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Posted to commits@commons.apache.org by lu...@apache.org on 2014/10/17 10:41:26 UTC
[2/8] git commit: MATH-1138 #comment Implemented new
BiCubicSplineInterpolator,
supporting Akima Spline Interpolator and updated tests
MATH-1138 #comment Implemented new BiCubicSplineInterpolator, supporting Akima Spline Interpolator and updated tests
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/d8bfc8c8
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/d8bfc8c8
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/d8bfc8c8
Branch: refs/heads/master
Commit: d8bfc8c8f8864f9c22e0409780d5dd3fb30497ff
Parents: a3fdeb4
Author: Hank Grabowski <ha...@applieddefense.com>
Authored: Wed Oct 15 10:15:14 2014 -0400
Committer: Hank Grabowski <ha...@applieddefense.com>
Committed: Wed Oct 15 10:15:14 2014 -0400
----------------------------------------------------------------------
.../interpolation/AkimaSplineInterpolator.java | 225 ++++++
.../BicubicSplineInterpolatingFunction.java | 620 +++------------
.../BicubicSplineInterpolator.java | 140 +---
.../TricubicSplineInterpolator.java | 35 +-
.../AkimaSplineInterpolatorTest.java | 227 ++++++
.../BicubicSplineInterpolatingFunctionTest.java | 746 +++++--------------
.../BicubicSplineInterpolatorTest.java | 217 ++++--
...PolynomialBicubicSplineInterpolatorTest.java | 10 +-
.../interpolation/SplineInterpolatorTest.java | 42 +-
.../TricubicSplineInterpolatorTest.java | 2 +-
10 files changed, 923 insertions(+), 1341 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d8bfc8c8/src/main/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolator.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolator.java
new file mode 100644
index 0000000..8fb896c
--- /dev/null
+++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolator.java
@@ -0,0 +1,225 @@
+/*
+ * 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.polynomials.PolynomialFunction;
+import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
+import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import org.apache.commons.math3.exception.NullArgumentException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.MathArrays;
+import org.apache.commons.math3.util.Precision;
+
+/**
+ * Computes a cubic spline interpolation for the data set using the Akima
+ * algorithm, as originally formulated by Hiroshi Akima in his 1970 paper
+ * "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures."
+ * J. ACM 17, 4 (October 1970), 589-602. DOI=10.1145/321607.321609
+ * http://doi.acm.org/10.1145/321607.321609
+ * <p>
+ * This implementation is based on the Akima implementation in the CubicSpline
+ * class in the Math.NET Numerics library. The method referenced is
+ * CubicSpline.InterpolateAkimaSorted
+ * <p>
+ * The {@link #interpolate(double[], double[])} method returns a
+ * {@link PolynomialSplineFunction} consisting of n cubic polynomials, defined
+ * over the subintervals determined by the x values, x[0] < x[i] ... < x[n]. The
+ * Akima algorithm requires that n >= 5.
+ * </p>
+ * <p>
+ */
+
+public class AkimaSplineInterpolator
+ implements UnivariateInterpolator {
+
+
+ /**
+ * The minimum number of points that are needed to compute the function
+ */
+ public static final int MINIMUM_NUMBER_POINTS = 5;
+
+ /**
+ * Default constructor. Builds an AkimaSplineInterpolator object
+ */
+ public AkimaSplineInterpolator() {
+
+ }
+
+ /**
+ * Computes an interpolating function for the data set.
+ *
+ * @param xvals the arguments for the interpolation points
+ * @param yvals the values for the interpolation points
+ * @return a function which interpolates the data set
+ * @throws DimensionMismatchException if {@code x} and {@code y} have
+ * different sizes.
+ * @throws NonMonotonicSequenceException if {@code x} is not sorted in
+ * strict increasing order.
+ * @throws NumberIsTooSmallException if the size of {@code x} is smaller
+ * than 5.
