limit_sample_space

float  limit_sample_space(float minu, float maxu, float u)

float  limit_sample_space(float maxu, float u)

minu

Minimum desired value of u. minu will be clamped to between 0 and 1. If not specified, minu is 0.

maxu

Maximum desired value of u. maxu will be clamped to between 0 and 1.

u

Number between 0 and 1.

If u is outside of [minu,maxu], u is wrapped in the space in such a way that uniform random u in [0,1) will yield uniform random samples in [minu,maxu] and returned. This avoids the extra samples at the bounds of the range that clamping to the range would introduce. It also avoids the changing of samples inside the range that fitting to the range would introduce, i.e. if u is already in the range, the return value is exactly u.

However, this is much slower than fitting or clamping, so only use it when both uniformity and consistency are needed. For example, it can be useful in avoiding outliers in probability distributions without affecting samples that are not outliers. It also introduces the issue that results will no longer be monotone increasing with respect to u. Fitting will often suffice for avoiding outliers too, at the expense of slightly affecting samples that are not outliers.

To find minu and maxu given a minvalue and maxvalue of some probability distribution, minu = CDF(minvalue) and maxu = CDF(maxvalue), where CDF is the cumulative distribution function (not inverse) of the probability distribution. The versions of sample_exponential, sample_cauchy, sample_normal, sample_lognormal, and sample_lognormal_by_median that take a minvalue or maxvalue use fitting instead of this limiting, because it maintains monotonicity, but this function can be applied to u before sampling, in order to have better consistency for samples in the range.