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Posted to commits@commons.apache.org by tn...@apache.org on 2015/02/25 23:02:46 UTC
[4/4] [math] Remove deprecated interpolation and fitter classes.
Remove deprecated interpolation and fitter classes.
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/0a5cd113
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/0a5cd113
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/0a5cd113
Branch: refs/heads/master
Commit: 0a5cd11327d50e5906fb4dc08bce5baea6b2d247
Parents: d389e94
Author: Thomas Neidhart <th...@gmail.com>
Authored: Wed Feb 25 23:02:30 2015 +0100
Committer: Thomas Neidhart <th...@gmail.com>
Committed: Wed Feb 25 23:02:30 2015 +0100
----------------------------------------------------------------------
.../BicubicSplineInterpolatingFunction.java | 638 ------------------
.../BicubicSplineInterpolator.java | 176 -----
...hingPolynomialBicubicSplineInterpolator.java | 171 -----
.../TricubicSplineInterpolatingFunction.java | 482 -------------
.../TricubicSplineInterpolator.java | 201 ------
.../math4/analysis/solvers/NewtonSolver.java | 92 ---
.../commons/math4/fitting/CurveFitter.java | 233 -------
.../commons/math4/fitting/GaussianFitter.java | 365 ----------
.../commons/math4/fitting/HarmonicFitter.java | 384 -----------
.../commons/math4/fitting/PolynomialFitter.java | 72 --
.../BicubicSplineInterpolatingFunctionTest.java | 670 -------------------
.../BicubicSplineInterpolatorTest.java | 186 -----
...PolynomialBicubicSplineInterpolatorTest.java | 181 -----
...TricubicSplineInterpolatingFunctionTest.java | 545 ---------------
.../TricubicSplineInterpolatorTest.java | 214 ------
.../analysis/solvers/NewtonSolverTest.java | 111 ---
.../commons/math4/fitting/CurveFitterTest.java | 143 ----
.../math4/fitting/GaussianFitterTest.java | 364 ----------
.../math4/fitting/HarmonicFitterTest.java | 187 ------
.../math4/fitting/PolynomialFitterTest.java | 288 --------
20 files changed, 5703 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/0a5cd113/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolatingFunction.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolatingFunction.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolatingFunction.java
deleted file mode 100644
index e9f7e19..0000000
--- a/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolatingFunction.java
+++ /dev/null
@@ -1,638 +0,0 @@
-/*
- * 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.math4.analysis.interpolation;
-
-import java.util.Arrays;
-
-import org.apache.commons.math4.analysis.BivariateFunction;
-import org.apache.commons.math4.exception.DimensionMismatchException;
-import org.apache.commons.math4.exception.NoDataException;
-import org.apache.commons.math4.exception.NonMonotonicSequenceException;
-import org.apache.commons.math4.exception.OutOfRangeException;
-import org.apache.commons.math4.util.MathArrays;
-
-/**
- * Function that implements the
- * <a href="http://en.wikipedia.org/wiki/Bicubic_interpolation">
- * bicubic spline interpolation</a>. Due to numerical accuracy issues this should not
- * be used.
- *
- * @since 2.1
- * @deprecated as of 3.4 replaced by
- * {@link org.apache.commons.math4.analysis.interpolation.PiecewiseBicubicSplineInterpolatingFunction}
- */
-@Deprecated
-public class BicubicSplineInterpolatingFunction
- implements BivariateFunction {
- /** Number of coefficients. */
- private static final int NUM_COEFF = 16;
- /**
- * Matrix to compute the spline coefficients from the function values
- * and function derivatives values
- */
- private static final double[][] AINV = {
- { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },
- { -3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0 },
- { 2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0 },
- { 0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0 },
- { 0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0 },
- { -3,0,3,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },
- { 0,0,0,0,-3,0,3,0,0,0,0,0,-2,0,-1,0 },
- { 9,-9,-9,9,6,3,-6,-3,6,-6,3,-3,4,2,2,1 },
- { -6,6,6,-6,-3,-3,3,3,-4,4,-2,2,-2,-2,-1,-1 },
- { 2,0,-2,0,0,0,0,0,1,0,1,0,0,0,0,0 },
- { 0,0,0,0,2,0,-2,0,0,0,0,0,1,0,1,0 },
- { -6,6,6,-6,-4,-2,4,2,-3,3,-3,3,-2,-1,-2,-1 },
- { 4,-4,-4,4,2,2,-2,-2,2,-2,2,-2,1,1,1,1 }
- };
-
- /** 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 BicubicSplineFunction[][] splines;
- /**
- * Partial derivatives.
- * The value of the first index determines the kind of derivatives:
- * 0 = first partial derivatives wrt x
- * 1 = first partial derivatives wrt y
- * 2 = second partial derivatives wrt x
- * 3 = second partial derivatives wrt y
- * 4 = cross partial derivatives
- */
- private final BivariateFunction[][][] partialDerivatives;
-
- /**
- * @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.
- * @param dFdX Values of the partial derivative of function with respect
- * to x on every grid point.
- * @param dFdY Values of the partial derivative of function with respect
- * to y on every grid point.
- * @param d2FdXdY Values of the cross partial derivative of function on
- * every grid point.
- * @throws DimensionMismatchException if the various arrays do not contain
- * the expected number of elements.
- * @throws NonMonotonicSequenceException if {@code x} or {@code y} are
- * not strictly increasing.
- * @throws NoDataException if any of the arrays has zero length.
- */
- public BicubicSplineInterpolatingFunction(double[] x,
- double[] y,
- double[][] f,
- double[][] dFdX,
- double[][] dFdY,
- double[][] d2FdXdY)
- throws DimensionMismatchException,
- NoDataException,
- NonMonotonicSequenceException {
- this(x, y, f, dFdX, dFdY, d2FdXdY, false);
- }
-
- /**
- * @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.
- * @param dFdX Values of the partial derivative of function with respect
- * to x on every grid point.
- * @param dFdY Values of the partial derivative of function with respect
- * to y on every grid point.
- * @param d2FdXdY Values of the cross partial derivative of function on
- * every grid point.
- * @param initializeDerivatives Whether to initialize the internal data
- * needed for calling any of the methods that compute the partial derivatives
- * this function.
- * @throws DimensionMismatchException if the various arrays do not contain
- * the expected number of elements.
- * @throws NonMonotonicSequenceException if {@code x} or {@code y} are
- * not strictly increasing.
- * @throws NoDataException if any of the arrays has zero length.
