
    Ug              
          d Z ddlZddlmZmZ ddlmZmZ ddlZ	ddl
mZ ddlmZmZmZmZmZmZ ddlmZ dd	lmZmZ dd
lmZmZ ddlmZ ddlmZmZ ddl m!Z!m"Z" g dZ#e ed          k    rddl
m$Z% nddl
m%Z% d Z&	 d)dZ'd Z(d*dZ)d Z*d Z+d Z, G d deeeeee           Z- G d! d"e-          Z. G d# d$e-          Z/ G d% d&e-          Z0 G d' d(eee          Z1dS )+zG
The :mod:`sklearn.pls` module implements Partial Least Squares (PLS).
    N)ABCMetaabstractmethod)IntegralReal)svd   )BaseEstimatorClassNamePrefixFeaturesOutMixinMultiOutputMixinRegressorMixinTransformerMixin_fit_context)ConvergenceWarning)check_arraycheck_consistent_length)Interval
StrOptions)svd_flip)parse_version
sp_version)FLOAT_DTYPEScheck_is_fitted)PLSCanonicalPLSRegressionPLSSVDz1.7)pinv)pinv2c           
         t          | dd          \  }}}|j        j                                        }ddd}t	          j        |          ||         z  t	          j        |          j        z  }t	          j        ||k              }|d d d |f         }||d |         z  }t	          j	        t	          j
        t	          j        ||d |                                       S )NF)full_matricescheck_finiteg     @@g    .A)fd)r   dtypecharlowernpmaxfinfoepssum	transpose	conjugatedot)ausvhtfactorcondranks           _/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/sklearn/cross_decomposition/_pls.py
_pinv2_oldr7   )   s     1E>>>HAq"	AS!!F6!99vay 28A;;?2D6!d(D	!!!UdU(A5D5MA<RVAr%4%y%9%9::;;;    A  ư>Fc                 n   t          j        | j                  j        	 t	          fd|j        D                       }n"# t          $ r}t          d          |d}~ww xY wd}|dk    rt          |           t          |          }
}	t          |          D ]r}|dk    rt          j	        |	|          }n0t          j	        | j        |          t          j	        ||          z  }|t          j
        t          j	        ||                    z   z  }t          j	        | |          }|dk    rt          j	        |
|          }n5t          j	        |j        |          t          j	        |j        |          z  }|r-|t          j
        t          j	        ||                    z   z  }t          j	        ||          t          j	        ||          z   z  }||z
  }t          j	        ||          |k     s|j        d         dk    r n|}t|dz   }||k    rt          j        dt                     |||fS )a?  Return the first left and right singular vectors of X'Y.

    Provides an alternative to the svd(X'Y) and uses the power method instead.
    With norm_y_weights to True and in mode A, this corresponds to the
    algorithm section 11.3 of the Wegelin's review, except this starts at the
    "update saliences" part.
    c              3   p   K   | ]0}t          j        t          j        |          k              ,|V  1d S N)r&   anyabs).0colr)   s     r6   	<genexpr>z;_get_first_singular_vectors_power_method.<locals>.<genexpr>H   s?      GGsRVBF3KK#4E-F-FGsGGGGGGr8   y residual is constantNd   B   z$Maximum number of iterations reached)r&   r(   r#   r)   nextTStopIterationr7   ranger-   sqrtshapewarningswarnr   )XYmodemax_itertolnorm_y_weightsy_scoreex_weights_oldX_pinvY_pinvi	x_weightsx_score	y_weightsx_weights_diffn_iterr)   s                    @r6   (_get_first_singular_vectors_power_methodra   ;   s-    (17


C=GGGGacGGGGG = = =4551<= Ms{{ $A
18__ " "3;;vw//IIqsG,,rvgw/G/GGIRWRVIy99::S@@	&I&&3;;vw//IIqsG,,rvgi/I/III 	E	9!=!=>>DDI&I&&"&I*F*F*LM"]26..11C77171:??E!UF<>PQQQi''s    A 
A!AA!c                     t          j        | j        |          }t          |d          \  }}}|dddf         |dddf         fS )zbReturn the first left and right singular vectors of X'Y.

