Repository: commons-math Updated Branches: refs/heads/master 09129d536 -> 753f278d1
MATH-1173: Tricubic interpolation New class "TricubicInterpolator" to replace "TricubicSplineInterpolator". Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/753f278d Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/753f278d Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/753f278d Branch: refs/heads/master Commit: 753f278d10fc0c92e912965379401ac182644101 Parents: 09129d5 Author: Gilles <er...@apache.org> Authored: Sun Dec 14 18:25:08 2014 +0100 Committer: Gilles <er...@apache.org> Committed: Sun Dec 14 18:25:08 2014 +0100 ---------------------------------------------------------------------- src/changes/changes.xml | 11 +- .../interpolation/TricubicInterpolator.java | 142 ++++++++++++ .../interpolation/TricubicInterpolatorTest.java | 225 +++++++++++++++++++ 3 files changed, 375 insertions(+), 3 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-math/blob/753f278d/src/changes/changes.xml ---------------------------------------------------------------------- diff --git a/src/changes/changes.xml b/src/changes/changes.xml index 22a5143..e54d71e 100644 --- a/src/changes/changes.xml +++ b/src/changes/changes.xml @@ -59,9 +59,10 @@ Most notable among the new features are: new distributions (Gumbel, Laplace, Logistic, Nakagami), and improvements on percentiles algorithms (better handling for NaNs in the regular algorithm, plus a new storeless implementation). - Bicubic splines interpolators have been fixed and new implementations - added. There have been numerous bug fixes and several improvements - on performances or robustness. See below for a full list) + Bicubic and tricubic interpolators have been fixed and new + implementations added. There have been numerous bug fixes and + several improvements on performances or robustness. See below + for a full list. The minimum version of the Java platform required to compile and use Apache Commons Math is Java 5. @@ -78,6 +79,10 @@ Users are encouraged to upgrade to this version as this release not 2. A few methods in the FastMath class are in fact slower that their counterpart in either Math or StrictMath (cf. MATH-740 and MATH-901). "> + <action dev="erans" type="add" issue="MATH-1173"> + New classes "TricubicInterpolatingFunction" and "TricubicInterpolator" to + replace "TricubicSplineInterpolatingFunction" and "TricubicSplineInterpolator". + </action> <action dev="erans" type="fix" issue="MATH-1178" due-to="Dmitriy"> Fixed example in userguide ("stat" section). </action> http://git-wip-us.apache.org/repos/asf/commons-math/blob/753f278d/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolator.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolator.java new file mode 100644 index 0000000..531e736 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolator.java @@ -0,0 +1,142 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.commons.math3.analysis.interpolation; + +import org.apache.commons.math3.exception.DimensionMismatchException; +import org.apache.commons.math3.exception.NoDataException; +import org.apache.commons.math3.exception.NonMonotonicSequenceException; +import org.apache.commons.math3.exception.NumberIsTooSmallException; +import org.apache.commons.math3.util.MathArrays; + +/** + * Generates a tricubic interpolating function. + * + * @since 3.4 + */ +public class TricubicInterpolator + implements TrivariateGridInterpolator { + /** + * {@inheritDoc} + */ + public TricubicInterpolatingFunction 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; + + // Approximation to the partial derivatives using finite differences. + final double[][][] dFdX = new double[xLen][yLen][zLen]; + final double[][][] dFdY = new double[xLen][yLen][zLen]; + final double[][][] dFdZ = new double[xLen][yLen][zLen]; + final double[][][] d2FdXdY = new double[xLen][yLen][zLen]; + final double[][][] d2FdXdZ = new double[xLen][yLen][zLen]; + final double[][][] d2FdYdZ = new double[xLen][yLen][zLen]; + final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen]; + + for (int i = 1; i < xLen - 1; i++) { + if (yval.length != fval[i].length) { + throw new DimensionMismatchException(yval.length, fval[i].length); + } + + final int nI = i + 1; + final int pI = i - 1; + + final double nX = xval[nI]; + final double pX = xval[pI]; + + final double deltaX = nX - pX; + + for (int j = 1; j < yLen - 1; j++) { + if (zval.length != fval[i][j].length) { + throw new DimensionMismatchException(zval.length, fval[i][j].length); + } + + final int nJ = j + 1; + final int pJ = j - 1; + + final double nY = yval[nJ]; + final double pY = yval[pJ]; + + final double deltaY = nY - pY; + final double deltaXY = deltaX * deltaY; + + for (int k = 1; k < zLen - 1; k++) { + final int nK = k + 1; + final int pK = k - 1; + + final double nZ = zval[nK]; + final double pZ = zval[pK]; + + final double deltaZ = nZ - pZ; + + dFdX[i][j][k] = (fval[nI][j][k] - fval[pI][j][k]) / deltaX; + dFdY[i][j][k] = (fval[i][nJ][k] - fval[i][pJ][k]) / deltaY; + dFdZ[i][j][k] = (fval[i][j][nK] - fval[i][j][pK]) / deltaZ; + + final double deltaXZ = deltaX * deltaZ; + final double deltaYZ = deltaY * deltaZ; + + d2FdXdY[i][j][k] = (fval[nI][nJ][k] - fval[nI][pJ][k] - fval[pI][nJ][k] + fval[pI][pJ][k]) / deltaXY; + d2FdXdZ[i][j][k] = (fval[nI][j][nK] - fval[nI][j][pK] - fval[pI][j][nK] + fval[pI][j][pK]) / deltaXZ; + d2FdYdZ[i][j][k] = (fval[i][nJ][nK] - fval[i][nJ][pK] - fval[i][pJ][nK] + fval[i][pJ][pK]) / deltaYZ; + + final double deltaXYZ = deltaXY * deltaZ; + + 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]) / deltaXYZ; + } + } + } + + // Create the interpolating function. + return new TricubicInterpolatingFunction(xval, yval, zval, fval, + dFdX, dFdY, dFdZ, + d2FdXdY, d2FdXdZ, d2FdYdZ, + d3FdXdYdZ) { + @Override + public boolean isValidPoint(double x, double y, double z) { + if (x < xval[1] || + x > xval[xval.length - 2] || + y < yval[1] || + y > yval[yval.length - 2] || + z < zval[1] || + z > zval[zval.length - 2]) { + return false; + } else { + return true; + } + } + }; + } +} http://git-wip-us.apache.org/repos/asf/commons-math/blob/753f278d/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatorTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatorTest.java b/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatorTest.java new file mode 100644 index 0000000..d66e2d6 --- /dev/null +++ b/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatorTest.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.exception.DimensionMismatchException; +import org.apache.commons.math3.exception.MathIllegalArgumentException; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.analysis.TrivariateFunction; +import org.junit.Assert; +import org.junit.Test; + +/** + * Test case for the {@link TricubicInterpolator tricubic interpolator}. + */ +public final class TricubicInterpolatorTest { + /** + * Test preconditions. + */ + @Test + public void testPreconditions() { + double[] xval = new double[] {3, 4, 5, 6.5}; + double[] yval = new double[] {-4, -3, -1, 2.5}; + double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5}; + double[][][] fval = new double[xval.length][yval.length][zval.length]; + + @SuppressWarnings("unused") + TrivariateFunction tcf = new TricubicInterpolator().interpolate(xval, yval, zval, fval); + + double[] wxval = new double[] {3, 2, 5, 6.5}; + try { + tcf = new TricubicInterpolator().interpolate(wxval, yval, zval, fval); + Assert.fail("an exception should have been thrown"); + } catch (MathIllegalArgumentException e) { + // Expected + } + double[] wyval = new double[] {-4, -1, -1, 2.5}; + try { + tcf = new TricubicInterpolator().interpolate(xval, wyval, zval, fval); + Assert.fail("an exception should have been thrown"); + } catch (MathIllegalArgumentException e) { + // Expected + } + double[] wzval = new double[] {-12, -8, -9, -3, 0, 2.5}; + try { + tcf = new TricubicInterpolator().interpolate(xval, yval, wzval, fval); + Assert.fail("an exception should have been thrown"); + } catch (MathIllegalArgumentException e) { + // Expected + } + double[][][] wfval = new double[xval.length - 1][yval.length][zval.length]; + try { + tcf = new TricubicInterpolator().interpolate(xval, yval, zval, wfval); + Assert.fail("an exception should have been thrown"); + } catch (DimensionMismatchException e) { + // Expected + } + wfval = new double[xval.length][yval.length - 1][zval.length]; + try { + tcf = new