Commons Math example source code file (ComplexTest.java)
The Commons Math ComplexTest.java source code/*
* 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,
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* See the License for the specific language governing permissions and
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*/
package org.apache.commons.math.complex;
import org.apache.commons.math.TestUtils;
import java.util.List;
import junit.framework.TestCase;
/**
* @version $Revision: 924345 $ $Date: 2010-03-17 12:03:56 -0400 (Wed, 17 Mar 2010) $
*/
public class ComplexTest extends TestCase {
private double inf = Double.POSITIVE_INFINITY;
private double neginf = Double.NEGATIVE_INFINITY;
private double nan = Double.NaN;
private double pi = Math.PI;
private Complex oneInf = new Complex(1, inf);
private Complex oneNegInf = new Complex(1, neginf);
private Complex infOne = new Complex(inf, 1);
private Complex infZero = new Complex(inf, 0);
private Complex infNaN = new Complex(inf, nan);
private Complex infNegInf = new Complex(inf, neginf);
private Complex infInf = new Complex(inf, inf);
private Complex negInfInf = new Complex(neginf, inf);
private Complex negInfZero = new Complex(neginf, 0);
private Complex negInfOne = new Complex(neginf, 1);
private Complex negInfNaN = new Complex(neginf, nan);
private Complex negInfNegInf = new Complex(neginf, neginf);
private Complex oneNaN = new Complex(1, nan);
private Complex zeroInf = new Complex(0, inf);
private Complex zeroNaN = new Complex(0, nan);
private Complex nanInf = new Complex(nan, inf);
private Complex nanNegInf = new Complex(nan, neginf);
private Complex nanZero = new Complex(nan, 0);
public void testConstructor() {
Complex z = new Complex(3.0, 4.0);
assertEquals(3.0, z.getReal(), 1.0e-5);
assertEquals(4.0, z.getImaginary(), 1.0e-5);
}
public void testConstructorNaN() {
Complex z = new Complex(3.0, Double.NaN);
assertTrue(z.isNaN());
z = new Complex(nan, 4.0);
assertTrue(z.isNaN());
z = new Complex(3.0, 4.0);
assertFalse(z.isNaN());
}
public void testAbs() {
Complex z = new Complex(3.0, 4.0);
assertEquals(5.0, z.abs(), 1.0e-5);
}
public void testAbsNaN() {
assertTrue(Double.isNaN(Complex.NaN.abs()));
Complex z = new Complex(inf, nan);
assertTrue(Double.isNaN(z.abs()));
}
public void testAbsInfinite() {
Complex z = new Complex(inf, 0);
assertEquals(inf, z.abs(), 0);
z = new Complex(0, neginf);
assertEquals(inf, z.abs(), 0);
z = new Complex(inf, neginf);
assertEquals(inf, z.abs(), 0);
}
public void testAdd() {
Complex x = new Complex(3.0, 4.0);
Complex y = new Complex(5.0, 6.0);
Complex z = x.add(y);
assertEquals(8.0, z.getReal(), 1.0e-5);
assertEquals(10.0, z.getImaginary(), 1.0e-5);
}
public void testAddNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.add(Complex.NaN);
assertTrue(z.isNaN());
z = new Complex(1, nan);
Complex w = x.add(z);
assertEquals(w.getReal(), 4.0, 0);
assertTrue(Double.isNaN(w.getImaginary()));
}
public void testAddInfinite() {
Complex x = new Complex(1, 1);
Complex z = new Complex(inf, 0);
Complex w = x.add(z);
assertEquals(w.getImaginary(), 1, 0);
assertEquals(inf, w.getReal(), 0);
x = new Complex(neginf, 0);
assertTrue(Double.isNaN(x.add(z).getReal()));
}
public void testConjugate() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.conjugate();
assertEquals(3.0, z.getReal(), 1.0e-5);
assertEquals(-4.0, z.getImaginary(), 1.0e-5);
}
public void testConjugateNaN() {
Complex z = Complex.NaN.conjugate();
