/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create square matrix
var matrix = new DenseMatrix(5);
var k = 0;
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix[i, j] = k++;
}
}
Console.WriteLine(@"Initial matrix");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create vector
var vector = new DenseVector(new[] { 50.0, 51.0, 52.0, 53.0, 54.0 });
Console.WriteLine(@"Sample vector");
Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 1. Insert new column
var result = matrix.InsertColumn(3, vector);
Console.WriteLine(@"1. Insert new column");
Console.WriteLine(result.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Insert new row
result = matrix.InsertRow(3, vector);
Console.WriteLine(@"2. Insert new row");
Console.WriteLine(result.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Set column values
matrix.SetColumn(2, (Vector)vector);
Console.WriteLine(@"3. Set column values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 4. Set row values.
matrix.SetRow(3, (double[])vector);
Console.WriteLine(@"4. Set row values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 5. Set diagonal values. SetRow/SetColumn/SetDiagonal accepts Vector and double[] as input parameter
matrix.SetDiagonal(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 });
Console.WriteLine(@"5. Set diagonal values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 6. Set submatrix values
matrix.SetSubMatrix(1, 3, 1, 3, DenseMatrix.Identity(3));
Console.WriteLine(@"6. Set submatrix values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Permutations.
// Initialize a new instance of the Permutation class. An array represents where each integer is permuted too:
// indices[i] represents that integer "i" is permuted to location indices[i]
var permutations = new Permutation(new[] { 0, 1, 3, 2, 4 });
// 7. Permute rows 3 and 4
matrix.PermuteRows(permutations);
Console.WriteLine(@"7. Permute rows 3 and 4");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 8. Permute columns 1 and 2, 3 and 5
permutations = new Permutation(new[] { 1, 0, 4, 3, 2 });
matrix.PermuteColumns(permutations);
Console.WriteLine(@"8. Permute columns 1 and 2, 3 and 5");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 9. Concatenate the matrix with the given matrix
var append = matrix.Append(matrix);
// Concatenate into result matrix
matrix.Append(matrix, append);
Console.WriteLine(@"9. Append matrix to matrix");
Console.WriteLine(append.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 10. Stack the matrix on top of the given matrix matrix
var stack = matrix.Stack(matrix);
// Stack into result matrix
matrix.Stack(matrix, stack);
Console.WriteLine(@"10. Stack the matrix on top of the given matrix matrix");
Console.WriteLine(stack.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 11. Diagonally stack the matrix on top of the given matrix matrix
var diagoinalStack = matrix.DiagonalStack(matrix);
// Diagonally stack into result matrix
matrix.DiagonalStack(matrix, diagoinalStack);
Console.WriteLine(@"11. Diagonally stack the matrix on top of the given matrix matrix");
Console.WriteLine(diagoinalStack.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}
private static void UseNormalEquation(DenseMatrix sourceX, DenseVector y)
{
Console.WriteLine("Solving with normal equation...");
var x = sourceX.InsertColumn(0, DenseVector.Create(sourceX.RowCount, i => 1));
var theta = NormalEquation(x, y);
Console.WriteLine("Theta computed (using normal equation): {0}", theta);
var price = new DenseVector(new[] { 1.0, 1650.0, 3.0 }) * theta;
Console.WriteLine("Predicted price of a 1650 sq-ft, 3 br house (using normal equation): {0}", price);
}
public void Train(DenseMatrix X, DenseVector d, DenseVector Kd)
{
int R = X.RowCount;
int N = X.ColumnCount;
int U = 0; //the number of neurons in the structure
var c = new DenseMatrix(R, 1);
var sigma = new DenseMatrix(R, 1);
var Q = new DenseMatrix((R + 1), (R + 1));
var O = new DenseMatrix(1, (R + 1));
var pT_n = new DenseMatrix((R + 1), 1);
double maxPhi = 0;
int maxIndex;
var Psi = new DenseMatrix(N, 1);
Console.WriteLine("Running...");
//for each observation n in X
for (int i = 0; i < N; i++)
{
Console.WriteLine(100*(i/(double) N) + "%");
var x = new DenseVector(R);
X.Column(i, x);
//if there are neurons in structure,
//update structure recursively.
