-is SrSSKrSSKrSSKrSSKrSSKrSSKJr SSK J r SSK J r SSK JrJrJrJr SSK Jr SSKJr SS KJrJrJrJr S r\R8"/S Q5R:r\R8"/S Q5R:r\"\5RA5r!\"S SS9r"\"S S9\"\"S SS9\"S S5\"S SS9-\"S S5\"S SS9-\"SS5-\"SS5\"S SS9-\"SS5-/r#\#Vs/sH o\":wdM UPM snr$\RJRMS\#5S5r'Sr(\RJRMS\$5S5r)\RJRMS\#5S5r*\RJRMS\#5S5r+\RJRMS\$5S5r,\RJRMS\$5S5r-\RJRMS\#5S5r.\RJRMS\#5S5r/\RJRMS\#5S 5r0S!r1\RJRMS\#5\RJRMS"\!\Rd"\RfS\RhS#9/5S$55r5S%r6S&r7\RJRMS\#5S'5r8S(r9S)r:\RJRMS\$5S*5r;S+r<\RJRMS\#5S,5r=S-r>S.r?S/r@\RJRMS\#5S05rAS1rB\RJRMS2S3\R"S450\DS54\"\R*\R4S69S7S8.\DS94/5S:5rFS;rGS<rH\RJRMS=S>S?/5\RJRMS@/SAQ5SB55rI\RJRMS=S>S?/5\RJRMS@/SAQ5SC55rJ\RJRMS@/SDQ5\RJRMSESFSG/5SH55rK\RJRMS@/SDQ5SI5rLSJrM"SKSL\5rNSMrOgs snf)Nz'Testing for Gaussian process regressionN) approx_fprime)ConvergenceWarning)GaussianProcessRegressor)RBF DotProductExpSineSquared WhiteKernel)ConstantKernel) MiniSeqKernel)assert_allcloseassert_almost_equalassert_array_almost_equalassert_array_lessc4U[R"U5-$)N)npsin)xs Z/var/www/html/venv/lib/python3.13/site-packages/sklearn/gaussian_process/tests/test_gpr.pyfr"s rvvay=)?g@g@g@g@g @)@g@g@g@g@rfixed length_scalelength_scale_boundsr)MbP?@@{Gz?Y@h㈵>)r#r"皙?kernelc&[RS::a[R"S5 [ US9R [ [5nUR[ SS9up#[U[5 [[R"U5S5 g)N#This test may fail on 32 bit Pythonr%T return_cov) sysmaxsizepytestxfailrfitXypredictr rdiag)r%gpry_predy_covs rtest_gpr_interpolationr98sd {{e :; #& 1 5 5a ;CKKdK3MF",rc [SS9n/SQn[R"/SQ5n[US9R X5nUR USS9upE[ U"USS9S R5S [R"[U55- R55 [ XB5 [ [R"U5S 5 g) Nr)baseline_similarity_bounds)ABC)r)Tr* eval_gradientr?r,) r rarrayrr1r4r raveleyelenr5)r%r2r3r6r7r8s r!test_gpr_interpolation_structuredrHEs g >FA A "& 1 5 5a ;CKKdK3MFq%a(..01rvvc!f~3E2L2L2N",rc"[RS::a[R"S5 [ US9R [ [5nURURR5URUR5:deg)Nr'r(r)) r-r.r/r0rr1r2r3log_marginal_likelihoodkernel_thetar%r6s rtest_lml_improvingrNTso {{e :; #& 1 5 5a ;C  & &s{{'8'8 9C  rc*[US9R[[5n[R "UR RR[RS9nURUSS9 [UR RUS5 g)Nr)dtypeF) clone_kernel) rr1r2r3ronesrKrLshapefloat64rJr )r%r6 input_thetas rtest_lml_without_cloning_kernelr[ish #& 1 5 5a ;C''#++++11DK %@ ));:rc[US9R[[5nUR UR R S5up#[R"[R"U5S:UR R UR RSS2S4:H-UR R UR RSS2S4:H-5(deg)Nr)T-C6?rr?) rr1r2r3rJrKrLrallabsbounds)r%r6lml lml_gradients rtest_converged_to_local_maximumrcss #& 1 5 5a ;C33CKK4E4EtLC 66   $ ;;   2 21a4 8 8 : ;;   2 21a4 8 8 :   rc[US9R[[5nURR n[ R"URRR5RnSnX2[ R"USS2S45)S4'[USS2S4URRU-5 [URRUSS2S4U-5 g)Nr)绽|=r?r) rr1r2r3rKr`rfinforLrTmaxisfiniter)r%r6r`max_tinys rtest_solution_inside_boundsrks #& 1 5 5a ;C [[  F 88CKK%%++ , 0 0D D,0BKKq!t % %q ()fQTlCKK$5$5$<=ckk''1)<=rc^[US9R[[5mTR UR S5up[ UR U4SjS5n[X#S5 g)Nr)Tc(>TRUS5$)NF)rJ)rLr6s r#test_lml_gradient..sC$?