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From ericbarnh...@apache.org
Subject [34/37] commons-numbers git commit: NUMBERS-22: Added file ComplexTest.java to file tracker
Date Fri, 26 Jan 2018 14:00:25 GMT
NUMBERS-22: Added file ComplexTest.java to file tracker


Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/fc70d935
Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/fc70d935
Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/fc70d935

Branch: refs/heads/master
Commit: fc70d935fdadc5d5a7862cf9a929da91b72b00d6
Parents: 16322d8
Author: Eric Barnhill <ericbarnhill@apache.org>
Authored: Fri Jan 26 14:54:16 2018 +0100
Committer: Eric Barnhill <ericbarnhill@apache.org>
Committed: Fri Jan 26 14:54:16 2018 +0100

----------------------------------------------------------------------
 .../commons/numbers/complex/ComplexTest.java    | 849 +++++++++++++++++++
 1 file changed, 849 insertions(+)
----------------------------------------------------------------------


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


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