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 * 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
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 *      http://www.apache.org/licenses/LICENSE-2.0
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 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math3.analysis.interpolation;

import java.util.Arrays;
import org.apache.commons.math3.analysis.BivariateFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.InsufficientDataException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NullArgumentException;
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
bicubic spline interpolation. This implementation currently uses AkimaSplineInterpolator as the underlying one-dimensional interpolator, which requires 5 sample points; insufficient data will raise an exception when the value method is called. 
Since:
3.4/**
 * Function that implements the
 * <a href="http://www.paulinternet.nl/?page=bicubic">bicubic spline</a>
 * interpolation.
 * This implementation currently uses {@link AkimaSplineInterpolator} as the
 * underlying one-dimensional interpolator, which requires 5 sample points;
 * insufficient data will raise an exception when the
 * {@link #value(double,double) value} method is called.
 *
 * @since 3.4
 */
public class PiecewiseBicubicSplineInterpolatingFunction
    implements BivariateFunction {
    
The minimum number of points that are needed to compute the function. /** The minimum number of points that are needed to compute the function. */
    private static final int MIN_NUM_POINTS = 5;
    
Samples x-coordinates /** Samples x-coordinates */
    private final double[] xval;
    
Samples y-coordinates /** Samples y-coordinates */
    private final double[] yval;
    
Set of cubic splines patching the whole data grid /** Set of cubic splines patching the whole data grid */
    private final double[][] fval;

    
Params:
x – Sample values of the x-coordinate, in increasing order.
y – Sample values of the y-coordinate, in increasing order.
f – Values of the function on every grid point. the expected number
       of elements.
Throws:
NonMonotonicSequenceException – if x or y are not strictly increasing.
NullArgumentException – if any of the arguments are null
NoDataException – if any of the arrays has zero length.
DimensionMismatchException – if the length of x and y don't match the row, column
        height of f/**
     * @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. the expected number
     *        of elements.
     * @throws NonMonotonicSequenceException if {@code x} or {@code y} are not
     *         strictly increasing.
     * @throws NullArgumentException if any of the arguments are null
     * @throws NoDataException if any of the arrays has zero length.
     * @throws DimensionMismatchException if the length of x and y don't match the row, column
     *         height of f
     */
    public PiecewiseBicubicSplineInterpolatingFunction(double[] x,
                                                       double[] y,
                                                       double[][] f)
        throws DimensionMismatchException,
               NullArgumentException,
               NoDataException,
               NonMonotonicSequenceException {
        if (x == null ||
            y == null ||
            f == null ||
            f[0] == null) {
            throw new NullArgumentException();
        }

        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 < MIN_NUM_POINTS ||
            yLen < MIN_NUM_POINTS ||
            f.length < MIN_NUM_POINTS ||
            f[0].length < MIN_NUM_POINTS) {
            throw new InsufficientDataException();
        }

        if (xLen != f.length) {
            throw new DimensionMismatchException(xLen, f.length);
        }

        if (yLen != f[0].length) {
            throw new DimensionMismatchException(yLen, f[0].length);
        }

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

        xval = x.clone();
        yval = y.clone();
        fval = f.clone();
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public double value(double x,
                        double y)
        throws OutOfRangeException {
        final AkimaSplineInterpolator interpolator = new AkimaSplineInterpolator();
        final int offset = 2;
        final int count = offset + 3;
        final int i = searchIndex(x, xval, offset, count);
        final int j = searchIndex(y, yval, offset, count);

        final double xArray[] = new double[count];
        final double yArray[] = new double[count];
        final double zArray[] = new double[count];
        final double interpArray[] = new double[count];

        for (int index = 0; index < count; index++) {
            xArray[index] = xval[i + index];
            yArray[index] = yval[j + index];
        }

        for (int zIndex = 0; zIndex < count; zIndex++) {
            for (int index = 0; index < count; index++) {
                zArray[index] = fval[i + index][j + zIndex];
            }
            final PolynomialSplineFunction spline = interpolator.interpolate(xArray, zArray);
            interpArray[zIndex] = spline.value(x);
        }

        final PolynomialSplineFunction spline = interpolator.interpolate(yArray, interpArray);

        double returnValue = spline.value(y);

        return returnValue;
    }

    
Indicates whether a point is within the interpolation range.
Params:
x – First coordinate.
y – Second coordinate.
Returns:
true if (x, y) is a valid point.
Since:
3.3/**
     * 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;
        }
    }

    
Params:
c – Coordinate.
val – Coordinate samples.
offset – how far back from found value to offset for querying
count – total number of elements forward from beginning that will be
       queried
Throws:
OutOfRangeException – if c is out of the range defined by the boundary values of val.
Returns:
the index in val corresponding to the interval containing c./**
     * @param c Coordinate.
     * @param val Coordinate samples.
     * @param offset how far back from found value to offset for querying
     * @param count total number of elements forward from beginning that will be
     *        queried
     * @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,
                            int offset,
                            int count) {
        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, which returns
            // negative
            // need to remove the negative sign for consistency
            r = -r - offset - 1;
        } else {
            r -= offset;
        }

        if (r < 0) {
            r = 0;
        }

        if ((r + count) >= val.length) {
            // "c" is the last sample of the range: Return the index
            // of the sample at the lower end of the last sub-interval.
            r = val.length - count;
        }

        return r;
    }
}