http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/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..1dbcce1 --- /dev/null +++ b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java @@ -0,0 +1,1477 @@ +/* + * 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 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); + + @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 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 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 = 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 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(Math.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() { + final double tol = Math.ulp(1d); + 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(), tol); + Complex iPi = Complex.I.multiply(new Complex(pi,0)); + TestUtils.assertEquals(Complex.ONE.negate(), + iPi.exp(), tol); + } + + @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()"); + // 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 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() { + final double tol = Math.ulp(1d); + TestUtils.assertEquals(new Complex(inf, pi / 2), + oneInf.log(), tol); + TestUtils.assertEquals(new Complex(inf, -pi / 2), + oneNegInf.log(), tol); + TestUtils.assertEquals(infZero, infOne.log(), tol); + TestUtils.assertEquals(new Complex(inf, pi), + negInfOne.log(), tol); + TestUtils.assertEquals(new Complex(inf, pi / 4), + infInf.log(), tol); + TestUtils.assertEquals(new Complex(inf, -pi / 4), + infNegInf.log(), tol); + TestUtils.assertEquals(new Complex(inf, 3d * pi / 4), + negInfInf.log(), tol); + TestUtils.assertEquals(new Complex(inf, - 3d * pi / 4), + negInfNegInf.log(), tol); + } + + @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() { + final double tol = Math.ulp(1d); + TestUtils.assertEquals(Complex.ZERO, + Complex.ZERO.pow(Complex.ONE), tol); + TestUtils.assertEquals(Complex.ZERO, + Complex.ZERO.pow(new Complex(2, 0)), tol); + 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), tol); + TestUtils.assertEquals(Complex.ONE, + Complex.I.pow(Complex.ZERO), tol); + TestUtils.assertEquals(Complex.ONE, + new Complex(-1, 3).pow(Complex.ZERO), tol); + } + + @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() { + final double tol = Math.ulp(1d); + TestUtils.assertEquals(Complex.ZERO, Complex.ZERO.pow(1.0), tol); + TestUtils.assertEquals(Complex.ZERO, Complex.ZERO.pow(2.0), tol); + TestUtils.assertSame(Complex.NaN, Complex.ZERO.pow(0.0)); + TestUtils.assertSame(Complex.NaN, Complex.ZERO.pow(-1.0)); + TestUtils.assertEquals(Complex.ONE, Complex.ONE.pow(0.0), tol); + TestUtils.assertEquals(Complex.ONE, Complex.I.pow(0.0), tol); + TestUtils.assertEquals(Complex.ONE, new Complex(-1, 3).pow(0.0), tol); + } + + @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() { + 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 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(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); + } + + } +}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexUtilsTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexUtilsTest.java b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexUtilsTest.java new file mode 100644 index 0000000..9a7a29d --- /dev/null +++ b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexUtilsTest.java @@ -0,0 +1,475 @@ +/* + * 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 org.apache.commons.numbers.complex.Complex; +import org.apache.commons.numbers.complex.ComplexUtils; +import org.junit.Assert; +import org.junit.Test; + +/** + */ +public class ComplexUtilsTest { + + private final double inf = Double.POSITIVE_INFINITY; + private final double negInf = Double.NEGATIVE_INFINITY; + private final double nan = Double.NaN; + private final double pi = Math.PI; + + private final Complex negInfInf = new Complex(negInf, inf); + private final Complex infNegInf = new Complex(inf, negInf); + private final Complex infInf = new Complex(inf, inf); + private final Complex negInfNegInf = new Complex(negInf, negInf); + private final Complex infNaN = new Complex(inf, nan); + + private static Complex c[]; // complex array with real values even and imag + // values odd + private static Complex cr[]; // complex array with real values consecutive + private static Complex ci[]; // complex array with imag values consecutive + private static double d[]; // real array with consecutive vals + private static double di[]; // real array with consecutive vals, + // 'interleaved' length + private static float f[]; // real array with consecutive vals + private static float fi[]; // real array with consec vals, interleaved + // length + private static double sr[]; // real component of split array, evens + private static double si[]; // imag component of split array, odds + private static float sfr[]; // real component of split array, float, evens + private static float sfi[]; // imag component of split array, float, odds + static Complex ans1, ans2; // answers to single value extraction methods + static Complex[] ansArrayc1r, ansArrayc1i, ansArrayc2r, ansArrayc2i, ansArrayc3, ansArrayc4; // answers + // to + // range + // extraction + // methods + static double[] ansArrayd1r, ansArrayd2r, ansArrayd1i, ansArrayd2i, ansArraydi1, ansArraydi2; + static float[] ansArrayf1r, ansArrayf2r, ansArrayf1i, ansArrayf2i, ansArrayfi1, ansArrayfi2; + static String msg; // error message for AssertEquals + static Complex[][] c2d, cr2d, ci2d; // for 2d methods + static Complex[][][] c3d, cr3d, ci3d; // for 3d methods + static double[][] d2d, di2d, sr2d, si2d; + static double[][][] d3d, di3d, sr3d, si3d; + static float[][] f2d, fi2d, sfr2d, sfi2d; + static float[][][] f3d, fi3d, sfr3d, sfi3d; + + private static void setArrays() { // initial setup method + c = new Complex[10]; + cr = new Complex[10]; + ci = new Complex[10]; + d = new double[10]; + f = new float[10]; + di = new double[20]; + fi = new float[20]; + sr = new double[10]; + si = new double[10]; + sfr = new float[10]; + sfi = new float[10]; + c2d = new Complex[10][10]; + cr2d = new Complex[10][10]; + ci2d = new Complex[10][10]; + c3d = new Complex[10][10][10]; + cr3d = new Complex[10][10][10]; + ci3d = new Complex[10][10][10]; + d2d = new double[10][10]; + d3d = new double[10][10][10]; + f2d = new float[10][10]; + f3d = new float[10][10][10]; + sr2d = new double[10][10]; + sr3d = new double[10][10][10]; + si2d = new double[10][10]; + si3d = new double[10][10][10]; + sfr2d = new float[10][10]; + sfr3d = new float[10][10][10]; + sfi2d = new float[10][10]; + sfi3d = new float[10][10][10]; + di2d = new double[10][20]; + di3d = new double[10][10][20]; + fi2d = new float[10][20]; + fi3d = new float[10][10][20]; + for (int i = 0; i < 20; i += 2) { + d[i / 2] = i / 2; + f[i / 2] = i / 2; + di[i] = i; + di[i + 1] = i + 1; + fi[i] = i; + fi[i + 1] = i + 1; + c[i / 2] = new Complex(i, i + 1); + cr[i / 2] = new Complex(i / 2); + ci[i / 2] = new Complex(0, i / 2); + sr[i / 2] = i; + si[i / 2] = i + 1; + sfr[i / 2] = i; + sfi[i / 2] = i + 1; + } + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 20; j += 2) { + d2d[i][j / 2] = 10 * i + j / 2; + f2d[i][j / 2] = 10 * i + j / 2; + sr2d[i][j / 2] = 10 * i + j; + si2d[i][j / 2] = 10 * i + j + 1; + sfr2d[i][j / 2] = 10 * i + j; + sfi2d[i][j / 2] = 10 * i + j + 1; + di2d[i][j] = 10 * i + j; + di2d[i][j + 1] = 10 * i + j + 1; + fi2d[i][j] = 10 * i + j; + fi2d[i][j + 1] = 10 * i + j + 1; + c2d[i][j / 2] = new Complex(10 * i + j, 10 * i + j + 1); + cr2d[i][j / 2] = new