- *
- * @see #partialDerivativeX(double,double)
- * @see #partialDerivativeY(double,double)
- * @see #partialDerivativeXX(double,double)
- * @see #partialDerivativeYY(double,double)
- * @see #partialDerivativeXY(double,double)
- */
- public BicubicSplineInterpolatingFunction(double[] x,
- double[] y,
- double[][] f,
- double[][] dFdX,
- double[][] dFdY,
- double[][] d2FdXdY,
- boolean initializeDerivatives)
- throws DimensionMismatchException,
- NoDataException,
- NonMonotonicSequenceException {
- 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 != f.length) {
- throw new DimensionMismatchException(xLen, f.length);
- }
- if (xLen != dFdX.length) {
- throw new DimensionMismatchException(xLen, dFdX.length);
- }
- if (xLen != dFdY.length) {
- throw new DimensionMismatchException(xLen, dFdY.length);
- }
- if (xLen != d2FdXdY.length) {
- throw new DimensionMismatchException(xLen, d2FdXdY.length);
- }
-
- MathArrays.checkOrder(x);
- MathArrays.checkOrder(y);
-
- xval = x.clone();
- yval = y.clone();
-
- final int lastI = xLen - 1;
- final int lastJ = yLen - 1;
- splines = new BicubicSplineFunction[lastI][lastJ];
-
- for (int i = 0; i < lastI; i++) {
- if (f[i].length != yLen) {
- throw new DimensionMismatchException(f[i].length, yLen);
- }
- if (dFdX[i].length != yLen) {
- throw new DimensionMismatchException(dFdX[i].length, yLen);
- }
- if (dFdY[i].length != yLen) {
- throw new DimensionMismatchException(dFdY[i].length, yLen);
- }
- if (d2FdXdY[i].length != yLen) {
- throw new DimensionMismatchException(d2FdXdY[i].length, yLen);
- }
- final int ip1 = i + 1;
- for (int j = 0; j < lastJ; j++) {
- final int jp1 = j + 1;
- final double[] beta = new double[] {
- f[i][j], f[ip1][j], f[i][jp1], f[ip1][jp1],
- dFdX[i][j], dFdX[ip1][j], dFdX[i][jp1], dFdX[ip1][jp1],
- dFdY[i][j], dFdY[ip1][j], dFdY[i][jp1], dFdY[ip1][jp1],
- d2FdXdY[i][j], d2FdXdY[ip1][j], d2FdXdY[i][jp1], d2FdXdY[ip1][jp1]
- };
-
- splines[i][j] = new BicubicSplineFunction(computeSplineCoefficients(beta),
- initializeDerivatives);
- }
- }
-
- if (initializeDerivatives) {
- // Compute all partial derivatives.
- partialDerivatives = new BivariateFunction[5][lastI][lastJ];
-
- for (int i = 0; i < lastI; i++) {
- for (int j = 0; j < lastJ; j++) {
- final BicubicSplineFunction bcs = splines[i][j];
- partialDerivatives[0][i][j] = bcs.partialDerivativeX();
- partialDerivatives[1][i][j] = bcs.partialDerivativeY();
- partialDerivatives[2][i][j] = bcs.partialDerivativeXX();
- partialDerivatives[3][i][j] = bcs.partialDerivativeYY();
- partialDerivatives[4][i][j] = bcs.partialDerivativeXY();
- }
- }
- } else {
- // Partial derivative methods cannot be used.
- partialDerivatives = null;
- }
- }
-
- /**
- * {@inheritDoc}
- */
- public double value(double x, double y)
- throws OutOfRangeException {
- final int i = searchIndex(x, xval);
- final int j = searchIndex(y, yval);
-
- final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
- final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
-
- return splines[i][j].value(xN, yN);
- }
-
- /**
- * 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 x x-coordinate.
- * @param y y-coordinate.
- * @return the value at point (x, y) of the first partial derivative with
- * respect to x.
- * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
- * the range defined by the boundary values of {@code xval} (resp.
- * {@code yval}).
- * @throws NullPointerException if the internal data were not initialized
- * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
- * double[][],double[][],double[][],boolean) constructor}).
- */
- public double partialDerivativeX(double x, double y)
- throws OutOfRangeException {
- return partialDerivative(0, x, y);
- }
- /**
- * @param x x-coordinate.
- * @param y y-coordinate.
- * @return the value at point (x, y) of the first partial derivative with
- * respect to y.
- * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
- * the range defined by the boundary values of {@code xval} (resp.
- * {@code yval}).
- * @throws NullPointerException if the internal data were not initialized
- * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
- * double[][],double[][],double[][],boolean) constructor}).
- */
- public double partialDerivativeY(double x, double y)
- throws OutOfRangeException {
- return partialDerivative(1, x, y);
- }
- /**
- * @param x x-coordinate.
- * @param y y-coordinate.
- * @return the value at point (x, y) of the second partial derivative with
- * respect to x.
- * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
- * the range defined by the boundary values of {@code xval} (resp.
- * {@code yval}).
- * @throws NullPointerException if the internal data were not initialized
- * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
- * double[][],double[][],double[][],boolean) constructor}).
- */
- public double partialDerivativeXX(double x, double y)
- throws OutOfRangeException {
- return partialDerivative(2, x, y);
- }
- /**
- * @param x x-coordinate.
- * @param y y-coordinate.
- * @return the value at point (x, y) of the second partial derivative with
- * respect to y.
- * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
- * the range defined by the boundary values of {@code xval} (resp.
- * {@code yval}).
- * @throws NullPointerException if the internal data were not initialized
- * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
- * double[][],double[][],double[][],boolean) constructor}).
- */
- public double partialDerivativeYY(double x, double y)
- throws OutOfRangeException {
- return partialDerivative(3, x, y);
- }
- /**
- * @param x x-coordinate.
- * @param y y-coordinate.
- * @return the value at point (x, y) of the second partial cross-derivative.
- * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
- * the range defined by the boundary values of {@code xval} (resp.
- * {@code yval}).
- * @throws NullPointerException if the internal data were not initialized
- * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
- * double[][],double[][],double[][],boolean) constructor}).
- */
- public double partialDerivativeXY(double x, double y)
- throws OutOfRangeException {
- return partialDerivative(4, x, y);
- }
-
- /**
- * @param which First index in {@link #partialDerivatives}.
- * @param x x-coordinate.
- * @param y y-coordinate.
- * @return the value at point (x, y) of the selected partial derivative.
- * @throws OutOfRangeException if {@code x} (resp. {@code y}) is outside
- * the range defined by the boundary values of {@code xval} (resp.
- * {@code yval}).
- * @throws NullPointerException if the internal data were not initialized
- * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
- * double[][],double[][],double[][],boolean) constructor}).
- */
- private double partialDerivative(int which, double x, double y)
- throws OutOfRangeException {
- final int i = searchIndex(x, xval);
- final int j = searchIndex(y, yval);
-
- final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
- final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
-
- return partialDerivatives[which][i][j].value(xN, yN);
- }
-
- /**
- * @param c Coordinate.
