-i |SrSSKJrJr SSKrSSKJr SSKJ r J r J r SSK J r JrJr SSKJrJr "S S \ \ \ \S 9rg) z)Principal Component Analysis Base Classes)ABCMetaabstractmethodN)linalg) BaseEstimatorClassNamePrefixFeaturesOutMixinTransformerMixin)_fill_or_add_to_diagonaldevice get_namespace)check_is_fitted validate_datac^\rSrSrSrSrSr\S Sj5rSr S Sjr S r \ S 5r S rg)_BasePCAzkBase class for PCA methods. Warning: This class should not be used directly. Use derived classes instead. c [UR5upURnURnUR(a(X1R USS2[ R 45-nX@R- nURX@R:UURS[U5URS95nURU-U-n[X`RU5 U$)a3Compute data covariance with the generative model. ``cov = components_.T * S**2 * components_ + sigma2 * eye(n_features)`` where S**2 contains the explained variances, and sigma2 contains the noise variances. Returns ------- cov : array of shape=(n_features, n_features) Estimated covariance of data. N)r dtype)r components_explained_variance_whitensqrtnpnewaxisnoise_variance_whereasarrayr rTr )selfxp_rexp_var exp_var_diffcovs N/var/www/html/venv/lib/python3.13/site-packages/sklearn/decomposition/_base.pyget_covariance_BasePCA.get_covariancesd../&& ** ;;%2:: 0F(GGK!5!55 xx ** *  JJs6'?'--J H }}|+{: &:&:B? c r[UR5upURRSnURS:XaUR U5UR - $U(aUR RnO[ RnUR S:XaU"UR55$URnURnUR(a(XQRUSS2[R45-nX`R - nURX`R :UURS[!U5S95nXUR"-UR - n[%USU- U5 UR"U"U5-U-nXR S-*-n[%USUR - U5 U$)aCompute data precision matrix with the generative model. Equals the inverse of the covariance but computed with the matrix inversion lemma for efficiency. Returns ------- precision : array, shape=(n_features, n_features) Estimated precision of data. rrN)r g?r)r rshape n_components_eyerrinvr&rrrrrrrr rr ) rr is_array_api_compliant n_features linalg_invrr"r# precisions r% get_precision_BasePCA.get_precision5s&343C3C%D"%%++A.     "66*%(<(<< < !JJ   3 &d1134 4&& ** ;;%2:: 0F(GGK!5!55 xx ** *  JJs6'?J 3  --/$2F2FF  C,,>CMMJy$99KG ++Q.//  C$2F2F,FKr(Ncg)aJPlaceholder for fit. Subclasses should implement this method! Fit the model with X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. Returns ------- self : object Returns the instance itself. N)rXys r%fit _BasePCA.fitbsr(c[XRUR5up#[U5 [ UUUR UR /SSS9nURXSS9$)a#Apply dimensionality reduction to X. X is projected on the first principal components previously extracted from a training set. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) New data, where `n_samples` is the number of samples and `n_features` is the number of features. Returns ------- X_new : array-like of shape (n_samples, n_components) Projection of X in the first principal components, where `n_samples` is the number of samples and `n_components` is the number of the components. )csrcscF)r accept_sparsereset)r x_is_centered)r rrr rfloat64float32 _transform)rr7r r!s r% transform_BasePCA.transformtsa$a!1!143K3KL   ::rzz*(  qu==r(cdXRR-nU(d5XBRURS5URR--nUR(aJUR UR 5nURUR5RnXeXV:'XE-nU$)N)r*) rrreshapemean_rrrfinforeps)rr7r r@ X_transformedscale min_scales r%rC_BasePCA._transforms,,...  ZZ G>(5@))r(r) metaclass)r[abcrrnumpyrscipyrbaserrr utils._array_apir r r utils.validationr rrr6r(r%res9/ (SSNN=z)#%5}PWz)r(