public override T norm(int order = 2, Normtype t = Normtype.Natural)
{
if (factor.ToFieldWrapper().Equals(Field.zero))
{
return(Field.zero);
}
switch (t)
{
case Normtype.Natural:
case Normtype.Infinity:
case Normtype.Max:
if (order != 1 && t == Normtype.Natural)
{
throw new NotSupportedException("cannot calculate norm of non-vector of more than first order");
}
return(factor);
}
throw new NotSupportedException(NOT_SUPPORTED_STRING);
}
public virtual T norm(int order = 2, Normtype t = Normtype.Natural)
{
var field = Fields.getField <T>();
T ord = field.fromInt(order);
switch (t)
{
case Normtype.Natural:
if (order == 0)
{
return(field.fromInt(rows));
}
if (this.isVector != VectorType.Collumn)
{
return(field.pow(this.Select(a => field.pow(field.abs(a), ord)).GetSum(), field.Invert(ord)));
}
if (order != 1)
{
throw new NotSupportedException("cannot calculate norm of non-vector of more than first order");
}
return(this.getCollumns().Select(a => a.Select(field.abs).GetSum()).GetMax(field));
case Normtype.Infinity:
return(this.getRows().Select(a => a.Select(field.abs).GetSum()).GetMax(field));
case Normtype.Frobenius:
return(field.pow((this.conjugate().transpose() * this).Trace(), field.fromFraction(1, 2)));
case Normtype.Entrywise:
return(field.pow(this.Select(a => field.pow(field.abs(a), ord)).GetSum(), field.Invert(ord)));
case Normtype.Max:
return(this.GetMax(field));
default:
throw new ArgumentException($"can't handle {nameof(Normtype)} " + t);
}
}
