NUBERS-17: Added further 4D functionality to Complex Utils (real 2 complex and complex 2 real)
Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/1de701b3 Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/1de701b3 Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/1de701b3 Branch: refs/heads/master Commit: 1de701b3e3c9dce998a1a0a7ed747ee5aa76cef4 Parents: 48464a3 Author: Eric Barnhill <ericbarnh...@apache.org> Authored: Wed Jul 12 10:16:39 2017 +0200 Committer: Eric Barnhill <ericbarnh...@apache.org> Committed: Wed Jul 12 10:16:39 2017 +0200 ---------------------------------------------------------------------- .../commons/numbers/complex/ComplexUtils.java | 136 +- .../commons/numbers/complex/CStandardTest.java | 282 ---- .../commons/numbers/complex/ComplexTest.java | 1366 ------------------ 3 files changed, 126 insertions(+), 1658 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/1de701b3/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java ---------------------------------------------------------------------- diff --git a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java index 4718ac5..e41709c 100644 --- a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java +++ b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java @@ -356,6 +356,24 @@ public class ComplexUtils { } /** + * Converts a 4D real {@code double[][][][]} array to a {@code Complex [][][][]} + * array. + * + * @param d 4D complex interleaved array + * @return 4D {@code Complex} array + * + * @since 1.0 + */ + public static Complex[][][][] real2Complex(double[][][][] d) { + final int w = d.length; + final Complex[][][][] c = new Complex[w][][][]; + for (int x = 0; x < w; x++) { + c[x] = ComplexUtils.real2Complex(d[x]); + } + return c; + } + + /** * Converts real component of {@code Complex[]} array to a {@code double[]} * array. * @@ -463,6 +481,41 @@ public class ComplexUtils { } /** + * Converts real component of a 4D {@code Complex[][][][]} array to a 4D + * {@code double[][][][]} array. + * + * @param c 4D complex interleaved array + * @return array of real component + * + * @since 1.0 + */ + public static double[][][][] complex2Real(Complex[][][][] c) { + final int length = c.length; + double[][][][] d = new double[length][][][]; + for (int n = 0; n < length; n++) { + d[n] = complex2Real(c[n]); + } + return d; + } + + /** + * Converts real component of a 4D {@code Complex[][][][]} array to a 4D + * {@code float[][][][]} array. + * + * @param c 4D {@code Complex} array + * @return {@code float[][][][]} of real component + * @since 1.0 + */ + public static float[][][][] complex2RealFloat(Complex[][][][] c) { + final int length = c.length; + float[][][][] f = new float[length][][][]; + for (int n = 0; n < length; n++) { + f[n] = complex2RealFloat(c[n]); + } + return f; + } + + /** * Converts a {@code double[]} array to an imaginary {@code Complex[]} * array. * @@ -510,8 +563,7 @@ public class ComplexUtils { */ public static Complex[][] imaginary2Complex(double[][] i) { int w = i.length; - int h = i[0].length; - Complex[][] c = new Complex[w][h]; + Complex[][] c = new Complex[w][]; for (int n = 0; n < w; n++) { c[n] = ComplexUtils.imaginary2Complex(i[n]); } @@ -529,13 +581,27 @@ public class ComplexUtils { */ public static Complex[][][] imaginary2Complex(double[][][] i) { int w = i.length; - int h = i[0].length; - int d = i[0].length; - Complex[][][] c = new Complex[w][h][d]; - for (int x = 0; x < w; x++) { - for (int y = 0; y < h; y++) { - c[x][y] = ComplexUtils.imaginary2Complex(i[x][y]); - } + Complex[][][] c = new Complex[w][][]; + for (int n = 0; n < w; n++) { + c[n] = ComplexUtils.imaginary2Complex(i[n]); + } + return c; + } + + /** + * Converts a 4D imaginary array {@code double[][][][]} to a 4D {@code Complex[][][][]} + * array. + * + * @param d 4D complex imaginary array + * @return 4D {@code Complex} array + * + * @since 1.0 + */ + public static Complex[][][][] imaginary2Complex(double[][][][] i) { + int w = i.length; + Complex[][][][] c = new Complex[w][][][]; + for (int n = 0; n < w; n++) { + c[n] = ComplexUtils.imaginary2Complex(i[n]); } return c; } @@ -647,6 +713,41 @@ public class ComplexUtils { return f; } + /** + * Converts imaginary component of a 4D {@code Complex[][][][]} array to a 4D + * {@code double[][][][]} array. + * + * @param