/// <summary>
/// Determina a soma de duas matrizes multidimensionais.
/// </summary>
/// <param name="right">A matriz multidimensional a ser somada.</param>
/// <param name="semiGroup">O semi-grupo responsável pelas operações sobre os coeficientes.</param>
/// <returns>O resultado da soma.</returns>
/// <exception cref="ArgumentNullException">Se um dos argumentos for nulo.</exception>
public MultiDimensionalMathRange <T> Sum(MultiDimensionalMathRange <T> right, ISemigroup <T> semiGroup)
{
if (right == null)
{
throw new ArgumentNullException("right");
}
if (semiGroup == null)
{
throw new ArgumentNullException("Semi group structure is needed.");
}
if (!this.CheckDimension(right.configuration))
{
throw new MathematicsException("Can only sum ranges with the same dimensions.");
}
var result = new MultiDimensionalMathRange <T>();
Array.Copy(this.configuration, result.configuration, this.configuration.Length);
var p = 1;
for (int i = 0; i < this.configuration.Length; ++i)
{
p *= this.configuration[i];
}
result.elements = new T[p];
for (int i = 0; i < this.elements.Length; ++i)
{
result.elements[i] = semiGroup.Add(this.elements[i], right.elements[i]);
}
return(result);
}
/// <summary>
/// Determina o produto de duas matrizes multidimensionais.
/// </summary>
/// <param name="right">A matriz multidimensional a ser somada.</param>
/// <param name="multiplyable">O objeto responsável pelas operações sobre os coeficientes.</param>
/// <returns>O resultado do produto.</returns>
/// <exception cref="ArgumentNullException">Se um dos argumentos for nulo.</exception>
public MultiDimensionalMathRange <T> Multiply(MultiDimensionalMathRange <T> right, IMultiplication <T> multiplyable)
{
if (right == null)
{
throw new ArgumentNullException("right");
}
if (multiplyable == null)
{
throw new ArgumentNullException("A multiplyable structure is needed.");
}
var result = new MultiDimensionalMathRange <T>();
if (this.configuration.Length == 0 || right.configuration.Length == 0)
{
result.configuration = new int[0];
result.elements = new T[0];
}
else
{
var p = 1;
var q = 1;
for (int i = 0; i < this.configuration.Length; ++i)
{
p *= this.configuration[i];
}
for (int i = 0; i < right.configuration[i]; ++i)
{
q *= right.configuration[i];
}
result.elements = new T[p * q];
result.configuration = new int[this.configuration.Length + right.configuration.Length];
for (int i = 0; i < this.configuration.Length; ++i)
{
result.configuration[i] = this.configuration[i];
}
for (int i = 0; i < right.configuration.Length; ++i)
{
result.configuration[this.configuration.Length + i] = right.configuration[i];
}
for (int i = 0; i < p; ++i)
{
for (int j = 0; j < q; ++j)
{
result.elements[j * p + i] = multiplyable.Multiply(this.elements[i], right.elements[j]);
}
}
}
return(result);
}
/// <summary>
/// Determina a contracção da matriz corrente segundo os índices espcificados.
/// </summary>
/// <param name="contractionIndices">A matriz multidimensional a ser somada.</param>
/// <param name="semiGroup">O objeto responsável pelas operações sobre os coeficientes.</param>
/// <returns>O resultado do produto.</returns>
/// <exception cref="ArgumentNullException">Se um dos argumentos for nulo.</exception>
public MultiDimensionalMathRange <T> Contract(int[] contractionIndices, ISemigroup <T> semiGroup)
{
if (contractionIndices == null)
{
throw new ArgumentNullException("contractionIndices");
}
if (semiGroup == null)
{
throw new MathematicsException("Parameter semiGroup can't be null.");
}
var result = new MultiDimensionalMathRange <T>();
this.CheckConversion(contractionIndices);
if (contractionIndices.Length == this.configuration.Length)
{
result.elements = new T[1];
var advance = 0;
for (int i = this.configuration.Length - 1; i > 0; --i)
{
advance *= this.configuration[i];
advance += 1;
}
var pos = advance;
for (int i = 1; i < this.configuration.Length; ++i)
{
result.elements[0] = semiGroup.Add(result.elements[0], this.elements[pos]);
pos += advance;
}
result.configuration = new[] { 0 };
}
else
{
var contractionMask = new int[this.configuration.Length];
var newConfigurationCount = 0;
for (int i = 0; i < this.configuration.Length; ++i)
{
if (!contractionIndices.Contains(i))
{
contractionMask[i] = 1;
}
else
{
++newConfigurationCount;
}
}
var newSize = 1;
result.configuration = new int[newConfigurationCount];
var pointer = 0;
for (int i = 0; i < this.configuration.Length; ++i)
{
if (contractionMask[i] == 1)
{
newSize *= this.configuration[i];
result.configuration[pointer++] = this.configuration[i];
}
}
var oldAdvances = new int[this.configuration.Length - newConfigurationCount];
var oldConfig = new int[oldAdvances.Length];
pointer = oldAdvances.Length;
var advance = 1;
for (int i = 0; i < this.configuration.Length; ++i)
{
if (contractionMask[i] == 0)
{
oldConfig[pointer] = this.configuration[i];
oldAdvances[pointer++] = advance;
}
advance *= this.configuration[i];
}
advance = 0;
for (int i = this.configuration.Length - 1; i > 0; --i)
{
advance *= this.configuration[i];
advance += contractionMask[i];
}
result.elements = new T[newSize];
var oldCoords = new int[oldConfig.Length];
pointer = 0;
for (int i = 0; i < newSize; ++i)
{
result.elements[i] = this.elements[pointer];
while (pointer < this.elements.Length)
{
result.elements[i] = semiGroup.Add(result.elements[i], result.elements[pointer]);
pointer += advance;
}
pointer = this.Increment(oldCoords, oldConfig, oldAdvances);
}
}
return(result);
}