    Here the whole SVD is computed.
    Fr   Nr   )r&   r-   rI   r   )rP   rQ   CU_Vts         r6   _get_first_singular_vectors_svdrh   v   sP    
 	qsAA1E***HAq"QQQT7Bq!!!tHr8   Tc                    |                      d          }| |z  } |                     d          }||z  }|rK|                     dd          }d||dk    <   | |z  } |                    dd          }d||dk    <   ||z  }n>t          j        | j        d                   }t          j        |j        d                   }| |||||fS )z{Center X, Y and scale if the scale parameter==True

    Returns
    -------
        X, Y, x_mean, y_mean, x_std, y_std
    r   axisrG   )rk   ddofg      ?        )meanstdr&   onesrM   )rP   rQ   scalex_meany_meanx_stdy_stds          r6   _center_scale_xyrv      s     VVV^^FKAVVV^^FKA 	$11%%!esl	U
11%%!esl	U

##
##a--r8   c                     t          j        t          j        |                     }t          j        | |                   }| |z  } ||z  }dS )z7Same as svd_flip but works on 1d arrays, and is inplaceN)r&   argmaxr@   sign)r/   vbiggest_abs_val_idxry   s       r6   _svd_flip_1dr|      sG     )BF1II..71()**DIAIAAAr8   c                 d    |-t          j        dt                     | t          d          |S | S )NzE`Y` is deprecated in 1.5 and will be removed in 1.7. Use `y` instead.z?Cannot use both `y` and `Y`. Use only `y` as `Y` is deprecated.)rN   rO   FutureWarning
ValueErroryrQ   s     r6   _deprecate_Y_when_optionalr      sI    }S	
 	
 	
 =Q   Hr8   c                 H    | |t          d          t          | |          S )Nzy is required.)r   r   r   s     r6   _deprecate_Y_when_requiredr      s*    yQY)***%a+++r8   c                   R   e Zd ZU dZ eeddd          gdg eddh          g ed	d
h          g eddh          g eeddd          g eeddd          gdgdZe	e
d<   e	 dddd	dddddd            Z ed          dd            ZddZddZd dZd!dZd ZdS )"_PLSa  Partial Least Squares (PLS)

    This class implements the generic PLS algorithm.

    Main ref: Wegelin, a survey of Partial Least Squares (PLS) methods,
    with emphasis on the two-block case
    https://stat.uw.edu/sites/default/files/files/reports/2000/tr371.pdf
    rG   Nleftclosedboolean
regression	canonicalr9   rF   r   nipalsr   n_componentsrq   deflation_moderR   	algorithmrS   rT   copy_parameter_constraintsr   Tr:   r;   )rq   r   rR   r   rS   rT   r   c                v    || _         || _        || _        || _        || _        || _        || _        || _        d S r>   )r   r   rR   rq   r   rS   rT   r   )	selfr   rq   r   rR   r   rS   rT   r   s	            r6   __init__z_PLS.__init__   sB     ),	
" 			r8   prefer_skip_nested_validationc           	      X   t          ||          }t          ||           |                     |t          j        d| j        d          }t          |dt          j        d| j        d          }|j        dk    rd| _        |	                    dd          }nd| _        |j
        d	         }|j
        d         }|j
        d         }| j        }| j        d
k    r|nt          |||          }||k    rt          d| d| d          | j        dk    | _        | j        }	t!          ||| j                  \  }
}| _        | _        | _        | _        t          j        ||f          | _        t          j        ||f          | _        t          j        ||f          | _        t          j        ||f          | _        t          j        ||f          | _        t          j        ||f          | _        g | _        t          j        |j                  j         }tC          |          D ]w}| j"        dk    rt          j#        t          j$        |          d|z  k     d	          }d|dd|f<   	 tK          |
|| j&        | j'        | j(        |	          \  }}}nD# tR          $ r7}tU          |          dk    r tW          j,        d|            Y d}~ nd}~ww xY w| j        -                    |           n| j"        dk    rt]          |
|          \  }}t_          ||           t          j0        |
|          }|	rd}nt          j0        ||          }t          j0        ||          |z  }t          j0        ||
          t          j0        ||          z  }|
t          j1        ||          z  }
| j        dk    rCt          j0        ||          t          j0        ||          z  }|t          j1        ||          z  }| j        d
k    rCt          j0        ||          t          j0        ||          z  }|t          j1        ||          z  }|| j        dd|f<   || j        dd|f<   || j        dd|f<   || j        dd|f<   || j        dd|f<   || j        dd|f<   yt          j0        | j        te          t          j0        | j        j3        | j                  d                    | _4        t          j0        | j        te          t          j0        | j        j3        | j                  d                    | _5        t          j0        | j4        | j        j3                  | _6        | j6        | j        z  j3        | j        z  | _6        | j        | _7        | j4        j
        d         | _8        | S )d  Fit model to data.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training vectors, where `n_samples` is the number of samples and
            `n_features` is the number of predictors.

