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Posted to commits@commons.apache.org by er...@apache.org on 2018/02/02 13:28:58 UTC
[03/50] commons-numbers git commit: NUMBERS-22: Added file
ComplexTest.java to file tracker
NUMBERS-22: Added file ComplexTest.java to file tracker
Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/fc70d935
Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/fc70d935
Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/fc70d935
Branch: refs/heads/feature__NUMBERS-51__field
Commit: fc70d935fdadc5d5a7862cf9a929da91b72b00d6
Parents: 16322d8
Author: Eric Barnhill <er...@apache.org>
Authored: Fri Jan 26 14:54:16 2018 +0100
Committer: Eric Barnhill <er...@apache.org>
Committed: Fri Jan 26 14:54:16 2018 +0100
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.../commons/numbers/complex/ComplexTest.java | 849 +++++++++++++++++++
1 file changed, 849 insertions(+)
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http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/fc70d935/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java
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diff --git a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java
new file mode 100644
index 0000000..b1ffab6
--- /dev/null
+++ b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java
@@ -0,0 +1,849 @@
+/*
+ * 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.numbers.complex;
+
+import java.util.List;
+
+import org.apache.commons.numbers.complex.Complex;
+import org.apache.commons.numbers.complex.ComplexUtils;
+import org.junit.Assert;
+import org.junit.Ignore;
+import org.junit.Test;
+
+
+/**
+ */
+public class ComplexTest {
+
+
+ private static final double inf = Double.POSITIVE_INFINITY;
+ private static final double neginf = Double.NEGATIVE_INFINITY;
+ private static final double nan = Double.NaN;
+ private static final double pi = Math.PI;
+ private static final Complex oneInf = new Complex(1, inf);
+ private static final Complex oneNegInf = new Complex(1, neginf);
+ private static final Complex infOne = new Complex(inf, 1);
+ private static final Complex infZero = new Complex(inf, 0);
+ private static final Complex infNaN = new Complex(inf, nan);
+ private static final Complex infNegInf = new Complex(inf, neginf);
+ private static final Complex infInf = new Complex(inf, inf);
+ private static final Complex negInfInf = new Complex(neginf, inf);
+ private static final Complex negInfZero = new Complex(neginf, 0);
+ private static final Complex negInfOne = new Complex(neginf, 1);
+ private static final Complex negInfNaN = new Complex(neginf, nan);
+ private static final Complex negInfNegInf = new Complex(neginf, neginf);
+ private static final Complex oneNaN = new Complex(1, nan);
+ private static final Complex zeroInf = new Complex(0, inf);
+ private static final Complex zeroNaN = new Complex(0, nan);
+ private static final Complex nanInf = new Complex(nan, inf);
+ private static final Complex nanNegInf = new Complex(nan, neginf);
+ private static final Complex nanZero = new Complex(nan, 0);
+
+ @Test
+ public void testConstructor() {
+ Complex z = new Complex(3.0, 4.0);
+ Assert.assertEquals(3.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(4.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testConstructorNaN() {
+ Complex z = new Complex(3.0, Double.NaN);
+ Assert.assertTrue(z.isNaN());
+
