Module ImportFrom alias Import alias identifier ImportFrom alias ImportFrom alias alias alias alias ImportFrom alias ImportFrom alias ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad body Assign TupleStore NameStore AttributeStore NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign TupleStore NameStore NameStore NameStore Call NameLoad NameLoad keyword NameLoad keyword NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad body Expr Str Assign TupleStore NameStore NameStore Call NameLoad NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad Return NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad Return NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam defaults body If NameLoad body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad orelse Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr keyword AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call NameLoad AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr ListLoad If CompareIsNot NameLoad NameLoad body Expr Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body If CompareIs NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad If UnaryOpNot Call NameLoad NameLoad AttributeLoad NameLoad attr body Assign NameStore SubscriptLoad Call AttributeLoad NameLoad attr NameLoad Slice NameLoad Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad Str attr NameLoad Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If Call NameLoad NameLoad NameLoad body If CompareLtLtE Num NameLoad Call AttributeLoad NameLoad attr body Assign NameStore BinOpAdd Call AttributeLoad NameLoad attr ListComp CompareLt NameLoad NameLoad comprehension NameStore Call AttributeLoad NameLoad attr Num orelse Raise Call NameLoad NameLoad If Call NameLoad NameLoad NameLoad body If CompareLt NameLoad Num body Raise Call NameLoad NameLoad orelse If CompareGtE NameLoad AttributeLoad NameLoad attr body If CompareLt AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr orelse Return If CompareLtLtE Num NameLoad AttributeLoad NameLoad attr body Assign AttributeStore NameLoad attr Call NameLoad NameLoad orelse Raise Call NameLoad NameLoad decorator_list AttributeLoad NameLoad attr FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr ExtSlice Slice AttributeLoad NameLoad attr Slice decorator_list AttributeLoad AttributeLoad NameLoad attr attr FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr Slice AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv AttributeLoad NameLoad attr SubscriptLoad Call AttributeLoad NameLoad attr BinOpAdd BinOpMult AttributeLoad NameLoad attr AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr ExtSlice Slice Index NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpAdd Call AttributeLoad AttributeLoad NameLoad attr attr Call AttributeLoad AttributeLoad NameLoad attr attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad AttributeLoad NameLoad attr attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad AttributeLoad NameLoad attr attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str If CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body If CompareNotEq AttributeLoad AttributeLoad NameLoad attr attr Num body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr orelse Assign NameStore Num orelse Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr TupleLoad SubscriptLoad AttributeLoad NameLoad attr Slice AttributeLoad NameLoad attr AttributeLoad NameLoad attr attr Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr If Call AttributeLoad NameLoad attr NameLoad Num body Raise Call NameLoad Str Return BinOpDiv Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad Num body Expr Str If NameLoad body Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Return BinOpAdd BinOpMult NameLoad SubscriptLoad AttributeLoad NameLoad attr Index NameLoad AttributeLoad NameLoad attr orelse Return SubscriptLoad AttributeLoad NameLoad attr Index NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If CompareGt NameLoad AttributeLoad NameLoad attr body Raise Call NameLoad Call AttributeLoad Str attr AttributeLoad NameLoad attr orelse Assign NameStore Call AttributeLoad NameLoad attr TupleLoad NameLoad AttributeLoad NameLoad attr keyword AttributeLoad AttributeLoad NameLoad attr attr Assign SubscriptStore NameLoad ExtSlice Ellipsis Slice NameLoad NameLoad Assign NameStore NameLoad If NameLoad body AugAssignMult NameStore BinOpPow AttributeLoad NameLoad attr Num Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad NameLoad ExtSlice Index NameLoad Slice keyword NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str If CompareIs NameLoad NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr NameLoad If CompareLt AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Slice NameLoad attr Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr TupleLoad AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Slice AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Slice NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr Return Call AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore AttributeLoad SubscriptLoad Call AttributeLoad AttributeLoad NameLoad attr attr Call AttributeLoad NameLoad attr TupleLoad AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr Index Num attr Assign AttributeStore NameLoad attr SubscriptLoad NameLoad ExtSlice Slice AttributeLoad NameLoad attr Slice Assign NameStore BinOpSub SubscriptLoad AttributeLoad NameLoad attr Index Num AttributeLoad NameLoad attr If CompareLt NameLoad AttributeLoad NameLoad attr body If CompareLt AttributeLoad NameLoad attr NameLoad body Assign NameStore AttributeLoad NameLoad attr orelse Assign NameStore NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad If CompareLt NameLoad NameLoad body Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr SubscriptLoad NameLoad ExtSlice Slice AttributeLoad NameLoad attr Slice decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num NameLoad body Expr Str Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign TupleStore NameStore NameStore NameStore Call NameLoad NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr keyword AttributeLoad NameLoad attr keyword NameLoad Assign NameStore CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad AugAssignAdd AttributeStore NameLoad attr NameLoad If NameLoad body Assign AttributeStore NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad Str Str Num NameLoad Str Num Str Str Num NameLoad Str Num Str Str TupleLoad Num Num NameLoad Str Num body Expr Str ImportFrom alias Return Call NameLoad Call NameLoad AttributeLoad NameLoad attr ListLoad AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword Str keyword Str keyword Str keyword ListLoad Num BinOpSub AttributeLoad NameLoad attr Num keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults TupleLoad Num Num Str body Expr Str TryExcept body ImportFrom alias handlers ExceptHandler body ImportFrom alias Raise Call NameLoad Expr Call NameLoad keyword Call NameLoad AttributeLoad NameLoad attr keyword ListLoad AttributeLoad NameLoad attr keyword ListLoad Str keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad Str Str Num NameLoad Str Num Str Str Num NameLoad Str Num Str Str TupleLoad Num Num NameLoad Str Num body Expr Str ImportFrom alias Return Call NameLoad Call NameLoad AttributeLoad NameLoad attr ListLoad Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword Str keyword Str keyword Str keyword ListLoad Num BinOpSub AttributeLoad NameLoad attr Num keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults TupleLoad Num Num Str body Expr Str TryExcept body ImportFrom alias handlers ExceptHandler body ImportFrom alias Raise Call NameLoad Expr Call NameLoad keyword Call NameLoad AttributeLoad NameLoad attr keyword ListLoad Call AttributeLoad NameLoad attr keyword ListLoad Str keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad Str Str Num NameLoad Str Num Str Str Num NameLoad Str Num Str Str TupleLoad Num Num NameLoad Str Num body Expr Str ImportFrom alias Return Call NameLoad Call NameLoad AttributeLoad NameLoad attr ListLoad Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword Str keyword Str keyword Str keyword ListLoad Num BinOpSub AttributeLoad NameLoad attr Num keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults TupleLoad Num Num Str body Expr Str TryExcept body ImportFrom alias handlers ExceptHandler body ImportFrom alias Raise Call NameLoad Expr Call NameLoad keyword Call NameLoad AttributeLoad NameLoad attr keyword ListLoad Call AttributeLoad NameLoad attr keyword ListLoad Str keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad Str attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad AttributeLoad NameLoad attr attr Return NameLoad decorator_list decorator_list ClassDef bases NameLoad NameLoad body Expr Str FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore Call NameLoad NameLoad keyword NameLoad keyword NameLoad keyword NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Expr Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad Expr Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad keyword NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Return NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad keyword Call AttributeLoad NameLoad attr keyword NameLoad keyword NameLoad Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Return NameLoad decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list Call NameLoad keyword Str FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list Call NameLoad keyword Str FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list Call NameLoad keyword Str FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Return Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad decorator_list Call NameLoad keyword Str FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad Num body Return Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad keyword NameLoad decorator_list Call NameLoad keyword Str FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list Call NameLoad keyword Str FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad Num body Expr Str Return Call AttributeLoad AttributeLoad NameLoad attr attr Call AttributeLoad NameLoad attr NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Return Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num NameLoad body Expr Str Assign NameStore Call NameLoad NameLoad keyword NameLoad keyword NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Expr Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad Str attr Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad AttributeLoad NameLoad attr attr Return NameLoad decorator_list decorator_list
N/A __future__ division N/A numpy np menpo.base doc_inherit menpo.math pca pcacov ipca as_matrix linear MeanLinearVectorModel vectorizable VectorizableBackedModel PCAVectorModel N/A MeanLinearVectorModel N/A N/A 
    A :map:`MeanLinearModel` where components are Principal Components.