+ */
+ public PolynomialSplineFunction interpolate(double[] xvals, double[] yvals)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ NonMonotonicSequenceException {
+ if (xvals == null || yvals == null) {
+ throw new NullArgumentException();
+ }
+
+ if (xvals.length != yvals.length) {
+ throw new DimensionMismatchException(xvals.length, yvals.length);
+ }
+
+ if (xvals.length < MINIMUM_NUMBER_POINTS) {
+ throw new NumberIsTooSmallException(
+ LocalizedFormats.NUMBER_OF_POINTS,
+ xvals.length,
+ MINIMUM_NUMBER_POINTS, true);
+ }
+
+ MathArrays.checkOrder(xvals);
+
+ final int numberOfDiffAndWeightElements = xvals.length - 1;
+
+ double differences[] = new double[numberOfDiffAndWeightElements];
+ double weights[] = new double[numberOfDiffAndWeightElements];
+
+ for (int i = 0; i < differences.length; i++) {
+ differences[i] = (yvals[i + 1] - yvals[i]) /
+ (xvals[i + 1] - xvals[i]);
+ }
+
+ for (int i = 1; i < weights.length; i++) {
+ weights[i] = FastMath.abs(differences[i] - differences[i - 1]);
+ }
+
+ /* Prepare Hermite interpolation scheme */
+
+ double firstDerivatives[] = new double[xvals.length];
+
+ for (int i = 2; i < firstDerivatives.length - 2; i++) {
+ if (Precision.equals(weights[i - 1], 0.0) &&
+ Precision.equals(weights[i + 1], 0.0)) {
+ firstDerivatives[i] = (((xvals[i + 1] - xvals[i]) * differences[i - 1]) + ((xvals[i] - xvals[i - 1]) * differences[i])) /
+ (xvals[i + 1] - xvals[i - 1]);
+ } else {
+ firstDerivatives[i] = ((weights[i + 1] * differences[i - 1]) + (weights[i - 1] * differences[i])) /
+ (weights[i + 1] + weights[i - 1]);
+ }
+ }
+
+ firstDerivatives[0] = this.differentiateThreePoint(xvals, yvals, 0, 0,
+ 1, 2);
+ firstDerivatives[1] = this.differentiateThreePoint(xvals, yvals, 1, 0,
+ 1, 2);
+ firstDerivatives[xvals.length - 2] = this
+ .differentiateThreePoint(xvals, yvals, xvals.length - 2,
+ xvals.length - 3, xvals.length - 2,
+ xvals.length - 1);
+ firstDerivatives[xvals.length - 1] = this
+ .differentiateThreePoint(xvals, yvals, xvals.length - 1,
+ xvals.length - 3, xvals.length - 2,
+ xvals.length - 1);
+
+ return this.interpolateHermiteSorted(xvals, yvals, firstDerivatives);
+ }
+
+ /**
+ * Three point differentiation helper, modeled off of the same method in the
+ * Math.NET CubicSpline class. This is used by both the Apache Math and the
+ * Math.NET Akima Cubic Spline algorithms
+ *
+ * @param xvals x values to calculate the numerical derivative with
+ * @param yvals y values to calculate the numerical derivative with
+ * @param indexOfDifferentiation index of the elemnt we are calculating the derivative around
+ * @param indexOfFirstSample index of the first element to sample for the three point method
+ * @param indexOfSecondsample index of the second element to sample for the three point method
+ * @param indexOfThirdSample index of the third element to sample for the three point method
+ * @return the derivative
+ */
+ private double differentiateThreePoint(double[] xvals, double[] yvals,
+ int indexOfDifferentiation,
+ int indexOfFirstSample,
+ int indexOfSecondsample,
+ int indexOfThirdSample) {
+ double x0 = yvals[indexOfFirstSample];
+ double x1 = yvals[indexOfSecondsample];
+ double x2 = yvals[indexOfThirdSample];
+
+ double t = xvals[indexOfDifferentiation] - xvals[indexOfFirstSample];
+ double t1 = xvals[indexOfSecondsample] - xvals[indexOfFirstSample];
+ double t2 = xvals[indexOfThirdSample] - xvals[indexOfFirstSample];
+
+ double a = (x2 - x0 - (t2 / t1 * (x1 - x0))) / (t2 * t2 - t1 * t2);
+ double b = (x1 - x0 - a * t1 * t1) / t1;
+ return (2 * a * t) + b;
+ }
+
+ /**
+ * Creates a Hermite cubic spline interpolation from the set of (x,y) value
+ * pairs and their derivatives. This is modeled off of the
+ * InterpolateHermiteSorted method in the Math.NET CubicSpline class.