+ z = new Complex(nan, 4.0);
+ Assert.assertTrue(z.isNaN());
+
+ z = new Complex(3.0, 4.0);
+ Assert.assertFalse(z.isNaN());
+ }
+
+ @Test
+ public void testAbs() {
+ Complex z = new Complex(3.0, 4.0);
+ Assert.assertEquals(5.0, z.abs(), 1.0e-5);
+ }
+
+ @Test
+ public void testAbsNaN() {
+ Assert.assertTrue(Double.isNaN(Complex.NaN.abs()));
+ Complex z = new Complex(inf, nan);
+ Assert.assertTrue(Double.isNaN(z.abs()));
+ }
+
+ @Test
+ public void testAdd() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex y = new Complex(5.0, 6.0);
+ Complex z = x.add(y);
+ Assert.assertEquals(8.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(10.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testAddInf() {
+ Complex x = new Complex(1, 1);
+ Complex z = new Complex(inf, 0);
+ Complex w = x.add(z);
+ Assert.assertEquals(w.getImaginary(), 1, 0);
+ Assert.assertEquals(inf, w.getReal(), 0);
+
+ x = new Complex(neginf, 0);
+ Assert.assertTrue(Double.isNaN(x.add(z).getReal()));
+ }
+
+
+ @Test
+ public void testScalarAdd() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = 2.0;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.add(yComplex), x.add(yDouble));
+ }
+
+ @Test
+ public void testScalarAddNaN() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = Double.NaN;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.add(yComplex), x.add(yDouble));
+ }
+
+ @Test
+ public void testScalarAddInf() {
+ Complex x = new Complex(1, 1);
+ double yDouble = Double.POSITIVE_INFINITY;
+
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.add(yComplex), x.add(yDouble));
+
+ x = new Complex(neginf, 0);
+ Assert.assertEquals(x.add(yComplex), x.add(yDouble));
+ }
+
+ @Test
+ public void testConjugate() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex z = x.conjugate();
+ Assert.assertEquals(3.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(-4.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testConjugateNaN() {
+ Complex z = Complex.NaN.conjugate();
+ Assert.assertTrue(z.isNaN());
+ }
+
+ @Test
+ public void testConjugateInfiinite() {
+ Complex z = new Complex(0, inf);
+ Assert.assertEquals(neginf, z.conjugate().getImaginary(), 0);
+ z = new Complex(0, neginf);
+ Assert.assertEquals(inf, z.conjugate().getImaginary(), 0);
+ }
+
+ @Test
+ public void testDivide() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex y = new Complex(5.0, 6.0);
+ Complex z = x.divide(y);
+ Assert.assertEquals(39.0 / 61.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(2.0 / 61.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testDivideReal() {
+ Complex x = new Complex(2d, 3d);
+ Complex y = new Complex(2d, 0d);
+ Assert.assertEquals(new Complex(1d, 1.5), x.divide(y));
+
+ }
+
+ @Test
+ public void testDivideImaginary() {
+ Complex x = new Complex(2d, 3d);
+ Complex y = new Complex(0d, 2d);
+ Assert.assertEquals(new Complex(1.5d, -1d), x.divide(y));
+ }
+
+ @Test
+ public void testDivideZero() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex z = x.divide(Complex.ZERO);
+ // Assert.assertEquals(z, Complex.INF); // See MATH-657
+ Assert.assertEquals(z, Complex.NaN);
+ }
+
+ @Test
+ public void testDivideZeroZero() {
+ Complex x = new Complex(0.0, 0.0);
+ Complex z = x.divide(Complex.ZERO);
+ Assert.assertEquals(z, Complex.NaN);
+ }
+
+ @Test
+ public void testDivideNaN() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex z = x.divide(Complex.NaN);
