生成一个m行n列的整数矩阵,如果m不等于n,对矩阵进行初等行变换,直至行阶梯形输出,计算矩阵的秩,如果m等于n,矩阵做初等行变换直至行阶梯形,输出,计算矩阵的秩,计算矩阵的行列式,java语言
时间: 2024-03-24 09:37:52 浏览: 66
好的,以下是 Java 代码:
```java
import java.util.Random;
public class Matrix {
private int[][] data;
private int m;
private int n;
public Matrix(int m, int n) {
this.m = m;
this.n = n;
data = new int[m][n];
Random rand = new Random();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
data[i][j] = rand.nextInt(10); // 生成 0 到 9 的随机整数
}
}
}
public void elementaryRowOperation() {
int lead = 0;
for (int r = 0; r < m; r++) {
if (lead >= n) {
break;
}
int i = r;
while (data[i][lead] == 0) {
i++;
if (i == m) {
i = r;
lead++;
if (lead == n) {
return;
}
}
}
swapRows(i, r);
int lv = data[r][lead];
multiplyRow(r, 1 / lv);
for (i = 0; i < m; i++) {
if (i != r) {
int lvi = data[i][lead];
addRow(i, r, -lvi);
}
}
lead++;
}
}
private void swapRows(int i, int j) {
int[] temp = data[i];
data[i] = data[j];
data[j] = temp;
}
private void multiplyRow(int i, int k) {
for (int j = 0; j < n; j++) {
data[i][j] *= k;
}
}
private void addRow(int i, int j, int k) {
for (int l = 0; l < n; l++) {
data[i][l] += k * data[j][l];
}
}
public int rank() {
Matrix copy = new Matrix(m, n);
copy.data = data.clone();
copy.elementaryRowOperation();
int rank = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (copy.data[i][j] != 0) {
rank++;
break;
}
}
}
return rank;
}
public int determinant() {
if (m != n) {
throw new IllegalArgumentException("Matrix is not square");
}
Matrix copy = new Matrix(m, n);
copy.data = data.clone();
int det = 1;
for (int i = 0; i < m; i++) {
int pivot = i;
for (int j = i + 1; j < m; j++) {
if (Math.abs(copy.data[j][i]) > Math.abs(copy.data[pivot][i])) {
pivot = j;
}
}
if (pivot != i) {
copy.swapRows(i, pivot);
det = -det;
}
det *= copy.data[i][i];
if (det == 0) {
return 0;
}
for (int j = i + 1; j < m; j++) {
int factor = copy.data[j][i] / copy.data[i][i];
for (int k = i + 1; k < n; k++) {
copy.data[j][k] -= factor * copy.data[i][k];
}
}
}
return det;
}
public void print() {
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
System.out.print(data[i][j] + " ");
}
System.out.println();
}
}
public static void main(String[] args) {
Matrix matrix = new Matrix(4, 5);
System.out.println("Original matrix:");
matrix.print();
System.out.println("After elementary row operation:");
matrix.elementaryRowOperation();
matrix.print();
System.out.println("Rank: " + matrix.rank());
System.out.println("Determinant: " + matrix.determinant());
}
}
```
这个程序会生成一个 m 行 n 列的随机整数矩阵,然后对其进行初等行变换,输出变换后的矩阵和矩阵的秩、行列式。其中,初等行变换函数 `elementaryRowOperation()` 会将矩阵变换为行阶梯形,秩即为行阶梯形中非零行的数量。行列式计算使用的是高斯消元法。
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