    Principal Component Analysis (PCA) by eigenvalue decomposition of the
    data's scatter matrix. For details of the implementation of PCA, see
    :map:`pca`.

    Parameters
    ----------
    samples : `ndarray` or `list` or `iterable` of `ndarray`
        List or iterable of numpy arrays to build the model from, or an
        existing data matrix.
    centre : `bool`, optional
        When ``True`` (default) PCA is performed after mean centering the data.
        If ``False`` the data is assumed to be centred, and the mean will be
        ``0``.
    n_samples : `int`, optional
        If provided then ``samples`` must be an iterator that yields
        ``n_samples``. If not provided then samples has to be a `list` (so we
        know how large the data matrix needs to be).
    max_n_components : `int`, optional
        The maximum number of components to keep in the model. Any components
        above and beyond this one are discarded.
    inplace : `bool`, optional
        If ``True`` the data matrix is modified in place. Otherwise, the data
        matrix is copied.
     __init__ N/A N/A self samples centre n_samples max_n_components inplace N/A True None None True N/A N/A N/A data N/A self n_samples N/A N/A self _data_to_matrix samples n_samples N/A N/A e_vectors e_values mean N/A pca data centre centre inplace inplace N/A N/A N/A self _constructor_helper eigenvalues e_values eigenvectors e_vectors mean mean centred centre max_n_components max_n_components N/A init_from_covariance_matrix N/A N/A cls C mean n_samples centred is_inverse max_n_components N/A True False None N/A N/A 
        Build the Principal Component Analysis (PCA) by eigenvalue
        decomposition of the provided covariance/scatter matrix. For details
        of the implementation of PCA, see :map:`pcacov`.

        Parameters
        ----------
        C : ``(n_features, n_features)`` `ndarray` or `scipy.sparse`
            The Covariance/Scatter matrix. If it is a precision matrix (inverse
            covariance), then set `is_inverse=True`.
        mean : ``(n_features, )`` `ndarray`
            The mean vector.
        n_samples : `int`
            The number of samples used to generate the covariance matrix.
        centred : `bool`, optional
            When ``True`` we assume that the data were centered before
            computing the covariance matrix.
        is_inverse : `bool`, optional
            It ``True``, then it is assumed that `C` is a precision matrix (
            inverse covariance). Thus, the eigenvalues will be inverted. If
            ``False``, then it is assumed that `C` is a covariance matrix.
        max_n_components : `int`, optional
            The maximum number of components to keep in the model. Any
            components above and beyond this one are discarded.
         N/A N/A e_vectors e_values N/A pcacov C is_inverse is_inverse N/A model N/A N/A PCAModel __new__ cls N/A N/A model n_samples n_samples N/A N/A N/A model _constructor_helper eigenvalues e_values eigenvectors e_vectors mean mean centred centred max_n_components max_n_components N/A model N/A classmethod init_from_components N/A N/A cls components eigenvalues mean n_samples centred max_n_components N/A None N/A N/A 
        Build the Principal Component Analysis (PCA) using the provided
        components (eigenvectors) and eigenvalues.

        Parameters
        ----------
        components : ``(n_components, n_features)`` `ndarray`
            The eigenvectors to be used.
        eigenvalues : ``(n_components, )`` `ndarray`
            The corresponding eigenvalues.
        mean : ``(n_features, )`` `ndarray`
            The mean vector.
        n_samples : `int`
            The number of samples used to generate the eigenvectors.
        centred : `bool`, optional
            When ``True`` we assume that the data were centered before
            computing the eigenvectors.
        max_n_components : `int`, optional
            The maximum number of components to keep in the model. Any
            components above and beyond this one are discarded.
         N/A model N/A N/A PCAModel __new__ cls N/A N/A model n_samples n_samples N/A N/A N/A model _constructor_helper eigenvalues eigenvalues eigenvectors components mean mean centred centred max_n_components max_n_components N/A model N/A classmethod _constructor_helper N/A N/A self eigenvalues eigenvectors mean centred max_n_components N/A N/A N/A centred N/A N/A N/A N/A MeanLinearVectorModel __init__ self eigenvectors mean N/A N/A N/A N/A MeanLinearVectorModel __init__ self eigenvectors N/A N/A np zeros N/A mean shape dtype N/A mean dtype N/A N/A self centred centred N/A N/A self _eigenvalues eigenvalues N/A N/A self _n_active_components N/A int N/A self n_components N/A N/A self _trimmed_eigenvalues N/A N/A np array N/A N/A N/A max_n_components None N/A N/A N/A N/A self trim_components max_n_components N/A _data_to_matrix N/A N/A self data n_samples N/A N/A N/A N/A n_samples None N/A N/A n_samples N/A len data N/A N/A N/A isinstance data N/A np ndarray N/A N/A data N/A N/A N/A np array data N/A n_samples N/A N/A data n_samples N/A n_active_components N/A N/A self N/A N/A N/A 
        The number of components currently in use on this model.

