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Java example source code file (BicubicSplineInterpolatingFunction.java)

This example Java source code file (BicubicSplineInterpolatingFunction.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

ainv, bicubicsplinefunction, bicubicsplineinterpolatingfunction, bivariatefunction, deprecated, dimensionmismatchexception, nodataexception, nonmonotonicsequenceexception, num_coeff, outofrangeexception, util

The BicubicSplineInterpolatingFunction.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 java.util.Arrays;
import org.apache.commons.math3.analysis.BivariateFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.util.MathArrays;

/**
 * Function that implements the
 * <a href="http://en.wikipedia.org/wiki/Bicubic_interpolation">
 * bicubic spline interpolation</a>. Due to numerical accuracy issues this should not
 * be used.
 *
 * @since 2.1
 * @deprecated as of 3.4 replaced by
 * {@link org.apache.commons.math3.analysis.interpolation.PiecewiseBicubicSplineInterpolatingFunction}
 */
@Deprecated
public class BicubicSplineInterpolatingFunction
    implements BivariateFunction {
    /** Number of coefficients. */
    private static final int NUM_COEFF = 16;
    /**
     * Matrix to compute the spline coefficients from the function values
     * and function derivatives values
     */
    private static final double[][] AINV = {
        { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
        { 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },
        { -3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0 },
        { 2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0 },
        { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
        { 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0 },
        { 0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0 },
        { 0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0 },
        { -3,0,3,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },
        { 0,0,0,0,-3,0,3,0,0,0,0,0,-2,0,-1,0 },
        { 9,-9,-9,9,6,3,-6,-3,6,-6,3,-3,4,2,2,1 },
        { -6,6,6,-6,-3,-3,3,3,-4,4,-2,2,-2,-2,-1,-1 },
        { 2,0,-2,0,0,0,0,0,1,0,1,0,0,0,0,0 },
        { 0,0,0,0,2,0,-2,0,0,0,0,0,1,0,1,0 },
        { -6,6,6,-6,-4,-2,4,2,-3,3,-3,3,-2,-1,-2,-1 },
        { 4,-4,-4,4,2,2,-2,-2,2,-2,2,-2,1,1,1,1 }
    };

    /** Samples x-coordinates */
    private final double[] xval;
    /** Samples y-coordinates */
    private final double[] yval;
    /** Set of cubic splines patching the whole data grid */
    private final BicubicSplineFunction[][] splines;
    /**
     * Partial derivatives.
     * The value of the first index determines the kind of derivatives:
     * 0 = first partial derivatives wrt x
     * 1 = first partial derivatives wrt y
     * 2 = second partial derivatives wrt x
     * 3 = second partial derivatives wrt y
     * 4 = cross partial derivatives
     */
    private final BivariateFunction[][][] partialDerivatives;

    /**
     * @param x Sample values of the x-coordinate, in increasing order.
     * @param y Sample values of the y-coordinate, in increasing order.
     * @param f Values of the function on every grid point.
     * @param dFdX Values of the partial derivative of function with respect
     * to x on every grid point.
     * @param dFdY Values of the partial derivative of function with respect
     * to y on every grid point.
     * @param d2FdXdY Values of the cross partial derivative of function on
     * every grid point.
     * @throws DimensionMismatchException if the various arrays do not contain
     * the expected number of elements.
     * @throws NonMonotonicSequenceException if {@code x} or {@code y} are
     * not strictly increasing.
     * @throws NoDataException if any of the arrays has zero length.
     */
    public BicubicSplineInterpolatingFunction(double[] x,
                                              double[] y,
                                              double[][] f,
                                              double[][] dFdX,
                                              double[][] dFdY,
                                              double[][] d2FdXdY)
        throws DimensionMismatchException,
               NoDataException,
               NonMonotonicSequenceException {
        this(x, y, f, dFdX, dFdY, d2FdXdY, false);
    }