        y : array-like of shape (n_samples,) or (n_samples, n_targets)
            Target vectors, where `n_samples` is the number of samples and
            `n_targets` is the number of response variables.

        Y : array-like of shape (n_samples,) or (n_samples, n_targets)
            Target vectors, where `n_samples` is the number of samples and
            `n_targets` is the number of response variables.

            .. deprecated:: 1.5
               `Y` is deprecated in 1.5 and will be removed in 1.7. Use `y` instead.

        Returns
        -------
        self : object
            Fitted model.
        Tr   r#   force_writeabler   ensure_min_samplesr   F
input_namer#   r   r   	ensure_2drG   r   r   `n_components` upper bound is . Got   instead. Reduce `n_components`.r   r   
   rj   rm   N)rR   rS   rT   rU   rD   z$y residual is constant at iteration r   )r    )9r   r   _validate_datar&   float64r   r   ndim_predict_1dreshaperM   r   r   minr   _norm_y_weightsrv   rq   _x_mean_y_mean_x_std_y_stdzeros
x_weights_
y_weights_	_x_scores	_y_scoresx_loadings_y_loadings_n_iter_r(   r#   r)   rK   r   allr@   ra   rR   rS   rT   rJ   strrN   rO   appendrh   r|   r-   outerr   rI   x_rotations_y_rotations_coef_
intercept__n_features_out)r   rP   r   rQ   npqr   rank_upper_boundrU   Xkyky_epskyk_maskr\   r^   r   rW   x_scoresy_ssy_scores
x_loadings
y_loadingss                           r6   fitz_PLS.fit   s   4 'q!,,1%%%*     
 
 * 
 
 
 6Q;;#D		"a  AA$DGAJGAJGAJ( !% 3| C C11QPQST***F1A F F#F F F  
  $2kA- HXq$*H
 H
DBdlDK (A|#455(A|#4551l"3441l"3448Q$5668Q$566
 ""&|$$ =	0 =	0A ~))&b5j!8qAAA!$111g:
 A!Y!% H'5  	!! %   1vv!999M"L"L"LMMMEEEEE	 ##G,,,,5(('Fr2'N'N$	9 I... vb),,H 4vi33vb),,t3H "--x0J0JJJ"(8Z000B"k11VHb11BF8X4N4NN
bhx444"l22VHb11BF8X4N4NN
bhx444$-DOAAAqD!$-DOAAAqD!#+DN111a4 #+DN111a4 %/DQQQT"%/DQQQT"" FO"&)+T_==ERRR
 
 FO"&)+T_==ERRR
 
 VD-t/?/ABB
j4;.1DK?
,#06q9s   +(J
K+KKc                    t          ||          }t          |            |                     ||t          d          }|| j        z  }|| j        z  }t          j        || j                  }|lt          |dd|t                    }|j
        dk    r|                    dd          }|| j        z  }|| j        z  }t          j        || j                  }||fS |S )a  Apply the dimension reduction.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Samples to transform.

        y : array-like of shape (n_samples, n_targets), default=None
            Target vectors.

        Y : array-like of shape (n_samples, n_targets), default=None
            Target vectors.

            .. deprecated:: 1.5
               `Y` is deprecated in 1.5 and will be removed in 1.7. Use `y` instead.

        copy : bool, default=True
            Whether to copy `X` and `Y`, or perform in-place normalization.

