public static double[] Solve(double c, double d)
{
if (d < 0)
{
return(Solve(c, -d).Reverse().Select(x => - x).ToArray());
}
// 最小の実数解
var x1 = d == 0 && c >= 0 ? 0 : SolveNegative();
// f(x) = (x - x_1) (x^2 + x_1 x + x_1^2 + c)
var det = -3 * x1 * x1 - 4 * c;
if (det < 0)
{
return new[] { x1 }
}
;
return(new[] { x1, (-x1 - Sqrt(det)) / 2, (-x1 + Sqrt(det)) / 2 });
double SolveNegative()
{
var f = CubicEquation1.CreateFunction(c, d);
var f1 = CubicEquation1.CreateDerivative(c);
var x0 = -1D;
while (f(x0) > 0)
{
x0 *= 2;
}
return(NewtonMethod.Solve(f, f1, x0));
}
}
}
static void Main(string[] args)
{
var watch = System.Diagnostics.Stopwatch.StartNew();
NewtonMethod equation = new NewtonMethod();
// Func<double,double> f = x => Math.Pow(x,3)-x-0.231;
// //derivative
// Func<double,double> g = x => 3*Math.Pow(x,2)-1;
// Func<double,double> f = x => x-Math.Sin(x) - 0.25;
// Func<double, double> g = x=> 1-Math.Cos(x);
// Func<double,double> f = x => Math.Pow(Math.E,-x)-5*x-3;
// Func<double,double> g = x => Math.Pow(Math.E,-x)-5;
Func <double, double> f = x => Math.Pow(x, 2) - 612;
Func <double, double> g = x => 2 * x;
//double? root = equation.ExecuteNewtonRaphson(f,g,3,0.00001);
double?root = equation.ExecuteNewtonRaphson(f, g, 20, 0.05);
watch.Stop();
Console.WriteLine($"Root is {root}");
System.Console.WriteLine("\nTime to run: " + watch.Elapsed.TotalMilliseconds + " milisec");
}
static void Main(string[] args)
{
var lb = 0.01f;
var ub = 0.0001f;
Console.WriteLine("Bisection methods:");
Console.WriteLine("#5");
Console.WriteLine(BisectionMethod.Evaluate(Function_5, 2, 3, lb));
Console.WriteLine(BisectionMethod.Evaluate(Function_5, 2, 3, ub));
Console.WriteLine("#9");
Console.WriteLine(BisectionMethod.Evaluate(Function_9, 0, (float)Math.PI * (3f / 2f), lb));
Console.WriteLine(BisectionMethod.Evaluate(Function_9, 0, (float)Math.PI * (3f / 2f), ub));
Console.WriteLine("#11");
Console.WriteLine(BisectionMethod.Evaluate(Function_11, 0.000000000001f, 2, lb));
Console.WriteLine(BisectionMethod.Evaluate(Function_11, 0.000000000001f, 2, ub));
Console.WriteLine("#15");
Console.WriteLine(BisectionMethod.Evaluate(Function_15, 0.2f, 2f, lb));
Console.WriteLine(BisectionMethod.Evaluate(Function_15, 0.2f, 2f, ub));
Console.WriteLine("Newton method");
Console.WriteLine("#5");
Console.WriteLine(NewtonMethod.Evaluate(Function_5, 2, 3, lb));
Console.WriteLine(NewtonMethod.Evaluate(Function_5, 2, 3, ub));
Console.WriteLine("#9");
Console.WriteLine(NewtonMethod.Evaluate(Function_9, 0, (float)Math.PI * (3f / 2f), lb));
Console.WriteLine(NewtonMethod.Evaluate(Function_9, 0, (float)Math.PI * (3f / 2f), ub));
Console.WriteLine("#11");
Console.WriteLine(NewtonMethod.Evaluate(Function_11, 0.000000000001f, 2, lb));
Console.WriteLine(NewtonMethod.Evaluate(Function_11, 0.000000000001f, 2, ub));
Console.WriteLine("#15");
Console.WriteLine(NewtonMethod.Evaluate(Function_15, 0.2f, 2f, lb));
Console.WriteLine(NewtonMethod.Evaluate(Function_15, 0.2f, 2f, ub));
}
// f(x) = ax^2 + bx + c = 0
public static double[] Solve(double a, double b, double c)
{
if (a == 0)
{
throw new ArgumentException("The value must not be 0.", nameof(a));
}
if (a < 0)
{
return(Solve(-a, -b, -c));
}
var det = b * b - 4 * a * c;
if (det.EqualsNearly(0))
{
return new[] { -b / (2 * a) }
}
;
if (det < 0)
{
return(new double[0]);
}
var f = CreateFunction(a, b, c);
var f1 = CreateDerivative(a, b);
var x01 = (-b - Math.Max(det, 1)) / (2 * a);
var x02 = (-b + Math.Max(det, 1)) / (2 * a);
return(new[] { NewtonMethod.Solve(f, f1, x01), NewtonMethod.Solve(f, f1, x02) });
