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||d| |ddd|f |fS ||d| |fS dS )a  Orthogonal Matching Pursuit step using the Cholesky decomposition.

    Parameters
    ----------
    X : ndarray of shape (n_samples, n_features)
        Input dictionary. Columns are assumed to have unit norm.

    y : ndarray of shape (n_samples,)
        Input targets.

    n_nonzero_coefs : int
        Targeted number of non-zero elements.

    tol : float, default=None
        Targeted squared error, if not None overrides n_nonzero_coefs.

    copy_X : bool, default=True
        Whether the design matrix X must be copied by the algorithm. A false
        value is only helpful if X is already Fortran-ordered, otherwise a
        copy is made anyway.

    return_path : bool, default=False
        Whether to return every value of the nonzero coefficients along the
        forward path. Useful for cross-validation.

    Returns
    -------
    gamma : ndarray of shape (n_nonzero_coefs,)
        Non-zero elements of the solution.

    idx : ndarray of shape (n_nonzero_coefs,)
        Indices of the positions of the elements in gamma within the solution
        vector.

    coef : ndarray of shape (n_features, n_nonzero_coefs)
        The first k values of column k correspond to the coefficient value
        for the active features at that step. The lower left triangle contains
        garbage. Only returned if ``return_path=True``.

    n_active : int
        Number of active features at convergence.
    Fnrm2swappotrsr   r   Ndtyper   
stacklevelTFZtransloweroverwrite_bZcheck_finiter   r   r!   r"   )copynpasfortranarrayfinfor   epsr   get_blas_funcsr   dotTemptyarangeshape
empty_likeargmaxabswarningswarn	prematureRuntimeWarningsolve_triangularZnormr   )Xyn_nonzero_coefstolcopy_Xreturn_path	min_floatr   r   r   alphaZresidualgamman_activeindicesmax_featuresLcoefslamvLkk_ rJ   =/tmp/pip-unpacked-wheel-zrfo1fqw/sklearn/linear_model/_omp.py_cholesky_omp   sp    +

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6
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t
d| f\}tt| }|}|}d}td}d}|dk	rt| n|}tj||f| jd}d|d< |rt|}tt|}||k s|| d	 |k rtjttd
d q|dkr| |d|f ||d|f< tj|d|d|f ||d|f ddddd |	||d|f d	 }| ||f | }||krtjttd
d qt||||f< nt| ||f |d< |
| | | | \| |< | |< |
| j| | j| \| j|< | j|< || ||  ||< ||< || ||  ||< ||< |d7 }||d|d|f |d| ddd\}}|r||d||d f< t| ddd|f |}|| }|dk	r||7 }t||d| }||8 }t||krqq||krqq|r$||d| |ddd|f |fS ||d| |fS dS )a  Orthogonal Matching Pursuit step on a precomputed Gram matrix.

    This function uses the Cholesky decomposition method.

    Parameters
    ----------
    Gram : ndarray of shape (n_features, n_features)
        Gram matrix of the input data matrix.

    Xy : ndarray of shape (n_features,)
        Input targets.

    n_nonzero_coefs : int
        Targeted number of non-zero elements.

    tol_0 : float, default=None
        Squared norm of y, required if tol is not None.

    tol : float, default=None
        Targeted squared error, if not None overrides n_nonzero_coefs.

    copy_Gram : bool, default=True
        Whether the gram matrix must be copied by the algorithm. A false
        value is only helpful if it is already Fortran-ordered, otherwise a
        copy is made anyway.

    copy_Xy : bool, default=True
        Whether the covariance vector Xy must be copied by the algorithm.
        If False, it may be overwritten.

    return_path : bool, default=False
        Whether to return every value of the nonzero coefficients along the
        forward path. Useful for cross-validation.

