public void CalculateTurningPointsTest2()
{
//y = x*x*x - x*x - x +1
//y' = 3x*x -2x -1 = (3x+1)(x-1)
//Stationary points solutions x = -1/3 (peak) , +1 (trough)
List <DPoint> points = new List <DPoint>();
for (double x = -10; x < 10; x = x + 0.01)
{
double y = x * x * x - x * x - x + 1;
points.Add(new DPoint(x, y));
}
Differentiator differentiator = new Differentiator(points);
differentiator.SampleSize = 9;
DPoint[] diffPoints = differentiator.Differentiate();
StationaryPoints target = new StationaryPoints(points.ToArray(), diffPoints);
target.Threshold = 0;
TurningPoint[] actual;
actual = target.CalculateTurningPoints();
Assert.AreEqual(2, actual.Length);
Assert.IsTrue(actual[0].IsPeak);
Assert.AreEqual("-0.33", actual[0].Point.X.ToString("0.00"));
Assert.IsFalse(actual[1].IsPeak);
Assert.AreEqual("1.00", actual[1].Point.X.ToString("0.00"));
}
public void Accuracy()
{
List <DPoint> points = new List <DPoint>();
for (int i = -100; i < 101; i++)
{
double x = (double)i;
double y = 3 * x * x - 2 * x + 1;
points.Add(new DPoint(x, y));
}
Differentiator target = new Differentiator(points);
DPoint[] diffPoints = target.Differentiate();
//x=0, y' = -2
Assert.AreEqual(0d, diffPoints[100].X);
Assert.AreEqual(-2d, diffPoints[100].Y);
//x=1, y'=4
Assert.AreEqual(1d, diffPoints[101].X);
Assert.AreEqual(4d, diffPoints[101].Y);
//x=-1, y'=-8
Assert.AreEqual(-1d, diffPoints[99].X);
Assert.AreEqual(-8d, diffPoints[99].Y);
//x=42, y'=250
Assert.AreEqual(42d, diffPoints[142].X);
Assert.AreEqual(250d, diffPoints[142].Y);
}
public void EndPoints()
{
DPoint[] points = createPoints();
Differentiator target = new Differentiator(points);
DPoint[] diffPoints = target.Differentiate();
Assert.AreEqual(0, diffPoints[0].X);
Assert.AreEqual(1, diffPoints[0].Y);
Assert.AreEqual(999, diffPoints[999].X);
Assert.AreEqual(-1, diffPoints[999].Y);
}
public void SampleSize()
{
Differentiator target = new Differentiator();
target.SampleSize = 9;
//y=2x+1
target.Add(new DPoint(0, 1));
target.Add(new DPoint(1, 3));
target.Add(new DPoint(2, 5));
DPoint[] diffPoints = target.Differentiate();
Assert.AreEqual(3, diffPoints.Length);
//expect best line fit, which has gadient of 2
Assert.AreEqual(2, diffPoints[0].Y);
Assert.AreEqual(2, diffPoints[1].Y);
Assert.AreEqual(2, diffPoints[2].Y);
}
public void Differentiate1()
{
DPoint[] points = createPoints();
Differentiator target = new Differentiator(points);
DPoint[] diffPoints = target.Differentiate();
Assert.AreEqual(points.Length, diffPoints.Length);
Assert.AreEqual(points[50].X, diffPoints[50].X);
Assert.AreEqual(points[500].X, diffPoints[500].X);
//gradient = 1
Assert.AreEqual(1d, diffPoints[50].Y);
//gradient = -1
Assert.AreEqual(-1d, diffPoints[150].Y);
//turning point
Assert.AreEqual(0d, diffPoints[100].Y);
}
public void CalculateTurningPointsTest2()
{
//y = x*x*x - x*x - x +1
//y' = 3x*x -2x -1 = (3x+1)(x-1)
//Stationary points solutions x = -1/3 (peak) , +1 (trough)
List<DPoint> points = new List<DPoint>();
for (double x = -10; x < 10; x=x+0.01)
{
double y = x * x * x - x * x - x + 1;
points.Add(new DPoint(x, y));
}
Differentiator differentiator = new Differentiator(points);
differentiator.SampleSize = 9;
DPoint[] diffPoints = differentiator.Differentiate();
StationaryPoints target = new StationaryPoints(points.ToArray(), diffPoints);
target.Threshold = 0;
TurningPoint[] actual;
actual = target.CalculateTurningPoints();
Assert.AreEqual(2, actual.Length);
Assert.IsTrue(actual[0].IsPeak);
Assert.AreEqual("-0.33", actual[0].Point.X.ToString("0.00"));
Assert.IsFalse(actual[1].IsPeak);
Assert.AreEqual("1.00", actual[1].Point.X.ToString("0.00"));
}
/// <summary>
/// Calculates this mathemarical expression.
