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Posted to dev@commons.apache.org by pi...@apache.org on 2005/09/05 00:00:43 UTC
svn commit: r278634 -
/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/
Author: pietsch
Date: Sun Sep 4 15:00:27 2005
New Revision: 278634
URL: http://svn.apache.org/viewcvs?rev=278634&view=rev
Log:
Preliminary checkin of SoC code.
Contributed by: Xiaogang Zhang
Added:
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/DividedDifferenceInterpolatorTest.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/Expm1Function.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/LaguerreSolverTest.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/MullerSolverTest.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/NevilleInterpolatorTest.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionLagrangeFormTest.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionNewtonFormTest.java (with props)
jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/RiddersSolverTest.java (with props)
Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/DividedDifferenceInterpolatorTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/DividedDifferenceInterpolatorTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/DividedDifferenceInterpolatorTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/DividedDifferenceInterpolatorTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,137 @@
+/*
+ * Copyright 2003-2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Divided Difference interpolator.
+ * <p>
+ * The error of polynomial interpolation is
+ * f(z) - p(z) = f^(n)(zeta) * (z-x[0])(z-x[1])...(z-x[n-1]) / n!
+ * where f^(n) is the n-th derivative of the approximated function and
+ * zeta is some point in the interval determined by x[] and z.
+ * <p>
+ * Since zeta is unknown, f^(n)(zeta) cannot be calculated. But we can bound
+ * it and use the absolute value upper bound for estimates. For reference,
+ * see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 2.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class DividedDifferenceInterpolatorTest extends TestCase {
+
+ /**
+ * Test of interpolator for the sine function.
+ * <p>
+ * |sin^(n)(zeta)| <= 1.0, zeta in [0, 2*PI]
+ */
+ public void testSinFunction() throws MathException {
+ UnivariateRealFunction f = new SinFunction();
+ UnivariateRealInterpolator interpolator = new DividedDifferenceInterpolator();
+ double x[], y[], z, expected, result, tolerance;
+
+ // 6 interpolating points on interval [0, 2*PI]
+ int n = 6;
+ double min = 0.0, max = 2 * Math.PI;
+ x = new double[n];
+ y = new double[n];
+ for (int i = 0; i < n; i++) {
+ x[i] = min + i * (max - min) / n;
+ y[i] = f.value(x[i]);
+ }
+ double derivativebound = 1.0;
+ UnivariateRealFunction p = interpolator.interpolate(x, y);
+
+ z = Math.PI / 4; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+
+ z = Math.PI * 1.5; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of interpolator for the exponential function.
+ * <p>
+ * |expm1^(n)(zeta)| <= e, zeta in [-1, 1]
+ */
+ public void testExpm1Function() throws MathException {
+ UnivariateRealFunction f = new Expm1Function();
+ UnivariateRealInterpolator interpolator = new DividedDifferenceInterpolator();
+ double x[], y[], z, expected, result, tolerance;
+
+ // 5 interpolating points on interval [-1, 1]
+ int n = 5;
+ double min = -1.0, max = 1.0;
+ x = new double[n];
+ y = new double[n];
+ for (int i = 0; i < n; i++) {
+ x[i] = min + i * (max - min) / n;
+ y[i] = f.value(x[i]);
+ }
+ double derivativebound = Math.E;
+ UnivariateRealFunction p = interpolator.interpolate(x, y);
+
+ z = 0.0; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+
+ z = 0.5; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+
+ z = -0.5; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of parameters for the interpolator.
+ */
+ public void testParameters() throws Exception {
+ UnivariateRealInterpolator interpolator = new DividedDifferenceInterpolator();
+
+ try {
+ // bad abscissas array
+ double x[] = { 1.0, 2.0, 2.0, 4.0 };
+ double y[] = { 0.0, 4.0, 4.0, 2.5 };
+ UnivariateRealFunction p = interpolator.interpolate(x, y);
+ p.value(0.0);
+ fail("Expecting MathException - bad abscissas array");
+ } catch (MathException ex) {
+ // expected
+ }
+ }
+
+ /**
+ * Returns the partial error term (z-x[0])(z-x[1])...(z-x[n-1])/n!