TricubicInterpolator().interpolate(xval, yval, zval, wfval); + Assert.fail("an exception should have been thrown"); + } catch (DimensionMismatchException e) { + // Expected + } + wfval = new double[xval.length][yval.length][zval.length - 1]; + try { + tcf = new TricubicInterpolator().interpolate(xval, yval, zval, wfval); + Assert.fail("an exception should have been thrown"); + } catch (DimensionMismatchException e) { + // Expected + } + } + + public void testIsValid() { + double[] xval = new double[] {3, 4, 5, 6.5}; + double[] yval = new double[] {-4, -3, -1, 2.5}; + double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5}; + double[][][] fval = new double[xval.length][yval.length][zval.length]; + + @SuppressWarnings("unused") + TricubicInterpolatingFunction tcf = new TricubicInterpolator().interpolate(xval, yval, zval, fval); + + // Valid. + Assert.assertTrue(tcf.isValidPoint(4, -3, -8)); + Assert.assertTrue(tcf.isValidPoint(5, -3, -8)); + Assert.assertTrue(tcf.isValidPoint(4, -1, -8)); + Assert.assertTrue(tcf.isValidPoint(5, -1, -8)); + Assert.assertTrue(tcf.isValidPoint(4, -3, 0)); + Assert.assertTrue(tcf.isValidPoint(5, -3, 0)); + Assert.assertTrue(tcf.isValidPoint(4, -1, 0)); + Assert.assertTrue(tcf.isValidPoint(5, -1, 0)); + + // Invalid. + Assert.assertFalse(tcf.isValidPoint(3.5, -3, -8)); + Assert.assertFalse(tcf.isValidPoint(4.5, -3.1, -8)); + Assert.assertFalse(tcf.isValidPoint(4.5, -2, 0)); + Assert.assertFalse(tcf.isValidPoint(4.5, 0, -3.5)); + Assert.assertFalse(tcf.isValidPoint(-10, 4.1, -1)); + } + + /** + * Test for a plane. + * <p> + * f(x, y, z) = 2 x - 3 y - 4 z + 5 + * </p> + */ + @Test + public void testPlane() { + double[] xval = new double[] {3, 4, 5, 6.5}; + double[] yval = new double[] {-4, -3, -1, 2, 2.5}; + double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5}; + + // Function values + TrivariateFunction f = new TrivariateFunction() { + public double value(double x, double y, double z) { + return 2 * x - 3 * y - 4 * z + 5; + } + }; + + double[][][] fval = new double[xval.length][yval.length][zval.length]; + + for (int i = 0; i < xval.length; i++) { + for (int j = 0; j < yval.length; j++) { + for (int k = 0; k < zval.length; k++) { + fval[i][j][k] = f.value(xval[i], yval[j], zval[k]); + } + } + } + + TrivariateFunction tcf = new TricubicInterpolator().interpolate(xval, + yval, + zval, + fval); + double x, y, z; + double expected, result; + + x = 4; + y = -3; + z = 0; + expected = f.value(x, y, z); + result = tcf.value(x, y, z); + Assert.assertEquals("On sample point", + expected, result, 1e-15); + + x = 4.5; + y = -1.5; + z = -4.25; + expected = f.value(x, y, z); + result = tcf.value(x, y, z); + Assert.assertEquals("Half-way between sample points (middle of the patch)", + expected, result, 1e-14); + } + + /** + * Sine wave. + * <p> + * f(x, y, z) = a cos [ω z - k<sub>y</sub> x - k<sub>y</sub> y] + * </p> + * with A = 0.2, ω = 0.5, k<sub>x</sub> = 2, k<sub>y</sub> = 1. + */ + @Test + public void testWave() { + double[] xval = new double[] {3, 4, 5, 6.5}; + double[] yval = new double[] {-4, -3, -1, 2, 2.5}; + double[] zval = new double[] {-12, -8, -5.5, -3, 0, 4}; + + final double a = 0.2; + final double omega = 0.5; + final double kx = 2; + final double ky = 1; + + // Function values + TrivariateFunction f = new TrivariateFunction() { + public double value(double x, double y, double z) { + return a * FastMath.cos(omega * z - kx * x - ky * y); + } + }; + + double[][][] fval = new double[xval.length][yval.length][zval.length]; + for (int i = 0; i < xval.length; i++) { + for (int j = 0; j < yval.length; j++) { + for (int k = 0; k < zval.length; k++) { + fval[i][j][k] = f.value(xval[i], yval[j], zval[k]); + } + } + } + + TrivariateFunction tcf = new TricubicInterpolator().interpolate(xval, + yval, + zval, + fval); + + double x, y, z; + double expected, result; + + x = 4; + y = -3; + z = 0; + expected = f.value(x, y, z); + result = tcf.value(x, y, z); + Assert.assertEquals("On sample point", + expected, result, 1e-14); + + x = 4.5; + y = -1.5; + z = -4.25; + expected = f.value(x, y, z); + result = tcf.value(x, y, z); + Assert.assertEquals("Half-way between sample points (middle of the patch)", + expected, result, 1e-1); // XXX Too high tolerance! + } +}
