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편집 파일: twodim_base.cpython-311.pyc
� �܋f�� � �F � d Z ddlZddlZddlmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZ ddlmZmZ ddlmZ ddlmZ ddl m Z g d�Z ej ej d � � � Z ee � � Z! ee � � Z" ee� � Z#d � Z$d � Z% e e%� � d � � � Z& e e%� � d� � � Z'e ed � � dde(dfdd�d�� � � � Z) e � � e)� � Z*d%d�Z+ e e+� � d&d�� � Z, e e+� � d&d�� � Z-e ed � � dde(fdd�d�� � � � Z. e � � e.� � Z/d%d�Z0 e e0� � d&d�� � Z1 e e0� � d&d�� � Z2d'd�Z3 e e3� � d(d�� � Z4 d)d �Z5 e e5� � d*d �� � Z6 ed � � d&d �� � Z7 ed � � d+d �� � Z8d%d!�Z9 e e9� � d&d"�� � Z: ed � � d+d#�� � Z; e e9� � d&d$�� � Z<dS ),z- Basic functions for manipulating 2d arrays � N)� asanyarray�arange�zeros� greater_equal�multiply�ones�asarray�where�int8�int16�int32�int64�intp�empty� promote_types�diagonal�nonzero�indices)�set_array_function_like_doc� set_module)� overrides)�iinfo)� broadcast_to)�diag�diagflat�eye�fliplr�flipud�tri�triu�tril�vander� histogram2d� mask_indices� tril_indices�tril_indices_from� triu_indices�triu_indices_from�numpy)�modulec � � |t j k r| t j k rt S |t j k r| t j k rt S |t j k r| t j k rt S t S )z# get small int that fits the range ) �i1�max�minr �i2r �i4r r )�low�highs �L/opt/cloudlinux/venv/lib64/python3.11/site-packages/numpy/lib/twodim_base.py�_min_intr4 ! sU � � �r�v�~�~�#���-�-�� � �r�v�~�~�#���-�-�� � �r�v�~�~�#���-�-�� � �L� c � � | fS �N� ��ms r3 �_flip_dispatcherr; , � � � �4�Kr5 c �r � t | � � } | j dk rt d� � �| dd�ddd�f S )ae Reverse the order of elements along axis 1 (left/right). For a 2-D array, this flips the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array, must be at least 2-D. Returns ------- f : ndarray A view of `m` with the columns reversed. Since a view is returned, this operation is :math:`\mathcal O(1)`. See Also -------- flipud : Flip array in the up/down direction. flip : Flip array in one or more dimensions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``. Requires the array to be at least 2-D. Examples -------- >>> A = np.diag([1.,2.,3.]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.fliplr(A) array([[0., 0., 1.], [0., 2., 0.], [3., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A) == A[:,::-1,...]) True � zInput must be >= 2-d.N����r �ndim� ValueErrorr9 s r3 r r 0 sB � �` �1� � �A��v��z�z��0�1�1�1� �Q�Q�Q���"��W�:�r5 c �n � t | � � } | j dk rt d� � �| ddd�df S )ax Reverse the order of elements along axis 0 (up/down). For a 2-D array, this flips the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array. Returns ------- out : array_like A view of `m` with the rows reversed. Since a view is returned, this operation is :math:`\mathcal O(1)`. See Also -------- fliplr : Flip array in the left/right direction. flip : Flip array in one or more dimensions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``. Requires the array to be at least 1-D. Examples -------- >>> A = np.diag([1.0, 2, 3]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.flipud(A) array([[0., 0., 3.], [0., 2., 0.], [1., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A) == A[::-1,...]) True >>> np.flipud([1,2]) array([2, 1]) � zInput must be >= 1-d.Nr? .r@ r9 s r3 r r f s> � �d �1� � �A��v��z�z��0�1�1�1� �T�T�r�T�3�Y�<�r5 �C)�likec � � |�t || ||||�� � S |�| }t | |f||�� � }||k r|S t j |� � }t j |� � }|dk r|}n| |z }d|d||z � j |d|dz �< |S )a Return a 2-D array with ones on the diagonal and zeros elsewhere. Parameters ---------- N : int Number of rows in the output. M : int, optional Number of columns in the output. If None, defaults to `N`. k : int, optional Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : data-type, optional