| /* |
| * 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.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 = Complex.ofCartesian(1, inf); |
| private static final Complex oneNegInf = Complex.ofCartesian(1, neginf); |
| private static final Complex infOne = Complex.ofCartesian(inf, 1); |
| private static final Complex infZero = Complex.ofCartesian(inf, 0); |
| private static final Complex infNaN = Complex.ofCartesian(inf, nan); |
| private static final Complex infNegInf = Complex.ofCartesian(inf, neginf); |
| private static final Complex infInf = Complex.ofCartesian(inf, inf); |
| private static final Complex negInfInf = Complex.ofCartesian(neginf, inf); |
| private static final Complex negInfZero = Complex.ofCartesian(neginf, 0); |
| private static final Complex negInfOne = Complex.ofCartesian(neginf, 1); |
| private static final Complex negInfNaN = Complex.ofCartesian(neginf, nan); |
| private static final Complex negInfNegInf = Complex.ofCartesian(neginf, neginf); |
| private static final Complex oneNaN = Complex.ofCartesian(1, nan); |
| private static final Complex zeroInf = Complex.ofCartesian(0, inf); |
| private static final Complex zeroNaN = Complex.ofCartesian(0, nan); |
| private static final Complex nanInf = Complex.ofCartesian(nan, inf); |
| private static final Complex nanNegInf = Complex.ofCartesian(nan, neginf); |
| private static final Complex nanZero = Complex.ofCartesian(nan, 0); |
| private static final Complex NAN = Complex.ofCartesian(nan, nan); |
| |
| @Test |
| public void testConstructor() { |
| Complex z = Complex.ofCartesian(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 = Complex.ofCartesian(3.0, Double.NaN); |
| Assert.assertTrue(z.isNaN()); |
| |
| z = Complex.ofCartesian(nan, 4.0); |
| Assert.assertTrue(z.isNaN()); |
| |
| z = Complex.ofCartesian(3.0, 4.0); |
| Assert.assertFalse(z.isNaN()); |
| } |
| |
| @Test |
| public void testAbs() { |
| Complex z = Complex.ofCartesian(3.0, 4.0); |
| Assert.assertEquals(5.0, z.abs(), 1.0e-5); |
| } |
| |
| @Test |
| public void testAbsNaN() { |
| Assert.assertTrue(Double.isNaN(NAN.abs())); |
| Complex z = Complex.ofCartesian(inf, nan); |
| Assert.assertTrue(Double.isNaN(z.abs())); |
| } |
| |
| @Test |
| public void testAdd() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(1, 1); |
| Complex z = Complex.ofCartesian(inf, 0); |
| Complex w = x.add(z); |
| Assert.assertEquals(w.getImaginary(), 1, 0); |
| Assert.assertEquals(inf, w.getReal(), 0); |
| |
| x = Complex.ofCartesian(neginf, 0); |
| Assert.assertTrue(Double.isNaN(x.add(z).getReal())); |
| } |
| |
| |
| @Test |
| public void testScalarAdd() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = 2.0; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.add(yComplex), x.add(yDouble)); |
| } |
| |
| @Test |
| public void testScalarAddNaN() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = Double.NaN; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.add(yComplex), x.add(yDouble)); |
| } |
| |
| @Test |
| public void testScalarAddInf() { |
| Complex x = Complex.ofCartesian(1, 1); |
| double yDouble = Double.POSITIVE_INFINITY; |
| |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.add(yComplex), x.add(yDouble)); |
| |
| x = Complex.ofCartesian(neginf, 0); |
| Assert.assertEquals(x.add(yComplex), x.add(yDouble)); |
| } |
| |
| @Test |
| public void testConjugate() { |
| Complex x = Complex.ofCartesian(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 = NAN.conjugate(); |
| Assert.assertTrue(z.isNaN()); |
| } |
| |
| @Test |
| public void testConjugateInfiinite() { |
| Complex z = Complex.ofCartesian(0, inf); |
| Assert.assertEquals(neginf, z.conjugate().getImaginary(), 0); |
