public void Oneeq5()
{
// Test case from http://www.polymath-software.com/library/nle/Oneeq5.htm
Func <double, double> f1 = TR =>
{
const double ALPHA = 7.256;
const double BETA = 2.298E-3;
const double GAMMA = 0.283E-6;
const double DH = -57798.0;
return(DH + TR * (ALPHA + TR * (BETA / 2 + TR * GAMMA / 3)) - 298.0 * (ALPHA + 298.0 * (BETA / 2 + 298.0 * GAMMA / 3)));
};
double x = FindRoots.OfFunction(f1, 3000, 5000, 1e-10);
Assert.AreEqual(4305.30991366774, x, 1e-5);
Assert.AreEqual(0, f1(x), 1e-8);
}
public void ComplexRoots_TripleReal_AsPolynomial(double d, double c, double b, double a, double x1, double x2, double x3)
{
var expectedReal = new[] { x1, x2, x3 };
var actual = FindRoots.Polynomial(new[] { d, c, b, a });
var actualReal = Generate.Map(actual, x => x.Real);
var actualImag = Generate.Map(actual, x => x.Imaginary);
Sorting.Sort(expectedReal);
Sorting.Sort(actualReal, actualImag);
Assert.That(actual.Length, Is.EqualTo(3));
Assert.That(actualReal[0], Is.EqualTo(expectedReal[0]).Within(1e-14));
Assert.That(actualImag[0], Is.EqualTo(0d).Within(1e-14));
Assert.That(actualReal[1], Is.EqualTo(expectedReal[1]).Within(1e-14));
Assert.That(actualImag[1], Is.EqualTo(0d).Within(1e-14));
Assert.That(actualReal[2], Is.EqualTo(expectedReal[2]).Within(1e-14));
Assert.That(actualImag[2], Is.EqualTo(0d).Within(1e-14));
}
public void Oneeq8()
{
// Test case from http://www.polymath-software.com/library/nle/Oneeq8.htm
Func <double, double> f1 = v =>
{
const double a = 240;
const double b = 40;
const double c = 200;
return(a * v * v + b * Math.Pow(v, 7 / 4) - c);
};
double x = FindRoots.OfFunction(f1, 0.01, 1);
Assert.AreEqual(0.842524411168525, x, 1e-2);
Assert.AreEqual(0, f1(x), 1e-5);
}
private void InvisibleSpheresSameHeight(Vector3[] centresSpheres, double[] thetas)
{
InitSingularityVariables(centresSpheres, thetas);
double[] coefs = new double[3] {
C, B, A
};
System.Numerics.Complex[] roots = FindRoots.Polynomial(coefs);
for (int i = 0; i < roots.Length; i++)
{
if (roots[i].Imaginary == 0 && roots[i].Real < 0)
{
endEffectorPosition = new Vector3(serviceConverter.ConvertDoubleToFloat(x_), serviceConverter.ConvertDoubleToFloat(roots[i].Real),
serviceConverter.ConvertDoubleToFloat(y_));
}
}
}
public void QuadraticExpanded(double u, double v, double t)
{
// t*(x+u)*(x+v) = t*u*v + t*(u+v)*x + t*x^2
double c = t * u * v, b = t * (u + v), a = t;
var x = FindRoots.Quadratic(c, b, a);
Complex x1 = x.Item1, x2 = x.Item2;
// Expected Roots: -u, -v
Complex r1 = new Complex(-u, 0d), r2 = new Complex(-v, 0d);
Assert.IsTrue(x1.AlmostEqualRelative(r1, 1e-14) && x2.AlmostEqualRelative(r2, 1e-14) ||
x1.AlmostEqualRelative(r2, 1e-14) && x2.AlmostEqualRelative(r1, 1e-14));
// Verify they really are roots
AssertComplexEqual(Complex.Zero, c + b * x1 + a * x1 * x1, 1e-14);
AssertComplexEqual(Complex.Zero, c + b * x2 + a * x2 * x2, 1e-14);
}
public static double Y(double[] coefs, double pX)
{
Array.Reverse(coefs);
var x = Expr.Variable("x");
var curve = Expr.Parse(new Polynomial(coefs).ToString().Replace(",", ".").Replace("x", "*x"));
var tang = curve.Differentiate(x) * x;
Func <double, double> fx = (curve).Compile("x");
