java 克里金插值

克里金插值（Kriging Interpolation）是一种空间插值方法，主要用于估计未知位置的数值或属性值。在Java中实现克里金插值可以使用第三方库，例如GeoTools、JTS Topology Suite等。下面以GeoTools为例给出实现代码：

import org.geotools.data.DataUtilities;
import org.geotools.geometry.jts.JTSFactoryFinder;
import org.geotools.grid.GridCoverage2D;
import org.geotools.grid.GridCoverageFactory;
import org.geotools.grid.Interpolator;
import org.geotools.referencing.CRS;
import org.geotools.referencing.crs.DefaultGeographicCRS;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.geom.GeometryFactory;

import javax.measure.quantity.Length;
import javax.measure.unit.SI;
import org.opengis.coverage.grid.GridCoordinates;
import org.opengis.coverage.grid.GridEnvelope;
import org.opengis.geometry.Envelope;
import org.opengis.referencing.crs.CoordinateReferenceSystem;
import org.opengis.referencing.operation.MathTransform;
import org.opengis.referencing.operation.TransformException;

public class KrigingInterpolation {
    public static void main(String[] args) throws TransformException {
        // 输入数据点坐标和属性值
        Coordinate[] inputPoints = {
                new Coordinate(0, 0),
                new Coordinate(1, 0),
                new Coordinate(2, 0),
                new Coordinate(0, 1),
                new Coordinate(1, 1),
                new Coordinate(2, 1),
                new Coordinate(0, 2),
                new Coordinate(1, 2),
                new Coordinate(2, 2)
        };
        double[] inputValues = {10, 20, 30, 15, 25, 35, 20, 30, 40};

        // 创建插值器
        GeometryFactory geometryFactory = JTSFactoryFinder.getGeometryFactory();
        Interpolator interpolator = new org.geotools.grid.kriging.KrigingInterpolator(geometryFactory);

        // 创建输入数据点的Geometry
        org.geotools.geometry.DirectPositionList positionList = new org.geotools.geometry.DirectPositionList();
        for (Coordinate inputPoint : inputPoints) {
            positionList.add(new org.geotools.geometry.DirectPosition(inputPoint.x, inputPoint.y));
        }
        org.locationtech.jts.geom.Point inputPointGeom = geometryFactory.createMultiPointFromCoords(positionList.toArray(new org.locationtech.jts.geom.Coordinate[positionList.size()])).getCentroid();

        // 创建输入数据点的属性值Feature
        org.geotools.feature.simple.SimpleFeatureType featureType = DataUtilities.createType("Input", "geom:Point:srid=4326,value:Double");
        org.geotools.feature.simple.SimpleFeatureBuilder featureBuilder = new org.geotools.feature.simple.SimpleFeatureBuilder(featureType);
        featureBuilder.add(inputPointGeom);
        featureBuilder.add(10.0);
        org.geotools.feature.simple.SimpleFeature feature = featureBuilder.buildFeature("1");
        feature.setDefaultGeometry(inputPointGeom);

        // 创建GridEnvelope和Envelope
        GridEnvelope gridEnvelope = new org.geotools.grid.GridEnvelope2D(new int[]{0, 0}, new int[]{2, 2});
        Envelope envelope = new org.geotools.geometry.EnvelopeImpl(new Coordinate(0, 0), new Coordinate(2, 2), DefaultGeographicCRS.WGS84);

        // 创建输出GridCoverage2D
        GridCoverageFactory gridCoverageFactory = new org.geotools.grid.GridCoverageFactory();
        GridCoverage2D outputGridCoverage2D = gridCoverageFactory.create("Output", feature, gridEnvelope, envelope);

        // 设置插值参数
        interpolator.setSearchRadius(10.0);
        interpolator.setSigma(100.0);
        interpolator.setAlpha(1.0);

        // 插值
        GridCoverage2D interpolatedGridCoverage2D = interpolator.interpolate(outputGridCoverage2D, inputPoints, inputValues);

        // 输出插值结果
        System.out.println("Interpolated grid coverage:");
        for (int i = 0; i < interpolatedGridCoverage2D.getNumRows(); i++) {
            for (int j = 0; j < interpolatedGridCoverage2D.getNumCols(); j++) {
                GridCoordinates gridCoordinates = new org.geotools.grid.GridCoordinates2D(i, j);
                org.opengis.geometry.DirectPosition directPosition = interpolatedGridCoverage2D.getGridGeometry().gridToWorld(gridCoordinates);
                double value = interpolatedGridCoverage2D.evaluate(directPosition).doubleValue(SI.METER);
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }
}

上述代码中，首先定义了输入数据点坐标和属性值，然后创建了克里金插值器对象。接着通过GeoTools创建输入数据点的Geometry和属性值Feature，以及GridEnvelope和Envelope，最后用这些对象创建输出GridCoverage2D。在插值前，设置了插值参数。最后调用插值器的interpolate方法进行插值，并输出插值结果。