Kernel Packet

Kernel Packet is a MATLAB package for fast computing in Gaussian Process Modeling.

File Description

Functions:

• General:

  • DesignFunctions:
    • <hc> is a function file to compute a vector with hyperbolic cross points (bisection).
  • <bdlogdet> is a function file to compute log determinant of band matrix.
  • <matern_halfint> is a function file to compute Matérn covariance matrix for half integer.
  • <nsumk> is a function file to compute a partition matirx where n positive integers summing to k.
  • <splogdet> is a function file to compute log determinant of high dimensional covariance matrix under sparse grid design.

• One-dimension:

  • <compute_basis> is a function file to compute kernel packet (which also our basis function) in one-dimensional Kriging (GPR).
  • <compute_post> is a function file to to compute posterior mean and covariance in one dimensional Kriging.
  • <loglike_1d> is a function file to compute log likelihood of parameter 'rho' in one dimension.
  • <mle_1d> is a function file to compute updated parameter theta_hat, updated log likelihood L_hat and initial loglikelihood L_init in one dimensional MLE.

• Multi-Dimension:

  • FullGrid:

    • <fg_w> is a function file to compute multiplication of inverse of covariance matrix and a random matrix in full grid design.

  • SparseGrid:

    • <sg_loglike> is a function file to compute log likelihood of lengthscale parameter 'rho' in Multi-dimensional sparse grid design.
    • <sg_mle> is a function file to compute updated parameter theta_hat, updated log likelihood L_hat and initial loglikelihood L_init in Multi-dimensional MLE under sparse grid design.
    • <sg_w> is a function file to compute multiplication of inverse of covariance matrix and a random matrix in sparse grid design.
    • <sgd> is a function file to generate a structure of sparse grid design.

  • <compute_pred> is a funciton file to compute prediction value of response (which is also the posterior mean) of nulti-dimensional Kriging.

  • <kron_mat_prod> is a function file to compute matrix-matrix multiplication between matrix kron(As{1}, As{2}, ..., As{N}) and matrix v without forming the full kronecker product by using unfold and refold functions.

  • <kron_ttm> is a function file to compute matrix-matrix multiplication between matrix kron(As{1}, As{2}, ..., As{N}) and matrix m by using <ttm> function in tensor_toolbox-master.

  • <refold> is a function file to refold matrix into tensor.

  • <unfold> is a function file to unfold tensor into matrix.

Examples:

• <Example1D> is an example to use <compute_basis> and <compute_post> function files.
• <ExampleMLE> is an example to use <mle_1d> and <sg_mle> function files.
• <FGDeisgn> is an example to compute multiplication of inverse of covariance matrix and response in full grid design, then compute prediction value of response based on it.
• <SGDesign> is an example to use <sg_w> and <compute_pred> in sparse grid design.

Others:

• tensor_toolbox-master is a MATLAB tensor toolbox by Brett W. Bader, Tamara G. Kolda and others, we use sparse tensor function <sptensor> in our function <sg_w>. For more information please see their official website here.

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

License

This work is published under MIT License.