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Editing: _measurements.cpython-311.pyc
� d�c� � � � d dl Z d dl ZddlmZ ddlmZ ddlmZ ddlmZ g d�Zd d�Zd d �Z dd �d �Z d!d �Z d� Z d"d�Z d d�Zd d�Zd d�Zd d�Zd d�Z d#d�Zd d�Zd d�Zd d�Zd d�Zd d�Zd d�Zd d �Zd d �Zd d �Z dS )$� N� )� _ni_support)� _ni_label)� _nd_image)� _morphology)�label� find_objects�labeled_comprehension�sum�mean�variance�standard_deviation�minimum�maximum�median�minimum_position�maximum_position�extrema�center_of_mass� histogram� watershed_ift� sum_labels� value_indicesc �n � t j | � � } t j | � � rt d� � �|�t j | j d� � }t j |t �� � }|j | j k rt d� � �|j D ]}|dk rt d� � ��| j dk }t |t j � � r"|j | j k rt d � � �d }nQd }|�3t j | j |r t j n t j � � }nt j | j |� � }| j d k s | j d k r%| j d k r| d k rdnd }||d < nd }|r|S ||fS t% j | ||� � }n�# t$ j $ r�}t j | j |r t j n t j � � } t% j | || � � }| d |d < t j || k � � st d� � |�Y d}~nd}~ww xY w|r|S ||fS )a� Label features in an array. Parameters ---------- input : array_like An array-like object to be labeled. Any non-zero values in `input` are counted as features and zero values are considered the background. structure : array_like, optional A structuring element that defines feature connections. `structure` must be centrosymmetric (see Notes). If no structuring element is provided, one is automatically generated with a squared connectivity equal to one. That is, for a 2-D `input` array, the default structuring element is:: [[0,1,0], [1,1,1], [0,1,0]] output : (None, data-type, array_like), optional If `output` is a data type, it specifies the type of the resulting labeled feature array. If `output` is an array-like object, then `output` will be updated with the labeled features from this function. This function can operate in-place, by passing output=input. Note that the output must be able to store the largest label, or this function will raise an Exception. Returns ------- label : ndarray or int An integer ndarray where each unique feature in `input` has a unique label in the returned array. num_features : int How many objects were found. If `output` is None, this function returns a tuple of (`labeled_array`, `num_features`). If `output` is a ndarray, then it will be updated with values in `labeled_array` and only `num_features` will be returned by this function. See Also -------- find_objects : generate a list of slices for the labeled features (or objects); useful for finding features' position or dimensions Notes ----- A centrosymmetric matrix is a matrix that is symmetric about the center. See [1]_ for more information. The `structure` matrix must be centrosymmetric to ensure two-way connections. For instance, if the `structure` matrix is not centrosymmetric and is defined as:: [[0,1,0], [1,1,0], [0,0,0]] and the `input` is:: [[1,2], [0,3]] then the structure matrix would indicate the entry 2 in the input is connected to 1, but 1 is not connected to 2. Examples -------- Create an image with some features, then label it using the default (cross-shaped) structuring element: >>> from scipy.ndimage import label, generate_binary_structure >>> import numpy as np >>> a = np.array([[0,0,1,1,0,0], ... [0,0,0,1,0,0], ... [1,1,0,0,1,0], ... [0,0,0,1,0,0]]) >>> labeled_array, num_features = label(a) Each of the 4 features are labeled with a different integer: >>> num_features 4 >>> labeled_array array([[0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0], [2, 2, 0, 0, 3, 0], [0, 0, 0, 4, 0, 0]]) Generate a structuring element that will consider features connected even if they touch diagonally: >>> s = generate_binary_structure(2,2) or, >>> s = [[1,1,1], ... [1,1,1], ... [1,1,1]] Label the image using the new structuring element: >>> labeled_array, num_features = label(a, structure=s) Show the 2 labeled features (note that features 1, 3, and 4 from above are now considered a single feature): >>> num_features 2 >>> labeled_array array([[0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0], [2, 2, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]]) References ---------- .. [1] James R. Weaver, "Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors." The American Mathematical Monthly 92.10 (1985): 711-717. �Complex type not supportedNr ��dtype�(structure and input must have equal rank� �'structure dimensions must be equal to 3i���zoutput shape not correctTFr .z/insufficient bit-depth in requested output type)�numpy�asarray� iscomplexobj� TypeErrorr �generate_binary_structure�ndim�bool� RuntimeError�shape� ValueError�size� isinstance�ndarray�np�empty�intp�int32r �_label� NeedMoreBits�all) �input� structure�output�ii� need_64bits�caller_provided_output�maxlabel� max_label�e� tmp_outputs �=/usr/lib/python3/dist-packages/scipy/ndimage/_measurements.pyr r , s{ � �J �M�%� � �E� ��%� � � 6��4�5�5�5��� �9�%�*�a�H�H� �� �i�t�4�4�4�I��~���#�#��E�F�F�F��o� H� H�� ��7�7� � F�G�G� G� � �*��+�K��&�%�-�(�(� 3� �<�5�;� &� &� � 7�8�8� 8�!%� � �!&� � �>��X�e�k�k�+O�2�7�7�r�x�P�P�F�F��X�e�k�6�2�2�F� �z�Q���%�*��/�/� �:��?�?� "�a�Z�Z�q�q�a�H�"�F�3�K�K� �H� !� $��O��8�#� #� � �$�U�I�v�>�>� � �� � !� � � � �X�e�k�k�+O�2�7�7�r�x�P�P� � �$�U�I�z�B�B� � ��o��s� ��v�f� �*�+�+� � �A�� �� � � � � � ����� ���� � !