c 4D complex interleaved array + * @return 4D {@code Complex} array + * + * @since 1.0 + */ + public static double[][][][] complex2Imaginary(Complex[][][][] c) { + final int length = c.length; + double[][][][] i = new double[length][][][]; + for (int n = 0; n < length; n++) { + i[n] = complex2Imaginary(c[n]); + } + return i; + } + + /** + * Converts imaginary component of a 4D {@code Complex[][][][]} array to a 4D + * {@code float[][][][]} array. + * + * @param c 4D {@code Complex} array + * @return {@code float[][][][]} of imaginary component + * @since 1.0 + */ + public static float[][][][] complex2ImaginaryFloat(Complex[][][][] c) { + final int length = c.length; + float[][][][] f = new float[length][][][]; + for (int n = 0; n < length; n++) { + f[n] = complex2ImaginaryFloat(c[n]); + } + return f; + } + // INTERLEAVED METHODS /** @@ -911,7 +1012,7 @@ public class ComplexUtils { /** * Converts a 3D {@code Complex[][][]} array to an interleaved complex - * {@code double[][][]} array. The third d level of the array is + * {@code double[][][]} array. The third level of the array is * interleaved. * * @param c 3D Complex array @@ -925,6 +1026,21 @@ public class ComplexUtils { } /** + * Converts a 4D {@code Complex[][][][]} array to an interleaved complex + * {@code double[][][][]} array. The fourth level of the array is + * interleaved. + * + * @param c 4D Complex array + * @return complex interleaved array alternating real and + * imaginary values + * + * @since 1.0 + */ + public static double[][][][] complex2Interleaved(Complex[][][][] c) { + return complex2Interleaved(c, 3); + } + + /** * Converts a 2D {@code Complex[][]} array to an interleaved complex * {@code float[][]} array. * http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/1de701b3/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java deleted file mode 100644 index 9c178f2..0000000 --- a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java +++ /dev/null @@ -1,282 +0,0 @@ -/* - * 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.Ignore; -import org.junit.Test; - -public class CStandardTest { - - private double inf = Double.POSITIVE_INFINITY; - private double negInf = Double.NEGATIVE_INFINITY; - private double nan = Double.NaN; - private double pi = Math.PI; - private double piOverFour = Math.PI / 4.0; - private double piOverTwo = Math.PI / 2.0; - private double threePiOverFour = 3.0*Math.PI/4.0; - private Complex oneOne = new Complex(1, 1); - private Complex oneZero = new Complex(1, 0); - private Complex oneInf = new Complex(1, inf); - private Complex oneNegInf = new Complex(1, negInf); - private Complex oneNaN = new Complex(1, nan); - private Complex zeroInf = new Complex(0, inf); - private Complex zeroNegInf = new Complex(0,negInf); - private Complex zeroNaN = new Complex(0, nan); - private Complex zeroPiTwo = new Complex(0.0, piOverTwo); - private Complex negZeroZero = new Complex(-0.0, 0); - private Complex negZeroNan = new Complex(-0.0, nan); - private Complex negI = new Complex(0.0, -1.0); - 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 infPiTwo = new Complex(inf, piOverTwo); - private Complex infPiFour = new Complex(inf, piOverFour); - private Complex infPi = new Complex(inf, Math.PI); - 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 negInfPosInf = new Complex(negInf, inf); - private Complex negInfPi = new Complex(negInf, Math.PI); - private Complex nanInf = new Complex(nan, inf); - private Complex nanNegInf = new Complex(nan, negInf); - private Complex nanZero = new Complex(nan, 0); - private Complex nanOne = new Complex(nan, 1); - private Complex piTwoNaN = new Complex(piOverTwo, nan); - private Complex piNegInf = new Complex(Math.PI, negInf); - private Complex piTwoNegInf = new Complex(piOverTwo, negInf); - private Complex piTwoNegZero = new Complex(piOverTwo, -0.0); - private Complex threePiFourNegInf = new Complex(threePiOverFour,negInf); - private Complex piFourNegInf = new Complex(piOverFour, negInf); - - public void assertComplex(Complex c1, Complex c2, double realTol, double imagTol) { - Assert.assertEquals(c1.getReal(), c2.getReal(), realTol); - Assert.assertEquals(c1.getImaginary(), c2.getImaginary(), imagTol); - } - - public void assertComplex(Complex c1, Complex