public void DerivativeTest1()
{
IExpression exp = new Arccos(new Variable("x"));
IExpression deriv = exp.Differentiate();
Assert.AreEqual("-(1 / sqrt(1 - (x ^ 2)))", deriv.ToString());
}
public void DerivativeTest2()
{
IExpression exp = new Arccos(new Mul(new Number(2), new Variable("x")));
IExpression deriv = exp.Differentiate();
Assert.AreEqual("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
}
public void CloneTest()
{
var exp = new Arccos(new Number(1));
var clone = exp.Clone();
Assert.Equal(exp, clone);
}
public void ExecuteComplexNumberTest()
{
var complex = new Complex(3, 2);
var exp = new Arccos(new ComplexNumber(complex));
var result = (Complex)exp.Execute();
Assert.Equal(Complex.Acos(complex), result);
Assert.Equal(0.60613782238729386, result.Real, 15);
Assert.Equal(-1.9686379257930964, result.Imaginary, 15);
}
public void DerivativeTest3()
{
// arccos(2x)
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Arccos(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
num.Value = 6;
Assert.AreEqual("arccos(6 * x)", exp.ToString());
Assert.AreEqual("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
}
public void CalculateRadianTest()
{
IExpression exp = new Arccos(new Number(1));
Assert.AreEqual(Math.Acos(1), exp.Calculate(AngleMeasurement.Radian));
}
public void CalculateDegreeTest()
{
IExpression exp = new Arccos(new Number(1));
Assert.AreEqual(Math.Acos(1) / Math.PI * 180, exp.Calculate(AngleMeasurement.Degree));
}
public void ArccosPartialDerivativeTest3()
{
var exp = new Arccos(new Variable("x"));
var deriv = Differentiate(exp, new Variable("y"));
Assert.Equal("0", deriv.ToString());
}
public void PartialDerivativeTest3()
{
IExpression exp = new Arccos(new Variable("x"));
IExpression deriv = exp.Differentiate(new Variable("y"));
Assert.AreEqual("0", deriv.ToString());
}
public void ArccosDerivativeTest2()
{
var exp = new Arccos(new Mul(new Number(2), new Variable("x")));
var deriv = Differentiate(exp);
Assert.Equal("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
}
public void ArccosDerivativeTest1()
{
var exp = new Arccos(new Variable("x"));
var deriv = Differentiate(exp);
Assert.Equal("-(1 / sqrt(1 - (x ^ 2)))", deriv.ToString());
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arccos(Arccos expression, Variable variable)
{
var pow = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), pow);
var sqrt = new Sqrt(sub);
var division = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
var unMinus = new UnaryMinus(division);
return unMinus;
}
public void ExecuteRadianTest()
{
var exp = new Arccos(new Number(1));
Assert.Equal(Math.Acos(1), exp.Execute(AngleMeasurement.Radian));
}
public void ExecuteDegreeTest()
{
var exp = new Arccos(new Number(1));
Assert.Equal(Math.Acos(1) / Math.PI * 180, exp.Execute(AngleMeasurement.Degree));
}
public void ArccosDerivativeTest3()
{
// arccos(2x)
var num = new Number(2);
var x = new Variable("x");
var mul = new Mul(num, x);
var exp = new Arccos(mul);
var deriv = Differentiate(exp);
Assert.Equal("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
num.Value = 6;
Assert.Equal("arccos(6 * x)", exp.ToString());
Assert.Equal("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
}
public void PartialDerivativeTest2()
{
IExpression exp = new Arccos(new Mul(new Variable("x"), new Variable("y")));
IExpression deriv = exp.Differentiate(new Variable("y"));
Assert.AreEqual("-((x * 1) / sqrt(1 - ((x * y) ^ 2)))", deriv.ToString());
}
public void ArccosPartialDerivativeTest2()
{
var exp = new Arccos(new Mul(new Variable("x"), new Variable("y")));
var deriv = Differentiate(exp, new Variable("y"));
Assert.Equal("-((x * 1) / sqrt(1 - ((x * y) ^ 2)))", deriv.ToString());
}
public void ArccosCos()
{
var exp = new Arccos(new Cos(new Variable("x")));
var expected = new Variable("x");
SimpleTest(exp, expected);
}
/// <summary>
/// Creates an expression object from <see cref="FunctionToken"/>.