����y� � s �F �H,�'A;H'�'H,c �� � t j | � � } t j | � � rt d� � �|dk r| � � � }t j | |� � S )a Find objects in a labeled array. Parameters ---------- input : ndarray of ints Array containing objects defined by different labels. Labels with value 0 are ignored. max_label : int, optional Maximum label to be searched for in `input`. If max_label is not given, the positions of all objects are returned. Returns ------- object_slices : list of tuples A list of tuples, with each tuple containing N slices (with N the dimension of the input array). Slices correspond to the minimal parallelepiped that contains the object. If a number is missing, None is returned instead of a slice. See Also -------- label, center_of_mass Notes ----- This function is very useful for isolating a volume of interest inside a 3-D array, that cannot be "seen through". Examples -------- >>> from scipy import ndimage >>> import numpy as np >>> a = np.zeros((6,6), dtype=int) >>> a[2:4, 2:4] = 1 >>> a[4, 4] = 1 >>> a[:2, :3] = 2 >>> a[0, 5] = 3 >>> a array([[2, 2, 2, 0, 0, 3], [2, 2, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0]]) >>> ndimage.find_objects(a) [(slice(2, 5, None), slice(2, 5, None)), (slice(0, 2, None), slice(0, 3, None)), (slice(0, 1, None), slice(5, 6, None))] >>> ndimage.find_objects(a, max_label=2) [(slice(2, 5, None), slice(2, 5, None)), (slice(0, 2, None), slice(0, 3, None))] >>> ndimage.find_objects(a == 1, max_label=2) [(slice(2, 5, None), slice(2, 5, None)), None] >>> loc = ndimage.find_objects(a)[0] >>> a[loc] array([[1, 1, 0], [1, 1, 0], [0, 0, 1]]) r r )r! r" r# r$ �maxr r )r5 r< s r? r r � s_ � �x �M�%� � �E� ��%� � � 6��4�5�5�5��1�}�}��I�I�K�K� � � !�%�� 3� 3�3� )� ignore_valuec � � t j d| j �� � }|du }|s |j � |� � |d< t j | ||� � }|S )a@ Find indices of each distinct value in given array. Parameters ---------- arr : ndarray of ints Array containing integer values. ignore_value : int, optional This value will be ignored in searching the `arr` array. If not given, all values found will be included in output. Default is None. Returns ------- indices : dictionary A Python dictionary of array indices for each distinct value. The dictionary is keyed by the distinct values, the entries are array index tuples covering all occurrences of the value within the array. This dictionary can occupy significant memory, usually several times the size of the input array. Notes ----- For a small array with few distinct values, one might use `numpy.unique()` to find all possible values, and ``(arr == val)`` to locate each value within that array. However, for large arrays, with many distinct values, this can become extremely inefficient, as locating each value would require a new search through the entire array. Using this function, there is essentially one search, with the indices saved for all distinct values. This is useful when matching a categorical image (e.g. a segmentation or classification) to an associated image of other data, allowing any per-class statistic(s) to then be calculated. Provides a more flexible alternative to functions like ``scipy.ndimage.mean()`` and ``scipy.ndimage.variance()``. Some other closely related functionality, with different strengths and weaknesses, can also be found in ``scipy.stats.binned_statistic()`` and the `scikit-image <https://scikit-image.org/>`_ function ``skimage.measure.regionprops()``. Note for IDL users: this provides functionality equivalent to IDL's REVERSE_INDICES option (as per the IDL documentation for the `HISTOGRAM <https://www.l3harrisgeospatial.com/docs/histogram.html>`_ function). .. versionadded:: 1.10.0 See Also -------- label, maximum, median, minimum_position, extrema, sum, mean, variance, standard_deviation, numpy.where, numpy.unique Examples -------- >>> import numpy as np >>> from scipy import ndimage >>> a = np.zeros((6, 6), dtype=int) >>> a[2:4, 2:4] = 1 >>> a[4, 4] = 1 >>> a[:2, :3] = 2 >>> a[0, 5] = 3 >>> a array([[2, 2, 2, 0, 0, 3], [2, 2, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0]]) >>> val_indices = ndimage.value_indices(a) The dictionary `val_indices` will have an entry for each distinct value in the input array. >>> val_indices.keys() dict_keys([0, 1, 2, 3]) The entry for each value is an index tuple, locating the elements with that value. >>> ndx1 = val_indices[1] >>> ndx1 (array([2, 2, 3, 3, 4]), array([2, 3, 2, 3, 4])) This can be used to index into the original array, or any other array with the same shape. >>> a[ndx1] array([1, 1, 1, 1, 1]) If the zeros were to be ignored, then the resulting dictionary would no longer have an entry for zero. >>> val_indices = ndimage.value_indices(a, ignore_value=0) >>> val_indices.keys() dict_keys([1, 2, 3]) )r r Nr )r! �zerosr �typer r )�arrrC �ignore_value_arr� ignoreIsNone� val_indicess r? r r 6 sf � �R �{�4�s�y�9�9�9�� �D�(�L� � H� .