- * @param val Coordinate samples.
- * @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) {
- final 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: Return the
- // index of the sample at the lower end of the sub-interval.
- return -r - 2;
- }
- final int last = val.length - 1;
- if (r == last) {
- // "c" is the last sample of the range: Return the index
- // of the sample at the lower end of the last sub-interval.
- return last - 1;
- }
-
- // "c" is another sample point.
- return r;
- }
-
- /**
- * Compute the spline coefficients from the list of function values and
- * function partial derivatives values at the four corners of a grid
- * element. They must be specified in the following order:
- * <ul>
- * <li>f(0,0)</li>
- * <li>f(1,0)</li>
- * <li>f(0,1)</li>
- * <li>f(1,1)</li>
- * <li>f<sub>x</sub>(0,0)</li>
- * <li>f<sub>x</sub>(1,0)</li>
- * <li>f<sub>x</sub>(0,1)</li>
- * <li>f<sub>x</sub>(1,1)</li>
- * <li>f<sub>y</sub>(0,0)</li>
- * <li>f<sub>y</sub>(1,0)</li>
- * <li>f<sub>y</sub>(0,1)</li>
- * <li>f<sub>y</sub>(1,1)</li>
- * <li>f<sub>xy</sub>(0,0)</li>
- * <li>f<sub>xy</sub>(1,0)</li>
- * <li>f<sub>xy</sub>(0,1)</li>
- * <li>f<sub>xy</sub>(1,1)</li>
- * </ul>
- * where the subscripts indicate the partial derivative with respect to
- * the corresponding variable(s).
- *
- * @param beta List of function values and function partial derivatives
- * values.
- * @return the spline coefficients.
- */
- private double[] computeSplineCoefficients(double[] beta) {
- final double[] a = new double[NUM_COEFF];
-
- for (int i = 0; i < NUM_COEFF; i++) {
- double result = 0;
- final double[] row = AINV[i];
- for (int j = 0; j < NUM_COEFF; j++) {
- result += row[j] * beta[j];
- }
- a[i] = result;
- }
-
- return a;
- }
-}
-
-/**
- * 2D-spline function.
- *
- */
-class BicubicSplineFunction implements BivariateFunction {
- /** Number of points. */
- private static final short N = 4;
- /** Coefficients */
- private final double[][] a;
- /** First partial derivative along x. */
- private final BivariateFunction partialDerivativeX;
- /** First partial derivative along y. */
- private final BivariateFunction partialDerivativeY;
- /** Second partial derivative along x. */
- private final BivariateFunction partialDerivativeXX;
- /** Second partial derivative along y. */
- private final BivariateFunction partialDerivativeYY;
- /** Second crossed partial derivative. */
- private final BivariateFunction partialDerivativeXY;
-
- /**
- * Simple constructor.
- *
- * @param coeff Spline coefficients.
- */
- public BicubicSplineFunction(double[] coeff) {
- this(coeff, false);
- }
-
- /**
- * Simple constructor.
- *
- * @param coeff Spline coefficients.
- * @param initializeDerivatives Whether to initialize the internal data
- * needed for calling any of the methods that compute the partial derivatives
- * this function.
- */
- public BicubicSplineFunction(double[] coeff,
- boolean initializeDerivatives) {
- a = new double[N][N];
- for (int i = 0; i < N; i++) {
- for (int j = 0; j < N; j++) {
- a[i][j] = coeff[i * N + j];
- }
- }
-
- if (initializeDerivatives) {
- // Compute all partial derivatives functions.
- final double[][] aX = new double[N][N];
- final double[][] aY = new double[N][N];
- final double[][] aXX = new double[N][N];
- final double[][] aYY = new double[N][N];
- final double[][] aXY = new double[N][N];
-
- for (int i = 0; i < N; i++) {
- for (int j = 0; j < N; j++) {
- final double c = a[i][j];
- aX[i][j] = i * c;
- aY[i][j] = j * c;
- aXX[i][j] = (i - 1) * aX[i][j];
- aYY[i][j] = (j - 1) * aY[i][j];
- aXY[i][j] = j * aX[i][j];
- }
- }
-
- partialDerivativeX = new BivariateFunction() {
- public double value(double x, double y) {
- final double x2 = x * x;
- final double[] pX = {0, 1, x, x2};
-
- final double y2 = y * y;
- final double y3 = y2 * y;
- final double[] pY = {1, y, y2, y3};
-
- return apply(pX, pY, aX);
- }
- };
- partialDerivativeY = new BivariateFunction() {
- public double value(double x, double y) {
- final double x2 = x * x;
- final double x3 = x2 * x;
- final double[] pX = {1, x, x2, x3};
-
- final double y2 = y * y;
- final double[] pY = {0, 1, y, y2};
-
- return apply(pX, pY, aY);
- }
- };
- partialDerivativeXX = new BivariateFunction() {
- public double value(double x, double y) {
- final double[] pX = {0, 0, 1, x};
-
- final double y2 = y * y;
- final double y3 = y2 * y;
- final double[] pY = {1, y, y2, y3};
-
- return apply(pX, pY, aXX);
- }
- };
- partialDerivativeYY = new BivariateFunction() {
- public double value(double x, double y) {
- final double x2 = x * x;
- final double x3 = x2 * x;
- final double[] pX = {1, x, x2, x3};
-
- final double[] pY = {0, 0, 1, y};
-
- return apply(pX, pY, aYY);
- }
- };
- partialDerivativeXY = new BivariateFunction() {
- public double value(double x, double y) {
- final double x2 = x * x;
- final double[] pX = {0, 1, x, x2};
-
- final double y2 = y * y;
- final double[] pY = {0, 1, y, y2};
-
- return apply(pX, pY, aXY);
- }
- };
- } else {
- partialDerivativeX = null;
- partialDerivativeY = null;
- partialDerivativeXX = null;
- partialDerivativeYY = null;
- partialDerivativeXY = null;
- }
- }
-
- /**
- * {@inheritDoc}
- */
- public double value(double x, double y) {
- if (x < 0 || x > 1) {
- throw new OutOfRangeException(x, 0, 1);
- }
- if (y < 0 || y > 1) {
- throw new OutOfRangeException(y, 0, 1);
- }
-
- final double x2 = x * x;
- final double x3 = x2 * x;
- final double[] pX = {1, x, x2, x3};
-
- final double y2 = y * y;
- final double y3 = y2 * y;
- final double[] pY = {1, y, y2, y3};
-
- return apply(pX, pY, a);
- }
-
- /**
- * Compute the value of the bicubic polynomial.
