public void ComplexTrigSpecialCases()
{
Assert.IsTrue(ComplexMath.Sin(0.0) == Complex.Zero);
Assert.IsTrue(ComplexMath.Cos(0.0) == Complex.One);
Assert.IsTrue(ComplexMath.Tan(0.0) == Complex.Zero);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(Math.PI / 2.0), 1.0, TestUtilities.RelativeTarget));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tan(Math.PI / 4.0), 1.0, TestUtilities.RelativeTarget));
}
public void ComplexNegativeAngles()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 16))
{
if (Math.Abs(z.Im) > Math.Log(Double.MaxValue / 10.0))
{
continue; // sin and cos blow up in imaginary part of argument gets too big
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(-z), -ComplexMath.Sin(z)), String.Format("remainder {0}", ComplexMath.Sin(-a) + ComplexMath.Sin(a)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(-z), ComplexMath.Cos(z)), String.Format("{0} vs. {1}", ComplexMath.Cos(-a), ComplexMath.Cos(a)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tan(-z), -ComplexMath.Tan(z)));
}
}
public void ComplexSecTanTest()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 10))
{
if (Math.Abs(z.Im) > Math.Log(Double.MaxValue / 10.0))
{
continue; // sin and cos blow up in imaginary part of argument gets too big
}
Complex sec = 1.0 / ComplexMath.Cos(z);
Complex tan = ComplexMath.Tan(z);
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(sec * sec, -tan * tan, 1));
}
}
public void ComplexSecTanTest()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-3, 1.0E3, 16))
{
// Since sin(z) and cos(z) have factors that go like e^{\pm Im(z)}, they will blow up if the imaginary
// part of z gets too big. We just skip over those problematic values.
if (Math.Abs(z.Im) > Math.Log(Double.MaxValue) / 2.0)
{
continue;
}
Complex sec = 1.0 / ComplexMath.Cos(z);
Complex tan = ComplexMath.Tan(z);
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(sec * sec, -tan * tan, 1));
}
}
public void ComplexTanTanh()
{
foreach (Complex x in TestUtilities.GenerateComplexValues(1.0E-3, 1.0E3, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tanh(x), -ComplexMath.I * ComplexMath.Tan(ComplexMath.I * x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tanh(-ComplexMath.I * x), -ComplexMath.I * ComplexMath.Tan(x)));
}
}