� 4� 9� 9�,� G� G�����)�#�|�=M�N�N�K� �rB Fc � ���� t j |� � }t j | � � } |r1t j | j � � � | j � � }��`|�t d� � �|s �| � � � � � S �| � � � |� � � � � S t j | �� � \ } �n"# t $ r} t d� � | �d} ~ ww xY w|�7|s �| �dk � � S �| �dk |�dk � � S t j |� � }t j |� �j � � � |j � � |k � � r t d|j �d�j �d�� � �|� �j � � }|� � � } |� � � } �| k �| k z } �| �| | } |r|| }�� � � } �| �| | } |r|| }|� � � }|| ����fd�}t j |j |� � }||dd�< |s || g|� � n || |g|� � t j |j |� � }|||< |r|d }|S ) a Roughly equivalent to [func(input[labels == i]) for i in index]. Sequentially applies an arbitrary function (that works on array_like input) to subsets of an N-D image array specified by `labels` and `index`. The option exists to provide the function with positional parameters as the second argument. Parameters ---------- input : array_like Data from which to select `labels` to process. labels : array_like or None Labels to objects in `input`. If not None, array must be same shape as `input`. If None, `func` is applied to raveled `input`. index : int, sequence of ints or None Subset of `labels` to which to apply `func`. If a scalar, a single value is returned. If None, `func` is applied to all non-zero values of `labels`. func : callable Python function to apply to `labels` from `input`. out_dtype : dtype Dtype to use for `result`. default : int, float or None Default return value when a element of `index` does not exist in `labels`. pass_positions : bool, optional If True, pass linear indices to `func` as a second argument. Default is False. Returns ------- result : ndarray Result of applying `func` to each of `labels` to `input` in `index`. Examples -------- >>> import numpy as np >>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> from scipy import ndimage >>> lbl, nlbl = ndimage.label(a) >>> lbls = np.arange(1, nlbl+1) >>> ndimage.labeled_comprehension(a, lbl, lbls, np.mean, float, 0) array([ 2.75, 5.5 , 6. ]) Falling back to `default`: >>> lbls = np.arange(1, nlbl+2) >>> ndimage.labeled_comprehension(a, lbl, lbls, np.mean, float, -1) array([ 2.75, 5.5 , 6. , -1. ]) Passing positions: >>> def fn(val, pos): ... print("fn says: %s : %s" % (val, pos)) ... return (val.sum()) if (pos.sum() % 2 == 0) else (-val.sum()) ... >>> ndimage.labeled_comprehension(a, lbl, lbls, fn, float, 0, True) fn says: [1 2 5 3] : [0 1 4 5] fn says: [4 7] : [ 7 11] fn says: [9 3] : [12 13] array([ 11., 11., -12., 0.]) Nz index without defined labelszMinput and labels must have the same shape (excepting dimensions with width 1)r z"Cannot convert index values from <z> to <z*> (labels' type) without loss of precisionc � ���� � j }t j � � d�� � }t j � � d�� � }t t |� � ||� � D ]"\ }����k r� ���fd�| D � � � ||< �#dS )zlabels must be sorted�left)�side�rightc �$ �� g | ] }|��� �� S � rQ )�.0�inp�h�ls ��r? � <listcomp>z9labeled_comprehension.<locals>.do_map.<locals>.<listcomp>1 s! �� � :� :� :�C�s�1�Q�3�x� :� :� :rB N)r+ r! � searchsorted�zip�range) �inputsr7 �nidx�lo�hi�irT rU �func�labels� sorted_indexs @@���r? �do_mapz%labeled_comprehension.<locals>.do_map% s� ���� �� �� � �� �6� B� B� B�� � �� �7� C� C� C���5��;�;��B�/�/� <� <�G�A�q�!��A�v�v�� �� :� :� :� :� :�6� :� :� :�;�F�1�I�I� <� <rB )r! �isscalarr" �aranger+ �reshaper) r* �ravel�broadcast_arrays� atleast_1dr. �any�astyper �minrA �argsortr/ rE )r5 r` �indexr_ � out_dtype�default�pass_positions� as_scalar� positionsr= r\ r] �mask� label_order� index_orderrb �tempr7 ra s ` ` @r? r r � s- ���� �L ��u�%�%�I� �M�%� � �E�� B��L���,�,�4�4�U�[�A�A� � �~� � � � ;�<�<� <� � :��4�� � � � �&�&� &��4�� � � � �y���'8�'8�9�9� 9�J� �.�u�f�=�=� ��v�v�� � J� J� J�� B� C� C�HI� J�����J���� �}� � B��4��f�q�j�)�*�*� *��4��f�q�j�)�9�V�a�Z�+@�A�A� A� � �U� #� #�E� �v�e�l�l�6�<�(�(�/�/�� �<�<��E�F�F� 9��j� "�[�[�[�&�,�,�,�8� 9� 9� 9� �L�L�� � &� &�E� �����B� �����B� �b�L�V�r�\� *�D� �D�\�F� �$�K�E�� $� �d�O� � �.�.�"�"�K� �K� �F� �+� �E�� +� �k�*� ��-�-�/�/�K���%�L� <� <� <� <� <� <� <� �;�u�{�I� .� .�D��D����G� � )����w�� � � � ����y�!�4�(�(�(� �[���i� 0� 0�F� �F�;��� ����� �Ms �C � C:�%C5�5C:c �� � t j t � � j }t j | t j � � r | j |k p)t j | t j � � o | j |k }|S )zCTest whether the NumPy data type `dt` can be safely cast to an int.)r. r �int�itemsize� issubdtype� signedinteger�unsignedinteger)�dt�int_size�safes r? �_safely_castable_to_intr� B s^ � ��x��}�}�%�H� �]�2�r� /� 0� 0� L�R�[�H�5L� O� �]�2�r� 1� 2� 2� M�r�{�X�7M� � �KrB c � � �� � � �fd�}|� |� � � S t j � |� � \ � }|� |� |dk � � S t j |� � r |� ||k � � S � � � fd�}t |j � � r5|� � � dk s |� � � |j k r�t j |d�� � \ }}t j |� � � t j |� � � � �� � � �r# ||� |j � � � � }t j ||� � } d| | |j k < || |k } n�t j |� � � � � � t j |� � � � � � � �� � � �r ||� � }t j |t j � � � � � } | dk | � j k z } d| | < � | � d� | < � | � d� | < �s� � fS || }d|| < � � |fS )a� Count, sum, and optionally compute (sum - centre)^2 of input by label Parameters ---------- input : array_like, N-D The input data to be analyzed. labels : array_like (N-D), optional The labels of the data in `input`. This array must be broadcast compatible with `input`; typically, it is the same shape as `input`. If `labels` is None, all nonzero values in `input` are treated as the single labeled group. index : label or sequence of labels, optional These are the labels of the groups for which the stats are computed. If `index` is None, the stats are computed for the single group where `labels` is greater than 0. centered : bool, optional If True, the centered sum of squares for each labeled group is also returned. Default is False. Returns ------- counts : int or ndarray of ints The number of elements in each labeled group. sums : scalar or ndarray of scalars The sums of the values in each labeled group. sums_c : scalar or ndarray of scalars, optional The sums of mean-centered squares of the values in each labeled group. This is only returned if `centered` is True. c �� �� �rZ| | � � � z }| j | � � � ||� � � z � � � fS | j | � � � fS )N)r r+ r � conjugate)�vals�vals_c�centereds �r? � single_groupz _stats.