/// <summary>
/// This method will find a root using regula falsi method
/// </summary>
/// <param name="source">
/// Function definition that implements IFunction interface.
/// </param>
/// <param name="args">
/// Arguments class containging info like max iterations value , first & second endpoints
/// of the interval given.
/// </param>
/// <returns>
/// Function root and metadata.
/// </returns>
public static FunctionRoot GetFunctionRootFalsi(IFunction source, GetFunctionRootArgs args)
{
int counter, side = 0;
double a = args.FromX, faVal = source.GetValue(args.FromX);
double b = args.ToX, fbVal = source.GetValue(args.ToX);
if (faVal * fbVal > 0)
{
throw new BoundaryFunctionValuesOfTheSameSignException
{
LeftValue = faVal,
RightValue = fbVal
}
}
;
for (counter = 1; counter < args.MaxIterations; counter++)
{
var x = (faVal * b - fbVal * a) / (faVal - fbVal);
var fxVal = source.GetValue(x);
if (Math.Abs(fxVal) < args.Approx)
{
return(new FunctionRoot
{
X = x,
Y = fxVal,
Iterated = counter,
Method_Used = "Falsi",
Group = source.TextRepresentation,
SourceId = source.Id,
Interval = $"[{args.FromX};{args.ToX}]"
});
}
if (fxVal * fbVal > 0)
{
b = x;
fbVal = fxVal;
if (side == -1)
{
faVal /= 2;
}
side = -1;
}
else
{
a = x;
faVal = fxVal;
if (side == 1)
{
fbVal /= 2;
}
side = 1;
}
}
throw new MaxIterationsReachedException();
}
}
/// <summary>
/// This method will find all roots of passed function using bisection.
/// </summary>
/// <param name="source">
/// Function definition that implements IFunction interface.
/// </param>
/// <param name="args">
/// Arguments class containging info like max iterations value , first & second endpoints
/// of the interval given.
/// </param>
/// <returns>
/// Function root and metadata.
/// </returns>
public static FunctionRoot GetFunctionRootBi(IFunction source, GetFunctionRootArgs args)
{
var counter = 1;
double val1 = source.GetValue(args.FromX),
val2 = source.GetValue(args.ToX);
double from = args.FromX, to = args.ToX;
if (val1 * val2 > 0)
{
throw new BoundaryFunctionValuesOfTheSameSignException
{
LeftValue = val1,
RightValue = val2
}
}
;
while (counter < args.MaxIterations)
{
var mid = (from + to) / 2;
var midVal = source.GetValue(mid);
if (Math.Abs(midVal) < args.Approx)
{
return(new FunctionRoot
{
X = mid,
Y = midVal,
Iterated = counter,
Method_Used = "Bi",
Group = source.TextRepresentation,
SourceId = source.Id,
Interval = $"[{args.FromX};{args.ToX}]"
});
}
mid = (from + to) / 2;
midVal = source.GetValue(mid);
if ((midVal < 0 && val1 < 0) || (midVal > 0 && val1 > 0))
{
from = mid;
}
else
{
to = mid;
}
counter++;
}
throw new MaxIterationsReachedException();
}
