rbf_kernel.cpp

/*
 * Copyright (c) 2017, The Regents of the University of California (Regents).
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 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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 * Please contact the author(s) of this library if you have any questions.
 * Authors: David Fridovich-Keil   ( dfk@eecs.berkeley.edu )
 */
///////////////////////////////////////////////////////////////////////////////
//
// Defines the RbfKernel class, which is derived from the Kernel base class.
// The RBF kernel is a function k(x, y) = exp(-0.5 (x-y)^T inv(L) (x-y)), where
// x, y are points in R^n and L is a diagonal matrix of squared length scales.
//
///////////////////////////////////////////////////////////////////////////////

#include <kernels/rbf_kernel.hpp>

#include <math.h>

namespace gp {

  // Factory method.
  Kernel::Ptr RbfKernel::Create(const VectorXd& lengths) {
    Kernel::Ptr ptr(new RbfKernel(lengths));
    return ptr;
  }

  // Constructor.
  RbfKernel::RbfKernel(const VectorXd& lengths)
    : Kernel(lengths) {}

  // Pure virtual methods to be implemented in a derived class.
  double RbfKernel::Evaluate(const VectorXd& x, const VectorXd& y) const {
    const VectorXd diff = x - y;

    return std::exp(-0.5 * diff.cwiseQuotient(params_).squaredNorm());
  }

  double RbfKernel::Partial(const VectorXd& x, const VectorXd& y,
                            size_t ii) const {
    CHECK_LT(ii, params_.size());
    const VectorXd diff = x - y;

    // Evaluate the kernel.
    const double kernel =
      std::exp(-0.5 * diff.cwiseQuotient(params_).squaredNorm());

    return kernel * diff(ii) * diff(ii) /
      (params_(ii) * params_(ii) * params_(ii));
  }

  void RbfKernel::Gradient(const VectorXd& x, const VectorXd& y,
                           VectorXd& gradient) const {
    const VectorXd diff = x - y;

    // Evaluate the kernel.
    const double kernel =
      std::exp(-0.5 * diff.cwiseQuotient(params_).squaredNorm());

    gradient = kernel * diff.cwiseProduct(diff).cwiseQuotient(
      params_.cwiseProduct(params_).cwiseProduct(params_));
  }


}  //\namespace gp