- *
- * @param pX Powers of the x-coordinate.
- * @param pY Powers of the y-coordinate.
- * @param coeff Spline coefficients.
- * @return the interpolated value.
- */
- private double apply(double[] pX, double[] pY, double[][] coeff) {
- double result = 0;
- for (int i = 0; i < N; i++) {
- for (int j = 0; j < N; j++) {
- result += coeff[i][j] * pX[i] * pY[j];
- }
- }
-
- return result;
- }
-
- /**
- * @return the partial derivative wrt {@code x}.
- */
- public BivariateFunction partialDerivativeX() {
- return partialDerivativeX;
- }
- /**
- * @return the partial derivative wrt {@code y}.
- */
- public BivariateFunction partialDerivativeY() {
- return partialDerivativeY;
- }
- /**
- * @return the second partial derivative wrt {@code x}.
- */
- public BivariateFunction partialDerivativeXX() {
- return partialDerivativeXX;
- }
- /**
- * @return the second partial derivative wrt {@code y}.
- */
- public BivariateFunction partialDerivativeYY() {
- return partialDerivativeYY;
- }
- /**
- * @return the second partial cross-derivative.
- */
- public BivariateFunction partialDerivativeXY() {
- return partialDerivativeXY;
- }
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/0a5cd113/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolator.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolator.java
deleted file mode 100644
index 53e726f..0000000
--- a/src/main/java/org/apache/commons/math4/analysis/interpolation/BicubicSplineInterpolator.java
+++ /dev/null
@@ -1,176 +0,0 @@
-/*
- * 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.math4.analysis.interpolation;
-
-import org.apache.commons.math4.analysis.UnivariateFunction;
-import org.apache.commons.math4.analysis.polynomials.PolynomialSplineFunction;
-import org.apache.commons.math4.exception.DimensionMismatchException;
-import org.apache.commons.math4.exception.NoDataException;
-import org.apache.commons.math4.exception.NonMonotonicSequenceException;
-import org.apache.commons.math4.exception.NumberIsTooSmallException;
-import org.apache.commons.math4.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.math4.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;
- }
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/0a5cd113/src/main/java/org/apache/commons/math4/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java
deleted file mode 100644
index 243da0c..0000000
--- a/src/main/java/org/apache/commons/math4/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java
+++ /dev/null
@@ -1,171 +0,0 @@
-/*
- * 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.math4.analysis.interpolation;
-
-import org.apache.commons.math4.analysis.polynomials.PolynomialFunction;
-import org.apache.commons.math4.exception.DimensionMismatchException;
-import org.apache.commons.math4.exception.NoDataException;
-import org.apache.commons.math4.exception.NonMonotonicSequenceException;
-import org.apache.commons.math4.exception.NotPositiveException;
-import org.apache.commons.math4.exception.NullArgumentException;
-import org.apache.commons.math4.fitting.PolynomialFitter;
-import org.apache.commons.math4.optim.SimpleVectorValueChecker;
-import org.apache.commons.math4.optim.nonlinear.vector.jacobian.GaussNewtonOptimizer;
-import org.apache.commons.math4.util.MathArrays;
-import org.apache.commons.math4.util.Precision;
-
-/**
- * Generates a bicubic interpolation function.
- * Prior to generating the interpolating function, the input is smoothed using
- * polynomial fitting.
- *
- * @since 2.2
- * @deprecated To be removed in 4.0 (see MATH-1166).
- */
-@Deprecated
-public class SmoothingPolynomialBicubicSplineInterpolator
- extends BicubicSplineInterpolator {
- /** Fitter for x. */
- private final PolynomialFitter xFitter;
- /** Degree of the fitting polynomial. */
- private final int xDegree;
- /** Fitter for y. */
- private final PolynomialFitter yFitter;
- /** Degree of the fitting polynomial. */
- private final int yDegree;
-
- /**
- * Default constructor. The degree of the fitting polynomials is set to 3.
- */
- public SmoothingPolynomialBicubicSplineInterpolator() {
- this(3);
- }
-
- /**
- * @param degree Degree of the polynomial fitting functions.
- * @exception NotPositiveException if degree is not positive
- */
- public SmoothingPolynomialBicubicSplineInterpolator(int degree)
- throws NotPositiveException {
- this(degree, degree);
- }
-
- /**
- * @param xDegree Degree of the polynomial fitting functions along the
- * x-dimension.
- * @param yDegree Degree of the polynomial fitting functions along the
- * y-dimension.
- * @exception NotPositiveException if degrees are not positive
- */
- public SmoothingPolynomialBicubicSplineInterpolator(int xDegree, int yDegree)
- throws NotPositiveException {
- if (xDegree < 0) {
- throw new NotPositiveException(xDegree);
- }
- if (yDegree < 0) {
- throw new NotPositiveException(yDegree);
- }
- this.xDegree = xDegree;
- this.yDegree = yDegree;
-
- final double safeFactor = 1e2;
- final SimpleVectorValueChecker checker
- = new SimpleVectorValueChecker(safeFactor * Precision.EPSILON,
- safeFactor * Precision.SAFE_MIN);
- xFitter = new PolynomialFitter(new GaussNewtonOptimizer(false, checker));
- yFitter = new PolynomialFitter(new GaussNewtonOptimizer(false, checker));
- }
-
- /**
- * {@inheritDoc}
- */
- @Override
- public BicubicSplineInterpolatingFunction interpolate(final double[] xval,
- final double[] yval,
- final double[][] fval)
- throws NoDataException, NullArgumentException,
- DimensionMismatchException, NonMonotonicSequenceException {
- 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);
- }
-
- final int xLen = xval.length;
- final int yLen = yval.length;
-
- for (int i = 0; i < xLen; i++) {
- if (fval[i].length != yLen) {
- throw new DimensionMismatchException(fval[i].length, yLen);
- }
- }
-
- MathArrays.checkOrder(xval);
- MathArrays.checkOrder(yval);
-
- // For each line y[j] (0 <= j < yLen), construct a polynomial, with
- // respect to variable x, fitting array fval[][j]
- final PolynomialFunction[] yPolyX = new PolynomialFunction[yLen];
- for (int j = 0; j < yLen; j++) {
- xFitter.clearObservations();
- for (int i = 0; i < xLen; i++) {
- xFitter.addObservedPoint(1, xval[i], fval[i][j]);
- }
-
- // Initial guess for the fit is zero for each coefficients (of which
- // there are "xDegree" + 1).
