Commons Math example source code file (SmoothingBicubicSplineInterpolator.java)

This example Commons Math source code file (SmoothingBicubicSplineInterpolator.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

bicubicsplineinterpolatingfunction, bicubicsplineinterpolatingfunction, bivariaterealfunction, bivariaterealgridinterpolator, illegalargumentexception, mathexception, polynomialsplinefunction, polynomialsplinefunction, smoothingbicubicsplineinterpolator, splineinterpolator, splineinterpolator, univariaterealfunction, univariaterealfunction

The Commons Math SmoothingBicubicSplineInterpolator.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.analysis.interpolation;

import org.apache.commons.math.DimensionMismatchException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.util.MathUtils;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.BivariateRealFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;

/**
 * Generates a bicubic interpolation function.
 * Before interpolating, smoothing of the input data is performed using
 * splines.
 * See <b>Handbook on splines for the user, ISBN 084939404X,
 * chapter 2.
 *
 * @version $Revision$ $Date$
 * @since 2.1
 */
public class SmoothingBicubicSplineInterpolator
    implements BivariateRealGridInterpolator {
    /**
     * {@inheritDoc}
     */
    public BivariateRealFunction interpolate(final double[] xval,
                                             final double[] yval,
                                             final double[][] zval)
        throws MathException, IllegalArgumentException {
        if (xval.length == 0 || yval.length == 0 || zval.length == 0) {
            throw MathRuntimeException.createIllegalArgumentException("no data");
        }
        if (xval.length != zval.length) {
            throw new DimensionMismatchException(xval.length, zval.length);
        }

        MathUtils.checkOrder(xval, 1, true);
        MathUtils.checkOrder(yval, 1, true);

        final int xLen = xval.length;
        final int yLen = yval.length;

        // Samples (first index is y-coordinate, i.e. subarray variable is x)
        // 0 <= i < xval.length
        // 0 <= j < yval.length
        // zX[j][i] = f(xval[i], yval[j])
        final double[][] zX = new double[yLen][xLen];
        for (int i = 0; i < xLen; i++) {
            if (zval[i].length != yLen) {
                throw new DimensionMismatchException(zval[i].length, yLen);
            }

            for (int j = 0; j < yLen; j++) {
                zX[j][i] = zval[i][j];
            }
        }

        final SplineInterpolator spInterpolator = new SplineInterpolator();

        // For each line y[j] (0 <= j < yLen), construct a 1D spline with
        // respect to variable x
        final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];
        for (int j = 0; j < yLen; j++) {
            ySplineX[j] = spInterpolator.interpolate(xval, zX[j]);
        }

        // For every knot (xval[i], yval[j]) of the grid, calculate corrected
        // values zY_1
        final double[][] zY_1 = new double[xLen][yLen];
        for (int j = 0; j < yLen; j++) {
            final PolynomialSplineFunction f = ySplineX[j];
            for (int i = 0; i < xLen; i++) {
                zY_1[i][j] = f.value(xval[i]);
            }
        }

        // For each line x[i] (0 <= i < xLen), construct a 1D spline with
        // respect to variable y generated by array zY_1[i]
        final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
        for (int i = 0; i < xLen; i++) {
            xSplineY[i] = spInterpolator.interpolate(yval, zY_1[i]);
        }

        // For every knot (xval[i], yval[j]) of the grid, calculate corrected
        // values zY_2
        final double[][] zY_2 = new double[xLen][yLen];
        for (int i = 0; i < xLen; i++) {
            final PolynomialSplineFunction f = xSplineY[i];
            for (int j = 0; j < yLen; j++) {
                zY_2[i][j] = f.value(yval[j]);
            }
        }

        // Partial derivatives with respect to x at the grid knots
        final double[][] dZdX = new double[xLen][yLen];
        for (int j = 0; j < yLen; j++) {
            final UnivariateRealFunction f = ySplineX[j].derivative();
            for (int i = 0; i < xLen; i++) {
                dZdX[i][j] = f.value(xval[i]);
            }
        }

        // Partial derivatives with respect to y at the grid knots
        final double[][] dZdY = new double[xLen][yLen];
        for (int i = 0; i < xLen; i++) {
            final UnivariateRealFunction f = xSplineY[i].derivative();
            for (int j = 0; j < yLen; j++) {
                dZdY[i][j] = f.value(yval[j]);
            }
        }

        // Cross partial derivatives
        final double[][] dZdXdY = new double[xLen][yLen];
        for (int i = 0; i < xLen ; i++) {
            final int nI = nextIndex(i, xLen);
            final int pI = previousIndex(i);
            for (int j = 0; j < yLen; j++) {
                final int nJ = nextIndex(j, yLen);
                final int pJ = previousIndex(j);
                dZdXdY[i][j] =  (zY_2[nI][nJ] - zY_2[nI][pJ] -
                                 zY_2[pI][nJ] + zY_2[pI][pJ]) /
                    ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ])) ;
            }
        }

        // Create the interpolating splines
        return new BicubicSplineInterpolatingFunction(xval, yval, zY_2,
                                                      dZdX, dZdY, dZdXdY);
    }

    /**
     * Compute the next index of an array, clipping if necessary.
     * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.
     *
     * @param i Index
     * @param max Upper limit of the array
     * @return the next index
     */
    private int nextIndex(int i, int max) {
        final int index = i + 1;
        return index < max ? index : index - 1;
    }
    /**
     * Compute the previous index of an array, clipping if necessary.
     * It is assumed (but not checked) that {@code i} is smaller than the size of the array.
     *
     * @param i Index
     * @return the previous index
     */
    private int previousIndex(int i) {
        final int index = i - 1;
        return index >= 0 ? index : 0;
    }
}