public static void Set(ManagedArray dst, double value)
{
for (var i = 0; i < dst.Length(); i++)
{
dst[i] = value;
}
}
public static double Fourier(ManagedArray x1, ManagedArray x2, ManagedArray k)
{
Vectorize(x1, x2);
var z = new ManagedArray(x1);
double prod = 0;
double m = k.Length() > 0 ? k[0] : 1;
for (var i = 0; i < x1.Length(); i++)
{
z[i] = Math.Sin(m + 0.5) * 2;
var d = x1[i] - x2[i];
z[i] = Math.Abs(d) > 0 ? Math.Sin(m + 0.5) * d / Math.Sin(d * 0.5) : z[i];
prod = (i == 0) ? z[i] : prod * z[i];
}
ManagedOps.Free(z);
return(prod);
}
public static double Sigmoid(ManagedArray x1, ManagedArray x2, ManagedArray k)
{
double m = k.Length() > 0 ? k[0] : 1;
double b = k.Length() > 1 ? k[1] : 0;
return(Math.Tanh(m * Multiply(x1, x2) / x1.Length() + b));
}
public static double Radial(ManagedArray x1, ManagedArray x2, ManagedArray k)
{
double sigma = k.Length() > 0 ? k[0] : 1;
double denum = 2 * sigma * sigma;
return(Math.Abs(denum) > 0 ? Math.Exp(-Math.Sqrt(SquaredDiff(x1, x2)) / denum) : 0);
}
public static double Gaussian(ManagedArray x1, ManagedArray x2, ManagedArray k)
{
var x = SquaredDiff(x1, x2);
double sigma = k.Length() > 0 ? k[0] : 1;
double denum = 2 * sigma * sigma;
return(Math.Abs(denum) > 0 ? Math.Exp(-x / denum) : 0);
}
static double SquaredDiff(ManagedArray x1, ManagedArray x2)
{
Vectorize(x1, x2);
double x = 0;
for (var i = 0; i < x1.Length(); i++)
{
var d = x1[i] - x2[i];
x += d * d;
}
return(x);
}
// Copies a 3D [x][y][z] to 4D [index][x][y][z]
public static void Copy3D4D(ManagedArray dst, ManagedArray src, int index)
{
MemCopy(dst, index * src.Length(), src, 0, src.Length());
}
// Copies a 4D [index][x][y][z] to 3D [x][y][z]
public static void Copy4D3D(ManagedArray dst, ManagedArray src, int index)
{
MemCopy(dst, 0, src, index * dst.Length(), dst.Length());
}
public void Setup(ManagedArray x, ManagedArray y, double c, KernelType kernel, ManagedArray param, double tolerance = 0.001, int maxpasses = 5, int category = 1)
{
ManagedOps.Free(dx, dy);
dx = new ManagedArray(x);
dy = new ManagedArray(y);
ManagedOps.Copy2D(dx, x, 0, 0);
ManagedOps.Copy2D(dy, y, 0, 0);
ktype = kernel;
// Data parameters
var m = Rows(dx);
Category = category;
MaxIterations = maxpasses;
Tolerance = tolerance;
C = c;
// Reset internal variables
ManagedOps.Free(K, kparam, E, alpha);
kparam = new ManagedArray(param);
ManagedOps.Copy2D(kparam, param, 0, 0);
// Variables
alpha = new ManagedArray(1, m);
E = new ManagedArray(1, m);
b = 0;
Iterations = 0;
// Pre-compute the Kernel Matrix since our dataset is small
// (In practice, optimized SVM packages that handle large datasets
// gracefully will *not* do this)
if (kernel == KernelType.LINEAR)
{
// Computation for the Linear Kernel
// This is equivalent to computing the kernel on every pair of examples
var tinput = ManagedMatrix.Transpose(dx);
K = ManagedMatrix.Multiply(dx, tinput);
double slope = kparam.Length() > 0 ? kparam[0] : 1;
double inter = kparam.Length() > 1 ? kparam[1] : 0;
ManagedMatrix.Multiply(K, slope);
ManagedMatrix.Add(K, inter);
ManagedOps.Free(tinput);
}
else if (kernel == KernelType.GAUSSIAN || kernel == KernelType.RADIAL)
{
// RBF Kernel
// This is equivalent to computing the kernel on every pair of examples
var pX2 = ManagedMatrix.Pow(dx, 2);
var rX2 = ManagedMatrix.RowSums(pX2);
var tX2 = ManagedMatrix.Transpose(rX2);
var trX = ManagedMatrix.Transpose(dx);
var tempK = new ManagedArray(m, m);
var temp1 = new ManagedArray(m, m);
var temp2 = ManagedMatrix.Multiply(dx, trX);
ManagedMatrix.Expand(rX2, m, 1, tempK);
ManagedMatrix.Expand(tX2, 1, m, temp1);
ManagedMatrix.Multiply(temp2, -2);
ManagedMatrix.Add(tempK, temp1);
ManagedMatrix.Add(tempK, temp2);
double sigma = kparam.Length() > 0 ? kparam[0] : 1;
var g = Math.Abs(sigma) > 0 ? Math.Exp(-1 / (2 * sigma * sigma)) : 0;
if (Type == KernelType.RADIAL)
{
ManagedMatrix.Sqrt(tempK);
}
K = ManagedMatrix.Pow(g, tempK);
ManagedOps.Free(pX2, rX2, tX2, trX, tempK, temp1, temp2);
}
else
{
// Pre-compute the Kernel Matrix
// The following can be slow due to the lack of vectorization
K = new ManagedArray(m, m);
var Xi = new ManagedArray(Cols(dx), 1);
var Xj = new ManagedArray(Cols(dx), 1);
for (var i = 0; i < m; i++)
{
ManagedOps.Copy2D(Xi, dx, 0, i);
for (var j = 0; j < m; j++)
{
ManagedOps.Copy2D(Xj, dx, 0, j);
K[j, i] = KernelFunction.Run(kernel, Xi, Xj, kparam);
// the matrix is symmetric
K[i, j] = K[j, i];
}
}
ManagedOps.Free(Xi, Xj);
}
eta = 0;
L = 0;
H = 0;
// Map 0 (or other categories) to -1
for (var i = 0; i < Rows(dy); i++)
{
dy[i] = (int)dy[i] != Category ? -1 : 1;
}
}
// SVMPREDICT returns a vector of predictions using a trained SVM model
//(svm_train).