        Returns
        -------
        x_scores, y_scores : array-like or tuple of array-like
            Return `x_scores` if `Y` is not given, `(x_scores, y_scores)` otherwise.
        Fr   r#   resetNr   )r   r   r   r#   rG   r   )r   r   r   r   r   r   r&   r-   r   r   r   r   r   r   r   )r   rP   r   rQ   r   r   r   s          r6   	transformz_PLS.transform  s    2 'q!,,LNN	T\	T[6!T.//=cU\  A v{{IIb!$$AAva!233HX%%r8   c                 x   t          ||          }t          |            t          |dt                    }t	          j        || j        j                  }|| j        z  }|| j	        z  }|Nt          |dt                    }t	          j        || j
        j                  }|| j        z  }|| j        z  }||fS |S )a  Transform data back to its original space.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_components)
            New data, where `n_samples` is the number of samples
            and `n_components` is the number of pls components.

        y : array-like of shape (n_samples,) or (n_samples, n_components)
            New target, where `n_samples` is the number of samples
            and `n_components` is the number of pls components.

        Y : array-like of shape (n_samples, n_components)
            New target, where `n_samples` is the number of samples
            and `n_components` is the number of pls components.

            .. deprecated:: 1.5
               `Y` is deprecated in 1.5 and will be removed in 1.7. Use `y` instead.

        Returns
        -------
        X_reconstructed : ndarray of shape (n_samples, n_features)
            Return the reconstructed `X` data.

        y_reconstructed : ndarray of shape (n_samples, n_targets)
            Return the reconstructed `X` target. Only returned when `y` is given.

        Notes
        -----
        This transformation will only be exact if `n_components=n_features`.
        rP   )r   r#   Nr   )r   r   r   r   r&   matmulr   rI   r   r   r   r   r   )r   rP   r   rQ   X_reconstructedy_reconstructeds         r6   inverse_transformz_PLS.inverse_transform  s    @ 'q!,,c>>>)At'7'9::4;&4<'=A#\BBBA i4+;+=>>Ot{*Ot|+O"O33r8   c                     t          |            |                     ||t          d          }|| j        z  }|| j        j        z  | j        z   }| j        r|                                n|S )aU  Predict targets of given samples.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Samples.

        copy : bool, default=True
            Whether to copy `X` and `Y`, or perform in-place normalization.

        Returns
        -------
        y_pred : ndarray of shape (n_samples,) or (n_samples, n_targets)
            Returns predicted values.

        Notes
        -----
        This call requires the estimation of a matrix of shape
        `(n_features, n_targets)`, which may be an issue in high dimensional
        space.
        Fr   )	r   r   r   r   r   rI   r   r   ravel)r   rP   r   Ypreds       r6   predictz_PLS.predict  si    , 	LNN	T\DJL 4?2 $ 0;u{{}}}e;r8   c                 V    |                      ||                              ||          S )a  Learn and apply the dimension reduction on the train data.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training vectors, where `n_samples` is the number of samples and
            `n_features` is the number of predictors.

        y : array-like of shape (n_samples, n_targets), default=None
            Target vectors, where `n_samples` is the number of samples and
            `n_targets` is the number of response variables.

        Returns
        -------
        self : ndarray of shape (n_samples, n_components)
            Return `x_scores` if `Y` is not given, `(x_scores, y_scores)` otherwise.
        r   r   r   rP   r   s      r6   fit_transformz_PLS.fit_transform  &    $ xx1~~''1---r8   c                     dddS )NTF)
poor_score
requires_y )r   s    r6   
_more_tagsz_PLS._more_tags*  s    "%888r8   r   NN)NNTTr>   )__name__
__module____qualname____doc__r   r   r   r   r   dict__annotations__r   r   r   r   r   r   r   r   r   r   r8   r6   r   r      s          "(AtFCCCD%:|[&ABBCS#J''( j%!2334Xh4???@q$v6667	$ 	$D 	 	 	   #    ^* \555f f f 65fP- - - -^3 3 3 3j< < < <:. . . .(9 9 9 9 9r8   r   )	metaclassc                        e Zd ZU dZi ej        Zeed<   dD ]Ze	                    e           	 dddddd fd	Z
d fd	Z xZS )r   a  PLS regression.