if (U == 0)
{
c = (DenseMatrix) x.ToColumnMatrix();
sigma = new DenseMatrix(R, 1, SigmaZero);
U = 1;
Psi = CalculatePsi(X, c, sigma);
UpdateStructure(X, Psi, d, ref Q, ref O);
pT_n =
(DenseMatrix)
(CalculateGreatPsi((DenseMatrix) x.ToColumnMatrix(), (DenseMatrix) Psi.Row(i).ToRowMatrix()))
.Transpose();
}
else
{
StructureRecurse(X, Psi, d, i, ref Q, ref O, ref pT_n);
}
bool KeepSpinning = true;
while (KeepSpinning)
{
//Calculate the error and if-part criteria
double ee = pT_n.Multiply(O)[0, 0];
double approximationError = Math.Abs(d[i] - ee);
DenseVector Phi;
double SumPhi;
CalculatePhi(x, c, sigma, out Phi, out SumPhi);
maxPhi = Phi.Maximum();
maxIndex = Phi.MaximumIndex();
if (approximationError > delta)
{
if (maxPhi < threshold)
{
var tempSigma = new DenseVector(R);
sigma.Column(maxIndex, tempSigma);
double minSigma = tempSigma.Minimum();
int minIndex = tempSigma.MinimumIndex();
sigma[minIndex, maxIndex] = k_sigma*minSigma;
Psi = CalculatePsi(X, c, sigma);
UpdateStructure(X, Psi, d, ref Q, ref O);
var psi = new DenseVector(Psi.ColumnCount);
Psi.Row(i, psi);
pT_n =
(DenseMatrix)
CalculateGreatPsi((DenseMatrix) x.ToColumnMatrix(), (DenseMatrix) psi.ToRowMatrix())
.Transpose();
}
else
{
//add a new neuron and update strucutre
double distance = 0;
var cTemp = new DenseVector(R);
var sigmaTemp = new DenseVector(R);
//foreach input variable
for (int j = 0; j < R; j++)
{
distance = Math.Abs(x[j] - c[j, 0]);
int distanceIndex = 0;
//foreach neuron past 1
for (int k = 1; k < U; k++)
{
if ((Math.Abs(x[j] - c[j, k])) < distance)
{
distanceIndex = k;
distance = Math.Abs(x[j] - c[j, k]);
}
}
if (distance < Kd[j])
{
cTemp[j] = c[j, distanceIndex];
sigmaTemp[j] = sigma[j, distanceIndex];
}
else
{
cTemp[j] = x[j];
sigmaTemp[j] = distance;
}
}
//end foreach
c = (DenseMatrix) c.InsertColumn(c.ColumnCount - 1, cTemp);
sigma = (DenseMatrix) sigma.InsertColumn(sigma.ColumnCount - 1, sigmaTemp);
Psi = CalculatePsi(X, c, sigma);
UpdateStructure(X, Psi, d, ref Q, ref O);
U++;
KeepSpinning = false;
}
}
else
{
if (maxPhi < threshold)
{
var tempSigma = new DenseVector(R);
sigma.Column(maxIndex, tempSigma);
double minSigma = tempSigma.Minimum();
int minIndex = tempSigma.MinimumIndex();
sigma[minIndex, maxIndex] = k_sigma*minSigma;
Psi = CalculatePsi(X, c, sigma);
UpdateStructure(X, Psi, d, ref Q, ref O);
var psi = new DenseVector(Psi.ColumnCount);
Psi.Row(i, psi);
pT_n =
(DenseMatrix)
CalculateGreatPsi((DenseMatrix) x.ToColumnMatrix(), (DenseMatrix) psi.ToRowMatrix())
.Transpose();
}
else
{
KeepSpinning = false;
}
}
}
}
out_C = c;
out_O = O;
out_Sigma = sigma;
Console.WriteLine("Done.");
}