}
}
public void quadric()
{
double func(Vector x) => x[0] * x[0];
NewtonMethod sut = new NewtonMethod()
{
Function = func,
MaxError = 1e-3,
MinPointChange = 1e-3,
Direction = 0,
};
var result = sut.FindMinimum(makePoint(0.0));
Assert.AreEqual(0.0, result.Value, 1e-3);
Assert.AreEqual(0.0, result.Point[0], 1e-3);
result = sut.FindMinimum(makePoint(2.0));
Assert.AreEqual(0.0, result.Value, 1e-3);
Assert.AreEqual(0.0, result.Point[0], 1e-3);
result = sut.FindMinimum(makePoint(200.0));
Assert.AreEqual(0.0, result.Value, 1e-3);
Assert.AreEqual(0.0, result.Point[0], 1e-3);
result = sut.FindMinimum(makePoint(-2000.0));
Assert.AreEqual(0.0, result.Value, 1e-3);
Assert.AreEqual(0.0, result.Point[0], 1e-3);
}
public static void Main()
{
NewtonMethod nm = new NewtonMethod();
// 解を計算(初期値, 収束条件)
double ah = nm.calc(1.0, 0.0001);
// 結果表示
System.Console.WriteLine(ah); // 解：2
}
static void Main(string[] args)
{
NewtonMethod a = new NewtonMethod();
double x;
x = a.MethodN(0.01,64, 2);
Console.Write("x=" + x);
Console.ReadKey();
}
public void NthRoot_3rdrootminus3_exceptionReturned()
{
var actual = NewtonMethod.NthRoot(-125, 3, 6);
double expected = -5;
Debug.WriteLine(expected - actual);
Assert.IsTrue(condition: Math.Abs(expected - actual) < Math.Pow(10, -6));
}
public void IsNewtonMethodCorrect()
{
Assert.That(NewtonMethod.Evaluate(new[] { 0d, 2, 3 }, new[] { 1d, 2, 1 }),
Is.EqualTo(new Polynomial(0, 1.5, -0.5)));
Assert.That(NewtonMethod.Evaluate(new [] { -1, 0, 0.5, 1 }, new [] { 0, 2, 9d / 8, 0 }),
Is.EqualTo(new Polynomial(2, -1, -2, 1)));
Assert.That(NewtonMethod.Evaluate(new [] { -2d, 0, 1 }, new [] { -4d, -1, -3 }),
Is.EqualTo(new Polynomial(11, -5d / 6, -7d / 6)));
}
public void TestMethodRightNumZero()
{
int deg = 3, a = 0;
double e = 0.001;
NewtonMethod c = new NewtonMethod();
double expected = 0.00;
double actual = Math.Round(c.MethodN(e, a, deg), 2);
Assert.AreEqual(expected, actual);
}
public void TestMethodDegZero()
{
int deg = 0, a = 125;
double e = 0.001;
NewtonMethod c = new NewtonMethod();
Boolean actual = double.IsNaN(c.MethodN(e,a,deg));
Assert.IsTrue(actual);
}
// f(x) = ax^3 + bx^2 + cx + d = 0
public static double[] Solve(double a, double b, double c, double d)
{
if (a == 0)
{
throw new ArgumentException("The value must not be 0.", nameof(a));
}
if (a < 0)
{
return(Solve(-a, -b, -c, -d));
}
var f = CreateFunction(a, b, c, d);
var xc = -b / (3 * a);
var yc = f(xc);
if (yc < 0)
{
return(Solve(a, -b, c, -d).Reverse().Select(x => - x).ToArray());
}
var f1 = CreateDerivative(a, b, c);
// 微修正
// 自明解
if (yc == 0 && f1(xc) > 0)
{
return new[] { xc }
}
;
if (yc == 0 && f1(xc) == 0)
{
return new[] { xc, xc, xc }
}
;
// xc より小さい実数解
var x1 = SolveNegative();
var p = a * x1 + b;
var q = p * x1 + c;
return(QuadraticEquation0.Solve(a, p, q).Prepend(x1).ToArray());
double SolveNegative()
{
var x0 = -1D;
while (f(xc + x0) > 0)
{
x0 *= 2;
}
return(NewtonMethod.Solve(f, f1, xc + x0));
}
}
}
public void NthRoot_sqrt2_Eps6Returned()
{
//A
var expected = 1.4142;
//A
var actual = NewtonMethod.NthRoot(2, 2, 4);
//A
Debug.WriteLine(expected - actual);
Assert.IsTrue(condition: Math.Abs(expected - actual) < Math.Pow(10, -4));
}
public void NewtonMethod_ValidData_ValidResult_Test()
{
double number = double.Parse(TestContext.DataRow["Number"].ToString());
double degrre = double.Parse(TestContext.DataRow["Degree"].ToString());
double accuracy = double.Parse(TestContext.DataRow["Accuracy"].ToString());
double expected = double.Parse(TestContext.DataRow["Expected"].ToString());