    PLSRegression is also known as PLS2 or PLS1, depending on the number of
    targets.

    For a comparison between other cross decomposition algorithms, see
    :ref:`sphx_glr_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py`.

    Read more in the :ref:`User Guide <cross_decomposition>`.

    .. versionadded:: 0.8

    Parameters
    ----------
    n_components : int, default=2
        Number of components to keep. Should be in `[1, n_features]`.

    scale : bool, default=True
        Whether to scale `X` and `Y`.

    max_iter : int, default=500
        The maximum number of iterations of the power method when
        `algorithm='nipals'`. Ignored otherwise.

    tol : float, default=1e-06
        The tolerance used as convergence criteria in the power method: the
        algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
        than `tol`, where `u` corresponds to the left singular vector.

    copy : bool, default=True
        Whether to copy `X` and `Y` in :term:`fit` before applying centering,
        and potentially scaling. If `False`, these operations will be done
        inplace, modifying both arrays.

    Attributes
    ----------
    x_weights_ : ndarray of shape (n_features, n_components)
        The left singular vectors of the cross-covariance matrices of each
        iteration.

    y_weights_ : ndarray of shape (n_targets, n_components)
        The right singular vectors of the cross-covariance matrices of each
        iteration.

    x_loadings_ : ndarray of shape (n_features, n_components)
        The loadings of `X`.

    y_loadings_ : ndarray of shape (n_targets, n_components)
        The loadings of `Y`.

    x_scores_ : ndarray of shape (n_samples, n_components)
        The transformed training samples.

    y_scores_ : ndarray of shape (n_samples, n_components)
        The transformed training targets.

    x_rotations_ : ndarray of shape (n_features, n_components)
        The projection matrix used to transform `X`.

    y_rotations_ : ndarray of shape (n_targets, n_components)
        The projection matrix used to transform `Y`.

    coef_ : ndarray of shape (n_target, n_features)
        The coefficients of the linear model such that `Y` is approximated as
        `Y = X @ coef_.T + intercept_`.

    intercept_ : ndarray of shape (n_targets,)
        The intercepts of the linear model such that `Y` is approximated as
        `Y = X @ coef_.T + intercept_`.

        .. versionadded:: 1.1

    n_iter_ : list of shape (n_components,)
        Number of iterations of the power method, for each
        component.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

    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

    See Also
    --------
    PLSCanonical : Partial Least Squares transformer and regressor.

    Examples
    --------
    >>> from sklearn.cross_decomposition import PLSRegression
    >>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [2.,5.,4.]]
    >>> y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
    >>> pls2 = PLSRegression(n_components=2)
    >>> pls2.fit(X, y)
    PLSRegression()
    >>> Y_pred = pls2.predict(X)

    For a comparison between PLS Regression and :class:`~sklearn.decomposition.PCA`, see
    :ref:`sphx_glr_auto_examples_cross_decomposition_plot_pcr_vs_pls.py`.
    r   r   rR   r   r   Tr:   r;   rq   rS   rT   r   c          
      Z    t                                          ||ddd|||           d S )Nr   r9   r   r   superr   r   r   rq   rS   rT   r   	__class__s         r6   r   zPLSRegression.__init__  sH     	%' 	 		
 		
 		
 		
 		
r8   Nc                     t          ||          }t                                          ||           | j        | _        | j        | _        | S )r   )r   r   r   r   	x_scores_r   	y_scores_)r   rP   r   rQ   r   s       r6   r   zPLSRegression.fit  sC    2 'q!,,Aqr8   r   r   )r   r   r   r   r   r   r   r   parampopr   r   __classcell__r   s   @r6   r   r   .  s         e eN $Cd&A#BDBBB8 * *""5)))) 
'+cu4
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         r8   r   c                        e Zd ZU dZi ej        Zeed<   dD ]Ze	                    e           	 ddddddd	 fd
Z
 xZS )r   a^  Partial Least Squares transformer and regressor.

    For a comparison between other cross decomposition algorithms, see
    :ref:`sphx_glr_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py`.

    Read more in the :ref:`User Guide <cross_decomposition>`.

