// <copyright file="ComplexTest.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
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using Complex = System.Numerics.Complex;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.ComplexTests
{
    /// <summary>
    /// Complex extension methods tests.
    /// </summary>
    [TestFixture]
    public class ComplexExtensionTest
    {
        /// <summary>
        /// Can compute exponential.
        /// </summary>
        /// <param name="real">Real part.</param>
        /// <param name="imag">Imaginary part.</param>
        /// <param name="expectedReal">Expected real part.</param>
        /// <param name="expectedImag">Expected imaginary part.</param>
        [TestCase(0.0, 0.0, 1.0, 0.0)]
        [TestCase(0.0, 1.0, 0.54030230586813977, 0.8414709848078965)]
        [TestCase(-1.0, 1.0, 0.19876611034641295, 0.30955987565311222)]
        [TestCase(-111.1, 111.1, -2.3259065941590448e-49, -5.1181940185795617e-49)]
        public void CanComputeExponential(double real, double imag, double expectedReal, double expectedImag)
        {
            var value = new Complex(real, imag);
            var expected = new Complex(expectedReal, expectedImag);
            AssertHelpers.AlmostEqualRelative(expected, value.Exp(), 14);
        }

        /// <summary>
        /// Can compute natural logarithm.
        /// </summary>
        /// <param name="real">Real part.</param>
        /// <param name="imag">Imaginary part.</param>
        /// <param name="expectedReal">Expected real part.</param>
        /// <param name="expectedImag">Expected imaginary part.</param>
        [TestCase(0.0, 0.0, double.NegativeInfinity, 0.0)]
        [TestCase(0.0, 1.0, 0.0, 1.5707963267948966)]
        [TestCase(-1.0, 1.0, 0.34657359027997264, 2.3561944901923448)]
        [TestCase(-111.1, 111.1, 5.0570042869255571, 2.3561944901923448)]
        [TestCase(111.1, -111.1, 5.0570042869255571, -0.78539816339744828)]
        public void CanComputeNaturalLogarithm(double real, double imag, double expectedReal, double expectedImag)
        {
            var value = new Complex(real, imag);
            var expected = new Complex(expectedReal, expectedImag);
            AssertHelpers.AlmostEqualRelative(expected, value.Ln(), 14);
        }

        /// <summary>
        /// Can compute power.
        /// </summary>
        [Test]
        public void CanComputePower()
        {
            var a = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
            var b = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(
                new Complex(9.99998047207974718744e-1, -1.76553541154378695012e-6), a.Power(b), 14);
            a = new Complex(0.0, 1.19209289550780998537e-7);
            b = new Complex(0.0, -1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(new Complex(1.00000018725172576491, 1.90048076369011843105e-6), a.Power(b), 14);
            a = new Complex(0.0, -1.19209289550780998537e-7);
            b = new Complex(0.0, 0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(-2.56488189382693049636e-1, -2.17823120666116144959), a.Power(b), 14);
            a = new Complex(0.0, 0.5);
            b = new Complex(0.0, -0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(2.06287223508090495171, 7.45007062179724087859e-1), a.Power(b), 14);
            a = new Complex(0.0, -0.5);
            b = new Complex(0.0, 1.0);
            AssertHelpers.AlmostEqualRelative(new Complex(3.70040633557002510874, -3.07370876701949232239), a.Power(b), 14);
            a = new Complex(0.0, 2.0);
            b = new Complex(0.0, -2.0);
            AssertHelpers.AlmostEqualRelative(new Complex(4.24532146387429353891, -2.27479427903521192648e1), a.Power(b), 14);
            a = new Complex(0.0, -8.388608e6);
            b = new Complex(1.19209289550780998537e-7, 0.0);
            AssertHelpers.AlmostEqualRelative(new Complex(1.00000190048219620166, -1.87253870018168043834e-7), a.Power(b), 14);
            a = new Complex(0.0, 0.0);
            b = new Complex(0.0, 0.0);
            AssertHelpers.AlmostEqualRelative(new Complex(1.0, 0.0), a.Power(b), 14);
            a = new Complex(0.0, 0.0);
            b = new Complex(1.0, 0.0);
            AssertHelpers.AlmostEqualRelative(new Complex(0.0, 0.0), a.Power(b), 14);

            a = new Complex(0.0, 0.0);
            b = new Complex(-1.0, 0.0);
            AssertHelpers.AlmostEqualRelative(new Complex(double.PositiveInfinity, 0.0), a.Power(b), 14);
            a = new Complex(0.0, 0.0);
            b = new Complex(-1.0, 1.0);
            AssertHelpers.AlmostEqualRelative(new Complex(double.PositiveInfinity, double.PositiveInfinity), a.Power(b), 14);
            a = new Complex(0.0, 0.0);
            b = new Complex(0.0, 1.0);
            Assert.That(a.Power(b).IsNaN());
        }

        /// <summary>
        /// Can compute root.
        /// </summary>
        [Test]
        public void CanComputeRoot()
        {
            var a = new Complex(0.0, -1.19209289550780998537e-7);
            var b = new Complex(0.0, 0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(0.038550761943650161, 0.019526430428319544), a.Root(b), 13);
            a = new Complex(0.0, 0.5);
            b = new Complex(0.0, -0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(0.007927894711475968, -0.042480480425152213), a.Root(b), 13);
            a = new Complex(0.0, -0.5);
            b = new Complex(0.0, 1.0);
            AssertHelpers.AlmostEqualRelative(new Complex(0.15990905692806806, 0.13282699942462053), a.Root(b), 13);
            a = new Complex(0.0, 2.0);
            b = new Complex(0.0, -2.0);
            AssertHelpers.AlmostEqualRelative(new Complex(0.42882900629436788, 0.15487175246424678), a.Root(b), 13);