/// </summary>
/// <param name="token">The function token.</param>
/// <returns>An expression.</returns>
protected virtual IExpression CreateFunction(FunctionToken token)
{
IExpression exp;
switch (token.Function)
{
case Functions.Add:
exp = new Add(); break;
case Functions.Sub:
exp = new Sub(); break;
case Functions.Mul:
exp = new Mul(); break;
case Functions.Div:
exp = new Div(); break;
case Functions.Pow:
exp = new Pow(); break;
case Functions.Absolute:
exp = new Abs(); break;
case Functions.Sine:
exp = new Sin(); break;
case Functions.Cosine:
exp = new Cos(); break;
case Functions.Tangent:
exp = new Tan(); break;
case Functions.Cotangent:
exp = new Cot(); break;
case Functions.Secant:
exp = new Sec(); break;
case Functions.Cosecant:
exp = new Csc(); break;
case Functions.Arcsine:
exp = new Arcsin(); break;
case Functions.Arccosine:
exp = new Arccos(); break;
case Functions.Arctangent:
exp = new Arctan(); break;
case Functions.Arccotangent:
exp = new Arccot(); break;
case Functions.Arcsecant:
exp = new Arcsec(); break;
case Functions.Arccosecant:
exp = new Arccsc(); break;
case Functions.Sqrt:
exp = new Sqrt(); break;
case Functions.Root:
exp = new Root(); break;
case Functions.Ln:
exp = new Ln(); break;
case Functions.Lg:
exp = new Lg(); break;
case Functions.Lb:
exp = new Lb(); break;
case Functions.Log:
exp = new Log(); break;
case Functions.Sineh:
exp = new Sinh(); break;
case Functions.Cosineh:
exp = new Cosh(); break;
case Functions.Tangenth:
exp = new Tanh(); break;
case Functions.Cotangenth:
exp = new Coth(); break;
case Functions.Secanth:
exp = new Sech(); break;
case Functions.Cosecanth:
exp = new Csch(); break;
case Functions.Arsineh:
exp = new Arsinh(); break;
case Functions.Arcosineh:
exp = new Arcosh(); break;
case Functions.Artangenth:
exp = new Artanh(); break;
case Functions.Arcotangenth:
exp = new Arcoth(); break;
case Functions.Arsecanth:
exp = new Arsech(); break;
case Functions.Arcosecanth:
exp = new Arcsch(); break;
case Functions.Exp:
exp = new Exp(); break;
case Functions.GCD:
exp = new GCD(); break;
case Functions.LCM:
exp = new LCM(); break;
case Functions.Factorial:
exp = new Fact(); break;
case Functions.Sum:
exp = new Sum(); break;
case Functions.Product:
exp = new Product(); break;
case Functions.Round:
exp = new Round(); break;
case Functions.Floor:
exp = new Floor(); break;
case Functions.Ceil:
exp = new Ceil(); break;
case Functions.Derivative:
exp = new Derivative(); break;
case Functions.Simplify:
exp = new Simplify(); break;
case Functions.Del:
exp = new Del(); break;
case Functions.Define:
exp = new Define(); break;
case Functions.Vector:
exp = new Vector(); break;
case Functions.Matrix:
exp = new Matrix(); break;
case Functions.Transpose:
exp = new Transpose(); break;
case Functions.Determinant:
exp = new Determinant(); break;
case Functions.Inverse:
exp = new Inverse(); break;
case Functions.If:
exp = new If(); break;
case Functions.For:
exp = new For(); break;
case Functions.While:
exp = new While(); break;
case Functions.Undefine:
exp = new Undefine(); break;
case Functions.Im:
exp = new Im(); break;
case Functions.Re:
exp = new Re(); break;
case Functions.Phase:
exp = new Phase(); break;
case Functions.Conjugate:
exp = new Conjugate(); break;
case Functions.Reciprocal:
exp = new Reciprocal(); break;
case Functions.Min:
exp = new Min(); break;
case Functions.Max:
exp = new Max(); break;
case Functions.Avg:
exp = new Avg(); break;
case Functions.Count:
exp = new Count(); break;
case Functions.Var:
exp = new Var(); break;
case Functions.Varp:
exp = new Varp(); break;
case Functions.Stdev:
exp = new Stdev(); break;
case Functions.Stdevp:
exp = new Stdevp(); break;
default:
exp = null; break;
}
var diff = exp as DifferentParametersExpression;
if (diff != null)
diff.ParametersCount = token.CountOfParams;
return exp;
}