c2) { - Assert.assertEquals(c1.getReal(), c2.getReal(),0.0); - Assert.assertEquals(c1.getImaginary(), c2.getImaginary(), 0.0); - } - - - /** - * ISO C Standard G.6.3 - */ - @Test - public void testSqrt1() { - Complex z1 = new Complex(-2.0, 0.0); - Complex z2 = new Complex(0.0, Math.sqrt(2)); - assertComplex(z1.sqrt(), z2); - z1 = new Complex(-2.0, -0.0); - z2 = new Complex(0.0, -Math.sqrt(2)); - assertComplex(z1.sqrt(), z2); - } - - @Test - public void testImplicitTrig() { - Complex z1 = new Complex(3.0); - Complex z2 = new Complex(0.0, 3.0); - assertComplex(z1.asin(), negI.multiply(z2.asinh())); - assertComplex(z1.atan(), negI.multiply(z2.atanh()), Math.ulp(1), Math.ulp(1)); - assertComplex(z1.cos(), z2.cosh()); - assertComplex(z1.sin(), negI.multiply(z2.sinh())); - assertComplex(z1.tan(), negI.multiply(z1.tanh())); - } - - /** - * ISO C Standard G.6.1.1 - */ - @Test - public void testAcos() { - assertComplex(oneOne.acos().conj(), oneOne.conj().acos(), Math.ulp(1), Math.ulp(1)); - assertComplex(Complex.ZERO.acos(), piTwoNegZero); - assertComplex(negZeroZero.acos(), piTwoNegZero); - assertComplex(zeroNaN.acos(), piTwoNaN); - assertComplex(oneInf.acos(), piTwoNegInf); - assertComplex(oneNaN.acos(), Complex.NaN); - assertComplex(negInfOne.acos(), piNegInf); - assertComplex(infOne.acos(), zeroNegInf); - assertComplex(negInfPosInf.acos(), threePiFourNegInf); - assertComplex(infInf.acos(), piFourNegInf); - assertComplex(infNaN.acos(), nanInf); - assertComplex(negInfNaN.acos(), nanNegInf); - assertComplex(nanOne.acos(), Complex.NaN); - assertComplex(nanInf.acos(), nanNegInf); - assertComplex(Complex.NaN.acos(), Complex.NaN); - } - - /** - * ISO C Standard G.6.2.2 - */ - @Test - public void testAsinh() { - // TODO: test for which Asinh is odd - assertComplex(oneOne.conj().asinh(), oneOne.asinh().conj()); - assertComplex(Complex.ZERO.asinh(), Complex.ZERO); - assertComplex(oneInf.asinh(), infPiTwo); - assertComplex(oneNaN.asinh(), Complex.NaN); - assertComplex(infOne.asinh(), infZero); - assertComplex(infInf.asinh(), infPiFour); - assertComplex(infNaN.asinh(), infNaN); - assertComplex(nanZero.asinh(), nanZero); - assertComplex(nanOne.asinh(), Complex.NaN); - assertComplex(nanInf.asinh(), infNaN); - assertComplex(Complex.NaN, Complex.NaN); - } - - /** - * ISO C Standard G.6.2.3 - */ - @Test - public void testAtanh() { - assertComplex(oneOne.conj().atanh(), oneOne.atanh().conj()); - assertComplex(Complex.ZERO.atanh(), Complex.ZERO); - assertComplex(zeroNaN.atanh(), zeroNaN); - assertComplex(oneZero.atanh(), infZero); - assertComplex(oneInf.atanh(),zeroPiTwo); - assertComplex(oneNaN.atanh(), Complex.NaN); - assertComplex(infOne.atanh(), zeroPiTwo); - assertComplex(infInf.atanh(), zeroPiTwo); - assertComplex(infNaN.atanh(), zeroNaN); - assertComplex(nanOne.atanh(), Complex.NaN); - assertComplex(nanInf.atanh(), zeroPiTwo); - assertComplex(Complex.NaN.atanh(), Complex.NaN); - } - - /** - * ISO C Standard G.6.2.4 - */ - @Test - public void testCosh() { - assertComplex(oneOne.cosh().conj(), oneOne.conj().cosh()); - assertComplex(Complex.ZERO.cosh(), Complex.ONE); - assertComplex(zeroInf.cosh(), nanZero); - assertComplex(zeroNaN.cosh(), nanZero); - assertComplex(oneInf.cosh(), Complex.NaN); - assertComplex(oneNaN.cosh(), Complex.NaN); - assertComplex(infZero.cosh(), infZero); - // the next test does not appear to make sense: - // (inf + iy) = inf + cis(y) - // skipped - assertComplex(infInf.cosh(), infNaN); - assertComplex(infNaN.cosh(), infNaN); - assertComplex(nanZero.cosh(), nanZero); - assertComplex(nanOne.cosh(), Complex.NaN); - assertComplex(Complex.NaN.cosh(), Complex.NaN); - } - - /** - * ISO C Standard G.6.2.5 - */ - @Test - public void testSinh() { - assertComplex(oneOne.sinh().conj(), oneOne.conj().sinh()); // AND CSINH IS ODD - assertComplex(Complex.ZERO.sinh(), Complex.ZERO); - assertComplex(zeroInf.sinh(), zeroNaN); - assertComplex(zeroNaN.sinh(), zeroNaN); - assertComplex(oneInf.sinh(), Complex.NaN); - assertComplex(oneNaN.sinh(), Complex.NaN); - assertComplex(infZero.sinh(), infZero); - // skipped test similar to previous section - assertComplex(infInf.sinh(), infNaN); - assertComplex(infNaN.sinh(), infNaN); - assertComplex(nanZero.sinh(), nanZero); - assertComplex(nanOne.sinh(), Complex.NaN); - assertComplex(Complex.NaN.sinh(), Complex.NaN); - } - - /** - * ISO C Standard