assertTrue(z.isNaN());
}
public void testConjugateInfiinite() {
Complex z = new Complex(0, inf);
assertEquals(neginf, z.conjugate().getImaginary(), 0);
z = new Complex(0, neginf);
assertEquals(inf, z.conjugate().getImaginary(), 0);
}
public void testDivide() {
Complex x = new Complex(3.0, 4.0);
Complex y = new Complex(5.0, 6.0);
Complex z = x.divide(y);
assertEquals(39.0 / 61.0, z.getReal(), 1.0e-5);
assertEquals(2.0 / 61.0, z.getImaginary(), 1.0e-5);
}
public void testDivideReal() {
Complex x = new Complex(2d, 3d);
Complex y = new Complex(2d, 0d);
assertEquals(new Complex(1d, 1.5), x.divide(y));
}
public void testDivideImaginary() {
Complex x = new Complex(2d, 3d);
Complex y = new Complex(0d, 2d);
assertEquals(new Complex(1.5d, -1d), x.divide(y));
}
public void testDivideInfinite() {
Complex x = new Complex(3, 4);
Complex w = new Complex(neginf, inf);
assertTrue(x.divide(w).equals(Complex.ZERO));
Complex z = w.divide(x);
assertTrue(Double.isNaN(z.getReal()));
assertEquals(inf, z.getImaginary(), 0);
w = new Complex(inf, inf);
z = w.divide(x);
assertTrue(Double.isNaN(z.getImaginary()));
assertEquals(inf, z.getReal(), 0);
w = new Complex(1, inf);
z = w.divide(w);
assertTrue(Double.isNaN(z.getReal()));
assertTrue(Double.isNaN(z.getImaginary()));
}
public void testDivideZero() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.divide(Complex.ZERO);
assertEquals(z, Complex.NaN);
}
public void testDivideNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.divide(Complex.NaN);
assertTrue(z.isNaN());
}
public void testDivideNaNInf() {
Complex z = oneInf.divide(Complex.ONE);
assertTrue(Double.isNaN(z.getReal()));
assertEquals(inf, z.getImaginary(), 0);
z = negInfNegInf.divide(oneNaN);
assertTrue(Double.isNaN(z.getReal()));
assertTrue(Double.isNaN(z.getImaginary()));
z = negInfInf.divide(Complex.ONE);
assertTrue(Double.isNaN(z.getReal()));
assertTrue(Double.isNaN(z.getImaginary()));
}
public void testMultiply() {
Complex x = new Complex(3.0, 4.0);
Complex y = new Complex(5.0, 6.0);
Complex z = x.multiply(y);
assertEquals(-9.0, z.getReal(), 1.0e-5);
assertEquals(38.0, z.getImaginary(), 1.0e-5);
}
public void testMultiplyNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.multiply(Complex.NaN);
assertTrue(z.isNaN());
}
public void testMultiplyNaNInf() {
Complex z = new Complex(1,1);
Complex w = z.multiply(infOne);
assertEquals(w.getReal(), inf, 0);
assertEquals(w.getImaginary(), inf, 0);
// [MATH-164]
assertTrue(new Complex( 1,0).multiply(infInf).equals(Complex.INF));
assertTrue(new Complex(-1,0).multiply(infInf).equals(Complex.INF));
assertTrue(new Complex( 1,0).multiply(negInfZero).equals(Complex.INF));
w = oneInf.multiply(oneNegInf);
assertEquals(w.getReal(), inf, 0);
assertEquals(w.getImaginary(), inf, 0);
w = negInfNegInf.multiply(oneNaN);
assertTrue(Double.isNaN(w.getReal()));
assertTrue(Double.isNaN(w.getImaginary()));
}
public void testScalarMultiply() {
Complex x = new Complex(3.0, 4.0);
double y = 2.0;
Complex z = x.multiply(y);
assertEquals(6.0, z.getReal(), 1.0e-5);
assertEquals(8.0, z.getImaginary(), 1.0e-5);
}
public void testScalarMultiplyNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.multiply(Double.NaN);
assertTrue(z.isNaN());
}
public void testScalarMultiplyInf() {
Complex z = new Complex(1,1);
Complex w = z.multiply(Double.POSITIVE_INFINITY);
assertEquals(w.getReal(), inf, 0);
assertEquals(w.getImaginary(), inf, 0);
w = z.multiply(Double.NEGATIVE_INFINITY);