    .. versionadded:: 0.8

    Parameters
    ----------
    n_components : int, default=2
        Number of components to keep. Should be in `[1, min(n_samples,
        n_features, n_targets)]`.

    scale : bool, default=True
        Whether to scale `X` and `Y`.

    algorithm : {'nipals', 'svd'}, default='nipals'
        The algorithm used to estimate the first singular vectors of the
        cross-covariance matrix. 'nipals' uses the power method while 'svd'
        will compute the whole SVD.

    max_iter : int, default=500
        The maximum number of iterations of the power method when
        `algorithm='nipals'`. Ignored otherwise.

    tol : float, default=1e-06
        The tolerance used as convergence criteria in the power method: the
        algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
        than `tol`, where `u` corresponds to the left singular vector.

    copy : bool, default=True
        Whether to copy `X` and `Y` in fit before applying centering, and
        potentially scaling. If False, these operations will be done inplace,
        modifying both arrays.

    Attributes
    ----------
    x_weights_ : ndarray of shape (n_features, n_components)
        The left singular vectors of the cross-covariance matrices of each
        iteration.

    y_weights_ : ndarray of shape (n_targets, n_components)
        The right singular vectors of the cross-covariance matrices of each
        iteration.

    x_loadings_ : ndarray of shape (n_features, n_components)
        The loadings of `X`.

    y_loadings_ : ndarray of shape (n_targets, n_components)
        The loadings of `Y`.

    x_rotations_ : ndarray of shape (n_features, n_components)
        The projection matrix used to transform `X`.

    y_rotations_ : ndarray of shape (n_targets, n_components)
        The projection matrix used to transform `Y`.

    coef_ : ndarray of shape (n_targets, n_features)
        The coefficients of the linear model such that `Y` is approximated as
        `Y = X @ coef_.T + intercept_`.

    intercept_ : ndarray of shape (n_targets,)
        The intercepts of the linear model such that `Y` is approximated as
        `Y = X @ coef_.T + intercept_`.

        .. versionadded:: 1.1

    n_iter_ : list of shape (n_components,)
        Number of iterations of the power method, for each
        component. Empty if `algorithm='svd'`.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

    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

    See Also
    --------
    CCA : Canonical Correlation Analysis.
    PLSSVD : Partial Least Square SVD.

    Examples
    --------
    >>> from sklearn.cross_decomposition import PLSCanonical
    >>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [2.,5.,4.]]
    >>> y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
    >>> plsca = PLSCanonical(n_components=2)
    >>> plsca.fit(X, y)
    PLSCanonical()
    >>> X_c, y_c = plsca.transform(X, y)
    r   )r   rR   r   Tr   r:   r;   )rq   r   rS   rT   r   c          
      Z    t                                          ||dd||||           d S )Nr   r9   r   r   )r   r   rq   r   rS   rT   r   r   s          r6   r   zPLSCanonical.__init__?  sH     	%& 	 		
 		
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 		
 		
r8   r   r   r   r   r   r   r   r   r   r   r   r   r   r   s   @r6   r   r     s         ` `D $Cd&A#BDBBB+ * *""5)))) 
 
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r8   r   c                        e Zd ZU dZi ej        Zeed<   dD ]Ze	                    e           	 d
ddddd fd	Z
 xZS )CCAa  Canonical Correlation Analysis, also known as "Mode B" PLS.

    For a comparison between other cross decomposition algorithms, see
    :ref:`sphx_glr_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py`.

    Read more in the :ref:`User Guide <cross_decomposition>`.

    Parameters
    ----------
    n_components : int, default=2
        Number of components to keep. Should be in `[1, min(n_samples,
        n_features, n_targets)]`.

    scale : bool, default=True
        Whether to scale `X` and `Y`.

    max_iter : int, default=500
        The maximum number of iterations of the power method.

    tol : float, default=1e-06
        The tolerance used as convergence criteria in the power method: the
        algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
        than `tol`, where `u` corresponds to the left singular vector.

    copy : bool, default=True
        Whether to copy `X` and `Y` in fit before applying centering, and
        potentially scaling. If False, these operations will be done inplace,
        modifying both arrays.