| z = Complex.ofCartesian(0, neginf); |
| Assert.assertEquals(inf, z.conjugate().getImaginary(), 0); |
| } |
| |
| @Test |
| public void testDivide() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(2d, 3d); |
| Complex y = Complex.ofCartesian(2d, 0d); |
| Assert.assertEquals(Complex.ofCartesian(1d, 1.5), x.divide(y)); |
| |
| } |
| |
| @Test |
| public void testDivideImaginary() { |
| Complex x = Complex.ofCartesian(2d, 3d); |
| Complex y = Complex.ofCartesian(0d, 2d); |
| Assert.assertEquals(Complex.ofCartesian(1.5d, -1d), x.divide(y)); |
| } |
| |
| @Test |
| public void testDivideZero() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Complex z = x.divide(Complex.ZERO); |
| Assert.assertEquals(z, Complex.INF); |
| } |
| |
| @Test |
| public void testDivideZeroZero() { |
| Complex x = Complex.ofCartesian(0.0, 0.0); |
| Complex z = x.divide(Complex.ZERO); |
| Assert.assertEquals(z, NAN); |
| } |
| |
| @Test |
| public void testDivideNaN() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Complex z = x.divide(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.isInfinite(z.getReal())); |
| Assert.assertTrue(Double.isInfinite(z.getImaginary())); |
| } |
| |
| @Test |
| public void testScalarDivide() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = 2.0; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.divide(yComplex), x.divide(yDouble)); |
| } |
| |
| @Test |
| public void testScalarDivideNaN() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = Double.NaN; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.divide(yComplex), x.divide(yDouble)); |
| } |
| |
| @Test |
| public void testScalarDivideZero() { |
| Complex x = Complex.ofCartesian(1,1); |
| TestUtils.assertEquals(x.divide(Complex.ZERO), x.divide(0), 0); |
| } |
| |
| @Test |
| public void testReciprocal() { |
| Complex z = Complex.ofCartesian(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 = Complex.ofCartesian(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 = Complex.ofCartesian(-2.0, 0.0); |
| Assert.assertTrue(Complex.equals(Complex.ofCartesian(-0.5, 0.0), z.reciprocal())); |
| } |
| |
| @Test |
| public void testReciprocalImaginary() { |
| Complex z = Complex.ofCartesian(0.0, -2.0); |
| Assert.assertEquals(Complex.ofCartesian(0.0, 0.5), z.reciprocal()); |
| } |
| |
| @Test |
| public void testReciprocalNaN() { |
| Assert.assertTrue(NAN.reciprocal().isNaN()); |
| } |
| |
| @Test |
| public void testMultiply() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = 2.0; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble)); |
| int zInt = -5; |
| Complex zComplex = Complex.ofReal(zInt); |
| Assert.assertEquals(x.multiply(zComplex), x.multiply(zInt)); |
| } |
| |
| @Test |
| public void testScalarMultiplyNaN() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = Double.NaN; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble)); |
| } |
| |
| @Test |
| public void testScalarMultiplyInf() { |
| Complex x = Complex.ofCartesian(1, 1); |
| double yDouble = Double.POSITIVE_INFINITY; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble)); |
| |
| yDouble = Double.NEGATIVE_INFINITY; |
| yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble)); |
| } |
| |
| @Test |
| public void testNegate() { |
| Complex x = Complex.ofCartesian(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 = NAN.negate(); |
| Assert.assertTrue(z.isNaN()); |
| } |
| |
| @Test |
| public void testSubtract() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(1, 1); |
| Complex z = Complex.ofCartesian(neginf, 0); |
| Complex w = x.subtract(z); |
| Assert.assertEquals(w.getImaginary(), 1, 0); |
| Assert.assertEquals(inf, w.getReal(), 0); |
