/**
* @brief Self [co]variance matrix between the test data, Kss(Z, Z)
* @param [in] logHyp The log hyperparameters
* - logHyp(0) = \f$\log(l)\f$
* - logHyp(1) = \f$\log(\sigma_f)\f$
* @param [in] testData The test data
* @param [in] fVarianceVector Flag for the return value
* - fVarianceVector = true : return \f$\mathbf{k}_{**} \in \mathbb{R}^{M \times 1}, \mathbf{k}_{**}^i = k(\mathbf{Z}_i, \mathbf{Z}_i)\f$ (default)
* - fVarianceVector = false: return \f$\mathbf{K}_{**} = \mathbf{K}(\mathbf{Z}, \mathbf{Z}) \in \mathbb{R}^{M \times M}\f$,\n
* which can be used for Bayesian Committee Machines.
* @return A matrix pointer\n
* - Mx1 (fVarianceVector == true)
* - MxM (fVarianceVector == false)\n
* M: The number of test data
*/
static MatrixPtr Kss(const Hyp &logHyp,
const TestData<Scalar> &testData,
const bool fVarianceVector = true)
{
// The number of test data
const int M = testData.M();
// Some constant values
const Scalar sigma_f2 = exp(static_cast<Scalar>(2.0) * logHyp(1)); // sigma_f^2
// Output
MatrixPtr pKss;
// K: self-variance vector (Mx1)
if(fVarianceVector)
{
// k(z, z) = sigma_f^2
pKss.reset(new Matrix(M, 1));
pKss->fill(sigma_f2);
}
// K: self-covariance matrix (MxM)
else
{
// K(r)
MatrixPtr pAbsDistXsXs = PairwiseOp<Scalar>::sqDist(testData.pXs()); // MxM
pAbsDistXsXs->noalias() = pAbsDistXsXs->cwiseSqrt();
pKss = K(logHyp, pAbsDistXsXs);
}
return pKss;
}
/**
* @brief Gets the cross absolute distances between the training and test inputs
* @param [in] pXs The M test inputs
* @return An matrix pointer
* \f[
* \mathbf{R} \in \mathbb{R}^{N \times M}, \quad
* \mathbf{R}_{ij} = |\mathbf{x}_i - \mathbf{z}_j|
* \f]
* @todo Include this matrix as a member variable like m_pDistXX
*/
MatrixPtr pAbsDistXXs(const TestData<Scalar> &testData) const
{
MatrixPtr pAbsDist = pSqDistXXs(testData); // NxM
pAbsDist->noalias() = pAbsDist->cwiseSqrt();
return pAbsDist;
}