+ Assert.assertTrue(z.isNaN());
+ }
+
+ @Test
+ public void testDivideNaNInf() {
+ Complex z = oneInf.divide(Complex.ONE);
+ Assert.assertTrue(Double.isNaN(z.getReal()));
+ Assert.assertEquals(inf, z.getImaginary(), 0);
+
+ z = negInfNegInf.divide(oneNaN);
+ Assert.assertTrue(Double.isNaN(z.getReal()));
+ Assert.assertTrue(Double.isNaN(z.getImaginary()));
+
+ z = negInfInf.divide(Complex.ONE);
+ Assert.assertTrue(Double.isNaN(z.getReal()));
+ Assert.assertTrue(Double.isNaN(z.getImaginary()));
+ }
+
+ @Test
+ public void testScalarDivide() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = 2.0;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.divide(yComplex), x.divide(yDouble));
+ }
+
+ @Test
+ public void testScalarDivideNaN() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = Double.NaN;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.divide(yComplex), x.divide(yDouble));
+ }
+
+ @Test
+ public void testScalarDivideZero() {
+ Complex x = new Complex(1,1);
+ TestUtils.assertEquals(x.divide(Complex.ZERO), x.divide(0), 0);
+ }
+
+ @Test
+ public void testReciprocal() {
+ Complex z = new Complex(5.0, 6.0);
+ Complex act = z.reciprocal();
+ double expRe = 5.0 / 61.0;
+ double expIm = -6.0 / 61.0;
+ Assert.assertEquals(expRe, act.getReal(), Math.ulp(expRe));
+ Assert.assertEquals(expIm, act.getImaginary(), Math.ulp(expIm));
+ }
+
+ @Test
+ public void testReciprocalReciprocal() {
+ Complex z = new Complex(5.0, 6.0);
+ Complex zRR = z.reciprocal().reciprocal();
+ final double tol = 1e-14;
+ Assert.assertEquals(zRR.getReal(), z.getReal(), tol);
+ Assert.assertEquals(zRR.getImaginary(), z.getImaginary(), tol);
+ }
+
+ @Test
+ public void testReciprocalReal() {
+ Complex z = new Complex(-2.0, 0.0);
+ Assert.assertTrue(Complex.equals(new Complex(-0.5, 0.0), z.reciprocal()));
+ }
+
+ @Test
+ public void testReciprocalImaginary() {
+ Complex z = new Complex(0.0, -2.0);
+ Assert.assertEquals(new Complex(0.0, 0.5), z.reciprocal());
+ }
+
+ @Test
+ public void testReciprocalNaN() {
+ Assert.assertTrue(Complex.NaN.reciprocal().isNaN());
+ }
+
+ @Test
+ public void testMultiply() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex y = new Complex(5.0, 6.0);
+ Complex z = x.multiply(y);
+ Assert.assertEquals(-9.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(38.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testMultiplyInfInf() {
+ // Assert.assertTrue(infInf.multiply(infInf).isNaN()); // MATH-620
+ Assert.assertTrue(infInf.multiply(infInf).isInfinite());
+ }
+
+ @Test
+ public void testScalarMultiply() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = 2.0;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
+ int zInt = -5;
+ Complex zComplex = new Complex(zInt);
+ Assert.assertEquals(x.multiply(zComplex), x.multiply(zInt));
+ }
+
+ @Test
+ public void testScalarMultiplyNaN() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = Double.NaN;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
+ }
+
+ @Test
+ public void testScalarMultiplyInf() {
+ Complex x = new Complex(1, 1);
+ double yDouble = Double.POSITIVE_INFINITY;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
+
+ yDouble = Double.NEGATIVE_INFINITY;
+ yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
+ }
+
+ @Test
+ public void testNegate() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex z = x.negate();
