/// <summary>
/// Creates a uniform distribution over strings that start with an upper case letter followed by
/// one or more letters, with length within the given bounds.
/// If <paramref name="maxLength"/> is set to <see langword="null"/>,
/// there will be no upper bound on the length, and the resulting distribution will thus be improper.
/// </summary>
/// <param name="minLength">The minimum possible string length. Defaults to 2.</param>
/// <param name="maxLength">
/// The maximum possible sequence length, or <see langword="null"/> for no upper bound on length.
/// Defaults to <see langword="null"/>.
/// </param>
/// <param name="allowUpperAfterFirst">Whether to allow upper case letters after the initial upper case letter. If false, only lower case letters will be allowed.</param>
/// <returns>The created distribution.</returns>
public static StringDistribution Capitalized(int minLength = 2, int?maxLength = null, bool allowUpperAfterFirst = false)
{
Argument.CheckIfInRange(minLength >= 1, "minLength", "The minimum length of a capitalized string should be 1 or more.");
Argument.CheckIfValid(!maxLength.HasValue || maxLength.Value >= minLength, "The maximum length cannot be less than the minimum length.");
var result = StringDistribution.Char(DiscreteChar.Upper());
if (maxLength.HasValue)
{
result.AppendInPlace(
allowUpperAfterFirst ? StringDistribution.Letters(minLength: minLength - 1, maxLength: maxLength.Value - 1)
: StringDistribution.Lower(minLength: minLength - 1, maxLength: maxLength.Value - 1));
}
else
{
// Concatenation with an improper distribution, need to adjust its scale so that the result is 1 on its support
double logNormalizer = result.GetLogAverageOf(result);
var lowercaseSuffixFunc = (allowUpperAfterFirst ? StringDistribution.Letters(minLength: minLength - 1)
: StringDistribution.Lower(minLength: minLength - 1)).GetNormalizedWorkspaceOrPoint();
var lowercaseSuffixFuncScaled = lowercaseSuffixFunc.ScaleLog(-logNormalizer);
result.AppendInPlace(StringDistribution.FromWorkspace(lowercaseSuffixFuncScaled));
}
return(result);
}