+ */
+ protected double partialerror(double x[], double z) throws
+ IllegalArgumentException {
+
+ if (x.length < 1) {
+ throw new IllegalArgumentException
+ ("Interpolation array cannot be empty.");
+ }
+ double out = 1;
+ for (int i = 0; i < x.length; i++) {
+ out *= (z - x[i]) / (i + 1);
+ }
+ return out;
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/DividedDifferenceInterpolatorTest.java
------------------------------------------------------------------------------
svn:executable = *
Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/Expm1Function.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/Expm1Function.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/Expm1Function.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/Expm1Function.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,39 @@
+/*
+ * Copyright 2003-2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.FunctionEvaluationException;
+
+/**
+ * Auxillary class for testing purposes.
+ *
+ * @version $Revision$ $Date$
+ */
+public class Expm1Function implements DifferentiableUnivariateRealFunction {
+
+ public double value(double x) throws FunctionEvaluationException {
+ // Math.expm1() is available in jdk 1.5 but not in jdk 1.4.2.
+ return Math.exp(x) - 1.0;
+ }
+
+ public UnivariateRealFunction derivative() {
+ return new UnivariateRealFunction() {
+ public double value(double x) throws FunctionEvaluationException {
+ return Math.exp(x);
+ }
+ };
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/Expm1Function.java
------------------------------------------------------------------------------
svn:executable = *
Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/LaguerreSolverTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/LaguerreSolverTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/LaguerreSolverTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/LaguerreSolverTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,178 @@
+/*
+ * Copyright 2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import org.apache.commons.math.complex.Complex;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Laguerre solver.
+ * <p>
+ * Laguerre's method is very efficient in solving polynomials. Test runs
+ * show that for a default absolute accuracy of 1E-6, it generally takes
+ * less than 5 iterations to find one root, provided solveAll() is not
+ * invoked, and 15 to 20 iterations to find all roots for quintic function.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class LaguerreSolverTest extends TestCase {
+
+ /**
+ * Test of solver for the linear function.
+ */
+ public void testLinearFunction() throws MathException {
+ double min, max, expected, result, tolerance;
+
+ // p(x) = 4x - 1
+ double coefficients[] = { -1.0, 4.0 };
+ PolynomialFunction f = new PolynomialFunction(coefficients);
+ UnivariateRealSolver solver = new LaguerreSolver(f);
+
+ min = 0.0; max = 1.0; expected = 0.25;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the quadratic function.
+ */
+ public void testQuadraticFunction() throws MathException {
+ double min, max, expected, result, tolerance;
+
+ // p(x) = 2x^2 + 5x - 3 = (x+3)(2x-1)
+ double coefficients[] = { -3.0, 5.0, 2.0 };
+ PolynomialFunction f = new PolynomialFunction(coefficients);
+ UnivariateRealSolver solver = new LaguerreSolver(f);
+
+ min = 0.0; max = 2.0; expected = 0.5;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -4.0; max = -1.0; expected = -3.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the quintic function.
+ */
+ public void testQuinticFunction() throws MathException {
+ double min, max, expected, result, tolerance;
+
+ // p(x) = x^5 - x^4 - 12x^3 + x^2 - x - 12 = (x+1)(x+3)(x-4)(x^2-x+1)
+ double coefficients[] = { -12.0, -1.0, 1.0, -12.0, -1.0, 1.0 };
+ PolynomialFunction f = new PolynomialFunction(coefficients);
+ UnivariateRealSolver solver = new LaguerreSolver(f);
+
+ min = -2.0; max = 2.0; expected = -1.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -5.0; max = -2.5; expected = -3.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = 3.0; max = 6.0; expected = 4.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the quintic function using solveAll().
+ */
+ public void testQuinticFunction2() throws MathException {
+ double initial = 0.0, tolerance;
+ Complex expected, result[];
+
+ // p(x) = x^5 + 4x^3 + x^2 + 4 = (x+1)(x^2-x+1)(x^2+4)
+ double coefficients[] = { 4.0, 0.0, 1.0, 4.0, 0.0, 1.0 };
+ PolynomialFunction f = new PolynomialFunction(coefficients);
+ LaguerreSolver solver = new LaguerreSolver(f);
+ result = solver.solveAll(coefficients, initial);
+
+ // The order of roots returned by solveAll() depends on
+ // initial value, solveAll() does no sorting.
