ForK Library

Subroutine used to determine the minimum or maximum value from a Kriging response surface (requires buildkriging to be called first)
Only Works for Ordinary Kriging (Constant Mean function)
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Functions/Subroutines  
subroutine  krigingextremefuncpredict (ndim, ntot, X, stot, H, beta, V, hyper, Xm, Ym, covarflagi, optflag, flag, Lb, Ub) 
This subroutine predicts the global minimum or maximum function values from the Kriging surface (constructed using buildkriging). Using an existing Kriging surface, the minimum or maximum value from the model is determined using either simplexsearch or patternsearch (specified with the optflagi). Within these optimization subroutines, the code krigingfuncpredict is invoked to predict the mean function value of the Kriging surface at a particular location. The optimization algorithms by design determine the minimum value of a function. To determine the maximum value (specified by flag=1), the objective is multiplied by \(1\) and minimization is performed. This optimization can only be performed on an Ordinary Kriging surface, meaning that the mean function is a constant value that is fitted during the construction of the mean function. From the universal Kriging framework used in buildkriging, ordinary Kriging can be recovered by using a \(p=0\) regression. This zeroth order regression requires a single term (meaning \(stot=1\)) and all the elements of the collocation matrix (H) are equal to one. 
Subroutine used to determine the minimum or maximum value from a Kriging response surface (requires buildkriging to be called first)
Only Works for Ordinary Kriging (Constant Mean function)
Definition in file krigingextremefuncpredict.f90.
subroutine krigingextremefuncpredict  (  integer,intent(in)  ndim, 
integer,intent(in)  ntot,  
real(8),dimension(ndim,ntot),intent(in)  X,  
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,  
integer,intent(in)  flag,  
real(8),dimension(ndim),intent(in)  Lb,  
real(8),dimension(ndim),intent(in)  Ub  
) 
This subroutine predicts the global minimum or maximum function values from the Kriging surface (constructed using buildkriging). Using an existing Kriging surface, the minimum or maximum value from the model is determined using either simplexsearch or patternsearch (specified with the optflagi). Within these optimization subroutines, the code krigingfuncpredict is invoked to predict the mean function value of the Kriging surface at a particular location. The optimization algorithms by design determine the minimum value of a function. To determine the maximum value (specified by flag=1), the objective is multiplied by \(1\) and minimization is performed.
This optimization can only be performed on an Ordinary Kriging surface, meaning that the mean function is a constant value that is fitted during the construction of the mean function. From the universal Kriging framework used in buildkriging, ordinary Kriging can be recovered by using a \(p=0\) regression. This zeroth order regression requires a single term (meaning \(stot=1\)) and all the elements of the collocation matrix (H) are equal to one.
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)  stot : Number of Terms in the regression 
in)  H: The collocation matrix for the regression (size=[stotxntot]) 
in)  beta: Regression coefficients based on the optimal estimate for the Kriging model (size=[stot]) Supplied by buildkriging subroutine 
in)  V: Processed Training Data (size=[ntot]) Supplied by buildkriging subroutine 
in)  hyper: Hyperparameters for the Kriging Model (size=[ndim+2]) Supplied by buildkriging subroutine 
in  out) Xm : Location of the extreme point (size=[ndim]) Starting point for the optimization is the input value for Xm. Final value overwrites this initial value. 
out)  Ym : Minimum or Maximum value 
in)  covarflagi: Flag to govern which covariance function is used

in)  optflagi: Flag to govern the optimization algorithm used to determine minimum or maximum value

in)  flag Determines whether minimum or maximum value is found

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 57 of file krigingextremefuncpredict.f90.
References patternsearch(), and simplexsearch().