$?u$MrrerA)rr1r2r3rJrLrr )r%rarblml_gradient_approxr6s @rtest_lml_gradientrqsX #& 1 5 5a ;C33FLL$GC' Mu 1=rcj[US9nUR[SS9up#[USS5 [ UR R 5S:aC[[R"U5[R"UR S5S5 g[[R"U5SS5 g)Nr)Tr*rr?) rr4r2r rGr%rLrr5exp)r%r6y_meanr8s r test_priorrvs~ #& 1CKKdK3MF1% 3::  q BGGENBFF6<<?,CQGBGGENAq1rc[US9R[[5nUR [ SS9up#UR [ S5n[U[R"US5S5 [[R"U5[R"U5R5- [R"US5[R"U5R5- S5 g)Nr)Tr*ir?) rr1r2r3r4X2sample_yr rmeanr5rgvar)r%r6rur8sampless rtest_sample_statisticsr}s #& 1 5 5a ;CKKtK4MFll2v&G 3Q7 ++-- wRWWU^//11 rc[S5n[USS9R[[5n[ R "URR5S:Xdeg)Nrr% optimizer) rrr1r2r3rrtrKrLrMs rtest_no_optimizerrsE XF "&D A E Ea KC 66#++## $ ++ +rtargetrScZ[RS::a[R"S5 [ US9R [ [5nUR[SS9up4UR[SS9up5[[R"[R"U55U5 g)Nr'r(r)Tr* return_std)r-r.r/r0rr1r2r3r4rxr rsqrtr5)r%rr6rur8y_stds rtest_predict_cov_vs_stdrsy {{e :; #& 1 5 5a ;CKKtK4MFKKtK4MF/7rc[RRS5nURSSS5nUSS2S4SUSS2S4--n[ SS/5n[ US9R X5n[R"URRS5[R"URRS5S-:deg) Nrr?)2r@r$rr)rs) rrandom RandomStateuniformrrr1rtrKrL)rngr2r3r%r6s rtest_anisotropic_kernelrs ))   "C B7#A !Q$#!Q$-A #s_F "& 1 5 5a ;C 66#++##A& '"&&1B1B11E*F*J JJ JrcSup[RRS5nURX5S-S- n[R"U5R SS9[R"SU-5R SS9-UR SUS9-n[S S 5[S /U-S /U-S 9-[S SS9-n[R*n[S5Hzn[UUSS9RX45nURURR 5n X[R""[R$5R&- :deU nM| g)N)r@rr@r?axisrAr$)scalesizerr )r]r"rr#)r#$@) noise_levelnoise_level_boundsrs)r%n_restarts_optimizer random_state)rrrrandnrsumnormalr>rr infrangerr1rJrKrLrffloat32eps) n_samples n_featuresrr2r3r%last_lmlrgpras rtest_random_startsrsI"I ))   "C )(1,q0A q 1  &&Q-    # $ **3Y* / 0 sK 3UZ'k]Z=W$EFFwH %a %!5  #a) (()9)9: 4 8 88888!)rc [R"[5n[R"[5n[U- U- n[ US9nUR [ U5 [ USS9nUR [ [5 UR[SS9upgXb-U-nXr-nUR[SS9up[Xh5 [Xy5 UR[SS9upXS--n UR[SS9up[X5 g)a Test normalization of the target values in GP Fitting non-normalizing GP on normalized y and fitting normalizing GP on unnormalized y should yield identical results. Note that, here, 'normalized y' refers to y that has been made zero mean and unit variance. r)Tr% normalize_yrr*r@N) rrzr3stdrr1r2r4rxr ) r%rury_normr6gpr_normr7 y_pred_std y_pred_normy_pred_std_norm_r8 y_cov_norms rtest_y_normalizationrsWWQZF FF1IE&jE !F #& 1CGGAv(v4HH LLARD9F ^f $F#J#+#3#3B4#3#H K, 4{{2${/HA 1H E$$RD$9MA*rc,S[-nSS0n[S0UD6n[USS9nUR[U5 UR [ SS9upE[R"/SQ5n[R"/SQ5n[XFS S S 9 [XWS S S 9 g )aR Here we test that, when noramlize_y=True, our GP can produce a sensible fit to training data whose variance is significantly larger than unity. This test was made in response to issue #15612. GP predictions are verified against predictions that were made using GPy which, here, is treated as the 'gold standard'. Note that we only investigate the RBF kernel here, as that is what was used in the GPy implementation. The following code can be used to recreate the GPy data: -------------------------------------------------------------------------- import GPy kernel_gpy = GPy.kern.RBF(input_dim=1, lengthscale=1.) gpy = GPy.models.GPRegression(X, np.vstack(y_large), kernel_gpy) gpy.optimize() y_pred_gpy, y_var_gpy = gpy.predict(X2) y_pred_std_gpy = np.sqrt(y_var_gpy) -------------------------------------------------------------------------- rrTrr)gy(V.@gV],;g6}~CgHW -@gƠKQ@)g ؼG'@gsr@g{u>5?g ?g.[ ?gQ?r)rtolatolg333333?N) r3rrr1r2r4rxrrDr )y_large RBF_paramsr%r6r7r y_pred_gpyy_pred_std_gpys rtest_large_variance_yr"s21fG!#&J  : F "&d CCGGAwRD9FKJ XXDNFT: JTBrc[R"[[S-45Rn[ SS9n[ USSS9nUR [[5 [ USSS9nUR [U5 UR[SS9upEUR[SS9upgUR[SS9upUR[SS9up[XFSS2S 45 [XFSS2S 4S- 5 [URS 5H#n [XWS U 45 [XS U 45 M% UR[S S 9n UR[S S 9n U RS:XdeU RS:Xde[XSS2S SS245 [Hn[ USS9nUR [[5 [ USS9nUR [[R"[[45R5 [URR URR S5 M g)Nr@rrF)r%rrTrr*rr?.rr)rsr)rsr@rr)rvstackr3Trrr1r2r4rxr rrXrykernelsrKrL)y_2dr%r6gpr_2d y_pred_1dy_std_1d y_pred_2dy_std_2dry_cov_1dy_cov_2dr y_sample_1d y_sample_2ds rtest_y_multioutputrYs 99aQZ " "Dc "F "&De TCGGAqM %VtQV WF JJq$++bT+:I ...=I++bT+2KA...5KA QT?3 QT?Q#67 1 &HsF{&;<HsF{&;<',,rR,0K//"/3K    '' '    ** * Aq%9:&f$G 1 )TJ 1biiA'))*CKK--v~~/C/CQGrcSn[XS9nUR[[5 UR UR R 5UR URR 5:deg)Nc V[RRS5nUU"USS9pT[S5Hqn[R"UR [R "SUSS2S45[R"SUSS2S4555nU"USS9nX:dMoXxpTMs XE4$)NrFrBrr?)rrrr atleast_1drmaximumminimum) obj_func initial_thetar`r theta_optfunc_minrrLrs rr(test_custom_optimizer..optimizersii##A&  ]% 8rAMM BJJr6!Q$<8"**QqRSt :UVEe4A|&+8 ""rr)rr1r2r3rJrKrLr%)r%rr6s rtest_custom_optimizerrsa # #& FCGGAqM  & &s{{'8'8 9C$>vRV$>$W!N 5 3rc0[SSS9[SSS9-n[5nUR[SS9up#UR[SS9up$[US9nUR[SS9up&UR[SS9up'[ X65 [ XG5 g) Nrr)constant_value_boundsrTrr*r))r>rrr4r2r)default_kernelgpr1ry_std1y_cov1gpr2y_std2y_cov2s