/// <summary>
/// Determine the value of the caplet using the Black-Caplet-formula
/// </summary>
/// <returns></returns>
public double Value(YieldCurve yieldCurve, double delta, Func <double, double> volatilityFunc)
{
// valuation date
var valuationDate = yieldCurve.SettleDate;
var T = Utilities.ConvertToDayCountFraction(valuationDate, FixingDate);
Func <double, double> func = t => volatilityFunc(T - t) * volatilityFunc(T - t);
var sigma = Math.Sqrt(1 / T * Integrate.OnClosedInterval(func, 0, T));
var tenor = Utilities.ConvertToDayCountFraction(FixingDate, ExpiryDate);
var bond = yieldCurve.GetDiscountFactors(new [] { FixingDate, ExpiryDate });
var kappa = CapRate / (Tenor * Principal) + delta;
var spotForwardRate = 1 / tenor * (bond[0] / bond[1] - 1);
var logLK = Math.Log((spotForwardRate + delta) / (kappa));
var gamma = T * sigma * sigma;
var dPlus = (logLK + 0.5 * gamma) / Math.Sqrt(gamma);
var dMinus = (logLK - 0.5 * gamma) / Math.Sqrt(gamma);
return(bond[1] * Principal * Tenor * (spotForwardRate * Normal.CDF(0, 1, dPlus) - kappa * Normal.CDF(0, 1, dMinus)));
}
public void TestIntegrateFacade()
{
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA),
1e-5,
"Interval");
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA, 1e-10),
1e-10,
"Interval, Target 1e-10");
Assert.AreEqual(
Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB),
TargetAreaB,
1e-12,
"Rectangle");
Assert.AreEqual(
Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB, 22),
TargetAreaB,
1e-10,
"Rectangle, Gauss-Legendre Order 22");
}
/// <summary>
/// Executes the example.
/// </summary>
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/Integrate.html"/>
/// <seealso cref="http://en.wikipedia.org/wiki/Trapezoidal_rule">Trapezoidal rule</seealso>
public override void ExecuteExample()
{
// 1. Integrate x*x on interval [0, 10]
Console.WriteLine(@"1. Integrate x*x on interval [0, 10]");
var result = Integrate.OnClosedInterval(x => x * x, 0, 10);
Console.WriteLine(result);
Console.WriteLine();
// 2. Integrate 1/(x^3 + 1) on interval [0, 1]
Console.WriteLine(@"2. Integrate 1/(x^3 + 1) on interval [0, 1]");
result = Integrate.OnClosedInterval(x => 1 / (Math.Pow(x, 3) + 1), 0, 1);
Console.WriteLine(result);
Console.WriteLine();
// 3. Integrate f(x) = exp(-x/5) (2 + sin(2 * x)) on [0, 10]
Console.WriteLine(@"3. Integrate f(x) = exp(-x/5) (2 + sin(2 * x)) on [0, 10]");
result = Integrate.OnClosedInterval(x => Math.Exp(-x / 5) * (2 + Math.Sin(2 * x)), 0, 100);
Console.WriteLine(result);
Console.WriteLine();
// 4. Integrate target function with absolute error = 1E-4
Console.WriteLine(@"4. Integrate target function with absolute error = 1E-4 on [0, 10]");
Console.WriteLine(@"public static double TargetFunctionA(double x) {
return Math.Exp(-x / 5) * (2 + Math.Sin(2 * x));
}");
result = Integrate.OnClosedInterval(TargetFunctionA, 0, 100, 1e-4);
Console.WriteLine(result);
Console.WriteLine();
}
private void AreaDetection()
{
double shortSum = 0, longSum = 0, shortAve, longAve;
for (int j = i; j > (i - shortNum + 1); j--)
{
double slope = (data[j, 1] - data[j - 1, 1]) / (data[j, 0] - data[j - 1, 0]);
double intercept = data[j, 1] - slope * data[j, 0];
var result1 = Integrate.OnClosedInterval(x => slope * x + intercept, data[j - 1, 0], (data[j, 0]));
shortSum += Math.Abs(result1);
}