    Returns
    -------
    gamma : ndarray of shape (n_nonzero_coefs,)
        Non-zero elements of the solution.

    idx : ndarray of shape (n_nonzero_coefs,)
        Indices of the positions of the elements in gamma within the solution
        vector.

    coefs : ndarray of shape (n_features, n_nonzero_coefs)
        The first k values of column k correspond to the coefficient value
        for the active features at that step. The lower left triangle contains
        garbage. Only returned if ``return_path=True``.

    n_active : int
        Number of active features at convergence.
    r   r   r   r   Nr   g      ?r#   r      r   r   TFr    r$   )r%   r&   r'   flags	writeabler(   r   r)   r   r*   r   r.   lenr-   r0   r1   r2   r3   r4   r5   r6   r7   r   r,   r+   inner)GramXyr:   Ztol_0r;   	copy_Gramcopy_Xyr=   r>   r   r   r   rB   r?   Ztol_currdeltar@   rA   rC   rD   rE   rF   rG   rH   rI   betarJ   rJ   rK   	_gram_omp   s    =



& 
  

$rX   )r:   r;   
precomputer<   r=   return_n_iterc             
   C   s  t | d|d} d}|jdkr(|dd}t |}|jd dkrBd}|dkrj|dkrjttd| jd  d}|dk	r|d	k rtd
|dkr|d	krtd|dkr|| jd krtd|dkr| jd	 | jd k}|r:t| j	| }t
|}t| j	|}	|dk	rtj|d d	d}
nd}
t||	|||
|d|dS |rdt| jd |jd | jd f}nt| jd |jd f}g }t|jd D ]}t| |dd|f ||||d}|r"|\}}}}|dddddt|f }t|j	D ]0\}}|d|d  ||d|d  ||f< qn|\}}}||||f< || q|jd dkr^|d	 }|rrt||fS t|S dS )a&  Orthogonal Matching Pursuit (OMP).

    Solves n_targets Orthogonal Matching Pursuit problems.
    An instance of the problem has the form:

    When parametrized by the number of non-zero coefficients using
    `n_nonzero_coefs`:
    argmin ||y - X\gamma||^2 subject to ||\gamma||_0 <= n_{nonzero coefs}

    When parametrized by error using the parameter `tol`:
    argmin ||\gamma||_0 subject to ||y - X\gamma||^2 <= tol

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

    Parameters
    ----------
    X : ndarray of shape (n_samples, n_features)
        Input data. Columns are assumed to have unit norm.

    y : ndarray of shape (n_samples,) or (n_samples, n_targets)
        Input targets.

    n_nonzero_coefs : int, default=None
        Desired number of non-zero entries in the solution. If None (by
        default) this value is set to 10% of n_features.

    tol : float, default=None
        Maximum norm of the residual. If not None, overrides n_nonzero_coefs.

    precompute : 'auto' or bool, default=False
        Whether to perform precomputations. Improves performance when n_targets
        or n_samples is very large.

    copy_X : bool, default=True
        Whether the design matrix X must be copied by the algorithm. A false
        value is only helpful if X is already Fortran-ordered, otherwise a
        copy is made anyway.

    return_path : bool, default=False
        Whether to return every value of the nonzero coefficients along the
        forward path. Useful for cross-validation.

    return_n_iter : bool, default=False
        Whether or not to return the number of iterations.

    Returns
    -------
    coef : ndarray of shape (n_features,) or (n_features, n_targets)
        Coefficients of the OMP solution. If `return_path=True`, this contains
        the whole coefficient path. In this case its shape is
        (n_features, n_features) or (n_features, n_targets, n_features) and
        iterating over the last axis generates coefficients in increasing order
        of active features.

    n_iters : array-like or int
        Number of active features across every target. Returned only if
        `return_n_iter` is set to True.

    See Also
    --------
    OrthogonalMatchingPursuit : Orthogonal Matching Pursuit model.
    orthogonal_mp_gram : Solve OMP problems using Gram matrix and the product X.T * y.
    lars_path : Compute Least Angle Regression or Lasso path using LARS algorithm.
    sklearn.decomposition.sparse_encode : Sparse coding.

    Notes
    -----
    Orthogonal matching pursuit was introduced in S. Mallat, Z. Zhang,
    Matching pursuits with time-frequency dictionaries, IEEE Transactions on
    Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415.
    (https://www.di.ens.fr/~mallat/papiers/MallatPursuit93.pdf)

    This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad,
    M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal
    Matching Pursuit Technical Report - CS Technion, April 2008.
    https://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf
    r   orderr%   Fr   TN皙?r   Epsilon cannot be negative$The number of atoms must be positive>The number of atoms cannot be more than the number of featuresautor   Zaxis)r:   r;   norms_squaredrT   rU   r=   )r<   r=   )r   ndimZreshaper/   maxint
ValueErrorr&   r+   r,   r'   sumorthogonal_mp_gramzerosrangerL   rP   	enumerateappendsqueeze)r8   r9   r:   r;   rY   r<   r=   rZ   GrS   rd   coefn_iterskoutrI   idxrE   n_iterrA   xrJ   rJ   rK   orthogonal_mp  s|    X


$     ,
rx   )r:   r;   rd   rT   rU   r=   rZ   c                C   sX  t | d|d} t|}|jdkr4|jd dkr4d}|jdkr^|ddtjf }|dk	r^|g}|sj|jjsr| }|dkr|dkrt	dt
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|rJt|	|
fS t|	S dS )a  Gram Orthogonal Matching Pursuit (OMP).