assertEquals(w.getReal(), inf, 0);
assertEquals(w.getImaginary(), inf, 0);
}
public void testNegate() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.negate();
assertEquals(-3.0, z.getReal(), 1.0e-5);
assertEquals(-4.0, z.getImaginary(), 1.0e-5);
}
public void testNegateNaN() {
Complex z = Complex.NaN.negate();
assertTrue(z.isNaN());
}
public void testSubtract() {
Complex x = new Complex(3.0, 4.0);
Complex y = new Complex(5.0, 6.0);
Complex z = x.subtract(y);
assertEquals(-2.0, z.getReal(), 1.0e-5);
assertEquals(-2.0, z.getImaginary(), 1.0e-5);
}
public void testSubtractNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.subtract(Complex.NaN);
assertTrue(z.isNaN());
}
public void testEqualsNull() {
Complex x = new Complex(3.0, 4.0);
assertFalse(x.equals(null));
}
public void testEqualsClass() {
Complex x = new Complex(3.0, 4.0);
assertFalse(x.equals(this));
}
public void testEqualsSame() {
Complex x = new Complex(3.0, 4.0);
assertTrue(x.equals(x));
}
public void testEqualsTrue() {
Complex x = new Complex(3.0, 4.0);
Complex y = new Complex(3.0, 4.0);
assertTrue(x.equals(y));
}
public void testEqualsRealDifference() {
Complex x = new Complex(0.0, 0.0);
Complex y = new Complex(0.0 + Double.MIN_VALUE, 0.0);
assertFalse(x.equals(y));
}
public void testEqualsImaginaryDifference() {
Complex x = new Complex(0.0, 0.0);
Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE);
assertFalse(x.equals(y));
}
public void testEqualsNaN() {
Complex realNaN = new Complex(Double.NaN, 0.0);
Complex imaginaryNaN = new Complex(0.0, Double.NaN);
Complex complexNaN = Complex.NaN;
assertTrue(realNaN.equals(imaginaryNaN));
assertTrue(imaginaryNaN.equals(complexNaN));
assertTrue(realNaN.equals(complexNaN));
}
public void testHashCode() {
Complex x = new Complex(0.0, 0.0);
Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE);
assertFalse(x.hashCode()==y.hashCode());
y = new Complex(0.0 + Double.MIN_VALUE, 0.0);
assertFalse(x.hashCode()==y.hashCode());
Complex realNaN = new Complex(Double.NaN, 0.0);
Complex imaginaryNaN = new Complex(0.0, Double.NaN);
assertEquals(realNaN.hashCode(), imaginaryNaN.hashCode());
assertEquals(imaginaryNaN.hashCode(), Complex.NaN.hashCode());
}
public void testAcos() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(0.936812, -2.30551);
TestUtils.assertEquals(expected, z.acos(), 1.0e-5);
TestUtils.assertEquals(new Complex(Math.acos(0), 0),
Complex.ZERO.acos(), 1.0e-12);
}
public void testAcosInf() {
TestUtils.assertSame(Complex.NaN, oneInf.acos());
TestUtils.assertSame(Complex.NaN, oneNegInf.acos());
TestUtils.assertSame(Complex.NaN, infOne.acos());
TestUtils.assertSame(Complex.NaN, negInfOne.acos());
TestUtils.assertSame(Complex.NaN, infInf.acos());
TestUtils.assertSame(Complex.NaN, infNegInf.acos());
TestUtils.assertSame(Complex.NaN, negInfInf.acos());
TestUtils.assertSame(Complex.NaN, negInfNegInf.acos());
}
public void testAcosNaN() {
assertTrue(Complex.NaN.acos().isNaN());
}
public void testAsin() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(0.633984, 2.30551);
TestUtils.assertEquals(expected, z.asin(), 1.0e-5);
}
public void testAsinNaN() {
assertTrue(Complex.NaN.asin().isNaN());
}
public void testAsinInf() {
TestUtils.assertSame(Complex.NaN, oneInf.asin());
TestUtils.assertSame(Complex.NaN, oneNegInf.asin());
TestUtils.assertSame(Complex.NaN, infOne.asin());
TestUtils.assertSame(Complex.NaN, negInfOne.asin());
TestUtils.assertSame(Complex.NaN, infInf.asin());