for (int j = i; j > (i - longNum + 1); j--)
{
double slope = (data[j, 1] - data[j - 1, 1]) / (data[j, 0] - data[j - 1, 0]);
double intercept = data[j, 1] - slope * data[j, 0];
var result2 = Integrate.OnClosedInterval(x => slope * x + intercept, data[j - 1, 0], (data[j, 0]));
longSum += Math.Abs(result2);
}
shortAve = shortSum / shortNum;
longAve = longSum / longNum;
if (Math.Abs((shortAve - longAve) / longAve) > ArgDetect)
{
Point point = new Point();
point = new Point(data[i, 0], data[i, 1]);
dataSource2.AppendAsync(base.Dispatcher, point);
flag = 2;
}
}
float TestReslut()
{
float e_pow = (Mathf.Pow(a, 2) - Mathf.Pow(b, 2)) / Mathf.Pow(a, 2);
float resulte = a * (float)Integrate.OnClosedInterval(x => Mathf.Sqrt(1 - e_pow * Mathf.Pow(Mathf.Cos((float)x), 2)), down * Mathf.Deg2Rad, up * Mathf.Deg2Rad);
return(Mathf.Abs(resulte));
}
public static double simpsonRuleEs(Expr expr, string varName, double a, double b, int n)
{
var f = expr.Compile(varName);
double srValue = SimpsonRule.IntegrateComposite(f, a, b, n);
double trueValue = Integrate.OnClosedInterval(f, a, b);
return(abs(trueValue - srValue));
}
public static double trapezoidalRuleEt(Expr expr, string varName, double a, double b, int n)
{
var f = expr.Compile(varName);
double trValue = NewtonCotesTrapeziumRule.IntegrateComposite(f, a, b, n);
double trueValue = Integrate.OnClosedInterval(f, a, b);
return(abs(trueValue - trValue));
}
public void TestPortal()
{
Assert.That(
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA),
NumericIs.AlmostEqualTo(TargetAreaA, 1e-5),
"Basic");
Assert.That(
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA, 1e-10),
NumericIs.AlmostEqualTo(TargetAreaA, 1e-10),
"Basic Target 1e-10");
}
public void TestIntegratePortal()
{
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA),
1e-5,
"Basic");
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA, 1e-10),
1e-10,
"Basic Target 1e-10");
}
Point3D ICompute.ElasticCenter()
{
double xcoord = Integrate.OnClosedInterval(
x => x * dL(x) / L,
-W / 2,
W / 2,
Prec
);
double zcoord = Integrate.OnClosedInterval(
x => F(x) * dL(x) / L,
-W / 2,
W / 2,
Prec
);
return(new Point3D(xcoord, 0, zcoord));
}
public List <PointLoad> DiscretizeForce(Func <double, double> force, Vault structure, UnitVector3D projection)
{
var res = new List <PointLoad>();
Boundaries bound = Boundaries[Axis];
for (int i = 0; i < structure.Points.MidSegment.Count; i++)
{
double coord_prev = structure.Points.Segment[i].ToVector3D().DotProduct(Axis);
double coord_next = structure.Points.Segment[i + 1].ToVector3D().DotProduct(Axis);
if (coord_prev > coord_next)
{
var temp = coord_next;
coord_next = coord_prev;
coord_prev = temp;
}
if (coord_next >= bound.Min && coord_prev <= bound.Max)
{
var point = structure.Points.MidSegment[i];
double min = Max(coord_prev, bound.Min);
double max = Min(coord_next, bound.Max);
double force_integral;
if (Abs(min - max) > Prec)
{
force_integral = Integrate.OnClosedInterval(force, min, max);
}
else
{
max = point.ToVector3D().DotProduct(Axis);
force_integral = 2 * Integrate.OnClosedInterval(force, min, max);
}
if (Abs(force_integral) > Prec)
{
res.Add(new VaultPointLoad(point, force_integral * projection));
}
}
}
return(res);
}
public virtual Length GetArcLength()
{
double length = GetFinalPoint().X.GetBasicVal();
if (Settings.Quantities.Α.IsRight() || length == 0)