+ Assert.assertEquals(-3.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(-4.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testNegateNaN() {
+ Complex z = Complex.NaN.negate();
+ Assert.assertTrue(z.isNaN());
+ }
+
+ @Test
+ public void testSubtract() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex y = new Complex(5.0, 6.0);
+ Complex z = x.subtract(y);
+ Assert.assertEquals(-2.0, z.getReal(), 1.0e-5);
+ Assert.assertEquals(-2.0, z.getImaginary(), 1.0e-5);
+ }
+
+ @Test
+ public void testSubtractInf() {
+ Complex x = new Complex(1, 1);
+ Complex z = new Complex(neginf, 0);
+ Complex w = x.subtract(z);
+ Assert.assertEquals(w.getImaginary(), 1, 0);
+ Assert.assertEquals(inf, w.getReal(), 0);
+
+ x = new Complex(neginf, 0);
+ Assert.assertTrue(Double.isNaN(x.subtract(z).getReal()));
+ }
+
+ @Test
+ public void testScalarSubtract() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = 2.0;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
+ }
+
+ @Test
+ public void testScalarSubtractNaN() {
+ Complex x = new Complex(3.0, 4.0);
+ double yDouble = Double.NaN;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
+ }
+
+ @Test
+ public void testScalarSubtractInf() {
+ Complex x = new Complex(1, 1);
+ double yDouble = Double.POSITIVE_INFINITY;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
+
+ x = new Complex(neginf, 0);
+ Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
+ }
+
+
+ @Test
+ public void testEqualsNull() {
+ Complex x = new Complex(3.0, 4.0);
+ Assert.assertFalse(x.equals(null));
+ }
+
+ @Test(expected=NullPointerException.class)
+ public void testFloatingPointEqualsPrecondition1() {
+ Complex.equals(new Complex(3.0, 4.0), null, 3);
+ }
+ @Test(expected=NullPointerException.class)
+ public void testFloatingPointEqualsPrecondition2() {
+ Complex.equals(null, new Complex(3.0, 4.0), 3);
+ }
+
+ @Test
+ public void testEqualsClass() {
+ Complex x = new Complex(3.0, 4.0);
+ Assert.assertFalse(x.equals(this));
+ }
+
+ @Test
+ public void testEqualsSame() {
+ Complex x = new Complex(3.0, 4.0);
+ Assert.assertTrue(x.equals(x));
+ }
+
+ @Test
+ public void testFloatingPointEquals() {
+ double re = -3.21;
+ double im = 456789e10;
+
+ final Complex x = new Complex(re, im);
+ Complex y = new Complex(re, im);
+
+ Assert.assertTrue(x.equals(y));
+ Assert.assertTrue(Complex.equals(x, y));
+
+ final int maxUlps = 5;
+ for (int i = 0; i < maxUlps; i++) {
+ re = Math.nextUp(re);
+ im = Math.nextUp(im);
+ }
+ y = new Complex(re, im);
+ Assert.assertTrue(Complex.equals(x, y, maxUlps));
+
+ re = Math.nextUp(re);
+ im = Math.nextUp(im);
+ y = new Complex(re, im);
+ Assert.assertFalse(Complex.equals(x, y, maxUlps));
+ }
+
+ @Test
+ public void testFloatingPointEqualsNaN() {
+ Complex c = new Complex(Double.NaN, 1);
+ Assert.assertFalse(Complex.equals(c, c));
+
+ c = new Complex(1, Double.NaN);
+ Assert.assertFalse(Complex.equals(c, c));
+ }
+
+ @Test
+ public void testFloatingPointEqualsWithAllowedDelta() {
+ final double re = 153.0000;
+ final double im = 152.9375;
+ final double tol1 = 0.0625;
+ final Complex x = new Complex(re, im);
+ final Complex y = new Complex(re + tol1, im + tol1);
+ Assert.assertTrue(Complex.equals(x, y, tol1));
+
+ final double tol2 = 0.0624;
+ Assert.assertFalse(Complex.equals(x, y, tol2));
+ }
+
+ @Test
+ public void testFloatingPointEqualsWithAllowedDeltaNaN() {
+ final Complex x = new Complex(0, Double.NaN);