+ *
+ * @param xvals x values for interpolation
+ * @param yvals y values for interpolation
+ * @param firstDerivatives first derivative values of the function
+ * @return polynomial that fits the function
+ */
+ private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals,
+ double[] yvals,
+ double[] firstDerivatives) {
+ if (xvals.length != yvals.length) {
+ throw new DimensionMismatchException(xvals.length, yvals.length);
+ }
+
+ if (xvals.length != firstDerivatives.length) {
+ throw new DimensionMismatchException(xvals.length,
+ firstDerivatives.length);
+ }
+
+ final int minimumLength = 2;
+ if (xvals.length < minimumLength) {
+ throw new NumberIsTooSmallException(
+ LocalizedFormats.NUMBER_OF_POINTS,
+ xvals.length, minimumLength,
+ true);
+ }
+
+ int size = xvals.length - 1;
+ final PolynomialFunction polynomials[] = new PolynomialFunction[size];
+ final double coefficients[] = new double[4];
+
+ for (int i = 0; i < polynomials.length; i++) {
+ double w = xvals[i + 1] - xvals[i];
+ double w2 = w * w;
+ coefficients[0] = yvals[i];
+ coefficients[1] = firstDerivatives[i];
+ coefficients[2] = (3 * (yvals[i + 1] - yvals[i]) / w - 2 *
+ firstDerivatives[i] - firstDerivatives[i + 1]) /
+ w;
+ coefficients[3] = (2 * (yvals[i] - yvals[i + 1]) / w +
+ firstDerivatives[i] + firstDerivatives[i + 1]) /
+ w2;
+ polynomials[i] = new PolynomialFunction(coefficients);
+ }
+
+ return new PolynomialSplineFunction(xvals, polynomials);
+
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d8bfc8c8/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolatingFunction.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolatingFunction.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolatingFunction.java
index 079e9fc..c0ce3c5 100644
--- a/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolatingFunction.java
+++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolatingFunction.java
@@ -18,143 +18,76 @@ package org.apache.commons.math3.analysis.interpolation;
import java.util.Arrays;
import org.apache.commons.math3.analysis.BivariateFunction;
+import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.InsufficientDataException;
import org.apache.commons.math3.exception.NoDataException;
+import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.util.MathArrays;
/**
- * Function that implements the
- * <a href="http://en.wikipedia.org/wiki/Bicubic_interpolation">
- * bicubic spline interpolation</a>.
+ * Function that implements the <a
+ * href="http://www.paulinternet.nl/?page=bicubic"> bicubic spline
+ * interpolation</a>.
*
* @since 2.1
*/
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;
+ private final double[][] fval;
/**
* @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.
+ * @param f Values of the function on every grid point. the expected number
+ * of elements.
+ * @throws NonMonotonicSequenceException if {@code x} or {@code y} are not
+ * strictly increasing.
+ * @throws NullArgumentException if any of the arguments are null
* @throws NoDataException if any of the arrays has zero length.