{
return(new Length(2.0 * GetHighestPoint().Y.GetBasicVal() - Settings.Quantities.H.GetBasicVal(), UnitLength.Basic));
}
return(new Length(
Integrate.OnClosedInterval(
x => Math.Sqrt(
1 + Math.Pow(
Math.Tan(Settings.Quantities.Α.GetBasicVal()) -
Settings.Quantities.G.GetBasicVal() /
Math.Pow(GetInitialPoint().Vx.GetBasicVal(), 2.0) * x, 2.0)
), 0, length
), UnitLength.Basic
));
}
double ICompute.IntZSq()
{
Func <double, double> func;
switch (Restraint)
{
case Restraint.Fixed:
double Oz = Points.ElasticCenter.Z;
func = u => Math.Pow(F(u) - Oz, 2) * dL(u);
break;
case Restraint.Pinned:
func = u => Math.Pow(F(u), 2) * dL(u);
break;
default:
var msg = "Restraint is unknown";
throw new InvalidOperationException(msg);
}
return(Integrate.OnClosedInterval(func, -W / 2, W / 2, Prec));
}
private void button1_Click(object sender, EventArgs e)
{
try
{
double xp = Double.Parse(textBox7.Text);
double xk = Double.Parse(textBox5.Text);
int n = Int32.Parse(textBox6.Text);
if (n % 2 == 0 && xp >= xk)
{
textBox1.Text = "" + MetodaProstokatow(h, xp, xk, n);
textBox3.Text = "" + MetodaTrapezow(h, xp, xk, n);
textBox4.Text = "" + Integrate.OnClosedInterval(h, xp, xk);
textBox2.Text = "" + MathNet.Numerics.Integration.Algorithms.SimpsonRule.IntegrateComposite(h, xp, xk, n);
}
else
{
MessageBox.Show("Zły przedział, lub granica górna jest mniejsza od dolnej");
}
}
catch (System.FormatException) { }
}
/// <summary>
/// Compute correlation matrix
/// </summary>
/// <param name="t"></param>
/// <param name="dt"></param>
/// <returns></returns>
private Matrix <double> CorrelationMatrix(double t, double dt)
{
var C = Matrix <double> .Build.Dense(NumRates, NumRates);
for (var i = 0; i < NumRates; i++)
{
for (var j = 0; j <= i; j++)
{
var i1 = i;
var j1 = j;
Func <double, double> func = x => Correlation[i1, j1] * Volatility[i1](T[i1] - x) * Volatility[j1](T[j1] - x);
var corr = Integrate.OnClosedInterval(func, t, t + dt);
C[i, j] = corr;
C[j, i] = corr;
}
}
return(C);
}
/// <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 virtual double XToLength(double x)
{
return(Integrate.OnClosedInterval(dL, -W / 2, x));
}
public void TestIntegrateFacade()
{
// TargetFunctionA
// integral_(0)^(10) exp(-x/5) (2 + sin(2 x)) dx = 9.1082
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA),
1e-5,
"Interval, Target 1e-08");
Assert.AreEqual(
TargetAreaA,
Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA, 1e-10),
1e-10,
"Interval, Target 1e-10");
// TargetFunctionB
// integral_(0)^(1) integral_(0)^(10) exp(-x/5) (2 + sin(2 y)) dx dy = 11.7079
Assert.AreEqual(
Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB),
TargetAreaB,
1e-12,
"Rectangle, order 32");
Assert.AreEqual(
Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB, 22),
TargetAreaB,
1e-10,
"Rectangle, Order 22");
// TargetFunctionC
// integral_(-oo)^(oo) 1/(1 + x^2) dx = pi
Assert.AreEqual(
TargetAreaC,
Integrate.DoubleExponential(TargetFunctionC, StartC, StopC),
1e-5,
"DoubleExponential, 1/(1 + x^2)");
Assert.AreEqual(
TargetAreaC,
Integrate.DoubleExponential(TargetFunctionC, StartC, StopC, 1e-10),
1e-10,
"DoubleExponential, 1/(1 + x^2)");
// TargetFunctionD
// integral_(0)^(1) log(x) dx = -1
Assert.AreEqual(
TargetAreaD,
Integrate.DoubleExponential(TargetFunctionD, StartD, StopD),
1e-10,
