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using System.Collections.Generic;
using ILNumerics;
namespace QUSMAML
{
public static class MultidimensionalScaling
{
/// <summary>
/// Multidimensional scaling/PCoA: transform distances to points in a coordinate system.
/// </summary>
/// <param name="input">A matrix of pairwise distances. Zero indicates identical objects.</param>
/// <returns>A matrix, the columns of which are coordinates in the nth dimension.
/// The rows are in the same order as the input.</returns>
public static ILArray<double> Scale(ILArray<double> input)
{
int n = input.Length;
ILArray<double> p = ILMath.eye<double>(n, n) - ILMath.repmat(1.0 / n, n, n);
ILArray<double> a = -.5 * ILMath.multiplyElem(input, input);
ILArray<double> b = ILMath.multiply(p, a, p);
ILArray<complex> V = ILMath.empty<complex>();
ILArray<complex> E = ILMath.eig((b + b.T) / 2, V);
ILArray<int> i = ILMath.empty<int>();
ILArray<double> e = ILMath.sort(ILMath.diag(ILMath.real(E)), i);
e = ILMath.flipud(e);
i = ILMath.toint32(ILMath.flipud(ILMath.todouble(i)));
ILArray<int> keep = ILMath.empty<int>();
for (int j = 0; j < e.Length; j++)
{
if (e[j] > 0.000000001)
{
keep.SetValue(j, keep.Length);
}
}
ILArray<double> Y;
if (ILMath.isempty(keep))
{
Y = ILMath.zeros(n, 1);
}
else
{
Y = ILMath.zeros<double>(V.S[0], keep.Length);
for (int j = 0; j < keep.Length; j++)
{
Y[ILMath.full, j] = ILMath.todouble(-V[ILMath.full, i[keep[j]]]) ;
}
Y = ILMath.multiply(Y, ILMath.diag(ILMath.sqrt(e[keep])));
}
ILArray<int> maxind = ILMath.empty<int>();
ILMath.max(ILMath.abs(Y), maxind, 0);
int d = Y.S[1];
ILArray<int> indices = maxind + ILMath.toint32(ILMath.array<int>(SteppedRange(0,n, (d-1)*n)));
ILArray<double> colsign = ILMath.sign(Y[indices]);
for (int j = 0; j < Y.S[1]; j++)
{
Y[ILMath.full, j] = Y[ILMath.full, j] * colsign[j];
}
return Y;
}
private static int[] SteppedRange(int start, int step, int end)
{
var values = new List<int>();
for (int i = start; i <= end; i = i + step)
{
values.Add(i);
}
return values.ToArray();
}
}
}