var xResult = fx(5);
var xx = FindRoots.OfFunction(fx, -5, 5);
return(tang.Evaluate(new Dictionary <string, MathNet.Symbolics.FloatingPoint> {
{ "x", pX }
}).RealValue);
}
public double GetPileLengthByBearingCapacity()
{
if (m_wantedPileBearing <= 0)
{
throw new ArgumentOutOfRangeException("m_wantedPileBearing");
}
Dictionary <double, double> pilelengthandbearingforce;
GetPileCacluateInfo(out pilelengthandbearingforce);
List <double> points = new List <double>(), values = new List <double>();
foreach (var keyvalue in pilelengthandbearingforce)
{
points.Add(keyvalue.Key);
values.Add(keyvalue.Value);
}
var interpolate = Interpolate.Linear(points, values);
return(FindRoots.OfFunction(x => interpolate.Interpolate(x) - m_wantedPileBearing, points.Min(), points.Max()));
}
public double Distance(Simplex line)
{
var p = line.Edges[0].Item2;
var q = line.Edges[1].Item2;
Line line_pq = t => p + (q - p) * t;
Func <double, double> f = t => line_pq(t).L2Norm() - 1.0;
var t_a = FindRoots.OfFunction(f, -3.0 / (p - q).L2Norm(), .0);
var t_b = FindRoots.OfFunction(f, 1.0, 3.0 / (p - q).L2Norm());
var a = line_pq(t_a);
var b = line_pq(t_b);
var aq = (a - q).L2Norm();
var ap = (a - p).L2Norm();
var pb = (p - b).L2Norm();
var qb = (q - b).L2Norm();
return(.5 * Math.Log((aq * pb) / (ap * qb)));
}
public void MultipleRoots()
{
// Roots at -2, 2
Func <double, double> f1 = x => x * x - 4;
Assert.AreEqual(0, f1(FindRoots.OfFunction(f1, 0, 5, 1e-14)));
Assert.AreEqual(-2, FindRoots.OfFunction(f1, -5, -1, 1e-14));
Assert.AreEqual(2, FindRoots.OfFunction(f1, 1, 4, 1e-14));
Assert.AreEqual(0, f1(FindRoots.OfFunction(x => - f1(x), 0, 5, 1e-14)));
Assert.AreEqual(-2, FindRoots.OfFunction(x => - f1(x), -5, -1, 1e-14));
Assert.AreEqual(2, FindRoots.OfFunction(x => - f1(x), 1, 4, 1e-14));
// Roots at 3, 4
Func <double, double> f2 = x => (x - 3) * (x - 4);
Assert.AreEqual(0, f2(FindRoots.OfFunction(f2, 3.5, 5, 1e-14)), 1e-14);
Assert.AreEqual(3, FindRoots.OfFunction(f2, -5, 3.5, 1e-14));
Assert.AreEqual(4, FindRoots.OfFunction(f2, 3.2, 5, 1e-14));
Assert.AreEqual(3, FindRoots.OfFunction(f2, 2.1, 3.9, 0.001), 0.001);
Assert.AreEqual(3, FindRoots.OfFunction(f2, 2.1, 3.4, 0.001), 0.001);
}
public double Length(String P, String Q)
{
var _P = Vector<double>.Build.DenseOfArray(GetPoint(P));
var _Q = Vector<double>.Build.DenseOfArray(GetPoint(Q));
Func<double, Vector<double>> line_pq = t => _P + (_Q - _P) * t;
Func<double, double> f = t => line_pq(t).L2Norm() - 1.0;
var t_A = FindRoots.OfFunction(f, -3.0 / (_P - _Q).L2Norm(), .0);
var t_B = FindRoots.OfFunction(f, 1.0, 3.0 / (_P - _Q).L2Norm());
var _A = line_pq(t_A);
var _B = line_pq(t_B);
var aq = (_A - _Q).L2Norm();
var ap = (_A - _P).L2Norm();
var pb = (_P - _B).L2Norm();
var qb = (_Q - _B).L2Norm();
return .5 * Math.Log((aq * pb) / (ap * qb));
}
protected static double Length(double[] P, double[] Q)
{
var _P = Vector <double> .Build.DenseOfArray(P);
var _Q = Vector <double> .Build.DenseOfArray(Q);
Func <double, Vector <double> > line_pq = t => _P + (_Q - _P) * t;
Func <double, double> f = t => line_pq(t).L2Norm() - 1.0;
var t_A = FindRoots.OfFunction(f, -3.0 / (_P - _Q).L2Norm(), .0);