<locals>.single_groupi sf �� � � )��D�I�I�K�K�'�F��9�d�h�h�j�j�6�F�4D�4D�4F�4F�+F�*K�*K�*M�*M�M� M��9�d�h�h�j�j�(� (rB Nr c �� �� ��z }�|| z }t j | � � � ||� � � z � � � �� � }|S )N��weights)r! �bincountrf r� )r` �means�centered_input�bc�countsr5 �sumss ���r? � _sum_centeredz _stats.<locals>._sum_centered| sg �� � �v� �� ��v� �.�� �^�F�L�L�N�N�'5�'5�'?�'?�'A�'A�(B�CH�5�7�7�L� L� L�� � rB T��return_inverser� )r! rg rc r� r rk rA r+ �uniquer� rf re r) rW � asanyarray�int_�copy) r5 r` rm r� r� r� � unique_labels� new_labels�sums_c�idxs�foundr� r� s ` ` @@r? �_statsr� J s� ����� �>)� )� )� )� )� �~��|�E�"�"�"� �*�5�&�9�9�M�E�6� �}��|�E�&�1�*� -�.�.�.� �~�e� � � 4��|�E�&�E�/� 2�3�3�3� � � � � � � � $�F�L� 1� 1� � �J�J�L�L�1� � �� � � � �v�{� :� :� %*�L���$M�$M�$M�!� �z�� � �+�+���~�j�%�+�+�-�-�@�@�@�� � E� #�]�:�#5�#5�f�l�#C�#C�D�D�F��!�-��7�7��+,��T�]�'� '�(� �t�$��-��� � �� � ���/�/���~�f�l�l�n�n�e�k�k�m�m�D�D�D�� � +�"�]�6�*�*�F�� ��u�z�2�2�7�7�9�9�����t�f�k� 1�2����e�V� � �D�\�F��F�E�6�N� ��:�D��D�%��L� � &���~� ��� �����v����f�%�%rB c �$ � t | ||� � S )a Calculate the sum of the values of the array. Notes ----- This is an alias for `ndimage.sum_labels` kept for backwards compatibility reasons, for new code please prefer `sum_labels`. See the `sum_labels` docstring for more details. )r �r5 r` rm s r? r r � s � � �e�V�U� +� +�+rB c �. � t | ||� � \ }}|S )a Calculate the sum of the values of the array. Parameters ---------- input : array_like Values of `input` inside the regions defined by `labels` are summed together. labels : array_like of ints, optional Assign labels to the values of the array. Has to have the same shape as `input`. index : array_like, optional A single label number or a sequence of label numbers of the objects to be measured. Returns ------- sum : ndarray or scalar An array of the sums of values of `input` inside the regions defined by `labels` with the same shape as `index`. If 'index' is None or scalar, a scalar is returned. See Also -------- mean, median Examples -------- >>> from scipy import ndimage >>> input = [0,1,2,3] >>> labels = [1,1,2,2] >>> ndimage.sum_labels(input, labels, index=[1,2]) [1.0, 5.0] >>> ndimage.sum_labels(input, labels, index=1) 1 >>> ndimage.sum_labels(input, labels) 6 )r� �r5 r` rm �countr s r? r r � s � �R ��v�u�-�-�J�E�3� �JrB c � � t | ||� � \ }}|t j |� � � t j � � z S )a� Calculate the mean of the values of an array at labels. Parameters ---------- input : array_like Array on which to compute the mean of elements over distinct regions. labels : array_like, optional Array of labels of same shape, or broadcastable to the same shape as `input`. All elements sharing the same label form one region over which the mean of the elements is computed. index : int or sequence of ints, optional Labels of the objects over which the mean is to be computed. Default is None, in which case the mean for all values where label is greater than 0 is calculated. Returns ------- out : list Sequence of same length as `index`, with the mean of the different regions labeled by the labels in `index`. See Also -------- variance, standard_deviation, minimum, maximum, sum, label Examples -------- >>> from scipy import ndimage >>> import numpy as np >>> a = np.arange(25).reshape((5,5)) >>> labels = np.zeros_like(a) >>> labels[3:5,3:5] = 1 >>> index = np.unique(labels) >>> labels array([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1]]) >>> index array([0, 1]) >>> ndimage.mean(a, labels=labels, index=index) [10.285714285714286, 21.0] )r� r! r� rj �float64r� s r? r r � s@ � �b ��v�u�-�-�J�E�3� ��!�%�(�(�/�/�� �>�>� >�>rB c � � t | ||d�� � \ }}}|t j |� � � t � � z S )a) Calculate the variance of the values of an N-D image array, optionally at specified sub-regions. Parameters ---------- input : array_like Nd-image data to process. labels : array_like, optional Labels defining sub-regions in `input`. If not None, must be same shape as `input`. index : int or sequence of ints, optional `labels` to include in output. If None (default), all values where `labels` is non-zero are used. Returns ------- variance : float or ndarray Values of variance, for each sub-region if `labels` and `index` are specified. See Also -------- label, standard_deviation, maximum, minimum, extrema Examples -------- >>> import numpy as np >>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> from scipy import ndimage >>> ndimage.variance(a) 7.609375 Features to process can be specified using `labels` and `index`: >>> lbl, nlbl = ndimage.label(a) >>> ndimage.variance(a, lbl, index=np.arange(1, nlbl+1)) array([ 2.1875, 2.25 , 9. ]) If no index is given, all non-zero `labels` are processed: >>> ndimage.variance(a, lbl) 6.1875 T)r� )r� r. r� rj �float)r5 r` rm r� r �sum_c_sqs r? r r % sE � �b "�%����F�F�F��E�3�� �b�m�E�*�*�1�1�%�8�8� 8�8rB c �H � t j t | ||� � � � S )am Calculate the standard deviation of the values of an N-D image array, optionally at specified sub-regions. Parameters ---------- input : array_like N-D image data to process. labels : array_like, optional Labels to identify sub-regions in `input`. If not None, must be same shape as `input`. index : int or sequence of ints, optional `labels` to include in output. If None (default), all values where `labels` is non-zero are used. Returns ------- standard_deviation : float or ndarray Values of standard deviation, for each sub-region if `labels` and `index` are specified. See Also -------- label, variance, maximum, minimum, extrema Examples -------- >>> import numpy as np >>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> from scipy import ndimage >>> ndimage.standard_deviation(a) 2.7585095613392387 Features to process can be specified using `labels` and `index`: >>> lbl, nlbl = ndimage.label(a) >>> ndimage.standard_deviation(a, lbl, index=np.arange(1, nlbl+1)) array([ 1.479, 1.5 , 3. ]) If no index is given, non-zero `labels` are processed: >>> ndimage.standard_deviation(a, lbl) 2.4874685927665499 )r! �sqrtr r� s r? r r Z s! � �b �:�h�u�f�e�4�4� 5� 5�5rB c �R ������ t j | � � } �p�}d} |r1t j | j � � � | j � � } �����fd�} |� | | | � � S t j | |� � \ } }|�$|dk } d} |r| | } | | | | � � S t j |� � r$||k } d} |r| | } | | | | � � S t |j � � r5|� � � dk s |� � � |j k rIt j |d�� � \ } }t j | |� � }d||| j k < | | |k }nPt j |t j � � � � � }|dk ||� � � k z }|� � � dz || < �r;t j | � � � |� � � f� � }n&| � � � � � � }| � � � | } |� � � | }|r| � � � | } g }�rRt j |� � � dz | j � � }| ddd� ||ddd� < ||| gz }�rRt j |� � � dz t( � � }| ddd� ||ddd� < ||| gz }�r@t j |� � � dz | j � � }| ||< ||| gz }�r@t j |� � � dz t( � � }| ||< ||| gz }��rft j t+ |� � � � }t j |� � � dz t j � � }|ddd� ||ddd� < t j |� � � dz t j � � }|||< || }|| }||z dz }||z }||z }t- j | j t, j � � s$t- j | j t, j � � r?|| | � d � � | | � d � � z d z gz }n|| | | | z d z gz }|S ) zOReturns min, max, or both, plus their positions (if requested), and median.Nc �P �� g }�r|| � � � gz }�r(||| | � � � k d gz }�r|| � � � gz }�r(||| | � � � k d gz }�r|t j | � � gz }|S �Nr )rk rA r! r )r� rr �result�find_max�find_max_positions� find_median�find_min�find_min_positionss �����r? r� z _select.<locals>.single_group� s� �� ��� � #� �t�x�x�z�z�l� "�F� � 9� �y�������!3�4�Q�7�8� 8�F� � #� �t�x�x�z�z�l� "�F� � 9� �y�������!3�4�Q�7�8� 8�F� � +� �u�|�D�)�)�*� *�F�� rB r Tr� r � ����dg @)r! r� rd r+ re r) rg rc r� r rk rA r� rW r� r� �lexsortrf rl rE rx �lenr. rz �integer�bool_rj )r5 r` rm r� r� r� r� r� �find_positionsrr r� rs �masked_positionsr� r� r� �orderr� �mins�minpos�maxs�maxpos�locsr\ r] �steps ````` r? �_selectr� � s ������ � � �U� #� #�E�'�=�+=�N��I�� B��L���,�,�4�4�U�[�A�A� � � � � � � � � � � �~��|�E�9�-�-�-� �*�5�&�9�9�M�E�6� �}��� �� �� � /� (��� ��|�E�$�K�)9�:�:�:� �~�e� � � ;��%��� �� � /� (��� ��|�E�$�K�)9�:�:�:� $�F�L� 1� 1� 5� �J�J�L�L�1� � �� � � � �v�{� :� :� %� �V�D� I� I� I� � �v��!�-��7�7�� ,-��T�]�'� '�(� �t�$��-��� � ��u�z�2�2�7�7�9�9�����t�v�z�z�|�|� 3�4���J�J�L�L�1�$�D�5��M�� (�� �u�{�{�}�}�f�l�l�n�n� =�>�>���� � � � �%�%�'�'�� �K�K�M�M�%� �E� �\�\�^�^�E� "�F�� -� �O�O�%�%�e�,� � �F�� ��{�6�:�:�<�<�!�+�U�[�9�9�� "�4�4�R�4�[��V�D�D�b�D�\���4��:�,� ��� !���V�Z�Z�\�\�A� -�s�3�3�� (���2����v�d�d��d�|� ��6�$�<�.� ��� ��{�6�:�:�<�<�!�+�U�[�9�9�� ��V� ��4��:�,� ��� !���V�Z�Z�\�\�A� -�s�3�3��"��v���6�$�<�.� ��� 6��|�C��K�K�(�(�� �[���� � ��)�5�:� 6� 6�� ���"��:��6�$�$�B�$�<�� �[���� � ��)�5�:� 6� 6����6� � ��X�� ��X�� �R��A�~�� �d� �� �d� �� �M�%�+�r�z� 2� 2� 6��=���b�h�7�7� 6� ��b� �(�(��-�-��b� �0@�0@��0E�0E�E��L�M� M�F�F� ��b� �E�"�I�-��4�5� 5�F� �MrB c �4 � t | ||d�� � d S )a� Calculate the minimum of the values of an array over labeled regions. Parameters ---------- input : array_like Array_like of values. For each region specified by `labels`, the minimal values of `input` over the region is computed. labels : array_like, optional An array_like of integers marking different regions over which the minimum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the minimum over the whole array is returned. index : array_like, optional A list of region labels that are taken into account for computing the minima. If index is None, the minimum over all elements where `labels` is non-zero is returned. Returns ------- minimum : float or list of floats List of minima of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a float is returned: the minimal value of `input` if `labels` is None, and the minimal value of elements where `labels` is greater than zero if `index` is None. See Also -------- label, maximum, median, minimum_position, extrema, sum, mean, variance, standard_deviation Notes ----- The function returns a Python list and not a NumPy array, use `np.array` to convert the list to an array. Examples -------- >>> from scipy import ndimage >>> import numpy as np >>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> labels, labels_nb = ndimage.label(a) >>> labels array([[1, 1, 0, 0], [1, 1, 0, 2], [0, 0, 0, 2], [3, 3, 0, 0]]) >>> ndimage.minimum(a, labels=labels, index=np.arange(1, labels_nb + 1)) [1.0, 4.0, 3.0] >>> ndimage.minimum(a) 0.0 >>> ndimage.minimum(a, labels=labels) 1.0 T)r� r �r� r� s r? r r s! � �x �5�&�%�$� 7� 7� 7�� :�:rB c �4 � t | ||d�� � d S )a� Calculate the maximum of the values of an array over labeled regions. Parameters ---------- input : array_like Array_like of values. For each region specified by `labels`, the maximal values of `input` over the region is computed. labels : array_like, optional An array of integers marking different regions over