public void TestRound(string input, int decimals, string expected)
{
var number = Number.Parse(input, CultureInfo.InvariantCulture);
var op = NumberMath.Round(number, decimals).ToString();
Assert.AreEqual(expected, op);
}
public void TestCos(double input, double expected)
{
NumberMath.AngleMode = AngleMode.Deg;
Number result = NumberMath.Cos(input);
AreEqual(expected, result, 1E-12);
}
public static PolynomialTerm Cos(PolynomialTerm name)
{
if (name.IsConstant)
{
return(NumberMath.RoundedCos((double)name));
}
else
{
return(IndeterminateExpression.Cos((char)name));
}
}
private void AreEqual(Number expected, Number result, Number diff)
{
if (result.State == NumberState.Value &&
expected.State == NumberState.Value)
{
bool assert = NumberMath.Abs(expected - result) < diff;
Assert.IsTrue(assert);
}
else
{
Assert.IsTrue(expected.State == result.State);
}
}
public static void AreEqual(Number expected, Number result, double delta = 0.0)
{
if (NumberAlgorithms.IsSpecialState(expected) &&
NumberAlgorithms.IsSpecialState(result) &&
expected.State != result.State)
{
Assert.Fail("Expected: {0}, result: {1}", expected, result);
}
else
{
Assert.Pass();
}
var diff = NumberMath.Abs(expected - result) < delta;
if (!diff)
{
Assert.Fail("Expected: {0}, result: {1}", expected, result);
}
Assert.Pass();
}
protected override Number Evaluate(Number number1, Number number2)
{
return(NumberMath.Pow(number1, number2));
}
public override IExpression?Differentiate(string byVariable)
{
if (Right is ConstantExpression)
{
// f(x) = g(x)^n
// f'(x) = n * g'(x) * g(x)^(n-1)
return
(new MultiplyExpression(new MultiplyExpression(Right, Left?.Differentiate(byVariable)),
new ExponentExpression(Left, new SubtractExpression(Right, new ConstantExpression(1)))));
}
var simple = Left?.Simplify();
if (simple is ConstantExpression constant)
{
// f(x) = a^g(x)
// f'(x) = (ln a) * g'(x) * a^g(x)
var a = constant.Value;
return(new MultiplyExpression(new MultiplyExpression(new ConstantExpression(NumberMath.Ln(a)), Right?.Differentiate(byVariable)), new ExponentExpression(simple, Right)));
}
throw new CannotDifferentiateException(Resources.CanotDifferentiate);
}
protected override Number Evaluate(Number number)
{
return(NumberMath.Round(NumberMath.Cos(number), 21));
}
public void TestFactorial(int n, double expected)
{
Number result = NumberMath.Factorial(n);
AreEqual(expected, result, 1E-9);
}
public void TestRadToGrad(double rad, double expectedGrad)
{
Number result = NumberMath.RadToGrad(rad);
AreEqual(expectedGrad, result, 1E-9);
}
private static Number FactorialWrapper(Number arg)
{
return(NumberMath.Factorial((int)arg.ToDouble()));
}
public void TestGradToDeg(double grad, double expectedDeg)
{
Number result = NumberMath.GradToDeg(grad);
AreEqual(expectedDeg, result, 1E-9);
}
public void TestDegToGrad(double deg, double expectedGrad)
{
Number result = NumberMath.DegToGrad(deg);
AreEqual(expectedGrad, result, 1E-9);
}
public void RoundedCosTests(double value, double expected)
{
NumberMath.RoundedCos(value).AssertIsEqualTo(expected);
}
protected override Number Evaluate(Number number)
{
return(NumberMath.Ln(number));
}
public void TestGradToRad(double grad, double expectedRad)
{
Number result = NumberMath.GradToRad(grad);
AreEqual(expectedRad, result, 1E-9);
}
/// <summary>
/// Integrates the expression with Simpson algorithm
/// </summary>
/// <param name="expression">Expression to integrate</param>
/// <param name="var">Integrate by which expression</param>
/// <param name="from">Start value</param>
/// <param name="to">End value</param>
/// <param name="steps">Number of steps</param>
/// <returns>Integration result</returns>
public static INumber Integrate(this IExpression expression, string var, INumber from, INumber to, int steps = 2048)
{
Number?_from = from as Number;
Number?_to = to as Number;
if (_from == null || _to == null)
{
throw new ExpressionEngineException();
}
if (_to < _from)
{
throw new ArgumentException(Resources.IntegrateErrorRange);
}
if (steps < 2 || (steps % 2 == 1))
{
throw new ArgumentException(Resources.InvalidSteps);
}
var flatExpression = expression.Flatten();
var vars = flatExpression.FirstOrDefault(e => e.Variables != null)?.Variables;
bool trigonometric = flatExpression.Any(e => IsTrigonometricNode(e));
if (trigonometric)
{
switch (NumberMath.AngleMode)
{
case AngleMode.Deg:
_from = NumberMath.DegToRad(_from);
_to = NumberMath.DegToRad(_to);
break;
case AngleMode.Grad:
_from = NumberMath.DegToGrad(_from);
_to = NumberMath.DegToGrad(_to);
break;
}
}
if (vars == null)
{
throw new InvalidOperationException(Resources.NoVariables);
}
if (string.IsNullOrEmpty(var))
{
throw new ArgumentNullException(nameof(var));
}
AngleMode old = NumberMath.AngleMode;
NumberMath.AngleMode = AngleMode.Rad;
Number h = (_to - _from) / steps;
Number x = _from + h;
Number s = 0.0;
for (int i = 1; i < steps / 2; i++)
{
vars[var] = x;
Number Fx = (expression.Evaluate() as Number) !;
vars[var] = x + h;
Number Fx2 = (expression.Evaluate() as Number) !;
s = s + (2 * Fx) + Fx2;
x += 2 * h;
}
vars[var] = from;
Number Fxa = (expression.Evaluate() as Number) !;
vars[var] = to;
Number Fxb = (expression.Evaluate() as Number) !;
vars[var] = _to - h;
Number Fxhb = (expression.Evaluate() as Number) !;
Number result = (h / 3) * ((2 * s) + Fxa + Fxb + (4 * Fxhb));
NumberMath.AngleMode = old;
return(NumberMath.Round(result, 15));
}