double result = NewtonMethod.FindNthRoot(number, degrre, accuracy);
Assert.AreEqual(expected, result, accuracy);
}
public void NthRoot_3thminus1000_Eps15Returned()
{
//A
double expected = -10;
//A
var actual = NewtonMethod.NthRoot(-1000, 3, 15);
//A
Debug.WriteLine(expected - actual);
Assert.IsTrue(condition: Math.Abs(expected - actual) < Math.Pow(10, -15));
}
public void NthRoot_maxvalue_Eps15Returned()
{
//A
var expected = Math.Pow(double.MaxValue, 0.01);
//A
var actual = NewtonMethod.NthRoot(double.MaxValue, 100, 15);
//A
Debug.WriteLine(expected - actual);
Assert.IsTrue(condition: Math.Abs(expected - actual) < Math.Pow(10, -15));
}
public void Function_11_Test()
{
var a = 0.000000000001f;
var b = 2f;
var expectedResult = 0f;
var result1 = NewtonMethod.Evaluate(Function_11, a, b, accuracyLowerBound);
var result2 = NewtonMethod.Evaluate(Function_11, a, b, accuracyUpperBound);
Assert.LessOrEqual(result2.Value, expectedResult);
Console.WriteLine(result1);
Console.WriteLine(result2);
}
public void Pow_5And_NegativeNumber5_ShouldThrowExeption()
{
//Arrange
var power = 5;
var epsilon = 0.0000001;
var number = 0;
//Act
void GetException() => NewtonMethod.Pow(power, number, epsilon);
//Assert
Assert.Throws <ArgumentException>(GetException);
}
public void Function_15_Test()
{
var a = 0.2f;
var b = 2f;
var expectedResult = 2f;
var result1 = NewtonMethod.Evaluate(Function_15, a, b, accuracyLowerBound);
var result2 = NewtonMethod.Evaluate(Function_15, a, b, accuracyUpperBound);
Assert.GreaterOrEqual(result2.Iterations, expectedResult);
Console.WriteLine(result1);
Console.WriteLine(result2);
}
public void DrawInterpolation(LambdaFunc func, float step)
{
DrawFunction((x) => (float)(50 * func(x / 100) + 100),
Color.Black);
double[] pointsX = new double[] { 0, Math.PI / 2, Math.PI, Math.PI * 3 / 2, Math.PI * 2 };
double[] pointsY = new double[] { func(pointsX[0]), func(pointsX[1]), func(pointsX[2]), func(pointsX[3]), func(pointsX[4]) };
DrawFunction((x) => (float)(50 * NewtonMethod.Newton(x / 100, pointsX, pointsY, (float)step) + 100), Color.Red);
DrawFunction((x) => (float)(50 * LagrangeMethod.Langrange(x / 100, pointsX, pointsY, (float)step - 0.6f) + 100), Color.Green);
}
public void Function_9_Test()
{
var a = 0f;
float b = (float)Math.PI * (3f / 2f);
var result1 = NewtonMethod.Evaluate(Function_9, a, b, accuracyLowerBound);
var result2 = NewtonMethod.Evaluate(Function_9, a, b, accuracyUpperBound);
Assert.LessOrEqual(result2.Value, result1.Value);
Assert.GreaterOrEqual(result2.Iterations, result1.Iterations);
Console.WriteLine(result1);
Console.WriteLine(result2);
}
public void Test_Function()
{
var a = 1.6f;
var b = 6f;
var result1 = NewtonMethod.Evaluate(TestFunction, a, b, accuracyLowerBound);
var result2 = NewtonMethod.Evaluate(TestFunction, a, b, accuracyUpperBound);
Assert.LessOrEqual(result2.Value, result1.Value);
Assert.GreaterOrEqual(result2.Iterations, result1.Iterations);
Console.WriteLine(result1);
Console.WriteLine(result2);
}
public static void Update(DiffirentialEquationInput input)
{
_lagrange = new LagrangeMethod();
_newton = new NewtonMethod();
_repo = new FunctionRepository();
FuncInit();
X0 = input.X0;
XN = input.XN;
Y0 = input.Y0;
Accuracy = input.Accuracy;
FuncType = input.FuncType;
}
private static void Lab1()
{
var newton = new NewtonMethod(F, Df, Constants.A, Constants.B);
Console.WriteLine(newton.GetAnswer());
var simple = new SimpleIterations(F, Phi, Dphi, Constants.A, Constants.B);
Console.WriteLine(simple.GetAnswer());