Complex(10 * i + j / 2); + ci2d[i][j / 2] = new Complex(0, 10 * i + j / 2); + } + } + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + for (int k = 0; k < 20; k += 2) { + d3d[i][j][k / 2] = 100 * i + 10 * j + k / 2; + f3d[i][j][k / 2] = 100 * i + 10 * j + k / 2; + sr3d[i][j][k / 2] = 100 * i + 10 * j + k; + si3d[i][j][k / 2] = 100 * i + 10 * j + k + 1; + sfr3d[i][j][k / 2] = 100 * i + 10 * j + k; + sfi3d[i][j][k / 2] = 100 * i + 10 * j + k + 1; + di3d[i][j][k] = 100 * i + 10 * j + k; + di3d[i][j][k + 1] = 100 * i + 10 * j + k + 1; + fi3d[i][j][k] = 100 * i + 10 * j + k; + fi3d[i][j][k + 1] = 100 * i + 10 * j + k + 1; + c3d[i][j][k / 2] = new Complex(100 * i + 10 * j + k, 100 * i + 10 * j + k + 1); + cr3d[i][j][k / 2] = new Complex(100 * i + 10 * j + k / 2); + ci3d[i][j][k / 2] = new Complex(0, 100 * i + 10 * j + k / 2); + } + } + } + ansArrayc1r = new Complex[] { new Complex(3), new Complex(4), new Complex(5), new Complex(6), new Complex(7) }; + ansArrayc2r = new Complex[] { new Complex(3), new Complex(5), new Complex(7) }; + ansArrayc1i = new Complex[] { new Complex(0, 3), new Complex(0, 4), new Complex(0, 5), new Complex(0, 6), + new Complex(0, 7) }; + ansArrayc2i = new Complex[] { new Complex(0, 3), new Complex(0, 5), new Complex(0, 7) }; + ansArrayc3 = new Complex[] { new Complex(6, 7), new Complex(8, 9), new Complex(10, 11), new Complex(12, 13), + new Complex(14, 15) }; + ansArrayc4 = new Complex[] { new Complex(6, 7), new Complex(10, 11), new Complex(14, 15) }; + ansArrayd1r = new double[] { 6, 8, 10, 12, 14 }; + ansArrayd1i = new double[] { 7, 9, 11, 13, 15 }; + ansArrayd2r = new double[] { 6, 10, 14 }; + ansArrayd2i = new double[] { 7, 11, 15 }; + ansArrayf1r = new float[] { 6, 8, 10, 12, 14 }; + ansArrayf1i = new float[] { 7, 9, 11, 13, 15 }; + ansArrayf2r = new float[] { 6, 10, 14 }; + ansArrayf2i = new float[] { 7, 11, 15 }; + ansArraydi1 = new double[] { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }; + ansArrayfi1 = new float[] { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }; + ansArraydi2 = new double[] { 6, 7, 10, 11, 14, 15 }; + ansArrayfi2 = new float[] { 6, 7, 10, 11, 14, 15 }; + msg = ""; + } + + @Test + public void testPolar2Complex() { + TestUtils.assertEquals(Complex.ONE, ComplexUtils.polar2Complex(1, 0), 10e-12); + TestUtils.assertEquals(Complex.ZERO, ComplexUtils.polar2Complex(0, 1), 10e-12); + TestUtils.assertEquals(Complex.ZERO, ComplexUtils.polar2Complex(0, -1), 10e-12); + TestUtils.assertEquals(Complex.I, ComplexUtils.polar2Complex(1, pi / 2), 10e-12); + TestUtils.assertEquals(Complex.I.negate(), ComplexUtils.polar2Complex(1, -pi / 2), 10e-12); + double r = 0; + for (int i = 0; i < 5; i++) { + r += i; + double theta = 0; + for (int j = 0; j < 20; j++) { + theta += pi / 6; + TestUtils.assertEquals(altPolar(r, theta), ComplexUtils.polar2Complex(r, theta), 10e-12); + } + theta = -2 * pi; + for (int j = 0; j < 20; j++) { + theta -= pi / 6; + TestUtils.assertEquals(altPolar(r, theta), ComplexUtils.polar2Complex(r, theta), 10e-12); + } + } + } + + protected Complex altPolar(double r, double theta) { + return Complex.I.multiply(new Complex(theta, 0)).exp().multiply(new Complex(r, 0)); + } + + @Test(expected = IllegalArgumentException.class) + public void testPolar2ComplexIllegalModulus() { + ComplexUtils.polar2Complex(-1, 0); + } + + @Test + public void testPolar2ComplexNaN() { + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(nan, 1)); + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(1, nan)); + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(nan, nan)); + } + + @Test + public void