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/*
* 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.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
* <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. */
private static final int MIN_NUM_POINTS = 5;
/** 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 double[][] fval;
/**
* @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}
*/
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.
*
* @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 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;
}
}
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