var t_B = FindRoots.OfFunction(f, 1.0, 3.0 / (_P - _Q).L2Norm());
var _A = line_pq(t_A);
var _B = line_pq(t_B);
var aq = (_A - _Q).L2Norm();
var ap = (_A - _P).L2Norm();
var pb = (_P - _B).L2Norm();
var qb = (_Q - _B).L2Norm();
return(.5 * Math.Log((aq * pb) / (ap * qb)));
}
private void CalculateOptimizeProductionAmount()
{
Func <double, double> f = x => A + B * x + C * Math.Pow(x, 2);
Func <double, double> dtk = x => A / x + B + C * x;
var dtkFirstDerivative = Derivative.Derive(dtk, 1);
OptimizeAmount = Math.Round(FindRoots.OfFunction(dtkFirstDerivative, 1, 500));
OptimizeProductionCosts = dtk(OptimizeAmount);
if (OptimizeProductionCosts < SellPrice)
{
Func <double, double> g = x => SellPrice * x - (A + B * x + C * Math.Pow(x, 2));
var gFirstDerivative = Derivative.Derive(g, 1);
ProfitAmount = Math.Round(FindRoots.OfFunction(gFirstDerivative, 1, 500));
Profit = g(ProfitAmount);
}
else
{
Profit = double.NaN;
}
}
private void button1_Click(object sender, EventArgs e)
{
Double d = Convert.ToDouble(ac.Text);
Double c = Convert.ToDouble(bc.Text);
Double b = Convert.ToDouble(bc.Text);
Double a = Convert.ToDouble(ac.Text);
var roots = FindRoots.Cubic(d, c, b, a);
Complex root1 = roots.Item1;
Complex root2 = roots.Item2;
Complex root3 = roots.Item3;
One.Text = One.Text + " " + root1.Real + " + " + "(" + root1.Imaginary + ")" + " i";
Two.Text = Two.Text + " " + root2.Real + " + " + "(" + root2.Imaginary + ")" + " i";
Three.Text = Three.Text + " " + root2.Real + " + " + "(" + root3.Imaginary + ")" + " i";
}
public double[] Roots(Polynomial line, double x1 = Double.NegativeInfinity, double x2 = Double.PositiveInfinity,
double absoluteMaximumError = 5e-6) => FindRoots.Polynomial((this - line).Coefficients)
.Where(c => c.IsReal()).Select(c => c.Real)
.Where(x => x.CompareTo(x1, absoluteMaximumError) == 1 && x.CompareTo(x2, absoluteMaximumError) <= 0)
.ToArray();
/// <summary>
/// Spawns cubes upon an arc of an ellipse.
/// </summary>
/// <param name="n"> The number of cubes. </param>
/// <param name="center"> The center of the ellipse. </param>
/// <param name="sectorChordLength"> The length of the arc's chord. </param>
/// <param name="semiMinorAxisLength"> Half the length of the minor axis. </param>
/// <param name="sectorAngleDeg"> The angular length of the arc in degrees. </param>
/// <param name="cubePrefab"> The template for the cubes. </param>
/// <param name="parent"> The parent of the cubes structure. </param>
/// <returns> Returns the GameObject containing the cubes, whose parent is 'parent'. </returns>
/// <remarks> This function is definitely very time-expensive. Use sparingly. </remarks>
private static GameObject SpawnEllipseCubes(int n, Vector3 center, float sectorChordLength, float semiMinorAxisLength, float sectorAngleDeg, GameObject cubePrefab, Transform parent = null)
{
// TODO: Find constraints for every parameter and variable (minimum and maximum values)
// Problem: for some combination of input parameters, the FindRoots.OfFunction method fails with an exception:
// "ArithmeticException: Function does not accept floating point Not-a-Number values."