| |
| x = Complex.ofCartesian(neginf, 0); |
| Assert.assertTrue(Double.isNaN(x.subtract(z).getReal())); |
| } |
| |
| @Test |
| public void testScalarSubtract() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = 2.0; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble)); |
| } |
| |
| @Test |
| public void testScalarSubtractNaN() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| double yDouble = Double.NaN; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble)); |
| } |
| |
| @Test |
| public void testScalarSubtractInf() { |
| Complex x = Complex.ofCartesian(1, 1); |
| double yDouble = Double.POSITIVE_INFINITY; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble)); |
| |
| x = Complex.ofCartesian(neginf, 0); |
| Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble)); |
| } |
| |
| |
| @Test |
| public void testEqualsNull() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Assert.assertFalse(x.equals(null)); |
| } |
| |
| @Test(expected=NullPointerException.class) |
| public void testFloatingPointEqualsPrecondition1() { |
| Complex.equals(Complex.ofCartesian(3.0, 4.0), null, 3); |
| } |
| @Test(expected=NullPointerException.class) |
| public void testFloatingPointEqualsPrecondition2() { |
| Complex.equals(null, Complex.ofCartesian(3.0, 4.0), 3); |
| } |
| |
| @Test |
| public void testEqualsClass() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Assert.assertFalse(x.equals(this)); |
| } |
| |
| @Test |
| public void testEqualsSame() { |
| Complex x = Complex.ofCartesian(3.0, 4.0); |
| Assert.assertTrue(x.equals(x)); |
| } |
| |
| @Test |
| public void testFloatingPointEquals() { |
| double re = -3.21; |
| double im = 456789e10; |
| |
| final Complex x = Complex.ofCartesian(re, im); |
| Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(re, im); |
| Assert.assertTrue(Complex.equals(x, y, maxUlps)); |
| |
| re = Math.nextUp(re); |
| im = Math.nextUp(im); |
| y = Complex.ofCartesian(re, im); |
| Assert.assertFalse(Complex.equals(x, y, maxUlps)); |
| } |
| |
| @Test |
| public void testFloatingPointEqualsNaN() { |
| Complex c = Complex.ofCartesian(Double.NaN, 1); |
| Assert.assertFalse(Complex.equals(c, c)); |
| |
| c = Complex.ofCartesian(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 = Complex.ofCartesian(re, im); |
| final Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(0, Double.NaN); |
| final Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(re, im); |
| final Complex y = Complex.ofCartesian(re * f, im * f); |
| Assert.assertTrue(Complex.equalsWithRelativeTolerance(x, y, tol)); |
| } |
| |
| @Test |
| public void testFloatingPointEqualsWithRelativeToleranceNaN() { |
| final Complex x = Complex.ofCartesian(0, Double.NaN); |
| final Complex y = Complex.ofCartesian(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 = Complex.ofCartesian(3.0, 4.0); |
| Complex y = Complex.ofCartesian(3.0, 4.0); |
| Assert.assertTrue(x.equals(y)); |
| } |
| |
| @Test |
| public void testEqualsRealDifference() { |
| Complex x = Complex.ofCartesian(0.0, 0.0); |
| Complex y = Complex.ofCartesian(0.0 + Double.MIN_VALUE, 0.0); |
| Assert.assertFalse(x.equals(y)); |
| } |
| |
| @Test |
| public void testEqualsImaginaryDifference() { |
| Complex x = Complex.ofCartesian(0.0, 0.0); |
| Complex y = Complex.ofCartesian(0.0, 0.0 + Double.MIN_VALUE); |
| Assert.assertFalse(x.equals(y)); |
| } |
| |
| @Test |
| public void testHashCode() { |
| Complex x = Complex.ofCartesian(0.0, 0.0); |
| Complex y = Complex.ofCartesian(0.0, 0.0 + Double.MIN_VALUE); |
| Assert.assertFalse(x.hashCode()==y.hashCode()); |
| y = Complex.ofCartesian(0.0 + Double.MIN_VALUE, 0.0); |