+ expected = new Complex(0.0, -2.0);
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected.abs() * solver.getRelativeAccuracy()));
+ assertEquals(0.0, (expected.subtract(result[0])).abs(), tolerance);
+
+ expected = new Complex(0.0, 2.0);
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected.abs() * solver.getRelativeAccuracy()));
+ assertEquals(0.0, (expected.subtract(result[1])).abs(), tolerance);
+
+ expected = new Complex(0.5, 0.5 * Math.sqrt(3.0));
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected.abs() * solver.getRelativeAccuracy()));
+ assertEquals(0.0, (expected.subtract(result[2])).abs(), tolerance);
+
+ expected = new Complex(-1.0, 0.0);
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected.abs() * solver.getRelativeAccuracy()));
+ assertEquals(0.0, (expected.subtract(result[3])).abs(), tolerance);
+
+ expected = new Complex(0.5, -0.5 * Math.sqrt(3.0));
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected.abs() * solver.getRelativeAccuracy()));
+ assertEquals(0.0, (expected.subtract(result[4])).abs(), tolerance);
+ }
+
+ /**
+ * Test of parameters for the solver.
+ */
+ public void testParameters() throws Exception {
+ double coefficients[] = { -3.0, 5.0, 2.0 };
+ PolynomialFunction f = new PolynomialFunction(coefficients);
+ UnivariateRealSolver solver = new LaguerreSolver(f);
+
+ try {
+ // bad interval
+ solver.solve(1, -1);
+ fail("Expecting IllegalArgumentException - bad interval");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ try {
+ // no bracketing
+ solver.solve(2, 3);
+ fail("Expecting IllegalArgumentException - no bracketing");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ try {
+ // bad function
+ UnivariateRealFunction f2 = new SinFunction();
+ UnivariateRealSolver solver2 = new LaguerreSolver(f2);
+ fail("Expecting IllegalArgumentException - bad function");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/LaguerreSolverTest.java
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svn:executable = *
Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/MullerSolverTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/MullerSolverTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/MullerSolverTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/MullerSolverTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,214 @@
+/*
+ * Copyright 2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Muller solver.
+ * <p>
+ * Muller's method converges almost quadratically near roots, but it can
+ * be very slow in regions far away from zeros. Test runs show that for
+ * reasonably good initial values, for a default absolute accuracy of 1E-6,
+ * it generally takes 5 to 10 iterations for the solver to converge.
+ * <p>
+ * Tests for the exponential function illustrate the situations where
+ * Muller solver performs poorly.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class MullerSolverTest extends TestCase {
+
+ /**
+ * Test of solver for the sine function.
+ */
+ public void testSinFunction() throws MathException {
+ UnivariateRealFunction f = new SinFunction();
+ UnivariateRealSolver solver = new MullerSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = 3.0; max = 4.0; expected = Math.PI;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -1.0; max = 1.5; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the sine function using solve2().
+ */
+ public void testSinFunction2() throws MathException {
+ UnivariateRealFunction f = new SinFunction();
+ MullerSolver solver = new MullerSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = 3.0; max = 4.0; expected = Math.PI;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -1.0; max = 1.5; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the quintic function.
+ */
+ public void testQuinticFunction() throws MathException {
+ UnivariateRealFunction f = new QuinticFunction();
+ UnivariateRealSolver solver = new MullerSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = -0.4; max = 0.2; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = 0.75; max = 1.5; expected = 1.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -0.9; max = -0.2; expected = -0.5;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the quintic function using solve2().
+ */
+ public void testQuinticFunction2() throws MathException {
+ UnivariateRealFunction f = new QuinticFunction();
+ MullerSolver solver = new MullerSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = -0.4; max = 0.2; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = 0.75; max = 1.5; expected = 1.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -0.9; max = -0.2; expected = -0.5;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the exponential function.
+ * <p>
+ * It takes 10 to 15 iterations for the last two tests to converge.
+ * In fact, if not for the bisection alternative, the solver would
+ * exceed the default maximal iteration of 100.