+ * @throws DimensionMismatchException if the length of x and y don't match the row, column
+ * height of f
*/
- 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 {
+ public BicubicSplineInterpolatingFunction(double[] x, double[] y,
+ double[][] f)
+ throws DimensionMismatchException, NullArgumentException,
+ NoDataException, NonMonotonicSequenceException {
+
+ final int minimumLength = AkimaSplineInterpolator.MINIMUM_NUMBER_POINTS;
+
+ if (x == null || y == null || f == null || f[0] == null) {
+ throw new NullArgumentException();
+ }
+
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 < minimumLength || yLen < minimumLength ||
+ f.length < minimumLength || f[0].length < minimumLength) {
+ throw new InsufficientDataException();
+ }
+
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);
+
+ if (yLen != f[0].length) {
+ throw new DimensionMismatchException(yLen, f[0].length);
}
MathArrays.checkOrder(x);
@@ -162,57 +95,7 @@ public class BicubicSplineInterpolatingFunction
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;
- }
+ fval = f.clone();
}
/**
@@ -220,13 +103,37 @@ public class BicubicSplineInterpolatingFunction
*/
public double value(double x, double y)
throws OutOfRangeException {
- final int i = searchIndex(x, xval);
- final int j = searchIndex(y, yval);
+ int index;
+ PolynomialSplineFunction spline;
+ AkimaSplineInterpolator interpolator = new AkimaSplineInterpolator();
+ final int offset = 2;
+ final int count = offset + 3;
+ final int i = searchIndex(x, xval, offset, count);
+ final int j = searchIndex(y, yval, offset, count);
+
+ double xArray[] = new double[count];
+ double yArray[] = new double[count];
+ double zArray[] = new double[count];
+ double interpArray[] = new double[count];
+
+ for (index = 0; index < count; index++) {
+ xArray[index] = xval[i + index];
+ yArray[index] = yval[j + index];
+ }
+
+ for (int zIndex = 0; zIndex < count; zIndex++) {
+ for (index = 0; index < count; index++) {
+ zArray[index] = fval[i + index][j + zIndex];
+ }
+ spline = interpolator.interpolate(xArray, zArray);
+ interpArray[zIndex] = spline.value(x);
+ }
+
+ spline = interpolator.interpolate(yArray, interpArray);
- final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
- final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
+ double returnValue = spline.value(y);
- return splines[i][j].value(xN, yN);
+ return returnValue;
}
/**
@@ -238,9 +145,7 @@ public class BicubicSplineInterpolatingFunction
* @since 3.3
*/
public boolean isValidPoint(double x, double y) {
- if (x < xval[0] ||
- x > xval[xval.length - 1] ||
- y < yval[0] ||
+ if (x < xval[0] || x > xval[xval.length - 1] || y < yval[0] ||
y > yval[yval.length - 1]) {
return false;
} else {
@@ -249,385 +154,42 @@ public class BicubicSplineInterpolatingFunction
}
/**
- * @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) {
+ * @param offset how far back from found value to offset for querying
+ * @param count total number of elements forward from beginning that will be
+ * queried
+ * @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, int offset, int count) {
+ 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);
- }
- };
+ // "c" in within an interpolation sub-interval, which returns
+ // negative
+ // need to remove the negative sign for consistency
+ r = -r - offset - 1;
} else {
- partialDerivativeX = null;
- partialDerivativeY = null;
- partialDerivativeXX = null;
- partialDerivativeYY = null;
- partialDerivativeXY = null;
+ r -= offset;
}
- }
- /**
- * {@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);
+ if (r < 0) {
+ r = 0;
}
- 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];
- }
+ if ((r + count) >= val.length) {
+ // "c" is the last sample of the range: Return the index
+ // of the sample at the lower end of the last sub-interval.
+ r = val.length - count;
}
- 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;
+ return r;
}
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d8bfc8c8/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolator.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolator.java
index 5e2c92f..36a9da2 100644
--- a/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolator.java
+++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolator.java
@@ -16,11 +16,10 @@
*/
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.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.MathArrays;
@@ -30,144 +29,37 @@ import org.apache.commons.math3.util.MathArrays;
* @since 2.2
*/
public class BicubicSplineInterpolator
- implements BivariateGridInterpolator {
- /** Whether to initialize internal data used to compute the analytical
- derivatives of the splines. */
- private final boolean initializeDerivatives;
+ implements BivariateGridInterpolator
+{
/**
* Default constructor.
