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Java example source code file (BicubicSplineInterpolator.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

bicubicsplineinterpolatingfunction, bicubicsplineinterpolator, bivariategridinterpolator, deprecated, dimensionmismatchexception, nodataexception, nonmonotonicsequenceexception, numberistoosmallexception, polynomialsplinefunction, univariatefunction

The BicubicSplineInterpolator.java Java example 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.math3.analysis.interpolation;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.MathArrays;

/**
 * Generates a bicubic interpolating function. Due to numerical accuracy issues this should not
 * be used.
 *
 * @since 2.2
 * @deprecated as of 3.4 replaced by {@link org.apache.commons.math3.analysis.interpolation.PiecewiseBicubicSplineInterpolator}
 */
@Deprecated
public class BicubicSplineInterpolator
    implements BivariateGridInterpolator {
    /** Whether to initialize internal data used to compute the analytical
        derivatives of the splines. */
    private final boolean initializeDerivatives;

    /**
     * Default constructor.
     * The argument {@link #BicubicSplineInterpolator(boolean) initializeDerivatives}
     * is set to {@code false}.
     */
    public BicubicSplineInterpolator() {
        this(false);
    }

    /**
     * Creates an interpolator.
     *
     * @param initializeDerivatives Whether to initialize the internal data
     * needed for calling any of the methods that compute the partial derivatives
     * of the {@link BicubicSplineInterpolatingFunction function} returned from
     * the call to {@link #interpolate(double[],double[],double[][]) interpolate}.
     */
    public BicubicSplineInterpolator(boolean initializeDerivatives) {
        this.initializeDerivatives = initializeDerivatives;
    }

    /**
     * {@inheritDoc}
     */
    public BicubicSplineInterpolatingFunction interpolate(final double[] xval,
                                                          final double[] yval,
                                                          final double[][] fval)
        throws NoDataException, DimensionMismatchException,
               NonMonotonicSequenceException, NumberIsTooSmallException {
        if (xval.length == 0 || yval.length == 0 || fval.length == 0) {
            throw new NoDataException();
        }
        if (xval.length != fval.length) {
            throw new DimensionMismatchException(xval.length, fval.length);
        }

        MathArrays.checkOrder(xval);
        MathArrays.checkOrder(yval);

        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
        // fX[j][i] = f(xval[i], yval[j])
        final double[][] fX = new double[yLen][xLen];
        for (int i = 0; i < xLen; i++) {
            if (fval[i].length != yLen) {
                throw new DimensionMismatchException(fval[i].length, yLen);
            }

            for (int j = 0; j < yLen; j++) {
                fX[j][i] = fval[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, fX[j]);
        }

        // For each line x[i] (0 <= i < xLen), construct a 1D spline with
        // respect to variable y generated by array fY_1[i]
        final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
        for (int i = 0; i < xLen; i++) {
            xSplineY[i] = spInterpolator.interpolate(yval, fval[i]);
        }

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

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

        // Cross partial derivatives
        final double[][] d2FdXdY = 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);
                d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] -
                                 fval[pI][nJ] + fval[pI][pJ]) /
                    ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
            }
        }

        // Create the interpolating splines
        return new BicubicSplineInterpolatingFunction(xval, yval, fval,
                                                      dFdX, dFdY, d2FdXdY,
                                                      initializeDerivatives);
    }

    /**
     * Computes the next index of an array, clipping if necessary.
     * It is assumed (but not checked) that {@code i >= 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;
    }
    /**
     * Computes 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;
    }
}

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