//var simpleV2 = new SimpleIterationsV2(F, Phi, Dphi, Constants.Av2, Constants.Bv2);
//Console.WriteLine(simpleV2.GetAnswer());
}
public void Pow_5And_Number10_ShouldReturnCorrectValue()
{
//Arrange
var power = 5;
var epsilon = 0.0000001;
var number = 10;
var expected = Math.Pow(10, (double)1 / 5);
//Act
var actual = NewtonMethod.Pow(power, number, epsilon);
//Assert
Assert.AreEqual(expected, actual, epsilon, "Pow 5 and number 10 test is successful");
}
public void multimodal()
{
// x ^ 4 - 0.5 * x ^ 3 - 2 * x ^ 2;
// max12 -> 0.0, 0.0
// min1 -> (-0.83 ~0.01, -0.617 ~0.002)
// min2 -> ( 1.20 ~0.01, -1.670 ~0.002)
double func(Vector x) => x[0] * x[0] * (x[0] * x[0] - 0.5 * x[0] - 2.0);
NewtonMethod sut = new NewtonMethod()
{
Function = func,
MaxError = 1e-3,
MinPointChange = 1e-3,
Direction = 0,
};
var result = sut.FindMinimum(makePoint(-100.0));
Assert.AreEqual(-0.617, result.Value, 2e-3);
Assert.AreEqual(-0.83, result.Point[0], 1e-2);
result = sut.FindMinimum(makePoint(-0.01));
Assert.AreEqual(-0.617, result.Value, 2e-3);
Assert.AreEqual(-0.83, result.Point[0], 1e-2);
result = sut.FindMinimum(makePoint(0.01));
Assert.AreEqual(-1.670, result.Value, 2e-3);
Assert.AreEqual(1.2, result.Point[0], 1e-2);
result = sut.FindMinimum(makePoint(1.201));
Assert.AreEqual(-1.670, result.Value, 2e-3);
Assert.AreEqual(1.2, result.Point[0], 1e-2);
result = sut.FindMinimum(makePoint(1000));
Assert.AreEqual(-1.670, result.Value, 2e-3);
Assert.AreEqual(1.2, result.Point[0], 1e-2);
result = sut.FindMinimum(makePoint(0.0));
Assert.AreEqual(-0.617, result.Value, 2e-3);
Assert.AreEqual(-0.83, result.Point[0], 1e-2);
}
public ScalarValue Function(FunctionValue f, ScalarValue x)
{
Func <double, double> lambda = t =>
{
var sv = f.Perform(Context, new ScalarValue(t));
if (!(sv is ScalarValue))
{
throw new YAMPArgumentInvalidException(Name, sv.Header, 1);
}
return(((ScalarValue)sv).Re);
};
var newton = new NewtonMethod(lambda, x.Re, 0.00001);
return(new ScalarValue(newton.Result[0, 0]));
}
float CalcAttenuateRate()
{
float n = maxSENum;
return(NewtonMethod.run(
delegate(float p)
{
return (1.0f - Mathf.Pow(p, n)) / (1.0f - p) - 1.0f / initVolume;
},
delegate(float p)
{
float ip = 1.0f - p;
float t0 = -n * Mathf.Pow(p, n - 1.0f) / ip;
float t1 = (1.0f - Mathf.Pow(p, n)) / ip / ip;
return t0 + t1;
},
0.9f, 100
));
}
private void drawPlot(Func <double, double> func, double x0, double h, int count)
{
var polynomial = NewtonMethod.Interpolate(func, x0, h, count);
//Отступ, чтобы отрезок интерполяции занимал 75% графика (отступы - 12.5% каждый)
double offsetNodes = count * 0.125;
double left = x0 - offsetNodes * h;
double right = x0 + (offsetNodes + count - 1) * h;
if (left > right)
{
double temp = left;
left = right;
right = temp;
}
var myModel = new PlotModel {
Title = "График"
};
myModel.Series.Add(new FunctionSeries(func, left, right, 0.1, "f(x)"));
myModel.Series.Add(new FunctionSeries(polynomial.ValueAt, left, right, 0.1, "P(x)"));
var scatterSeries = new ScatterSeries {
MarkerType = MarkerType.Circle
};
for (int i = 0; i < count; i++)
{
double xn = x0 + i * h;
scatterSeries.Points.Add(new ScatterPoint(xn, func(xn), 5, 255));
}
myModel.Series.Add(scatterSeries);
plotView.Model = myModel;
}
public void Sqrt_ThrowsArgumentOutOfRangeException(double number, int n, double precision)
{
Assert.Throws <ArgumentOutOfRangeException>(() => NewtonMethod.Sqrt(number, n, precision));
}
public void NthRoot_sqrt2_sqrt2AccuracyEps16Returned()
{
var actual = NewtonMethod.NthRoot(2, 2, 16);
}
public void ExecuteMethod(
string nameMethod,
double param1,