        :type: `int`
         N/A N/A self _n_active_components N/A property n_active_components N/A N/A self value N/A N/A N/A 
        Sets an updated number of active components on this model. The number
        of active components represents the number of principal components
        that will be used for generative purposes. Note that this therefore
        makes the model stateful. Also note that setting the number of
        components will not affect memory unless :meth:`trim_components`
        is called.

        Parameters
        ----------
        value : `int`
            The new number of active components.

        Raises
        ------
        ValueError
            Tried setting n_active_components to {value} - value needs to be a
            float 0.0 < n_components < self._total_kept_variance_ratio ({}) or
            an integer 1 < n_components < self.n_components ({})
         N/A err_str N/A N/A Tried setting n_active_components to {} - value needs to be a float 0.0 < n_components < self._total_kept_variance_ratio ({}) or an integer 1 < n_components < self.n_components ({}) format value N/A N/A self _total_variance_ratio N/A self n_components N/A N/A isinstance value float N/A N/A N/A 0.0 value N/A N/A self _total_variance_ratio N/A N/A value N/A N/A N/A np sum N/A N/A r value N/A r N/A N/A self _total_eigenvalues_cumulative_ratio 1 N/A N/A N/A ValueError err_str N/A N/A isinstance value int N/A N/A N/A value 1 N/A N/A N/A ValueError err_str N/A N/A N/A value N/A self n_components N/A N/A N/A N/A self n_active_components N/A self n_components N/A N/A value N/A self n_components N/A N/A N/A N/A 0 value N/A self n_components N/A N/A N/A self _n_active_components N/A int value N/A N/A N/A ValueError err_str N/A N/A n_active_components setter components N/A N/A self N/A N/A N/A 
        Returns the active components of the model.

        :type: ``(n_active_components, n_features)`` `ndarray`
         N/A N/A N/A self _components N/A N/A N/A self n_active_components N/A N/A N/A N/A MeanLinearVectorModel components getter eigenvalues N/A N/A self N/A N/A N/A 
        Returns the eigenvalues associated with the active components of the
        model, i.e. the amount of variance captured by each active component,
        sorted form largest to smallest.

        :type: ``(n_active_components,)`` `ndarray`
         N/A N/A N/A self _eigenvalues N/A N/A self n_active_components N/A property whitened_components N/A N/A self N/A N/A N/A 
        Returns the active components of the model, whitened.

        Returns
        -------
        whitened_components : ``(n_active_components, n_features)`` `ndarray`
            The whitened components.
         N/A N/A N/A self components N/A N/A N/A np sqrt N/A N/A N/A self eigenvalues N/A self n_samples N/A N/A self noise_variance N/A N/A N/A None N/A original_variance N/A N/A self N/A N/A N/A 
        Returns the total amount of variance captured by the original model,
        i.e. the amount of variance present on the original samples.

        Returns
        -------
        optional_variance : `float`
            The variance captured by the model.
         N/A N/A N/A N/A N/A self _eigenvalues sum N/A N/A N/A self _trimmed_eigenvalues sum N/A variance N/A N/A self N/A N/A N/A 
        Returns the total amount of variance retained by the active
        components.

        Returns
        -------
        variance : `float`
            Total variance captured by the active components.
         N/A N/A N/A N/A self eigenvalues sum N/A _total_variance N/A N/A self N/A N/A N/A 
        Returns the total amount of variance retained by all components
        (active and inactive). Useful when the model has been trimmed.

        Returns
        -------
        total_variance : `float`
            Total variance captured by all components.
         N/A N/A N/A N/A self _eigenvalues sum N/A variance_ratio N/A N/A self N/A N/A N/A 
        Returns the ratio between the amount of variance retained by the
        active components and the total amount of variance present on the
        original samples.

        Returns
        -------
        variance_ratio : `float`
            Ratio of active components variance and total variance present
            in original samples.
         N/A N/A N/A N/A self variance N/A N/A self original_variance N/A _total_variance_ratio N/A N/A self N/A N/A N/A 
        Returns the ratio between the total amount of variance retained by
        all components (active and inactive) and the total amount of variance
        present on the original samples.

        Returns
        -------
        total_variance_ratio : `float`
            Ratio of total variance over the original variance.
         N/A N/A N/A N/A self _total_variance N/A N/A self original_variance N/A eigenvalues_ratio N/A N/A self N/A N/A N/A 
        Returns the ratio between the variance captured by each active
        component and the total amount of variance present on the original
        samples.

        Returns
        -------
        eigenvalues_ratio : ``(n_active_components,)`` `ndarray`
            The active eigenvalues array scaled by the original variance.
         N/A N/A N/A self eigenvalues N/A N/A self original_variance N/A _total_eigenvalues_ratio N/A N/A self N/A N/A N/A 
        Returns the ratio between the variance captured by each active
        component and the total amount of variance present on the original
        samples.

        Returns
        -------
        total_eigenvalues_ratio : ``(n_components,)`` `ndarray`
            Array of eigenvalues scaled by the original variance.
         N/A N/A N/A self _eigenvalues N/A N/A self original_variance N/A eigenvalues_cumulative_ratio N/A N/A self N/A N/A N/A 
        Returns the cumulative ratio between the variance captured by the
        active components and the total amount of variance present on the
        original samples.

        Returns
        -------
        eigenvalues_cumulative_ratio : ``(n_active_components,)`` `ndarray`
            Array of cumulative eigenvalues.
         N/A N/A N/A np cumsum N/A N/A self eigenvalues_ratio N/A _total_eigenvalues_cumulative_ratio N/A N/A self N/A N/A N/A 
        Returns the cumulative ratio between the variance captured by the
        active components and the total amount of variance present on the
        original samples.

        Returns
        -------
        total_eigenvalues_cumulative_ratio : ``(n_active_components,)`` `ndarray`
            Array of total cumulative eigenvalues.
         N/A N/A N/A np cumsum N/A N/A self _total_eigenvalues_ratio N/A noise_variance N/A N/A self N/A N/A N/A 
        Returns the average variance captured by the inactive components,
        i.e. the sample noise assumed in a Probabilistic PCA formulation.

        If all components are active, then ``noise_variance == 0.0``.

        Returns
        -------
        noise_variance : `float`
            The mean variance of the inactive components.
         N/A N/A N/A self n_active_components N/A self n_components N/A N/A N/A N/A N/A self _trimmed_eigenvalues size 0 N/A N/A noise_variance N/A N/A N/A self _trimmed_eigenvalues mean N/A N/A noise_variance 0.0 N/A N/A noise_variance N/A N/A N/A N/A np hstack N/A N/A N/A self _eigenvalues N/A N/A self n_active_components N/A self _trimmed_eigenvalues mean N/A noise_variance N/A noise_variance_ratio N/A N/A self N/A N/A N/A 
        Returns the ratio between the noise variance and the total amount of
        variance present on the original samples.