+ final Complex y = new Complex(Double.NaN, 0);
+ Assert.assertFalse(Complex.equals(x, Complex.ZERO, 0.1));
+ Assert.assertFalse(Complex.equals(x, x, 0.1));
+ Assert.assertFalse(Complex.equals(x, y, 0.1));
+ }
+
+ @Test
+ public void testFloatingPointEqualsWithRelativeTolerance() {
+ final double tol = 1e-4;
+ final double re = 1;
+ final double im = 1e10;
+
+ final double f = 1 + tol;
+ final Complex x = new Complex(re, im);
+ final Complex y = new Complex(re * f, im * f);
+ Assert.assertTrue(Complex.equalsWithRelativeTolerance(x, y, tol));
+ }
+
+ @Test
+ public void testFloatingPointEqualsWithRelativeToleranceNaN() {
+ final Complex x = new Complex(0, Double.NaN);
+ final Complex y = new Complex(Double.NaN, 0);
+ Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, Complex.ZERO, 0.1));
+ Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, x, 0.1));
+ Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, y, 0.1));
+ }
+
+ @Test
+ public void testEqualsTrue() {
+ Complex x = new Complex(3.0, 4.0);
+ Complex y = new Complex(3.0, 4.0);
+ Assert.assertTrue(x.equals(y));
+ }
+
+ @Test
+ public void testEqualsRealDifference() {
+ Complex x = new Complex(0.0, 0.0);
+ Complex y = new Complex(0.0 + Double.MIN_VALUE, 0.0);
+ Assert.assertFalse(x.equals(y));
+ }
+
+ @Test
+ public void testEqualsImaginaryDifference() {
+ Complex x = new Complex(0.0, 0.0);
+ Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE);
+ Assert.assertFalse(x.equals(y));
+ }
+
+ @Test
+ public void testHashCode() {
+ Complex x = new Complex(0.0, 0.0);
+ Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE);
+ Assert.assertFalse(x.hashCode()==y.hashCode());
+ y = new Complex(0.0 + Double.MIN_VALUE, 0.0);
+ Assert.assertFalse(x.hashCode()==y.hashCode());
+ Complex realNaN = new Complex(Double.NaN, 0.0);
+ Complex imaginaryNaN = new Complex(0.0, Double.NaN);
+ Assert.assertEquals(realNaN.hashCode(), imaginaryNaN.hashCode());
+ Assert.assertEquals(imaginaryNaN.hashCode(), Complex.NaN.hashCode());
+
+ // MATH-1118
+ // "equals" and "hashCode" must be compatible: if two objects have
+ // different hash codes, "equals" must return false.
+ final String msg = "'equals' not compatible with 'hashCode'";
+
+ x = new Complex(0.0, 0.0);
+ y = new Complex(0.0, -0.0);
+ Assert.assertTrue(x.hashCode() != y.hashCode());
+ Assert.assertFalse(msg, x.equals(y));
+
+ x = new Complex(0.0, 0.0);
+ y = new Complex(-0.0, 0.0);
+ Assert.assertTrue(x.hashCode() != y.hashCode());
+ Assert.assertFalse(msg, x.equals(y));
+ }
+
+ @Test
+ @Ignore
+ public void testJava() {// TODO more debug
+ System.out.println(">>testJava()");
+ // MathTest#testExpSpecialCases() checks the following:
+ // Assert.assertEquals("exp of -infinity should be 0.0", 0.0, Math.exp(Double.NEGATIVE_INFINITY), Precision.EPSILON);
+ // Let's check how well Math works:
+ System.out.println("Math.exp="+Math.exp(Double.NEGATIVE_INFINITY));
+ String props[] = {
+ "java.version", // Java Runtime Environment version
+ "java.vendor", // Java Runtime Environment vendor
+ "java.vm.specification.version", // Java Virtual Machine specification version
+ "java.vm.specification.vendor", // Java Virtual Machine specification vendor
+ "java.vm.specification.name", // Java Virtual Machine specification name
+ "java.vm.version", // Java Virtual Machine implementation version
+ "java.vm.vendor", // Java Virtual Machine implementation vendor