- yPolyX[j] = new PolynomialFunction(xFitter.fit(new double[xDegree + 1]));
- }
-
- // For every knot (xval[i], yval[j]) of the grid, calculate corrected
- // values fval_1
- final double[][] fval_1 = new double[xLen][yLen];
- for (int j = 0; j < yLen; j++) {
- final PolynomialFunction f = yPolyX[j];
- for (int i = 0; i < xLen; i++) {
- fval_1[i][j] = f.value(xval[i]);
- }
- }
-
- // For each line x[i] (0 <= i < xLen), construct a polynomial, with
- // respect to variable y, fitting array fval_1[i][]
- final PolynomialFunction[] xPolyY = new PolynomialFunction[xLen];
- for (int i = 0; i < xLen; i++) {
- yFitter.clearObservations();
- for (int j = 0; j < yLen; j++) {
- yFitter.addObservedPoint(1, yval[j], fval_1[i][j]);
- }
-
- // Initial guess for the fit is zero for each coefficients (of which
- // there are "yDegree" + 1).
- xPolyY[i] = new PolynomialFunction(yFitter.fit(new double[yDegree + 1]));
- }
-
- // For every knot (xval[i], yval[j]) of the grid, calculate corrected
- // values fval_2
- final double[][] fval_2 = new double[xLen][yLen];
- for (int i = 0; i < xLen; i++) {
- final PolynomialFunction f = xPolyY[i];
- for (int j = 0; j < yLen; j++) {
- fval_2[i][j] = f.value(yval[j]);
- }
- }
-
- return super.interpolate(xval, yval, fval_2);
- }
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/0a5cd113/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolatingFunction.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolatingFunction.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolatingFunction.java
deleted file mode 100644
index fa5f76c..0000000
--- a/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolatingFunction.java
+++ /dev/null
@@ -1,482 +0,0 @@
-/*
- * 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.math4.analysis.interpolation;
-
-import org.apache.commons.math4.analysis.TrivariateFunction;
-import org.apache.commons.math4.exception.DimensionMismatchException;
-import org.apache.commons.math4.exception.NoDataException;
-import org.apache.commons.math4.exception.NonMonotonicSequenceException;
-import org.apache.commons.math4.exception.OutOfRangeException;
-import org.apache.commons.math4.util.MathArrays;
-
-/**
- * Function that implements the
- * <a href="http://en.wikipedia.org/wiki/Tricubic_interpolation">
- * tricubic spline interpolation</a>, as proposed in
- * <quote>
- * Tricubic interpolation in three dimensions<br/>
- * F. Lekien and J. Marsden<br/>
- * <em>Int. J. Numer. Meth. Engng</em> 2005; <b>63</b>:455-471
- * </quote>
- *
- * @since 2.2
- * @deprecated To be removed in 4.0 (see MATH-1166).
- */
-@Deprecated
-public class TricubicSplineInterpolatingFunction
- implements TrivariateFunction {
- /**
- * Matrix to compute the spline coefficients from the function values
- * and function derivatives values
- */
- private static final double[][] AINV = {
- { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { -3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { -3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 9,-9,-9,9,0,0,0,0,6,3,-6,-3,0,0,0,0,6,-6,3,-3,0,0,0,0,0,0,0,0,0,0,0,0,4,2,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { -6,6,6,-6,0,0,0,0,-3,-3,3,3,0,0,0,0,-4,4,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { -6,6,6,-6,0,0,0,0,-4,-2,4,2,0,0,0,0,-3,3,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 4,-4,-4,4,0,0,0,0,2,2,-2,-2,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,6,3,-6,-3,0,0,0,0,6,-6,3,-3,0,0,0,0,4,2,2,1,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,3,3,0,0,0,0,-4,4,-2,2,0,0,0,0,-2,-2,-1,-1,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,-4,-2,4,2,0,0,0,0,-3,3,-3,3,0,0,0,0,-2,-1,-2,-1,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,2,-2,2,-2,0,0,0,0,1,1,1,1,0,0,0,0 },
- {-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 9,-9,0,0,-9,9,0,0,6,3,0,0,-6,-3,0,0,0,0,0,0,0,0,0,0,6,-6,0,0,3,-3,0,0,0,0,0,0,0,0,0,0,4,2,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { -6,6,0,0,6,-6,0,0,-3,-3,0,0,3,3,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,6,3,0,0,-6,-3,0,0,0,0,0,0,0,0,0,0,6,-6,0,0,3,-3,0,0,4,2,0,0,2,1,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,0,0,6,-6,0,0,0,0,0,0,0,0,0,0,-3,-3,0,0,3,3,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,-2,2,0,0,-2,-2,0,0,-1,-1,0,0 },
- { 9,0,-9,0,-9,0,9,0,0,0,0,0,0,0,0,0,6,0,3,0,-6,0,-3,0,6,0,-6,0,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,2,0,2,0,1,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,9,0,-9,0,-9,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,3,0,-6,0,-3,0,6,0,-6,0,3,0,-3,0,0,0,0,0,0,0,0,0,4,0,2,0,2,0,1,0 },
- { -27,27,27,-27,27,-27,-27,27,-18,-9,18,9,18,9,-18,-9,-18,18,-9,9,18,-18,9,-9,-18,18,18,-18,-9,9,9,-9,-12,-6,-6,-3,12,6,6,3,-12,-6,12,6,-6,-3,6,3,-12,12,-6,6,-6,6,-3,3,-8,-4,-4,-2,-4,-2,-2,-1 },
- { 18,-18,-18,18,-18,18,18,-18,9,9,-9,-9,-9,-9,9,9,12,-12,6,-6,-12,12,-6,6,12,-12,-12,12,6,-6,-6,6,6,6,3,3,-6,-6,-3,-3,6,6,-6,-6,3,3,-3,-3,8,-8,4,-4,4,-4,2,-2,4,4,2,2,2,2,1,1 },
- { -6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,-3,0,-3,0,3,0,3,0,-4,0,4,0,-2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-2,0,-1,0,-1,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,-6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,-3,0,3,0,3,0,-4,0,4,0,-2,0,2,0,0,0,0,0,0,0,0,0,-2,0,-2,0,-1,0,-1,0 },
- { 18,-18,-18,18,-18,18,18,-18,12,6,-12,-6,-12,-6,12,6,9,-9,9,-9,-9,9,-9,9,12,-12,-12,12,6,-6,-6,6,6,3,6,3,-6,-3,-6,-3,8,4,-8,-4,4,2,-4,-2,6,-6,6,-6,3,-3,3,-3,4,2,4,2,2,1,2,1 },