double param2,
double param3,
double param4,
string testFunction,
int rangeArray,
double[] LinSysMasA,
double[,] LinSysMatrixB,
double[] massX,
double[] massF,
double[] massW,
double pointInterpolation,
double[,] MatrixAlgebraA,
double pointPercentile,
double pointGenerator)
{
TestFunction = testFunction;
switch (nameMethod)
{
//*** Approximate decision of equalization f(x)=0 ***
case "Bisection Method":
{
Bisection bisect = new Bisection(new FunctionOne(TestFunBisection), param1, param2, param3);
result = "\n Result of the program: \n" +
" x= " + string.Format("{0:f" + precision + "}", bisect.Result);
}
break;
case "Chord Method":
{
Сhord chord = new Сhord(new FunctionOne(TestFunNewton), new FunctionOne(TestFunNewton2), param1, param2, param3, param4);
result = "\n Result of the program: \n" +
" x= " + string.Format("{0:f" + precision + "}", chord.GetSolution());
}
break;
case "Iteration Method":
{
IterationMethod itermet = new IterationMethod(new FunctionOne(TestFunIteration), param1, param2, param3, param4);
result = "\n Result of the program: \n" +
" x= " + string.Format("{0:f" + precision + "}", itermet.GetSolution());
}
break;
case "Newton Method":
{
Newton newton = new Newton(new FunctionOne(TestFunNewton), new FunctionOne(TestFunNewton2), param1, param2, param3, param4);
result = "\n Result of the program: \n" +
" x= " + string.Format("{0:f" + precision + "}", newton.GetSolution());
}
break;
//*** Differential Equations ***
case "Euler Simple":
{
EulerSimple eulersimpl = new EulerSimple(new Function(TestFunDifferEquations), param1, param2, param3, Convert.ToInt32(param4));
var result_eulersimpl = eulersimpl.Result;
for (int j = 0; j < Convert.ToInt32(param4); j++)
{
result = result + string.Format("{0:f" + precision + "}", result_eulersimpl[0, j])
+ " : "
+ string.Format("{0:f" + precision + "}", result_eulersimpl[1, j]) + "\n";
}
}
break;
case "Euler Modified":
{
EulerModified eulerModif = new EulerModified(new Function(TestFunDifferEquations), param1, param2, param3, Convert.ToInt32(param4));
var result_eulerModif = eulerModif.Result;
for (int j = 0; j < Convert.ToInt32(param4); j++)
{
result = result + string.Format("{0:f" + precision + "}", result_eulerModif[0, j])
+ " : " + string.Format("{0:f" + precision + "}", result_eulerModif[1, j]) + "\n";
// result = result + "fun=\n";
// result = result +Convert.ToString( TestFunDifferEquations);
}
}
break;
case "Euler Corrected":
{
EulerCorrected eulerCorrect = new EulerCorrected(new Function(TestFunDifferEquations), param1, param2, param3, Convert.ToInt32(param4));
var result_eulerCorrect = eulerCorrect.Result;
for (int j = 0; j < Convert.ToInt32(param4); j++)
{
result = result + string.Format("{0:f" + precision + "}", result_eulerCorrect[0, j])
+ " : " + string.Format("{0:f" + precision + "}", result_eulerCorrect[1, j]) + "\n";
}
}
break;
case "Runge-Kutta4":
{
RungeKutta4 rungeKutta4 = new RungeKutta4(new Function(TestFunDifferEquations), param1, param2, param3, Convert.ToInt32(param4));
var result_rungeKutta4 = rungeKutta4.Result;
for (int j = 0; j < Convert.ToInt32(param4); j++)
{
result = result + string.Format("{0:f" + precision + "}", result_rungeKutta4[0, j])
+ " : " + string.Format("{0:f" + precision + "}", result_rungeKutta4[1, j]) + "\n";
}
}
break;
//*** Integration ***
case "Chebishev":
Chebishev chebish = new Chebishev(new FunctionOne(TestFunInteger), param1, param2, Convert.ToInt32(param3));
var result_chebish = chebish.GetSolution();
for (int j = 0; j <= Convert.ToInt32(param3); j++)
{
