/// <summary>
/// Checks whether a function is a real metric distance, i.e. respects
/// the triangle inequality. Please note that a function can still pass
/// this test and not respect the triangle inequality.
/// </summary>
///
public static bool IsMetric(Func <int[], int[], double> value)
{
// Direct test
double z = value(new[] { 1 }, new[] { 1 });
if (z > 2 || z < 0)
{
return(false);
}
int size = 3;
int[] zero = new int[size];
foreach (var a in Combinatorics.Sequences(3, size, inPlace: true))
{
foreach (var b in Combinatorics.Sequences(3, size, inPlace: true))
{
double dza = value(zero, a);
double dzb = value(zero, b);
double dab = value(a, b);
if (dab > dza + dzb)
{
return(false);
}
double daz = value(a, zero);
double dbz = value(b, zero);
double dba = value(b, a);
if (daz != dza || dbz != dzb || dab != dba)
{
return(false);
}
}
}
return(true);
}
/// <summary>
/// Creates a vector containing every index that can be used to
/// address a given <paramref name="array"/>, in order.
/// </summary>
///
/// <param name="array">The array whose indices will be returned.</param>
///
/// <returns>
/// An enumerable object that can be used to iterate over all
/// positions of the given <paramref name="array">System.Array</paramref>.
/// </returns>
///
/// <example>
/// <code>
/// double[,] a =
/// {
/// { 5.3, 2.3 },
/// { 4.2, 9.2 }
/// };
///
/// foreach (int[] idx in Indices.From(a))
/// {
/// // Get the current element
/// double e = (double)a.GetValue(idx);
/// }
/// </code>
/// </example>
///
public static IEnumerable <int[]> From(this Array array)
{
int[] dimensions = array.GetDimensions();
return(Combinatorics.Sequences(dimensions, inPlace: true));
}