- { -12,12,12,-12,12,-12,-12,12,-6,-6,6,6,6,6,-6,-6,-6,6,-6,6,6,-6,6,-6,-8,8,8,-8,-4,4,4,-4,-3,-3,-3,-3,3,3,3,3,-4,-4,4,4,-2,-2,2,2,-4,4,-4,4,-2,2,-2,2,-2,-2,-2,-2,-1,-1,-1,-1 },
- { 2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { -6,6,0,0,6,-6,0,0,-4,-2,0,0,4,2,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 4,-4,0,0,-4,4,0,0,2,2,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,0,0,6,-6,0,0,0,0,0,0,0,0,0,0,-4,-2,0,0,4,2,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,-3,3,0,0,-2,-1,0,0,-2,-1,0,0 },
- { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,2,2,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,2,-2,0,0,1,1,0,0,1,1,0,0 },
- { -6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,-4,0,-2,0,4,0,2,0,-3,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,-2,0,-1,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,-6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,-2,0,4,0,2,0,-3,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,0,-2,0,-1,0,-2,0,-1,0 },
- { 18,-18,-18,18,-18,18,18,-18,12,6,-12,-6,-12,-6,12,6,12,-12,6,-6,-12,12,-6,6,9,-9,-9,9,9,-9,-9,9,8,4,4,2,-8,-4,-4,-2,6,3,-6,-3,6,3,-6,-3,6,-6,3,-3,6,-6,3,-3,4,2,2,1,4,2,2,1 },
- { -12,12,12,-12,12,-12,-12,12,-6,-6,6,6,6,6,-6,-6,-8,8,-4,4,8,-8,4,-4,-6,6,6,-6,-6,6,6,-6,-4,-4,-2,-2,4,4,2,2,-3,-3,3,3,-3,-3,3,3,-4,4,-2,2,-4,4,-2,2,-2,-2,-1,-1,-2,-2,-1,-1 },
- { 4,0,-4,0,-4,0,4,0,0,0,0,0,0,0,0,0,2,0,2,0,-2,0,-2,0,2,0,-2,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0 },
- { 0,0,0,0,0,0,0,0,4,0,-4,0,-4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,-2,0,-2,0,2,0,-2,0,2,0,-2,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0 },
- { -12,12,12,-12,12,-12,-12,12,-8,-4,8,4,8,4,-8,-4,-6,6,-6,6,6,-6,6,-6,-6,6,6,-6,-6,6,6,-6,-4,-2,-4,-2,4,2,4,2,-4,-2,4,2,-4,-2,4,2,-3,3,-3,3,-3,3,-3,3,-2,-1,-2,-1,-2,-1,-2,-1 },
- { 8,-8,-8,8,-8,8,8,-8,4,4,-4,-4,-4,-4,4,4,4,-4,4,-4,-4,4,-4,4,4,-4,-4,4,4,-4,-4,4,2,2,2,2,-2,-2,-2,-2,2,2,-2,-2,2,2,-2,-2,2,-2,2,-2,2,-2,2,-2,1,1,1,1,1,1,1,1 }
- };
-
- /** Samples x-coordinates */
- private final double[] xval;
- /** Samples y-coordinates */
- private final double[] yval;
- /** Samples z-coordinates */
- private final double[] zval;
- /** Set of cubic splines pacthing the whole data grid */
- private final TricubicSplineFunction[][][] splines;
-
- /**
- * @param x Sample values of the x-coordinate, in increasing order.
- * @param y Sample values of the y-coordinate, in increasing order.
- * @param z Sample values of the y-coordinate, in increasing order.
- * @param f Values of the function on every grid point.
- * @param dFdX Values of the partial derivative of function with respect to x on every grid point.
- * @param dFdY Values of the partial derivative of function with respect to y on every grid point.
- * @param dFdZ Values of the partial derivative of function with respect to z on every grid point.
- * @param d2FdXdY Values of the cross partial derivative of function on every grid point.
- * @param d2FdXdZ Values of the cross partial derivative of function on every grid point.
- * @param d2FdYdZ Values of the cross partial derivative of function on every grid point.
- * @param d3FdXdYdZ Values of the cross partial derivative of function on every grid point.
- * @throws NoDataException if any of the arrays has zero length.
- * @throws DimensionMismatchException if the various arrays do not contain the expected number of elements.
- * @throws NonMonotonicSequenceException if {@code x}, {@code y} or {@code z} are not strictly increasing.
- */
- public TricubicSplineInterpolatingFunction(double[] x,
- double[] y,
- double[] z,
- double[][][] f,
- double[][][] dFdX,
- double[][][] dFdY,
- double[][][] dFdZ,
- double[][][] d2FdXdY,
- double[][][] d2FdXdZ,
- double[][][] d2FdYdZ,
- double[][][] d3FdXdYdZ)
- throws NoDataException,
- DimensionMismatchException,
- NonMonotonicSequenceException {
- final int xLen = x.length;
- final int yLen = y.length;
- final int zLen = z.length;
-
- if (xLen == 0 || yLen == 0 || z.length == 0 || f.length == 0 || f[0].length == 0) {
- throw new NoDataException();
- }
- if (xLen != f.length) {
- throw new DimensionMismatchException(xLen, f.length);
- }
- if (xLen != dFdX.length) {
- throw new DimensionMismatchException(xLen, dFdX.length);
- }
- if (xLen != dFdY.length) {
- throw new DimensionMismatchException(xLen, dFdY.length);
- }
- if (xLen != dFdZ.length) {
- throw new DimensionMismatchException(xLen, dFdZ.length);
- }
- if (xLen != d2FdXdY.length) {
- throw new DimensionMismatchException(xLen, d2FdXdY.length);
- }
- if (xLen != d2FdXdZ.length) {
- throw new DimensionMismatchException(xLen, d2FdXdZ.length);
- }
- if (xLen != d2FdYdZ.length) {
- throw new DimensionMismatchException(xLen, d2FdYdZ.length);
- }
- if (xLen != d3FdXdYdZ.length) {
- throw new DimensionMismatchException(xLen, d3FdXdYdZ.length);
- }
-
- MathArrays.checkOrder(x);
- MathArrays.checkOrder(y);
- MathArrays.checkOrder(z);
-
- xval = x.clone();
- yval = y.clone();
- zval = z.clone();
-
- final int lastI = xLen - 1;
- final int lastJ = yLen - 1;
- final int lastK = zLen - 1;
- splines = new TricubicSplineFunction[lastI][lastJ][lastK];
-
- for (int i = 0; i < lastI; i++) {
- if (f[i].length != yLen) {
- throw new DimensionMismatchException(f[i].length, yLen);
- }
- if (dFdX[i].length != yLen) {
- throw new DimensionMismatchException(dFdX[i].length, yLen);
- }
- if (dFdY[i].length != yLen) {
- throw new DimensionMismatchException(dFdY[i].length, yLen);