- * The argument {@link #BicubicSplineInterpolator(boolean) initializeDerivatives}
- * is set to {@code false}.
*/
- public BicubicSplineInterpolator() {
- this(false);
- }
+ public BicubicSplineInterpolator()
+ {
- /**
- * 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,
+ 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();
+ throws DimensionMismatchException, NullArgumentException, NoDataException, NonMonotonicSequenceException
+ {
+ if ( xval == null || yval == null || fval == null || fval[0] == null )
+ {
+ throw new NullArgumentException();
}
- if (xval.length != fval.length) {
- throw new DimensionMismatchException(xval.length, fval.length);
+
+ if ( xval.length == 0 || yval.length == 0 || fval.length == 0 )
+ {
+ throw new NoDataException();
}
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;
+ return new BicubicSplineInterpolatingFunction( xval, yval, fval );
}
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d8bfc8c8/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolator.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolator.java
index cda6a33..0faa274 100644
--- a/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolator.java
+++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolator.java
@@ -76,7 +76,7 @@ public class TricubicSplineInterpolator
}
}
- final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator(true);
+ final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();
// For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
final BicubicSplineInterpolatingFunction[] xSplineYZ
@@ -103,46 +103,13 @@ public class TricubicSplineInterpolator
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];
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d8bfc8c8/src/test/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolatorTest.java b/src/test/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolatorTest.java
new file mode 100644
index 0000000..017241a
--- /dev/null
+++ b/src/test/java/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolatorTest.java
@@ -0,0 +1,227 @@
+/*
+ * 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.distribution.UniformRealDistribution;
+import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import org.apache.commons.math3.exception.NullArgumentException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.Precision;
+import org.junit.Assert;
+import org.junit.Test;
+
+import static org.junit.Assert.*;
+
+public class AkimaSplineInterpolatorTest
+{
+
+ @Test
+ public void testIllegalArguments()
+ {
+ // Data set arrays of different size.
+ UnivariateInterpolator i = new AkimaSplineInterpolator();
+
+ try
+ {
+ double yval[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
+ i.interpolate( null, yval );
+ Assert.fail( "Failed to detect x null pointer" );
+ }
+ catch ( NullArgumentException iae )
+ {
+ // Expected.
+ }
+
+ try
+ {
+ double xval[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
+ i.interpolate( xval, null );
+ Assert.fail( "Failed to detect y null pointer" );
+ }
+ catch ( NullArgumentException iae )
+ {
+ // Expected.
+ }
+
+ try
+ {
+ double xval[] = { 0.0, 1.0, 2.0, 3.0 };
+ double yval[] = { 0.0, 1.0, 2.0, 3.0 };
+ i.interpolate( xval, yval );
+ Assert.fail( "Failed to detect insufficient data" );
+ }
+ catch ( NumberIsTooSmallException iae )
+ {
+ // Expected.
+ }
+
+ try
+ {
+ double xval[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
+ double yval[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
+ i.interpolate( xval, yval );
+ Assert.fail( "Failed to detect data set array with different sizes." );
+ }
+ catch ( DimensionMismatchException iae )
+ {
+ // Expected.
+ }
+
+ // X values not sorted.
+ try
+ {
+ double xval[] = { 0.0, 1.0, 0.5, 7.0, 3.5, 2.2, 8.0 };
+ double yval[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+ i.interpolate( xval, yval );
+ Assert.fail( "Failed to detect unsorted arguments." );
+ }
+ catch ( NonMonotonicSequenceException iae )
+ {
+ // Expected.