        Returns
        -------
        noise_variance_ratio : `float`
            The ratio between the noise variance and the variance present
            in the original samples.
         N/A N/A N/A N/A self noise_variance N/A N/A self original_variance N/A inverse_noise_variance N/A N/A self N/A N/A N/A 
        Returns the inverse of the noise variance.

        Returns
        -------
        inverse_noise_variance : `float`
            Inverse of the noise variance.

        Raises
        ------
        ValueError
            If ``noise_variance() == 0``
         N/A noise_variance N/A N/A self noise_variance N/A N/A N/A np allclose noise_variance 0 N/A N/A N/A ValueError noise variance is effectively 0 - cannot take the inverse N/A N/A 1.0 noise_variance N/A component N/A N/A self index with_mean scale N/A True 1.0 N/A N/A 
        A particular component of the model, in vectorized form.

        Parameters
        ----------
        index : `int`
            The component that is to be returned
        with_mean: `bool`, optional
            If ``True``, the component will be blended with the mean vector
            before being returned. If not, the component is returned on it's
            own.
        scale : `float`, optional
            A scale factor that should be applied to the component. Only
            valid in the case where with_mean is ``True``. The scale is applied
            in units of standard deviations (so a scale of ``1.0``
            `with_mean` visualizes the mean plus ``1`` std. dev of the component
            in question).

        Returns
        -------
        component_vector : ``(n_features,)`` `ndarray`
            The component vector of the given index.
         N/A with_mean N/A N/A scaled_eigval N/A scale N/A N/A np sqrt N/A N/A self eigenvalues N/A index N/A N/A N/A scaled_eigval N/A N/A self components N/A index N/A self _mean N/A N/A N/A N/A self components N/A index N/A instance_vectors N/A N/A self weights normalized_weights N/A False N/A N/A 
        Creates new vectorized instances of the model using the first
        components in a particular weighting.

        Parameters
        ----------
        weights : ``(n_vectors, n_weights)`` `ndarray` or `list` of `lists`
            The weightings for the first `n_weights` components that
            should be used per instance that is to be produced

            ``weights[i, j]`` is the linear contribution of the j'th
            principal component to the i'th instance vector produced. Note
            that if ``n_weights < n_components``, only the first ``n_weight``
            components are used in the reconstruction (i.e. unspecified
            weights are implicitly ``0``).
        normalized_weights : `bool`, optional
            If ``True``, the weights are assumed to be normalized w.r.t the
            eigenvalues. This can be easier to create unique instances by
            making the weights more interpretable.

        Returns
        -------
        vectors : ``(n_vectors, n_features)`` `ndarray`
            The instance vectors for the weighting provided.

        Raises
        ------
        ValueError
            If n_weights > n_components
         N/A weights N/A N/A np asarray weights N/A N/A n_instances n_weights N/A weights shape N/A N/A n_weights N/A self n_active_components N/A N/A N/A ValueError N/A N/A Number of weightings cannot be greater than {} format N/A self n_active_components N/A N/A full_weights N/A N/A np zeros N/A n_instances N/A self n_active_components dtype N/A N/A self _components dtype N/A N/A full_weights N/A N/A N/A n_weights weights N/A weights full_weights N/A normalized_weights N/A N/A weights N/A N/A self eigenvalues 0.5 N/A N/A N/A self _instance_vectors_for_full_weights weights N/A instance N/A N/A self weights normalized_weights N/A False N/A N/A 
        Creates a new vector instance of the model by weighting together the
        components.

        Parameters
        ----------
        weights : ``(n_weights,)`` `ndarray` or `list`
            The weightings for the first `n_weights` components that should be
            used.

            ``weights[j]`` is the linear contribution of the j'th principal
            component to the instance vector.
        normalized_weights : `bool`, optional
            If ``True``, the weights are assumed to be normalized w.r.t the
            eigenvalues. This can be easier to create unique instances by
            making the weights more interpretable.

        Returns
        -------
        vector : ``(n_features,)`` `ndarray`
            The instance vector for the weighting provided.
         N/A weights N/A N/A np asarray weights N/A N/A N/A N/A N/A self instance_vectors N/A weights N/A N/A None N/A normalized_weights normalized_weights flatten N/A trim_components N/A N/A self n_components N/A None N/A N/A 
        Permanently trims the components down to a certain amount. The number of
        active components will be automatically reset to this particular value.

        This will reduce `self.n_components` down to `n_components`
        (if ``None``, `self.n_active_components` will be used), freeing up
        memory in the process.

        Once the model is trimmed, the trimmed components cannot be recovered.

        Parameters
        ----------
        n_components: `int` >= ``1`` or `float` > ``0.0`` or ``None``, optional
            The number of components that are kept or else the amount (ratio)
            of variance that is kept. If ``None``, `self.n_active_components` is
            used.

        Notes
        -----
        In case `n_components` is greater than the total number of components or
        greater than the amount of variance currently kept, this method does
        not perform any action.
         N/A N/A n_components None N/A N/A n_components N/A self n_active_components N/A N/A self n_active_components n_components N/A N/A N/A self n_active_components N/A self n_components N/A N/A nac N/A self n_active_components N/A N/A self _components N/A N/A N/A N/A self _components N/A nac copy N/A N/A self _trimmed_eigenvalues N/A N/A np hstack N/A N/A self _trimmed_eigenvalues N/A N/A self _eigenvalues N/A N/A self n_active_components N/A N/A self _eigenvalues N/A N/A N/A N/A self _eigenvalues N/A nac copy N/A project_whitened N/A N/A self vector_instance N/A N/A N/A 
        Projects the `vector_instance` onto the whitened components,
        retrieving the whitened linear weightings.

        Parameters
        ----------
        vector_instance : ``(n_features,)`` `ndarray`
            A novel vector.

        Returns
        -------
        projected : ``(n_features,)`` `ndarray`
            A vector of whitened linear weightings
         N/A whitened_components N/A N/A self whitened_components N/A N/A N/A np dot vector_instance N/A whitened_components T N/A orthonormalize_against_inplace N/A N/A self linear_model N/A N/A N/A 
        Enforces that the union of this model's components and another are
        both mutually orthonormal.

        Note that the model passed in is guaranteed to not have it's number
        of available components changed. This model, however, may loose some
        dimensionality due to reaching a degenerate state.

        The removed components will always be trimmed from the end of
        components (i.e. the components which capture the least variance).
        If trimming is performed, `n_components` and `n_available_components`
        would be altered - see :meth:`trim_components` for details.