    /**
     * @param x Sample values of the x-coordinate, in increasing order.
     * @param y Sample values of the y-coordinate, in increasing order.
     * @param f Values of the function on every grid point.
     * @param dFdX Values of the partial derivative of function with respect
     * to x on every grid point.
     * @param dFdY Values of the partial derivative of function with respect
     * to y on every grid point.
     * @param d2FdXdY Values of the cross partial derivative of function on
     * every grid point.
     * @param initializeDerivatives Whether to initialize the internal data
     * needed for calling any of the methods that compute the partial derivatives
     * this function.
     * @throws DimensionMismatchException if the various arrays do not contain
     * the expected number of elements.
     * @throws NonMonotonicSequenceException if {@code x} or {@code y} are
     * not strictly increasing.
     * @throws NoDataException if any of the arrays has zero length.
     *
     * @see #partialDerivativeX(double,double)
     * @see #partialDerivativeY(double,double)
     * @see #partialDerivativeXX(double,double)
     * @see #partialDerivativeYY(double,double)
     * @see #partialDerivativeXY(double,double)
     */
    public BicubicSplineInterpolatingFunction(double[] x,
                                              double[] y,
                                              double[][] f,
                                              double[][] dFdX,
                                              double[][] dFdY,
                                              double[][] d2FdXdY,
                                              boolean initializeDerivatives)
        throws DimensionMismatchException,
               NoDataException,
               NonMonotonicSequenceException {
        final int xLen = x.length;
        final int yLen = y.length;

        if (xLen == 0 || yLen == 0 || f.length == 0 || f[0].length == 0) {
            throw new NoDataException();
        }
        if (xLen != f.length) {
            throw new DimensionMismatchException(xLen, f.length);
        }
        if (xLen != dFdX.length) {
            throw new DimensionMismatchException(xLen, dFdX.length);
        }
        if (xLen != dFdY.length) {
            throw new DimensionMismatchException(xLen, dFdY.length);
        }
        if (xLen != d2FdXdY.length) {
            throw new DimensionMismatchException(xLen, d2FdXdY.length);
        }

        MathArrays.checkOrder(x);
        MathArrays.checkOrder(y);

        xval = x.clone();
        yval = y.clone();

        final int lastI = xLen - 1;
        final int lastJ = yLen - 1;
        splines = new BicubicSplineFunction[lastI][lastJ];

        for (int i = 0; i < lastI; i++) {
            if (f[i].length != yLen) {
                throw new DimensionMismatchException(f[i].length, yLen);
            }
            if (dFdX[i].length != yLen) {
                throw new DimensionMismatchException(dFdX[i].length, yLen);
            }
            if (dFdY[i].length != yLen) {
                throw new DimensionMismatchException(dFdY[i].length, yLen);
            }
            if (d2FdXdY[i].length != yLen) {
                throw new DimensionMismatchException(d2FdXdY[i].length, yLen);
            }
            final int ip1 = i + 1;
            for (int j = 0; j < lastJ; j++) {
                final int jp1 = j + 1;
                final double[] beta = new double[] {
                    f[i][j], f[ip1][j], f[i][jp1], f[ip1][jp1],
                    dFdX[i][j], dFdX[ip1][j], dFdX[i][jp1], dFdX[ip1][jp1],
                    dFdY[i][j], dFdY[ip1][j], dFdY[i][jp1], dFdY[ip1][jp1],
                    d2FdXdY[i][j], d2FdXdY[ip1][j], d2FdXdY[i][jp1], d2FdXdY[ip1][jp1]
                };

                splines[i][j] = new BicubicSplineFunction(computeSplineCoefficients(beta),
                                                          initializeDerivatives);
            }
        }

        if (initializeDerivatives) {
            // Compute all partial derivatives.
            partialDerivatives = new BivariateFunction[5][lastI][lastJ];

            for (int i = 0; i < lastI; i++) {
                for (int j = 0; j < lastJ; j++) {
                    final BicubicSplineFunction bcs = splines[i][j];
                    partialDerivatives[0][i][j] = bcs.partialDerivativeX();
                    partialDerivatives[1][i][j] = bcs.partialDerivativeY();
                    partialDerivatives[2][i][j] = bcs.partialDerivativeXX();
                    partialDerivatives[3][i][j] = bcs.partialDerivativeYY();
                    partialDerivatives[4][i][j] = bcs.partialDerivativeXY();
                }
            }
        } else {
            // Partial derivative methods cannot be used.
            partialDerivatives = null;
        }
    }

