/// <summary>
/// Approximates a value for a differential equation using Euler's formula
/// </summary>
/// <param name="formula">Differential formula to approximate</param>
/// <param name="step">How far forwards to go each step</param>
/// <param name="x">Initial x value</param>
/// <param name="y">Initial y value</param>
/// <param name="iterations">How many steps to take</param>
/// <returns>A double indicating y value at final value of x</returns>
public static double Eulers(Queue <Element> formula, double step, double x, double y, int iterations)
{
for (int i = iterations; i > 0; i--)
{
y += step * RPN.Compute(formula, ("x", x), ("y", y));
x += step;
}
return(y);
}
public void ComplexReset()
{
RPN test = new RPN("x^2").Compute();
PostFix math = new PostFix(test);
Assert.AreEqual(4, math.SetVariable("x", 2).Compute());
test.SetEquation("2x");
test.Compute();
math = new PostFix(test);
Assert.AreEqual(6, math.SetVariable("x", 3).Compute());
}
public void MixedDivisionMultiplication()
{
RPN test = new RPN("1/2x");
test.Data.ImplicitMultiplicationPriority = true;
test.Compute();
Assert.AreEqual("1 2 x * /", test.Polish.Print());
test.SetEquation("8/2(2 + 2)").Compute();
Assert.AreEqual("8 2 4 * /", test.Polish.Print());
test.Data.ImplicitMultiplicationPriority = false;
test.SetEquation("1/2x").Compute();
Assert.AreEqual("x 2 /", test.Polish.Print());
test.SetEquation("8/2(2 + 2)").Compute();
Assert.AreEqual("16", test.Polish.Print());
}
/// <summary>
/// Integrates a function using the mid-ordinate approximation
/// </summary>
/// <param name="function">Function to integrate</param>
/// <param name="lowerBound">Lower bound of integration</param>
/// <param name="upperBound">Upper bound of integration</param>
/// <param name="numOrdinates">Number of ordinates to integrate with</param>
/// <returns>A double? where null means it was an invalid operation</returns>
public static double?MidOrdinate(Queue <Element> function, double lowerBound, double upperBound, double numOrdinates)
{
//if lower bound is higher than upper bound, then it's invalid
if (lowerBound >= upperBound)
{
return(null);
}
//find the distance between ordinates
double h = (upperBound - lowerBound) / numOrdinates;
double sum = 0;
//compute the function at midpoints between the ordinates, and add up
for (double i = lowerBound; i < upperBound; i += h)
{
sum += RPN.Compute(function, ("x", i + h / 2));
}
sum *= h;
return(sum);
}
/// <summary>
/// Integrates a function using simpson's approximation
/// </summary>
/// <param name="function">Function to integrate</param>
/// <param name="lowerBound">Lower bound of integration</param>
/// <param name="upperBound">Upper bound of integration</param>
/// <param name="numOrdinates">Number of ordinates to integrate with</param>
/// <returns>A double? where null means it was an invalid operation</returns>
public static double?Simpsons(Queue <Element> function, double lowerBound, double upperBound, double numOrdinates)
{
//if lower bound is higher than upper bound, then it's invalid
if (lowerBound >= upperBound)
{
return(null);
}
//find the distance between ordinates
double h = (upperBound - lowerBound) / numOrdinates;
//calculate the sum of the first and last ordinate
double firstSum = RPN.Compute(function, ("x", lowerBound)) + RPN.Compute(function, ("x", upperBound));
//calculate the sum of the odd ordinates
double secondSum = 0;
for (double i = lowerBound + h; i < upperBound; i += 2 * h)
{
secondSum += RPN.Compute(function, ("x", i));
}
//calculate the sum of the even ordinates
double thirdSum = 0;
for (double i = lowerBound + 2 * h; i < upperBound; i += 2 * h)
{
thirdSum += RPN.Compute(function, ("x", i));
}
//find total sum from the calculated values
double sum = firstSum + 4 * secondSum + 2 * thirdSum;
sum *= h / 3;
return(sum);
}
public void ComputeTests(double expected, string input, double xValue = 0)
{
Queue <Element> elements = new();
foreach (string token in input.Split(' '))
{
if (double.TryParse(token, out double number))
{
elements.Enqueue(new Value(number));
}
else if (OperatorsHelper.TryParse(token, out Operators op))
{
elements.Enqueue(new Operator(op));
}
else
{
elements.Enqueue(new Variable(token));
}
}
double value = RPN.Compute(elements, ("x", xValue));
Assert.AreEqual(expected, value, 1e-6);
}
static void Main(string[] args)
{
Console.Title = "AbMath v1.0.4";
Console.WindowWidth = Console.BufferWidth;
Console.WriteLine("(C) 2018. Abhishek Sathiabalan");
Console.WriteLine("Recent Changes:");
Console.WriteLine("Unary negative is now implemented.");
Console.WriteLine("Composite Function bug should now be fixed.");
Console.WriteLine("Implicit multiplication.");
Console.WriteLine("Variadic Function Support");
Console.WriteLine();
while (true)
{
Console.ForegroundColor = ConsoleColor.Gray;
string equation = string.Empty;
while (string.IsNullOrWhiteSpace(equation))
{
Console.Write("Equation>");
equation = Console.ReadLine();
if (equation.Length == 0)
{
Console.Clear();
}
}
RPN = new RPN(equation);
if (RPN.Data.MarkdownTables)
{
Console.Clear();
Console.WriteLine($"Equation>``{equation}``");
}
RPN.Logger += Write;
RPN.Output += Write;
RPN.Compute();
PostFix postFix = new PostFix(RPN);
postFix.Logger += Write;
if (RPN.ContainsVariables)
{
Console.WriteLine("Set the variables");
for (int i = 0; i < RPN.Data.Variables.Count; i++)
{
Console.Write(RPN.Data.Variables[i] + "=");
postFix.SetVariable(RPN.Data.Variables[i], Console.ReadLine());
}
}
Console.ForegroundColor = ConsoleColor.White;
double answer = postFix.Compute();
if (RPN.Data.MarkdownTables)
{
Console.Write($"Answer: ``{answer}``");
}
else
{
Console.Write($"Answer: {answer}");
}
Console.WriteLine();
Console.WriteLine(RPN.Data.TimeRecords().ToString());
Console.WriteLine();
Console.ForegroundColor = ConsoleColor.Gray;
Console.Write("Press any key to continue...");
Console.ReadKey(true);
Console.Clear();
}
void Write(object sender, string Event)
{
Console.WriteLine(Event);
}
}
public void RPNIntegrationTests(double expected, string input, double xValue = 0)
{
Queue <Element> calculated = RPN.SYA(input);
Assert.AreEqual(expected, RPN.Compute(calculated, ("x", xValue)), 1e-6);
}