    Solves n_targets Orthogonal Matching Pursuit problems using only
    the Gram matrix X.T * X and the product X.T * y.

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

    Parameters
    ----------
    Gram : ndarray of shape (n_features, n_features)
        Gram matrix of the input data: X.T * X.

    Xy : ndarray of shape (n_features,) or (n_features, n_targets)
        Input targets multiplied by X: X.T * y.

    n_nonzero_coefs : int, default=None
        Desired number of non-zero entries in the solution. If None (by
        default) this value is set to 10% of n_features.

    tol : float, default=None
        Maximum norm of the residual. If not None, overrides n_nonzero_coefs.

    norms_squared : array-like of shape (n_targets,), default=None
        Squared L2 norms of the lines of y. Required if tol is not None.

    copy_Gram : bool, default=True
        Whether the gram matrix must be copied by the algorithm. A false
        value is only helpful if it is already Fortran-ordered, otherwise a
        copy is made anyway.

    copy_Xy : bool, default=True
        Whether the covariance vector Xy must be copied by the algorithm.
        If False, it may be overwritten.

    return_path : bool, default=False
        Whether to return every value of the nonzero coefficients along the
        forward path. Useful for cross-validation.

    return_n_iter : bool, default=False
        Whether or not to return the number of iterations.

    Returns
    -------
    coef : ndarray of shape (n_features,) or (n_features, n_targets)
        Coefficients of the OMP solution. If `return_path=True`, this contains
        the whole coefficient path. In this case its shape is
        (n_features, n_features) or (n_features, n_targets, n_features) and
        iterating over the last axis yields coefficients in increasing order
        of active features.

    n_iters : array-like or int
        Number of active features across every target. Returned only if
        `return_n_iter` is set to True.

    See Also
    --------
    OrthogonalMatchingPursuit : Orthogonal Matching Pursuit model (OMP).
    orthogonal_mp : Solves n_targets Orthogonal Matching Pursuit problems.
    lars_path : Compute Least Angle Regression or Lasso path using
        LARS algorithm.
    sklearn.decomposition.sparse_encode : Generic sparse coding.
        Each column of the result is the solution to a Lasso problem.

    Notes
    -----
    Orthogonal matching pursuit was introduced in G. Mallat, Z. Zhang,
    Matching pursuits with time-frequency dictionaries, IEEE Transactions on
    Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415.
    (https://www.di.ens.fr/~mallat/papiers/MallatPursuit93.pdf)

    This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad,
    M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal
    Matching Pursuit Technical Report - CS Technion, April 2008.
    https://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf
    r   r[   r   TNr^   zSGram OMP needs the precomputed norms in order to evaluate the error sum of squares.r   r_   r`   ra   r   F)rT   rU   r=   )r   r&   Zasarrayre   r/   newaxisrN   rO   r%   rg   rP   rh   rk   r   rl   rX   rm   r,   rn   ro   )rR   rS   r:   r;   rd   rT   rU   r=   rZ   rq   rr   rs   rt   rI   ru   rE   rv   rA   rw   rJ   rJ   rK   rj     sh    W

&
,
rj   c                   @   s   e Zd ZU dZeedddddgeedddddgdgdeedhged	hdgd
Z	e
ed< ddddd	d
ddZdd ZdS )OrthogonalMatchingPursuita  Orthogonal Matching Pursuit model (OMP).