    /**
     * {@inheritDoc}
     */
    public double value(double x, double y)
        throws OutOfRangeException {
        final int i = searchIndex(x, xval);
        final int j = searchIndex(y, yval);

        final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
        final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);

        return splines[i][j].value(xN, yN);
    }

    /**
     * Indicates whether a point is within the interpolation range.
     *
     * @param x First coordinate.
     * @param y Second coordinate.
     * @return {@code true} if (x, y) is a valid point.
     * @since 3.3
     */
    public boolean isValidPoint(double x, double y) {
        if (x < xval[0] ||
            x > xval[xval.length - 1] ||
            y < yval[0] ||
            y > yval[yval.length - 1]) {
            return false;
        } else {
            return true;
        }
    }

    /**
     * @param x x-coordinate.
     * @param y y-coordinate.
     * @return the value at point (x, y) of the first partial derivative with
     * respect to x.
     * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
     * the range defined by the boundary values of {@code xval} (resp.
     * {@code yval}).
     * @throws NullPointerException if the internal data were not initialized
     * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
     *             double[][],double[][],double[][],boolean) constructor}).
     */
    public double partialDerivativeX(double x, double y)
        throws OutOfRangeException {
        return partialDerivative(0, x, y);
    }
    /**
     * @param x x-coordinate.
     * @param y y-coordinate.
     * @return the value at point (x, y) of the first partial derivative with
     * respect to y.
     * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
     * the range defined by the boundary values of {@code xval} (resp.
     * {@code yval}).
     * @throws NullPointerException if the internal data were not initialized
     * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
     *             double[][],double[][],double[][],boolean) constructor}).
     */
    public double partialDerivativeY(double x, double y)
        throws OutOfRangeException {
        return partialDerivative(1, x, y);
    }
    /**
     * @param x x-coordinate.
     * @param y y-coordinate.
     * @return the value at point (x, y) of the second partial derivative with
     * respect to x.
     * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
     * the range defined by the boundary values of {@code xval} (resp.
     * {@code yval}).
     * @throws NullPointerException if the internal data were not initialized
     * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
     *             double[][],double[][],double[][],boolean) constructor}).
     */
    public double partialDerivativeXX(double x, double y)
        throws OutOfRangeException {
        return partialDerivative(2, x, y);
    }
    /**
     * @param x x-coordinate.
     * @param y y-coordinate.
     * @return the value at point (x, y) of the second partial derivative with
     * respect to y.
     * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
     * the range defined by the boundary values of {@code xval} (resp.
     * {@code yval}).
     * @throws NullPointerException if the internal data were not initialized
     * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
     *             double[][],double[][],double[][],boolean) constructor}).
     */
    public double partialDerivativeYY(double x, double y)
        throws OutOfRangeException {
        return partialDerivative(3, x, y);
    }
    /**
     * @param x x-coordinate.
     * @param y y-coordinate.
     * @return the value at point (x, y) of the second partial cross-derivative.
     * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
     * the range defined by the boundary values of {@code xval} (resp.
     * {@code yval}).
     * @throws NullPointerException if the internal data were not initialized
     * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
     *             double[][],double[][],double[][],boolean) constructor}).
     */
    public double partialDerivativeXY(double x, double y)
        throws OutOfRangeException {
        return partialDerivative(4, x, y);
    }