which the maximum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the maximum over the whole array is returned. index : array_like, optional A list of region labels that are taken into account for computing the maxima. If index is None, the maximum over all elements where `labels` is non-zero is returned. Returns ------- output : float or list of floats List of maxima of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a float is returned: the maximal value of `input` if `labels` is None, and the maximal value of elements where `labels` is greater than zero if `index` is None. See Also -------- label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation Notes ----- The function returns a Python list and not a NumPy array, use `np.array` to convert the list to an array. Examples -------- >>> import numpy as np >>> a = np.arange(16).reshape((4,4)) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) >>> labels = np.zeros_like(a) >>> labels[:2,:2] = 1 >>> labels[2:, 1:3] = 2 >>> labels array([[1, 1, 0, 0], [1, 1, 0, 0], [0, 2, 2, 0], [0, 2, 2, 0]]) >>> from scipy import ndimage >>> ndimage.maximum(a) 15.0 >>> ndimage.maximum(a, labels=labels, index=[1,2]) [5.0, 14.0] >>> ndimage.maximum(a, labels=labels) 14.0 >>> b = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> labels, labels_nb = ndimage.label(b) >>> labels array([[1, 1, 0, 0], [1, 1, 0, 2], [0, 0, 0, 2], [3, 3, 0, 0]]) >>> ndimage.maximum(b, labels=labels, index=np.arange(1, labels_nb + 1)) [5.0, 7.0, 9.0] T)r� r r� r� s r? r r A s! � �Z �5�&�%�$� 7� 7� 7�� :�:rB c �4 � t | ||d�� � d S )a� Calculate the median of the values of an array over labeled regions. Parameters ---------- input : array_like Array_like of values. For each region specified by `labels`, the median value of `input` over the region is computed. labels : array_like, optional An array_like of integers marking different regions over which the median value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the median over the whole array is returned. index : array_like, optional A list of region labels that are taken into account for computing the medians. If index is None, the median over all elements where `labels` is non-zero is returned. Returns ------- median : float or list of floats List of medians of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a float is returned: the median value of `input` if `labels` is None, and the median value of elements where `labels` is greater than zero if `index` is None. See Also -------- label, minimum, maximum, extrema, sum, mean, variance, standard_deviation Notes ----- The function returns a Python list and not a NumPy array, use `np.array` to convert the list to an array. Examples -------- >>> from scipy import ndimage >>> import numpy as np >>> a = np.array([[1, 2, 0, 1], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> labels, labels_nb = ndimage.label(a) >>> labels array([[1, 1, 0, 2], [1, 1, 0, 2], [0, 0, 0, 2], [3, 3, 0, 0]]) >>> ndimage.median(a, labels=labels, index=np.arange(1, labels_nb + 1)) [2.5, 4.0, 6.0] >>> ndimage.median(a) 1.0 >>> ndimage.median(a, labels=labels) 3.0 T)r� r r� r� s r? r r � s! � �v �5�&�%�T� :� :� :�1� =�=rB c � � t j t j | � � j � � }t j dgt |ddd� � � z � � ddd� }t | ||d�� � d }t j |� � rt ||z |z � � S d� |� dd� � |z |z D � � S )a� Find the positions of the minimums of the values of an array at labels. Parameters ---------- input : array_like Array_like of values. labels : array_like, optional An array of integers marking different regions over which the position of the minimum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the location of the first minimum over the whole array is returned. The `labels` argument only works when `index` is specified. index : array_like, optional A list of region labels that are taken into account for finding the location of the minima. If `index` is None, the ``first`` minimum over all elements where `labels` is non-zero is returned. The `index` argument only works when `labels` is specified. Returns ------- output : list of tuples of ints Tuple of ints or list of tuples of ints that specify the location of minima of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a tuple of ints is returned specifying the location of the first minimal value of `input`. See Also -------- label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation Examples -------- >>> import numpy as np >>> a = np.array([[10, 20, 30], ... [40, 80, 100], ... [1, 100, 200]]) >>> b = np.array([[1, 2, 0, 1], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> from scipy import ndimage >>> ndimage.minimum_position(a) (2, 0) >>> ndimage.minimum_position(b) (0, 2) Features to process can be specified using `labels` and `index`: >>> label, pos = ndimage.label(a) >>> ndimage.minimum_position(a, label, index=np.arange(1, pos+1)) [(2, 0)] >>> label, pos = ndimage.label(b) >>> ndimage.minimum_position(b, label, index=np.arange(1, pos+1)) [(0, 0), (0, 3), (3, 1)] r Nr r� T)r� c �, � g | ]}t |� � ��S rQ ��tuple�rR �vs r? rV z$minimum_position.<locals>.<listcomp> � � � I� I� I��E�!�H�H� I� I� IrB � r! �arrayr" r) �cumprod�listr� rc r� re �r5 r` rm �dims�dim_prodr� s r? r r � s� � �F �;�u�}�U�+�+�1� 2� 2�D��}�a�S�4��U�a��U� �#4�#4� 4�5�5�d�d��d�;�H� �U�F�E�d� C� C� C�A� F�F� �~�f� � � 2��f��(�D�0�1�1�1� I� I�v�~�~�b�!