public static Matrix<double> Scale(Matrix<double> input)
{
int n = input.RowCount;
Matrix<double> p = DenseMatrix.Build.DenseIdentity(n) - DenseMatrix.Create(n,n, (_, __) => 1.0 / n);
Matrix<double> a = -.5 * input.PointwiseMultiply(input);
Matrix<double> b = p.Multiply(p.Multiply(a));
b = (b + b.Transpose()).Divide(2.0);
var evd = b.Evd();
Vector<double> E = DenseVector.OfEnumerable(evd.EigenValues.Select(x => x.Real));
Matrix<double> V = evd.EigenVectors;
DenseVector i = DenseVector.Create(E.Count, x => x);
Sorting.Sort(E, i);
var e = DenseVector.OfEnumerable(E.Reverse());
i = DenseVector.OfEnumerable(i.Reverse());
Vector keep = DenseVector.Create(e.Count(x => x > 0.000000001), _ => 0);
int counter = 0;
for (int j = 0; j < e.Count; j++)
{
if (e[j] > 0.000000001)
{
keep[j] = counter;
counter++;
}
}
Matrix<double> Y;
if (e.Count(x => x > 0.000000001) == 0)
{
Y = DenseMatrix.Create(n, n, (_, __) => 0);
}
else
{
Y = DenseMatrix.Create(V.RowCount, keep.Count, (_, __) => 0);
for (int j = 0; j < keep.Count; j++)
{
Y.SetColumn(j, (V.Column((int)(i[(int)(keep[j] + 0.5)] + 0.5)).ToArray()));
}
Y = Y.Multiply(DiagonalMatrix.OfDiagonal(keep.Count, keep.Count, e.Where((x, j) => keep.Contains(j)).Select(Math.Sqrt)));
}
//Enforce a sign convention on the solution -- the largest element
//in each coordinate will have a positive sign.
List<int> maxIndices = Y.EnumerateColumns().Select(x => x.AbsoluteMaximumIndex()).ToList();
var colSigns = maxIndices.Select((x, j) => Math.Sign(Y[x, j])).ToList();
for (int j = 0; j < Y.ColumnCount; j++)
{
Y.SetColumn(j, Y.Column(j) * colSigns[j]);
}
return Y;
}
public void Test(Matrix<double> targetPattern, double activationCriterion, double inactivationCriterion, out List<double> meanSEList, out List<double> meanSSList, out List<double> meanCEList, out List<bool> correctnessList, out List<double> meanActivationList, out List<double> meanAUActivationList, out List<double> meanIUActivationList)
{
meanSEList = ((targetPattern - LayerActivationMatrix).PointwisePower(2).RowSums() / 2.0 / UnitCount).ToList();
meanSSList = ((((LayerActivationMatrix.PointwiseMultiply(LayerActivationMatrix.PointwiseLog()) + ((1 - LayerActivationMatrix).PointwiseMultiply((1 - LayerActivationMatrix).PointwiseLog()))) / Math.Log(2)) + 1).RowSums() / UnitCount).ToList();
meanCEList = (((targetPattern.PointwiseMultiply(LayerActivationMatrix.PointwiseLog()) + (1 - targetPattern).PointwiseMultiply((1 - LayerActivationMatrix).PointwiseLog())) / Math.Log(Math.E)).RowSums() * -1 / UnitCount).ToList();
meanActivationList = (LayerActivationMatrix.RowSums() / UnitCount).ToList();
correctnessList = new List<bool>(LayerActivationMatrix.RowCount);
meanAUActivationList = new List<double>(LayerActivationMatrix.RowCount);
meanIUActivationList = new List<double>(LayerActivationMatrix.RowCount);
for (int index = 0; index < LayerActivationMatrix.RowCount; index++)
{
correctnessList.Add(true);
meanAUActivationList.Add(0);
meanIUActivationList.Add(0);
}
Matrix<double> activeUnitMatrix = DenseMatrix.Create(LayerActivationMatrix.RowCount, LayerActivationMatrix.ColumnCount, 0);
Matrix<double> inactiveUnitMatrix = DenseMatrix.Create(LayerActivationMatrix.RowCount, LayerActivationMatrix.ColumnCount, 0);
Matrix<double> countActive = DenseMatrix.Create(LayerActivationMatrix.RowCount, 1, 0);
Matrix<double> countInactive = DenseMatrix.Create(LayerActivationMatrix.RowCount, 1, 0);
for (int rowIndex = 0;rowIndex<LayerActivationMatrix.RowCount;rowIndex++)
{
for (int columnIndex = 0; columnIndex < LayerActivationMatrix.ColumnCount; columnIndex++)
{
if (targetPattern[rowIndex, columnIndex] > activationCriterion)
{
if(LayerActivationMatrix[rowIndex, columnIndex] < activationCriterion) correctnessList[rowIndex] = false;
activeUnitMatrix[rowIndex, columnIndex] = 1;
countActive[rowIndex, 0]++;
}
if (targetPattern[rowIndex, columnIndex] < inactivationCriterion)
{
if (LayerActivationMatrix[rowIndex, columnIndex] > activationCriterion) correctnessList[rowIndex] = false;
inactiveUnitMatrix[rowIndex, columnIndex] = 1;
countInactive[rowIndex, 0]++;
}
}
}
meanAUActivationList = LayerActivationMatrix.PointwiseMultiply(activeUnitMatrix).RowSums().ToList();
meanIUActivationList = LayerActivationMatrix.PointwiseMultiply(inactiveUnitMatrix).RowSums().ToList();
for (int rowIndex = 0; rowIndex < LayerActivationMatrix.RowCount; rowIndex++)
{
if (countActive[rowIndex, 0] > 0) meanAUActivationList[rowIndex] = meanAUActivationList[rowIndex] / countActive[rowIndex,0];
else
{
meanAUActivationList[rowIndex] = double.NaN;
}
if (countInactive[rowIndex, 0] > 0) meanIUActivationList[rowIndex] = meanIUActivationList[rowIndex] / countInactive[rowIndex,0];
else
{
meanIUActivationList[rowIndex] = double.NaN;
}
}
}