def test_index_generator( self ):
index_generator = IndexGenerator()
# num_dims = 2, max_level = 3 index_norm_order = 1
num_dims = 2
max_level = 3
index_generator.set_parameters( num_dims, max_level,
index_norm_order = 1,
priority_weight = 1. )
index_generator.build_isotropic_index_set()
indices = index_generator.get_all_indices()
true_indices = [[0, 0],
[1, 0],
[2, 0],
[0, 1],
[1, 1],
[0, 2],
[1, 2],
[2, 1],
[3, 0],
[0, 3]]
indices_list = []
for i, index in enumerate( indices ):
indices_list.append( index.uncompressed_data( num_dims ) )
indices = unique_matrix_rows( numpy.array( indices_list ))
true_indices = unique_matrix_rows( numpy.array( true_indices ) )
assert numpy.allclose( true_indices, indices )
# num_dims = 3, max_level = 2 index_norm_order = 1
num_dims = 3
max_level = 2
index_generator.set_parameters( num_dims, max_level,
index_norm_order = 1,
priority_weight = 1. )
index_generator.build_isotropic_index_set()
indices = index_generator.get_all_indices()
true_indices = [[0, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[2, 0, 0],
[1, 1, 0],
[0, 2, 0],
[1, 0, 1],
[0, 1, 1],
[0, 0, 2]]
indices_list = []
for i, index in enumerate( indices ):
indices_list.append( index.uncompressed_data( num_dims ) )
indices = unique_matrix_rows( numpy.array( indices_list ))
true_indices = unique_matrix_rows( numpy.array( true_indices ) )
assert numpy.allclose( true_indices, indices )
# num_dims = 2, max_level = 3 index_norm_order = 0.5
num_dims = 2
max_level = 3
index_generator = IndexGenerator()
index_generator.set_parameters( num_dims, max_level,
index_norm_order = 0.5,
priority_weight = 1. )
index_generator.build_isotropic_index_set()
indices = index_generator.get_all_indices()
true_indices = [[0, 0],
[1, 0],
[2, 0],
[3, 0],
[0, 1],
[0, 2],
[0, 3]]
indices_list = []
for i, index in enumerate( indices ):
indices_list.append( index.uncompressed_data( num_dims ) )
indices = unique_matrix_rows( numpy.array( indices_list ) )
true_indices = unique_matrix_rows( numpy.array( true_indices ) )
assert numpy.allclose( true_indices, indices )
# num_dims = 2, max_level = 6 index_norm_order = 0.5
num_dims = 2
max_level = 6
index_generator = IndexGenerator()
index_generator.set_parameters( num_dims, max_level,
index_norm_order = 0.5,
priority_weight = 1. )
index_generator.build_isotropic_index_set()
indices = index_generator.get_all_indices()
true_indices = [[0, 0],
[1, 0],
[2, 0],
[3, 0],
[4, 0],
[5, 0],
[6, 0],
[1, 1],
[2, 1],
[1, 2],
[0, 1],
[0, 2],
[0, 3],
[0, 4],
[0, 5],
[0, 6]]
indices_list = []
for i, index in enumerate( indices ):
indices_list.append( index.uncompressed_data( num_dims ) )
indices = unique_matrix_rows( numpy.array( indices_list ) )
true_indices = unique_matrix_rows( numpy.array( true_indices ) )
assert numpy.allclose( true_indices, indices )
from utilities.indexing import PolynomialIndex, IndexGenerator
# num_dims = 2, max_level = 6 index_norm_order = 0.5
num_dims = 10
max_level = 30
index_generator = IndexGenerator()
index_generator.set_parameters( num_dims, max_level, index_norm_order = 0.5,
priority_weight = 1. )
index_generator.build_isotropic_index_set()
indices = index_generator.get_all_indices()
print index_generator.num_indices
def pce_study( build_pts, build_vals, domain,
test_pts, test_vals,
results_file = None,
cv_file = None, solver_type = 2 ):
num_dims = build_pts.shape[0]
index_generator = IndexGenerator()
poly_1d = [ LegendrePolynomial1D() ]
basis = TensorProductBasis( num_dims, poly_1d )
pce = PCE( num_dims, order = 0, basis = basis, func_domain = domain )
if ( solver_type == 1 ):
num_folds = build_pts.shape[1]
else:
num_folds = 20
index_norm_orders = numpy.linspace( 0.4, 1.0, 4 )
#solvers = numpy.array( [solver_type], numpy.int32 )
#cv_params_grid_array = cartesian_product( [solvers,orders] )
cv_params_grid = []
for index_norm_order in index_norm_orders:
level = 2
# determine what range of orders to consider.
# spefically consider any order that results in a pce with terms <= 3003
while ( True ):
index_generator.set_parameters( num_dims, level,
index_norm_order = index_norm_order )
index_generator.build_isotropic_index_set()
print level, index_norm_order, index_generator.num_indices
if ( index_generator.num_indices > 3003 ):
break
cv_params = {}
cv_params['solver'] = solver_type
cv_params['order'] = level
cv_params['index_norm_order'] = index_norm_order
if ( cv_params['solver'] > 1 or
index_generator.num_indices <= build_pts.shape[1] ):
# only do least squares on over-determined systems
cv_params_grid.append( cv_params )
else:
break
level += 1
print cv_params_grid
# cv_iterator = LeaveOneOutCrossValidationIterator()
cv_iterator = KFoldCrossValidationIterator( num_folds = num_folds )
CV = GridSearchCrossValidation( cv_iterator, pce,
use_predictor_cross_validation = True,
use_fast_predictor_cross_validation = True )
t0 = time.time()
CV.run( build_pts, build_vals, cv_params_grid )
time_taken = time.time() - t0
print 'cross validation took ', time_taken, ' seconds'
print "################"
print "Best cv params: ", CV.best_cv_params
print "Best cv score: ", CV.best_score
print "################"
#for i in xrange( len( CV.cv_params_set ) ):
# print CV.cv_params_set[i], CV.scores[i]
best_order = CV.best_cv_params['order']
best_index_norm_order = CV.best_cv_params['index_norm_order']
best_pce = PCE( num_dims,
order = best_order,
basis = basis,
func_domain = domain,
index_norm_order = best_index_norm_order)
V = best_pce.vandermonde( build_pts ).T
best_pce.set_solver( CV.best_cv_params['solver'] )
if cv_params['solver'] > 1 :
best_res_tol = CV.best_cv_params['norm_residual']
best_pce.linear_solver.residual_tolerance = best_res_tol
sols, sol_metrics = best_pce.linear_solver.solve( V, build_vals )
coeff = sols[:,-1]
best_pce.set_coefficients( coeff )
error = abs( build_vals - best_pce.evaluate_set( build_pts ) )
print max( error )
print 'Evaluating best pce at test points'
num_test_pts = test_pts.shape[1]
pce_vals_pred = best_pce.evaluate_set( test_pts ).T
print test_vals.shape, pce_vals_pred.shape
error = test_vals.squeeze() - pce_vals_pred
linf_error = numpy.max( numpy.absolute( error ) )
l2_error = numpy.sqrt( numpy.dot( error.T, error ) / num_test_pts )
mean = numpy.mean( pce_vals_pred )
var = numpy.var( pce_vals_pred )
pce_mean = best_pce.mean()
pce_var = best_pce.variance()
if results_file is not None:
results_file.write( '%1.15e' %linf_error + ',' + '%1.15e' %l2_error +
',' + '%1.15e' %mean + ',' + '%1.15e' %var +
',%1.15e' %pce_mean + ',' + '%1.15e' %pce_var + '\n')
print "linf error: ", linf_error
print "l2 error: ", l2_error
print "mean: ", mean
print "var: ", var
print "pce mean: ", pce_mean
print "pce var: ", pce_var
me, te, ie = best_pce.get_sensitivities()
interaction_values, interaction_terms = best_pce.get_interactions()
show = False
fignum = 1
filename = 'oscillator-individual-interactions.png'
plot_interaction_values( interaction_values, interaction_terms, title = 'Sobol indices', truncation_pct = 0.95, filename = filename, show = show,
fignum = fignum )
fignum += 1
filename = 'oscillator-dimension-interactions.png'
plot_interaction_effects( ie, title = 'Dimension-wise joint effects', truncation_pct = 0.95, filename = filename, show = show,fignum = fignum )
fignum += 1
filename = 'oscillator-main-effects.png'
plot_main_effects( me, truncation_pct = 0.95, title = 'Main effect sensitivity indices', filename = filename, show = show, fignum = fignum )
fignum += 1
filename = 'oscillator-total-effects.png'
plot_total_effects( te, truncation_pct = 0.95, title = 'Total effect sensitivity indices', filename = filename, show = show, fignum = fignum )
fignum += 1
from scipy.stats.kde import gaussian_kde
pylab.figure( fignum )
pce_kde = gaussian_kde( pce_vals_pred )
pce_kde_x = numpy.linspace( pce_vals_pred.min(), pce_vals_pred.max(), 100 )
pce_kde_y = pce_kde( pce_kde_x )
pylab.plot( pce_kde_x, pce_kde_y,label = 'pdf of surrogate' )
true_kde = gaussian_kde( test_vals )
true_kde_x = numpy.linspace( test_vals.min(), test_vals.max(), 100 )
true_kde_y = true_kde( true_kde_x )
pylab.plot( true_kde_x, true_kde_y, label = 'true pdf' )
pylab.legend(loc=2)
pylab.show()