+ */
+ public void testExpm1Function() throws MathException {
+ UnivariateRealFunction f = new Expm1Function();
+ UnivariateRealSolver solver = new MullerSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = -1.0; max = 2.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -20.0; max = 10.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -50.0; max = 100.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the exponential function using solve2().
+ * <p>
+ * It takes 25 to 50 iterations for the last two tests to converge.
+ */
+ public void testExpm1Function2() throws MathException {
+ UnivariateRealFunction f = new Expm1Function();
+ MullerSolver solver = new MullerSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = -1.0; max = 2.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -20.0; max = 10.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -50.0; max = 100.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve2(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of parameters for the solver.
+ */
+ public void testParameters() throws Exception {
+ UnivariateRealFunction f = new SinFunction();
+ UnivariateRealSolver solver = new MullerSolver(f);
+
+ try {
+ // bad interval
+ solver.solve(1, -1);
+ fail("Expecting IllegalArgumentException - bad interval");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ try {
+ // no bracketing
+ solver.solve(2, 3);
+ fail("Expecting IllegalArgumentException - no bracketing");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/MullerSolverTest.java
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svn:executable = *
Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/NevilleInterpolatorTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/NevilleInterpolatorTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/NevilleInterpolatorTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/NevilleInterpolatorTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,137 @@
+/*
+ * Copyright 2003-2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Neville interpolator.
+ * <p>
+ * The error of polynomial interpolation is
+ * f(z) - p(z) = f^(n)(zeta) * (z-x[0])(z-x[1])...(z-x[n-1]) / n!
+ * where f^(n) is the n-th derivative of the approximated function and
+ * zeta is some point in the interval determined by x[] and z.
+ * <p>
+ * Since zeta is unknown, f^(n)(zeta) cannot be calculated. But we can bound
+ * it and use the absolute value upper bound for estimates. For reference,
+ * see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 2.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class NevilleInterpolatorTest extends TestCase {
+
+ /**
+ * Test of interpolator for the sine function.
+ * <p>
+ * |sin^(n)(zeta)| <= 1.0, zeta in [0, 2*PI]
+ */
+ public void testSinFunction() throws MathException {
+ UnivariateRealFunction f = new SinFunction();
+ UnivariateRealInterpolator interpolator = new NevilleInterpolator();
+ double x[], y[], z, expected, result, tolerance;
+
+ // 6 interpolating points on interval [0, 2*PI]
+ int n = 6;
+ double min = 0.0, max = 2 * Math.PI;
+ x = new double[n];
+ y = new double[n];
+ for (int i = 0; i < n; i++) {
+ x[i] = min + i * (max - min) / n;
+ y[i] = f.value(x[i]);
+ }
+ double derivativebound = 1.0;
+ UnivariateRealFunction p = interpolator.interpolate(x, y);
+
+ z = Math.PI / 4; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+
+ z = Math.PI * 1.5; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of interpolator for the exponential function.
+ * <p>
+ * |expm1^(n)(zeta)| <= e, zeta in [-1, 1]
+ */
+ public void testExpm1Function() throws MathException {
+ UnivariateRealFunction f = new Expm1Function();
+ UnivariateRealInterpolator interpolator = new NevilleInterpolator();
+ double x[], y[], z, expected, result, tolerance;
+
+ // 5 interpolating points on interval [-1, 1]
+ int n = 5;
+ double min = -1.0, max = 1.0;
+ x = new double[n];
+ y = new double[n];
+ for (int i = 0; i < n; i++) {
+ x[i] = min + i * (max - min) / n;
+ y[i] = f.value(x[i]);
+ }
+ double derivativebound = Math.E;
+ UnivariateRealFunction p = interpolator.interpolate(x, y);
+
+ z = 0.0; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+
+ z = 0.5; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+
+ z = -0.5; expected = f.value(z); result = p.value(z);
+ tolerance = Math.abs(derivativebound * partialerror(x, z));
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of parameters for the interpolator.