result = result + "\n h = " + string.Format("{0:f" + precision + "}", result_chebish[1, j]) + " \t integral = "
+ string.Format("{0:f" + precision + "}", result_chebish[0, j]);
}
break;
case "Simpson":
Simpson simps = new Simpson(new FunctionOne(TestFunInteger), param1, param2, Convert.ToInt32(param3));
var result_simps = simps.GetSolution();
for (int j = 0; j <= Convert.ToInt32(param3); j++)
{
result = result + "\n h = " + string.Format("{0:f" + precision + "}", result_simps[1, j]) +
" \t integral = " + string.Format("{0:f" + precision + "}", result_simps[0, j]);
}
break;
case "Simpson2":
Simpson2 simps2 = new Simpson2(new FunctionOne(TestFunInteger), param1, param2, Convert.ToInt32(param3));
var result_simps2 = simps2.GetSolution();
result = "\n\n integral = " + string.Format("{0:f" + precision + "}", result_simps2);
break;
case "Trapezium":
Trapezium trapez = new Trapezium(new FunctionOne(TestFunInteger), param1, param2, Convert.ToInt32(param3));
var result_trapez = trapez.GetSolution();
for (int j = 0; j <= Convert.ToInt32(param3); j++)
{
result = result + "\n h = " + string.Format("{0:f" + precision + "}", result_trapez[1, j])
+ " \t integral = " + string.Format("{0:f" + precision + "}", result_trapez[0, j]);
}
break;
//*** Non Linear equalization ***
case "Half Division":
HalfDivision halfdiv = new HalfDivision(new FunctionOne(TestFunNonLinearEquations), param1, param2, param3);
result = "\n X = " + string.Format("{0:f" + precision + "}", halfdiv.GetSolution()[0, 0])
+ " Iterations = " + string.Format("{0:f" + precision + "}", halfdiv.GetSolution()[1, 0]);
break;
case "Hord Metod":
HordMetod hormet = new HordMetod(new FunctionOne(TestFunNonLinearEquations), param1, param2, Convert.ToInt32(param3));
result = "\n X = " + string.Format("{0:f" + precision + "}", hormet.GetSolution()[0, 0])
+ " Iterations = " + string.Format("{0:f" + precision + "}", hormet.GetSolution()[1, 0]);
break;
case "Newton Metod":
NewtonMethod newt = new NewtonMethod(new FunctionOne(TestFunNonLinearEquations), param1, param2);
result = "\n X = " + string.Format("{0:f" + precision + "}", newt.GetSolution()[0, 0])
+ " Iterations = " + string.Format("{0:f" + precision + "}", newt.GetSolution()[1, 0]);
break;
case "Secant Metod":
Secant sec = new Secant(new FunctionOne(TestFunNonLinearEquations), param1, param2);
result = "\n X = " + string.Format("{0:f" + precision + "}", sec.GetSolution()[0, 0])
+ " Iterations = " + string.Format("{0:f" + precision + "}", sec.GetSolution()[1, 0]);
break;
default:
result = "";
break;
//*** Linear Systems ***
case "Gaus":
double[,] LinSysMatrix;
LinSysMatrix = new double[100, 100];
for (int l = 0; l < rangeArray; l++)
{
for (int j = 0; j < rangeArray; j++)
{
LinSysMatrix[l, j] = LinSysMatrixB[l, j];
}
LinSysMatrix[l, rangeArray] = LinSysMasA[l];
}
Gaus gaus = new Gaus(4, LinSysMatrix);
var result_gaus = gaus.GetSolution();
result = "";
for (int j = 0; j < result_gaus.Length; j++)
{
result = result + "\n X" + j + " = "
+ string.Format("{0:f" + precision + "}", result_gaus[j]) + ";";
}
break;
case "Zeidel":
Zeidel zeidel = new Zeidel(4, LinSysMatrixB, LinSysMasA);
var result_zeidel = zeidel.GetSolution();
result = "";
for (int j = 0; j < result_zeidel.Length; j++)
{
result = result + "\n X" + j + " = "
+ string.Format("{0:f" + precision + "}", result_zeidel[j]) + ";";
}
break;
//*** Interpolation ***
case "Lagrange Interpolator":
LagrangeInterpolator lagran = new LagrangeInterpolator(massX, massF, 6, pointInterpolation);
result = "\n A value interpolation polynomial is in the point of interpolation.";