        Parameters
        ----------
        linear_model : :map:`LinearModel`
            A second linear model to orthonormalize this against.
         N/A Q N/A N/A N/A N/A N/A np linalg qr N/A N/A np hstack N/A N/A N/A linear_model _components T N/A N/A self _components T N/A 0 T N/A N/A linear_model components N/A Q N/A N/A N/A linear_model n_components N/A N/A n_available_components N/A N/A N/A Q shape N/A 0 N/A linear_model n_components N/A N/A n_available_components N/A self n_components N/A N/A N/A N/A self n_active_components n_available_components N/A N/A n_active_components N/A self n_active_components N/A N/A n_active_components n_available_components N/A N/A N/A self trim_components n_components n_available_components N/A N/A n_active_components n_available_components N/A N/A N/A self n_active_components n_active_components N/A N/A self components N/A Q N/A N/A N/A linear_model n_components N/A N/A increment N/A N/A self data n_samples forgetting_factor verbose N/A None 1.0 False N/A N/A 
        Update the eigenvectors, eigenvalues and mean vector of this model
        by performing incremental PCA on the given samples.

        Parameters
        ----------
        samples : `list` of :map:`Vectorizable`
            List of new samples to update the model from.
        n_samples : `int`, optional
            If provided then ``samples``  must be an iterator that yields
            ``n_samples``. If not provided then samples has to be a
            list (so we know how large the data matrix needs to be).
        forgetting_factor : ``[0.0, 1.0]`` `float`, optional
            Forgetting factor that weights the relative contribution of new
            samples vs old samples. If 1.0, all samples are weighted equally
            and, hence, the results is the exact same as performing batch
            PCA on the concatenated list of old and new simples. If <1.0,
            more emphasis is put on the new samples. See [1] for details.

        References
        ----------
        .. [1] David Ross, Jongwoo Lim, Ruei-Sung Lin, Ming-Hsuan Yang.
           "Incremental Learning for Robust Visual Tracking". IJCV, 2007.
         N/A N/A data n_new_samples N/A N/A self _data_to_matrix data n_samples N/A N/A e_vectors e_values m_vector N/A ipca data N/A self _components N/A self _eigenvalues N/A self n_samples m_a N/A self _mean f forgetting_factor N/A reset N/A N/A self n_active_components N/A self n_components N/A N/A self _mean m_vector N/A N/A self _components e_vectors N/A N/A self _eigenvalues e_values N/A N/A self n_samples n_new_samples N/A reset N/A N/A N/A self n_active_components N/A self n_components N/A plot_eigenvalues N/A N/A self figure_id new_figure render_lines line_colour line_style line_width render_markers marker_style marker_size marker_face_colour marker_edge_colour marker_edge_width render_axes axes_font_name axes_font_size axes_font_style axes_font_weight figure_size render_grid grid_line_style grid_line_width N/A None False True b - 2 True o 6 b k 1.0 True sans-serif 10 normal normal N/A 10 6 True -- 0.5 N/A N/A 
        Plot of the eigenvalues.

        Parameters
        ----------
        figure_id : `object`, optional
            The id of the figure to be used.
        new_figure : `bool`, optional
            If ``True``, a new figure is created.
        render_lines : `bool`, optional
            If ``True``, the line will be rendered.
        line_colour : See Below, optional
            The colour of the lines.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        line_style : {``-``, ``--``, ``-.``, ``:``}, optional
            The style of the lines.
        line_width : `float`, optional
            The width of the lines.
        render_markers : `bool`, optional
            If ``True``, the markers will be rendered.
        marker_style : See Below, optional
            The style of the markers.
            Example options ::

                {``.``, ``,``, ``o``, ``v``, ``^``, ``<``, ``>``, ``+``,
                 ``x``, ``D``, ``d``, ``s``, ``p``, ``*``, ``h``, ``H``,
                 ``1``, ``2``, ``3``, ``4``, ``8``}

        marker_size : `int`, optional
            The size of the markers in points.
        marker_face_colour : See Below, optional
            The face (filling) colour of the markers.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        marker_edge_colour : See Below, optional
            The edge colour of the markers.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        marker_edge_width : `float`, optional
            The width of the markers' edge.
        render_axes : `bool`, optional
            If ``True``, the axes will be rendered.
        axes_font_name : See Below, optional
            The font of the axes.
            Example options ::

                {``serif``, ``sans-serif``, ``cursive``, ``fantasy``,
                 ``monospace``}

        axes_font_size : `int`, optional
            The font size of the axes.
        axes_font_style : {``normal``, ``italic``, ``oblique``}, optional
            The font style of the axes.
        axes_font_weight : See Below, optional
            The font weight of the axes.
            Example options ::

                {``ultralight``, ``light``, ``normal``, ``regular``,
                 ``book``, ``medium``, ``roman``, ``semibold``,
                 ``demibold``, ``demi``, ``bold``, ``heavy``,
                 ``extra bold``, ``black``}

        figure_size : (`float`, `float`) or ``None``, optional
            The size of the figure in inches.
        render_grid : `bool`, optional
            If ``True``, the grid will be rendered.
        grid_line_style : {``-``, ``--``, ``-.``, ``:``}, optional
            The style of the grid lines.
        grid_line_width : `float`, optional
            The width of the grid lines.

        Returns
        -------
        viewer : :map:`MatplotlibRenderer`
            The viewer object.
         menpo.visualize plot_curve N/A N/A plot_curve N/A range N/A self n_active_components N/A N/A self eigenvalues figure_id figure_id new_figure new_figure legend_entries None title Eigenvalues x_label Component Number y_label Eigenvalue axes_x_limits N/A 0 N/A N/A self n_active_components 1 axes_y_limits None axes_x_ticks None axes_y_ticks None render_lines render_lines line_colour line_colour line_style line_style line_width line_width render_markers render_markers marker_style marker_style marker_size marker_size marker_face_colour marker_face_colour marker_edge_colour marker_edge_colour marker_edge_width marker_edge_width render_legend False render_axes render_axes axes_font_name axes_font_name axes_font_size axes_font_size axes_font_style axes_font_style axes_font_weight axes_font_weight figure_size figure_size render_grid render_grid grid_line_style grid_line_style grid_line_width grid_line_width N/A plot_eigenvalues_widget N/A N/A self figure_size style N/A N/A 10 6 coloured N/A N/A 
        Plot of the eigenvalues using an interactive widget.