+ }
+ }
+
+ /*
+ * Interpolate a straight line. <p> y = 2 x - 5 <p> Tolerances determined by performing same calculation using
+ * Math.NET over ten runs of 100 random number draws for the same function over the same span with the same number
+ * of elements
+ */
+ @Test
+ public void testInterpolateLine()
+ {
+ final int numberOfElements = 10;
+ final double minimumX = -10;
+ final double maximumX = 10;
+ final int numberOfSamples = 100;
+ final double interpolationTolerance = 1e-15;
+ final double maxTolerance = 1e-15;
+
+ UnivariateFunction f = new UnivariateFunction()
+ {
+ public double value( double x )
+ {
+ return 2 * x - 5;
+ }
+ };
+
+ testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance,
+ maxTolerance );
+ }
+
+ /*
+ * Interpolate a straight line. <p> y = 3 x<sup>2</sup> - 5 x + 7 <p> Tolerances determined by performing same
+ * calculation using Math.NET over ten runs of 100 random number draws for the same function over the same span with
+ * the same number of elements
+ */
+
+ @Test
+ public void testInterpolateParabola()
+ {
+ final int numberOfElements = 10;
+ final double minimumX = -10;
+ final double maximumX = 10;
+ final int numberOfSamples = 100;
+ final double interpolationTolerance = 7e-15;
+ final double maxTolerance = 6e-14;
+
+ UnivariateFunction f = new UnivariateFunction()
+ {
+ public double value( double x )
+ {
+ return ( 3 * x * x ) - ( 5 * x ) + 7;
+ }
+ };
+
+ testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance,
+ maxTolerance );
+ }
+
+ /*
+ * Interpolate a straight line. <p> y = 3 x<sup>3</sup> - 0.5 x<sup>2</sup> + x - 1 <p> Tolerances determined by
+ * performing same calculation using Math.NET over ten runs of 100 random number draws for the same function over
+ * the same span with the same number of elements
+ */
+ @Test
+ public void testInterpolateCubic()
+ {
+ final int numberOfElements = 10;
+ final double minimumX = -3;
+ final double maximumX = 3;
+ final int numberOfSamples = 100;
+ final double interpolationTolerance = 0.37;
+ final double maxTolerance = 3.8;
+
+ UnivariateFunction f = new UnivariateFunction()
+ {
+ public double value( double x )
+ {
+ return ( 3 * x * x * x ) - ( 0.5 * x * x ) + ( 1 * x ) - 1;
+ }
+ };
+
+ testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance,
+ maxTolerance );
+ }
+
+ private void testInterpolation( double minimumX, double maximumX, int numberOfElements, int numberOfSamples,
+ UnivariateFunction f, double tolerance, double maxTolerance )
+ {
+ double expected;
+ double actual;
+ double currentX;
+ final double delta = ( maximumX - minimumX ) / ( (double) numberOfElements );
+ double xValues[] = new double[numberOfElements];
+ double yValues[] = new double[numberOfElements];
+
+ for ( int i = 0; i < numberOfElements; i++ )
+ {
+ xValues[i] = minimumX + delta * (double) i;
+ yValues[i] = f.value( xValues[i] );
+ }
+
+ UnivariateFunction interpolation = new AkimaSplineInterpolator().interpolate( xValues, yValues );
+
+ for ( int i = 0; i < numberOfElements; i++ )
+ {
+ currentX = xValues[i];
+ expected = f.value( currentX );
+ actual = interpolation.value( currentX );
+ assertTrue( Precision.equals( expected, actual ) );
+ }
+
+ final RandomGenerator rng = new Well19937c( 1234567L ); // "tol" depends on the seed.
+ final UniformRealDistribution distX =
+ new UniformRealDistribution( rng, xValues[0], xValues[xValues.length - 1] );
+
+ double sumError = 0;
+ for ( int i = 0; i < numberOfSamples; i++ )
+ {
+ currentX = distX.sample();
+ expected = f.value( currentX );
+ actual = interpolation.value( currentX );
+ sumError += FastMath.abs( actual - expected );
+ assertEquals( expected, actual, maxTolerance );
+ }
+
+ assertEquals( 0.0, ( sumError / (double) numberOfSamples ), tolerance );
+ }
+}