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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.math.analysis.interpolation;
+
+import org.apache.commons.math.DimensionMismatchException;
+import org.apache.commons.math.MathException;
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
+import org.apache.commons.math.exception.NoDataException;
+import org.apache.commons.math.util.MathUtils;
+
+/**
+ * Generates a bicubic interpolating function.
+ *
+ * @version $Revision: 980944 $ $Date: 2010-07-30 22:31:11 +0200 (ven. 30 juil. 2010) $
+ * @since 2.2
+ */
+public class BicubicSplineInterpolator
+ implements BivariateRealGridInterpolator {
+ /**
+ * {@inheritDoc}
+ */
+ public BicubicSplineInterpolatingFunction interpolate(final double[] xval,
+ final double[] yval,
+ final double[][] fval)
+ throws MathException, IllegalArgumentException {
+ 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);
+ }
+
+ MathUtils.checkOrder(xval);
+ MathUtils.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 UnivariateRealFunction 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 UnivariateRealFunction 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);
+ }
+
+ /**
+ * Compute the next index of an array, clipping if necessary.
+ * It is assumed (but not checked) that {@code i} is larger than or equal to 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;
+ }
+ /**
+ * Compute 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;
+ }
+}