/*
* 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.math4.complex;
import java.util.List;
import org.apache.commons.math4.TestUtils;
import org.apache.commons.math4.complex.Complex;
import org.apache.commons.math4.complex.ComplexUtils;
import org.apache.commons.math4.exception.NullArgumentException;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Ignore;
import org.junit.Test;
/**
*/
public class ComplexTest {
private double inf = Double.POSITIVE_INFINITY;
private double neginf = Double.NEGATIVE_INFINITY;
private double nan = Double.NaN;
private double pi = FastMath.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);
@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 testAbsInfinite() {
Complex z = new Complex(inf, 0);
Assert.assertEquals(inf, z.abs(), 0);
z = new Complex(0, neginf);
Assert.assertEquals(inf, z.abs(), 0);
z = new Complex(inf, neginf);
Assert.assertEquals(inf, z.abs(), 0);
}
@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 testAddNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.add(Complex.NaN);
Assert.assertSame(Complex.NaN, z);
z = new Complex(1, nan);
Complex w = x.add(z);
Assert.assertSame(Complex.NaN, w);
}
@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 testDivideInf() {
Complex x = new Complex(3, 4);
Complex w = new Complex(neginf, inf);
Assert.assertTrue(x.divide(w).equals(Complex.ZERO));
Complex z = w.divide(x);
Assert.assertTrue(Double.isNaN(z.getReal()));
Assert.assertEquals(inf, z.getImaginary(), 0);
w = new Complex(inf, inf);
z = w.divide(x);
Assert.assertTrue(Double.isNaN(z.getImaginary()));
Assert.assertEquals(inf, z.getReal(), 0);
w = new Complex(1, inf);
z = w.divide(w);
Assert.assertTrue(Double.isNaN(z.getReal()));
Assert.assertTrue(Double.isNaN(z.getImaginary()));
}
@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 testScalarDivideInf() {
Complex x = new Complex(1,1);
double yDouble = Double.POSITIVE_INFINITY;
Complex yComplex = new Complex(yDouble);
TestUtils.assertEquals(x.divide(yComplex), x.divide(yDouble), 0);
yDouble = Double.NEGATIVE_INFINITY;
yComplex = new Complex(yDouble);
TestUtils.assertEquals(x.divide(yComplex), x.divide(yDouble), 0);
x = new Complex(1, Double.NEGATIVE_INFINITY);
TestUtils.assertEquals(x.divide(yComplex), x.divide(yDouble), 0);
}
@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(), FastMath.ulp(expRe));
Assert.assertEquals(expIm, act.getImaginary(), FastMath.ulp(expIm));
}
@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 testReciprocalInf() {
Complex z = new Complex(neginf, inf);
Assert.assertTrue(z.reciprocal().equals(Complex.ZERO));
z = new Complex(1, inf).reciprocal();
Assert.assertEquals(z, Complex.ZERO);
}
@Test
public void testReciprocalZero() {
Assert.assertEquals(Complex.ZERO.reciprocal(), Complex.INF);
}
@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 testMultiplyNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.multiply(Complex.NaN);
Assert.assertSame(Complex.NaN, z);
z = Complex.NaN.multiply(5);
Assert.assertSame(Complex.NaN, z);
}
@Test
public void testMultiplyInfInf() {
// Assert.assertTrue(infInf.multiply(infInf).isNaN()); // MATH-620
Assert.assertTrue(infInf.multiply(infInf).isInfinite());
}
@Test
public void testMultiplyNaNInf() {
Complex z = new Complex(1,1);
Complex w = z.multiply(infOne);
Assert.assertEquals(w.getReal(), inf, 0);
Assert.assertEquals(w.getImaginary(), inf, 0);
// [MATH-164]
Assert.assertTrue(new Complex( 1,0).multiply(infInf).equals(Complex.INF));
Assert.assertTrue(new Complex(-1,0).multiply(infInf).equals(Complex.INF));
Assert.assertTrue(new Complex( 1,0).multiply(negInfZero).equals(Complex.INF));
w = oneInf.multiply(oneNegInf);
