0PhgHdZddlZddlmZmZddlZddlmZddl m Z m Z m Z m Z ddlmZddlmZmZmZdd lmZmZmZmZdd lmZmZd d gZd ZdZdZdZ d#dZ!dZ"dZ#edgdgdgdgdd d#ddddddddddddd d!Z$Gd"d e e e Z%dS)$z Python implementation of the fast ICA algorithms. Reference: Tables 8.3 and 8.4 page 196 in the book: Independent Component Analysis, by Hyvarinen et al. N)IntegralReal)linalg) BaseEstimatorClassNamePrefixFeaturesOutMixinTransformerMixin _fit_context)ConvergenceWarning)as_float_array check_arraycheck_random_state)IntervalOptions StrOptionsvalidate_params)check_is_fitted validate_datafasticaFastICAcz|tj||d|j|d|gz}|S)a Orthonormalize w wrt the first j rows of W. Parameters ---------- w : ndarray of shape (n,) Array to be orthogonalized W : ndarray of shape (p, n) Null space definition j : int < p The no of (from the first) rows of Null space W wrt which w is orthogonalized. Notes ----- Assumes that W is orthogonal w changed in place N)npr multi_dotT)wWjs ^/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/sklearn/decomposition/_fastica.py_gs_decorrelationrs<*  a2A2!BQB%0 1 11A HcDtjtj||j\}}tj|tj|jjd}tj |dtj |z z|j|gS)z@Symmetric decorrelation i.e. W <- (W * W.T) ^{-1/2} * W N)a_mina_max?) reighrdotrclipfinfodtypetinyrsqrt)rsus r_sym_decorrelationr.8s} ;rva~~ & &DAq !'**/t<<r c  t|}~t|jd}t|D]}|t j|||\} } tt j| |j|z | ddtjf|zz } ~ ~ tttt j d| |dz } | }| |krntj dt||dzfS)zCParallel FastICA. Used internally by FastICA --main loop r1Nzij,ij->iz\FastICA did not converge. Consider increasing tolerance or the maximum number of iterations.)r.floatr4r6rr&rnewaxisr<r:einsumwarningswarnr ) r=r>r?r@rArBrp_iirFrGW1rIs r_ica_parrTjs 6""A qwqz  BHoo  aq! h// e tQS 1 1B 6qqq"*}9MPQ9Q Q R R %#c")JA6677!;<<==  99 E   A      b1f9r c |dd}||z}tj||}tj|jd|j}t |D]%\}}|d|dzz z||<&||fS)Nalphar$rr0r1r)getrtanhemptyr4r) enumerater9)xr@rVgxg_xrEgx_is r_logcoshr_s LL# & &EJA AB (171:QW - - -CR==0041tQw;'--//A s7Nr ctj|dz dz }||z}d|dzz |z}||dfS)Nrr1r2)rexpr9)r[r@rbr\r]s r_exprcsO &1a41  C SB q!t8s C sxxRx   r cD|dzd|dzzdfS)Nrrar2)r9)r[r@s r_cuberfs' a4!ad(b)) ))r array-likeboolean)r= return_X_meancompute_sources return_n_iterFprefer_skip_nested_validationparallel unit-variancelogcosh-C6?svdT) algorithmwhitenfunr@rAr>rB whiten_solver random_staterirjrkc @t||||||||| |  }|||| }|jdvr|j}|j}nd}d}||j|g}| r||| r||j|S)a#Perform Fast Independent Component Analysis. The implementation is based on [1]_. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. n_components : int, default=None Number of components to use. If None is passed, all are used. algorithm : {'parallel', 'deflation'}, default='parallel' Specify which algorithm to use for FastICA. whiten : str or bool, default='unit-variance' Specify the whitening strategy to use. - If 'arbitrary-variance', a whitening with variance arbitrary is used. - If 'unit-variance', the whitening matrix is rescaled to ensure that each recovered source has unit variance. - If False, the data is already considered to be whitened, and no whitening is performed. .. versionchanged:: 1.3 The default value of `whiten` changed to 'unit-variance' in 1.3. fun : {'logcosh', 'exp', 'cube'} or callable, default='logcosh' The functional form of the G function used in the approximation to neg-entropy. Could be either 'logcosh', 'exp', or 'cube'. You can also provide your own function. It should return a tuple containing the value of the function, and of its derivative, in the point. The derivative should be averaged along its last dimension. Example:: def my_g(x): return x ** 3, (3 * x ** 2).mean(axis=-1) fun_args : dict, default=None Arguments to send to the functional form. If empty or None and if fun='logcosh', fun_args will take value {'alpha' : 1.0}. max_iter : int, default=200 Maximum number of iterations to perform. tol : float, default=1e-4 A positive scalar giving the tolerance at which the un-mixing matrix is considered to have converged. w_init : ndarray of shape (n_components, n_components), default=None Initial un-mixing array. If `w_init=None`, then an array of values drawn from a normal