result = result + "\n\n P = " + string.Format("{0:f" + precision + "}", lagran.GetSolution());
break;
case "Newton Interpolator":
NewtonInterpolator newinterpol = new NewtonInterpolator(massX, massF, 6, pointInterpolation);
result = "\n A value interpolation polynomial is in the point of interpolation.";
result = result + "\n\n P = " + string.Format("{0:f" + precision + "}", newinterpol.GetSolution());
break;
case "Neville Interpolator":
NevilleInterpolator newill = new NevilleInterpolator(massX, massF, 6, pointInterpolation);
result = "\n A value interpolation polynomial is in the point of interpolation.";
result = result + "\n\n P = " + string.Format("{0:f" + precision + "}", newill.GetSolution());
break;
case "Spline Interpolator":
SplineInterpolator spline = new SplineInterpolator(massX, massF, 6, pointInterpolation);
result = "\n A value interpolation polynomial is in the point of interpolation.";
result = result + "\n\n P = " + string.Format("{0:f" + precision + "}", spline.GetSolution());
break;
case "Barycentric Interpolator":
BarycentricInterpolation barycen = new BarycentricInterpolation(massX, massF, massW, 6, pointInterpolation);
result = "\n A value interpolation polynomial is in the point of interpolation.";
result = result + "\n\n P = " + string.Format("{0:f" + precision + "}", barycen.GetSolution());
break;
//*** Matrix Algebra ***
case "Matrix Determinant":
MatrixDeterminant matrdet = new MatrixDeterminant();
result = " \n\n\n Determinant = " + string.Format("{0:f" + precision + "}", matrdet.MatrixDet(MatrixAlgebraA, rangeArray)) + ";\n";
break;
case "RMatrix LU":
MatrixLU matrlu = new MatrixLU(MatrixAlgebraA, rangeArray, rangeArray);
var result_matrlu = matrlu.GetSolution();
var result_matrlu2 = matrlu.GetSolution2();
result = "A:\n";
for (int ii = 0; ii < rangeArray; ii++)
{
for (int j = 0; j < rangeArray; j++)
{
result = result + " \t " + string.Format("{0:f" + precision + "}", result_matrlu[ii, j]);
}
result = result + " \n";
}
result = result + "\nL:\n";
for (int ii = 0; ii < rangeArray; ii++)
{
result = result + " " + string.Format("{0:f" + precision + "}", result_matrlu2[ii]);
}
result = result + " \n ";
break;
case "Matrix Inverse LU":
RMatrixLuInverse matrluinv = new RMatrixLuInverse();
MatrixLU matrlu2 = new MatrixLU(MatrixAlgebraA, rangeArray, rangeArray);
if (matrluinv.rmatrixluinverse(MatrixAlgebraA, rangeArray, matrlu2.GetSolution2()) == true)
{
result = "\n An inverse matrix exists \n\n ";
var result_matrluinv = matrluinv.GetSolution();
for (int ii = 0; ii < rangeArray; ii++)
{
for (int j = 0; j < rangeArray; j++)
{
result = result + " \t" + string.Format("{0:f" + precision + "}", result_matrluinv[ii, j]);
}
result = result + "\n\n";
}
}
else
{
result = "\n An inverse matrix does not exist";
}
break;
//*** Optimizing***
case "Brentopt":
Brentopt brent = new Brentopt(new FunctionOne(TestFunOptimizing), param1, param2, param3);
result = "\n Point of the found minimum :";
result = result + "\n\n XMin = " + string.Format("{0:f" + precision + "}", brent.GetSolution());
result = result + "\n\n A value of function is in the found minimum :";
result = result + "\n\n F(XMin) = " + string.Format("{0:f" + precision + "}", brent.GetSolutionFunction());
break;
case "Golden Section":
GoldenSection godsection = new GoldenSection(new FunctionOne(TestFunOptimizing), param1, param2, Convert.ToInt32(param3));
result = "\n Scopes of segment which a decision of task is on .";
result = result + "\n\n a = " + string.Format("{0:f" + precision + "}", godsection.GetSolutionA());