G.6.2.6 - */ - @Test - public void testTanh() { - assertComplex(oneOne.tanh().conj(), oneOne.conj().tanh()); // AND CSINH IS ODD - assertComplex(Complex.ZERO.tanh(), Complex.ZERO); - assertComplex(oneInf.tanh(), Complex.NaN); - assertComplex(oneNaN.tanh(), Complex.NaN); - //Do Not Understand the Next Test - assertComplex(infInf.tanh(), oneZero); - assertComplex(infNaN.tanh(), oneZero); - assertComplex(nanZero.tanh(), nanZero); - assertComplex(nanOne.tanh(), Complex.NaN); - assertComplex(Complex.NaN.tanh(), Complex.NaN); - } - - /** - * ISO C Standard G.6.3.1 - */ - @Test - public void testExp() { - assertComplex(oneOne.conj().exp(), oneOne.exp().conj()); - assertComplex(Complex.ZERO.exp(), oneZero); - assertComplex(negZeroZero.exp(), oneZero); - assertComplex(oneInf.exp(), Complex.NaN); - assertComplex(oneNaN.exp(), Complex.NaN); - assertComplex(infZero.exp(), infZero); - // Do not understand next test - assertComplex(negInfInf.exp(), Complex.ZERO); - assertComplex(infInf.exp(), infNaN); - assertComplex(negInfNaN.exp(), Complex.ZERO); - assertComplex(infNaN.exp(), infNaN); - assertComplex(nanZero.exp(), nanZero); - assertComplex(nanOne.exp(), Complex.NaN); - assertComplex(Complex.NaN.exp(), Complex.NaN); - } - - /** - * ISO C Standard G.6.3.2 - */ - @Test - public void testLog() { - assertComplex(oneOne.log().conj(), oneOne.conj().log()); - assertComplex(negZeroZero.log(), negInfPi); - assertComplex(Complex.ZERO.log(), negInfZero); - assertComplex(oneInf.log(), infPiTwo); - assertComplex(oneNaN.log(), Complex.NaN); - assertComplex(negInfOne.log(), infPi); - assertComplex(infOne.log(), infZero); - assertComplex(infInf.log(), infPiFour); - assertComplex(infNaN.log(), infNaN); - assertComplex(nanOne.log(), Complex.NaN); - assertComplex(nanInf.log(), infNaN); - assertComplex(Complex.NaN.log(), Complex.NaN); - } - - /** - * ISO C Standard G.6.4.2 - */ - @Test - public void testSqrt2() { - assertComplex(oneOne.sqrt().conj(), oneOne.conj().sqrt()); - assertComplex(Complex.ZERO.sqrt(), Complex.ZERO); - assertComplex(oneInf.sqrt(), infInf); - assertComplex(negInfOne.sqrt(), zeroNaN); - assertComplex(infOne.sqrt(), infZero); - assertComplex(negInfNaN.sqrt(), nanInf); - assertComplex(infNaN.sqrt(), infNaN); - assertComplex(nanOne.sqrt(), Complex.NaN); - assertComplex(Complex.NaN.sqrt(), Complex.NaN); - } -} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/1de701b3/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 deleted file mode 100644 index 99a9624..0000000 --- a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java +++ /dev/null @@ -1,1366 +0,0 @@ -/* - * 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(), 0); - Assert.assertEquals(4.0, z.getImaginary(), 0); - } - - @Test - public void testAbs() { - Complex z = new Complex(3.0, 4.0); - Assert.assertEquals(5.0, z.abs(), 0); - } - - @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(), 0); - Assert.assertEquals(10.0, z.getImaginary(), 0); - } - - @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 testConjugateInfinite() { - 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 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 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 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 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 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); - assertFalseComplex(x, y); - } - - @Test - public void testEqualsImaginaryDifference() { - Complex x = new Complex(0.0, 0.0); - Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE); - assertFalseComplex(x, 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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); - Complex infcmplx = (Complex)TestUtils.serializeAndRecover(infInf); - Assert.assertEquals(infInf, infcmplx); - 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); - TestComplex inftcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(infInf)); - Assert.assertEquals(infInf, inftcmplx); - } - - /** - * 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); - } - - } - - private static void assertFalseComplex(Complex a, Complex b) { - Assert.assertFalse("Difference not detected", new Double(a.getReal()).equals(new Double(b.getReal())) && new Double(a.getImaginary()).equals(new Double(b.getImaginary()))); - } - -}
