[RNG-130] UnitSphereSampler for 1 dimension can return invalid length samples

• Type: Bug
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Affects Version/s: 1.3
• Fix Version/s: 1.4
• Component/s: sampling
• Assignee: Alex Herbert
• Reporter: Alex Herbert
• Created: 12/Apr/21 21:21
• Updated: 13/Sep/21 10:41
• Resolved: 15/Apr/21 22:04

Description

The UnitSphereSampler for 1 dimension currently creates a sample from a standard normal distribution and then normalises it to unit length. This can create values that are not 1 or -1.

The following code shows this occurs approximately 14% of the time:

final UniformRandomProvider rng =
    RandomSource.create(RandomSource.XO_RO_SHI_RO_128_PP, 0x1a2b3cL);
final UnitSphereSampler generator = new UnitSphereSampler(1, rng);
int count = 0;
int size = 1000000;
for (int i = size; i-- > 0; ) {
    final double[] v = generator.nextVector();
    if (Math.abs(v[0]) != 1.0) {
        count++;
    }
}
System.out.printf("%d / %d (%.3f)%n", count, size, 100.0 * count / size);

Outputs:

139977 / 1000000 (13.998)

This can be fixed by switching the sampling algorithm to use a bit from the random generator to pick either a 1 or -1 for the return value. This can be fixed as part of RNG-129 which is creating specialisations for sampling for lower order dimensions.

Issue Links

• is fixed by: RNG-129 Performance improvement for UnitSphereSampler
• is related to: RNG-129 Performance improvement for UnitSphereSampler