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Kriging 克里金算法Java实现

网友: 文章列表 2024-03-21 17:34:58

Kriging 克里金算法Java实现

  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
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);}
}

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
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);}
}

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
  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
}

在 main 函数中，定义了一个样本点列表，包含了四个空间点，然后定义了克里金插值的一些参数，包括 nugget，range 和 sill。接着定义了一个待插值的空间点，然后调用克里金的 interpolate 方法进行插值计算，并将结果打印出来。

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