-iABSrSSKrSSKJr SSKJr Sr"SS5rg) zA Loss functions for linear models with raw_prediction = X @ coef N)sparse) squared_normcURSn[R"U5(a6UR[R"US4X"4S9-U-R 5$USS2S4U-nURU-$)z/Compute the sandwich product X.T @ diag(W) @ X.rshapeN)rrissparseT dia_matrixtoarray)XW n_samplesWXs T/var/www/html/venv/lib/python3.13/site-packages/sklearn/linear_model/_linear_loss.py sandwich_dotrsq I q CC&##QF92HI IA M ')  q$wZ!^ssRxc\rSrSrSrSrSSjrSrSrSr SS jr SS jr SS jr SS jr SS jrSrg)LinearModelLoss%aJGeneral class for loss functions with raw_prediction = X @ coef + intercept. Note that raw_prediction is also known as linear predictor. The loss is the average of per sample losses and includes a term for L2 regularization:: loss = 1 / s_sum * sum_i s_i loss(y_i, X_i @ coef + intercept) + 1/2 * l2_reg_strength * ||coef||_2^2 with sample weights s_i=1 if sample_weight=None and s_sum=sum_i s_i. Gradient and hessian, for simplicity without intercept, are:: gradient = 1 / s_sum * X.T @ loss.gradient + l2_reg_strength * coef hessian = 1 / s_sum * X.T @ diag(loss.hessian) @ X + l2_reg_strength * identity Conventions: if fit_intercept: n_dof = n_features + 1 else: n_dof = n_features if base_loss.is_multiclass: coef.shape = (n_classes, n_dof) or ravelled (n_classes * n_dof,) else: coef.shape = (n_dof,) The intercept term is at the end of the coef array: if base_loss.is_multiclass: if coef.shape (n_classes, n_dof): intercept = coef[:, -1] if coef.shape (n_classes * n_dof,) intercept = coef[n_features::n_dof] = coef[(n_dof-1)::n_dof] intercept.shape = (n_classes,) else: intercept = coef[-1] Shape of gradient follows shape of coef. gradient.shape = coef.shape But hessian (to make our lives simpler) are always 2-d: if base_loss.is_multiclass: hessian.shape = (n_classes * n_dof, n_classes * n_dof) else: hessian.shape = (n_dof, n_dof) Note: If coef has shape (n_classes * n_dof,), the 2d-array can be reconstructed as coef.reshape((n_classes, -1), order="F") The option order="F" makes coef[:, i] contiguous. This, in turn, makes the coefficients without intercept, coef[:, :-1], contiguous and speeds up matrix-vector computations. Note: If the average loss per sample is wanted instead of the sum of the loss per sample, one can simply use a rescaled sample_weight such that sum(sample_weight) = 1. Parameters ---------- base_loss : instance of class BaseLoss from sklearn._loss. fit_intercept : bool cXlX lgN base_loss fit_intercept)selfrrs r__init__LinearModelLoss.__init__hs "*rNcURSnURRnUR(aUS-nOUnURR(a[ R "XU4USS9nU$[ R "XUS9nU$)aAllocate coef of correct shape with zeros. Parameters: ----------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. dtype : data-type, default=None Overrides the data type of coef. With dtype=None, coef will have the same dtype as X. Returns ------- coef : ndarray of shape (n_dof,) or (n_classes, n_dof) Coefficients of a linear model. F)rdtypeorder)rr")rr n_classesr is_multiclassnp zeros_like)rr r" n_featuresr$n_dofcoefs rinit_zero_coefLinearModelLoss.init_zero_coeflsz WWQZ NN,,   NEE >> ' '==e*11rcPURS:XaX-O [U5nSU-U-$)z5Compute L2 penalty term l2_reg_strength/2 *||w||_2^2.r g?)r1r)rr4l2_reg_strengthnorm2_ws r l2_penaltyLinearModelLoss.l2_penaltys,'.||q'8'#l7>S_$w..rcUcURX5upnOURU5upURRUUSUS9n [R "XS9n XR X5-$)aGCompute the loss as weighted average over point-wise losses. Parameters ---------- coef : ndarray of shape (n_dof,), (n_classes, n_dof) or (n_classes * n_dof,) Coefficients of a linear model. If shape (n_classes * n_dof,), the classes of one feature are contiguous, i.e. one reconstructs the 2d-array via coef.reshape((n_classes, -1), order="F"). X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. y : contiguous array of shape (n_samples,) Observed, true target values. sample_weight : None or