� 4� 4�� @�D� H� I� I� I�IrB c � � t j t j | � � j � � }t j dgt |ddd� � � z � � ddd� }t | ||d�� � d }t j |� � rt ||z |z � � S d� |� dd� � |z |z D � � S )a Find the positions of the maximums of the values of an array at labels. For each region specified by `labels`, the position of the maximum value of `input` within the region is returned. Parameters ---------- input : array_like Array_like of values. labels : array_like, optional An array of integers marking different regions over which the position of the maximum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the location of the first maximum over the whole array is returned. The `labels` argument only works when `index` is specified. index : array_like, optional A list of region labels that are taken into account for finding the location of the maxima. If `index` is None, the first maximum over all elements where `labels` is non-zero is returned. The `index` argument only works when `labels` is specified. Returns ------- output : list of tuples of ints List of tuples of ints that specify the location of maxima of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a tuple of ints is returned specifying the location of the ``first`` maximal value of `input`. See also -------- label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation Examples -------- >>> from scipy import ndimage >>> import numpy as np >>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> ndimage.maximum_position(a) (3, 0) Features to process can be specified using `labels` and `index`: >>> lbl = np.array([[0, 1, 2, 3], ... [0, 1, 2, 3], ... [0, 1, 2, 3], ... [0, 1, 2, 3]]) >>> ndimage.maximum_position(a, lbl, 1) (1, 1) If no index is given, non-zero `labels` are processed: >>> ndimage.maximum_position(a, lbl) (2, 3) If there are no maxima, the position of the first element is returned: >>> ndimage.maximum_position(a, lbl, 2) (0, 2) r Nr r� T)r� c �, � g | ]}t |� � ��S rQ r� r� s r? rV z$maximum_position.<locals>.<listcomp>p r� rB r� r� s r? r r s� � �R �;�u�}�U�+�+�1� 2� 2�D��}�a�S�4��U�a��U� �#4�#4� 4�5�5�d�d��d�;�H� �U�F�E�d� C� C� C�A� F�F� �~�f� � � 2��f��(�D�0�1�1�1� I� I�v�~�~�b�!� 4� 4�� @�D� H� I� I� I�IrB c � � t j t j | � � j � � }t j dgt |ddd� � � z � � ddd� }t | ||dddd�� � \ }}}}t j |� � r,||t ||z |z � � t ||z |z � � fS d� |� dd� � |z |z D � � }d� |� dd� � |z |z D � � }||||fS ) a� Calculate the minimums and maximums of the values of an array at labels, along with their positions. Parameters ---------- input : ndarray N-D image data to process. labels : ndarray, optional Labels of features in input. If not None, must be same shape as `input`. index : int or sequence of ints, optional Labels to include in output. If None (default), all values where non-zero `labels` are used. Returns ------- minimums, maximums : int or ndarray Values of minimums and maximums in each feature. min_positions, max_positions : tuple or list of tuples Each tuple gives the N-D coordinates of the corresponding minimum or maximum. See Also -------- maximum, minimum, maximum_position, minimum_position, center_of_mass Examples -------- >>> import numpy as np >>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> from scipy import ndimage >>> ndimage.extrema(a) (0, 9, (0, 2), (3, 0)) Features to process can be specified using `labels` and `index`: >>> lbl, nlbl = ndimage.label(a) >>> ndimage.extrema(a, lbl, index=np.arange(1, nlbl+1)) (array([1, 4, 3]), array([5, 7, 9]), [(0, 0), (1, 3), (3, 1)], [(1, 0), (2, 3), (3, 0)]) If no index is given, non-zero `labels` are processed: >>> ndimage.extrema(a, lbl) (1, 9, (0, 0), (3, 0)) r Nr r� T)r� r� r� r� c �, � g | ]}t |� � ��S rQ r� r� s r? rV zextrema.<locals>.<listcomp>� � � �Y�Y�Y�!�U�1�X�X�Y�Y�YrB c �, � g | ]}t |� � ��S rQ r� r� s r? rV zextrema.<locals>.<listcomp>� r� rB r� ) r5 r` rm r� r� �minimums� min_positions�maximums� max_positionss r? r r s sA � �l �;�u�}�U�+�+�1� 2� 2�D��}�a�S�4��U�a��U� �#4�#4� 4�5�5�d�d��d�;�H�7>�u�f�?D�HL�HL�RV�RV� 8X� 8X� 8X�4�H�m�X�}� �~�h� � � ;��(�E�=�H�+D��*L�$M�$M��}��0�D�8�9�9�;� ;� Z�Y� �(=�(=�b�!�(D�(D��(P�TX�'X�Y�Y�Y�M�Y�Y� �(=�(=�b�!�(D�(D��(P�TX�'X�Y�Y�Y�M� �X�}�m� ;�;rB c �P � ����� t � ��� � �t j d� � j D � � ���� ��fd�t � j � � D � � }t j |d � � rt |� � S d� t j |� � j D � � S )a� Calculate the center of mass of the values of an array at labels. Parameters ---------- input : ndarray Data from which to calculate center-of-mass. The masses can either be positive or negative. labels : ndarray, optional Labels for objects in `input`, as generated by `ndimage.label`. Only used with `index`. Dimensions must be the same as `input`. index : int or sequence of ints, optional Labels for which to calculate centers-of-mass. If not specified, the combined center of mass of all labels greater than zero will be calculated. Only used with `labels`. Returns ------- center_of_mass : tuple, or list of tuples Coordinates of centers-of-mass. Examples -------- >>> import numpy as np >>> a = np.array(([0,0,0,0], ... [0,1,1,0], ... [0,1,1,0], ... [0,1,1,0])) >>> from scipy import ndimage >>> ndimage.center_of_mass(a) (2.0, 1.5) Calculation of multiple objects in an image >>> b = np.array(([0,1,1,0], ... [0,1,0,0], ... [0,0,0,0], ... [0,0,1,1], ... [0,0,1,1])) >>> lbl = ndimage.label(b)[0] >>> ndimage.center_of_mass(b, lbl, [1,2]) [(0.33333333333333331, 1.3333333333333333), (3.5, 2.5)] Negative masses are also accepted, which can occur for example when bias is removed from measured data due to random noise. >>> c = np.array(([-1,0,0,0], ... [0,-1,-1,0], ... [0,1,-1,0], ... [0,1,1,0])) >>> ndimage.center_of_mass(c) (-4.0, 1.0) If there are division by zero issues, the function does not raise an error but rather issues a RuntimeWarning before returning inf and/or NaN. >>> d = np.array([-1, 1]) >>> ndimage.center_of_mass(d) (inf,) c �. � g | ]}t d |� � ��S �r )�slice)rR r^ s r? rV z"center_of_mass.