Assert.assertEquals(w.getReal(), inf, 0);
Assert.assertEquals(w.getImaginary(), inf, 0);
w = negInfNegInf.multiply(oneNaN);
Assert.assertTrue(Double.isNaN(w.getReal()));
Assert.assertTrue(Double.isNaN(w.getImaginary()));
z = new Complex(1, neginf);
Assert.assertSame(Complex.INF, z.multiply(z));
}
@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 testSubtractNaN() {
Complex x = new Complex(3.0, 4.0);
Complex z = x.subtract(Complex.NaN);
Assert.assertSame(Complex.NaN, z);
z = new Complex(1, nan);
Complex w = x.subtract(z);
Assert.assertSame(Complex.NaN, w);
}
@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 = FastMath.nextUp(re);
im = FastMath.nextUp(im);
}
y = new Complex(re, im);
Assert.assertTrue(Complex.equals(x, y, maxUlps));
re = FastMath.nextUp(re);
im = FastMath.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 testEqualsNaN() {
Complex realNaN = new Complex(Double.NaN, 0.0);
Complex imaginaryNaN = new Complex(0.0, Double.NaN);
Complex complexNaN = Complex.NaN;
Assert.assertTrue(realNaN.equals(imaginaryNaN));
Assert.assertTrue(imaginaryNaN.equals(complexNaN));
Assert.assertTrue(realNaN.equals(complexNaN));
}
@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
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(FastMath.acos(0), 0),
Complex.ZERO.acos(), 1.0e-12);
}
@Test
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());
}
@Test
public void testAcosNaN() {
Assert.assertTrue(Complex.NaN.acos().isNaN());
}
@Test
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);
}
@Test
public void testAsinNaN() {
Assert.assertTrue(Complex.NaN.asin().isNaN());
}
@Test
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());
}
@Test
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);
}
@Test
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());
}
@Test
public void testAtanI() {
Assert.assertTrue(Complex.I.atan().isNaN());
}
@Test
public void testAtanNaN() {
Assert.assertTrue(Complex.NaN.atan().isNaN());
}
@Test
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);
}
@Test
public void testCosNaN() {
Assert.assertTrue(Complex.NaN.cos().isNaN());
}
@Test
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());
}
@Test
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);
}
@Test
public void testCoshNaN() {
Assert.assertTrue(Complex.NaN.cosh().isNaN());
}
@Test
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());
}
@Test
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);
}
@Test
public void testExpNaN() {
Assert.assertTrue(Complex.NaN.exp().isNaN());
}
@Test
public void testExpInf1() {
TestUtils.assertSame(Complex.NaN, oneInf.exp());
}
@Test
public void testExpInf2() {
TestUtils.assertSame(Complex.NaN, oneNegInf.exp());
}
@Test
public void testExpInf3() {
TestUtils.assertSame(infInf, infOne.exp());
}
@Test
@Ignore
public void testJava() {// TODO more debug
System.out.println(">>testJava()");
// FastMathTest#testExpSpecialCases() checks the following:
// Assert.assertEquals("exp of -infinity should be 0.0", 0.0, FastMath.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 testExpInf4() {
final Complex exp = negInfOne.exp();
TestUtils.assertSame(Complex.ZERO, exp);
}
@Test
public void testExpInf5() {
TestUtils.assertSame(Complex.NaN, infInf.exp());
}
@Test
public void testExpInf6() {
TestUtils.assertSame(Complex.NaN, infNegInf.exp());
}
@Test
public void testExpInf7() {
TestUtils.assertSame(Complex.NaN, negInfInf.exp());
}
@Test
public void testExpInf8() {
TestUtils.assertSame(Complex.NaN, negInfNegInf.exp());
}
@Test
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);
}
@Test
public void testLogNaN() {
Assert.assertTrue(Complex.NaN.log().isNaN());