rtest_no_fit_default_predictrss':S >N $ %D Q4 0IA Q4 0IA #> :D Q4 0IA Q4 0IAf-f-rcZ[SS/S9n[US9nSn[R"[US9 UR [ [5 SSS5 [SS/S9[SS /S9-n[US9n[R"S S 9n[R"S 5 UR [ [5 [U5S :Xde[USR[5(deUSRR SS:Xde[USR[5(deUSRR SS:XdeSSS5 ["R$"[ S 5n[SS/SS/S9n[US9n[R"S S 9n[R"S 5 UR U[5 [U5S :Xde[USR[5(deUSRR SS:Xde[USR[5(deUSRR SS:XdeSSS5 g!,(df  GN4=f!,(df  GN;=f!,(df  g=f)Nr#rrr)zThe optimal value found for dimension 0 of parameter length_scale is close to the specified upper bound 0.001. Increasing the bound and calling fit again may find a better value.rrrgj@T)recordalwaysr@rzThe optimal value found for dimension 0 of parameter k1__noise_level is close to the specified upper bound 0.001. Increasing the bound and calling fit again may find a better value.r?zThe optimal value found for dimension 0 of parameter k2__length_scale is close to the specified lower bound 1000.0. Decreasing the bound and calling fit again may find a better value.rrrr"rzThe optimal value found for dimension 0 of parameter length_scale is close to the specified lower bound 10.0. Decreasing the bound and calling fit again may find a better value.zThe optimal value found for dimension 1 of parameter length_scale is close to the specified lower bound 10.0. Decreasing the bound and calling fit again may find a better value.)rrr/warnsrr1r2r3r warningscatch_warnings simplefilterrG issubclasscategoryrargsrtile) r%r6warning_message kernel_sumgpr_sumrX_tile kernel_dimsgpr_dimss rtest_warning_boundsrsy dD\ 2F "& 1C  ( @ 1  At = #JAJ'j9G   -h' Aq6{a&),,.@AAAA 1I   " "1 %*1 1  1&),,.@AAAA 1I   " "1 %*1 1  1% .4WWQ]FC:C:NK'{;H   -h' VQ6{a&),,.@AAAA 1I   " "1 %*1 1  1&),,.@AAAA 1I   " "1 %*1 1  1% . -K A @ . -< . -s%I8CJ $C J8 J J J*c|S[SS9-n[SSSS9nX-n[US9R[[ 5 g)Ng@gI@rrr)r periodicityperiodicity_boundsr))rrrr1r2r3)k1k2r%s r%test_bound_check_fixed_hyperparameterr!sB 3D) )B cg BWFF+//15rcd[R"[RS[RS9n[ USS9nUR [U5 UR[R"S5:XdeUR[SS9up4[X15 [[R"U5SSS 9 [RSS pe[RRS5n[R"UR!US 4S 9[R""US 4S S 9/S S9nUR [U5 UR[SS9up[U SS2S 4S 5 [[R"U S5SSS 9 U RXV4:XdeU RXUU4:Xdeg)zCheck that the std. dev. is affected to 1 when normalizing a constant feature. Non-regression test for: https://github.com/scikit-learn/scikit-learn/issues/18318 NaN where affected to the target when scaling due to null std. dev. with constant target. rrSTrrr*r,g& .