+ */
+ public void testParameters() throws Exception {
+ UnivariateRealInterpolator interpolator = new NevilleInterpolator();
+
+ try {
+ // bad abscissas array
+ double x[] = { 1.0, 2.0, 2.0, 4.0 };
+ double y[] = { 0.0, 4.0, 4.0, 2.5 };
+ UnivariateRealFunction p = interpolator.interpolate(x, y);
+ p.value(0.0);
+ fail("Expecting MathException - bad abscissas array");
+ } catch (MathException ex) {
+ // expected
+ }
+ }
+
+ /**
+ * Returns the partial error term (z-x[0])(z-x[1])...(z-x[n-1])/n!
+ */
+ protected double partialerror(double x[], double z) throws
+ IllegalArgumentException {
+
+ if (x.length < 1) {
+ throw new IllegalArgumentException
+ ("Interpolation array cannot be empty.");
+ }
+ double out = 1;
+ for (int i = 0; i < x.length; i++) {
+ out *= (z - x[i]) / (i + 1);
+ }
+ return out;
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/NevilleInterpolatorTest.java
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Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionLagrangeFormTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionLagrangeFormTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionLagrangeFormTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionLagrangeFormTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,149 @@
+/*
+ * Copyright 2003-2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Lagrange form of polynomial function.
+ * <p>
+ * We use n+1 points to interpolate a polynomial of degree n. This should
+ * give us the exact same polynomial as result. Thus we can use a very
+ * small tolerance to account only for round-off errors.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class PolynomialFunctionLagrangeFormTest extends TestCase {
+
+ /**
+ * Test of polynomial for the linear function.
+ */
+ public void testLinearFunction() throws MathException {
+ PolynomialFunctionLagrangeForm p;
+ double c[], z, expected, result, tolerance = 1E-12;
+
+ // p(x) = 1.5x - 4
+ double x[] = { 0.0, 3.0 };
+ double y[] = { -4.0, 0.5 };
+ p = new PolynomialFunctionLagrangeForm(x, y);
+
+ z = 2.0; expected = -1.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 4.5; expected = 2.75; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 6.0; expected = 5.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ assertEquals(1, p.degree());
+
+ c = p.getCoefficients();
+ assertEquals(2, c.length);
+ assertEquals(-4.0, c[0], tolerance);
+ assertEquals(1.5, c[1], tolerance);
+ }
+
+ /**
+ * Test of polynomial for the quadratic function.
+ */
+ public void testQuadraticFunction() throws MathException {
+ PolynomialFunctionLagrangeForm p;
+ double c[], z, expected, result, tolerance = 1E-12;
+
+ // p(x) = 2x^2 + 5x - 3 = (2x - 1)(x + 3)
+ double x[] = { 0.0, -1.0, 0.5 };
+ double y[] = { -3.0, -6.0, 0.0 };
+ p = new PolynomialFunctionLagrangeForm(x, y);
+
+ z = 1.0; expected = 4.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 2.5; expected = 22.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = -2.0; expected = -5.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ assertEquals(2, p.degree());
+
+ c = p.getCoefficients();
+ assertEquals(3, c.length);
+ assertEquals(-3.0, c[0], tolerance);
+ assertEquals(5.0, c[1], tolerance);
+ assertEquals(2.0, c[2], tolerance);
+ }
+
+ /**
+ * Test of polynomial for the quintic function.
+ */
+ public void testQuinticFunction() throws MathException {
+ PolynomialFunctionLagrangeForm p;
+ double c[], z, expected, result, tolerance = 1E-12;
+
+ // p(x) = x^5 - x^4 - 7x^3 + x^2 + 6x = x(x^2 - 1)(x + 2)(x - 3)
+ double x[] = { 1.0, -1.0, 2.0, 3.0, -3.0, 0.5 };
+ double y[] = { 0.0, 0.0, -24.0, 0.0, -144.0, 2.34375 };
+ p = new PolynomialFunctionLagrangeForm(x, y);
+
+ z = 0.0; expected = 0.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = -2.0; expected = 0.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 4.0; expected = 360.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ assertEquals(5, p.degree());
+
+ c = p.getCoefficients();
+ assertEquals(6, c.length);
+ assertEquals(0.0, c[0], tolerance);
+ assertEquals(6.0, c[1], tolerance);
+ assertEquals(1.0, c[2], tolerance);
+ assertEquals(-7.0, c[3], tolerance);
+ assertEquals(-1.0, c[4], tolerance);
+ assertEquals(1.0, c[5], tolerance);
+ }
+
+ /**
+ * Test of parameters for the polynomial.
