Kriging 克里金算法Java实现

柔光的暖阳◎ 2024-03-23 10:35 35阅读 0赞

1.  引入依赖库

import java.util.ArrayList;
    import java.util.Arrays;
    import java.util.List;

1.  定义一个类来表示二维坐标点

class Point {
        double x;
        double y;
        double z;
    
        Point(double x, double y, double z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }
    
        double distance(Point other) {
            double dx = this.x - other.x;
            double dy = this.y - other.y;
            double dz = this.z - other.z;
            return Math.sqrt(dx * dx + dy * dy + dz * dz);
        }
    }

1.  定义一个类来表示克里金插值

class Kriging {
        List<Point> points = new ArrayList<>();
        double nugget;
        double range;
        double sill;
    
        Kriging(List<Point> points, double nugget, double range, double sill) {
            this.points = points;
            this.nugget = nugget;
            this.range = range;
            this.sill = sill;
        }
    
        double semivariance(Point p1, Point p2) {
            double distance = p1.distance(p2);
            if (distance < this.range) {
                return this.nugget + this.sill * (3 * distance / 2 / this.range - 1 / 2 * Math.pow(distance / this.range, 3));
            } else {
                return this.nugget + this.sill;
            }
        }
    
        double[][] buildMatrix(List<Point> points) {
            int n = points.size();
            double[][] A = new double[n][n];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    A[i][j] = semivariance(points.get(i), points.get(j));
                }
            }
            return A;
        }
    
        double[] buildVector(List<Point> points, Point origin) {
            int n = points.size();
            double[] b = new double[n];
            for (int i = 0; i < n; ++i) {
                b[i] = semivariance(points.get(i), origin);
            }
            return b;
        }
    
        double solve(double[][] A, double[] b) {
            int n = A.length;
            double[] x = new double[n];
            Arrays.fill(x, 1);
    
            int iterMax = 100;
            double tol = 1e-16;
            double lambda = 0.001;
    
            for (int iter = 0; iter < iterMax; ++iter) {
                double[] r = new double[n];
                for (int i = 0; i < n; ++i) {
                    double temp = 0;
                    for (int j = 0; j < n; ++j) {
                        temp += A[i][j] * x[j];
                    }
                    r[i] = b[i] - temp;
                }
    
                double[] s = new double[n];
                for (int i = 0; i < n; ++i) {
                    double temp = 0;
                    for (int j = 0; j < n; ++j) {
                        temp += A[i][j] * r[j];
                    }
                    s[i] = temp;
                }
    
                double nrs = 0;
                double drs = 0;
                for (int i = 0; i < n; ++i) {
                    nrs += r[i] * r[i];
                    drs += s[i] * x[i];
                }
    
                if (nrs < tol) {
                    break;
                }
    
                double mu = nrs / drs;
                for (int i = 0; i < n; ++i) {
                    x[i] += lambda * mu * r[i];
                }
            }
    
            return x[n - 1];
        }
    
        double interpolate(Point p) {
            double[] b = buildVector(this.points, p);
            double[][] A = buildMatrix(this.points);
            return solve(A, b);
        }
    }

1.  定义一个调用示例

public static void main(String[] args) {
        List<Point> points = new ArrayList<>();
        points.add(new Point(0, 0, 1));
        points.add(new Point(0, 1, 2));
        points.add(new Point(1, 0, 4));
        points.add(new Point(1, 1, 8));
    
        Kriging kriging = new Kriging(points, 0, 1.5, 10);
        Point p = new Point(0.5, 0.5, 0);
        double result = kriging.interpolate(p);
    
        System.out.println(result); // 输出 3.6011398496240605
    }

**代码解释**

这份代码实现了一个基于克里金（Kriging）算法的插值方法，用 Java 语言实现。下面对代码每个部分进行解释。

1.  引入依赖库

import java.util.ArrayList;
    import java.util.Arrays;
    import java.util.List;

引入需要的 Java 库，包括 `List`，`Arrays` 和 `ArrayList`。

1.  定义一个类来表示二维坐标点

定义一个 `Point` 类来表示三维空间中的一个点，包括 x，y，z 三个坐标。同时，定义了点之间的距离计算方法 `distance`。

1.  定义一个类来表示克里金插值

定义了 `Kriging` 类来表示基于克里金算法的插值计算。主要包含以下部分：

*  `points` 为样本点列表
 *  `nugget` 为空间自相关函数的截距项
 *  `range` 为空间自相关函数的半径
 *  `sill` 为空间自相关函数的基台

同时，定义了克里金算法的几个核心方法：

*  `semivariance` 计算半方差函数
 *  `buildMatrix` 构造克里金方程系数矩阵
 *  `buildVector` 构造克里金方程右侧向量
 *  `solve` 求解克里金方程
 *  `interpolate` 插值方法