- }
- if (dFdZ[i].length != yLen) {
- throw new DimensionMismatchException(dFdZ[i].length, yLen);
- }
- if (d2FdXdY[i].length != yLen) {
- throw new DimensionMismatchException(d2FdXdY[i].length, yLen);
- }
- if (d2FdXdZ[i].length != yLen) {
- throw new DimensionMismatchException(d2FdXdZ[i].length, yLen);
- }
- if (d2FdYdZ[i].length != yLen) {
- throw new DimensionMismatchException(d2FdYdZ[i].length, yLen);
- }
- if (d3FdXdYdZ[i].length != yLen) {
- throw new DimensionMismatchException(d3FdXdYdZ[i].length, yLen);
- }
-
- final int ip1 = i + 1;
- for (int j = 0; j < lastJ; j++) {
- if (f[i][j].length != zLen) {
- throw new DimensionMismatchException(f[i][j].length, zLen);
- }
- if (dFdX[i][j].length != zLen) {
- throw new DimensionMismatchException(dFdX[i][j].length, zLen);
- }
- if (dFdY[i][j].length != zLen) {
- throw new DimensionMismatchException(dFdY[i][j].length, zLen);
- }
- if (dFdZ[i][j].length != zLen) {
- throw new DimensionMismatchException(dFdZ[i][j].length, zLen);
- }
- if (d2FdXdY[i][j].length != zLen) {
- throw new DimensionMismatchException(d2FdXdY[i][j].length, zLen);
- }
- if (d2FdXdZ[i][j].length != zLen) {
- throw new DimensionMismatchException(d2FdXdZ[i][j].length, zLen);
- }
- if (d2FdYdZ[i][j].length != zLen) {
- throw new DimensionMismatchException(d2FdYdZ[i][j].length, zLen);
- }
- if (d3FdXdYdZ[i][j].length != zLen) {
- throw new DimensionMismatchException(d3FdXdYdZ[i][j].length, zLen);
- }
-
- final int jp1 = j + 1;
- for (int k = 0; k < lastK; k++) {
- final int kp1 = k + 1;
-
- final double[] beta = new double[] {
- f[i][j][k], f[ip1][j][k],
- f[i][jp1][k], f[ip1][jp1][k],
- f[i][j][kp1], f[ip1][j][kp1],
- f[i][jp1][kp1], f[ip1][jp1][kp1],
-
- dFdX[i][j][k], dFdX[ip1][j][k],
- dFdX[i][jp1][k], dFdX[ip1][jp1][k],
- dFdX[i][j][kp1], dFdX[ip1][j][kp1],
- dFdX[i][jp1][kp1], dFdX[ip1][jp1][kp1],
-
- dFdY[i][j][k], dFdY[ip1][j][k],
- dFdY[i][jp1][k], dFdY[ip1][jp1][k],
- dFdY[i][j][kp1], dFdY[ip1][j][kp1],
- dFdY[i][jp1][kp1], dFdY[ip1][jp1][kp1],
-
- dFdZ[i][j][k], dFdZ[ip1][j][k],
- dFdZ[i][jp1][k], dFdZ[ip1][jp1][k],
- dFdZ[i][j][kp1], dFdZ[ip1][j][kp1],
- dFdZ[i][jp1][kp1], dFdZ[ip1][jp1][kp1],
-
- d2FdXdY[i][j][k], d2FdXdY[ip1][j][k],
- d2FdXdY[i][jp1][k], d2FdXdY[ip1][jp1][k],
- d2FdXdY[i][j][kp1], d2FdXdY[ip1][j][kp1],
- d2FdXdY[i][jp1][kp1], d2FdXdY[ip1][jp1][kp1],
-
- d2FdXdZ[i][j][k], d2FdXdZ[ip1][j][k],
- d2FdXdZ[i][jp1][k], d2FdXdZ[ip1][jp1][k],
- d2FdXdZ[i][j][kp1], d2FdXdZ[ip1][j][kp1],
- d2FdXdZ[i][jp1][kp1], d2FdXdZ[ip1][jp1][kp1],
-
- d2FdYdZ[i][j][k], d2FdYdZ[ip1][j][k],
- d2FdYdZ[i][jp1][k], d2FdYdZ[ip1][jp1][k],
- d2FdYdZ[i][j][kp1], d2FdYdZ[ip1][j][kp1],
- d2FdYdZ[i][jp1][kp1], d2FdYdZ[ip1][jp1][kp1],
-
- d3FdXdYdZ[i][j][k], d3FdXdYdZ[ip1][j][k],
- d3FdXdYdZ[i][jp1][k], d3FdXdYdZ[ip1][jp1][k],
- d3FdXdYdZ[i][j][kp1], d3FdXdYdZ[ip1][j][kp1],
- d3FdXdYdZ[i][jp1][kp1], d3FdXdYdZ[ip1][jp1][kp1],
- };
-
- splines[i][j][k] = new TricubicSplineFunction(computeSplineCoefficients(beta));
- }
- }
- }
- }
-
- /**
- * {@inheritDoc}
- *
- * @throws OutOfRangeException if any of the variables is outside its interpolation range.
- */
- public double value(double x, double y, double z)
- throws OutOfRangeException {
- final int i = searchIndex(x, xval);
- if (i == -1) {
- throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]);
- }
- final int j = searchIndex(y, yval);
- if (j == -1) {
- throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]);
- }
- final int k = searchIndex(z, zval);
- if (k == -1) {
- throw new OutOfRangeException(z, zval[0], zval[zval.length - 1]);
- }
-
- final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
- final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
- final double zN = (z - zval[k]) / (zval[k + 1] - zval[k]);
-
- return splines[i][j][k].value(xN, yN, zN);
- }
-
- /**
- * @param c Coordinate.
- * @param val Coordinate samples.
- * @return the index in {@code val} corresponding to the interval containing {@code c}, or {@code -1}
- * if {@code c} is out of the range defined by the end values of {@code val}.
- */
- private int searchIndex(double c, double[] val) {
- if (c < val[0]) {
- return -1;
- }
-
- final int max = val.length;
- for (int i = 1; i < max; i++) {
- if (c <= val[i]) {
- return i - 1;
- }
- }
-
- return -1;
- }
-
- /**
- * Compute the spline coefficients from the list of function values and
- * function partial derivatives values at the four corners of a grid
- * element. They must be specified in the following order:
- * <ul>
- * <li>f(0,0,0)</li>
- * <li>f(1,0,0)</li>
- * <li>f(0,1,0)</li>
- * <li>f(1,1,0)</li>
- * <li>f(0,0,1)</li>
- * <li>f(1,0,1)</li>
- * <li>f(0,1,1)</li>
- * <li>f(1,1,1)</li>
- *
- * <li>f<sub>x</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>x</sub>(1,1,1)</li>
- *
- * <li>f<sub>y</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>y</sub>(1,1,1)</li>
- *
- * <li>f<sub>z</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>z</sub>(1,1,1)</li>
- *
- * <li>f<sub>xy</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>xy</sub>(1,1,1)</li>
- *
- * <li>f<sub>xz</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>xz</sub>(1,1,1)</li>
- *
- * <li>f<sub>yz</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>yz</sub>(1,1,1)</li>
- *
- * <li>f<sub>xyz</sub>(0,0,0)</li>
- * <li>... <em>(same order as above)</em></li>
- * <li>f<sub>xyz</sub>(1,1,1)</li>
- * </ul>
- * where the subscripts indicate the partial derivative with respect to
- * the corresponding variable(s).