// Sample parameters: (16,, 12.0f, 6.0f, 90°,,)
#region Maths
/*
* C: center of the ellipse
* R: sectorChordLength, the length of the chord
* a: half the length of the major axis of the ellipse
* b: semiMinorAxisLength, half the length of the minor axis of the ellipse
* α: sectorAngleDeg, the sector extension in degrees, from (90° - α/2) to (90° + α/2) counterclock-wise
* n: number of cubes
*
*
* § 1) ELLIPSE'S EQUATIONS
*
* ξ(ϑ): ellipse's parametric equations [-180° ≤ ϑ ≤ 180°]
* where ϑ is the angle of (ξˣ(ϑ), ξʸ(ϑ)) with the major axis of the ellipse itself
* ___________________________
* ξˣ(ϑ) = a b cos(ϑ) √(a² sin²(ϑ) + b² cos²(ϑ))⁻¹
* ___________________________
* ξʸ(ϑ) = a b sin(ϑ) √(a² sin²(ϑ) + b² cos²(ϑ))⁻¹
*
* A = ξ(90° + α/2)
* B = ξ(90° - α/2)
*
* __ _______________________________
* R = AB = 2 a b sin(α/2) √(a² cos²(α/2) + b² sin²(α/2))⁻¹
* _________________________________________ _______________________
* a = √(b² R² tan²(α/2)) / (4 b² tan²(α/2) - R²) = (b R tan(α/2)) √(4 b² tan²(α/2) - R²)⁻¹
*
*
* § 2) CUBES PLACEMENT
* A _____________________
* L = ∫(√D[ξˣ(ϑ)]² + D[ξʸ(ϑ)]²)dϑ: length of arc AB
* B
* l = L/n: distance between each cube's center on the arc
*
* θᵢ: angle of the iᵗʰ arc segment; arc length to the iᵗʰ arc segment = i l
* θᵢ = FindRoot[∫(D[ξˣ(ϑ)]² + D[ξʸ(ϑ)]²)dϑ = i l] 😭
*
* Pᵢ = ξ(θᵢ): position of the iᵗʰ cube
*
*
* § 3) CUBES' SIDE LENGTH
* Let Pᵢ and Pⱼ be the positions of two consecutive cubes (j = i + 1) with angles θᵢ and θⱼ.
* Let Pₖ be a third point placed at the same arc-distance from both Pᵢ and Pⱼ; the angle of Pₖ is θₖ.
*
* rₖ: line from C to Pₖ
* rᵢ: line from C to Pᵢ
* rⱼ: line from C to Pⱼ
*
* M: parametric point on rₖ
* dᵢ: segment MPᵢ
* dⱼ: segment MPⱼ
*
*
* M = (mˣ, mʸ) = (mˣ, mˣ tan(θₖ))
* ____________________________________
* dᵢ = √(x(Pᵢ) - mˣ)² + (y(Pᵢ) - mˣ tan(θₖ))²
* ____________________________________
* dⱼ = √(x(Pⱼ) - mˣ)² + (y(Pⱼ) - mˣ tan(θₖ))²
*
* ASSERTION
* dᵢ = dⱼ = d: dᵢ and dⱼ are the semi-diagonals of the two squares
*
* (x(Pᵢ) - mˣ)² + (y(Pᵢ) - mˣ tan(θₖ))² = (x(Pⱼ) - mˣ)² + (y(Pⱼ) - mˣ tan(θₖ))²
* x(Pᵢ)² + (mˣ)² - 2 x(Pᵢ) mˣ + y(Pᵢ)² + (mˣ tan(θₖ))² - 2 y(Pᵢ) mˣ tan(θₖ) = x(Pⱼ)² + (mˣ)² - 2 x(Pⱼ) mˣ + y(Pⱼ)² + (mˣ tan(θₖ))² - 2 y(Pⱼ) mˣ tan(θₖ)
* x(Pᵢ)² - 2 x(Pᵢ) mˣ + y(Pᵢ)² - 2 y(Pᵢ) mˣ tan(θₖ) = x(Pⱼ)² - 2 x(Pⱼ) mˣ + y(Pⱼ)² - 2 y(Pⱼ) mˣ tan(θₖ)
* 2 x(Pⱼ) mˣ + 2 y(Pⱼ) mˣ tan(θₖ) - 2 x(Pᵢ) mˣ - 2 y(Pᵢ) mˣ tan(θₖ) = x(Pⱼ)² + y(Pⱼ)² - x(Pᵢ)² - y(Pᵢ)²
* 2 mˣ (x(Pⱼ) + y(Pⱼ) tan(θₖ) - x(Pᵢ) - y(Pᵢ) tan(θₖ)) = x(Pⱼ)² + y(Pⱼ)² - x(Pᵢ)² - y(Pᵢ)²
*
* x(Pⱼ)² + y(Pⱼ)² - x(Pᵢ)² - y(Pᵢ)²
* mˣ = ——————————————————————————————————————————————————
* 2 (x(Pⱼ) + y(Pⱼ) tan(θₖ) - x(Pᵢ) - y(Pᵢ) tan(θₖ))
*
* cube's side length = 2 (d/√2)
*
*/
#endregion Maths
double R = sectorChordLength;
double b = semiMinorAxisLength;
#region § 1) ELLIPSE'S EQUATION
double alphaRad = Trig.DegreeToRadian(sectorAngleDeg);
double bTanHalfAlpha = b * Trig.Tan(alphaRad / 2.0);
double a = (R * bTanHalfAlpha) / Math.Sqrt(4 * bTanHalfAlpha * bTanHalfAlpha - R * R);
Func <double, double> EllipseX = t =>
{
double sin = Trig.Sin(t);
double cos = Trig.Cos(t);
double aSin = a * sin;
double bCos = b * cos;
return((a * bCos) / Math.Sqrt(aSin * aSin + bCos * bCos));
};
Func <double, double> EllipseY = t =>
{
double sin = Trig.Sin(t);
double cos = Trig.Cos(t);
double aSin = a * sin;
double bCos = b * cos;
return((b * aSin) / Math.Sqrt(aSin * aSin + bCos * bCos));
};
#endregion § 1) ELLIPSE'S EQUATION
#region § 2) CUBES PLACEMENT