}
@Test
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);
}
@Test
public void testLogZero() {
TestUtils.assertSame(negInfZero, Complex.ZERO.log());
}
@Test
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);
}
@Test
public void testPowNaNBase() {
Complex x = new Complex(3, 4);
Assert.assertTrue(Complex.NaN.pow(x).isNaN());
}
@Test
public void testPowNaNExponent() {
Complex x = new Complex(3, 4);
Assert.assertTrue(x.pow(Complex.NaN).isNaN());
}
@Test
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));
}
@Test
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);
}
@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 testScalarPowInf() {
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(Double.POSITIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(Double.NEGATIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,infOne.pow(1.0));
TestUtils.assertSame(Complex.NaN,negInfOne.pow(1.0));
TestUtils.assertSame(Complex.NaN,infInf.pow(1.0));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(1.0));
TestUtils.assertSame(Complex.NaN,negInfInf.pow(10));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(1.0));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(Double.POSITIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(Double.POSITIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,infInf.pow(Double.POSITIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,infInf.pow(Double.NEGATIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(Double.NEGATIVE_INFINITY));
TestUtils.assertSame(Complex.NaN,infNegInf.pow(Double.POSITIVE_INFINITY));
}
@Test
public void testScalarPowZero() {
TestUtils.assertSame(Complex.NaN, Complex.ZERO.pow(1.0));
TestUtils.assertSame(Complex.NaN, Complex.ZERO.pow(0.0));
TestUtils.assertEquals(Complex.ONE, Complex.ONE.pow(0.0), 10e-12);
TestUtils.assertEquals(Complex.ONE, Complex.I.pow(0.0), 10e-12);
TestUtils.assertEquals(Complex.ONE, new Complex(-1, 3).pow(0.0), 10e-12);
}
@Test(expected=NullArgumentException.class)
public void testpowNull() {
Complex.ONE.pow(null);
}
@Test
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);
}
@Test
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());
}
@Test
public void testSinNaN() {
Assert.assertTrue(Complex.NaN.sin().isNaN());
}
@Test
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);
}
@Test
public void testSinhNaN() {
Assert.assertTrue(Complex.NaN.sinh().isNaN());
}
@Test
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());
}
@Test
public void testSqrtRealPositive() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(2, 1);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
@Test
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);
}
@Test
public void testSqrtRealNegative() {
Complex z = new Complex(-3.0, 4);
Complex expected = new Complex(1, 2);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
@Test
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);
}
@Test
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);
}
@Test
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(FastMath.sqrt(r), theta / 2);
TestUtils.assertEquals(sqrtz, z.sqrt(), 10e-12);
}
}
}
@Test
public void testSqrtNaN() {
Assert.assertTrue(Complex.NaN.sqrt().isNaN());
}
@Test
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());
}
@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
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);
/* Check that no overflow occurs (MATH-722) */
Complex actual = new Complex(3.0, 1E10).tan();
expected = new Complex(0, 1);
TestUtils.assertEquals(expected, actual, 1.0e-5);
actual = new Complex(3.0, -1E10).tan();
