通用线性分段查找表

Question

I am looking for a generic optimized lookup object that takes a function f(x) and creates a linear piecewise approximation with configurable parameters for the range of x and the intervals of population.

Obviously this is not hard to write, but given that it is useful for a lot of expensive functions (trig, yield, distance), I thought a generic one might already exist. Please let me know.

Another useful feature would be to serialize / deserialize the lookup table as a rather precise 100,000 point+ table can take several minutes to construct.

Answer 1

I don't believe anything exists in the .NET class libraries directly. Something may exist in a third party library ( like C5 perhaps ).

Creating a generic version of a function that can accept ranges is a bit tricky in C#, since there is no unifying type or interface which provides arithmetic operators. However, with some creativity, it's possible to craft something:

// generic linear lookup class, supports any comparable type T
public class LinearLookup<T>  where T : IComparable<T>
{
    private readonly List<T> m_DomainValues = new List<T>();

    public LinearLookup( Func<T,T> domainFunc, Func<T,T> rangeFunc, 
          T lowerBound, T upperBound )
    {
        m_DomainValues = Range( domainFunc, rangeFunc, 
                                lowerBound, upperBound )
                           .ToList();
    }

    public T Lookup( T rangeValue )
    {
        // this could be improved for numeric types
        var index = m_DomainValues.BinarySearch( rangeValue );
        if( index < 0 )
            index = (-index)-1;
        return m_DomainValues[index];
    }

    private static IEnumerable<T> Range( Func<T,T> domainFunc, 
         Func<T,T> rangeFunc, T lower, T upper )
    {
        var rangeVal = lower;
        do
        {
            yield return domainFunc( rangeVal );

            rangeVal = rangeFunc( rangeVal );

        } while( rangeVal.CompareTo( upper ) < 0 );
    }
}

This class will precompute a set of domain values for the function domainFunc over the range [lower,upper>. It uses binary search for lookup - a compromise that allows any comparable type to be used - not just built in numeric types. The function rangeFunc allows the increment to be controlled by external code. So, here's a linear lookup for Math.Sin over the range [0,PI/2> with an increment of 0.01:

var sinLookup = new LinearLookup( Math.Sin, x => x + 0.01d, 0, Math.PI/2 );
var lookupPI4 = sinLookup[Math.PI/4]; // fetch the value sin(π/4)