Data-type of the returned array. order : {'C', 'F'}, optional Whether the output should be stored in row-major (C-style) or column-major (Fortran-style) order in memory. .. versionadded:: 1.14.0 ${ARRAY_FUNCTION_LIKE} .. versionadded:: 1.20.0 Returns ------- I : ndarray of shape (N,M) An array where all elements are equal to zero, except for the `k`-th diagonal, whose values are equal to one. See Also -------- identity : (almost) equivalent function diag : diagonal 2-D array from a 1-D array specified by the user. Examples -------- >>> np.eye(2, dtype=int) array([[1, 0], [0, 1]]) >>> np.eye(3, k=1) array([[0., 1., 0.], [0., 0., 1.], [0., 0., 0.]]) N)�M�k�dtype�order)rJ rK r rD )�_eye_with_liker �operator�index�flat)�NrH rI rJ rK rF r: �is r3 r r � s� � �b �� �d�A��a�u�E�J�J�J�J��y� �� �q�!�f�E��/�/�/�A��A�v�v��� ��q���A���q���A��A�v�v� ����R�1�H�� �A�d�q��s�d�G�L���A�a�C��� �Hr5 c � � | fS r7 r8 )�vrI s r3 �_diag_dispatcherrT � r< r5 c �n � t | � � } | j }t |� � dk r[|d t |� � z }t ||f| j � � }|dk r|}n| |z }| |d||z � j |d|dz �< |S t |� � dk rt | |� � S t d� � �)a� Extract a diagonal or construct a diagonal array. See the more detailed documentation for ``numpy.diagonal`` if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using. Parameters ---------- v : array_like If `v` is a 2-D array, return a copy of its `k`-th diagonal. If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th diagonal. k : int, optional Diagonal in question. The default is 0. Use `k>0` for diagonals above the main diagonal, and `k<0` for diagonals below the main diagonal. Returns ------- out : ndarray The extracted diagonal or constructed diagonal array. See Also -------- diagonal : Return specified diagonals. diagflat : Create a 2-D array with the flattened input as a diagonal. trace : Sum along diagonals. triu : Upper triangle of an array. tril : Lower triangle of an array. Examples -------- >>> x = np.arange(9).reshape((3,3)) >>> x array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> np.diag(x) array([0, 4, 8]) >>> np.diag(x, k=1) array([1, 5]) >>> np.diag(x, k=-1) array([3, 7]) >>> np.diag(np.diag(x)) array([[0, 0, 0], [0, 4, 0], [0, 0, 8]]) rD r Nr> zInput must be 1- or 2-d.) r �shape�len�absr rJ rO r rB )rS rI �s�n�resrQ s r3 r r � s� � �n �1� � �A� ��A� �1�v�v��{�{� �a�D��Q���K���Q��F�A�G�$�$�� ��6�6��A�A���q��A�!"��D�Q�q�S�D� ��q�v�!�A�#�v� �� � �Q���1�����1�~�~� ��3�4�4�4r5 c � � | j }n# t $ r d}Y nw xY wt | � � � � � } t | � � }|t |� � z }t ||f| j � � }|dk r&t d||z t �� � }||z ||z z }n%t d||z t �� � }|||z |z z }| |j |< |s|S ||� � S )a� Create a two-dimensional array with the flattened input as a diagonal. Parameters ---------- v : array_like Input data, which is flattened and set as the `k`-th diagonal of the output. k : int, optional Diagonal to set; 0, the default, corresponds to the "main" diagonal, a positive (negative) `k` giving the number of the diagonal above (below) the main. Returns ------- out : ndarray The 2-D output array. See Also -------- diag : MATLAB work-alike for 1-D and 2-D arrays. diagonal : Return specified diagonals. trace : Sum along diagonals. Examples -------- >>> np.diagflat([[1,2], [3,4]]) array([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) >>> np.diagflat([1,2], 1) array([[0, 1, 0], [0, 0, 2], [0, 0, 0]]) Nr �rJ ) �__array_wrap__�AttributeErrorr �ravelrW rX r rJ r r rO )rS rI �wraprY rZ r[ rQ �fis r3 r r 2 s� � �P�� ���� � � � ����������� � �����A� �A���A� �C��F�F� �A� ��A���� � �C� �Q��� �1�a��c�� &� &� &�� �q�S��1��W��� �1�a��c�� &� &� &�� ��!