解线性方程组
编程技术 / houtizong 发布于 2年前 210
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>();result.add(line);for(int j = 0; j <= columnNum; j++){line.add(Double.valueOf(lineDataArr[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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