TestUtils.assertSame(Complex.NaN, infNegInf.asin());
TestUtils.assertSame(Complex.NaN, negInfInf.asin());
TestUtils.assertSame(Complex.NaN, negInfNegInf.asin());
}
public void testAtan() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(1.44831, 0.158997);
TestUtils.assertEquals(expected, z.atan(), 1.0e-5);
}
public void testAtanInf() {
TestUtils.assertSame(Complex.NaN, oneInf.atan());
TestUtils.assertSame(Complex.NaN, oneNegInf.atan());
TestUtils.assertSame(Complex.NaN, infOne.atan());
TestUtils.assertSame(Complex.NaN, negInfOne.atan());
TestUtils.assertSame(Complex.NaN, infInf.atan());
TestUtils.assertSame(Complex.NaN, infNegInf.atan());
TestUtils.assertSame(Complex.NaN, negInfInf.atan());
TestUtils.assertSame(Complex.NaN, negInfNegInf.atan());
}
public void testAtanNaN() {
assertTrue(Complex.NaN.atan().isNaN());
assertTrue(Complex.I.atan().isNaN());
}
public void testCos() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(-27.03495, -3.851153);
TestUtils.assertEquals(expected, z.cos(), 1.0e-5);
}
public void testCosNaN() {
assertTrue(Complex.NaN.cos().isNaN());
}
public void testCosInf() {
TestUtils.assertSame(infNegInf, oneInf.cos());
TestUtils.assertSame(infInf, oneNegInf.cos());
TestUtils.assertSame(Complex.NaN, infOne.cos());
TestUtils.assertSame(Complex.NaN, negInfOne.cos());
TestUtils.assertSame(Complex.NaN, infInf.cos());
TestUtils.assertSame(Complex.NaN, infNegInf.cos());
TestUtils.assertSame(Complex.NaN, negInfInf.cos());
TestUtils.assertSame(Complex.NaN, negInfNegInf.cos());
}
public void testCosh() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(-6.58066, -7.58155);
TestUtils.assertEquals(expected, z.cosh(), 1.0e-5);
}
public void testCoshNaN() {
assertTrue(Complex.NaN.cosh().isNaN());
}
public void testCoshInf() {
TestUtils.assertSame(Complex.NaN, oneInf.cosh());
TestUtils.assertSame(Complex.NaN, oneNegInf.cosh());
TestUtils.assertSame(infInf, infOne.cosh());
TestUtils.assertSame(infNegInf, negInfOne.cosh());
TestUtils.assertSame(Complex.NaN, infInf.cosh());
TestUtils.assertSame(Complex.NaN, infNegInf.cosh());
TestUtils.assertSame(Complex.NaN, negInfInf.cosh());
TestUtils.assertSame(Complex.NaN, negInfNegInf.cosh());
}
public void testExp() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(-13.12878, -15.20078);
TestUtils.assertEquals(expected, z.exp(), 1.0e-5);
TestUtils.assertEquals(Complex.ONE,
Complex.ZERO.exp(), 10e-12);
Complex iPi = Complex.I.multiply(new Complex(pi,0));
TestUtils.assertEquals(Complex.ONE.negate(),
iPi.exp(), 10e-12);
}
public void testExpNaN() {
assertTrue(Complex.NaN.exp().isNaN());
}
public void testExpInf() {
TestUtils.assertSame(Complex.NaN, oneInf.exp());
TestUtils.assertSame(Complex.NaN, oneNegInf.exp());
TestUtils.assertSame(infInf, infOne.exp());
TestUtils.assertSame(Complex.ZERO, negInfOne.exp());
TestUtils.assertSame(Complex.NaN, infInf.exp());
TestUtils.assertSame(Complex.NaN, infNegInf.exp());
TestUtils.assertSame(Complex.NaN, negInfInf.exp());
TestUtils.assertSame(Complex.NaN, negInfNegInf.exp());
}
public void testLog() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(1.60944, 0.927295);
TestUtils.assertEquals(expected, z.log(), 1.0e-5);
}
public void testLogNaN() {
assertTrue(Complex.NaN.log().isNaN());
}
public void testLogInf() {
TestUtils.assertEquals(new Complex(inf, pi / 2),
oneInf.log(), 10e-12);
TestUtils.assertEquals(new Complex(inf, -pi / 2),
oneNegInf.log(), 10e-12);
TestUtils.assertEquals(infZero, infOne.log(), 10e-12);
