public void CanAddSparseMatricesBothWays()
{
var m1 = new SparseMatrix(1, 3);
var m2 = new SparseMatrix(new double[, ] {
{ 0, 1, 1 }
});
var sum1 = m1 + m2;
var sum2 = m2 + m1;
Assert.IsTrue(sum1.Equals(m2));
Assert.IsTrue(sum1.Equals(sum2));
var sparseResult = new SparseMatrix(1, 3);
sparseResult.Add(m2, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = new SparseMatrix(new double[, ] {
{ 0, 1, 1 }
});
sparseResult.Add(m1, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = new SparseMatrix(new double[, ] {
{ 0, 1, 1 }
});
m1.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = new SparseMatrix(new double[, ] {
{ 0, 1, 1 }
});
sparseResult.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(2 * sum1));
var denseResult = new DenseMatrix(1, 3);
denseResult.Add(m2, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
denseResult = new DenseMatrix(new double[, ] {
{ 0, 1, 1 }
});
denseResult.Add(m1, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
var m3 = new DenseMatrix(new double[, ] {
{ 0, 1, 1 }
});
var sum3 = m1 + m3;
var sum4 = m3 + m1;
Assert.IsTrue(sum3.Equals(m3));
Assert.IsTrue(sum3.Equals(sum4));
}
/// <summary>
/// Transform to a sparse matrix.
/// </summary>
/// <param name="ratings"></param>
/// <returns></returns>
public static SparseMatrix <double> ToSparseMatrix(this List <Rating> ratings)
{
SparseMatrix <double> matrix = new SparseMatrix <double>();
foreach (var r in ratings)
{
if (!matrix.HasEntry(r.UserId, r.ItemId))
{
matrix.Add(r.UserId, r.ItemId, r.Score);
}
}
return(matrix);
}
public void CanAddSparseMatricesBothWays()
{
var m1 = new SparseMatrix(1, 3);
var m2 = new SparseMatrix(new Complex32[,] { { 0, 1, 1 } });
var sum1 = m1 + m2;
var sum2 = m2 + m1;
Assert.IsTrue(sum1.Equals(m2));
Assert.IsTrue(sum1.Equals(sum2));
var sparseResult = new SparseMatrix(1, 3);
sparseResult.Add(m2, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = new SparseMatrix(new Complex32[,] { { 0, 1, 1 } });
sparseResult.Add(m1, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = new SparseMatrix(new Complex32[,] { { 0, 1, 1 } });
m1.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = new SparseMatrix(new Complex32[,] { { 0, 1, 1 } });
sparseResult.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(2 * sum1));
var denseResult = new DenseMatrix(1, 3);
denseResult.Add(m2, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
denseResult = new DenseMatrix(new Complex32[,] { { 0, 1, 1 } });
denseResult.Add(m1, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
var m3 = new DenseMatrix(new Complex32[,] { { 0, 1, 1 } });
var sum3 = m1 + m3;
var sum4 = m3 + m1;
Assert.IsTrue(sum3.Equals(m3));
Assert.IsTrue(sum3.Equals(sum4));
}
/// <summary>
/// GP Regression Method
/// </summary>
/// <param name="targets">the actual y value of the data points</param>
/// <param name="future_point_count">the future point count to predict</param>
/// <param name="sigma_0">amplitude of SE covariance</param>
/// <param name="lambda">length scale of SE covariance</param>
/// <param name="sigma_n">standard deviation of output noise</param>
/// <param name="fstar">mean of GP</param>
/// <param name="Vfstar">variance of GP</param>
/// <param name="logpyX">log p(y|X)</param>
public static void Predict(double[] targets, int future_point_count, double sigma_0, double lambda, double sigma_n, out double[] fstar, out double[] Vfstar, out double logpyX)
{
int n = targets.Length;
double[,] cov = GetDataCovar(n, sigma_0, lambda, sigma_n);
double mean = targets.Sum() / n;
for (int i = 0; i < targets.Length; i++)
{
targets[i] -= mean;
}
//column matrix y
SparseMatrix y = new SparseMatrix(n, 1, targets);
SparseMatrix K = new SparseMatrix(cov);
//identity matrix for I
SparseMatrix I = SparseMatrix.Identity(targets.Length);
//choleski(K + sigman^2*I)
var temp_matrix = K.Add(I.Multiply(System.Math.Pow(sigma_n, 2)));
var cholesky = temp_matrix.Cholesky();
var L = cholesky.Factor;
//inverse of L_transpose()
//var L2 = L.LU().L;
var L_transpose_inverse = L.Transpose().Inverse();
//inverse of L
var L_inverse = L.Inverse();
//alpha = L'\(L\y)
var alpha = L_transpose_inverse.Multiply(L_inverse).Multiply(y);
double L_diag = 0.0;
for (int i = 0; i < L.ColumnCount; i++)
{
L_diag += System.Math.Log(L[i, i]);
}
logpyX = -y.Transpose().Multiply(alpha).Multiply(0.5)[0, 0] - L_diag - future_point_count * System.Math.Log(2 * System.Math.PI) * 0.5;
fstar = new double[targets.Length + future_point_count];
Vfstar = new double[targets.Length + future_point_count];
for (int i = 0; i < n + future_point_count; i++)
{
double[] kstar = new double[targets.Length];
for (int j = 0; j < n; j++)
{
kstar[j] = GetCov_SE(j, i, sigma_0, lambda, sigma_n);
}
var column_vector_kstar = new SparseMatrix(n, 1, kstar);
//f*=k_*^T * alpha
fstar[i] = column_vector_kstar.Transpose().Multiply(alpha)[0, 0];
fstar[i] += mean;
//v = L\k_*
var v = L_inverse.Multiply(column_vector_kstar);
//V[fstar] = k(x_*,x_*) - v^T*v
Vfstar[i] = GetCov_SE(i, i, sigma_0, lambda, sigma_n) - v.Transpose().Multiply(v)[0, 0] + System.Math.Pow(sigma_n, 2);
}
}
