public IEnumerable <IShape> GenerateIllustrationForCurrentStep(IEnumerable <double> actualPoints, IDifferentiableTwice analyzedFunction, int iterationNumber)
{
if (!actualPoints.IsEnoughOfParams(4))
{
MethodsHelper.ThrowGreedlyException(actualPoints, 4);
}
var lastPoints = actualPoints.GetLastN(4);
var x1 = lastPoints[0];
var x2 = lastPoints[1];
var x3 = lastPoints[2];
var y1 = analyzedFunction.Compute(lastPoints[0]);
var y2 = analyzedFunction.Compute(lastPoints[1]);
var y3 = analyzedFunction.Compute(lastPoints[2]);
double B1;
double C1;
var A1 = ParabolaCoeffs(x1, x2, x3, y2, y1, y3, out B1, out C1);
yield return(new ShapeKeeper <IFunction>(new SimpleFunctionKeeper(x => x * x * A1 + x * B1 + C1),
new UsualExpandingDomain().Update(lastPoints[0]).Update(lastPoints[1]).Update(lastPoints[2]).Update(lastPoints[3]),
string.Format("Parabola on {0}x*x+{1}*x+{2} N{3}", A1, B1, C1, iterationNumber)
));
var rightRoot = (-B1 + Sign * Math.Sqrt(B1 * B1 - 4 * A1 * C1)) / (2 * A1);
yield return(new VerticalSegment(0, analyzedFunction.Compute(rightRoot), rightRoot, string.Format("Parabola step N{0}", iterationNumber)));
}
public IEnumerable <IShape> GenerateIllustrationForCurrentStep(IEnumerable <double> actualPoints, IFunction analyzedFunction, int iterationNumber)
{
if (!actualPoints.IsEnoughOfParams(3))
{
MethodsHelper.ThrowGreedlyException(actualPoints, 3);
}
var start = actualPoints.First();
var lastPoints = actualPoints.GetLastN(2);
yield return(new LineShape(new UsualExpandingDomain().Update(start).Update(lastPoints[0]).Update(lastPoints[1]),
new Point2D
{
X = start,
Y = analyzedFunction.Compute(start)
},
new Point2D()
{
X = lastPoints[0], Y = analyzedFunction.Compute(lastPoints[0])
},
string.Format("Chord of {0} step", iterationNumber)
));
yield return(new VerticalSegment(0,
analyzedFunction.Compute(lastPoints[1]),
lastPoints[1], string.Format("Chord step N{0}", iterationNumber)));
}
public IEnumerable <IShape> GenerateIllustrationForCurrentStep(IEnumerable <double> actualPoints, IDifferentiableTwice analyzedFunction, int iterationNumber)
{
if (!actualPoints.IsEnoughOfParams(4))
{
MethodsHelper.ThrowGreedlyException(actualPoints, 4);
}
var lastPoints = actualPoints.GetLastN(4);
var x1 = lastPoints[0];
var x2 = lastPoints[1];
var x3 = lastPoints[2];
var y1 = analyzedFunction.Compute(lastPoints[0]);
var y2 = analyzedFunction.Compute(lastPoints[1]);
var y3 = analyzedFunction.Compute(lastPoints[2]);
var denom = (x1 - x2) * (x1 - x3) * (x2 - x3);
var A1 = (x3 * (y2 - y1) + x2 * (y1 - y3) + x1 * (y3 - y2)) / denom;
var B1 = (Math.Pow(x3, 2) * (y1 - y2) + Math.Pow(x2, 2) * (y3 - y1) + Math.Pow(x1, 2) * (y2 - y3)) / denom;
var C1 = (x2 * x3 * (x2 - x3) * y1 + x3 * x1 * (x3 - x1) * y2 + x1 * x2 * (x1 - x2) * y3) / denom;
yield return(new ShapeKeeper <IFunction>(new SimpleFunctionKeeper(x => analyzedFunction.Compute(x3)
+ analyzedFunction.FirstDerivative.Compute(x3) * (x - x3)
- MaximumOfDoubleDiff * Math.Pow(x - x3, 2) / 2),
new UsualExpandingDomain().Update(lastPoints[0]).Update(lastPoints[1]).Update(lastPoints[2]).Update(lastPoints[3]),
string.Format("Porabola on {0}x*x+{1}*x+{2} N{3}", A1, B1, C1, iterationNumber)
));
yield return(new VerticalSegment(0, analyzedFunction.Compute(lastPoints[3]), lastPoints[3], string.Format("Mullers step N{0}", iterationNumber)));
}
public IEnumerable <double> ComputeNext(IEnumerable <double> previuosPoints, IFunction analyzedFunction)
{
if (!previuosPoints.IsEnoughOfParams(2))
{
MethodsHelper.ThrowGreedlyException(previuosPoints, 2);
}
yield return(MethodStep(previuosPoints.First(), previuosPoints.Last(), analyzedFunction.Compute));
}
public IEnumerable <double> ComputeNext(IEnumerable <double> previuosPoints, IFunction analyzedFunction)
{
if (!previuosPoints.IsEnoughOfParams(2))
{
MethodsHelper.ThrowGreedlyException(previuosPoints, 2);
}
var lastPoints = previuosPoints.GetLastN(2);
yield return(MethodStep(lastPoints[0], lastPoints[1], analyzedFunction.Compute));
}
public IEnumerable <double> ComputeNext(IEnumerable <double> previuosPoints, IDifferentiableTwice analyzedFunction)
{
if (!previuosPoints.IsEnoughOfParams(3))
{
MethodsHelper.ThrowGreedlyException(previuosPoints, 3);
}
var lastPoints = previuosPoints.GetLastN(3);
