ForK Library

# krigingmaxeipredictGEK.f90 File Reference

Subroutine to Predict maximum expected improvement from Gradient-Enhanced Kriging Surface based on a current minimum value(requires buildkrigingGEK to be called first)
Only Works for Ordinary Kriging (Constant Mean function) More...

Go to the source code of this file.

## Functions/Subroutines

subroutine krigingmaxeipredictGEK (ndim, ntot, X, gtot, pts, dims, stot, H, beta, V, hyper, Xm, Ym, covarflagi, optflag, Lb, Ub, Ymin)
See documentation for krigingmaxeipredict for details. This subroutine is the gradient-enhanced version and is functionally the same as the function-only subroutine.

## Detailed Description

Subroutine to Predict maximum expected improvement from Gradient-Enhanced Kriging Surface based on a current minimum value(requires buildkrigingGEK to be called first)
Only Works for Ordinary Kriging (Constant Mean function)

Definition in file krigingmaxeipredictGEK.f90.

## Function Documentation

 subroutine krigingmaxeipredictGEK ( 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),intent(in) H, real(8),dimension(stot),intent(in) Beta, real(8),dimension(ntot),intent(in) V, real(8),dimension(ndim+2),intent(in) hyper, real(8),dimension(ndim),intent(out) Xm, real(8),intent(out) Ym, integer,intent(in) covarflagi, integer,intent(in) optflag, real(8),dimension(ndim),intent(in) Lb, real(8),dimension(ndim),intent(in) Ub, real(8),intent(in) Ymin )

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

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 out) Xm : Location of the maximum Expected Improvement (size=[ndim]) out) Eim : Maximum Expected Improvement 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. in) optflagi: Flag to govern the optimization algorithm used to determine maximum Expected Improvement optflag=0 Simplex Search (Nelder-Mead Method) to determine maximum Expected Improvement Local optimization technique using simplex elements to determine search direction and line search to determine step sizes Fastest method but inherently sequential and may stall on local optimum optflag=1 Pattern Search used to determine maximum Expected Improvement Global optimization method with fixed search directions (forward and backward in each direction) Each iteration requires $$2*ndim$$ function evaluations; however, these may be performed in parallel using openmp (Each thread performs own likelihood evaluation so OMP_STACK_SIZE must be set large enough) in) Lb Lower Bound for each variable (size = [ndim]) Should be the minimum possible value of Xm in each dimension in) Ub Upper Bound for each variable (size = [ndim]) Should be the maximum possible value of Xm in each dimension in) Ymin The current minimum value that the new candidate improves on. In the context of optimization, Ymin is the minimum value for the current optimization iteration. The expected improvement at a point uses the mean and variance from the Kriging model to predict the improvement in the minimum value if a new simulation is performed at that location. Hence, the maximum expected improvement is the location in the design space most likely to reduce the minimum value by the largest amount.

Definition at line 62 of file krigingmaxeipredictGEK.f90.

References patternsearch(), and simplexsearch().