    /**
     * @param which First index in {@link #partialDerivatives}.
     * @param x x-coordinate.
     * @param y y-coordinate.
     * @return the value at point (x, y) of the selected partial derivative.
     * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
     * the range defined by the boundary values of {@code xval} (resp.
     * {@code yval}).
     * @throws NullPointerException if the internal data were not initialized
     * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
     *             double[][],double[][],double[][],boolean) constructor}).
     */
    private double partialDerivative(int which, double x, double y)
        throws OutOfRangeException {
        final int i = searchIndex(x, xval);
        final int j = searchIndex(y, yval);

        final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
        final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);

        return partialDerivatives[which][i][j].value(xN, yN);
    }

    /**
     * @param c Coordinate.
     * @param val Coordinate samples.
     * @return the index in {@code val} corresponding to the interval
     * containing {@code c}.
     * @throws OutOfRangeException if {@code c} is out of the
     * range defined by the boundary values of {@code val}.
     */
    private int searchIndex(double c, double[] val) {
        final int r = Arrays.binarySearch(val, c);

        if (r == -1 ||
            r == -val.length - 1) {
            throw new OutOfRangeException(c, val[0], val[val.length - 1]);
        }

        if (r < 0) {
            // "c" in within an interpolation sub-interval: Return the
            // index of the sample at the lower end of the sub-interval.
            return -r - 2;
        }
        final int last = val.length - 1;
        if (r == last) {
            // "c" is the last sample of the range: Return the index
            // of the sample at the lower end of the last sub-interval.
            return last - 1;
        }

        // "c" is another sample point.
        return r;
    }

    /**
     * Compute the spline coefficients from the list of function values and
     * function partial derivatives values at the four corners of a grid
     * element. They must be specified in the following order:
     * <ul>
     *  <li>f(0,0)
     *  <li>f(1,0)
     *  <li>f(0,1)
     *  <li>f(1,1)
     *  <li>fx(0,0)
     *  <li>fx(1,0)
     *  <li>fx(0,1)
     *  <li>fx(1,1)
     *  <li>fy(0,0)
     *  <li>fy(1,0)
     *  <li>fy(0,1)
     *  <li>fy(1,1)
     *  <li>fxy(0,0)
     *  <li>fxy(1,0)
     *  <li>fxy(0,1)
     *  <li>fxy(1,1)
     * </ul>
     * where the subscripts indicate the partial derivative with respect to
     * the corresponding variable(s).
     *
     * @param beta List of function values and function partial derivatives
     * values.
     * @return the spline coefficients.
     */
    private double[] computeSplineCoefficients(double[] beta) {
        final double[] a = new double[NUM_COEFF];

        for (int i = 0; i < NUM_COEFF; i++) {
            double result = 0;
            final double[] row = AINV[i];
            for (int j = 0; j < NUM_COEFF; j++) {
                result += row[j] * beta[j];
            }
            a[i] = result;
        }

        return a;
    }
}

/**
 * 2D-spline function.
 *
 */
class BicubicSplineFunction implements BivariateFunction {
    /** Number of points. */
    private static final short N = 4;
    /** Coefficients */
    private final double[][] a;
    /** First partial derivative along x. */
    private final BivariateFunction partialDerivativeX;
    /** First partial derivative along y. */
    private final BivariateFunction partialDerivativeY;
    /** Second partial derivative along x. */
    private final BivariateFunction partialDerivativeXX;
    /** Second partial derivative along y. */
    private final BivariateFunction partialDerivativeYY;
    /** Second crossed partial derivative. */
    private final BivariateFunction partialDerivativeXY;

    /**
     * Simple constructor.
     *
     * @param coeff Spline coefficients.
     */
    BicubicSplineFunction(double[] coeff) {
        this(coeff, false);
    }

    /**
     * Simple constructor.
     *
     * @param coeff Spline coefficients.
     * @param initializeDerivatives Whether to initialize the internal data
     * needed for calling any of the methods that compute the partial derivatives
     * this function.
     */
    BicubicSplineFunction(double[] coeff, boolean initializeDerivatives) {
        a = new double[N][N];
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                a[i][j] = coeff[i * N + j];
            }
        }

        if (initializeDerivatives) {
            // Compute all partial derivatives functions.
            final double[][] aX = new double[N][N];
            final double[][] aY = new double[N][N];
            final double[][] aXX = new double[N][N];
            final double[][] aYY = new double[N][N];
            final double[][] aXY = new double[N][N];

