
while(flag){
String num = scanner.next();
if(StringUtils.isNotBlank(num)){
try {
lineNum = Integer.valueOf(num);
} catch (Exception e) {
lineNum = 0;
}
if(lineNum < 1){
System.out.println("请重新输入(需是整数且大于零)");
}else{
flag = false;
}
}else{
System.out.println("请重新输入(需是整数且大于零)");
}
}
int columnNum = lineNum;
List<List<Double>> result = new ArrayList<List<Double>>();
for(int i = 0; i < lineNum; i++){
List<Double> temp = new ArrayList<Double>();
for(int j = 0; j < columnNum; j++){
temp.add((double) (int)(Math.random()*10 + 1));
}
result.add(temp);
}
DeterminantCalculation determinant = new DeterminantCalculation(result);
System.out.println("初始化行列式:");
determinant.print();
determinant.transpose();
determinant.print();
try {
determinant.chang2UpperTriangle();
} catch (Exception e) {
e.printStackTrace();
}
determinant.print();
System.out.println("行列式值为:" + determinant.getValue());
}
}
JAVA实现的N阶行列式计算，一起分享学习，有不足之处还望指正批评。