distribution is used. whiten_solver : {"eigh", "svd"}, default="svd" The solver to use for whitening. - "svd" is more stable numerically if the problem is degenerate, and often faster when `n_samples <= n_features`. - "eigh" is generally more memory efficient when `n_samples >= n_features`, and can be faster when `n_samples >= 50 * n_features`. .. versionadded:: 1.2 random_state : int, RandomState instance or None, default=None Used to initialize ``w_init`` when not specified, with a normal distribution. Pass an int, for reproducible results across multiple function calls. See :term:`Glossary `. return_X_mean : bool, default=False If True, X_mean is returned too. compute_sources : bool, default=True If False, sources are not computed, but only the rotation matrix. This can save memory when working with big data. Defaults to True. return_n_iter : bool, default=False Whether or not to return the number of iterations. Returns ------- K : ndarray of shape (n_components, n_features) or None If whiten is 'True', K is the pre-whitening matrix that projects data onto the first n_components principal components. If whiten is 'False', K is 'None'. W : ndarray of shape (n_components, n_components) The square matrix that unmixes the data after whitening. The mixing matrix is the pseudo-inverse of matrix ``W K`` if K is not None, else it is the inverse of W. S : ndarray of shape (n_samples, n_components) or None Estimated source matrix. X_mean : ndarray of shape (n_features,) The mean over features. Returned only if return_X_mean is True. n_iter : int If the algorithm is "deflation", n_iter is the maximum number of iterations run across all components. Else they are just the number of iterations taken to converge. This is returned only when return_n_iter is set to `True`. Notes ----- The data matrix X is considered to be a linear combination of non-Gaussian (independent) components i.e. X = AS where columns of S contain the independent components and A is a linear mixing matrix. In short ICA attempts to `un-mix' the data by estimating an un-mixing matrix W where ``S = W K X.`` While FastICA was proposed to estimate as many sources as features, it is possible to estimate less by setting n_components < n_features. It this case K is not a square matrix and the estimated A is the pseudo-inverse of ``W K``. This implementation was originally made for data of shape [n_features, n_samples]. Now the input is transposed before the algorithm is applied. This makes it slightly faster for Fortran-ordered input. References ---------- .. [1] A. Hyvarinen and E. Oja, "Fast Independent Component Analysis", Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430. Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.decomposition import fastica >>> X, _ = load_digits(return_X_y=True) >>> K, W, S = fastica(X, n_components=7, random_state=0, whiten='unit-variance') >>> K.shape (7, 64) >>> W.shape (7, 7) >>> S.shape (1797, 7) rCrtrurvr@rAr>rBrwrxrj)roarbitrary-varianceN) r_validate_params_fit_transformru whitening_mean_ _unmixingr;n_iter_)r=rCrtrurvr@rAr>rBrwrxrirjrkestSKX_meanreturned_valuess rrrsZ !  #!   C 1o>>A z<<< N #-+O'v&&&,s{+++ r c eZdZUdZeeddddgeddhgedd heed hgehd e ge dgeedddgee d ddgd dgeddhgdgd Z e e d< d!dd dddddddd fd Zd"dZedd!dZedd!dZd#dZd#dZedZfd ZxZS)$raFastICA: a fast algorithm for Independent Component Analysis. The implementation is based on [1]_. Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, default=None Number of components to use. If None is passed, all are used. algorithm : {'parallel', 'deflation'}, default='parallel' Specify which algorithm to use for FastICA. whiten : str or bool, default='unit-variance' Specify the whitening strategy to use. - If 'arbitrary-variance', a whitening with variance arbitrary is used. - If 'unit-variance', the whitening matrix is rescaled to ensure that each recovered source has unit variance. - If False, the data is already considered to be whitened, and no whitening is performed. .. versionchanged:: 1.3 