Alex D Herbert created RNG-55:
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Summary: UnitSphereSampler
Key: RNG-55
URL: https://issues.apache.org/jira/browse/RNG-55
Project: Commons RNG
Issue Type: Bug
Components: sampling
Affects Versions: 1.1
Reporter: Alex D Herbert
The {{UnitSphereSampler}} does not check for zero length dimension. This doesn't cause a fail but maybe should be raised as an error? The user will find out when they call {{nextVector()}} with an {{NegativeArraySizeException}} anyway.
However the algorithm can fail under the extremely unlikely condition that the {{NormalizedGaussianSampler}} returns {{0}} for each dimension. This is more likely when using {{dimension==1}}.
The returned vector will be {{Double.NaN}} for each dimension due to the use of {{1 / Math.sqrt(0)}}:
{code:java}
// f will be Double.POSITIVE_INFINITY
final double f = 1 / Math.sqrt(normSq);
for (int i = 0; i < dimension; i++) {
// v will be Double.NaN as 0 * Double.POSITIVE_INFINITY is Double.NaN
v[i] *= f;
}
{code}
Here is a test that demonstrates it. All it requires in the RNG to provide a long of 0 to the internal {{ZigguratNormalizedGaussianSampler}}:
{code:java}
@Test
public void testBadRNG() {
final UniformRandomProvider rng = new UniformRandomProvider() {
public long nextLong(long n) { return 0; }
public long nextLong() { return 0; }
public int nextInt(int n) { return 0; }
public int nextInt() { return 0; }
public float nextFloat() { return 0; }
public double nextDouble() { return 0;}
public void nextBytes(byte[] bytes, int start, int len) {}
public void nextBytes(byte[] bytes) {}
public boolean nextBoolean() { return false; }
};
UnitSphereSampler s = new UnitSphereSampler(1, rng);
double[] v = s.nextVector();
Assert.assertNotNull(v);
Assert.assertEquals(1, v.length);
Assert.assertTrue(Double.isNaN(v[0]));
}
{code}
This can be fixed by an outer loop:
{code:java}
/**
* @return a random normalized Cartesian vector.
*/
public double[] nextVector() {
final double[] v = new double[dimension];
// Pick a point by choosing a standard Gaussian for each element,
// and then normalize to unit length.
double normSq = 0;
while (normSq == 0) {
for (int i = 0; i < dimension; i++) {
final double comp = sampler.sample();
v[i] = comp;
normSq += comp * comp;
}
}
final double f = 1 / Math.sqrt(normSq);
for (int i = 0; i < dimension; i++) {
v[i] *= f;
}
return v;
}
{code}
But this can then infinite loop if the {{NormalizedGaussianSampler}} always returns 0 (as for the dummy test case above).
Q. What is the lesser evil of a vector with NaN (as with the current implementation) or never returning in an extreme edge case?
Throwing an exception would change the API.
Returning the vector [1,0,0,....] would fix the edge case but not alert the user to a broken RNG:
{code:java}
/**
* @return a random normalized Cartesian vector.
*/
public double[] nextVector() {
final double[] v = new double[dimension];
// Pick a point by choosing a standard Gaussian for each element,
// and then normalize to unit length.
double normSq = 0;
for (int i = 0; i < dimension; i++) {
final double comp = sampler.sample();
v[i] = comp;
normSq += comp * comp;
}
if (normSq == 0) {
// Extreme edge case
if (dimension != 0)
v[0] = 1;
return v;
}
final double f = 1 / Math.sqrt(normSq);
for (int i = 0; i < dimension; i++) {
v[i] *= f;
}
return v;
}
{code}
This is all extremely unlikely however I noticed as I was reviewing new classes in V1.1 and saw this problem that I have hit before in a random walk simulation.
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