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 V Average <S, V>(this IVectorSpace <S, V> space, IArray <S> factors, IArray <V> vectors)
{
var summands = new Array <V>(
size: factors.Size,
atF: index => space.Scale(factors[index], vectors[index]));
return(space.Adding().Join(summands));
}
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)));
}));
}