��Q�w�Y���C�H�R�L� � �� � �4��9�9�s � � �c � � |�t || |||�� � S |�| }t j t | t d| � � �� � t | ||z t | ||z � � �� � � � }|� |d�� � }|S )a\ An array with ones at and below the given diagonal and zeros elsewhere. Parameters ---------- N : int Number of rows in the array. M : int, optional Number of columns in the array. By default, `M` is taken equal to `N`. k : int, optional The sub-diagonal at and below which the array is filled. `k` = 0 is the main diagonal, while `k` < 0 is below it, and `k` > 0 is above. The default is 0. dtype : dtype, optional Data type of the returned array. The default is float. ${ARRAY_FUNCTION_LIKE} .. versionadded:: 1.20.0 Returns ------- tri : ndarray of shape (N, M) Array with its lower triangle filled with ones and zero elsewhere; in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise. Examples -------- >>> np.tri(3, 5, 2, dtype=int) array([[1, 1, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 1, 1]]) >>> np.tri(3, 5, -1) array([[0., 0., 0., 0., 0.], [1., 0., 0., 0., 0.], [1., 1., 0., 0., 0.]]) N)rH rI rJ r r] F)�copy)�_tri_with_liker �outerr r4 �astype)rP rH rI rJ rF r: s r3 r r n s� � �T �� �d�A��a�u�=�=�=�=��y� ����F�1�H�Q��N�N� ;� ;� ;� "�A�2�q��s�(�A�2�q�1�u�2E�2E� F� F� F� H� H�A� ����U��#�#�A� �Hr5 c � � | fS r7 r8 )r: rI s r3 �_trilu_dispatcherri � r< r5 c � � t | � � } t | j dd� |t d��}t || t d| j � � � � S )a$ Lower triangle of an array. Return a copy of an array with elements above the `k`-th diagonal zeroed. For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two axes. Parameters ---------- m : array_like, shape (..., M, N) Input array. k : int, optional Diagonal above which to zero elements. `k = 0` (the default) is the main diagonal, `k < 0` is below it and `k > 0` is above. Returns ------- tril : ndarray, shape (..., M, N) Lower triangle of `m`, of same shape and data-type as `m`. See Also -------- triu : same thing, only for the upper triangle Examples -------- >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 0, 0, 0], [ 4, 0, 0], [ 7, 8, 0], [10, 11, 12]]) >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5)) array([[[ 0, 0, 0, 0, 0], [ 5, 6, 0, 0, 0], [10, 11, 12, 0, 0], [15, 16, 17, 18, 0]], [[20, 0, 0, 0, 0], [25, 26, 0, 0, 0], [30, 31, 32, 0, 0], [35, 36, 37, 38, 0]], [[40, 0, 0, 0, 0], [45, 46, 0, 0, 0], [50, 51, 52, 0, 0], [55, 56, 57, 58, 0]]]) ���N�rI rJ rD �r r rV �boolr r rJ �r: rI �masks r3 r! r! � sL � �b �1� � �A� ������ ��� .� .� .�D� ��q�%��1�7�+�+� ,� ,�,r5 c � � t | � � } t | j dd� |dz t d��}t |t d| j � � | � � S )a� Upper triangle of an array. Return a copy of an array with the elements below the `k`-th diagonal zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the final two axes. Please refer to the documentation for `tril` for further details. See Also -------- tril : lower triangle of an array Examples -------- >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 1, 2, 3], [ 4, 5, 6], [ 0, 8, 9], [ 0, 0, 12]]) >>> np.triu(np.arange(3*4*5).reshape(3, 4, 5)) array([[[ 0, 1, 2, 3, 4], [ 0, 6, 7, 8, 9], [ 0, 0, 12, 13, 14], [ 0, 0, 0, 18, 19]], [[20, 21, 22, 23, 24], [ 0, 26, 27, 28, 29], [ 0, 0, 32, 33, 34], [ 0, 0, 0, 38, 39]], [[40, 41, 42, 43, 44], [ 0, 46, 47, 48, 49], [ 0, 0, 52, 53, 54], [ 0, 0, 0, 58, 59]]]) rk NrD rl rm ro s r3 r r � sP � �L �1� � �A� ������ ��!��4� 0� 0� 0�D� ��u�Q���(�(�!