| Assert.assertFalse(x.hashCode()==y.hashCode()); |
| Complex realNaN = Complex.ofCartesian(Double.NaN, 0.0); |
| Complex imaginaryNaN = Complex.ofCartesian(0.0, Double.NaN); |
| Assert.assertEquals(realNaN.hashCode(), imaginaryNaN.hashCode()); |
| Assert.assertEquals(imaginaryNaN.hashCode(), 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 = Complex.ofCartesian(0.0, 0.0); |
| y = Complex.ofCartesian(0.0, -0.0); |
| Assert.assertTrue(x.hashCode() != y.hashCode()); |
| Assert.assertFalse(msg, x.equals(y)); |
| |
| x = Complex.ofCartesian(0.0, 0.0); |
| y = Complex.ofCartesian(-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 = Complex.ofCartesian(3, 4); |
| double yDouble = 5.0; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.pow(yComplex), x.pow(yDouble)); |
| } |
| |
| @Test |
| public void testScalarPowNaNBase() { |
| Complex x = NAN; |
| double yDouble = 5.0; |
| Complex yComplex = Complex.ofReal(yDouble); |
| Assert.assertEquals(x.pow(yComplex), x.pow(yDouble)); |
| } |
| |
| @Test |
| public void testScalarPowNaNExponent() { |
| Complex x = Complex.ofCartesian(3, 4); |
| double yDouble = Double.NaN; |
| Complex yComplex = Complex.ofReal(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 = Complex.ofPolar(r, theta); |
| Complex sqrtz = Complex.ofPolar(Math.sqrt(r), theta / 2); |
| TestUtils.assertEquals(sqrtz, z.sqrt(), tol); |
| } |
| } |
| } |
| |
| /** |
| * 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 testNthRootNormalThirdRoot() { |
| // The complex number we want to compute all third-roots for. |
| Complex z = Complex.ofCartesian(-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 testNthRootNormalFourthRoot() { |
| // The complex number we want to compute all third-roots for. |
| Complex z = Complex.ofCartesian(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 testNthRootCornercaseThirdRootImaginaryPartEmpty() { |
| // 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 = Complex.ofCartesian(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 testNthRootCornercaseThirdRootRealPartZero() { |
| // complex number with only imaginary part |
| Complex z = Complex.ofCartesian(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: compute <b>third roots</b> using a negative argument |
| * to go clockwise around the unit circle. Fourth roots of one |
| * are taken in both directions around the circle using |
| * positive and negative arguments. |
| * <pre> |
| * <code> |
| * <b>z = 1</b> |
| * => z_0 = Positive: 1,0 ; Negative: 1,0 |
| * => z_1 = Positive: 0,1 ; Negative: 0,-1 |
| * => z_2 = Positive: -1,0 ; Negative: -1,0 |
| * => z_3 = Positive: 0,-1 ; Negative: 0,1 |
| * </code> |
| * </pre> |
| */ |
| @Test |
| public void testNthRootNegativeArg() { |
| // The complex number we want to compute all third-roots for. |
| Complex z = Complex.ofCartesian(1, 0); |
| // The List holding all fourth roots |
| Complex[] fourthRootsOfZ = z.nthRoot(4).toArray(new Complex[0]); |
| // test z_0 |
| Assert.assertEquals(1, fourthRootsOfZ[0].getReal(), 1.0e-5); |
| Assert.assertEquals(0, fourthRootsOfZ[0].getImaginary(), 1.0e-5); |
| // test z_1 |
| Assert.assertEquals(0, fourthRootsOfZ[1].getReal(), 1.0e-5); |
| Assert.assertEquals(1, fourthRootsOfZ[1].getImaginary(), 1.0e-5); |
| // test z_2 |
| Assert.assertEquals(-1, fourthRootsOfZ[2].getReal(), 1.0e-5); |
| Assert.assertEquals(0, fourthRootsOfZ[2].getImaginary(), 1.0e-5); |
| // test z_3 |
| Assert.assertEquals(0, fourthRootsOfZ[3].getReal(), 1.0e-5); |
| Assert.assertEquals(-1, fourthRootsOfZ[3].getImaginary(), 1.0e-5); |
| // go clockwise around the unit circle using negative argument |
| fourthRootsOfZ = z.nthRoot(-4).toArray(new Complex[0]); |