TestUtils.assertEquals(new Complex(inf, pi),
negInfOne.log(), 10e-12);
TestUtils.assertEquals(new Complex(inf, pi / 4),
infInf.log(), 10e-12);
TestUtils.assertEquals(new Complex(inf, -pi / 4),
infNegInf.log(), 10e-12);
TestUtils.assertEquals(new Complex(inf, 3d * pi / 4),
negInfInf.log(), 10e-12);
TestUtils.assertEquals(new Complex(inf, - 3d * pi / 4),
negInfNegInf.log(), 10e-12);
}
public void testLogZero() {
TestUtils.assertSame(negInfZero, Complex.ZERO.log());
}
public void testPow() {
Complex x = new Complex(3, 4);
Complex y = new Complex(5, 6);
Complex expected = new Complex(-1.860893, 11.83677);
TestUtils.assertEquals(expected, x.pow(y), 1.0e-5);
}
public void testPowNaNBase() {
Complex x = new Complex(3, 4);
assertTrue(Complex.NaN.pow(x).isNaN());
}
public void testPowNaNExponent() {
Complex x = new Complex(3, 4);
assertTrue(x.pow(Complex.NaN).isNaN());
}
public void testPowInf() {
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(oneInf));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(oneNegInf));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(infOne));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(infInf));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(infNegInf));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(negInfInf));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(negInfNegInf));
TestUtils.assertSame(Complex.NaN,infOne.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,negInfOne.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,infInf.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,negInfInf.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(infNegInf));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(negInfNegInf));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(infInf));
TestUtils.assertSame(Complex.NaN,infInf.pow(infNegInf));
TestUtils.assertSame(Complex.NaN,infInf.pow(negInfNegInf));
TestUtils.assertSame(Complex.NaN,infInf.pow(infInf));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(infNegInf));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(negInfNegInf));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(infInf));
}
public void testPowZero() {
TestUtils.assertSame(Complex.NaN,
Complex.ZERO.pow(Complex.ONE));
TestUtils.assertSame(Complex.NaN,
Complex.ZERO.pow(Complex.ZERO));
TestUtils.assertSame(Complex.NaN,
Complex.ZERO.pow(Complex.I));
TestUtils.assertEquals(Complex.ONE,
Complex.ONE.pow(Complex.ZERO), 10e-12);
TestUtils.assertEquals(Complex.ONE,
Complex.I.pow(Complex.ZERO), 10e-12);
TestUtils.assertEquals(Complex.ONE,
new Complex(-1, 3).pow(Complex.ZERO), 10e-12);
}
public void testpowNull() {
try {
Complex.ONE.pow(null);
fail("Expecting NullPointerException");
} catch (NullPointerException ex) {
// expected
}
}
public void testSin() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(3.853738, -27.01681);
TestUtils.assertEquals(expected, z.sin(), 1.0e-5);
}
public void testSinInf() {
TestUtils.assertSame(infInf, oneInf.sin());
TestUtils.assertSame(infNegInf, oneNegInf.sin());
TestUtils.assertSame(Complex.NaN, infOne.sin());
TestUtils.assertSame(Complex.NaN, negInfOne.sin());
TestUtils.assertSame(Complex.NaN, infInf.sin());
TestUtils.assertSame(Complex.NaN, infNegInf.sin());
TestUtils.assertSame(Complex.NaN, negInfInf.sin());
TestUtils.assertSame(Complex.NaN, negInfNegInf.sin());
}
public void testSinNaN() {
assertTrue(Complex.NaN.sin().isNaN());
}
public void testSinh() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(-6.54812, -7.61923);
