/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">The p value.</param>
/// <returns>Scalar <c>ret = (sum(abs(this[i])^p))^(1/p)</c></returns>
public override Complex32 Norm(double p)
{
if (1 > p)
{
throw new ArgumentOutOfRangeException("p");
}
if (NonZerosCount == 0)
{
return(Complex32.Zero);
}
if (2.0 == p)
{
return(_nonZeroValues.Aggregate(Complex32.Zero, SpecialFunctions.Hypotenuse).Magnitude);
}
if (Double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(0, NonZerosCount, (index, localData) => Math.Max(localData, _nonZeroValues[index].Magnitude), Common.Max));
}
var sum = 0.0;
for (var index = 0; index < NonZerosCount; index++)
{
sum += Math.Pow(_nonZeroValues[index].Magnitude, p);
}
return((float)Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">The p value.</param>
/// <returns>Scalar <c>ret = (sum(abs(this[i])^p))^(1/p)</c></returns>
public override double Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (1.0 == p)
{
return(SumMagnitudes());
}
if (2.0 == p)
{
return(Data.Aggregate(0.0, SpecialFunctions.Hypotenuse));
}
if (Double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, Math.Abs(Data[index])),
Math.Max));
}
var sum = 0.0;
for (var index = 0; index < Count; index++)
{
sum += Math.Pow(Math.Abs(Data[index]), p);
}
return(Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">
/// The p value.
/// </param>
/// <returns>
/// <c>Scalar ret = (sum(abs(At(i))^p))^(1/p)</c>
/// </returns>
public override Complex32 Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, At(index).Magnitude),
Common.Max));
}
var sum = 0.0;
for (var index = 0; index < Count; index++)
{
sum += Math.Pow(At(index).Magnitude, p);
}
return((float)Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">The p value.</param>
/// <returns>Scalar <c>ret = (sum(abs(this[i])^p))^(1/p)</c></returns>
public override Complex32 Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (1.0 == p)
{
return(SumMagnitudes());
}
if (2.0 == p)
{
return(Data.Aggregate(Complex32.Zero, SpecialFunctions.Hypotenuse).Magnitude);
}
if (Double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, Data[index].Magnitude),
Common.Max));
}
var sum = 0.0;
for (var i = 0; i < Count; i++)
{
sum += Math.Pow(Data[i].Magnitude, p);
}
return((float)Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">
/// The p value.
/// </param>
/// <returns>
/// <c>Scalar ret = (sum(abs(this[i])^p))^(1/p)</c>
/// </returns>
public override double Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (Double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, Math.Abs(At(index))),
Math.Max));
}
var sum = 0.0;
for (var index = 0; index < Count; index++)
{
sum += Math.Pow(Math.Abs(At(index)), p);
}
return(Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">
/// The p value.
/// </param>
/// <returns>
/// <c>Scalar ret = (sum(abs(this[i])^p))^(1/p)</c>
/// </returns>
public override float Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (float.IsPositiveInfinity((float)p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, Math.Abs(this[index])),
Common.Max));
}
var sum = CommonParallel.Aggregate(
0,
Count,
index => Math.Pow(Math.Abs(this[index]), p));
return((float)Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">
/// The p value.
/// </param>
/// <returns>
/// <c>Scalar ret = (sum(abs(this[i])^p))^(1/p)</c>
/// </returns>
public override Complex Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, this[index].Magnitude),
Math.Max));
}
var sum = CommonParallel.Aggregate(
0,
Count,
index => Math.Pow(this[index].Magnitude, p));
return(Math.Pow(sum, 1.0 / p));
}
/// <summary>
/// Computes the p-Norm.
/// </summary>
/// <param name="p">The p value.</param>
/// <returns>Scalar <c>ret = (sum(abs(this[i])^p))^(1/p)</c></returns>
public override Complex Norm(double p)
{
if (p < 0.0)
{
throw new ArgumentOutOfRangeException("p");
}
if (1.0 == p)
{
return(CommonParallel.Aggregate(
0,
Count,
index => Data[index].Magnitude));
}
if (2.0 == p)
{
return(Data.Aggregate(Complex.Zero, SpecialFunctions.Hypotenuse).Magnitude);
}
if (Double.IsPositiveInfinity(p))
{
return(CommonParallel.Select(
0,
Count,
(index, localData) => Math.Max(localData, Data[index].Magnitude),
Math.Max));
}
var sum = CommonParallel.Aggregate(
0,
Count,
index => Math.Pow(Data[index].Magnitude, p));
return(Math.Pow(sum, 1.0 / p));
}