/// </summary>
/// <param name="parameters">An object that contains all parameters and functions for expressions.</param>
/// <returns>
/// A result of the calculation.
/// </returns>
/// <seealso cref="ExpressionParameters" />
public override object Calculate(ExpressionParameters parameters)
{
var differentiator = new Differentiator ();
var derivat = differentiator.Differentiate ( this.Expression, this.Variable );
return derivat.Calculate ( parameters );
}
public void Accuracy()
{
List<DPoint> points = new List<DPoint>();
for (int i = -100; i < 101; i++)
{
double x = (double)i;
double y = 3 * x * x - 2 * x + 1;
points.Add(new DPoint(x, y));
}
Differentiator target = new Differentiator(points);
DPoint[] diffPoints = target.Differentiate();
//x=0, y' = -2
Assert.AreEqual(0d, diffPoints[100].X);
Assert.AreEqual(-2d, diffPoints[100].Y);
//x=1, y'=4
Assert.AreEqual(1d, diffPoints[101].X);
Assert.AreEqual(4d, diffPoints[101].Y);
//x=-1, y'=-8
Assert.AreEqual(-1d, diffPoints[99].X);
Assert.AreEqual(-8d, diffPoints[99].Y);
//x=42, y'=250
Assert.AreEqual(42d, diffPoints[142].X);
Assert.AreEqual(250d, diffPoints[142].Y);
}
public void SampleSize()
{
Differentiator target = new Differentiator();
target.SampleSize = 9;
//y=2x+1
target.Add(new DPoint(0, 1));
target.Add(new DPoint(1, 3));
target.Add(new DPoint(2, 5));
DPoint[] diffPoints = target.Differentiate();
Assert.AreEqual(3, diffPoints.Length);
//expect best line fit, which has gadient of 2
Assert.AreEqual(2, diffPoints[0].Y);
Assert.AreEqual(2, diffPoints[1].Y);
Assert.AreEqual(2, diffPoints[2].Y);
}
public void EndPoints()
{
DPoint[] points = createPoints();
Differentiator target = new Differentiator(points);
DPoint[] diffPoints = target.Differentiate();
Assert.AreEqual(0, diffPoints[0].X);
Assert.AreEqual(1, diffPoints[0].Y);
Assert.AreEqual(999, diffPoints[999].X);
Assert.AreEqual(-1, diffPoints[999].Y);
}
public void Differentiate1()
{
DPoint[] points = createPoints();
Differentiator target = new Differentiator(points);
DPoint[] diffPoints = target.Differentiate();
Assert.AreEqual(points.Length, diffPoints.Length);
Assert.AreEqual(points[50].X, diffPoints[50].X);
Assert.AreEqual(points[500].X, diffPoints[500].X);
//gradient = 1
Assert.AreEqual(1d, diffPoints[50].Y);
//gradient = -1
Assert.AreEqual(-1d, diffPoints[150].Y);
//turning point
Assert.AreEqual(0d, diffPoints[100].Y);
}
public static void TestDifferentiation(string expression, string answer)
{
Assert.Equal(answer, Differentiator.Differentiate(expression));
}