TestUtils.assertEquals(expected, z.sinh(), 1.0e-5);
}
public void testSinhNaN() {
assertTrue(Complex.NaN.sinh().isNaN());
}
public void testSinhInf() {
TestUtils.assertSame(Complex.NaN, oneInf.sinh());
TestUtils.assertSame(Complex.NaN, oneNegInf.sinh());
TestUtils.assertSame(infInf, infOne.sinh());
TestUtils.assertSame(negInfInf, negInfOne.sinh());
TestUtils.assertSame(Complex.NaN, infInf.sinh());
TestUtils.assertSame(Complex.NaN, infNegInf.sinh());
TestUtils.assertSame(Complex.NaN, negInfInf.sinh());
TestUtils.assertSame(Complex.NaN, negInfNegInf.sinh());
}
public void testSqrtRealPositive() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(2, 1);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtRealZero() {
Complex z = new Complex(0.0, 4);
Complex expected = new Complex(1.41421, 1.41421);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtRealNegative() {
Complex z = new Complex(-3.0, 4);
Complex expected = new Complex(1, 2);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtImaginaryZero() {
Complex z = new Complex(-3.0, 0.0);
Complex expected = new Complex(0.0, 1.73205);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtImaginaryNegative() {
Complex z = new Complex(-3.0, -4.0);
Complex expected = new Complex(1.0, -2.0);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtPolar() {
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(), 10e-12);
}
}
}
public void testSqrtNaN() {
assertTrue(Complex.NaN.sqrt().isNaN());
}
public void testSqrtInf() {
TestUtils.assertSame(infNaN, oneInf.sqrt());
TestUtils.assertSame(infNaN, oneNegInf.sqrt());
TestUtils.assertSame(infZero, infOne.sqrt());
TestUtils.assertSame(zeroInf, negInfOne.sqrt());
TestUtils.assertSame(infNaN, infInf.sqrt());
TestUtils.assertSame(infNaN, infNegInf.sqrt());
TestUtils.assertSame(nanInf, negInfInf.sqrt());
TestUtils.assertSame(nanNegInf, negInfNegInf.sqrt());
}
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);
}
public void testSqrt1zNaN() {
assertTrue(Complex.NaN.sqrt1z().isNaN());
}
public void testTan() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(-0.000187346, 0.999356);
TestUtils.assertEquals(expected, z.tan(), 1.0e-5);
}
public void testTanNaN() {
assertTrue(Complex.NaN.tan().isNaN());
}
public void testTanInf() {
TestUtils.assertSame(zeroNaN, oneInf.tan());
TestUtils.assertSame(zeroNaN, oneNegInf.tan());
TestUtils.assertSame(Complex.NaN, infOne.tan());
TestUtils.assertSame(Complex.NaN, negInfOne.tan());
TestUtils.assertSame(Complex.NaN, infInf.tan());
TestUtils.assertSame(Complex.NaN, infNegInf.tan());
TestUtils.assertSame(Complex.NaN, negInfInf.tan());
TestUtils.assertSame(Complex.NaN, negInfNegInf.tan());
}
public void testTanCritical() {
TestUtils.assertSame(infNaN, new Complex(pi/2, 0).tan());
TestUtils.assertSame(negInfNaN, new Complex(-pi/2, 0).tan());
}
public void testTanh() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(1.00071, 0.00490826);
TestUtils.assertEquals(expected, z.tanh(), 1.0e-5);
}
public void testTanhNaN() {
assertTrue(Complex.NaN.tanh().isNaN());
}
public void testTanhInf() {
TestUtils.assertSame(Complex.NaN, oneInf.tanh());
TestUtils.assertSame(Complex.NaN, oneNegInf.tanh());
TestUtils.assertSame(nanZero, infOne.tanh());
TestUtils.assertSame(nanZero, negInfOne.tanh());
TestUtils.assertSame(Complex.NaN, infInf.tanh());
TestUtils.assertSame(Complex.NaN, infNegInf.tanh());
TestUtils.assertSame(Complex.NaN, negInfInf.tanh());