        Parameters
        ----------
        figure_size : (`float`, `float`) or ``None``, optional
            The size of the figure in inches.
        style : {``'coloured'``, ``'minimal'``}, optional
            If ``'coloured'``, then the style of the widget will be coloured. If
            ``minimal``, then the style is simple using black and white colours.
         N/A N/A menpowidgets plot_graph N/A N/A N/A menpo.visualize.base MenpowidgetsMissingError N/A N/A MenpowidgetsMissingError N/A N/A plot_graph x_axis N/A range N/A self n_active_components y_axis N/A N/A self eigenvalues legend_entries N/A Eigenvalues figure_size figure_size style style N/A plot_eigenvalues_ratio N/A N/A self figure_id new_figure render_lines line_colour line_style line_width render_markers marker_style marker_size marker_face_colour marker_edge_colour marker_edge_width render_axes axes_font_name axes_font_size axes_font_style axes_font_weight figure_size render_grid grid_line_style grid_line_width N/A None False True b - 2 True o 6 b k 1.0 True sans-serif 10 normal normal N/A 10 6 True -- 0.5 N/A N/A 
        Plot of the variance ratio captured by the eigenvalues.

        Parameters
        ----------
        figure_id : `object`, optional
            The id of the figure to be used.
        new_figure : `bool`, optional
            If ``True``, a new figure is created.
        render_lines : `bool`, optional
            If ``True``, the line will be rendered.
        line_colour : See Below, optional
            The colour of the lines.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        line_style : {``-``, ``--``, ``-.``, ``:``}, optional
            The style of the lines.
        line_width : `float`, optional
            The width of the lines.
        render_markers : `bool`, optional
            If ``True``, the markers will be rendered.
        marker_style : See Below, optional
            The style of the markers.
            Example options ::

                {``.``, ``,``, ``o``, ``v``, ``^``, ``<``, ``>``, ``+``,
                 ``x``, ``D``, ``d``, ``s``, ``p``, ``*``, ``h``, ``H``,
                 ``1``, ``2``, ``3``, ``4``, ``8``}

        marker_size : `int`, optional
            The size of the markers in points.
        marker_face_colour : See Below, optional
            The face (filling) colour of the markers.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        marker_edge_colour : See Below, optional
            The edge colour of the markers.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        marker_edge_width : `float`, optional
            The width of the markers' edge.
        render_axes : `bool`, optional
            If ``True``, the axes will be rendered.
        axes_font_name : See Below, optional
            The font of the axes.
            Example options ::

                {``serif``, ``sans-serif``, ``cursive``, ``fantasy``,
                 ``monospace``}

        axes_font_size : `int`, optional
            The font size of the axes.
        axes_font_style : {``normal``, ``italic``, ``oblique``}, optional
            The font style of the axes.
        axes_font_weight : See Below, optional
            The font weight of the axes.
            Example options ::

                {``ultralight``, ``light``, ``normal``, ``regular``,
                 ``book``, ``medium``, ``roman``, ``semibold``,
                 ``demibold``, ``demi``, ``bold``, ``heavy``,
                 ``extra bold``, ``black``}

        figure_size : (`float`, `float`) or `None`, optional
            The size of the figure in inches.
        render_grid : `bool`, optional
            If ``True``, the grid will be rendered.
        grid_line_style : {``-``, ``--``, ``-.``, ``:``}, optional
            The style of the grid lines.
        grid_line_width : `float`, optional
            The width of the grid lines.

        Returns
        -------
        viewer : :map:`MatplotlibRenderer`
            The viewer object.
         menpo.visualize plot_curve N/A N/A plot_curve N/A range N/A self n_active_components N/A N/A N/A self eigenvalues_ratio figure_id figure_id new_figure new_figure legend_entries None title Variance Ratio of Eigenvalues x_label Component Number y_label Variance Ratio axes_x_limits N/A 0 N/A N/A self n_active_components 1 axes_y_limits None axes_x_ticks None axes_y_ticks None render_lines render_lines line_colour line_colour line_style line_style line_width line_width render_markers render_markers marker_style marker_style marker_size marker_size marker_face_colour marker_face_colour marker_edge_colour marker_edge_colour marker_edge_width marker_edge_width render_legend False render_axes render_axes axes_font_name axes_font_name axes_font_size axes_font_size axes_font_style axes_font_style axes_font_weight axes_font_weight figure_size figure_size render_grid render_grid grid_line_style grid_line_style grid_line_width grid_line_width N/A plot_eigenvalues_ratio_widget N/A N/A self figure_size style N/A N/A 10 6 coloured N/A N/A 
        Plot of the variance ratio captured by the eigenvalues using an
        interactive widget.

        Parameters
        ----------
        figure_size : (`float`, `float`) or ``None``, optional
            The size of the figure in inches.
        style : {``'coloured'``, ``'minimal'``}, optional
            If ``'coloured'``, then the style of the widget will be coloured. If
            ``minimal``, then the style is simple using black and white colours.
         N/A N/A menpowidgets plot_graph N/A N/A N/A menpo.visualize.base MenpowidgetsMissingError N/A N/A MenpowidgetsMissingError N/A N/A plot_graph x_axis N/A range N/A self n_active_components y_axis N/A N/A N/A self eigenvalues_ratio legend_entries N/A Eigenvalues ratio figure_size figure_size style style N/A plot_eigenvalues_cumulative_ratio N/A N/A self figure_id new_figure render_lines line_colour line_style line_width render_markers marker_style marker_size marker_face_colour marker_edge_colour marker_edge_width render_axes axes_font_name axes_font_size axes_font_style axes_font_weight figure_size render_grid grid_line_style grid_line_width N/A None False True b - 2 True o 6 b k 1.0 True sans-serif 10 normal normal N/A 10 6 True -- 0.5 N/A N/A 
        Plot of the cumulative variance ratio captured by the eigenvalues.

        Parameters
        ----------
        figure_id : `object`, optional
            The id of the figure to be used.
        new_figure : `bool`, optional
            If ``True``, a new figure is created.
        render_lines : `bool`, optional
            If ``True``, the line will be rendered.
        line_colour : See Below, optional
            The colour of the lines.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        line_style : {``-``, ``--``, ``-.``, ``:``}, optional
            The style of the lines.
        line_width : `float`, optional
            The width of the lines.
        render_markers : `bool`, optional
            If ``True``, the markers will be rendered.
        marker_style : See Below, optional
            The style of the markers.
            Example options ::

                {``.``, ``,``, ``o``, ``v``, ``^``, ``<``, ``>``, ``+``,
                 ``x``, ``D``, ``d``, ``s``, ``p``, ``*``, ``h``, ``H``,
                 ``1``, ``2``, ``3``, ``4``, ``8``}

        marker_size : `int`, optional
            The size of the markers in points.
        marker_face_colour : See Below, optional
            The face (filling) colour of the markers.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        marker_edge_colour : See Below, optional
            The edge colour of the markers.
            Example options ::

                {``r``, ``g``, ``b``, ``c``, ``m``, ``k``, ``w``}
                or 
                ``(3, )`` `ndarray`
                or
                `list` of length ``3``

        marker_edge_width : `float`, optional
            The width of the markers' edge.
        render_axes : `bool`, optional
            If ``True``, the axes will be rendered.
        axes_font_name : See Below, optional
            The font of the axes.
            Example options ::

