Full Factorial about smt HOT 3 CLOSED

Could you provide the code examples to show the problem?

from smt.

The script i use is the following :

from __future__ import print_function, division
import numpy as np
from scipy import linalg
from smt.utils import compute_rms_error

from smt.problems import  WingWeight, Sphere
from smt.sampling_methods import LHS, Random, FullFactorial
from smt.surrogate_models import LS, QP, KPLS, KRG, KPLSK, GEKPL

try:
    import matplotlib.pyplot as plt
    plot_status = True
except:
    plot_status = False

import scipy.interpolate

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import pylab

########### Initialization of the problem, construction of the training and validation points

ndim = 10 #number of variables
ndoe = 300


#Construction of the DOE for the fuction
fun = WingWeight(ndim = ndim)
sampling = FullFactorial(xlimits = fun.xlimits)
b = sampling(ndoe)
#Compute the outputs
f = fun(b)   



# Construction of the validation points
nval = 100
  
sampling = LHS(xlimits = fun.xlimits, criterion = 'cm' )
bval = sampling(nval)
fval = fun(bval)


#plot of validation vs sampling points
fig = plt.figure(1)
ax = fig.add_subplot(2, 1, 1)
ax.plot(f, f, "o" , label = 'sampling points')
ax.plot(fval, fval, 'r.', label = 'validation points')

ax.set_xlabel('F')
ax.set_ylabel('F')

ax.legend(loc='upper left')
plt.title('Plot of validation vs sampling points')
ax.grid()
pylab.show()



#-------------------------- The KPLSK model--------------------------------#   
t = KPLSK(n_comp = ndim, theta0 = [1e-2]*ndim , poly = 'linear', corr = 'squar_exp')
t.set_training_values(b,f)

t.train()


# Prediction of the validation points
fnew = t.predict_values(bval) 
print('KPLSK model,  err: '+ str(compute_rms_error(t,bval,fval)))


if plot_status:    
# Plot the function, the prediction and the 95% confidence interval based on
# the MSE
    fig = plt.figure()
    plt.plot(fval, fval, '-', label='$F_{true}$')
    plt.plot(fval, fnew, 'r.', label='$\hat{F}$')
   
    plt.xlabel('$F_{true}$')
    plt.ylabel('$\hat{F}$')
    
    plt.legend(loc='upper left')
    plt.title('KPLSK model: validation of the prediction model')   

if plot_status:
    plt.show()

# Value of theta
print("theta values",  t.optimal_theta) 

Which comes with the following error for number of training points ndoe < 600 :

*Training ...
/home/dmitris/.local/lib/python3.8/site-packages/sklearn/cross_decomposition/_pls.py:353: UserWarning: X scores are null at iteration 9
warnings.warn('X scores are null at iteration %s' % k)
capi_return is NULL
Call-back cb_calcfc_in__cobyla__user__routines failed.
Traceback (most recent call last):
File "KPLSK_easy_wing.py", line 73, in
t.train()
File "/home/dmitris/Programs/SMT/smt-master/smt/surrogate_models/surrogate_model.py", line 248, in train
self._train()
File "/home/dmitris/Programs/SMT/smt-master/smt/surrogate_models/krg_based.py", line 123, in _train
self._new_train()
File "/home/dmitris/Programs/SMT/smt-master/smt/surrogate_models/krg_based.py", line 111, in _new_train
self.optimal_rlf_value, self.optimal_par, self.optimal_theta = self._optimize_hyperparam(
File "/home/dmitris/Programs/SMT/smt-master/smt/surrogate_models/krg_based.py", line 450, in _optimize_hyperparam
optimal_theta = 10.0 ** optimize.fmin_cobyla(
File "/usr/lib/python3/dist-packages/scipy/optimize/cobyla.py", line 166, in fmin_cobyla
sol = _minimize_cobyla(func, x0, args, constraints=con,
File "/usr/lib/python3/dist-packages/scipy/optimize/cobyla.py", line 250, in _minimize_cobyla
xopt, info = _cobyla.minimize(calcfc, m=m, x=np.copy(x0), rhobeg=rhobeg,
File "/usr/lib/python3/dist-packages/scipy/optimize/cobyla.py", line 242, in calcfc
f = fun(x, args)
File "/home/dmitris/Programs/SMT/smt-master/smt/surrogate_models/krg_based.py", line 414, in minus_reduced_likelihood_function
return -self._reduced_likelihood_function(theta=10.0 ** log10t)[0]
File "/home/dmitris/Programs/SMT/smt-master/smt/surrogate_models/krg_based.py", line 207, in _reduced_likelihood_function
raise Exception(
Exception: F is too ill conditioned. Poor combination of regression model and observations.

For ndoe >= 600 :

When the number of training points exceeds a specific number, the training process proceeds uninterrupted

from smt.

If you try with LHS it works fine. The thing is with FullFactorial points are "aligned" and this can lead too ill-conditionned kriging matrix. Moreover using KPLSK you should take of number of components n_comp smaller than ndim. Indeed the purpose is to solve the problem in the reduced space of principal components.

from smt.