� ,� ,�,r5 c � � | fS r7 r8 )�xrP � increasings r3 �_vander_dispatcherru r< r5 Fc �� � t | � � } | j dk rt d� � �|�t | � � }t t | � � |ft | j t � � �� � }|s|dd�ddd�f n|}|dk r d|dd�df< |dk rD| dd�df |dd�dd�f< t j |dd�dd�f |dd�dd�f d�� � |S )ar Generate a Vandermonde matrix. The columns of the output matrix are powers of the input vector. The order of the powers is determined by the `increasing` boolean argument. Specifically, when `increasing` is False, the `i`-th output column is the input vector raised element-wise to the power of ``N - i - 1``. Such a matrix with a geometric progression in each row is named for Alexandre- Theophile Vandermonde. Parameters ---------- x : array_like 1-D input array. N : int, optional Number of columns in the output. If `N` is not specified, a square array is returned (``N = len(x)``). increasing : bool, optional Order of the powers of the columns. If True, the powers increase from left to right, if False (the default) they are reversed. .. versionadded:: 1.9.0 Returns ------- out : ndarray Vandermonde matrix. If `increasing` is False, the first column is ``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `increasing` is True, the columns are ``x^0, x^1, ..., x^(N-1)``. See Also -------- polynomial.polynomial.polyvander Examples -------- >>> x = np.array([1, 2, 3, 5]) >>> N = 3 >>> np.vander(x, N) array([[ 1, 1, 1], [ 4, 2, 1], [ 9, 3, 1], [25, 5, 1]]) >>> np.column_stack([x**(N-1-i) for i in range(N)]) array([[ 1, 1, 1], [ 4, 2, 1], [ 9, 3, 1], [25, 5, 1]]) >>> x = np.array([1, 2, 3, 5]) >>> np.vander(x) array([[ 1, 1, 1, 1], [ 8, 4, 2, 1], [ 27, 9, 3, 1], [125, 25, 5, 1]]) >>> np.vander(x, increasing=True) array([[ 1, 1, 1, 1], [ 1, 2, 4, 8], [ 1, 3, 9, 27], [ 1, 5, 25, 125]]) The determinant of a square Vandermonde matrix is the product of the differences between the values of the input vector: >>> np.linalg.det(np.vander(x)) 48.000000000000043 # may vary >>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1) 48 rD z.x must be a one-dimensional array or sequence.Nr] r? r )�out�axis) r rA rB rW r r rJ �intr � accumulate)rs rP rt rS �tmps r3 r" r" s � �R �� � �A��v��{�{��I�J�J�J��y� ��F�F�� �s�1�v�v�q�k� �q�w��!<�!<�=�=�=�A� &� -�!�A�A�A�t�t��t�G�*�*�A�C��1�u�u���A�A�A�q�D� ��1�u�u��q�q�q�$�w�Z��A�A�A�q�r�r�E� ���C����1�2�2��J�C����1�2�2��J�Q�?�?�?�?� �Hr5 c # � K � | V � |V � t |� � }n# t $ r d}Y nw xY w|dk r |E d {V �� n|V � |V � d S )NrD r> )rW � TypeError)rs �y�bins�range�density�weightsrP s r3 �_histogram2d_dispatcherr� q s� � � � � �G�G�G� �G�G�G�� ��I�I���� � � � � ���������A�v�v����������� � � � �M�M�M�M�Ms � � +�+� c �> � ddl m} t | � � t |� � k rt d� � � t |� � }n# t $ r d}Y nw xY w|dk r|dk rt |� � x}} || g} || |g||||� � \ } } | | d | d fS )a# Compute the bi-dimensional histogram of two data samples. Parameters ---------- x : array_like, shape (N,) An array containing the x coordinates of the points to be histogrammed. y : array_like, shape (N,) An array containing the y coordinates of the points to be histogrammed. bins : int or array_like or [int, int] or [array, array], optional The bin specification: * If int, the number of bins for the two dimensions (nx=ny=bins). * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins). * If [int, int], the number of bins in each dimension (nx, ny = bins). * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins). * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges. range : array_like, shape(2,2), optional The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range will be considered outliers and not tallied in the histogram. density : bool, optional If False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, ``bin_count / sample_count / bin_area``. weights : array_like, shape(N,), optional An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. Weights are normalized to 1 if `density` is True. If `density` is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray, shape(nx, ny) The bi-dimensional histogram of samples `x` and `y`. Values in `x` are histogrammed along the first dimension and values in `y` are histogrammed along the second dimension. xedges : ndarray, shape(nx+1,) The bin edges along the first dimension. yedges : ndarray, shape(ny+1,) The bin edges along the second dimension. See Also -------- histogram : 1D histogram histogramdd : Multidimensional histogram Notes ----- When `density` is True, then the returned histogram is the sample density, defined such that the sum over bins of the product ``bin_value * bin_area`` is 1. Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y` values on the ordinate axis. Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y` along the second dimension of the array (horizontal). This ensures compatibility with `histogramdd`. Examples -------- >>> from matplotlib.image import NonUniformImage >>> import matplotlib.pyplot as plt Construct a 2-D histogram with variable bin width. First define the bin edges: >>> xedges = [0, 1, 3, 5] >>> yedges = [0, 2, 3, 4, 6] Next we create a histogram H with random bin content: >>> x = np.random.normal(2, 1, 100) >>> y = np.random.normal(1, 1, 100) >>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges)) >>> # Histogram does not follow Cartesian convention (see Notes), >>> # therefore transpose H for visualization purposes. >>> H = H.T :func:`imshow <matplotlib.pyplot.imshow>` can only display square bins: >>> fig = plt.figure(figsize=(7, 3)) >>> ax = fig.add_subplot(131, title='imshow: square bins') >>> plt.imshow(H, interpolation='nearest', origin='lower', ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) <matplotlib.image.AxesImage object at 0x...> :func:`pcolormesh <matplotlib.pyplot.pcolormesh>` can display actual edges: >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges', ... aspect='equal') >>> X, Y = np.meshgrid(xedges, yedges) >>> ax.pcolormesh(X, Y, H) <matplotlib.collections.QuadMesh object at 0x...> :class:`NonUniformImage <matplotlib.image.NonUniformImage>` can be used to display actual bin edges with interpolation: >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated', ... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]]) >>> im = NonUniformImage(ax, interpolation='bilinear') >>> xcenters = (xedges[:-1] + xedges[1:]) / 2 >>> ycenters = (yedges[:-1] + yedges[1:]) / 2 >>> im.set_data(xcenters, ycenters, H) >>> ax.add_image(im) >>> plt.show() It is also possible to construct a 2-D histogram without specifying bin edges: >>> # Generate non-symmetric test data >>> n = 10000 >>> x = np.linspace(1, 100, n) >>> y = 2*np.log(x) + np.random.rand(n) - 0.5 >>> # Compute 2d histogram. Note the order of x/y and xedges/yedges >>> H, yedges, xedges = np.histogram2d(y, x, bins=20) Now we can plot the histogram using :func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a :func:`hexbin <matplotlib.pyplot.hexbin>` for comparison. >>> # Plot histogram using pcolormesh >>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True) >>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow') >>> ax1.plot(x, 2*np.log(x), 'k-') >>> ax1.set_xlim(x.min(), x.max()) >>> ax1.set_ylim(y.min(), y.max()) >>> ax1.set_xlabel('x') >>> ax1.set_ylabel('y') >>> ax1.set_title('histogram2d') >>> ax1.grid() >>> # Create hexbin plot for comparison >>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow') >>> ax2.plot(x, 2*np.log(x), 'k-') >>> ax2.set_title('hexbin') >>> ax2.set_xlim(x.min(), x.max()) >>> ax2.set_xlabel('x') >>> ax2.grid() >>> plt.show() r )� histogramddz"x and y must have the same length.rD r> )r) r� rW rB r} r ) rs r~ r r� r� r� r� rP �xedges�yedges�hist�edgess r3 r# r# � s� � �p "�!�!�!�!�!� �1�v�v��Q������=�>�>�>�� ��I�I���� � � � � �������� �A�v�v�!