+ */
+ public void testParameters() throws Exception {
+ PolynomialFunctionLagrangeForm p;
+
+ try {
+ // bad input array length
+ double x[] = { 1.0 };
+ double y[] = { 2.0 };
+ p = new PolynomialFunctionLagrangeForm(x, y);
+ fail("Expecting IllegalArgumentException - bad input array length");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ try {
+ // mismatch input arrays
+ double x[] = { 1.0, 2.0, 3.0, 4.0 };
+ double y[] = { 0.0, -4.0, -24.0 };
+ p = new PolynomialFunctionLagrangeForm(x, y);
+ fail("Expecting IllegalArgumentException - mismatch input arrays");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionLagrangeFormTest.java
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Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionNewtonFormTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionNewtonFormTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionNewtonFormTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionNewtonFormTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,148 @@
+/*
+ * Copyright 2003-2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Newton form of polynomial function.
+ * <p>
+ * The small tolerance number is used only to account for round-off errors.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class PolynomialFunctionNewtonFormTest extends TestCase {
+
+ /**
+ * Test of polynomial for the linear function.
+ */
+ public void testLinearFunction() throws MathException {
+ PolynomialFunctionNewtonForm p;
+ double coefficients[], z, expected, result, tolerance = 1E-12;
+
+ // p(x) = 1.5x - 4 = 2 + 1.5(x-4)
+ double a[] = { 2.0, 1.5 };
+ double c[] = { 4.0 };
+ p = new PolynomialFunctionNewtonForm(a, c);
+
+ z = 2.0; expected = -1.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 4.5; expected = 2.75; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 6.0; expected = 5.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ assertEquals(1, p.degree());
+
+ coefficients = p.getCoefficients();
+ assertEquals(2, coefficients.length);
+ assertEquals(-4.0, coefficients[0], tolerance);
+ assertEquals(1.5, coefficients[1], tolerance);
+ }
+
+ /**
+ * Test of polynomial for the quadratic function.
+ */
+ public void testQuadraticFunction() throws MathException {
+ PolynomialFunctionNewtonForm p;
+ double coefficients[], z, expected, result, tolerance = 1E-12;
+
+ // p(x) = 2x^2 + 5x - 3 = 4 + 3(x-1) + 2(x-1)(x+2)
+ double a[] = { 4.0, 3.0, 2.0 };
+ double c[] = { 1.0, -2.0 };
+ p = new PolynomialFunctionNewtonForm(a, c);
+
+ z = 1.0; expected = 4.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 2.5; expected = 22.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = -2.0; expected = -5.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ assertEquals(2, p.degree());
+
+ coefficients = p.getCoefficients();
+ assertEquals(3, coefficients.length);
+ assertEquals(-3.0, coefficients[0], tolerance);
+ assertEquals(5.0, coefficients[1], tolerance);
+ assertEquals(2.0, coefficients[2], tolerance);
+ }
+
+ /**
+ * Test of polynomial for the quintic function.
+ */
+ public void testQuinticFunction() throws MathException {
+ PolynomialFunctionNewtonForm p;
+ double coefficients[], z, expected, result, tolerance = 1E-12;
+
+ // p(x) = x^5 - x^4 - 7x^3 + x^2 + 6x
+ // = 6x - 6x^2 -6x^2(x-1) + x^2(x-1)(x+1) + x^2(x-1)(x+1)(x-2)
+ double a[] = { 0.0, 6.0, -6.0, -6.0, 1.0, 1.0 };
+ double c[] = { 0.0, 0.0, 1.0, -1.0, 2.0 };
+ p = new PolynomialFunctionNewtonForm(a, c);
+
+ z = 0.0; expected = 0.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = -2.0; expected = 0.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ z = 4.0; expected = 360.0; result = p.value(z);
+ assertEquals(expected, result, tolerance);
+
+ assertEquals(5, p.degree());
+
+ coefficients = p.getCoefficients();
+ assertEquals(6, coefficients.length);
+ assertEquals(0.0, coefficients[0], tolerance);
+ assertEquals(6.0, coefficients[1], tolerance);
+ assertEquals(1.0, coefficients[2], tolerance);
+ assertEquals(-7.0, coefficients[3], tolerance);
+ assertEquals(-1.0, coefficients[4], tolerance);
+ assertEquals(1.0, coefficients[5], tolerance);
+ }
+
+ /**
+ * Test of parameters for the polynomial.