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

    Parameters
    ----------
    n_nonzero_coefs : int, default=None
        Desired number of non-zero entries in the solution. If None (by
        default) this value is set to 10% of n_features.

    tol : float, default=None
        Maximum norm of the residual. If not None, overrides n_nonzero_coefs.

    fit_intercept : bool, default=True
        Whether to calculate the intercept for this model. If set
        to false, no intercept will be used in calculations
        (i.e. data is expected to be centered).

    normalize : bool, default=False
        This parameter is ignored when ``fit_intercept`` is set to False.
        If True, the regressors X will be normalized before regression by
        subtracting the mean and dividing by the l2-norm.
        If you wish to standardize, please use
        :class:`~sklearn.preprocessing.StandardScaler` before calling ``fit``
        on an estimator with ``normalize=False``.

        .. versionchanged:: 1.2
           default changed from True to False in 1.2.

        .. deprecated:: 1.2
            ``normalize`` was deprecated in version 1.2 and will be removed in 1.4.

    precompute : 'auto' or bool, default='auto'
        Whether to use a precomputed Gram and Xy matrix to speed up
        calculations. Improves performance when :term:`n_targets` or
        :term:`n_samples` is very large. Note that if you already have such
        matrices, you can pass them directly to the fit method.

    Attributes
    ----------
    coef_ : ndarray of shape (n_features,) or (n_targets, n_features)
        Parameter vector (w in the formula).

    intercept_ : float or ndarray of shape (n_targets,)
        Independent term in decision function.

    n_iter_ : int or array-like
        Number of active features across every target.

    n_nonzero_coefs_ : int
        The number of non-zero coefficients in the solution. If
        `n_nonzero_coefs` is None and `tol` is None this value is either set
        to 10% of `n_features` or 1, whichever is greater.

    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

    See Also
    --------
    orthogonal_mp : Solves n_targets Orthogonal Matching Pursuit problems.
    orthogonal_mp_gram :  Solves n_targets Orthogonal Matching Pursuit
        problems using only the Gram matrix X.T * X and the product X.T * y.
    lars_path : Compute Least Angle Regression or Lasso path using LARS algorithm.
    Lars : Least Angle Regression model a.k.a. LAR.
    LassoLars : Lasso model fit with Least Angle Regression a.k.a. Lars.
    sklearn.decomposition.sparse_encode : Generic sparse coding.
        Each column of the result is the solution to a Lasso problem.
    OrthogonalMatchingPursuitCV : Cross-validated
        Orthogonal Matching Pursuit model (OMP).

    Notes
    -----
    Orthogonal matching pursuit was introduced in G. Mallat, Z. Zhang,
    Matching pursuits with time-frequency dictionaries, IEEE Transactions on
    Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415.
    (https://www.di.ens.fr/~mallat/papiers/MallatPursuit93.pdf)

    This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad,
    M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal
    Matching Pursuit Technical Report - CS Technion, April 2008.
    https://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf

    Examples
    --------
    >>> from sklearn.linear_model import OrthogonalMatchingPursuit
    >>> from sklearn.datasets import make_regression
    >>> X, y = make_regression(noise=4, random_state=0)
    >>> reg = OrthogonalMatchingPursuit().fit(X, y)
    >>> reg.score(X, y)
    0.9991...
    >>> reg.predict(X[:1,])
    array([-78.3854...])
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            Training data.

        y : array-like of shape (n_samples,) or (n_samples, n_targets)
            Target values. Will be cast to X's dtype if necessary.

        Returns
        -------
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a  Compute the residues on left-out data for a full LARS path.

    Parameters
    ----------
    X_train : ndarray of shape (n_samples, n_features)
        The data to fit the LARS on.

    y_train : ndarray of shape (n_samples)
        The target variable to fit LARS on.

    X_test : ndarray of shape (n_samples, n_features)
        The data to compute the residues on.

    y_test : ndarray of shape (n_samples)
        The target variable to compute the residues on.

    copy : bool, default=True
        Whether X_train, X_test, y_train and y_test should be copied.  If
        False, they may be overwritten.

    fit_intercept : bool, default=True
        Whether to calculate the intercept for this model. If set
        to false, no intercept will be used in calculations
        (i.e. data is expected to be centered).

    normalize : bool, default=False
        This parameter is ignored when ``fit_intercept`` is set to False.
        If True, the regressors X will be normalized before regression by
        subtracting the mean and dividing by the l2-norm.
        If you wish to standardize, please use
        :class:`~sklearn.preprocessing.StandardScaler` before calling ``fit``
        on an estimator with ``normalize=False``.

        .. versionchanged:: 1.2
           default changed from True to False in 1.2.

