import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
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);
}
}
class Kriging {
List points = new ArrayList<>();
double nugget;
double range;
double sill;
Kriging(List 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 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 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);
}
}
public static void main(String[] args) {
List 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。
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
。
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
。
class Kriging {
List points = new ArrayList<>();
double nugget;
double range;
double sill;
Kriging(List 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 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 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public static void main(String[] args) {
List 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。