testPolar2ComplexInf() { + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(1, inf)); + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(1, negInf)); + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(inf, inf)); + TestUtils.assertSame(Complex.NaN, ComplexUtils.polar2Complex(inf, negInf)); + TestUtils.assertSame(infInf, ComplexUtils.polar2Complex(inf, pi / 4)); + TestUtils.assertSame(infNaN, ComplexUtils.polar2Complex(inf, 0)); + TestUtils.assertSame(infNegInf, ComplexUtils.polar2Complex(inf, -pi / 4)); + TestUtils.assertSame(negInfInf, ComplexUtils.polar2Complex(inf, 3 * pi / 4)); + TestUtils.assertSame(negInfNegInf, ComplexUtils.polar2Complex(inf, 5 * pi / 4)); + } + + @Test + public void testCExtract() { + final double[] real = new double[] { negInf, -123.45, 0, 1, 234.56, pi, inf }; + final Complex[] complex = ComplexUtils.real2Complex(real); + + for (int i = 0; i < real.length; i++) { + Assert.assertEquals(real[i], complex[i].getReal(), 0d); + } + } + + // EXTRACTION METHODS + + @Test + public void testExtractionMethods() { + setArrays(); + // Extract complex from real double array, index 3 + TestUtils.assertSame(new Complex(3), ComplexUtils.extractComplexFromRealArray(d, 3)); + // Extract complex from real float array, index 3 + TestUtils.assertSame(new Complex(3), ComplexUtils.extractComplexFromRealArray(f, 3)); + // Extract real double from complex array, index 3 + TestUtils.assertSame(6, ComplexUtils.extractRealFromComplexArray(c, 3)); + // Extract real float from complex array, index 3 + TestUtils.assertSame(6, ComplexUtils.extractRealFloatFromComplexArray(c, 3)); + // Extract complex from interleaved double array, index 3 + TestUtils.assertSame(new Complex(6, 7), ComplexUtils.extractComplexFromInterleavedArray(d, 3)); + // Extract complex from interleaved float array, index 3 + TestUtils.assertSame(new Complex(6, 7), ComplexUtils.extractComplexFromInterleavedArray(f, 3)); + // Extract interleaved double from complex array, index 3 + TestUtils.assertEquals(msg, new double[] { 6, 7 }, ComplexUtils.extractInterleavedFromComplexArray(c, 3), + Math.ulp(1)); + // Extract interleaved float from complex array, index 3 + TestUtils.assertEquals(msg, new double[] { 6, 7 }, ComplexUtils.extractInterleavedFromComplexArray(c, 3), + Math.ulp(1)); + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + // REAL <-> COMPLEX + + @Test + public void testRealToComplex() { + setArrays(); + // Real double to complex, range 3-7, increment 1, entered as ints + // Real double to complex, whole array + TestUtils.assertEquals(msg, cr, ComplexUtils.real2Complex(d),Math.ulp(1.0)); + // Real float to complex, whole array + TestUtils.assertEquals(msg, cr, ComplexUtils.real2Complex(f),Math.ulp(1.0)); + // 2d + for (int i = 0; i < 10; i++) { + // Real double to complex, 2d + TestUtils.assertEquals(msg, cr2d[i], ComplexUtils.real2Complex(d2d[i]),Math.ulp(1.0)); + // Real float to complex, 2d + TestUtils.assertEquals(msg, cr2d[i], ComplexUtils.real2Complex(f2d[i]),Math.ulp(1.0)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Real double to complex, 3d + TestUtils.assertEquals(msg, cr3d[i][j], ComplexUtils.real2Complex(d3d[i][j]),Math.ulp(1.0)); + // Real float to complex, 3d + TestUtils.assertEquals(msg, cr3d[i][j], ComplexUtils.real2Complex(f3d[i][j]),Math.ulp(1.0)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + @Test + public void testComplexToReal() { + setArrays(); + // Real complex to double, whole array + TestUtils.assertEquals(msg, sr, ComplexUtils.complex2Real(c),Math.ulp(1.0)); + // Real complex to float, whole array + TestUtils.assertEquals(msg, sfr, ComplexUtils.complex2RealFloat(c),Math.ulp(1.0f)); + // 2d + for (int i = 0; i < 10; i++) { + // Real complex to double, 2d + TestUtils.assertEquals(msg, sr2d[i], ComplexUtils.complex2Real(c2d[i]),Math.ulp(1.0)); + // Real complex to float, 2d + TestUtils.assertEquals(msg, sfr2d[i], ComplexUtils.complex2RealFloat(c2d[i]),Math.ulp(1.0f)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Real complex to double, 3d + TestUtils.assertEquals(msg, sr3d[i][j], ComplexUtils.complex2Real(c3d[i][j]),Math.ulp(1.0)); + // Real complex to float, 3d + TestUtils.assertEquals(msg, sfr3d[i][j], ComplexUtils.complex2RealFloat(c3d[i][j]),Math.ulp(1.0f)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + // IMAGINARY <-> COMPLEX + + @Test + public void testImaginaryToComplex() { + setArrays(); + // Imaginary double to complex, whole array + TestUtils.assertEquals(msg, ci, ComplexUtils.imaginary2Complex(d),Math.ulp(1.0)); + // Imaginary float to complex, whole array + TestUtils.assertEquals(msg, ci, ComplexUtils.imaginary2Complex(f),Math.ulp(1.0)); + // 2d + for (int i = 0; i < 10; i++) { + // Imaginary double to complex, 2d + TestUtils.assertEquals(msg, ci2d[i], ComplexUtils.imaginary2Complex(d2d[i]),Math.ulp(1.0)); + // Imaginary float to complex, 2d + TestUtils.assertEquals(msg, ci2d[i], ComplexUtils.imaginary2Complex(f2d[i]),Math.ulp(1.0)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Imaginary double to complex, 3d + TestUtils.assertEquals(msg, ci3d[i][j], ComplexUtils.imaginary2Complex(d3d[i][j]),Math.ulp(1.0)); + // Imaginary float to complex, 3d + TestUtils.assertEquals(msg, ci3d[i][j], ComplexUtils.imaginary2Complex(f3d[i][j]),Math.ulp(1.0)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + @Test + public void testComplexToImaginary() { + setArrays(); + // Imaginary complex to double, whole array + TestUtils.assertEquals(msg, si, ComplexUtils.complex2Imaginary(c),Math.ulp(1.0)); + // Imaginary complex to float, whole array + TestUtils.assertEquals(msg, sfi, ComplexUtils.complex2ImaginaryFloat(c),Math.ulp(1.0f)); + // 2d + for (int i = 0; i < 10; i++) { + // Imaginary complex to double, 2d + TestUtils.assertEquals(msg, si2d[i], ComplexUtils.complex2Imaginary(c2d[i]),Math.ulp(1.0)); + // Imaginary complex to float, 2d + TestUtils.assertEquals(msg, sfi2d[i], ComplexUtils.complex2ImaginaryFloat(c2d[i]),Math.ulp(1.0f)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Imaginary complex to double, 3d + TestUtils.assertEquals(msg, si3d[i][j], ComplexUtils.complex2Imaginary(c3d[i][j]),Math.ulp(1.0)); + // Imaginary complex to float, 3d + TestUtils.assertEquals(msg, sfi3d[i][j], ComplexUtils.complex2ImaginaryFloat(c3d[i][j]),Math.ulp(1.0f)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + // INTERLEAVED <-> COMPLEX + + @Test + public void testInterleavedToComplex() { + setArrays(); + // Interleaved double to complex, whole array + TestUtils.assertEquals(msg, c, ComplexUtils.interleaved2Complex(di),Math.ulp(1.0)); + // Interleaved float to complex, whole array + TestUtils.assertEquals(msg, c, ComplexUtils.interleaved2Complex(fi),Math.ulp(1.0)); + // 2d + for (int i = 0; i < 10; i++) { + // Interleaved double to complex, 2d + TestUtils.assertEquals(msg, c2d[i], ComplexUtils.interleaved2Complex(di2d[i]),Math.ulp(1.0)); + // Interleaved float to complex, 2d + TestUtils.assertEquals(msg, c2d[i], ComplexUtils.interleaved2Complex(fi2d[i]),Math.ulp(1.0)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Interleaved double to complex, 3d + TestUtils.assertEquals(msg, c3d[i][j], ComplexUtils.interleaved2Complex(di3d[i][j]),Math.ulp(1.0)); + // Interleaved float to complex, 3d + TestUtils.assertEquals(msg, c3d[i][j], ComplexUtils.interleaved2Complex(fi3d[i][j]),Math.ulp(1.0)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + @Test + public void testComplexToInterleaved() { + setArrays(); + TestUtils.assertEquals(msg, di, ComplexUtils.complex2Interleaved(c),Math.ulp(1.0)); + // Interleaved complex to float, whole array + TestUtils.assertEquals(msg, fi, ComplexUtils.complex2InterleavedFloat(c),Math.ulp(1.0f)); + // 