| // test z_0 |
| Assert.assertEquals(1, fourthRootsOfZ[0].getReal(), 1.0e-5); |
| Assert.assertEquals(0, fourthRootsOfZ[0].getImaginary(), 1.0e-5); |
| // test z_1 |
| Assert.assertEquals(0, fourthRootsOfZ[1].getReal(), 1.0e-5); |
| Assert.assertEquals(-1, fourthRootsOfZ[1].getImaginary(), 1.0e-5); |
| // test z_2 |
| Assert.assertEquals(-1, fourthRootsOfZ[2].getReal(), 1.0e-5); |
| Assert.assertEquals(0, fourthRootsOfZ[2].getImaginary(), 1.0e-5); |
| // test z_3 |
| Assert.assertEquals(0, fourthRootsOfZ[3].getReal(), 1.0e-5); |
| Assert.assertEquals(1, fourthRootsOfZ[3].getImaginary(), 1.0e-5); |
| } |
| /** |
| * Test standard values |
| */ |
| @Test |
| public void testGetArgument() { |
| Complex z = Complex.ofCartesian(1, 0); |
| Assert.assertEquals(0.0, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(1, 1); |
| Assert.assertEquals(Math.PI/4, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(0, 1); |
| Assert.assertEquals(Math.PI/2, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(-1, 1); |
| Assert.assertEquals(3 * Math.PI/4, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(-1, 0); |
| Assert.assertEquals(Math.PI, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(-1, -1); |
| Assert.assertEquals(-3 * Math.PI/4, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(0, -1); |
| Assert.assertEquals(-Math.PI/2, z.getArgument(), 1.0e-12); |
| |
| z = Complex.ofCartesian(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(NAN.getArgument())); |
| } |
| |
| @Test |
| public void testParse() { |
| Assert.assertTrue(Complex.ZERO.equals(Complex.parse(Complex.ZERO.toString()))); |
| Assert.assertTrue(Complex.ONE.equals(Complex.parse(Complex.ONE.toString()))); |
| Assert.assertTrue(Complex.I.equals(Complex.parse(Complex.I.toString()))); |
| Assert.assertTrue(Complex.INF.equals(Complex.parse(Complex.INF.toString()))); |
| Assert.assertTrue(NAN.equals(Complex.parse(NAN.toString()))); |
| Assert.assertTrue(oneInf.equals(Complex.parse(oneInf.toString()))); |
| Assert.assertTrue(negInfZero.equals(Complex.parse(negInfZero.toString()))); |
| Assert.assertTrue(Complex.ofReal(pi).equals(Complex.parse(Complex.ofReal(pi).toString()))); |
| Assert.assertTrue(Complex.ofPolar(2, pi).equals(Complex.parse(Complex.ofPolar(2, pi).toString()))); |
| Assert.assertTrue(Complex.ofCis(pi).equals(Complex.parse(Complex.ofCis(pi).toString()))); |
| } |
| |
| @Test(expected=IllegalArgumentException.class) |
| public void testParseWrongStart() { |
| final String re = "1.234"; |
| final String im = "5.678"; |
| Complex.parse(re + "," + im + ")"); |
| } |
| @Test(expected=IllegalArgumentException.class) |
| public void testParseWrongEnd() { |
| final String re = "1.234"; |
| final String im = "5.678"; |
| Complex.parse("(" + re + "," + im); |
| } |
| @Test(expected=IllegalArgumentException.class) |
| public void testParseMissingSeparator() { |
| final String re = "1.234"; |
| final String im = "5.678"; |
| Complex.parse("(" + re + " " + im + ")"); |
| } |
| @Test(expected=IllegalArgumentException.class) |
| public void testParseInvalidRe() { |
| final String re = "I.234"; |
| final String im = "5.678"; |
| Complex.parse("(" + re + "," + im + ")"); |
| } |
| @Test(expected=IllegalArgumentException.class) |
| public void testParseInvalidIm() { |
| final String re = "1.234"; |
| final String im = "5.G78"; |
| Complex.parse("(" + re + "," + im + ")"); |
| } |
| |
| @Test |
| public void testParseSpaceAllowedAroundNumbers() { |
| final double re = 1.234; |
| final double im = 5.678; |
| final String str = "( " + re + " , " + im + " )"; |
| Assert.assertTrue(Complex.ofCartesian(re, im).equals(Complex.parse(str))); |
| } |
| } |
