解线性方程组
关于数值分析的相关实验源码可以访问我的github获取： JavaOs467/project at main · os467/JavaOs467 (github.com)
下面采用的是消主元法，也是我们通常最常用的解线性方程组方法，本质上就是带入消元法。
package project.lab5;
/**
* 消主元法
*/
public class Miss {
/* private float[][] matrix = {
{10F,-1F,-2F,7.2F},
{-1F,10F,-2F,8.3F},
{-1F,-1F,5F,4.2F}
};*/
/* private float[][] matrix =
{
{-3F,2F,6F,4F},
{10F,-7F,0F,7F},
{5F,-1F,5F,6F}
};*/
/*private float[][] matrix =
{
{2F,3F,5F,5F},
{3F,4F,7F,6F},
{1F,3F,3F,5F}
};*/
/*private float[][] matrix =
{
{6F,18F,-15F,-17F,14F,-17F,24F},
{-4F,-19F,11F,12F,-4F,15F,12F},
{-7F,-2F,-22F,6F,-13F,21F,13F},
{-24F,-10F,-21F,10F,8F,-11F,24F},
{12F,-22F,9F,8F,-3F,-4F,24F},
{-5F,-18F,13F,4F,22F,15F,3F}
};*/
private float[][] matrix =
{
{226F,18F,-15F,-17F,14F,-17F,24F},
{-4F,201F,11F,12F,-4F,15F,12F},
{-7F,-2F,-198F,6F,-13F,21F,13F},
{-24F,-10F,-21F,230F,8F,-11F,24F},
{12F,-22F,9F,8F,217F,-4F,24F},
{-5F,-18F,13F,4F,22F,235F,3F}
};
//行数量
private int r;
//列数量
private int c;
//已扫描行
private int pass = 0;
//原始矩阵副本
private float[][] matrixOrigin;
//解集
private float[] x;
public static void main(String[] args) {
Miss guss = new Miss();
guss.d();
}
private void d() {
//检查矩阵合法性并初始化参数
if (checkMatrix()) return;
//打印矩阵
printMatrix();
//先记录以下原矩阵
matrixOrigin = new float[r][c];
for (int i = 0; i < r; i++) {
for (int j = 0; j < c; j++) {
matrixOrigin[i][j] = matrix[i][j];
}
}
//先消去x1,然后x2，最后解出x3,x2,x1
for (int i = 0; i < c - 2; i++) {
//将系数最大的行选出
Float max = null;
Integer maxRow = null;
//比大小找最大主元行
for (int j = 0; j < r; j++) {
if (max == null || Math.abs(matrix[j][i]) > Math.abs(max)){
max = matrix[j][i];
maxRow = j;
}
}
//交换已扫描行最大行
exchangeRow(pass,maxRow);
maxRow = pass;
pass++;
//maxRow行的系数更新
for (int j = 0; j < c; j++) {
matrix[maxRow][j] /= max;
}
//更新其它行的系数值
for (int j = pass; j < r; j++) {
float a = matrix[j][i];
//消去a
matrix[j][i] = 0;
//更改每行b值
matrix[j][c-1] += -a * matrix[maxRow][c-1];
//更改每行其它系数值
for (int k = 0; k < c - 1; k++) {
if (k != i){
matrix[j][k] += a * -matrix[maxRow][k];
}
}
}
}
//开始回解
for (int i = r-1; i >= 0 ; i--) {
float sumDiv = 0;
for (int j = 0; j < c - 1; j++) {
sumDiv+=matrix[i][j];
}
x[i] = matrix[i][c-1]/sumDiv;
//消去其它行的未知数
for (int j = i - 1; j >= 0; j--) {
//更新b值
matrix[j][c-1] -= matrix[j][i] * x[i];
//系数置0
matrix[j][i] = 0;
}
}
//打印结果
printAns();
}
private void exchangeRow(int pass, Integer maxRow) {
if (pass == maxRow) return;
for (int i = 0; i < c; i++) {
matrix[maxRow][i] += matrix[pass][i];
matrix[pass][i] = matrix[maxRow][i] - matrix[pass][i];
matrix[maxRow][i] -= matrix[pass][i];
}
}
private void printAns() {
float[] lrMiss = new float[r];
//计算左边 - 右边
for (int i = 0; i < r; i++) {
float sum = 0;
for (int j = 0; j < c - 1; j++) {
sum += matrixOrigin[i][j] * x[j];
}
lrMiss[i] = sum - matrixOrigin[i][c-1];
}
int padding = 20;
for (int i = 0; i < r; i++) {
String ansX = "x"+(i+1)+" = "+ (Math.abs(x[i]) < 0.00001F ? 0 : x[i]);
System.out.print(ansX);
for (int j = 0; j < padding - ansX.length(); j++) {
System.out.print(" ");
}
System.out.print("|");
System.out.println("\t\t 左边 - 右边 = "+lrMiss[i]);
}
}
private void printMatrix() {
System.out.println("解目标方程组:");
for (int i = 0; i < r; i++) {
for (int j = 0; j < c - 1; j++) {
if (j != 0){
System.out.print(Math.abs(matrix[i][j])+"x"+(j+1)+"\t");
}else {
System.out.print(matrix[i][j]+"x"+(j+1)+"\t");
}
if (j != c-2){
if (matrix[i][j+1] > 0){
System.out.print("+\t");
}else {
System.out.print("-\t");
}
}
}
System.out.println(" = \t\t"+matrix[i][c-1]);
}
System.out.println("\n\n");
}
private boolean checkMatrix() {
r = matrix.length;
if (r == 0) return true;
c = matrix[0].length;
x = new float[c-1];
return false;
}
}
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