+ "java.vm.name", // Java Virtual Machine implementation name
+ "java.specification.version", // Java Runtime Environment specification version
+ "java.specification.vendor", // Java Runtime Environment specification vendor
+ "java.specification.name", // Java Runtime Environment specification name
+ "java.class.version", // Java class format version number
+ };
+ for(String t : props) {
+ System.out.println(t + "=" + System.getProperty(t));
+ }
+ System.out.println("<<testJava()");
+ }
+
+
+ @Test
+ public void testScalarPow() {
+ Complex x = new Complex(3, 4);
+ double yDouble = 5.0;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.pow(yComplex), x.pow(yDouble));
+ }
+
+ @Test
+ public void testScalarPowNaNBase() {
+ Complex x = Complex.NaN;
+ double yDouble = 5.0;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.pow(yComplex), x.pow(yDouble));
+ }
+
+ @Test
+ public void testScalarPowNaNExponent() {
+ Complex x = new Complex(3, 4);
+ double yDouble = Double.NaN;
+ Complex yComplex = new Complex(yDouble);
+ Assert.assertEquals(x.pow(yComplex), x.pow(yDouble));
+ }
+ @Test
+ public void testSqrtPolar() {
+ final double tol = 1e-12;
+ double r = 1;
+ for (int i = 0; i < 5; i++) {
+ r += i;
+ double theta = 0;
+ for (int j = 0; j < 11; j++) {
+ theta += pi / 12;
+ Complex z = ComplexUtils.polar2Complex(r, theta);
+ Complex sqrtz = ComplexUtils.polar2Complex(Math.sqrt(r), theta / 2);
+ TestUtils.assertEquals(sqrtz, z.sqrt(), tol);
+ }
+ }
+ }
+
+ @Test
+ public void testSqrt1z() {
+ Complex z = new Complex(3, 4);
+ Complex expected = new Complex(4.08033, -2.94094);
+ TestUtils.assertEquals(expected, z.sqrt1z(), 1.0e-5);
+ }
+
+ @Test
+ public void testSqrt1zNaN() {
+ Assert.assertTrue(Complex.NaN.sqrt1z().isNaN());
+ }
+
+ /**
+ * Test: computing <b>third roots</b> of z.
+ * <pre>
+ * <code>
+ * <b>z = -2 + 2 * i</b>
+ * => z_0 = 1 + i
+ * => z_1 = -1.3660 + 0.3660 * i
+ * => z_2 = 0.3660 - 1.3660 * i
+ * </code>
+ * </pre>
+ */
+ @Test
+ public void testNthRoot_normal_thirdRoot() {
+ // The complex number we want to compute all third-roots for.
+ Complex z = new Complex(-2,2);
+ // The List holding all third roots
+ Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
+ // Returned Collection must not be empty!
+ Assert.assertEquals(3, thirdRootsOfZ.length);
+ // test z_0
+ Assert.assertEquals(1.0, thirdRootsOfZ[0].getReal(), 1.0e-5);
+ Assert.assertEquals(1.0, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
+ // test z_1
+ Assert.assertEquals(-1.3660254037844386, thirdRootsOfZ[1].getReal(), 1.0e-5);
+ Assert.assertEquals(0.36602540378443843, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
+ // test z_2
+ Assert.assertEquals(0.366025403784439, thirdRootsOfZ[2].getReal(), 1.0e-5);
+ Assert.assertEquals(-1.3660254037844384, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
+ }
+
+
+ /**
+ * Test: computing <b>fourth roots</b> of z.
+ * <pre>
+ * <code>
+ * <b>z = 5 - 2 * i</b>
+ * => z_0 = 1.5164 - 0.1446 * i
+ * => z_1 = 0.1446 + 1.5164 * i
+ * => z_2 = -1.5164 + 0.1446 * i
+ * => z_3 = -1.5164 - 0.1446 * i
+ * </code>
+ * </pre>
+ */
+ @Test
+ public void testNthRoot_normal_fourthRoot() {
+ // The complex number we want to compute all third-roots for.
+ Complex z = new Complex(5,-2);
+ // The List holding all fourth roots
+ Complex[] fourthRootsOfZ = z.nthRoot(4).toArray(new Complex[0]);
+ // Returned Collection must not be empty!