TestUtils.assertSame(Complex.NaN, negInfNegInf.tanh());
}
public void testTanhCritical() {
TestUtils.assertSame(nanInf, new Complex(0, pi/2).tanh());
}
/** test issue MATH-221 */
public void testMath221() {
assertEquals(new Complex(0,-1), new Complex(0,1).multiply(new Complex(-1,0)));
}
/**
* Test: computing <b>third roots of z.
* <pre>
* <code>
* <b>z = -2 + 2 * i
* => z_0 = 1 + i
* => z_1 = -1.3660 + 0.3660 * i
* => z_2 = 0.3660 - 1.3660 * i
* </code>
* </pre>
*/
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!
assertEquals(3, thirdRootsOfZ.length);
// test z_0
assertEquals(1.0, thirdRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(1.0, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(-1.3660254037844386, thirdRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(0.36602540378443843, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(0.366025403784439, thirdRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(-1.3660254037844384, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
}
/**
* Test: computing <b>fourth roots of z.
* <pre>
* <code>
* <b>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
* </code>
* </pre>
*/
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!
assertEquals(4, fourthRootsOfZ.length);
// test z_0
assertEquals(1.5164629308487783, fourthRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(-0.14469266210702247, fourthRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(0.14469266210702256, fourthRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(1.5164629308487783, fourthRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(-1.5164629308487783, fourthRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(0.14469266210702267, fourthRootsOfZ[2].getImaginary(), 1.0e-5);
// test z_3
assertEquals(-0.14469266210702275, fourthRootsOfZ[3].getReal(), 1.0e-5);
assertEquals(-1.5164629308487783, fourthRootsOfZ[3].getImaginary(), 1.0e-5);
}
/**
* Test: computing <b>third roots of z.
* <pre>
* <code>
* <b>z = 8
* => z_0 = 2
* => z_1 = -1 + 1.73205 * i
* => z_2 = -1 - 1.73205 * i
* </code>
* </pre>
*/
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!
assertEquals(3, thirdRootsOfZ.length);
// test z_0
assertEquals(2.0, thirdRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(0.0, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(-1.0, thirdRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(1.7320508075688774, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(-1.0, thirdRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(-1.732050807568877, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
}
/**
* Test: computing <b>third roots of z with real part 0.
* <pre>
* <code>
* <b>z = 2 * i
* => z_0 = 1.0911 + 0.6299 * i
* => z_1 = -1.0911 + 0.6299 * i
* => z_2 = -2.3144 - 1.2599 * i
* </code>
* </pre>
*/
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!
assertEquals(3, thirdRootsOfZ.length);
// test z_0
assertEquals(1.0911236359717216, thirdRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(0.6299605249474365, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(-1.0911236359717216, thirdRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(0.6299605249474365, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(-2.3144374213981936E-16, thirdRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(-1.2599210498948732, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
}
/**
* Test cornercases with NaN and Infinity.
