/// <summary>
/// Q-R Decomposition
/// </summary>
/// <param name="A">Source matrix</param>
/// <returns>{Q,R} in array form</returns>
public static RealMatrix[] QR(RealMatrix A)
{
int m = A.Height;
int n = A.Width;
var Q = RealMatrix.I(m);
var R = new RealMatrix(A);
for (int k = 0; k < n; k++)
{
var x = new RVector(R.Submatrix(k, k, 0, 1));
var e = RVector.Zeros(x.Length);
e[0] = 1;
var u = -Math.Sign(x[0]) * x.Norm2 * e + x;
u = u / u.Norm2;
var qn = RealMatrix.I(u.Length) - 2 * u.Outer(u);
//var r = R.Submatrix(k, k) - 2 * u.Outer(u) * R.Submatrix(k, k);
var q = RealMatrix.I(Q.Height);
q.Update(k, k, qn);
Q = Q * q;
R = Q.Transpose * A;
}
return(new[] { Q, R });
}
/// <summary>
/// Day dream - Reconstruct a randrom matrix (An interesting way of seeing strong features the machine has learnt).
///
/// Randomly initialize the visible units once, and start running alternating Gibbs sampling steps
/// (where each step consists of updating all the hidden units, and then updating all of the visible units),
/// taking a sample of the visible units at each step.
///
/// Note that we only initialize the network "once", so these samples are correlated.
/// ---------
/// samples: A matrix, where each row is a sample of the visible units produced while the network was daydreaming。
/// </summary>
/// <param name="numberOfSamples">How many images/dreams</param>
/// <returns>Array of Reconstructed dreams</returns>
public double[][] DayDream(int numberOfSamples)
{
//Create a matrix, where each row is to be a sample of of the visible units
//(with an extra bias unit), initialized to all ones.
var data = RealMatrix.Ones(numberOfSamples, m_numVisibleElements + 1);
//Take the first sample from a uniform distribution.
data.Update(0, 1, Distributions.UniformRandromMatrixBool(1, m_numVisibleElements), 1);
//Start the alternating Gibbs sampling.
//Note that we keep the hidden units binary states, but leave the
//visible units as real probabilities.
//See section 3 of Hinton's "A Practical Guide to Training Restricted Boltzmann Machines" for more on why.
for (int i = 0; i < numberOfSamples; i++)
{
var visible = data.Submatrix(i, 0, 1).ToVector();
//Calculate the activations of the hidden units.
var hidden_activations = (visible * m_weights).ToVector();
//Calculate the probabilities of turning the hidden units on.
var hidden_probs = ActivationFunctions.Logistic(hidden_activations);
//Turn the hidden units on with their specified probabilities.
var hidden_states = hidden_probs > RVector.Random(m_numHiddenElements + 1);
//Always fix the bias unit to 1.
hidden_states[0] = 1;
//Recalculate the probabilities that the visible units are on.
var visible_activations = (hidden_states * m_weights.Transpose).ToVector();
var visible_probs = ActivationFunctions.Logistic(visible_activations);
var visible_states = visible_probs > RVector.Random(m_numVisibleElements + 1);
data.Update(visible_states, 0, false, i, 0);
}
return(data.Submatrix(0, 1).ToArray());
}
public static RVector operator *(double scalar, RVector v)
{
var newVector = new RVector(v.Length);
Parallel.For(0, v.Length, i =>
{
newVector[i] = v[i] * scalar;
});
return(newVector);
}
public static double Dot(this RVector v1, RVector v2)
{
double r = 0;
Parallel.For(0, v1.Length, i =>
{
r += v1[i] * v2[i];
});
return(r);
}
public static RVector Ones(int size)
{
var v = new RVector(size);
for (int i = 0; i < size; i++)
{
v[i] = 1;
}
return(v);
}
public static RVector operator >(RVector c1, RVector c2)
{
var result = new RVector(c1.Length);
Parallel.For(0, c1.Length, i =>
{
result[i] = Convert.ToDouble(c1[i] > c2[i]);
});
return(result);
}
public static RVector operator -(RVector u, RVector v)
{
var x = new RVector(u.Length);
Parallel.For(0, u.Length, i =>
{
x[i] = u[i] - v[i];
});
return(x);
}
/// <summary>
/// Uniform Random Vector
/// </summary>
/// <param name="numElements"></param>
/// <returns></returns>
public static RVector UniformRandromVector(int numElements)
{
var vector = new RVector(numElements);
Parallel.For(0, numElements, i =>
{
vector[i] = GetRandomDouble();
});
return(vector);
}
public static RVector Logistic(RVector vector)
{
var result = new RVector(vector.Length);
for (int i = 0; i < vector.Length; i++)
{
result[i] = Logistic(vector[i]);
}
return(result);
}
public static RealMatrix Outer(this RVector u, RVector v)
{
var A = new RealMatrix(u.Length, v.Length);
Parallel.For(0, u.Length, i =>
Parallel.For(0, v.Length, j =>
{
A[i, j] = u[i] * v[j];
}));
return(A);
}
/// <summary>
/// Update a selection with a source vector
/// </summary>
/// <param name="matrix"></param>
/// <param name="src"></param>
/// <param name="length"></param>
/// <param name="isVertical"></param>
/// <param name="mPos"></param>
/// <param name="nPos"></param>
public static void Update(this RealMatrix matrix, RVector src, int length = 0, bool isVertical = true,
int mPos = 0, int nPos = 0)
{
length = length == 0 ? src.Length : length;
for (int i = 0; i < length; i++)
{
if (isVertical)
{
matrix[mPos + i, nPos] = src[i];
}
else
{
matrix[mPos, nPos + i] = src[i];
}
}
}