internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial result = poly1 + poly2 - (poly1 * poly2);
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, result));
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial sum = poly1 + poly2;
BinaryInterval temp = new BinaryInterval(operands.LowerBound, operands.UpperBound, sum.Coefficients, (new Polynomial(1)).Coefficients);
GetMinMax(temp, ref output, true);
}
internal virtual void Operate(BinaryInterval operands, ref IntervalSet output )
{
throw new NotImplementedException();
}
/// <summary>
/// Builds minimum/maximum function for the given interval. The method is used directly in AndM and OrM, and as a part of calculation in other operators.
/// </summary>
/// <param name="operands"></param>
/// <param name="output"></param>
/// <param name="minimum"></param>
internal static void GetMinMax(BinaryInterval operands, ref IntervalSet output, bool minimum)
{
//Find all points where operand1 = operand2 for the given interval
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial difference = poly1 - poly2;
if (Interval.IsEmpty(difference)) //both opearands are equal
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, poly1));
else
{
decimal[] roots = Interval.RealRoots(difference, operands.LowerBound, operands.UpperBound);
if (roots.Length == 0)
{ //just find out which function is higher for the whole interval
double r1 = poly1.Evaluate(new Complex((double)operands.LowerBound)).Re;
double r2 = poly2.Evaluate(new Complex((double)operands.LowerBound)).Re;
if ((minimum && r1 <= r2) || (!minimum && r1 > r2))
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, poly1));
else
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, poly2));
}
else
{
List<decimal> crossPoints = new List<decimal>();
crossPoints.AddRange(roots);
if (! crossPoints.Contains(operands.LowerBound))
crossPoints.Add(operands.LowerBound);
if (!crossPoints.Contains(operands.UpperBound))
crossPoints.Add(operands.UpperBound);
crossPoints.Sort();
//Declares that value of operand1 is higher than the value of operand2 for the given range;
for (int i = 0; i < crossPoints.Count() - 1; i++)
{
bool firstIsPreffered;
if (roots.Contains(crossPoints[i]))
{
double deriv1 = poly1.Differentiate(new Complex((double)crossPoints[i])).Re;
double deriv2 = poly2.Differentiate(new Complex((double)crossPoints[i])).Re;
firstIsPreffered = (minimum && deriv1 < deriv2) || (!minimum && deriv1 > deriv2);
}
else
{ //it must be the second one, then
double deriv1 = poly1.Differentiate(new Complex((double)crossPoints[i + 1])).Re;
double deriv2 = poly2.Differentiate(new Complex((double)crossPoints[i + 1])).Re;
firstIsPreffered = (minimum && deriv2 < deriv1) || (!minimum && deriv2 > deriv1);
}
output.AddInterval(new Interval(output, crossPoints[i], crossPoints[i + 1], firstIsPreffered ? poly1 : poly2));
}
}
}
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial multipl = (Operand1Power ? poly1^2 : poly1) + (Operand2Power ? poly2^2 : poly2);
if (this.FinalDivision)
multipl = multipl / RssDescendantCount;
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, multipl));
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
GetMinMax(operands, ref output, true);
}