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krigingeipredictGEK.f90 File Reference

Subroutine to Predict Expected improvement from Gradient-enhanced Kriging Surface based on a given minimum value (requires buildkrigingGEK to be called first) More...

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Functions/Subroutines

subroutine krigingeipredictGEK (ndim, ntot, X, gtot, pts, dims, stot, H, beta, V, hyper, mtot, Xm, Hm, EI, covarflagi, Ymin)
 See documentation for krigingeipredict for details. This subroutine is the gradient-enhanced version and is functionally the same as the function-only subroutine.

Detailed Description

Subroutine to Predict Expected improvement from Gradient-enhanced Kriging Surface based on a given minimum value (requires buildkrigingGEK to be called first)

Definition in file krigingeipredictGEK.f90.


Function Documentation

subroutine krigingeipredictGEK ( integer,intent(in)  ndim,
integer,intent(in)  ntot,
real(8),dimension(ndim,ntot),intent(in)  X,
integer,intent(in)  gtot,
integer,dimension(gtot),intent(in)  pts,
integer,dimension(gtot),intent(in)  dims,
integer,intent(in)  stot,
real(8),dimension(stot,ntot+gtot),intent(in)  H,
real(8),dimension(stot),intent(in)  Beta,
real(8),dimension(ntot+gtot),intent(in)  V,
real(8),dimension(ndim+3),intent(in)  hyper,
integer,intent(in)  mtot,
real(8),dimension(ndim,mtot),intent(in)  Xm,
real(8),dimension(stot,mtot),intent(in)  Hm,
real(8),dimension(mtot),intent(out)  EI,
integer,intent(in)  covarflagi,
real(8),intent(in)  Ymin 
)

See documentation for krigingeipredict for details. This subroutine is the gradient-enhanced version and is functionally the same as the function-only subroutine.

Author:
Brian Lockwood Department of Mechanical Engineering University of Wyoming
Date:
May 2, 2012
Parameters:
in)ndim : The dimension of the problem
in)ntot : The number of Training points
in)X : The location of the training points (size=[ndimxntot])
in)gtot: Number of derivative values included in training data (ndim*ntot if all derivatives are included at the training points)
in)pts: List identifying what point the derivative value is enforced at (size=[gtot] with values ranging from 1 to ntot)
in)dims: List identifying the dimension the derivative is taken with respect to (size=[gtot] with values ranging from 1 to ndim)
in)stot : Number of Terms in the regression
in)H: The collocation matrix for the regression including derivative values. (size=[stotxntot+gtot])
Columns 1:ntot are the basis evaluated at the training points
Columns ntot+1:ntot+gtot are the derivative of the basis evaluated at the training points
in) beta: Regression coefficients based on the optimal estimate for the Kriging model (size=[stot])
Supplied by buildkrigingGEK subroutine
in)V: Processed Training Data (size=[ntot+gtot])
Supplied by buildkrigingGEK subroutine
in)hyper: Hyperparameters for the Kriging Model (size=[ndim+3])
Supplied by buildkrigingGEK subroutine
in)mtot : The number of test points, the places where function prediction are desired
in)Xm : The location of the test points (size=[ndimxmtot])
in)Hm : The collocation matrix evaluated at the test points. The derivative of the basis is NOT required for the test points to predict function values (size=[stotxmtot])
out)Ym: The predicted function values (size=[mtot])
Using the processed data V, predicting function values is essentially linear with respect to the number of test points so mtot can be set to one and this subroutine can be called multiple times.
Often the function values at a set of test points is required, hence the ability to make the predictions in a single function call.
in)covarflagi: Flag to govern which covariance function is used

  • covarflag==1 Uses Matern function with \(\nu=3/2\)
  • covarflag==2 Uses Matern function with \(\nu=5/2\)


The parameter \(\nu\) governs the smoothness and differentiability of the covariance function.
When using gradient values, \(\nu=1/2\) is not differentiable enough so \(\nu \geq 3/2\) must be used
Must supply the same covariance flag as used in buildkrigingGEK.

Definition at line 48 of file krigingeipredictGEK.f90.

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