/// <summary>
/// Combines vectors into their product vector.
/// for example: [ v1, v2 ] => v3: {Value:v1 * v2, Index:[v1.Index, v2.Index]
/// </summary>
/// <param name="vectors">vectors to combine</param>
/// <param name="vectorSize">the size of the passed vectors</param>
/// <returns>combined vector</returns>
public static IndexedVector Combine(IEnumerable <IndexedVector> vectors, int vectorSize)
{
var result = new IndexedVector
{
Index = Enumerable.Empty <int>().ToHashSet(),
Value = Vector.One(vectorSize)
};
foreach (var vector in vectors)
{
result.Value = result.Value.Multiply(vector.Value);
result.Index.UnionWith(vector.Index);
}
return(result);
}
/// <summary>
/// Gets the 'characteristic' vectors for a given matrix row(IndexedVector).
/// </summary>
/// <param name="vector">row to get the vectors for</param>
/// <returns>characteristic vectors</returns>
public IList <Vector> GetCharacteristicVectorsFor(IndexedVector vector)
{
var contains = _characteristicVectors.TryGetValue(vector.Index, out var result);
if (contains)
{
return(result);
}
var indices = vector.GetCharacteristicVectorIndices(M);
var indicesWithInverse = indices
//get index and the 'inverse' of the index
.SelectMany(index => new[] { -index, index })
.ToList();
var combinations = indicesWithInverse
//get all combinations of the indices in indices.Count means.
.GetCombinations(indices.Count)
//convert to hashset
.Select(index => index.ToHashSet())
//skip indexes like {...,x, ..., -x, ...}
.Where(index => index.All(part => !index.Contains(-part)))
.ToList();
var characteristics = new List <Vector>(combinations.Count);
foreach (var combination in combinations)
{
var characteristicVector = Vector.One(VectorSize);
foreach (var index in combination)
{
//Get either the inverse of the vector (complement), or the vector itself
bool isInverse = index < 0;
var row = this[new HashSet <int> {
Math.Abs(index)
}].Value;
var toMultiply = isInverse ? row.Complement() : row;
characteristicVector = characteristicVector.Multiply(toMultiply);
}
characteristics.Add(characteristicVector);
}
_characteristicVectors.Add(vector.Index, characteristics);
return(characteristics);
}
/// <summary>
/// Generates the matrix rows using R and M parameters.
/// Stores the result in _rows;
/// </summary>
private void Generate()
{
var baseVectors = GetBaseVectors().ToList();
// if R <= 1, then there is no need to generate the products from vector combinations
if (R <= 1)
{
Rows = baseVectors;
return;
}
//get all possible combinations from the base vectors in collections of size 2 - R.
//skip the first 'base' vector, as it's equivalent to 1, and when multiplying by it later, the resulting vector is simply itself.
var combinations = baseVectors.Skip(1).GetCombinations(2, R);
var indexedCombinedVectors = combinations
.Select(combination => IndexedVector.Combine(combination, VectorSize));
Rows = baseVectors
.Concat(indexedCombinedVectors)
.ToList();
}