contiguous array of shape (n_samples,), default=None Sample weights. l2_reg_strength : float, default=0.0 L2 regularization strength n_threads : int, default=1 Number of OpenMP threads to use. raw_prediction : C-contiguous array of shape (n_samples,) or array of shape (n_samples, n_classes) Raw prediction values (in link space). If provided, these are used. If None, then raw_prediction = X @ coef + intercept is calculated. Returns ------- loss : float Weighted average of losses per sample, plus penalty. Ny_truer8 sample_weight n_threadsr4)r9r5rlossr&averager>) rr*r yrCr<rDr8r4r3rFs rrFLinearModelLoss.lossszN  !151J1J41S .G!%!6!6t!< G~~"") #  zz$6oog???rcURURRsupn U [UR5-n UcUR X5upnOUR U5upURRUUUUS9upUcUO[R"U5nUR5U- nXRX5- nUU-nURR(d][R"XRS9nURU-X\--USU &UR(aUR5US'UU4$[R"X4U RSS9nURU-X\--USS2SU 24'UR(aURSS9USS2S4'UR S :XaUR#SS 9nUU4$) aComputes the sum of loss and gradient w.r.t. coef. Parameters ---------- coef : ndarray of shape (n_dof,), (n_classes, n_dof) or (n_classes * n_dof,) Coefficients of a linear model. If shape (n_classes * n_dof,), the classes of one feature are contiguous, i.e. one reconstructs the 2d-array via coef.reshape((n_classes, -1), order="F"). X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. y : contiguous array of shape (n_samples,) Observed, true target values. sample_weight : None or contiguous array of shape (n_samples,), default=None Sample weights. l2_reg_strength : float, default=0.0 L2 regularization strength n_threads : int, default=1 Number of OpenMP threads to use. raw_prediction : C-contiguous array of shape (n_samples,) or array of shape (n_samples, n_classes) Raw prediction values (in link space). If provided, these are used. If None, then raw_prediction = X @ coef + intercept is calculated. Returns ------- loss : float Weighted average of losses per sample, plus penalty. gradient : ndarray of shape coef.shape The gradient of the loss. NrAr"r.r!r"r#raxisr r0)rrr$intrr9r5 loss_gradientr&sumr>r% empty_liker"r emptyr1ravel)rr*r rHrCr<rDr8rr(r$r)r4r3rFgrad_pointwisesw_sumgrads rrPLinearModelLoss.loss_gradient sT./WWdnn6N6N*S!3!344  !151J1J41S .G!%!6!6t!< G#~~;;)' <  ,3 9NxxzF" 99& ~~++==]];D !n 47P PD* !!)--/RTz88Y.gmm3OD#1#3#3a#7/:S#SDKZK !!,00a08QU yyA~zzz,Tzrc@URURRsupn U [UR5-n UcUR X5upnOUR U5upURRUUUUS9nUcUO[R"U5nX-nURR(d[[R"XRS9nURU-X\--USU &UR(aUR5US'U$[R"X4U RSS9nURU-X\--USS2SU 24'UR(aURSS9USS2S4'URS :XaUR!SS 9$U$) a-Computes the gradient w.r.t. coef. Parameters ---------- coef : ndarray of shape (n_dof,), (n_classes, n_dof) or (n_classes * n_dof,) Coefficients of a linear model. If shape (n_classes * n_dof,), the classes of one feature are contiguous, i.e. one reconstructs the 2d-array via coef.reshape((n_classes, -1), order="F"). X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. y : contiguous array of shape (n_samples,) Observed, true target values. sample_weight : None or contiguous array of shape (n_samples,), default=None Sample weights. l2_reg_strength : float, default=0.0 L2 regularization strength n_threads : int, default=1 Number of OpenMP threads to use. raw_prediction : C-contiguous array of shape (n_samples,) or array of shape (n_samples, n_classes) Raw prediction values (in link space). If provided, these are used. If None, then raw_prediction = X @ coef + intercept is calculated. Returns ------- gradient : ndarray of shape coef.shape The gradient of the loss. NrArKr.r!rLrrMr r0)rrr$rOrr9r5gradientr&rQr%rRr"r rSr1rT)rr*r rHrCr<rDr8rr(r$r)r4r3rUrVrWs rrZLinearModelLoss.gradientXsN./WWdnn6N6N*S!3!344  !151J1J41S .G!%!6!6t!< G00)' 1  ,3 9N ~~++==]];D !n 47P PD* !!)