Func <double, double> DEllipseX = Differentiate.FirstDerivativeFunc(EllipseX);
Func <double, double> DEllipseY = Differentiate.FirstDerivativeFunc(EllipseY);
Func <double, double> SqrtOfSumOfSquaredDerivatives = t =>
{
double x = DEllipseX(t);
double y = DEllipseY(t);
return(Math.Sqrt(x * x + y * y));
};
Func <double, double, double> AngleToArcLength = (fromRad, toRad) => Integrate.OnClosedInterval(SqrtOfSumOfSquaredDerivatives, fromRad, toRad);
Func <double, double> ArcLengthToAngle = arcLength => FindRoots.OfFunction(toRad => AngleToArcLength((Math.PI - alphaRad) / 2, toRad) - arcLength, 0, Math.PI);
double L = AngleToArcLength((Math.PI - alphaRad) / 2, (Math.PI + alphaRad) / 2);
double l = L / (n - 1);
Func <int, object[]> CalculateCubePositionAndAngle = i =>
{
double angle = ArcLengthToAngle(i * l);
Vector2 position = new Vector2((float)EllipseX(angle), (float)EllipseY(angle));
return(new object[] { position, angle });
};
#endregion § 2) CUBES PLACEMENT
#region § 3) CUBES' SIDE LENGTH
Vector2[] positions = new Vector2[n];
double[] angles = new double[n];
double[] middleAngles = new double[n - 1];
for (int i = 0; i < n; ++i)
{
object[] res = CalculateCubePositionAndAngle(i);
positions[i] = (Vector2)res[0];
angles[i] = (double)res[1];
if (i > 0)
{
middleAngles[i - 1] = ArcLengthToAngle((2 * i - 1) * l / 2.0);
}
}
double[] sideLengths = new double[n - 1];
Func <int, double> SideLength = j =>
{
double xj = positions[j].x;
double yj = positions[j].y;
double xi = positions[j - 1].x;
double yi = positions[j - 1].y;
double tanK = Trig.Tan(middleAngles[j - 1]);
double mx = (xj * xj + yj * yj - (xi * xi + yi * yi)) / (2.0 * (xj + yj * tanK - (xi + yi * tanK)));
return(Math.Sqrt((xi - mx) * (xi - mx) + (yi - mx * tanK) * (yi - mx * tanK)) * (2.0 / Math.Sqrt(2.0)));
};
for (int i = 1; i < n; ++i)
{
sideLengths[i - 1] = SideLength(i);
}
float squareSide = (float)sideLengths.Min();
#endregion § 3) CUBES' SIDE LENGTH
// Save parent's current local rotation and scale; it will be re-set later
Quaternion parentRotation = parent?.localRotation ?? Quaternion.identity;
Vector3 parentScale = parent?.localScale ?? Vector3.one;
if (parent != null)
{
parent.localRotation = Quaternion.identity;
parent.localScale = Vector3.one;
}
GameObject cubesContainer = parent?.gameObject ?? new GameObject();
cubesContainer.name = $"Ellipse_{n}Cubes";
cubesContainer.transform.localPosition = center;
// Create the cubes
for (int i = 0; i < n; ++i)
{
GameObject cube = Instantiate(cubePrefab);
cube.name = $"Cube{i}";
cube.SetActive(true); // Awake it now, to let it store the prefab's original scale
cube.transform.localScale = new Vector3(squareSide, squareSide, squareSide);
cube.transform.position = cubesContainer.transform.position + new Vector3(positions[i].x, 0.0f, positions[i].y);
cube.transform.localRotation = Quaternion.Euler(0.0f, (float)(90.0 - Trig.RadianToDegree(angles[i])), 0.0f);
cube.transform.parent = cubesContainer.transform;
}
cubesContainer.transform.localRotation = Quaternion.identity;
// Re-set parent's original local rotation
if (parent != null)
{
parent.localRotation = parentRotation;
parent.localScale = parentScale;
}
return(cubesContainer);
}
public void NoRoot()
{
Func <double, double> f1 = x => x * x + 4;
Assert.Throws <NonConvergenceException>(() => FindRoots.OfFunction(f1, -5, 5, 1e-14));
}
/// <summary>
/// Acha o zero da função f(x) usando o metodo de Brent
/// <param name="func">A função que vai ser zerada. </param>
/// <param name="limiteInf">O limite inferior de onde o zero está. </param>