>)rr@r?)r)rX fill_valuerN).r?)rrWr2rXrYrr1 _y_train_stdr/rPr4r r5rr concatenaterfull) r% y_constantr6r7r8r n_targetsrr3Y_predY_covs rtest_constant_targetr&-sb2::6J "&d CCGGAz   v}}S1 11 1KKdK3MFF'BGGENCd3771:qy ))   "C  JJYNJ + GG9a.Q 7   AGGAqMKKdK3MFF1a4L!$BGGE&M*Cd; <rr rrrDr1r4r rdiagonal) r%r6X_trainy_trainrpred1rpred2covs r2test_gpr_consistency_std_cov_non_invertible_kernelr.VsE}m ,s  & 0%&F #&T JChh #J  % #  +   $ * %   Ghh     O     O   GGGG XX + &  % * %  $  FV5JEV5JECS!12>rzparams, TypeError, err_msgrrzCalpha must be a scalar or an array with same number of entries as yrr@)r%rz#requires that all bounds are finitec[S0UD6n[R"XS9 UR[[ 5 SSS5 g!,(df  g=f)z0Check that expected error are raised during fit.rNr)rr/rr1r2r3)params TypeErrorerr_msgr6s rtest_gpr_fit_errorr3s6( # ,V ,C y 0 1  1 0 0s A Ac[[5S9R[[5nSn[ R "[US9 URSS9 SSS5 g!,(df  g=f)z7Check that we raise the proper error in the LML method.r)z.Gradient can only be evaluated for theta!=NonerTrBN) rrr1r2r3r/r ValueErrorrJr6r2s rtest_gpr_lml_errorr7sK "#% 0 4 4Q :C>G z 1 ##$#7 2 1 1s A A,c[[5S9R[[5nSn[ R "[US9 UR[SSS9 SSS5 g!,(df  g=f)z4Check that we raise the proper error during predict.r)z9At most one of return_std or return_cov can be requested.rT)r+rN) rrr1r2r3r/r RuntimeErrorr4r6s rtest_gpr_predict_errorr:sL "#% 0 4 4Q :CIG |7 3 A$4 8 4 3 3s A$$ A2rTFr#)Nr?rc[RRS5nSup4nU4nUbXa4-nU4nUb US:aXq4-nURXC5nURXS5n UR"U6n [ US9n U R X5 U R U SS9upU R U SS9upU RU:XdeU RU:XdeURU4U-:Xdeg) aCheck the shapes of y_mean, y_std, and y_cov in single-output (n_targets=None) and multi-output settings, including the edge case when n_targets=1, where the sklearn convention is to squeeze the predictions. Non-regression test for: https://github.com/scikit-learn/scikit-learn/issues/17394 https://github.com/scikit-learn/scikit-learn/issues/18065 https://github.com/scikit-learn/scikit-learn/issues/22174 )r rVNr?rTrr*)rrrrrr1r4rX)rr#rrn_samples_trainn_samples_test y_train_shape y_test_shaper)rr*modelr7rrr8s rtest_predict_shapesrDs ))   %C29/J$&M% 4 #$LQ#l2 ii4G YY~ 2Fii'G $ =E IIgMM&TM:MF}}V}5HA <<< '' ' ;;, && & ;;>+l: :: :rcb[RRS5nSup4SnSnU4nUbXq4-nUb US:aXQU4nOXV4nURXC5n URXS5n UR"U6n [ US9n U R X5 U R XS9n U RU:Xdeg) aCheck the shapes of y_samples in single-output (n_targets=0) and multi-output settings, including the edge case when n_targets=1, where the sklearn