+ */
+ public void testParameters() throws Exception {
+ PolynomialFunctionNewtonForm p;
+
+ try {
+ // bad input array length
+ double a[] = { 1.0 };
+ double c[] = { 2.0 };
+ p = new PolynomialFunctionNewtonForm(a, c);
+ fail("Expecting IllegalArgumentException - bad input array length");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ try {
+ // mismatch input arrays
+ double a[] = { 1.0, 2.0, 3.0, 4.0 };
+ double c[] = { 4.0, 3.0, 2.0, 1.0 };
+ p = new PolynomialFunctionNewtonForm(a, c);
+ fail("Expecting IllegalArgumentException - mismatch input arrays");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/PolynomialFunctionNewtonFormTest.java
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Added: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/RiddersSolverTest.java
URL: http://svn.apache.org/viewcvs/jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/RiddersSolverTest.java?rev=278634&view=auto
==============================================================================
--- jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/RiddersSolverTest.java (added)
+++ jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/RiddersSolverTest.java Sun Sep 4 15:00:27 2005
@@ -0,0 +1,131 @@
+/*
+ * Copyright 2005 The Apache Software Foundation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis;
+
+import org.apache.commons.math.MathException;
+import junit.framework.TestCase;
+
+/**
+ * Testcase for Ridders solver.
+ * <p>
+ * Ridders' method converges superlinearly, more specific, its rate of
+ * convergence is sqrt(2). Test runs show that for a default absolute
+ * accuracy of 1E-6, it generally takes less than 5 iterations for close
+ * initial bracket and 5 to 10 iterations for distant initial bracket
+ * to converge.
+ *
+ * @version $Revision$ $Date$
+ */
+public final class RiddersSolverTest extends TestCase {
+
+ /**
+ * Test of solver for the sine function.
+ */
+ public void testSinFunction() throws MathException {
+ UnivariateRealFunction f = new SinFunction();
+ UnivariateRealSolver solver = new RiddersSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = 3.0; max = 4.0; expected = Math.PI;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -1.0; max = 1.5; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the quintic function.
+ */
+ public void testQuinticFunction() throws MathException {
+ UnivariateRealFunction f = new QuinticFunction();
+ UnivariateRealSolver solver = new RiddersSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = -0.4; max = 0.2; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = 0.75; max = 1.5; expected = 1.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -0.9; max = -0.2; expected = -0.5;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of solver for the exponential function.
+ */
+ public void testExpm1Function() throws MathException {
+ UnivariateRealFunction f = new Expm1Function();
+ UnivariateRealSolver solver = new RiddersSolver(f);
+ double min, max, expected, result, tolerance;
+
+ min = -1.0; max = 2.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -20.0; max = 10.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+
+ min = -50.0; max = 100.0; expected = 0.0;
+ tolerance = Math.max(solver.getAbsoluteAccuracy(),
+ Math.abs(expected * solver.getRelativeAccuracy()));
+ result = solver.solve(min, max);
+ assertEquals(expected, result, tolerance);
+ }
+
+ /**
+ * Test of parameters for the solver.
+ */
+ public void testParameters() throws Exception {
+ UnivariateRealFunction f = new SinFunction();
+ UnivariateRealSolver solver = new RiddersSolver(f);
+
+ try {
+ // bad interval
+ solver.solve(1, -1);
+ fail("Expecting IllegalArgumentException - bad interval");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ try {
+ // no bracketing
+ solver.solve(2, 3);
+ fail("Expecting IllegalArgumentException - no bracketing");
+ } catch (IllegalArgumentException ex) {
+ // expected
+ }
+ }
+}
Propchange: jakarta/commons/proper/math/trunk/src/test/org/apache/commons/math/analysis/RiddersSolverTest.java
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