/*
* 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;
}
}