            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    final double c = a[i][j];
                    aX[i][j] = i * c;
                    aY[i][j] = j * c;
                    aXX[i][j] = (i - 1) * aX[i][j];
                    aYY[i][j] = (j - 1) * aY[i][j];
                    aXY[i][j] = j * aX[i][j];
                }
            }

            partialDerivativeX = new BivariateFunction() {
                    /** {@inheritDoc} */
                    public double value(double x, double y)  {
                        final double x2 = x * x;
                        final double[] pX = {0, 1, x, x2};

                        final double y2 = y * y;
                        final double y3 = y2 * y;
                        final double[] pY = {1, y, y2, y3};

                        return apply(pX, pY, aX);
                    }
                };
            partialDerivativeY = new BivariateFunction() {
                    /** {@inheritDoc} */
                    public double value(double x, double y)  {
                        final double x2 = x * x;
                        final double x3 = x2 * x;
                        final double[] pX = {1, x, x2, x3};

                        final double y2 = y * y;
                        final double[] pY = {0, 1, y, y2};

                        return apply(pX, pY, aY);
                    }
                };
            partialDerivativeXX = new BivariateFunction() {
                    /** {@inheritDoc} */
                    public double value(double x, double y)  {
                        final double[] pX = {0, 0, 1, x};

                        final double y2 = y * y;
                        final double y3 = y2 * y;
                        final double[] pY = {1, y, y2, y3};

                        return apply(pX, pY, aXX);
                    }
                };
            partialDerivativeYY = new BivariateFunction() {
                    /** {@inheritDoc} */
                    public double value(double x, double y)  {
                        final double x2 = x * x;
                        final double x3 = x2 * x;
                        final double[] pX = {1, x, x2, x3};

                        final double[] pY = {0, 0, 1, y};

                        return apply(pX, pY, aYY);
                    }
                };
            partialDerivativeXY = new BivariateFunction() {
                    /** {@inheritDoc} */
                    public double value(double x, double y)  {
                        final double x2 = x * x;
                        final double[] pX = {0, 1, x, x2};

                        final double y2 = y * y;
                        final double[] pY = {0, 1, y, y2};

                        return apply(pX, pY, aXY);
                    }
                };
        } else {
            partialDerivativeX = null;
            partialDerivativeY = null;
            partialDerivativeXX = null;
            partialDerivativeYY = null;
            partialDerivativeXY = null;
        }
    }

    /**
     * {@inheritDoc}
     */
    public double value(double x, double y) {
        if (x < 0 || x > 1) {
            throw new OutOfRangeException(x, 0, 1);
        }
        if (y < 0 || y > 1) {
            throw new OutOfRangeException(y, 0, 1);
        }

        final double x2 = x * x;
        final double x3 = x2 * x;
        final double[] pX = {1, x, x2, x3};

        final double y2 = y * y;
        final double y3 = y2 * y;
        final double[] pY = {1, y, y2, y3};

        return apply(pX, pY, a);
    }

    /**
     * Compute the value of the bicubic polynomial.
     *
     * @param pX Powers of the x-coordinate.
     * @param pY Powers of the y-coordinate.
     * @param coeff Spline coefficients.
     * @return the interpolated value.
     */
    private double apply(double[] pX, double[] pY, double[][] coeff) {
        double result = 0;
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                result += coeff[i][j] * pX[i] * pY[j];
            }
        }

        return result;
    }

    /**
     * @return the partial derivative wrt {@code x}.
     */
    public BivariateFunction partialDerivativeX() {
        return partialDerivativeX;
    }
    /**
     * @return the partial derivative wrt {@code y}.
     */
    public BivariateFunction partialDerivativeY() {
        return partialDerivativeY;
    }
    /**
     * @return the second partial derivative wrt {@code x}.
     */
    public BivariateFunction partialDerivativeXX() {
        return partialDerivativeXX;
    }
    /**
     * @return the second partial derivative wrt {@code y}.
     */
    public BivariateFunction partialDerivativeYY() {
        return partialDerivativeYY;
    }
    /**
     * @return the second partial cross-derivative.
     */
    public BivariateFunction partialDerivativeXY() {
        return partialDerivativeXY;
    }
}

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