public void ComplexExecuteTest()
{
var complex = new Complex(5, 3);
var exp = new Sqrt(new ComplexNumber(complex));
Assert.Equal(Complex.Sqrt(complex), exp.Execute());
}
public void NegativeComplexNumberExecuteTest()
{
var complex = new Complex(-25, 13);
var exp = new Sqrt(new ComplexNumber(complex));
Assert.Equal(Complex.Sqrt(complex), exp.Execute());
}
public void NegativeNumberExecuteTest2()
{
var exp = new Sqrt(new Number(-1));
Assert.Equal(new Complex(0, 1), exp.Execute());
}
public void ExecuteTest1()
{
var exp = new Sqrt(new Number(4));
Assert.Equal(Math.Sqrt(4), exp.Execute());
}
public void SqrtDerivativeTest2()
{
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Sqrt(mul);
IExpression deriv = Differentiate(exp);
Assert.AreEqual("(2 * 1) / (2 * sqrt(2 * x))", deriv.ToString());
num.Value = 3;
Assert.AreEqual("sqrt(3 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) / (2 * sqrt(2 * x))", deriv.ToString());
}
public void SqrtDerivativeTest1()
{
var exp = new Sqrt(new Mul(new Number(2), new Variable("x")));
var deriv = Differentiate(exp);
Assert.Equal("(2 * 1) / (2 * sqrt(2 * x))", deriv.ToString());
}
public void SqrtPartialDerivativeTest1()
{
// sqrt(2xy)
var exp = new Sqrt(new Mul(new Mul(new Number(2), new Variable("x")), new Variable("y")));
var deriv = Differentiate(exp);
Assert.Equal("(2 * 1 * y) / (2 * sqrt(2 * x * y))", 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 Arcsec(Arcsec expression, Variable variable)
{
var abs = new Abs(expression.Argument.Clone());
var sqr = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(sqr, new Number(1));
var sqrt = new Sqrt(sub);
var mul = new Mul(abs, sqrt);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
return div;
}
/// <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 Arcsin(Arcsin expression, Variable variable)
{
var involution = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), involution);
var sqrt = new Sqrt(sub);
var division = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
return division;
}
/// <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 Arcosh(Arcosh expression, Variable variable)
{
var sqr = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(sqr, new Number(1));
var sqrt = new Sqrt(sub);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
return div;
}
/// <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 Arcsch(Arcsch expression, Variable variable)
{
var inv = new Pow(expression.Argument.Clone(), new Number(2));
var add = new Add(new Number(1), inv);
var sqrt = new Sqrt(add);
var abs = new Abs(expression.Argument.Clone());
var mul = new Mul(abs, sqrt);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
var unMinus = new UnaryMinus(div);
return unMinus;
}
/// <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 SqrtPartialDerivativeTest2()
{
IExpression exp = new Sqrt(new Variable("y"));
IExpression deriv = Differentiate(exp);
Assert.AreEqual("0", deriv.ToString());
}
public void SqrtPartialDerivativeTest1()
{
// sqrt(2xy)
IExpression exp = new Sqrt(new Mul(new Mul(new Number(2), new Variable("x")), new Variable("y")));
IExpression deriv = Differentiate(exp);
Assert.AreEqual("((2 * 1) * y) / (2 * sqrt((2 * x) * y))", deriv.ToString());
}
public void CalculateTest()
{
IExpression exp = new Sqrt(new Number(4));
Assert.AreEqual(Math.Sqrt(4), exp.Calculate());
}
/// <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 Arsech(Arsech expression, Variable variable)
{
var inv = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), inv);
var sqrt = new Sqrt(sub);
var mul = new Mul(expression.Argument.Clone(), sqrt);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
var unMinus = new UnaryMinus(div);
return unMinus;
}
public void NegativeNumberCalculateTest()
{
var exp = new Sqrt(new Number(-25));
Assert.AreEqual(double.NaN, exp.Calculate());
}
/// <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 Arsinh(Arsinh expression, Variable variable)
{
var sqr = new Pow(expression.Argument.Clone(), new Number(2));
var add = new Add(sqr, new Number(1));
var sqrt = new Sqrt(add);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
return div;
}
public void SqrtDerivativeTest2()
{
var num = new Number(2);
var x = new Variable("x");
var mul = new Mul(num, x);
var exp = new Sqrt(mul);
var deriv = Differentiate(exp);
Assert.Equal("(2 * 1) / (2 * sqrt(2 * x))", deriv.ToString());
num.Value = 3;
Assert.Equal("sqrt(3 * x)", exp.ToString());
Assert.Equal("(2 * 1) / (2 * sqrt(2 * x))", 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 Sqrt(Sqrt expression, Variable variable)
{
var mul = new Mul(new Number(2), expression.Clone());
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
return div;
}
public void SqrtPartialDerivativeTest2()
{
var exp = new Sqrt(new Variable("y"));
var deriv = Differentiate(exp);
Assert.Equal("0", deriv.ToString());
}
/// <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;
}