Kernel Class Reference

Kernel functions for the Gaussian Process surrogate. More...

Inheritance diagram for Kernel:

Public Member Functions
virtual void	compute_gram (const std::vector< MatrixXd > &dists2, const VectorXd &theta_values, MatrixXd &gram)=0
	Compute a Gram matrix given a vector of squared distances and kernel hyperparameters. More...
virtual void	compute_gram_derivs (const MatrixXd &gram, const std::vector< MatrixXd > &dists2, const VectorXd &theta_values, std::vector< MatrixXd > &gram_derivs)=0
	Compute the derivatives of the Gram matrix with respect to the kernel hyperparameters. More...
virtual MatrixXd	compute_first_deriv_pred_gram (const MatrixXd &pred_gram, const std::vector< MatrixXd > &mixed_dists, const VectorXd &theta_values, const int index)=0
	Compute the first derivatve of the prediction matrix for a given component. More...
virtual MatrixXd	compute_second_deriv_pred_gram (const MatrixXd &pred_gram, const std::vector< MatrixXd > &mixed_dists, const VectorXd &theta_values, const int index_i, const int index_j)=0
	Compute the second derivatve of the prediction matrix for a pair of components. More...

Protected Member Functions
void	compute_Dbar (const std::vector< MatrixXd > &cw_dists2, const VectorXd &theta_values, bool take_sqrt=true)
	Compute the `‘Dbar’' matrices of scaled distances. More...

Protected Attributes
MatrixXd	Dbar
MatrixXd	Dbar2

Detailed Description

Kernel functions for the Gaussian Process surrogate.

Member Function Documentation

compute_gram()

virtual void compute_gram ( const std::vector< MatrixXd > &  dists2, const VectorXd &  theta_values, MatrixXd &  gram  )

pure virtual

Compute a Gram matrix given a vector of squared distances and kernel hyperparameters.

Parameters

[in]	dists2	Vector of squared distance matrices.
[in]	theta_values	Vector of hyperparameters.
[in,out]	gram	Gram matrix.

Returns

Gram matrix.

Implemented in Matern52Kernel, Matern32Kernel, and SquaredExponentialKernel.

compute_gram_derivs()

virtual void compute_gram_derivs ( const MatrixXd &  gram, const std::vector< MatrixXd > &  dists2, const VectorXd &  theta_values, std::vector< MatrixXd > &  gram_derivs  )

pure virtual

Compute the derivatives of the Gram matrix with respect to the kernel hyperparameters.

Parameters

[in]	gram	Gram Matrix
[in]	dists2	Vector of squared distance matrices.
[in]	theta_values	Vector of hyperparameters.
[in,out]	gram_derivs	Vector of Gram matrix derivatives.

Returns

Derivatives of the Gram matrix w.r.t. the hyperparameters.

Implemented in Matern52Kernel, Matern32Kernel, and SquaredExponentialKernel.

compute_first_deriv_pred_gram()

virtual MatrixXd compute_first_deriv_pred_gram ( const MatrixXd &  pred_gram, const std::vector< MatrixXd > &  mixed_dists, const VectorXd &  theta_values, const int  index  )

pure virtual

Compute the first derivatve of the prediction matrix for a given component.

Parameters

[in]	pred_gram	Prediction Gram matrix - Rectangular matrix of kernel evaluations between the surrogate and prediction points.
[in]	mixed_dists	Component-wise signed distances between the prediction and build points.
[in]	theta_values	Vector of hyperparameters.
[in]	index	Specifies the component of the derivative.

Returns

first_deriv_pred_gram First derivative of the prediction Gram matrix for a given component.

Implemented in Matern52Kernel, Matern32Kernel, and SquaredExponentialKernel.

compute_second_deriv_pred_gram()

virtual MatrixXd compute_second_deriv_pred_gram ( const MatrixXd &  pred_gram, const std::vector< MatrixXd > &  mixed_dists, const VectorXd &  theta_values, const int  index_i, const int  index_j  )

pure virtual

Compute the second derivatve of the prediction matrix for a pair of components.

Parameters

[in]	pred_gram	Prediction Gram matrix - Rectangular matrix of kernel evaluations between the surrogate and prediction points.
[in]	mixed_dists	Component-wise signed distances between the prediction and build points.
[in]	theta_values	Vector of hyperparameters.
[in]	index_i	Specifies the first component of the second derivative.
[in]	index_j	Specifies the second component of the second derivative.

Returns

second_deriv_pred_gram Second derivative of the prediction matrix for a pair of components.

Implemented in Matern52Kernel, Matern32Kernel, and SquaredExponentialKernel.

compute_Dbar()

void compute_Dbar ( const std::vector< MatrixXd > &  cw_dists2, const VectorXd &  theta_values, bool  take_sqrt = true  )

protected

Compute the `‘Dbar’' matrices of scaled distances.

Parameters

[in]	cw_dists2	Vector of component-wise squared distance matrices.
[in]	theta_values	Vector of hyperparameters.
[in]	take_sqrt	Flag for computing the square root of Dbar2.

Returns

Matrix of hyperparameter-scaled distances.

Referenced by Matern32Kernel::compute_first_deriv_pred_gram(), Matern52Kernel::compute_first_deriv_pred_gram(), SquaredExponentialKernel::compute_gram(), Matern32Kernel::compute_gram(), Matern52Kernel::compute_gram(), Matern32Kernel::compute_gram_derivs(), Matern52Kernel::compute_gram_derivs(), and Matern52Kernel::compute_second_deriv_pred_gram().

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The documentation for this class was generated from the following files:

• SurrogatesGPKernels.hpp
• SurrogatesGPKernels.cpp