2d + for (int i = 0; i < 10; i++) { + // Interleaved complex to double, 2d + TestUtils.assertEquals(msg, di2d[i], ComplexUtils.complex2Interleaved(c2d[i]),Math.ulp(1.0)); + // Interleaved complex to float, 2d + TestUtils.assertEquals(msg, fi2d[i], ComplexUtils.complex2InterleavedFloat(c2d[i]),Math.ulp(1.0f)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Interleaved complex to double, 3d + TestUtils.assertEquals(msg, di3d[i][j], ComplexUtils.complex2Interleaved(c3d[i][j]),Math.ulp(1.0)); + // Interleaved complex to float, 3d + TestUtils.assertEquals(msg, fi3d[i][j], ComplexUtils.complex2InterleavedFloat(c3d[i][j]),Math.ulp(1.0f)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + // SPLIT TO COMPLEX + @Test + public void testSplit2Complex() { + setArrays(); + // Split double to complex, whole array + TestUtils.assertEquals(msg, c, ComplexUtils.split2Complex(sr, si),Math.ulp(1.0)); + + // 2d + for (int i = 0; i < 10; i++) { + // Split double to complex, 2d + TestUtils.assertEquals(msg, c2d[i], ComplexUtils.split2Complex(sr2d[i], si2d[i]),Math.ulp(1.0)); + } + // 3d + for (int i = 0; i < 10; i++) { + for (int j = 0; j < 10; j++) { + // Split double to complex, 3d + TestUtils.assertEquals(msg, c3d[i][j], ComplexUtils.split2Complex(sr3d[i][j], si3d[i][j]),Math.ulp(1.0)); + } + } + if (!msg.equals("")) { + throw new RuntimeException(msg); + } + } + + // INITIALIZATION METHODS + + @Test + public void testInitialize() { + Complex[] c = new Complex[10]; + ComplexUtils.initialize(c); + for (Complex cc : c) { + TestUtils.assertEquals(new Complex(0, 0), cc, Math.ulp(0)); + } + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/RootsOfUnityTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/RootsOfUnityTest.java b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/RootsOfUnityTest.java new file mode 100644 index 0000000..df40f99 --- /dev/null +++ b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/RootsOfUnityTest.java @@ -0,0 +1,84 @@ +/* + * 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 org.junit.Assert; +import org.junit.Test; + + +/** + * Unit tests for the {@link RootsOfUnity} class. + * + */ +public class RootsOfUnityTest { + @Test(expected = IllegalArgumentException.class) + public void testPrecondition() { + new RootsOfUnity(0); + } + @Test(expected = IndexOutOfBoundsException.class) + public void testGetRootPrecondition1() { + final int n = 3; + final RootsOfUnity roots = new RootsOfUnity(n); + roots.getRoot(-1); + } + @Test(expected = IndexOutOfBoundsException.class) + public void testGetRootPrecondition2() { + final int n = -2; + final RootsOfUnity roots = new RootsOfUnity(n); + roots.getRoot(2); + } + + @Test + public void testGetNumberOfRoots1() { + final int n = 5; + final RootsOfUnity roots = new RootsOfUnity(n); + Assert.assertEquals(n, roots.getNumberOfRoots()); + Assert.assertTrue(roots.isCounterClockwise()); + } + @Test + public void testGetNumberOfRoots2() { + final int n = -4; + final RootsOfUnity roots = new RootsOfUnity(n); + Assert.assertEquals(Math.abs(n), roots.getNumberOfRoots()); + Assert.assertFalse(roots.isCounterClockwise()); + } + + @Test + public void testComputeRoots() { + final double tol = Math.ulp(1d); + final org.apache.commons.math3.complex.RootsOfUnity cmRoots = + new org.apache.commons.math3.complex.RootsOfUnity(); + for (int n = -10; n < 11; n++) { + final int absN = Math.abs(n); + if (n != 0) { + cmRoots.computeRoots(n); + final RootsOfUnity roots = new RootsOfUnity(n); + for (int k = 0; k < absN; k++) { + final Complex z = roots.getRoot(k); + Assert.assertEquals("n=" + n + " k=" + k, + cmRoots.getReal(k), + z.getReal(), + tol); + Assert.assertEquals("n=" + n + " k=" + k, + cmRoots.getImaginary(k), + z.getImaginary(), + tol); + } + } + } + } +}