+ Assert.assertEquals(4, fourthRootsOfZ.length);
+ // test z_0
+ Assert.assertEquals(1.5164629308487783, fourthRootsOfZ[0].getReal(), 1.0e-5);
+ Assert.assertEquals(-0.14469266210702247, fourthRootsOfZ[0].getImaginary(), 1.0e-5);
+ // test z_1
+ Assert.assertEquals(0.14469266210702256, fourthRootsOfZ[1].getReal(), 1.0e-5);
+ Assert.assertEquals(1.5164629308487783, fourthRootsOfZ[1].getImaginary(), 1.0e-5);
+ // test z_2
+ Assert.assertEquals(-1.5164629308487783, fourthRootsOfZ[2].getReal(), 1.0e-5);
+ Assert.assertEquals(0.14469266210702267, fourthRootsOfZ[2].getImaginary(), 1.0e-5);
+ // test z_3
+ Assert.assertEquals(-0.14469266210702275, fourthRootsOfZ[3].getReal(), 1.0e-5);
+ Assert.assertEquals(-1.5164629308487783, fourthRootsOfZ[3].getImaginary(), 1.0e-5);
+ }
+
+ /**
+ * Test: computing <b>third roots</b> of z.
+ * <pre>
+ * <code>
+ * <b>z = 8</b>
+ * => z_0 = 2
+ * => z_1 = -1 + 1.73205 * i
+ * => z_2 = -1 - 1.73205 * i
+ * </code>
+ * </pre>
+ */
+ @Test
+ public void testNthRoot_cornercase_thirdRoot_imaginaryPartEmpty() {
+ // The number 8 has three third roots. One we all already know is the number 2.
+ // But there are two more complex roots.
+ Complex z = new Complex(8,0);
+ // The List holding all third roots
+ Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
+ // Returned Collection must not be empty!
+ Assert.assertEquals(3, thirdRootsOfZ.length);
+ // test z_0
+ Assert.assertEquals(2.0, thirdRootsOfZ[0].getReal(), 1.0e-5);
+ Assert.assertEquals(0.0, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
+ // test z_1
+ Assert.assertEquals(-1.0, thirdRootsOfZ[1].getReal(), 1.0e-5);
+ Assert.assertEquals(1.7320508075688774, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
+ // test z_2
+ Assert.assertEquals(-1.0, thirdRootsOfZ[2].getReal(), 1.0e-5);
+ Assert.assertEquals(-1.732050807568877, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
+ }
+
+
+ /**
+ * Test: computing <b>third roots</b> of z with real part 0.
+ * <pre>
+ * <code>
+ * <b>z = 2 * i</b>
+ * => z_0 = 1.0911 + 0.6299 * i
+ * => z_1 = -1.0911 + 0.6299 * i
+ * => z_2 = -2.3144 - 1.2599 * i
+ * </code>
+ * </pre>
+ */
+ @Test
+ public void testNthRoot_cornercase_thirdRoot_realPartZero() {
+ // complex number with only imaginary part
+ Complex z = new Complex(0,2);
+ // The List holding all third roots
+ Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
+ // Returned Collection must not be empty!
