ForK Library

# krigingextremefuncpredictGEK.f90 File Reference

Subroutine to Predict mean function values from Gradient-Enhanced Kriging Surface (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 krigingextremefuncpredictGEK (ndim, ntot, X, gtot, pts, dims, stot, H, beta, V, hyper, Xm, Ym, covarflagi, optflag, flag, Lb, Ub)
See documentation for krigingextremefuncpredict for details. This subroutine is the gradient-enhanced version and is functionally the same as the function-only subroutine.

## Detailed Description

Subroutine to Predict mean function values from Gradient-Enhanced Kriging Surface (requires buildkrigingGEK to be called first)
Only Works for Ordinary Kriging (Constant Mean function)

Definition in file krigingextremefuncpredictGEK.f90.

## Function Documentation

 subroutine krigingextremefuncpredictGEK ( 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, real(8),dimension(ndim),intent(out) Xm, real(8),intent(out) Ym, integer,intent(in) covarflagi, integer,intent(in) optflag, integer,intent(in) flag, real(8),dimension(ndim),intent(in) Lb, real(8),dimension(ndim),intent(in) Ub )

See documentation for krigingextremefuncpredict 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 extreme point (size=[ndim]) out) Ym : Minimum or Maximum value 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 minimum or maximum value optflag=0 Simplex Search (Nelder-Mead Method) to determine extreme value 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 extreme value 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) flag Determines whether minimum or maximum value is found flag = 0 Subroutine finds the minimum value flag = 1 Subroutine finds the maximum value 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

Definition at line 61 of file krigingextremefuncpredictGEK.f90.

References patternsearch(), and simplexsearch().