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Java example source code file (TricubicSplineInterpolator.java)

This example Java source code file (TricubicSplineInterpolator.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

bicubicsplineinterpolatingfunction, bicubicsplineinterpolator, deprecated, dimensionmismatchexception, nodataexception, nonmonotonicsequenceexception, numberistoosmallexception, tricubicsplineinterpolatingfunction, tricubicsplineinterpolator, trivariategridinterpolator

The TricubicSplineInterpolator.java Java example source code

/*
 * 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.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 tricubic interpolating function.
 *
 * @since 2.2
 * @deprecated To be removed in 4.0 (see MATH-1166).
 */
@Deprecated
public class TricubicSplineInterpolator
    implements TrivariateGridInterpolator {
    /**
     * {@inheritDoc}
     */
    public TricubicSplineInterpolatingFunction interpolate(final double[] xval,
                                                           final double[] yval,
                                                           final double[] zval,
                                                           final double[][][] fval)
        throws NoDataException, NumberIsTooSmallException,
               DimensionMismatchException, NonMonotonicSequenceException {
        if (xval.length == 0 || yval.length == 0 || zval.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);
        MathArrays.checkOrder(zval);

        final int xLen = xval.length;
        final int yLen = yval.length;
        final int zLen = zval.length;

        // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets
        // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])
        // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])
        final double[][][] fvalXY = new double[zLen][xLen][yLen];
        final double[][][] fvalZX = new double[yLen][zLen][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++) {
                if (fval[i][j].length != zLen) {
                    throw new DimensionMismatchException(fval[i][j].length, zLen);
                }

                for (int k = 0; k < zLen; k++) {
                    final double v = fval[i][j][k];
                    fvalXY[k][i][j] = v;
                    fvalZX[j][k][i] = v;
                }
            }
        }

        final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator(true);

        // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
        final BicubicSplineInterpolatingFunction[] xSplineYZ
            = new BicubicSplineInterpolatingFunction[xLen];
        for (int i = 0; i < xLen; i++) {
            xSplineYZ[i] = bsi.interpolate(yval, zval, fval[i]);
        }

        // For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x
        final BicubicSplineInterpolatingFunction[] ySplineZX
            = new BicubicSplineInterpolatingFunction[yLen];
        for (int j = 0; j < yLen; j++) {
            ySplineZX[j] = bsi.interpolate(zval, xval, fvalZX[j]);
        }

        // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
        final BicubicSplineInterpolatingFunction[] zSplineXY
            = new BicubicSplineInterpolatingFunction[zLen];
        for (int k = 0; k < zLen; k++) {
            zSplineXY[k] = bsi.interpolate(xval, yval, fvalXY[k]);
        }

        // Partial derivatives wrt x and wrt y
        final double[][][] dFdX = new double[xLen][yLen][zLen];
        final double[][][] dFdY = new double[xLen][yLen][zLen];
        final double[][][] d2FdXdY = new double[xLen][yLen][zLen];
        for (int k = 0; k < zLen; k++) {
            final BicubicSplineInterpolatingFunction f = zSplineXY[k];
            for (int i = 0; i < xLen; i++) {
                final double x = xval[i];
                for (int j = 0; j < yLen; j++) {
                    final double y = yval[j];
                    dFdX[i][j][k] = f.partialDerivativeX(x, y);
                    dFdY[i][j][k] = f.partialDerivativeY(x, y);
                    d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y);
                }
            }
        }

        // Partial derivatives wrt y and wrt z
        final double[][][] dFdZ = new double[xLen][yLen][zLen];
        final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];
        for (int i = 0; i < xLen; i++) {
            final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
            for (int j = 0; j < yLen; j++) {
                final double y = yval[j];
                for (int k = 0; k < zLen; k++) {
                    final double z = zval[k];
                    dFdZ[i][j][k] = f.partialDerivativeY(y, z);
                    d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z);
                }
            }
        }

        // Partial derivatives wrt x and wrt z
        final double[][][] d2FdZdX = new double[xLen][yLen][zLen];
        for (int j = 0; j < yLen; j++) {
            final BicubicSplineInterpolatingFunction f = ySplineZX[j];
            for (int k = 0; k < zLen; k++) {
                final double z = zval[k];
                for (int i = 0; i < xLen; i++) {
                    final double x = xval[i];
                    d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);
                }
            }
        }

        // Third partial cross-derivatives
        final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];
        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);
                for (int k = 0; k < zLen; k++) {
                    final int nK = nextIndex(k, zLen);
                    final int pK = previousIndex(k);

                    // XXX Not sure about this formula
                    d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] -
                                          fval[pI][nJ][nK] + fval[pI][pJ][nK] -
                                          fval[nI][nJ][pK] + fval[nI][pJ][pK] +
                                          fval[pI][nJ][pK] - fval[pI][pJ][pK]) /
                        ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]) * (zval[nK] - zval[pK])) ;
                }
            }
        }

        // Create the interpolating splines
        return new TricubicSplineInterpolatingFunction(xval, yval, zval, fval,
                                                       dFdX, dFdY, dFdZ,
                                                       d2FdXdY, d2FdZdX, d2FdYdZ,
                                                       d3FdXdYdZ);
    }

    /**
     * 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;
    }
}

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