    Attributes
    ----------
    x_weights_ : ndarray of shape (n_features, n_components)
        The left singular vectors of the cross-covariance matrices of each
        iteration.

    y_weights_ : ndarray of shape (n_targets, n_components)
        The right singular vectors of the cross-covariance matrices of each
        iteration.

    x_loadings_ : ndarray of shape (n_features, n_components)
        The loadings of `X`.

    y_loadings_ : ndarray of shape (n_targets, n_components)
        The loadings of `Y`.

    x_rotations_ : ndarray of shape (n_features, n_components)
        The projection matrix used to transform `X`.

    y_rotations_ : ndarray of shape (n_targets, n_components)
        The projection matrix used to transform `Y`.

    coef_ : ndarray of shape (n_targets, n_features)
        The coefficients of the linear model such that `Y` is approximated as
        `Y = X @ coef_.T + intercept_`.

    intercept_ : ndarray of shape (n_targets,)
        The intercepts of the linear model such that `Y` is approximated as
        `Y = X @ coef_.T + intercept_`.

        .. versionadded:: 1.1

    n_iter_ : list of shape (n_components,)
        Number of iterations of the power method, for each
        component.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

    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

    See Also
    --------
    PLSCanonical : Partial Least Squares transformer and regressor.
    PLSSVD : Partial Least Square SVD.

    Examples
    --------
    >>> from sklearn.cross_decomposition import CCA
    >>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]]
    >>> y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
    >>> cca = CCA(n_components=1)
    >>> cca.fit(X, y)
    CCA(n_components=1)
    >>> X_c, Y_c = cca.transform(X, y)
    r   r   r   Tr:   r;   r   c          
      Z    t                                          ||ddd|||           d S )Nr   rF   r   r   r   r   s         r6   r   zCCA.__init__  sH     	%& 	 		
 		
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 		
r8   r   r  r   s   @r6   r  r  U  s         X Xt $Cd&A#BDBBB8 * *""5)))) 
'+cu4
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r8   r  c                       e Zd ZU dZ eeddd          gdgdgdZeed<   dd
d
ddZ	 e
d
          dd            ZddZddZdS )r   a  Partial Least Square SVD.

    This transformer simply performs a SVD on the cross-covariance matrix
    `X'Y`. It is able to project both the training data `X` and the targets
    `Y`. The training data `X` is projected on the left singular vectors, while
    the targets are projected on the right singular vectors.

    Read more in the :ref:`User Guide <cross_decomposition>`.

    .. versionadded:: 0.8

    Parameters
    ----------
    n_components : int, default=2
        The number of components to keep. Should be in `[1,
        min(n_samples, n_features, n_targets)]`.

    scale : bool, default=True
        Whether to scale `X` and `Y`.

    copy : bool, default=True
        Whether to copy `X` and `Y` in fit before applying centering, and
        potentially scaling. If `False`, these operations will be done inplace,
        modifying both arrays.

    Attributes
    ----------
    x_weights_ : ndarray of shape (n_features, n_components)
        The left singular vectors of the SVD of the cross-covariance matrix.
        Used to project `X` in :meth:`transform`.

    y_weights_ : ndarray of (n_targets, n_components)
        The right singular vectors of the SVD of the cross-covariance matrix.
        Used to project `X` in :meth:`transform`.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

    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

    See Also
    --------
    PLSCanonical : Partial Least Squares transformer and regressor.
    CCA : Canonical Correlation Analysis.

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.cross_decomposition import PLSSVD
    >>> X = np.array([[0., 0., 1.],
    ...               [1., 0., 0.],
    ...               [2., 2., 2.],
    ...               [2., 5., 4.]])
    >>> y = np.array([[0.1, -0.2],
    ...               [0.9, 1.1],
    ...               [6.2, 5.9],
    ...               [11.9, 12.3]])
    >>> pls = PLSSVD(n_components=2).fit(X, y)
    >>> X_c, y_c = pls.transform(X, y)
    >>> X_c.shape, y_c.shape
    ((4, 2), (4, 2))
    rG   Nr   r   r   r   rq   r   r   r   T)rq   r   c                0    || _         || _        || _        d S r>   r  )r   r   rq   r   s       r6   r   zPLSSVD.__init__  s    (
			r8   r   c                 :   t          ||          }t          ||           |                     |t          j        d| j        d          }t          |dt          j        d| j        d          }|j        dk    r|                    dd          }| j	        }t          |j        d	         |j        d         |j        d                   }||k    rt          d
| d| d          t          ||| j                  \  }}| _        | _        | _        | _        t          j        |j        |          }t+          |d          \  }}}	|ddd|f         }|	d|         }	t-          ||	          \  }}	|	j        }
|| _        |
| _        | j        j        d         | _        | S )a  Fit model to data.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training samples.