                {``serif``, ``sans-serif``, ``cursive``, ``fantasy``,
                 ``monospace``}

        axes_font_size : `int`, optional
            The font size of the axes.
        axes_font_style : {``normal``, ``italic``, ``oblique``}, optional
            The font style of the axes.
        axes_font_weight : See Below, optional
            The font weight of the axes.
            Example options ::

                {``ultralight``, ``light``, ``normal``, ``regular``,
                 ``book``, ``medium``, ``roman``, ``semibold``,
                 ``demibold``, ``demi``, ``bold``, ``heavy``,
                 ``extra bold``, ``black``}

        figure_size : (`float`, `float`) or `None`, optional
            The size of the figure in inches.
        render_grid : `bool`, optional
            If ``True``, the grid will be rendered.
        grid_line_style : {``-``, ``--``, ``-.``, ``:``}, optional
            The style of the grid lines.
        grid_line_width : `float`, optional
            The width of the grid lines.

        Returns
        -------
        viewer : :map:`MatplotlibRenderer`
            The viewer object.
         menpo.visualize plot_curve N/A N/A plot_curve N/A range N/A self n_active_components N/A N/A N/A self eigenvalues_cumulative_ratio figure_id figure_id new_figure new_figure legend_entries None title Cumulative Variance Ratio of Eigenvalues x_label Component Number y_label Cumulative Variance Ratio axes_x_limits N/A 0 N/A N/A self n_active_components 1 axes_y_limits None axes_x_ticks None axes_y_ticks None render_lines render_lines line_colour line_colour line_style line_style line_width line_width render_markers render_markers marker_style marker_style marker_size marker_size marker_face_colour marker_face_colour marker_edge_colour marker_edge_colour marker_edge_width marker_edge_width render_legend False render_axes render_axes axes_font_name axes_font_name axes_font_size axes_font_size axes_font_style axes_font_style axes_font_weight axes_font_weight figure_size figure_size render_grid render_grid grid_line_style grid_line_style grid_line_width grid_line_width N/A plot_eigenvalues_cumulative_ratio_widget N/A N/A self figure_size style N/A N/A 10 6 coloured N/A N/A 
        Plot of the cumulative variance ratio captured by the eigenvalues using
        an interactive widget.

        Parameters
        ----------
        figure_size : (`float`, `float`) or ``None``, optional
            The size of the figure in inches.
        style : {``'coloured'``, ``'minimal'``}, optional
            If ``'coloured'``, then the style of the widget will be coloured. If
            ``minimal``, then the style is simple using black and white colours.
         N/A N/A menpowidgets plot_graph N/A N/A N/A menpo.visualize.base MenpowidgetsMissingError N/A N/A MenpowidgetsMissingError N/A N/A plot_graph x_axis N/A range N/A self n_active_components y_axis N/A N/A N/A self eigenvalues_cumulative_ratio legend_entries N/A Eigenvalues cumulative ratio figure_size figure_size style style N/A __str__ N/A N/A self N/A N/A N/A str_out N/A N/A PCA Vector Model 
 - centred:              {}
 - # features:           {}
 - # active components:  {}
 - kept variance:        {:.2}  {:.1%}
 - noise variance:       {:.2}  {:.1%}
 - total # components:   {}
 - components shape:     {}
 format N/A self centred N/A self n_features N/A self n_active_components N/A N/A self variance N/A N/A self variance_ratio N/A N/A self noise_variance N/A N/A self noise_variance_ratio N/A self n_components N/A N/A self components shape N/A str_out N/A N/A PCAModel N/A VectorizableBackedModel PCAVectorModel N/A N/A 
    A :map:`MeanLinearModel` where components are Principal Components
    and the components are vectorized instances.

    Principal Component Analysis (PCA) by eigenvalue decomposition of the
    data's scatter matrix. For details of the implementation of PCA, see
    :map:`pca`.

    Parameters
    ----------
    samples : `list` or `iterable` of :map:`Vectorizable`
        List or iterable of samples to build the model from.
    centre : `bool`, optional
        When ``True`` (default) PCA is performed after mean centering the data.
        If ``False`` the data is assumed to be centred, and the mean will be
        ``0``.
    n_samples : `int`, optional
        If provided then ``samples``  must be an iterator that yields
        ``n_samples``. If not provided then samples has to be a `list` (so we
        know how large the data matrix needs to be).
    max_n_components : `int`, optional
        The maximum number of components to keep in the model. Any components
        above and beyond this one are discarded.
    inplace : `bool`, optional
        If ``True`` the data matrix is modified in place. Otherwise, the data
        matrix is copied.
    verbose : `bool`, optional
        Whether to print building information or not.
      __init__ N/A N/A self samples centre n_samples max_n_components inplace verbose N/A True None None True False N/A N/A N/A data template N/A as_matrix samples length n_samples return_template True verbose verbose N/A n_samples N/A N/A data shape N/A 0 N/A N/A N/A PCAVectorModel __init__ self data centre centre max_n_components max_n_components n_samples n_samples inplace inplace N/A N/A N/A VectorizableBackedModel __init__ self template N/A init_from_covariance_matrix N/A N/A cls C mean n_samples centred is_inverse max_n_components N/A True False None N/A N/A 
        Build the Principal Component Analysis (PCA) by eigenvalue
        decomposition of the provided covariance/scatter matrix. For details
        of the implementation of PCA, see :map:`pcacov`.

        Parameters
        ----------
        C : ``(n_features, n_features)`` `ndarray` or `scipy.sparse`
            The Covariance/Scatter matrix. If it is a precision matrix (inverse
            covariance), then set `is_inverse=True`.
        mean : :map:`Vectorizable`
            The mean instance. It must be a :map:`Vectorizable` and *not* an
            `ndarray`.
        n_samples : `int`
            The number of samples used to generate the covariance matrix.
        centred : `bool`, optional
            When ``True`` we assume that the data were centered before
            computing the covariance matrix.
        is_inverse : `bool`, optional
            It ``True``, then it is assumed that `C` is a precision matrix (
            inverse covariance). Thus, the eigenvalues will be inverted. If
            ``False``, then it is assumed that `C` is a covariance matrix.
        max_n_components : `int`, optional
            The maximum number of components to keep in the model. Any
            components above and beyond this one are discarded.
         N/A self_model N/A N/A PCAVectorModel __new__ cls N/A N/A self_model n_samples n_samples N/A N/A e_vectors e_values N/A pcacov C is_inverse is_inverse N/A N/A N/A self_model _constructor_helper eigenvalues e_values eigenvectors e_vectors mean N/A N/A mean as_vector centred centred max_n_components max_n_components N/A N/A N/A VectorizableBackedModel __init__ self_model mean N/A self_model N/A classmethod init_from_components N/A N/A cls components eigenvalues mean n_samples centred max_n_components N/A None N/A N/A 
        Build the Principal Component Analysis (PCA) using the provided
        components (eigenvectors) and eigenvalues.

