/// <summary>
/// Computes the quotient of two multi-intervals
/// </summary>.
public static MultiInterval Divide(MultiInterval dividend, MultiInterval divisor)
{
List <Interval> aIntervals = dividend._intervals;
List <Interval> bIntervals = divisor._intervals;
MultiInterval multiInterval = new MultiInterval();
for (int i = 0; i < aIntervals.Count; i++)
{
for (int j = 0; j < bIntervals.Count; j++)
{
Interval intervalDivisor = bIntervals[j];
if (intervalDivisor.Contains(0))
{
multiInterval.Add(Interval.Divide(aIntervals[i], new Interval(0, intervalDivisor.UpperBound)));
multiInterval.Add(Interval.Divide(aIntervals[i], new Interval(intervalDivisor.LowerBound, 0)));
}
else
{
multiInterval.Add(Interval.Divide(aIntervals[i], intervalDivisor));
}
}
}
return(multiInterval);
}
/// <summary>
/// Computes the union of two multi-intervals
/// </summary>
public static MultiInterval Union(MultiInterval a, MultiInterval b)
{
MultiInterval multiInterval = a.Clone();
foreach (var interval in b._intervals)
{
multiInterval.Add(interval);
}
return(multiInterval);
}
/// <summary>
/// Extends the multi-interval to contain the specified value.
/// </summary>
public MultiInterval Extend(double value)
{
MultiInterval multiInterval = new MultiInterval();
for (int i = 0; i < _intervals.Count; i++)
{
Interval extended = _intervals[i].Extend(value);
multiInterval.Add(extended);
}
return(multiInterval);
}
/// <summary>
/// Computes the product of two multi-intervals
/// </summary>
public static MultiInterval Multiply(MultiInterval a, MultiInterval b)
{
List <Interval> aIntervals = a._intervals;
List <Interval> bIntervals = b._intervals;
MultiInterval multiInterval = new MultiInterval();
for (int i = 0; i < aIntervals.Count; i++)
{
for (int j = 0; j < bIntervals.Count; j++)
{
Interval product = Interval.Multiply(aIntervals[i], bIntervals[j]);
multiInterval.Add(product);
}
}
return(multiInterval);
}
/// <summary>
/// Subtracts two multi-intervals
/// </summary>
public static MultiInterval Subtract(MultiInterval a, MultiInterval b)
{
List <Interval> aIntervals = a._intervals;
List <Interval> bIntervals = b._intervals;
MultiInterval multiInterval = new MultiInterval();
for (int i = 0; i < aIntervals.Count; i++)
{
for (int j = 0; j < bIntervals.Count; j++)
{
Interval difference = Interval.Subtract(aIntervals[i], bIntervals[j]);
multiInterval.Add(difference);
}
}
return(multiInterval);
}
/// <summary>
/// Computes and returns the intersection between <paramref name="a"/> and <paramref name="b"/>
/// </summary>
public static MultiInterval Intersection(MultiInterval a, MultiInterval b)
{
List <Interval> aIntervals = a._intervals;
List <Interval> bIntervals = b._intervals;
MultiInterval multiInterval = new MultiInterval();
for (int i = 0; i < aIntervals.Count; i++)
{
for (int j = 0; j < bIntervals.Count; j++)
{
Interval intersection = Interval.Intersection(aIntervals[i], bIntervals[j]);
if (!intersection.IsEmpty)
{
multiInterval.Add(intersection);
}
}
}
return(multiInterval);
}