<locals>.<listcomp>� s � �:�:�:���q�!���:�:�:rB c �z �� g | ]7}t ��| � t � � z ��� � �z ��8S rQ )r rj r� )rR �dir�gridsrm r5 r` � normalizers �����r? rV z"center_of_mass.<locals>.<listcomp>� sQ �� � -� -� -�� �5�5��:�,�,�U�3�3�3�V�U�C�C�j�P� -� -� -rB r c �, � g | ]}t |� � ��S rQ r� r� s r? rV z"center_of_mass.<locals>.<listcomp> s � � 5� 5� 5��E�!�H�H� 5� 5� 5rB ) r r! �ogridr) rY r& rc r� r� �T)r5 r` rm �resultsr� r� s ``` @@r? r r � s� ������ �z �U�F�E�*�*�J� �K�:�:�e�k�:�:�:� ;�E�-� -� -� -� -� -� -� -� �� �+�+�-� -� -�G� �~�g�a�j�!�!� ��W�~�~� � 5� 5�e�k�'� 2� 2� 4� 5� 5� 5�5rB c �v �� t j |||dz � � ��fd�}t | |||t dd�� � S )a� Calculate the histogram of the values of an array, optionally at labels. Histogram calculates the frequency of values in an array within bins determined by `min`, `max`, and `bins`. The `labels` and `index` keywords can limit the scope of the histogram to specified sub-regions within the array. Parameters ---------- input : array_like Data for which to calculate histogram. min, max : int Minimum and maximum values of range of histogram bins. bins : int Number of bins. labels : array_like, optional Labels for objects in `input`. If not None, must be same shape as `input`. index : int or sequence of ints, optional Label or labels for which to calculate histogram. If None, all values where label is greater than zero are used Returns ------- hist : ndarray Histogram counts. Examples -------- >>> import numpy as np >>> a = np.array([[ 0. , 0.2146, 0.5962, 0. ], ... [ 0. , 0.7778, 0. , 0. ], ... [ 0. , 0. , 0. , 0. ], ... [ 0. , 0. , 0.7181, 0.2787], ... [ 0. , 0. , 0.6573, 0.3094]]) >>> from scipy import ndimage >>> ndimage.histogram(a, 0, 1, 10) array([13, 0, 2, 1, 0, 1, 1, 2, 0, 0]) With labels and no indices, non-zero elements are counted: >>> lbl, nlbl = ndimage.label(a) >>> ndimage.histogram(a, 0, 1, 10, lbl) array([0, 0, 2, 1, 0, 1, 1, 2, 0, 0]) Indices can be used to count only certain objects: >>> ndimage.histogram(a, 0, 1, 10, lbl, 2) array([0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) r c �: �� t j | �� � d S r� )r! r )r� �_binss �r? �_histzhistogram.<locals>._hist> s �� ���t�U�+�+�A�.�.rB NF)rp )r! �linspacer �object)r5 rk rA �binsr` rm r� r� s @r? r r s^ �� �j �N�3��T�A�X� .� .�E�/� /� /� /� /� !����u�f�d�05� 7� 7� 7� 7rB c �� � t j | � � } | j j t j t j fvrt d� � �|�t j | j d� � }t j |t �� � }|j | j k rt d� � �|j D ]}|dk rt d� � ��|j j s|� � � }t j |� � }| j |j k rt d� � �t j t j t j t j t j t j t j g}|j j |vrt d � � �t/ |t j � � r |j j |vrt d � � �n|j }t3 j || � � }t7 j | |||� � |S ) a Apply watershed from markers using image foresting transform algorithm. Parameters ---------- input : array_like Input. markers : array_like Markers are points within each watershed that form the beginning of the process. Negative markers are considered background markers which are processed after the other markers. structure : structure element, optional A structuring element defining the connectivity of the object can be provided. If None, an element is generated with a squared connectivity equal to one. output : ndarray, optional An output array can optionally be provided. The same shape as input. Returns ------- watershed_ift : ndarray Output. Same shape as `input`. References ---------- .. [1] A.X. Falcao, J. Stolfi and R. de Alencar Lotufo, "The image foresting transform: theory, algorithms, and applications", Pattern Analysis and Machine Intelligence, vol. 26, pp. 19-29, 2004. z+only 8 and 16 unsigned inputs are supportedNr r r r r z'input and markers must have equal shapez marker should be of integer typez output should be of integer type) r! r" r rF �uint8�uint16r$ r r% r& r' r( r) �flags� contiguousr� �int8�int16r1 r� �int64�intcr0 r, r- r � _get_outputr r )r5 �markersr6 r7 r8 �integral_typess r? r r E s� � �> �M�%� � �E� �{��� �U�\� :�:�:��E�F�F�F��� �9�%�*�a�H�H� �� �i�t�4�4�4�I��~���#�#��E�F�F�F��o� J� J�� ��7�7� � H�I�I� I� � �?� %� %� �N�N�$�$� ��m�G�$�$�G� �{�g�m�#�#��D�E�E�E��j��k��k��j��k��j��j� "�N� �}�� �/�/��=�>�>�>��&�%�-�(�(� � �<� �N� 2� 2� � A�B�B� B� 3� � �� � $�V�U� 3� 3�F� ��E�7�I�v�>�>�>� �MrB )NNr� )F)NNF)NNFFFFF) r! r. � r r r r �__all__r r r r r� r� r r r r r r� r r r r r r r r r rQ rB r? �<module>r s� ��> � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � H� H� H�� A!� A!� A!� A!�HC4� C4� C4� C4�L (,� o� o� o� o� o�dW� W� W� W�t� � �h&� h&� h&� h&�V ,� ,� ,� ,� *� *� *� *�Z2?� 2?� 2?� 2?�j29� 29� 29� 29�j16� 16� 16� 16�h FK�9>� �q� q� q� q�h<;� <;� <;� <;�~M;� M;� M;� M;�`;>� ;>� ;>� ;>�|LJ� LJ� LJ� LJ�^RJ� RJ� RJ� RJ�jH<� H<� H<� H<�VF6� F6� F6� F6�R;7� ;7� ;7� ;7�|E� E� E� E� E� ErB
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