expected = new Complex(0, -1);
TestUtils.assertEquals(expected, actual, 1.0e-5);
}
@Test
public void testTanNaN() {
Assert.assertTrue(Complex.NaN.tan().isNaN());
}
@Test
public void testTanInf() {
TestUtils.assertSame(Complex.valueOf(0.0, 1.0), oneInf.tan());
TestUtils.assertSame(Complex.valueOf(0.0, -1.0), 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());
}
@Test
public void testTanCritical() {
TestUtils.assertSame(infNaN, new Complex(pi/2, 0).tan());
TestUtils.assertSame(negInfNaN, new Complex(-pi/2, 0).tan());
}
@Test
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);
/* Check that no overflow occurs (MATH-722) */
Complex actual = new Complex(1E10, 3.0).tanh();
expected = new Complex(1, 0);
TestUtils.assertEquals(expected, actual, 1.0e-5);
actual = new Complex(-1E10, 3.0).tanh();
expected = new Complex(-1, 0);
TestUtils.assertEquals(expected, actual, 1.0e-5);
}
@Test
public void testTanhNaN() {
Assert.assertTrue(Complex.NaN.tanh().isNaN());
}
@Test
public void testTanhInf() {
TestUtils.assertSame(Complex.NaN, oneInf.tanh());
TestUtils.assertSame(Complex.NaN, oneNegInf.tanh());
TestUtils.assertSame(Complex.valueOf(1.0, 0.0), infOne.tanh());
TestUtils.assertSame(Complex.valueOf(-1.0, 0.0), 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());
}
@Test
public void testTanhCritical() {
TestUtils.assertSame(nanInf, new Complex(0, pi/2).tanh());
}
/** test issue MATH-221 */
@Test
public void testMath221() {
Assert.assertTrue(Complex.equals(new Complex(0,-1),
new Complex(0,1).multiply(new Complex(-1,0))));
}
/**
* 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 cornercases with NaN and Infinity.
*/
@Test
public void testNthRoot_cornercase_NAN_Inf() {
// NaN + finite -> NaN
List<Complex> roots = oneNaN.nthRoot(3);
Assert.assertEquals(1,roots.size());
Assert.assertEquals(Complex.NaN, roots.get(0));
roots = nanZero.nthRoot(3);
Assert.assertEquals(1,roots.size());
Assert.assertEquals(Complex.NaN, roots.get(0));
// NaN + infinite -> NaN
roots = nanInf.nthRoot(3);
Assert.assertEquals(1,roots.size());
Assert.assertEquals(Complex.NaN, roots.get(0));
// finite + infinite -> Inf
roots = oneInf.nthRoot(3);
Assert.assertEquals(1,roots.size());
Assert.assertEquals(Complex.INF, roots.get(0));
// infinite + infinite -> Inf
roots = negInfInf.nthRoot(3);
Assert.assertEquals(1,roots.size());
Assert.assertEquals(Complex.INF, roots.get(0));
}
/**
* 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(FastMath.PI/4, z.getArgument(), 1.0e-12);
z = new Complex(0, 1);
Assert.assertEquals(FastMath.PI/2, z.getArgument(), 1.0e-12);
z = new Complex(-1, 1);
Assert.assertEquals(3 * FastMath.PI/4, z.getArgument(), 1.0e-12);
z = new Complex(-1, 0);
Assert.assertEquals(FastMath.PI, z.getArgument(), 1.0e-12);
z = new Complex(-1, -1);
Assert.assertEquals(-3 * FastMath.PI/4, z.getArgument(), 1.0e-12);
z = new Complex(0, -1);
Assert.assertEquals(-FastMath.PI/2, z.getArgument(), 1.0e-12);
z = new Complex(1, -1);
Assert.assertEquals(-FastMath.PI/4, z.getArgument(), 1.0e-12);
}
/**
* Verify atan2-style handling of infinite parts
*/
@Test
public void testGetArgumentInf() {
Assert.assertEquals(FastMath.PI/4, infInf.getArgument(), 1.0e-12);
Assert.assertEquals(FastMath.PI/2, oneInf.getArgument(), 1.0e-12);
Assert.assertEquals(0.0, infOne.getArgument(), 1.0e-12);
Assert.assertEquals(FastMath.PI/2, zeroInf.getArgument(), 1.0e-12);
Assert.assertEquals(0.0, infZero.getArgument(), 1.0e-12);
Assert.assertEquals(FastMath.PI, negInfOne.getArgument(), 1.0e-12);
Assert.assertEquals(-3.0*FastMath.PI/4, negInfNegInf.getArgument(), 1.0e-12);
Assert.assertEquals(-FastMath.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);
}
}
}