From commits-return-61064-archive-asf-public=cust-asf.ponee.io@commons.apache.org Fri Jan 26 15:00:03 2018 Return-Path: X-Original-To: archive-asf-public@eu.ponee.io Delivered-To: archive-asf-public@eu.ponee.io Received: from cust-asf.ponee.io (cust-asf.ponee.io [163.172.22.183]) by mx-eu-01.ponee.io (Postfix) with ESMTP id 6D45C18076D for ; Fri, 26 Jan 2018 15:00:03 +0100 (CET) Received: by cust-asf.ponee.io (Postfix) id 5C8A2160C53; Fri, 26 Jan 2018 14:00:03 +0000 (UTC) Delivered-To: archive-asf-public@cust-asf.ponee.io Received: from mail.apache.org (hermes.apache.org [140.211.11.3]) by cust-asf.ponee.io (Postfix) with SMTP id DD5BF160C3E for ; Fri, 26 Jan 2018 15:00:01 +0100 (CET) Received: (qmail 69042 invoked by uid 500); 26 Jan 2018 13:59:54 -0000 Mailing-List: contact commits-help@commons.apache.org; run by ezmlm Precedence: bulk List-Help: List-Unsubscribe: List-Post: List-Id: Reply-To: dev@commons.apache.org Delivered-To: mailing list commits@commons.apache.org Received: (qmail 67693 invoked by uid 99); 26 Jan 2018 13:59:54 -0000 Received: from git1-us-west.apache.org (HELO git1-us-west.apache.org) (140.211.11.23) by apache.org (qpsmtpd/0.29) with ESMTP; Fri, 26 Jan 2018 13:59:54 +0000 Received: by git1-us-west.apache.org (ASF Mail Server at git1-us-west.apache.org, from userid 33) id 5A4A4F4DC8; Fri, 26 Jan 2018 13:59:52 +0000 (UTC) Content-Type: text/plain; charset="us-ascii" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit From: ericbarnhill@apache.org To: commits@commons.apache.org Date: Fri, 26 Jan 2018 14:00:25 -0000 Message-Id: <411761540bd0442a852c269655cc0356@git.apache.org> In-Reply-To: <93fa054182d04057be924a12467eb287@git.apache.org> References: <93fa054182d04057be924a12467eb287@git.apache.org> X-Mailer: ASF-Git Admin Mailer Subject: [34/37] 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/master Commit: fc70d935fdadc5d5a7862cf9a929da91b72b00d6 Parents: 16322d8 Author: Eric Barnhill Authored: Fri Jan 26 14:54:16 2018 +0100 Committer: Eric Barnhill Committed: Fri Jan 26 14:54:16 2018 +0100 ---------------------------------------------------------------------- .../commons/numbers/complex/ComplexTest.java | 849 +++++++++++++++++++ 1 file changed, 849 insertions(+) ---------------------------------------------------------------------- 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 ---------------------------------------------------------------------- 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("<third roots of z. + * 
+     * 
+     * z = -2 + 2 * i
+     *   => z_0 =  1      +          i
+     *   => z_1 = -1.3660 + 0.3660 * i
+     *   => z_2 =  0.3660 - 1.3660 * i
+     * 
+     *
+ */ + @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 fourth roots of z. + * 
+     * 
+     * z = 5 - 2 * i
+     *   => 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
+     * 
+     *
+ */ + @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 third roots of z. + * 
+     * 
+     * z = 8
+     *   => z_0 =  2
+     *   => z_1 = -1 + 1.73205 * i
+     *   => z_2 = -1 - 1.73205 * i
+     * 
+     *
+ */ + @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 third roots of z with real part 0. + * 
+     * 
+     * z = 2 * i
+     *   => z_0 =  1.0911 + 0.6299 * i
+     *   => z_1 = -1.0911 + 0.6299 * i
+     *   => z_2 = -2.3144 - 1.2599 * i
+     * 
+     *
+ */ + @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); + } + + } +}