*/
public void testNthRoot_cornercase_NAN_Inf() {
// NaN + finite -> NaN
List<Complex> roots = oneNaN.nthRoot(3);
assertEquals(1,roots.size());
assertEquals(Complex.NaN, roots.get(0));
roots = nanZero.nthRoot(3);
assertEquals(1,roots.size());
assertEquals(Complex.NaN, roots.get(0));
// NaN + infinite -> NaN
roots = nanInf.nthRoot(3);
assertEquals(1,roots.size());
assertEquals(Complex.NaN, roots.get(0));
// finite + infinite -> Inf
roots = oneInf.nthRoot(3);
assertEquals(1,roots.size());
assertEquals(Complex.INF, roots.get(0));
// infinite + infinite -> Inf
roots = negInfInf.nthRoot(3);
assertEquals(1,roots.size());
assertEquals(Complex.INF, roots.get(0));
}
/**
* Test standard values
*/
public void testGetArgument() {
Complex z = new Complex(1, 0);
assertEquals(0.0, z.getArgument(), 1.0e-12);
z = new Complex(1, 1);
assertEquals(Math.PI/4, z.getArgument(), 1.0e-12);
z = new Complex(0, 1);
assertEquals(Math.PI/2, z.getArgument(), 1.0e-12);
z = new Complex(-1, 1);
assertEquals(3 * Math.PI/4, z.getArgument(), 1.0e-12);
z = new Complex(-1, 0);
assertEquals(Math.PI, z.getArgument(), 1.0e-12);
z = new Complex(-1, -1);
assertEquals(-3 * Math.PI/4, z.getArgument(), 1.0e-12);
z = new Complex(0, -1);
assertEquals(-Math.PI/2, z.getArgument(), 1.0e-12);
z = new Complex(1, -1);
assertEquals(-Math.PI/4, z.getArgument(), 1.0e-12);
}
/**
* Verify atan2-style handling of infinite parts
*/
public void testGetArgumentInf() {
assertEquals(Math.PI/4, infInf.getArgument(), 1.0e-12);
assertEquals(Math.PI/2, oneInf.getArgument(), 1.0e-12);
assertEquals(0.0, infOne.getArgument(), 1.0e-12);
assertEquals(Math.PI/2, zeroInf.getArgument(), 1.0e-12);
assertEquals(0.0, infZero.getArgument(), 1.0e-12);
assertEquals(Math.PI, negInfOne.getArgument(), 1.0e-12);
assertEquals(-3.0*Math.PI/4, negInfNegInf.getArgument(), 1.0e-12);
assertEquals(-Math.PI/2, oneNegInf.getArgument(), 1.0e-12);
}
/**
* Verify that either part NaN results in NaN
*/
public void testGetArgumentNaN() {
assertEquals(nan, nanZero.getArgument());
assertEquals(nan, zeroNaN.getArgument());
assertEquals(nan, Complex.NaN.getArgument());
}
public void testSerial() {
Complex z = new Complex(3.0, 4.0);
assertEquals(z, TestUtils.serializeAndRecover(z));
Complex ncmplx = (Complex)TestUtils.serializeAndRecover(oneNaN);
assertEquals(nanZero, ncmplx);
assertTrue(ncmplx.isNaN());
Complex infcmplx = (Complex)TestUtils.serializeAndRecover(infInf);
assertEquals(infInf, infcmplx);
assertTrue(infcmplx.isInfinite());
TestComplex tz = new TestComplex(3.0, 4.0);
assertEquals(tz, TestUtils.serializeAndRecover(tz));
TestComplex ntcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(oneNaN));
assertEquals(nanZero, ntcmplx);
assertTrue(ntcmplx.isNaN());
TestComplex inftcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(infInf));
assertEquals(infInf, inftcmplx);
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);
}
}
}
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