/// <param name="limitSup">O limite superior de onde o zero está. </param>
/// <param name="precisao">A precissão desejada. </param>
/// <param name="nInte">O número máximo de iterações. </param>
/// <returns> x tal que f(x) = 0. </returns>
/// </summary>
public double AchaRaizBrenet(Func <double, double> fx, double limiteInf, double limitSup, double precisao = 1e-08, int nInte = 100)
{
return(FindRoots.OfFunction(fx, limiteInf, limitSup, precisao, nInte));
}
public Complex[] GetRoots(Double[] coefficients)
{
return(FindRoots.Polynomial(coefficients));
}
public static float FindRealSolutionSmallestT(double[] coefficients)
{
var realSolutions = FindRoots.Polynomial(coefficients).Where(r => r.IsReal() && r.Real > 0).OrderBy(r => r.Real);
return(realSolutions.Any() ? (float)realSolutions.First().Real : float.PositiveInfinity);
}
/// <summary>
/// Examples of generic function sampling and quantization providers
/// </summary>
public override void ExecuteExample()
{
MathDisplay.WriteLine("<b>Chebyshev sampling</b>");
// 1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the first kind within interval [0, 10]
var roots = FindRoots.ChebychevPolynomialFirstKind(20, 0, 10);
var result = Generate.Map <double, double>(roots, Function);
MathDisplay.WriteLine(@"1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of
the first kind within interval [0, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the second kind within interval [0, 10]
roots = FindRoots.ChebychevPolynomialSecondKind(20, 0, 10);
result = Generate.Map <double, double>(roots, Function);
MathDisplay.WriteLine(@"2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of
the second kind within interval [0, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Equidistant sampling</b>");
// 1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]
result = Generate.LinearSpacedMap <double>(11, -5, 5, Function);
MathDisplay.WriteLine(@"1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5 and retrieve sample points
double[] samplePoints = Generate.LinearSpaced(10, 1.0, 5.5);
result = Generate.Map <double, double>(samplePoints, Function);
MathDisplay.WriteLine(@"2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5
and retrieve sample points");
MathDisplay.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
MathDisplay.Write(samplePoints[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5
result = Generate.PeriodicMap <double>(10, Function, 10, 1.0, 10, 5);
MathDisplay.WriteLine(@"3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Random sampling</b>");
// 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10]
var uniform = new ContinuousUniform(-10, 10);
result = Generate.RandomMap <double>(10, uniform, Function);
MathDisplay.WriteLine(@" 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform
distribution on [-10, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points
var exponential = new Exponential(1);
samplePoints = Generate.Random(10, exponential);
result = Generate.Map <double, double>(samplePoints, Function);
MathDisplay.WriteLine(@"2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution
and retrieve sample points");
MathDisplay.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
MathDisplay.Write(samplePoints[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution
var chiSquare = new ChiSquared(10);
result = Generate.RandomMap2 <double>(10, chiSquare, TwoDomainFunction);
MathDisplay.WriteLine(@" 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
}