 Dakota  Version 6.15 Explore and Predict with Confidence
Kernel Class Referenceabstract

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...

MatrixXd Dbar

MatrixXd Dbar2

## Detailed Description

Kernel functions for the Gaussian Process surrogate.

## Member Function Documentation

 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.

 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.

 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.

 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.

 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.

The documentation for this class was generated from the following files:
• SurrogatesGPKernels.hpp
• SurrogatesGPKernels.cpp