- *
- * @param beta List of function values and function partial derivatives values.
- * @return the spline coefficients.
- */
- private double[] computeSplineCoefficients(double[] beta) {
- final int sz = 64;
- final double[] a = new double[sz];
-
- for (int i = 0; i < sz; i++) {
- double result = 0;
- final double[] row = AINV[i];
- for (int j = 0; j < sz; j++) {
- result += row[j] * beta[j];
- }
- a[i] = result;
- }
-
- return a;
- }
-}
-
-/**
- * 3D-spline function.
- *
- */
-class TricubicSplineFunction
- implements TrivariateFunction {
- /** Number of points. */
- private static final short N = 4;
- /** Coefficients */
- private final double[][][] a = new double[N][N][N];
-
- /**
- * @param aV List of spline coefficients.
- */
- public TricubicSplineFunction(double[] aV) {
- for (int i = 0; i < N; i++) {
- for (int j = 0; j < N; j++) {
- for (int k = 0; k < N; k++) {
- a[i][j][k] = aV[i + N * (j + N * k)];
- }
- }
- }
- }
-
- /**
- * @param x x-coordinate of the interpolation point.
- * @param y y-coordinate of the interpolation point.
- * @param z z-coordinate of the interpolation point.
- * @return the interpolated value.
- * @throws OutOfRangeException if {@code x}, {@code y} or
- * {@code z} are not in the interval {@code [0, 1]}.
- */
- public double value(double x, double y, double z)
- throws OutOfRangeException {
- if (x < 0 || x > 1) {
- throw new OutOfRangeException(x, 0, 1);
- }
- if (y < 0 || y > 1) {
- throw new OutOfRangeException(y, 0, 1);
- }
- if (z < 0 || z > 1) {
- throw new OutOfRangeException(z, 0, 1);
- }
-
- final double x2 = x * x;
- final double x3 = x2 * x;
- final double[] pX = { 1, x, x2, x3 };
-
- final double y2 = y * y;
- final double y3 = y2 * y;
- final double[] pY = { 1, y, y2, y3 };
-
- final double z2 = z * z;
- final double z3 = z2 * z;
- final double[] pZ = { 1, z, z2, z3 };
-
- double result = 0;
- for (int i = 0; i < N; i++) {
- for (int j = 0; j < N; j++) {
- for (int k = 0; k < N; k++) {
- result += a[i][j][k] * pX[i] * pY[j] * pZ[k];
- }
- }
- }
-
- return result;
- }
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/0a5cd113/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolator.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolator.java
deleted file mode 100644
index c068f74..0000000
--- a/src/main/java/org/apache/commons/math4/analysis/interpolation/TricubicSplineInterpolator.java
+++ /dev/null
@@ -1,201 +0,0 @@
-/*
- * 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.math4.analysis.interpolation;
-
-import org.apache.commons.math4.exception.DimensionMismatchException;
-import org.apache.commons.math4.exception.NoDataException;
-import org.apache.commons.math4.exception.NonMonotonicSequenceException;
-import org.apache.commons.math4.exception.NumberIsTooSmallException;
-import org.apache.commons.math4.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;
- }
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/0a5cd113/src/main/java/org/apache/commons/math4/analysis/solvers/NewtonSolver.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/analysis/solvers/NewtonSolver.java b/src/main/java/org/apache/commons/math4/analysis/solvers/NewtonSolver.java
deleted file mode 100644
index f377030..0000000
--- a/src/main/java/org/apache/commons/math4/analysis/solvers/NewtonSolver.java
+++ /dev/null
@@ -1,92 +0,0 @@
-/*
- * 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.math4.analysis.solvers;
-
-import org.apache.commons.math4.analysis.DifferentiableUnivariateFunction;
-import org.apache.commons.math4.exception.TooManyEvaluationsException;
-import org.apache.commons.math4.util.FastMath;
-
-/**
- * Implements <a href="http://mathworld.wolfram.com/NewtonsMethod.html">
- * Newton's Method</a> for finding zeros of real univariate functions.
- * <p>
- * The function should be continuous but not necessarily smooth.</p>
- *
- * @deprecated as of 3.1, replaced by {@link NewtonRaphsonSolver}
- */
-@Deprecated
-public class NewtonSolver extends AbstractDifferentiableUnivariateSolver {
- /** Default absolute accuracy. */
- private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
-
- /**
- * Construct a solver.
- */
- public NewtonSolver() {
- this(DEFAULT_ABSOLUTE_ACCURACY);
- }
- /**
- * Construct a solver.
- *
- * @param absoluteAccuracy Absolute accuracy.
- */
- public NewtonSolver(double absoluteAccuracy) {
- super(absoluteAccuracy);
- }
-
- /**
- * Find a zero near the midpoint of {@code min} and {@code max}.
- *
- * @param f Function to solve.
- * @param min Lower bound for the interval.
- * @param max Upper bound for the interval.
- * @param maxEval Maximum number of evaluations.
- * @return the value where the function is zero.
- * @throws org.apache.commons.math4.exception.TooManyEvaluationsException
- * if the maximum evaluation count is exceeded.
- * @throws org.apache.commons.math4.exception.NumberIsTooLargeException
- * if {@code min >= max}.
- */
- @Override
- public double solve(int maxEval, final DifferentiableUnivariateFunction f,
- final double min, final double max)
- throws TooManyEvaluationsException {
- return super.solve(maxEval, f, UnivariateSolverUtils.midpoint(min, max));
- }
-
- /**
- * {@inheritDoc}
- */
- @Override
- protected double doSolve()
- throws TooManyEvaluationsException {
- final double startValue = getStartValue();
- final double absoluteAccuracy = getAbsoluteAccuracy();
-
- double x0 = startValue;
- double x1;
- while (true) {
- x1 = x0 - (computeObjectiveValue(x0) / computeDerivativeObjectiveValue(x0));
- if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
- return x1;
- }
-
- x0 = x1;
- }
- }
-}