--/RK88Y.gmm3OD#1#3#3a#7/:S#SDKZK !!,00a08QU yyA~zzz,, rc f URURRsupn U [UR5-n U cUR X5upn OUR U5upUcU O[R"U5nUc [R"XRSS9nOURUR:wa&[SURSURS35eURR(a&URR(d [S5eUnURnUc"[R "UU4URS9nOURUU4:wa[S UU4S UR<S35eURR(aAURR"(d&URR(d [S 5eUnURR(GdEURR%UU UUS 9unnUU-nUU-n[R&"US :*US9S:n[R("U5nUR*U-X^--USU &UR(aUR5US'U(aUUU4$[-UU5USU 2SU 24'US :aBURR"(aSOSnUR/SUS9SX-U S-2==U- ss'UR(a4UR*U-nUUSS2S4'UUSSS24'UR5US'GOcURR1UU UUS 9unnUU-nUR/X4SS9nUR*U-X^--USS2SU 24'UR(aURS S9USS2S4'UR2S:XaUR5SS9nUbUU- nOSU- n[7U 5GHZnUSS2U4SUSS2U4- -U-n[-UU5UUX-U 2UX-U 24'UR(aPUR*U-nUUUX-U 2X-U-4'UUX-U-UX-U 24'UR5UX-U-X-U-4'[7US-U 5HnUSS2U4*USS2U4-U-n[-UU5UUX-U 2UX-U 24'UR(aPUR*U-nUUUX-U 2X-U-4'UUX-U-UX-U 24'UR5UX-U-X-U-4'UUSU 2USU 24UUSU 2USU 24'M GM] US :aKURR"(aSOSnUR/SUS9SU S-U -U -X-S-2==U- ss'SnUUU4$)afComputes gradient and hessian w.r.t. coef. Parameters ---------- coef : ndarray of shape (n_dof,), (n_classes, n_dof) or (n_classes * n_dof,) Coefficients of a linear model. If shape (n_classes * n_dof,), the classes of one feature are contiguous, i.e. one reconstructs the 2d-array via coef.reshape((n_classes, -1), order="F"). X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. y : contiguous array of shape (n_samples,) Observed, true target values. sample_weight : None or contiguous array of shape (n_samples,), default=None Sample weights. l2_reg_strength : float, default=0.0 L2 regularization strength n_threads : int, default=1 Number of OpenMP threads to use. gradient_out : None or ndarray of shape coef.shape A location into which the gradient is stored. If None, a new array might be created. hessian_out : None or ndarray of shape (n_dof, n_dof) or (n_classes * n_dof, n_classes * n_dof) A location into which the hessian is stored. If None, a new array might be created. raw_prediction : C-contiguous array of shape (n_samples,) or array of shape (n_samples, n_classes) Raw prediction values (in link space). If provided, these are used. If None, then raw_prediction = X @ coef + intercept is calculated. Returns ------- gradient : ndarray of shape coef.shape The gradient of the loss. hessian : ndarray of shape (n_dof, n_dof) or (n_classes, n_dof, n_dof, n_classes) Hessian matrix. hessian_warning : bool True if pointwise hessian has more than 25% of its elements non-positive. 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FM  VVN3N !n 47P PD* !!)--/RT?22-9!^-LD*kzk) *" $zz66C Ru -.R1CPQ .RS#S!!SS>) "SbS"W "R"W -113V %)NN$A$A-+# %B% !NE f $N<< 2#<>D#1#3#3a#7/:S#SDKZK !!,00a08QU yyA~zzz,L("V+6\9%!Q$K1uQT{?3b8!A& .: .:<%%qBI2Y>!.24!.2I2Y>@ /!3Y5Ka5OOPq1ui0Aq!t uQT{2R7A%Q*I2Y>I2Y>@))SS1W 6B%2Q68%2Q6 6BD EEGY3a79ORS9SST8[R"U5n[R"T5(aTRTUST--UST&O2[R R TRTUST/5UST&UST===TUST-- sss&TR(a(UST===UST-- sss&TUST-TUS--US'U$)Nr.)r&rRrr r linalg multi_dotr) sretr hXhX_sum hessian_sumr<r(rs rhessp7LinearModelLoss.gradient_hessian_product..hesspsmmA&??1%%'(ssb1[j>.A'BC $')yy':':ACCQ{ ^;T'UC $KZ Oa n$DD %% $"6$$q*~5 ae8KKCG rr!rLcR> URTS4SS9nT R(aUSS2S4nUSS2SS24nOSnTUR-U-nUT *U-RSS9SS2[R 4- nUT -nT bUT SS2[R 4-n[R "TT4TRSS9nURT-T - TU--USS2ST 24'T R(aURSS9T - USS2S4'TRS:XaURSS9$U$)Nr.r!r0rr rMrL) r2rr rQr&newaxisrSr"r1rT)ry s_intercepttmp hess_prodr r*r<r$r)r(rorCrrVr4s rr~rs8IIy"oSI9%%"#ArE(K!SbS& A"#K!##g + ))q)1!RZZ-@@u  ,=BJJ77CHHi%7w}}TWX -0UUQY&,@?UVCV,V ![j[.)%%'*wwAw'?Iae$99>$???55$$rr r0)rrr$rOrr9r&rQr%rdrRr"r rr r rsqueezeasarray atleast_1drfrSr1rT)rr*r rHrCr<rDrr3r8rUrlrWr~r{r|r}r$r)r(rorVr4s``` `` @@@@@@@@@rgradient_hessian_product(LinearModelLoss.gradient_hessian_products@./WWdnn6N6N*JS!3!344-1-F-FtQ-O*+3 9N~~+++-1^^-L-L-+# .M. *N f $N f $N==W]];D !n 47P PD* !!)--/R),,.Kq!!%%~q&9)AWX $ArzzM2Q6!!BJJrvv1v~$>?v.  \{w%)NN$A$A-+# %B% !NE f $N88Y.gmm3OD#1#3#3a#7/G:S#SDKZK !!,00a08QU . % %.yyA~zzz,e33{rrr)Nr/r N)Nr/r NNN)Nr/r )__name__ __module__ __qualname____firstlineno____doc__rr+r5r9r>rFrPrZrdr__static_attributes__rrrr%s@D+8%"N2@/4@vLfG\+DNOWrr) rnumpyr&scipyr utils.extmathrrrrrrrs&(.T T r