/// <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);
}
public static EigenObject GetEigen(double[,] a)
{
int width = a.GetLength(0);
double[] array = new double[width * width];
for (int i = 0; i < width; i++)
{
for (int j = 0; j < width; j++)
{
array[i * width + j] = a[i, j];
}
}
ILRetArray <double> A = ILMath.array(
array, width, width);
ILArray <complex> eigVectors = ILMath.array(new complex(0, 0), width * width);
ILArray <complex> eigValues = ILMath.eig(A, eigVectors);
return(new EigenObject(eigVectors, eigValues, width));
}
public static EigenObject GetEigen(Bitmap bmp)
{
int width = bmp.Width;
double[] array = new double[width * width];
for (int i = 0; i < width; i++)
{
for (int j = 0; j < width; j++)
{
array[i * width + j] = bmp.GetPixel(i, j).R;
}
}
ILArray <double> A = ILMath.array(
array, width, width);
ILArray <complex> eigVectors = ILMath.array(new complex(0, 0), width * width);
ILArray <complex> eigValues = ILMath.eig(A, eigVectors);
return(new EigenObject(eigVectors, eigValues, width));
}
public static ILScene Plot(Func <double, double, double> zOfxy, double x0, double xf, double y0, double yf, double pointsPerDimension = 700)
{
// create some test data (RBF)
ILArray <float> Y = 1;
double dx = (xf - x0) / pointsPerDimension;
double dy = (yf - y0) / pointsPerDimension;
ILArray <float> result = ILMath.array <float>(new ILSize(xf, yf));
for (double x = x0; x < xf; x += dx)
{
for (double y = y0; y < yf; y += dy)
{
result[x, y] = (float)zOfxy(x, y);
}
}
//ILArray<float> X = ILMath.meshgrid(
// ILMath.linspace<float>(-2f, 2f, 100),
// ILMath.linspace<float>(-2f, 2f, 100), Y);
//Y = X * X;
//Y = X * X + Y * Y;
//ILArray<float> A = 1 - ILMath.exp(-Y * 2f);Charting.Plot(xyz, 0, 10, 0, 15)
// create new scene, add plot cube
var scene = new ILScene {
new ILPlotCube(twoDMode: false)
{
// rotate around X axis only
Rotation = Matrix4.Rotation(new Vector3(1, 0, 0), 1.1f),
// set perspective projection
Projection = Projection.Perspective,
// add plot cube contents
Childs =
{
// add surface plot, default configuration
//new ILSurface(A, 1 - A) { Alpha = 0.9f },
new ILSurface(result)
{
Alpha = 0.9f
},
//new ILSurface(A) { Alpha = 0.9f },
// add contour plot in 3D, configure individual levels
//new ILContourPlot(A, new List<ContourLevel> {
// new ContourLevel() { Value = 0.8f, LineWidth = 4, ShowLabel = false },
// new ContourLevel() { Value = 0.5f, LineWidth = 4, ShowLabel = false },
// new ContourLevel() { Value = 0.2f, LineWidth = 4, ShowLabel = false, LineColor = 1 },
// new ContourLevel() { Value = 0.02f, LineWidth = 4, ShowLabel = false},
//}, create3D: true),
//// add contour plot in 2D, default levels, no labels
//new ILContourPlot(1 - A, showLabels: false),
//// add legend, label first contour plots levels only
//new ILLegend("0.8","0.5","0.2","0.02") {
// // move legend to upper right corner
// Location = new System.Drawing.PointF(0.97f,0.05f),
// Anchor = new System.Drawing.PointF(1,0)
//}
}
}
};
return(scene);
}
//Finalval is the result of the look up of Lambda and Beta in the CP map.
//The function uses a bilinear interpolation method, and has been developed
//to replace interpn in an embedded matlab environment
public void Interpolate(double Beta, double Lambda, ILArray <double> table2, ILArray <double> Betavec2, ILArray <double> Lambdavec2, out double Finalval)
{
ILArray <int> Bt;
int B1;
int B2;
ILArray <int> Lt;
int L1;
int L2;
ILArray <double> Yvals;
ILArray <double> Yintervals;
//Setting up persistent variables
//Function initialization
//The first time the function is run, it stores supplied map as a persistent
//variable.
if (_persistentCt == null)// Is only run once
{
_persistentCt = new PersistentVariables();
_persistentCt.Table = table2.C;
_persistentCt.Betavec = Betavec2.C;
_persistentCt.Lambdavec = Lambdavec2.C;
}
//Step 1, finding two adjecent indexes of the BetaVec, which contain the
//supplied beta value
Bt = ILMath.empty <int>();
ILMath.min(ILMath.abs(_persistentCt.Betavec - Beta), Bt); //Finding index 1
B1 = Bt.GetValue(0); //Necessary specification in embedded
//matlab
if (Beta > _persistentCt.Betavec.GetValue(B1)) //Finding index 2
{
if (B1 == (_persistentCt.Betavec.Length - 1)) //testing if endpoint-extrapolation
{
B2 = B1; //should be used
B1 = B1 - 1;
}
else
{
B2 = B1 + 1;
}
}
else
{
if (B1 == 0)
{
B1 = 1;
B2 = 0;
}
else
{
B2 = B1 - 1;
}
}
//Step 2, finding two adjecent indexes of the LambdaVec, which contain the
//supplied Lambda value
Lt = ILMath.empty <int>();
ILMath.min(ILMath.abs(_persistentCt.Lambdavec - Lambda), Lt);
L1 = Lt.GetValue(0);
if (Lambda > _persistentCt.Lambdavec.GetValue(L1)) //Need to work out of indexes
{
if (L1 == (_persistentCt.Lambdavec.Length - 1))
{
L2 = L1;
L1 = L1 - 1;
}
else
{
L2 = L1 + 1;
}
}
else
{
if (L1 == 0)
{
L1 = 1;
L2 = 0;
}
else
{
L2 = L1 - 1;
}
}
//Step 3
//Finding the four indexed values by means of the indexes
Yvals = new double[, ] {
{ _persistentCt.Table.GetValue(B1, L1), _persistentCt.Table.GetValue(B2, L1) },
{ _persistentCt.Table.GetValue(B1, L2), _persistentCt.Table.GetValue(B2, L2) }
};
//Step 4
//Making two sets of linear interpolations by using the different lambda values
Yintervals = ILMath.array(new double[] {
((Yvals.GetValue(0, 1) - Yvals.GetValue(0, 0))
/ (_persistentCt.Lambdavec.GetValue(L2) - _persistentCt.Lambdavec.GetValue(L1))
* (Lambda - _persistentCt.Lambdavec.GetValue(L1))
+ Yvals.GetValue(0, 0)),
((Yvals.GetValue(1, 1) - Yvals.GetValue(1, 0))
/ (_persistentCt.Lambdavec.GetValue(L2) - _persistentCt.Lambdavec.GetValue(L1))
* (Lambda - _persistentCt.Lambdavec.GetValue(L1))
+ Yvals.GetValue(1, 0))
},
2, 1);
//Step 5
//Making the final linear interpolation on the results obtained in
//stepp 4
Finalval = ((Yintervals.GetValue(1) - Yintervals.GetValue(0)) / (_persistentCt.Betavec.GetValue(B2) - _persistentCt.Betavec.GetValue(B1)))
* (Beta - _persistentCt.Betavec.GetValue(B1))
+ Yintervals.GetValue(0);
}
public Vector(int dimension, int dimensionMDF, double value)
{
this.values = ILMath.array <double>(value, dimension);
this.valuesMDF = ILMath.array <double>(value, dimensionMDF);
}