"DoubleExponential, log(x)");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussLegendre(TargetFunctionD, StartD, StopD, order: 1024),
1e-10,
"GaussLegendre, log(x), order 1024");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 15),
1e-10,
"GaussKronrod, log(x), order 15");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 21),
1e-10,
"GaussKronrod, log(x), order 21");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 31),
1e-10,
"GaussKronrod, log(x), order 31");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 41),
1e-10,
"GaussKronrod, log(x), order 41");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 51),
1e-10,
"GaussKronrod, log(x), order 51");
Assert.AreEqual(
TargetAreaD,
Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, 1e-10, order: 61),
1e-10,
"GaussKronrod, log(x), order 61");
double error, L1;
var Q = Integrate.GaussKronrod(TargetFunctionD, StartD, StopD, out error, out L1, 1e-10, order: 15);
Assert.AreEqual(
Math.Abs(TargetAreaD),
Math.Abs(L1),
1e-10,
"GaussKronrod, L1");
// TargetFunctionE
// integral_(0)^(1) log^2(x) dx = 2
Assert.AreEqual(
TargetAreaE,
Integrate.DoubleExponential(TargetFunctionE, StartE, StopE),
1e-10,
"DoubleExponential, log^2(x)");
Assert.AreEqual(
TargetAreaE,
Integrate.GaussLegendre(TargetFunctionE, StartE, StopE, order: 128),
1e-5,
"GaussLegendre, log^2(x), order 128");
Assert.AreEqual(
TargetAreaE,
Integrate.GaussKronrod(TargetFunctionE, StartE, StopE, 1e-10, order: 15),
1e-10,
"GaussKronrod, log^2(x), order 15");
// TargetFunctionF
// integral_(0)^(oo) exp(-x) cos(x) dx = 1/2
Assert.AreEqual(
TargetAreaF,
Integrate.DoubleExponential(TargetFunctionF, StartF, StopF),
1e-10,
"DoubleExponential, e^(-x) cos(x)");
Assert.AreEqual(
TargetAreaF,
Integrate.GaussLegendre(TargetFunctionF, StartF, StopF, order: 128),
1e-10,
"GaussLegendre, e^(-x) cos(x), order 128");
Assert.AreEqual(
TargetAreaF,
Integrate.GaussKronrod(TargetFunctionF, StartF, StopF, 1e-10, order: 15),
1e-10,
"GaussKronrod, e^(-x) cos(x), order 15");
// TargetFunctionG
// integral_(0)^(1) sqrt(x)/sqrt(1 - x^2) dx = 1.19814
Assert.AreEqual(
TargetAreaG,
Integrate.DoubleExponential(TargetFunctionG, StartG, StopG),
1e-5,
"DoubleExponential, sqrt(x)/sqrt(1 - x^2)");
Assert.AreEqual(
TargetAreaG,
Integrate.GaussLegendre(TargetFunctionG, StartG, StopG, order: 128),
1e-10,
"GaussLegendre, sqrt(x)/sqrt(1 - x^2), order 128");
Assert.AreEqual(
TargetAreaG,
Integrate.GaussKronrod(TargetFunctionG, StartG, StopG, 1e-10, order: 15),
1e-10,
"GaussKronrod, sqrt(x)/sqrt(1 - x^2), order 15");
}
public static double integral(Expr expr, string varName, double a, double b)
{
var f = expr.Compile(varName);
return(Integrate.OnClosedInterval(f, a, b));
}
public static double RealResult()
{
return(Integrate.OnClosedInterval(Integral, 1.5, 2.3, 1e-15));
}
//计算信噪比
public double SNR(double reflectivity, double altitudeAngle, double AOD,
double viewAngle, double sensorSize, double cameraSize,
double initialBand, double endBand, double integralTime)
{
double f = 1.0 / (2 * integralTime);
double tao = Math.Exp(-1 * AOD);
double A0 = 3.14 * (cameraSize / 2.0) * (cameraSize / 2.0);
double D = cameraSize * Math.Sqrt(sensorSize * f);//D不确定
double snr = D * reflectivity * viewAngle * A0 * tao * Math.Cos(altitudeAngle) * Math.Sqrt(integralTime) * Integrate.OnClosedInterval(x => x * x, 0, 10);
return(snr);
}