/// <summary>
/// Takes an array of doubles as
/// input, and returns a randomly-selected index into the array
/// as an `Int`. The probability of selecting a specific index
/// is proportional to the value of the array element at that index.
/// Array elements that are equal to zero are ignored and their indices
/// are never returned.If any array element is less than zero, or if
/// no array element is greater than zero, then the operation fails.
/// As a source of randomness uses a number uniformly distributed between 0 and 1.
/// Used for Quantum.Intrinsic.Random
/// </summary>
/// <param name="uniformZeroOneSample"> Number between Zero and one, uniformly distributed</param>
public static long SampleDistribution(IQArray <double> unnormalizedDistribution, double uniformZeroOneSample)
{
if (unnormalizedDistribution.Any(prob => prob < 0.0))
{
throw new ExecutionFailException("Random expects array of non-negative doubles.");
}
var total = unnormalizedDistribution.Sum();
if (total == 0)
{
throw new ExecutionFailException("Random expects array of non-negative doubles with positive sum.");
}
var sample = uniformZeroOneSample * total;
return(unnormalizedDistribution
// Get the unnormalized CDF of the distribution.
.SelectAggregates((double acc, double x) => acc + x)
// Look for the first index at which the CDF is bigger
// than the random sample of 𝑈(0, 1) that we were given
// as a parameter.
.Select((cumulativeProb, idx) => (cumulativeProb, idx))
.Where(item => item.cumulativeProb >= sample)
// Cast that index to long, and default to returning
// the last item.
.Select(
item => (long)item.idx
)
.DefaultIfEmpty(
unnormalizedDistribution.Length - 1
)
.First());
}