        Parameters
        ----------
        components : ``(n_components, n_features)`` `ndarray`
            The eigenvectors to be used.
        eigenvalues : ``(n_components, )`` `ndarray`
            The corresponding eigenvalues.
        mean : :map:`Vectorizable`
            The mean instance. It must be a :map:`Vectorizable` and *not* an
            `ndarray`.
        n_samples : `int`
            The number of samples used to generate the eigenvectors.
        centred : `bool`, optional
            When ``True`` we assume that the data were centered before
            computing the eigenvectors.
        max_n_components : `int`, optional
            The maximum number of components to keep in the model. Any
            components above and beyond this one are discarded.
         N/A self_model N/A N/A PCAVectorModel __new__ cls N/A N/A self_model n_samples n_samples N/A N/A N/A self_model _constructor_helper eigenvalues eigenvalues eigenvectors components mean N/A N/A mean as_vector centred centred max_n_components max_n_components N/A N/A N/A VectorizableBackedModel __init__ self_model mean N/A self_model N/A classmethod mean N/A N/A self N/A N/A N/A 
        Return the mean of the model.

        :type: :map:`Vectorizable`
         N/A N/A N/A N/A self template_instance from_vector N/A self _mean N/A mean_vector N/A N/A self N/A N/A N/A 
        Return the mean of the model as a 1D vector.

        :type: `ndarray`
         N/A N/A self _mean N/A property project_out_vector N/A N/A self instance_vector N/A N/A N/A N/A N/A PCAVectorModel project_out self instance_vector N/A N/A doc_inherit name project_out reconstruct_vector N/A N/A self instance_vector N/A N/A N/A N/A N/A PCAVectorModel reconstruct self instance_vector N/A N/A doc_inherit name reconstruct project_vector N/A N/A self instance_vector N/A N/A N/A N/A N/A PCAVectorModel project self instance_vector N/A N/A doc_inherit name project instance_vector N/A N/A self weights normalized_weights N/A False N/A N/A N/A N/A PCAVectorModel instance self weights normalized_weights normalized_weights N/A N/A doc_inherit name instance component_vector N/A N/A self index with_mean scale N/A True 1.0 N/A N/A N/A N/A PCAVectorModel component self index with_mean with_mean scale scale N/A N/A doc_inherit name component project_whitened_vector N/A N/A self vector_instance N/A N/A N/A N/A N/A PCAVectorModel project_whitened self vector_instance N/A N/A doc_inherit name project_whitened component N/A N/A self index with_mean scale N/A True 1.0 N/A N/A 
        Return a particular component of the linear model.

        Parameters
        ----------
        index : `int`
            The component that is to be returned
        with_mean: `bool`, optional
            If ``True``, the component will be blended with the mean vector
            before being returned. If not, the component is returned on it's
            own.
        scale : `float`, optional
            A scale factor that should be applied to the component. Only
            valid in the case where ``with_mean == True``. See
            :meth:`component_vector` for how this scale factor is interpreted.

        Returns
        -------
        component : `type(self.template_instance)`
            The requested component instance.
         N/A N/A N/A N/A self template_instance from_vector N/A N/A self component_vector index with_mean with_mean scale scale N/A instance N/A N/A self weights normalized_weights N/A False N/A N/A 
        Creates a new instance of the model using the first ``len(weights)``
        components.

        Parameters
        ----------
        weights : ``(n_weights,)`` `ndarray` or `list`
            ``weights[i]`` is the linear contribution of the i'th component
            to the instance vector.
        normalized_weights : `bool`, optional
            If ``True``, the weights are assumed to be normalized w.r.t the
            eigenvalues. This can be easier to create unique instances by
            making the weights more interpretable.
        Raises
        ------
        ValueError
            If n_weights > n_components

        Returns
        -------
        instance : `type(self.template_instance)`
            An instance of the model.
         N/A v N/A N/A self instance_vector weights normalized_weights normalized_weights N/A N/A N/A N/A self template_instance from_vector v N/A project_whitened N/A N/A self instance N/A N/A N/A 
        Projects the `instance` onto the whitened components, retrieving the 
        whitened linear weightings.

        Parameters
        ----------
        instance : :map:`Vectorizable`
            A novel instance.

        Returns
        -------
        projected : (n_components,)
            A vector of whitened linear weightings
         N/A N/A N/A self project_whitened_vector N/A N/A instance as_vector N/A increment N/A N/A self samples n_samples forgetting_factor verbose N/A None 1.0 False N/A N/A 
        Update the eigenvectors, eigenvalues and mean vector of this model
        by performing incremental PCA on the given samples.

        Parameters
        ----------
        samples : `list` of :map:`Vectorizable`
            List of new samples to update the model from.
        n_samples : `int`, optional
            If provided then ``samples``  must be an iterator that yields
            ``n_samples``. If not provided then samples has to be a
            list (so we know how large the data matrix needs to be).
        forgetting_factor : ``[0.0, 1.0]`` `float`, optional
            Forgetting factor that weights the relative contribution of new
            samples vs old samples. If 1.0, all samples are weighted equally
            and, hence, the results is the exact same as performing batch
            PCA on the concatenated list of old and new simples. If <1.0,
            more emphasis is put on the new samples. See [1] for details.

        References
        ----------
        .. [1] David Ross, Jongwoo Lim, Ruei-Sung Lin, Ming-Hsuan Yang.
           "Incremental Learning for Robust Visual Tracking". IJCV, 2007.
         N/A data N/A as_matrix samples length n_samples verbose verbose N/A n_new_samples N/A N/A data shape N/A 0 N/A N/A N/A PCAVectorModel increment self data n_samples n_new_samples forgetting_factor forgetting_factor verbose verbose N/A __str__ N/A N/A self N/A N/A N/A str_out N/A N/A PCA Model 
 - instance class:       {}
 - centred:              {}
 - # features:           {}
 - # active components:  {}
 - kept variance:        {:.2}  {:.1%}
 - noise variance:       {:.2}  {:.1%}
 - total # components:   {}
 - components shape:     {}
 format N/A type N/A self template_instance N/A self centred N/A self n_features N/A self n_active_components N/A N/A self variance N/A N/A self variance_ratio N/A N/A self noise_variance N/A N/A self noise_variance_ratio N/A self n_components N/A N/A self components shape N/A str_out N/A N/A