//
// pred = SVMPREDICT(model, X) returns a vector of predictions using a
// trained SVM model (svm_train). X is a mxn matrix where there each
// example is a row. model is a svm model returned from svm_train.
// predictions pred is a m x 1 column of predictions of {0, 1} values.
//
// Converted to R by: SD Separa (2016/03/18)
// Converted to C# by: SD Separa (2018/09/29)
public ManagedArray Predict(ManagedArray input)
{
var predictions = new ManagedArray(1, Rows(input));
if (Trained)
{
var x = new ManagedArray(input);
if (Cols(x) == 1)
{
ManagedMatrix.Transpose(x, input);
}
else
{
ManagedOps.Copy2D(x, input, 0, 0);
}
var m = Rows(x);
predictions.Resize(1, m);
if (Type == KernelType.LINEAR)
{
ManagedMatrix.Multiply(predictions, x, W);
ManagedMatrix.Add(predictions, B);
}
else if (Type == KernelType.GAUSSIAN || Type == KernelType.RADIAL)
{
// RBF Kernel
// This is equivalent to computing the kernel on every pair of examples
var pX1 = ManagedMatrix.Pow(x, 2);
var pX2 = ManagedMatrix.Pow(ModelX, 2);
var rX2 = ManagedMatrix.RowSums(pX2);
var X1 = ManagedMatrix.RowSums(pX1);
var X2 = ManagedMatrix.Transpose(rX2);
var tX = ManagedMatrix.Transpose(ModelX);
var tY = ManagedMatrix.Transpose(ModelY);
var tA = ManagedMatrix.Transpose(Alpha);
var rows = Rows(X1);
var cols = Cols(X2);
var tempK = new ManagedArray(cols, rows);
var temp1 = new ManagedArray(cols, rows);
var temp2 = ManagedMatrix.Multiply(x, tX);
ManagedMatrix.Multiply(temp2, -2);
ManagedMatrix.Expand(X1, cols, 1, tempK);
ManagedMatrix.Expand(X2, 1, rows, temp1);
ManagedMatrix.Add(tempK, temp1);
ManagedMatrix.Add(tempK, temp2);
var sigma = KernelParam.Length() > 0 ? KernelParam[0] : 1;
if (Type == KernelType.RADIAL)
{
ManagedMatrix.Sqrt(tempK);
}
var g = Math.Abs(sigma) > 0 ? Math.Exp(-1 / (2 * sigma * sigma)) : 0;
var Kernel = ManagedMatrix.Pow(g, tempK);
var tempY = new ManagedArray(Cols(tY), rows);
var tempA = new ManagedArray(Cols(tA), rows);
ManagedMatrix.Expand(tY, 1, rows, tempY);
ManagedMatrix.Expand(tA, 1, rows, tempA);
ManagedMatrix.Product(Kernel, tempY);
ManagedMatrix.Product(Kernel, tempA);
var p = ManagedMatrix.RowSums(Kernel);
ManagedOps.Copy2D(predictions, p, 0, 0);
ManagedMatrix.Add(predictions, B);
ManagedOps.Free(pX1, pX2, rX2, X1, X2, tempK, temp1, temp2, tX, tY, tA, tempY, tempA, Kernel, p);
}
else
{
var Xi = new ManagedArray(Cols(x), 1);
var Xj = new ManagedArray(Cols(ModelX), 1);
for (var i = 0; i < m; i++)
{
double prediction = 0;
ManagedOps.Copy2D(Xi, x, 0, i);
for (var j = 0; j < Rows(ModelX); j++)
{
ManagedOps.Copy2D(Xj, ModelX, 0, j);
prediction += Alpha[j] * ModelY[j] * KernelFunction.Run(Type, Xi, Xj, KernelParam);
}
predictions[i] = prediction + B;
}
ManagedOps.Free(Xi, Xj);
}
ManagedOps.Free(x);
}
return(predictions);
}