        .. deprecated:: 1.2
            ``normalize`` was deprecated in version 1.2 and will be removed in 1.4.

    max_iter : int, default=100
        Maximum numbers of iterations to perform, therefore maximum features
        to include. 100 by default.

    Returns
    -------
    residues : ndarray of shape (n_samples, max_features)
        Residues of the prediction on the test data.
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ddZdd ZdS )OrthogonalMatchingPursuitCVa  Cross-validated Orthogonal Matching Pursuit model (OMP).

    See glossary entry for :term:`cross-validation estimator`.

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

    Parameters
    ----------
    copy : bool, default=True
        Whether the design matrix X must be copied by the algorithm. A false
        value is only helpful if X is already Fortran-ordered, otherwise a
        copy is made anyway.

    fit_intercept : bool, default=True
        Whether to calculate the intercept for this model. If set
        to false, no intercept will be used in calculations
        (i.e. data is expected to be centered).

    normalize : bool, default=False
        This parameter is ignored when ``fit_intercept`` is set to False.
        If True, the regressors X will be normalized before regression by
        subtracting the mean and dividing by the l2-norm.
        If you wish to standardize, please use
        :class:`~sklearn.preprocessing.StandardScaler` before calling ``fit``
        on an estimator with ``normalize=False``.

        .. versionchanged:: 1.2
           default changed from True to False in 1.2.

        .. deprecated:: 1.2
            ``normalize`` was deprecated in version 1.2 and will be removed in 1.4.

    max_iter : int, default=None
        Maximum numbers of iterations to perform, therefore maximum features
        to include. 10% of ``n_features`` but at least 5 if available.

    cv : int, cross-validation generator or iterable, default=None
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross-validation,
        - integer, to specify the number of folds.
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, :class:`KFold` is used.

        Refer :ref:`User Guide <cross_validation>` for the various
        cross-validation strategies that can be used here.

        .. versionchanged:: 0.22
            ``cv`` default value if None changed from 3-fold to 5-fold.

    n_jobs : int, default=None
        Number of CPUs to use during the cross validation.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

    verbose : bool or int, default=False
        Sets the verbosity amount.

    Attributes
    ----------
    intercept_ : float or ndarray of shape (n_targets,)
        Independent term in decision function.

    coef_ : ndarray of shape (n_features,) or (n_targets, n_features)
        Parameter vector (w in the problem formulation).

    n_nonzero_coefs_ : int
        Estimated number of non-zero coefficients giving the best mean squared
        error over the cross-validation folds.

    n_iter_ : int or array-like
        Number of active features across every target for the model refit with
        the best hyperparameters got by cross-validating across all folds.

    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

    See Also
    --------
    orthogonal_mp : Solves n_targets Orthogonal Matching Pursuit problems.
    orthogonal_mp_gram : Solves n_targets Orthogonal Matching Pursuit
        problems using only the Gram matrix X.T * X and the product X.T * y.
    lars_path : Compute Least Angle Regression or Lasso path using LARS algorithm.
    Lars : Least Angle Regression model a.k.a. LAR.
    LassoLars : Lasso model fit with Least Angle Regression a.k.a. Lars.
    OrthogonalMatchingPursuit : Orthogonal Matching Pursuit model (OMP).
    LarsCV : Cross-validated Least Angle Regression model.
    LassoLarsCV : Cross-validated Lasso model fit with Least Angle Regression.
    sklearn.decomposition.sparse_encode : Generic sparse coding.
        Each column of the result is the solution to a Lasso problem.

    Notes
    -----
    In `fit`, once the optimal number of non-zero coefficients is found through
    cross-validation, the model is fit again using the entire training set.

    Examples
    --------
    >>> from sklearn.linear_model import OrthogonalMatchingPursuitCV
    >>> from sklearn.datasets import make_regression
    >>> X, y = make_regression(n_features=100, n_informative=10,
    ...                        noise=4, random_state=0)
    >>> reg = OrthogonalMatchingPursuitCV(cv=5).fit(X, y)
    >>> reg.score(X, y)
    0.9991...
    >>> reg.n_nonzero_coefs_
    10
    >>> reg.predict(X[:1,])
    array([-78.3854...])
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            Training data.

        y : array-like of shape (n_samples,)
            Target values. Will be cast to X's dtype if necessary.

        Returns
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