The default value of `whiten` changed to 'unit-variance' in 1.3. fun : {'logcosh', 'exp', 'cube'} or callable, default='logcosh' The functional form of the G function used in the approximation to neg-entropy. Could be either 'logcosh', 'exp', or 'cube'. You can also provide your own function. It should return a tuple containing the value of the function, and of its derivative, in the point. The derivative should be averaged along its last dimension. Example:: def my_g(x): return x ** 3, (3 * x ** 2).mean(axis=-1) fun_args : dict, default=None Arguments to send to the functional form. If empty or None and if fun='logcosh', fun_args will take value {'alpha' : 1.0}. max_iter : int, default=200 Maximum number of iterations during fit. tol : float, default=1e-4 A positive scalar giving the tolerance at which the un-mixing matrix is considered to have converged. w_init : array-like of shape (n_components, n_components), default=None Initial un-mixing array. If `w_init=None`, then an array of values drawn from a normal distribution is used. whiten_solver : {"eigh", "svd"}, default="svd" The solver to use for whitening. - "svd" is more stable numerically if the problem is degenerate, and often faster when `n_samples <= n_features`. - "eigh" is generally more memory efficient when `n_samples >= n_features`, and can be faster when `n_samples >= 50 * n_features`. .. versionadded:: 1.2 random_state : int, RandomState instance or None, default=None Used to initialize ``w_init`` when not specified, with a normal distribution. Pass an int, for reproducible results across multiple function calls. See :term:`Glossary `. Attributes ---------- components_ : ndarray of shape (n_components, n_features) The linear operator to apply to the data to get the independent sources. This is equal to the unmixing matrix when ``whiten`` is False, and equal to ``np.dot(unmixing_matrix, self.whitening_)`` when ``whiten`` is True. mixing_ : ndarray of shape (n_features, n_components) The pseudo-inverse of ``components_``. It is the linear operator that maps independent sources to the data. mean_ : ndarray of shape(n_features,) The mean over features. Only set if `self.whiten` is True. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 n_iter_ : int If the algorithm is "deflation", n_iter is the maximum number of iterations run across all components. Else they are just the number of iterations taken to converge. whitening_ : ndarray of shape (n_components, n_features) Only set if whiten is 'True'. This is the pre-whitening matrix that projects data onto the first `n_components` principal components. See Also -------- PCA : Principal component analysis (PCA). IncrementalPCA : Incremental principal components analysis (IPCA). KernelPCA : Kernel Principal component analysis (KPCA). MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. SparsePCA : Sparse Principal Components Analysis (SparsePCA). References ---------- .. [1] A. Hyvarinen and E. Oja, Independent Component Analysis: Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430. Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.decomposition import FastICA >>> X, _ = load_digits(return_X_y=True) >>> transformer = FastICA(n_components=7, ... random_state=0, ... whiten='unit-variance') >>> X_transformed = transformer.fit_transform(X) >>> X_transformed.shape (1797, 7) r1Nleft)closedrn deflationr|roF>rbcuberpgrgr%rsrxrz_parameter_constraintsrprqrr) rtrurvr@rAr>rBrwrxc t||_||_||_||_||_||_||_||_ | |_ | |_ dSN) super__init__rCrtrurvr@rAr>rBrwrx) selfrCrtrurvr@rAr>rBrwrx __class__s rrzFastICA.__init__sj ("      *(r c t|jtjtjgdj}jinj}tj}| dd}d|cxkrdksntdj dkrt}n?j d krt}n,j d krt}ntj rfd }|j\}} j} js| d} t%jd | t)| |} | t)| |kr't)| |} t%jd | zjr|d} || ddtjfz}jdkrt1j||\} } tj| ddd}tj| jjdz}| |k}tj|rt%jd|| |<tj | | | || dd|f} } n-jdkr"t1j!|dddd\} } | tj"| dz} | | z jd| }~ ~ tj||}|tj | z}ntG|d}j$}|2tj%|&| | f|j}n7tj%|}|j| | fkrtdd| | fizj'||j(|d}j)dkrtU|fi|\}}nj)dkrtW|fi|\}}~|_,|rJjr(tj-|||gj}ntj||j}nd}jrjd krO|s'tj-|||gj}tj.