        y : array-like of shape (n_samples,) or (n_samples, n_targets)
            Targets.

        Y : array-like of shape (n_samples,) or (n_samples, n_targets)
            Targets.

            .. deprecated:: 1.5
               `Y` is deprecated in 1.5 and will be removed in 1.7. Use `y` instead.

        Returns
        -------
        self : object
            Fitted estimator.
        Tr   r   r   Fr   rG   r   r   r   r   r   rc   N)r   r   r   r&   r   r   r   r   r   r   r   rM   r   rv   rq   r   r   r   r   r-   rI   r   r   r   r   r   )r   rP   r   rQ   r   r   rd   re   r0   rg   Vs              r6   r   z
PLSSVD.fit  s   . 'q!,,1%%%*     
 
 * 
 
 
 6Q;;		"a  A
 (qwqz171:qwqzBB***F1A F F#F F F  
 FVq$*F
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B1dlDL$+t{
 F13NNq...1baaa,B2D#4Q7r8   c                    t          ||          }t          |            |                     |t          j        d          }|| j        z
  | j        z  }t          j        || j                  }|nt          |ddt          j                  }|j
        dk    r|                    dd          }|| j        z
  | j        z  }t          j        || j                  }||fS |S )a  
        Apply the dimensionality reduction.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Samples to be transformed.

        y : array-like of shape (n_samples,) or (n_samples, n_targets),                 default=None
            Targets.

        Y : array-like of shape (n_samples,) or (n_samples, n_targets),                 default=None
            Targets.

            .. deprecated:: 1.5
               `Y` is deprecated in 1.5 and will be removed in 1.7. Use `y` instead.

        Returns
        -------
        x_scores : array-like or tuple of array-like
            The transformed data `X_transformed` if `Y is not None`,
            `(X_transformed, Y_transformed)` otherwise.
        F)r#   r   Nr   )r   r   r#   rG   r   )r   r   r   r&   r   r   r   r-   r   r   r   r   r   r   r   )r   rP   r   rQ   Xrr   yrr   s           r6   r   zPLSSVD.transformY  s    4 'q!,,5AA$,$+-6"do..=A#bjQQQAv{{IIb!$$dl"dk1Bvb$/22HX%%r8   c                 V    |                      ||                              ||          S )a  Learn and apply the dimensionality reduction.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training samples.

        y : array-like of shape (n_samples,) or (n_samples, n_targets),                 default=None
            Targets.

        Returns
        -------
        out : array-like or tuple of array-like
            The transformed data `X_transformed` if `Y is not None`,
            `(X_transformed, Y_transformed)` otherwise.
        r   r   s      r6   r   zPLSSVD.fit_transform  r   r8   r   r   r>   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r8   r6   r   r     s         A AH "(AtFCCCD$ $D   4     
 \555D D D 65DL& & & &P. . . . . .r8   r   )r9   r:   r;   Fr   )2r   rN   abcr   r   numbersr   r   numpyr&   scipy.linalgr   baser	   r
   r   r   r   r   
exceptionsr   utilsr   r   utils._param_validationr   r   utils.extmathr   utils.fixesr   r   utils.validationr   r   __all__r   r   r7   ra   rh   rv   r|   r   r   r   r   r   r  r   r   r8   r6   <module>r     s)     ' ' ' ' ' ' ' ' " " " " " " " "                          , + + + + + 8 8 8 8 8 8 8 8 : : : : : : : : $ $ $ $ $ $ 3 3 3 3 3 3 3 3 < < < < < < < <
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