convention is to squeeze the predictions. Non-regression test for: https://github.com/scikit-learn/scikit-learn/issues/22175 r<)rr=rVrsNr?r>r)rrrrrr1ryrX)rr#rrr?n_samples_X_testn_samples_y_testrArBr)rr*rC y_sampless rtest_sample_y_shapesrIs ))   %C"&J$&M% 4 Q(5EF (; ii4G YY' 4Fii'G $ =E IIgvBI ??l ** *r)Nr?r@rArr?rsc:[RRS5nURSS5nURSUbUOS5n[ US9nUR X1S9R nURX45 UR X1S9R nXg:Xdeg)zJCheck the output shape of `sample_y` is consistent before and after `fit`.rrANr?r#r)rrrrrryrXr1)r#rrr2r3rCshape_before_fitshape_after_fits rtest_sample_y_shape_with_priorrOs ))   %C "aA "9#8ia@A $y 9E~~a~=CC IIaOnnQn<BBO  .. .rc[RRS5nSnURUS5nURX bUOS5n[ US9nUR USS9upgUR USS 9upUR X45 UR USS9upUR USS 9upURU R:XdeURU R:XdeU RU R:Xdeg) zIAFA $y 9E!MM!M=J==t=4LA IIaO--d-;I--d-3KA   y .. . ??hnn ,, , ??hnn ,, ,rc$[RRS5nURSS5nURSS5n[ SS9n[ R "[SS9 URX5 S S S 5 g !,(df  g =f) zeCheck that an error is raised when the number of targets seen at fit is inconsistent with n_targets. rrrAr@r?rLz!The number of targets seen in `y`rN) rrrrrr/rr5r1)rr2r3rCs rtest_n_targets_errorrZ,si ))   "C "aA "aA $q 1E z)L M ! N M Ms &B Bc\rSrSrSrSrSrg) CustomKerneli9z A custom kernel that has a diag method that returns the first column of the input matrix X. This is a helper for the test to check that the input matrix X is not mutated. cUSS2S4$)Nrr)selfr2s rr5CustomKernel.diag@sAwrrN)__name__ __module__ __qualname____firstlineno____doc__r5__static_attributes__rrrr\r\9s  rr\c[[5S9R[[5n[ R "[5nUR[SS9u n[[U5 g)z Check that the input X is not modified by the predict method of the GaussianProcessRegressor when setting return_std=True. Non-regression test for: https://github.com/scikit-learn/scikit-learn/issues/24340 r)TrN) rr\r1r2r3rcopyrxr4r )r6X2_copyrs r#test_gpr_predict_input_not_modifiedriDsJ #,. 9 = =a CCggbkG ;;rd; +DAqB r)Prdrr-r numpyrr/scipy.optimizersklearn.exceptionsrsklearn.gaussian_processr sklearn.gaussian_process.kernelsrrrr r r>4sklearn.gaussian_process.tests._mini_sequence_kernelr sklearn.utils._testingr r rrr atleast_2drr2rxrEr3 fixed_kernelrnon_fixed_kernelsmark parametrizer9rHrNrQr[rcrkrqrvr}rrWrXrYrrrrrrrrrrrrr&r.zerosr5rr3r7r:rDrIrOrXrZr\rir)s0rrws0-   (1= OMM0133]],-//aDJJLA SSk:c;#3KPPc;#3KPPkc;#3KPPk +2L'|5KV'L7+ -, - -#4567+,7+;,;#45 6 #45 >6 >7+ >, >7+ 2, 27+,",7+Arwwqwwqz'L#MN8O,8 K67+$+,$+N4Cn+H\#4564 7+4,4*."F R 67+%<,% R>