BicubicSplineInterpolator.java
- /*
- * 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;
- }
- }