public static Func <Fraction, V> Interpolate <V>(this IVectorSpace <Fraction, V> space, V start, V end)
{
return(scale =>
{
return space.Add(space.Scale(scale.Complement(), start), space.Scale(scale, end));
});
}
public static IVectorSpace <S, IPoint <V> > Geometry <S, V>(this IVectorSpace <S, V> space)
{
return(new VectorSpace <S, IPoint <V> >(
zero: new Point <V>(axis => space.Zero),
addF: (left, right) =>
{
return new Point <V>(axis => space.Add(left.On(axis), right.On(axis)));
},
scaleF: (scale, point) =>
{
return new Point <V>(axis => space.Scale(scale, point.On(axis)));
}));
}
/// <summary>
/// Obtém uma base ortogonalizada a partir da base actual.
/// </summary>
/// <param name="coefficientsField">O corpo responsável pelas operações sobre os coeficientes.</param>
/// <param name="vectorSpace">O espaço responsável pela multiplicação de um escalar com um vector.</param>
/// <param name="scalarProduct">O produto escalar.</param>
/// <returns>A base ortogonalizada.</returns>
/// <exception cref="ArgumentNullException">Se algum dos argumentos for nulo.</exception>
public VectorSpaceGenerator <CoeffType> GetOrthogonalizedBase(
IField <CoeffType> coefficientsField,
IVectorSpace <CoeffType, IMathVector <CoeffType> > vectorSpace,
IScalarProductSpace <IMathVector <CoeffType>, CoeffType> scalarProduct)
{
if (coefficientsField == null)
{
throw new ArgumentNullException("coefficientsField");
}
else if (vectorSpace == null)
{
throw new ArgumentNullException("vectorSpace");
}
else if (scalarProduct == null)
{
throw new ArgumentNullException("scalarProduct");
}
else
{
var result = new List <IMathVector <CoeffType> >();
// Mantém a lista de resultados intermédios
var intermediaryResults = new List <CoeffType>();
if (this.basisVectors.Count > 0)
{
var basisCount = this.basisVectors.Count;
var i = -1;
var control = 0;
while (control < basisCount)
{
var currentVector = this.basisVectors[control];
if (!currentVector.IsNull(coefficientsField))
{
i = control;
control = basisCount;
}
else
{
++control;
}
}
if (i != -1)
{
--basisCount;
var currentVector = this.basisVectors[i];
result.Add(currentVector);
if (i < basisCount)
{
var denom = scalarProduct.Multiply(currentVector, currentVector);
intermediaryResults.Add(denom);
++i;
for (; i < basisCount; ++i)
{
currentVector = this.basisVectors[i];
for (int j = 0; j < result.Count; ++j)
{
denom = intermediaryResults[j];
if (!coefficientsField.IsAdditiveUnity(denom))
{
var orthoVector = result[j];
var num = scalarProduct.Multiply(currentVector, orthoVector);
if (!coefficientsField.IsAdditiveUnity(num))
{
var scalar = coefficientsField.Multiply(
num,
coefficientsField.MultiplicativeInverse(denom));
scalar = coefficientsField.AdditiveInverse(scalar);
if (!coefficientsField.IsMultiplicativeUnity(scalar))
{
orthoVector = vectorSpace.MultiplyScalar(scalar, orthoVector);
currentVector = vectorSpace.Add(currentVector, orthoVector);
}
}
}
}
// Já foi calculado o vector ortogonal
denom = scalarProduct.Multiply(currentVector, currentVector);
if (coefficientsField.IsAdditiveUnity(denom))
{
if (!currentVector.IsNull(coefficientsField))
{
intermediaryResults.Add(denom);
result.Add(currentVector);
}
}
else
{
intermediaryResults.Add(denom);
result.Add(currentVector);
}
}
// Na útlima iteração não é necessário calcular o produto escalar
currentVector = this.basisVectors[i];
for (int j = 0; j < result.Count; ++j)
{
denom = intermediaryResults[j];
if (!coefficientsField.IsAdditiveUnity(denom))
{
var orthoVector = result[j];
var num = scalarProduct.Multiply(currentVector, orthoVector);
if (!coefficientsField.IsAdditiveUnity(num))
{
var scalar = coefficientsField.Multiply(
num,
coefficientsField.MultiplicativeInverse(denom));
scalar = coefficientsField.AdditiveInverse(scalar);
if (!coefficientsField.IsMultiplicativeUnity(scalar))
{
orthoVector = vectorSpace.MultiplyScalar(scalar, orthoVector);
currentVector = vectorSpace.Add(currentVector, orthoVector);
}
}
}
}
// Já foi calculado o vector ortogonal
if (!currentVector.IsNull(coefficientsField))
{
result.Add(currentVector);
}
}
}
}
return(new VectorSpaceGenerator <CoeffType>(
this.vectorSpaceDimension,
result));
}
}