result = result + "\n\n b = " + string.Format("{0:f" + precision + "}", godsection.GetSolutionB());
break;
case "Pijavsky":
Pijavsky pijavsky = new Pijavsky(new FunctionOne(TestFunOptimizing), param1, param2, param3, Convert.ToInt32(param4));
result = "\n Abscissa of the best point from found..";
result = result + "\n\n F = " + string.Format("{0:f" + precision + "}", pijavsky.GetSolution());
break;
//*** Statistics ***
case "Correlation Pearson":
CorrelationPearson corelperson = new CorrelationPearson(massX, massF, 6);
result = "\n Pearson product-moment correlation coefficient.";
result = result + "\n\n K = " + string.Format("{0:f" + precision + "}", corelperson.GetSolution());
break;
case "Correlation Spearmans Rank":
CorrelationSpearmansRank corelspear = new CorrelationSpearmansRank(massX, massF, 6);
result = "\n Pearson product-moment correlation coefficient.";
result = result + "\n\n K = " + string.Format("{0:f" + precision + "}", corelspear.GetSolution());
break;
case "Descriptive Statistics Median":
DescriptiveStatisticsADevMedian desceripM = new DescriptiveStatisticsADevMedian(massX, 6);
result = "\n Output parameters:";
result = result + "\n\n M = " + string.Format("{0:f" + precision + "}", desceripM.GetSolution());
break;
case "Descriptive Statistics Moments":
DescriptiveStatisticsMoments desceripMo = new DescriptiveStatisticsMoments(massX, 6);
result = "\n Output parameters:";
result = result + "\n\n M = " + string.Format("{0:f" + precision + "}", desceripMo.GetSolution());
result = result + "\n\n Variance = " + string.Format("{0:f" + precision + "}", desceripMo.variance);
result = result + "\n\n Skewness = " + string.Format("{0:f" + precision + "}", desceripMo.skewness) + " (if variance<>0; zero otherwise)";
result = result + "\n\n Kurtosis = " + string.Format("{0:f" + precision + "}", desceripMo.kurtosis) + " (if variance<>0; zero otherwise)";
break;
case "Descriptive Statistics Percentile":
DescriptiveStatisticsPercentile desceripP = new DescriptiveStatisticsPercentile(massX, 6, pointPercentile);
result = "\n Output parameters:";
result = result + "\n\n V = " + string.Format("{0:f" + precision + "}", desceripP.GetSolution());
break;
case "Generator 1":
RandomGeneratorsMethod1 random1 = new RandomGeneratorsMethod1();
result = "\n Output parameters:";
result = result + "\n\n Random = " + string.Format("{0:f" + precision + "}", random1.GetSolution());
break;
case "Generator 2":
RandomGeneratorsMethod2 random2 = new RandomGeneratorsMethod2(Convert.ToInt32(pointGenerator));
result = "\n Output parameters:";
result = result + "\n\n Random = " + string.Format("{0:f" + precision + "}", random2.GetSolution());
break;
case "Generator 3":
RandomGeneratorsMethod3 random3 = new RandomGeneratorsMethod3();
result = "\n Output parameters:";
result = result + "\n\n Random = " + string.Format("{0:f" + precision + "}", random3.GetSolution());
break;
case "Generator 4":
RandomGeneratorsMethod4 random4 = new RandomGeneratorsMethod4();
result = "\n Output parameters:";
result = result + "\n\n Random = " + string.Format("{0:f" + precision + "}", random4.GetSolution());
break;
case "Generator 5":
RandomGeneratorsMethod5 random5 = new RandomGeneratorsMethod5(pointGenerator);
result = "\n Output parameters:";
result = result + "\n\n Random = " + string.Format("{0:f" + precision + "}", random5.GetSolution());
break;
}
}
public double Sqrt_PositiveTest(double number, int n, double precision = 0.000001)
{
return(NewtonMethod.Sqrt(number, n, precision));
}