            //a = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
            //b = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
            //AssertHelpers.AlmostEqual(new Complex(0.0, 0.0), a.Root(b), 15);
            a = new Complex(0.0, -8.388608e6);
            b = new Complex(1.19209289550780998537e-7, 0.0);
            AssertHelpers.AlmostEqualRelative(new Complex(double.PositiveInfinity, double.NegativeInfinity), a.Root(b), 14);
        }

        /// <summary>
        /// Can compute square.
        /// </summary>
        [Test]
        public void CanComputeSquare()
        {
            var complex = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(new Complex(0, 2.8421709430403888e-14), complex.Square(), 15);
            complex = new Complex(0.0, 1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(new Complex(-1.4210854715201944e-14, 0.0), complex.Square(), 15);
            complex = new Complex(0.0, -1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(new Complex(-1.4210854715201944e-14, 0.0), complex.Square(), 15);
            complex = new Complex(0.0, 0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(-0.25, 0.0), complex.Square(), 15);
            complex = new Complex(0.0, -0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(-0.25, 0.0), complex.Square(), 15);
            complex = new Complex(0.0, -8.388608e6);
            AssertHelpers.AlmostEqualRelative(new Complex(-70368744177664.0, 0.0), complex.Square(), 15);
        }

        /// <summary>
        /// Can compute square root.
        /// </summary>
        [Test]
        public void CanComputeSquareRoot()
        {
            var complex = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(
                new Complex(0.00037933934912842666, 0.00015712750315077684), complex.SquareRoot(), 14);
            complex = new Complex(0.0, 1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(
                new Complex(0.00024414062499999973, 0.00024414062499999976), complex.SquareRoot(), 14);
            complex = new Complex(0.0, -1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(
                new Complex(0.00024414062499999973, -0.00024414062499999976), complex.SquareRoot(), 14);
            complex = new Complex(0.0, 0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(0.5, 0.5), complex.SquareRoot(), 14);
            complex = new Complex(0.0, -0.5);
            AssertHelpers.AlmostEqualRelative(new Complex(0.5, -0.5), complex.SquareRoot(), 14);
            complex = new Complex(0.0, -8.388608e6);
            AssertHelpers.AlmostEqualRelative(new Complex(2048.0, -2048.0), complex.SquareRoot(), 14);
            complex = new Complex(8.388608e6, 1.19209289550780998537e-7);
            AssertHelpers.AlmostEqualRelative(new Complex(2896.3093757400989, 2.0579515874459933e-11), complex.SquareRoot(), 14);
            complex = new Complex(0.0, 0.0);
            AssertHelpers.AlmostEqualRelative(Complex.Zero, complex.SquareRoot(), 14);
        }

        /// <summary>
        /// Can determine if imaginary is unit.
        /// </summary>
        [Test]
        public void CanDetermineIfImaginaryUnit()
        {
            var complex = new Complex(0, 1);
            Assert.IsTrue(complex.IsImaginaryOne(), "Imaginary unit");
        }

        /// <summary>
        /// Can determine if a complex is infinity.
        /// </summary>
        [Test]
        public void CanDetermineIfInfinity()
        {
            var complex = new Complex(double.PositiveInfinity, 1);
            Assert.IsTrue(complex.IsInfinity(), "Real part is infinity.");
            complex = new Complex(1, double.NegativeInfinity);
            Assert.IsTrue(complex.IsInfinity(), "Imaginary part is infinity.");
            complex = new Complex(double.NegativeInfinity, double.PositiveInfinity);
            Assert.IsTrue(complex.IsInfinity(), "Both parts are infinity.");
        }

        /// <summary>
        /// Can determine if a complex is not a number.
        /// </summary>
        [Test]
        public void CanDetermineIfNaN()
        {
            var complex = new Complex(double.NaN, 1);
            Assert.IsTrue(complex.IsNaN(), "Real part is NaN.");
            complex = new Complex(1, double.NaN);
            Assert.IsTrue(complex.IsNaN(), "Imaginary part is NaN.");
            complex = new Complex(double.NaN, double.NaN);
            Assert.IsTrue(complex.IsNaN(), "Both parts are NaN.");
        }

        /// <summary>
        /// Can determine Complex number with a value of one.
        /// </summary>
        [Test]
        public void CanDetermineIfOneValueComplexNumber()
        {
            var complex = new Complex(1, 0);
            Assert.IsTrue(complex.IsOne(), "Complex number with a value of one.");
        }

        /// <summary>
        /// Can determine if a complex is a real non-negative number.
        /// </summary>
        [Test]
        public void CanDetermineIfRealNonNegativeNumber()
        {
            var complex = new Complex(1, 0);
            Assert.IsTrue(complex.IsReal(), "Is a real non-negative number.");
        }

        /// <summary>
        /// Can determine if a complex is a real number.
        /// </summary>
        [Test]
        public void CanDetermineIfRealNumber()
        {
            var complex = new Complex(-1, 0);
            Assert.IsTrue(complex.IsReal(), "Is a real number.");
        }

        /// <summary>
        /// Can determine if a complex is a zero number.
        /// </summary>
        [Test]
        public void CanDetermineIfZeroValueComplexNumber()
        {
            var complex = new Complex(0, 0);
            Assert.IsTrue(complex.IsZero(), "Zero complex number.");
        }
    }
}