+ Assert.assertEquals(3, thirdRootsOfZ.length);
+ // test z_0
+ Assert.assertEquals(1.0911236359717216, thirdRootsOfZ[0].getReal(), 1.0e-5);
+ Assert.assertEquals(0.6299605249474365, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
+ // test z_1
+ Assert.assertEquals(-1.0911236359717216, thirdRootsOfZ[1].getReal(), 1.0e-5);
+ Assert.assertEquals(0.6299605249474365, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
+ // test z_2
+ Assert.assertEquals(-2.3144374213981936E-16, thirdRootsOfZ[2].getReal(), 1.0e-5);
+ Assert.assertEquals(-1.2599210498948732, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
+ }
+
+ /**
+ * Test standard values
+ */
+ @Test
+ public void testGetArgument() {
+ Complex z = new Complex(1, 0);
+ Assert.assertEquals(0.0, z.getArgument(), 1.0e-12);
+
+ z = new Complex(1, 1);
+ Assert.assertEquals(Math.PI/4, z.getArgument(), 1.0e-12);
+
+ z = new Complex(0, 1);
+ Assert.assertEquals(Math.PI/2, z.getArgument(), 1.0e-12);
+
+ z = new Complex(-1, 1);
+ Assert.assertEquals(3 * Math.PI/4, z.getArgument(), 1.0e-12);
+
+ z = new Complex(-1, 0);
+ Assert.assertEquals(Math.PI, z.getArgument(), 1.0e-12);
+
+ z = new Complex(-1, -1);
+ Assert.assertEquals(-3 * Math.PI/4, z.getArgument(), 1.0e-12);
+
+ z = new Complex(0, -1);
+ Assert.assertEquals(-Math.PI/2, z.getArgument(), 1.0e-12);
+
+ z = new Complex(1, -1);
+ Assert.assertEquals(-Math.PI/4, z.getArgument(), 1.0e-12);
+
+ }
+
+ /**
+ * Verify atan2-style handling of infinite parts
+ */
+ @Test
+ public void testGetArgumentInf() {
+ Assert.assertEquals(Math.PI/4, infInf.getArgument(), 1.0e-12);
+ Assert.assertEquals(Math.PI/2, oneInf.getArgument(), 1.0e-12);
+ Assert.assertEquals(0.0, infOne.getArgument(), 1.0e-12);
+ Assert.assertEquals(Math.PI/2, zeroInf.getArgument(), 1.0e-12);
+ Assert.assertEquals(0.0, infZero.getArgument(), 1.0e-12);
+ Assert.assertEquals(Math.PI, negInfOne.getArgument(), 1.0e-12);
+ Assert.assertEquals(-3.0*Math.PI/4, negInfNegInf.getArgument(), 1.0e-12);
+ Assert.assertEquals(-Math.PI/2, oneNegInf.getArgument(), 1.0e-12);
+ }
+
+ /**
+ * Verify that either part NaN results in NaN
+ */
+ @Test
+ public void testGetArgumentNaN() {
+ Assert.assertTrue(Double.isNaN(nanZero.getArgument()));
+ Assert.assertTrue(Double.isNaN(zeroNaN.getArgument()));
+ Assert.assertTrue(Double.isNaN(Complex.NaN.getArgument()));
+ }
+
+ /*
+ @Test
+ public void testSerial() {
+ Complex z = new Complex(3.0, 4.0);
+ Assert.assertEquals(z, TestUtils.serializeAndRecover(z));
+ Complex ncmplx = (Complex)TestUtils.serializeAndRecover(oneNaN); Assert.assertEquals(nanZero, ncmplx); Assert.assertTrue(ncmplx.isNaN());
+ Complex infcmplx = (Complex)TestUtils.serializeAndRecover(infInf);
+ Assert.assertEquals(infInf, infcmplx);
+ Assert.assertTrue(infcmplx.isInfinite());
+ TestComplex tz = new TestComplex(3.0, 4.0);
+ Assert.assertEquals(tz, TestUtils.serializeAndRecover(tz));
+ TestComplex ntcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(oneNaN));
+ Assert.assertEquals(nanZero, ntcmplx);
+ Assert.assertTrue(ntcmplx.isNaN());
+ TestComplex inftcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(infInf));
+ Assert.assertEquals(infInf, inftcmplx);
+ Assert.assertTrue(inftcmplx.isInfinite());
+ }
+ */
+
+ /**
+ * Class to test extending Complex
+ */
+ public static class TestComplex extends Complex {
+
+ /**
+ * Serialization identifier.
+ */
+ private static final long serialVersionUID = 3268726724160389237L;
+
+ public TestComplex(double real, double imaginary) {
+ super(real, imaginary);
+ }
+
+ public TestComplex(Complex other){
+ this(other.getReal(), other.getImaginary());
+ }
+
+ @Override
+ protected TestComplex createComplex(double real, double imaginary){
+ return new TestComplex(real, imaginary);
+ }
+
+ }
+}