private void InitInterpolationWithBoundedError(double maxPermittedError)
{
int rank = 1, startRank = 1, midPointRank = 1;
var prevPdf = PDF(rank);
var prevCdf = prevPdf;
var midPointCdf = prevCdf;
InterpolationCDFRanks.Add(1);
InterpolationCDFValues.Add(prevCdf);
// Advance three pointers, one at the start of the segment, one at the midpoint, and one at the end.
// The midpoint advances at half the speed of the end of the segment.
for (rank = 2; rank <= N - 1; rank++)
{
var currPdf = PDF(rank);
var currCdf = Min(1.0, prevCdf + currPdf);
if ((rank - startRank) % 2 == 0)
{
midPointRank++;
midPointCdf += PDF(midPointRank);
}
// No need to interpolate if the segment has no gap that needs interpolating.
if (rank - startRank >= 2)
{
// Add a provisional interpolation point.
InterpolationCDFRanks.Add(rank);
InterpolationCDFValues.Add(currCdf);
// Calculate the interpolation error for the midpoint.
// If it is still small enough, remove the provisional interpolation point.
var endPointPosition = InterpolationSize - 1;
var cdfInterpolator = CDFInterpolator(endPointPosition);
var estimatedMidpointCdf = Min(1.0, cdfInterpolator.Y(midPointRank));
var relativeError = Abs(midPointCdf - estimatedMidpointCdf) / midPointCdf;
InterpolationCDFRanks.RemoveAt(endPointPosition);
InterpolationCDFValues.RemoveAt(endPointPosition);
// It is not guaranteed that the midpoint of the segment is where the worst error would be found.
// Thus permit less error than requested in the hope that this will keep the true maximum error
// below maxPermittedError as well.
if (relativeError >= maxPermittedError / 7)
{
// We decided we need an interpolation point, thus are starting a new segment.
midPointRank = startRank = rank - 1;
midPointCdf = prevCdf;
InterpolationCDFRanks.Add(rank - 1);
InterpolationCDFValues.Add(prevCdf);
}
}
prevPdf = currPdf;
prevCdf = currCdf;
}
// Close out the last segment.
InterpolationCDFRanks.Add(N);
InterpolationCDFValues.Add(1);
}
/// <summary>
/// Perform no interpolation; store CDF values for all ranks, which may consume much memory.
/// </summary>
private void InitInterpolationWithZeroError()
{
var cdf = 0.0;
for (var rank = 1; rank <= N; rank++)
{
cdf += PDF(rank);
InterpolationCDFRanks.Add(rank);
InterpolationCDFValues.Add(cdf);
}
}