var differed = analyzedFunction.FirstDerivative.Compute(lastPoints[2]);
var deltaXi = (-differed + Sign * Math.Sqrt(differed * differed + 2 * MaximumOfDoubleDiff * (analyzedFunction.Compute(lastPoints[2])))) / (-MaximumOfDoubleDiff);
yield return(deltaXi + lastPoints[2]);
}
public IEnumerable <IShape> GenerateIllustrationForCurrentStep(IEnumerable <double> actualPoints, IFunction analyzedFunction, int iterationNumber)
{
if (!actualPoints.IsEnoughOfParams(2))
{
MethodsHelper.ThrowGreedlyException(actualPoints, 2);
}
var lastPoints = actualPoints.GetLastN(2);
for (var i = 0; i < 2; i++)
{
var onLinePoint = analyzedFunction.Compute(lastPoints[i]);
yield return(new VerticalSegment(onLinePoint + 1, onLinePoint - 1, lastPoints[i], String.Format("Bound({0}) N{1}", lastPoints[i], iterationNumber)));
}
}
public IEnumerable <double> ComputeNext(IEnumerable <double> previuosPoints, IDifferentiableOnce analyzedFunction)
{
if (!previuosPoints.IsEnoughOfParams(1))
{
MethodsHelper.ThrowGreedlyException(previuosPoints, 1);
}
var prevPoint = previuosPoints.Last();
if (prevPoint < 0)
{
throw new Exception("Метод Ньютона - тыква. Касательная ушла не туда. Надо попробовать начать метод с другой стороны от корня.");
}
var inPoint = analyzedFunction.Compute(prevPoint);
var inPointDerivative = analyzedFunction.FirstDerivative.Compute(prevPoint);
yield return(prevPoint - inPoint / inPointDerivative);
}
public IEnumerable <double> ComputeNext(IEnumerable <double> previuosPoints, IFunction analyzedFunction)
{
if (!previuosPoints.IsEnoughOfParams(2))
{
MethodsHelper.ThrowGreedlyException(previuosPoints, 2);
}
var lastPoints = previuosPoints.GetLastN(2);
var bisect = lastPoints.Average();
if (Math.Abs(analyzedFunction.Compute(bisect)) < double.Epsilon)
{
return(Enumerable.Empty <double>());
}
var firstSegment = analyzedFunction.Compute(lastPoints[0]) * analyzedFunction.Compute(bisect);
if (firstSegment < 0)
{
return new[] { lastPoints[0], bisect }
}
;
var seconsSegment = analyzedFunction.Compute(bisect) * analyzedFunction.Compute(lastPoints[1]);
if (seconsSegment < 0)
{
return new[] { bisect, lastPoints[1] }
}
;
throw new Exception(string.Format("Метод деления пополам сломался. Выбран отрезок с концами одного знака(f({0}) = {1},f({2}) = {3})",
lastPoints[0],
analyzedFunction.Compute(lastPoints[0]),
lastPoints[1],
analyzedFunction.Compute(lastPoints[1])));
}
public IEnumerable <IShape> GenerateIllustrationForCurrentStep(IEnumerable <double> actualPoints, IDifferentiableOnce analyzedFunction, int iterationNumber)
{
if (!actualPoints.IsEnoughOfParams(2))
{
MethodsHelper.ThrowGreedlyException(actualPoints, 2);
}
var lastPoints = actualPoints.GetLastN(2);
yield return(new LineShape(new UsualExpandingDomain().Update(lastPoints[0]).Update(lastPoints[1]),
new Point2D {
X = lastPoints[0], Y = analyzedFunction.Compute(lastPoints[0])
},
new Point2D {
X = lastPoints[1], Y = 0
},
string.Format("Secant N{0}", iterationNumber)));
yield return(new VerticalSegment(0,
analyzedFunction.Compute(lastPoints[1]),
lastPoints[1],
string.Format("Newton step N{0}", iterationNumber)));
}
public IEnumerable <double> ComputeNext(IEnumerable <double> previuosPoints, IDifferentiableTwice analyzedFunction)
{
if (!previuosPoints.IsEnoughOfParams(3))
{
MethodsHelper.ThrowGreedlyException(previuosPoints, 3);
}
var lastPoints = previuosPoints.GetLastN(3).ToList();
lastPoints.Sort();
var x1 = lastPoints[0];
var x2 = lastPoints[1];
var x3 = lastPoints[2];
var y1 = analyzedFunction.Compute(lastPoints[0]);
var y2 = analyzedFunction.Compute(lastPoints[1]);
var y3 = analyzedFunction.Compute(lastPoints[2]);
double B1;
double C1;
var A1 = ParabolaCoeffs(x1, x2, x3, y2, y1, y3, out B1, out C1);
var root = (-B1 + Sign * Math.Sqrt(B1 * B1 - 4 * A1 * C1)) / (2 * A1);
if (x1 < root && root < x2)
{
return new List <double> {
x1, root, x2
}
}
;
if (x2 < root && root < x3)
{
return new List <double> {
x2, root, x3
}
}
;
root = (-B1 - Sign * Math.Sqrt(B1 * B1 - 4 * A1 * C1)) / (2 * A1);
if (x1 < root && root < x2)
{
return new List <double> {
x1, root, x2
}
}
;
if (x2 < root && root < x3)
{
return new List <double> {
x2, root, x3
}
}
;
return(new List <double> {
x2, root, x3
});
throw new Exception();
}