|dd!"}||z}||jz}tj||_/| _0|_1n|_/t1j2j/d#_3|_4|S)$adFit the model. 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. compute_sources : bool, default=False If False, sources are not computes but only the rotation matrix. This can save memory when working with big data. Defaults to False. Returns ------- S : ndarray of shape (n_samples, n_components) or None Sources matrix. `None` if `compute_sources` is `False`. r)r7r)ensure_min_samplesNrVr$r1zalpha must be in [1,2]rprbrc j|fi|Sr)rv)r[r@rs rr?z!FastICA._fit_transform..gIstx..X...r z(Ignoring n_components with whiten=False.z/n_components is too large: it will be set to %srar2r% zfThere are some small singular values, using whiten_solver = 'svd' might lead to more accurate results.)outrsF) full_matrices check_finiter)r7)sizer0z/w_init has invalid shape -- should be %(shape)sr4)r>r?r@rArBrnrroT)r3keepdims)r)5rrurfloat64float32rr@rrxrW ValueErrorrvr_rcrfcallabler4rCrOrPminr9rMrwrr%r&argsortr(r)epsanyr+rssignr rBasarraynormalr>rArtrTrJrrstd components_rrpinvmixing_r)rr=rjXTr@rxrVr? n_features n_samplesrCrdr- sort_indicesrdegenerate_idxrX1rBkwargsrrDrS_stds` rr~zFastICA._fit_transform!s;$  :rz*    .22DM)$*;<<  Wc**EQ566 6 8y AA X  AA X  AA dh   / / / / / /!# I( { F|7L MD E E E  y*55L #i44 4 4y*55L MALP    ;$ 0WW"W%%F &BJ' 'B!V++{266!99--1!z!}}TTrT2 hqw''+b0!"S6.))M, %(.!q!!!!!!!\/(:1#u,,z"ENNNrPQrR1 1 AQ -<-(A12B "')$$ $BB ///B >Z##, )E#FFbhFF Z''F| l;;; E| <=> 8      >Z ' ' ..v..IAvv ^{ * * ..v..IAv   { $I''Ar 335F1bMMOA ; !{o--&: ++Q2J779Aqq4888U UW !va||D DJDOO D {4#3%HHH r Trlc0||dS)a5Fit the model and recover the sources from 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. y : Ignored Not used, present for API consistency by convention. Returns ------- X_new : ndarray of shape (n_samples, n_components) Estimated sources obtained by transforming the data with the estimated unmixing matrix. Tr{r~rr=ys r fit_transformzFastICA.fit_transforms&""1d";;;r c4||d|S)aFit the model to 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. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. Fr{rrs rfitz FastICA.fits"$ Au555 r ct|t|||o|jtjtjgd}|jr ||jz}tj||jj S)a_Recover the sources from X (apply the unmixing matrix). Parameters ---------- X : array-like of shape (n_samples, n_features) Data to transform, where `n_samples` is the number of samples and `n_features` is the number of features. copy : bool, default=True If False, data passed to fit can be overwritten. Defaults to True. Returns ------- X_new : ndarray of shape (n_samples, n_components) Estimated sources obtained by transforming the data with the estimated unmixing matrix. F)r7r)reset) rrrurrrrr&rrrr=r7s r transformzFastICA.transformst$    &4;:rz*     ;  OAva)+,,,r ct|t||o|jtjtjg}tj||jj}|jr ||j z }|S)a1Transform the sources back to the mixed data (apply mixing matrix). Parameters ---------- X : array-like of shape (n_samples, n_components) Sources, where `n_samples` is the number of samples and `n_components` is the number of components. copy : bool, default=True If False, data passed to fit are overwritten. Defaults to True. Returns ------- X_new : ndarray of shape (n_samples, n_features) Reconstructed data obtained with the mixing matrix. )r7r)) rr rurrrr&rrrrs rinverse_transformzFastICA.inverse_transformse  !5$+rz2:>V W W W F1dln % % ;  OAr c&|jjdS)z&Number of transformed output features.r)rr4)rs r_n_features_outzFastICA._n_features_outs%a((r cdt}ddg|j_|S)Nrr)r__sklearn_tags__transformer_tagspreserves_dtype)rtagsrs rrzFastICA.__sklearn_tags__!s-ww''))1:I0F- r r)F)T)__name__ __module__ __qualname____doc__rrrrboolrdictrr__annotations__rr~r rrrrpropertyrr __classcell__)rs@rrros9EEP"(AtFCCCTJ j*k!:;;< J,o> ? ? GD5' " "  55566A4LXh4???@sD8889&$*fe_556'($$D$)  )))))))4VVVVp\555<<<65<(\55565(----@2))X)r r)&rrOnumbersrrnumpyrscipyrbaserrr r exceptionsr utilsr r rutils._param_validationrrrrutils.validationrr__all__rr.rJrTr_rcrfrrr rrsN"""""""" ,+++++CCCCCCCCCCTTTTTTTTTTTT======== i    2 A A A   FD    !!!***^#%;#  #(@    @@@@@Fuuuuu-/?uuuuur