�q�&�&�!�$�-�-�'����� �� �+�q�!�f�d�E�7�G�D�D�K�D�%� ��q��5��8� #�#s �A � A�Ac �n � t | | ft � � } |||� � }t |dk � � S )a� Return the indices to access (n, n) arrays, given a masking function. Assume `mask_func` is a function that, for a square array a of size ``(n, n)`` with a possible offset argument `k`, when called as ``mask_func(a, k)`` returns a new array with zeros in certain locations (functions like `triu` or `tril` do precisely this). Then this function returns the indices where the non-zero values would be located. Parameters ---------- n : int The returned indices will be valid to access arrays of shape (n, n). mask_func : callable A function whose call signature is similar to that of `triu`, `tril`. That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`. `k` is an optional argument to the function. k : scalar An optional argument which is passed through to `mask_func`. Functions like `triu`, `tril` take a second argument that is interpreted as an offset. Returns ------- indices : tuple of arrays. The `n` arrays of indices corresponding to the locations where ``mask_func(np.ones((n, n)), k)`` is True. See Also -------- triu, tril, triu_indices, tril_indices Notes ----- .. versionadded:: 1.4.0 Examples -------- These are the indices that would allow you to access the upper triangular part of any 3x3 array: >>> iu = np.mask_indices(3, np.triu) For example, if `a` is a 3x3 array: >>> a = np.arange(9).reshape(3, 3) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> a[iu] array([0, 1, 2, 4, 5, 8]) An offset can be passed also to the masking function. This gets us the indices starting on the first diagonal right of the main one: >>> iu1 = np.mask_indices(3, np.triu, 1) with which we now extract only three elements: >>> a[iu1] array([1, 2, 5]) r )r ry r )rZ � mask_funcrI r: �as r3 r$ r$ , s7 � �D �a��V�S���A�� �!�Q���A� �1��6�?�?�r5 c � �� t | ||t �� � �t �fd�t �j d�� � D � � � � S )ap Return the indices for the lower-triangle of an (n, m) array. Parameters ---------- n : int The row dimension of the arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `tril` for details). m : int, optional .. versionadded:: 1.9.0 The column dimension of the arrays for which the returned arrays will be valid. By default `m` is taken equal to `n`. Returns ------- inds : tuple of arrays The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array. See also -------- triu_indices : similar function, for upper-triangular. mask_indices : generic function accepting an arbitrary mask function. tril, triu Notes ----- .. versionadded:: 1.4.0 Examples -------- Compute two different sets of indices to access 4x4 arrays, one for the lower triangular part starting at the main diagonal, and one starting two diagonals further right: >>> il1 = np.tril_indices(4) >>> il2 = np.tril_indices(4, 2) Here is how they can be used with a sample array: >>> 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]]) Both for indexing: >>> a[il1] array([ 0, 4, 5, ..., 13, 14, 15]) And for assigning values: >>> a[il1] = -1 >>> a array([[-1, 1, 2, 3], [-1, -1, 6, 7], [-1, -1, -1, 11], [-1, -1, -1, -1]]) These cover almost the whole array (two diagonals right of the main one): >>> a[il2] = -10 >>> a array([[-10, -10, -10, 3], [-10, -10, -10, -10], [-10, -10, -10, -10], [-10, -10, -10, -10]]) rl c 3 �N �K � | ] }t |�j � � � V � � d S r7 �r rV ��.0�inds�tri_s �r3 � <genexpr>z tril_indices.<locals>.<genexpr>� �H �� � � � ?� ?�� �d�D�J�/�/��5� ?� ?� ?� ?� ?� ?r5 T��sparse�r rn �tupler rV �rZ rI r: r� s @r3 r% r% s sc �� �\ �q�!�q�� %� %� %�D� � ?� ?� ?� ?� $�T�Z�� =� =� =�?� ?� ?� ?� ?� ?r5 c � � | fS r7 r8 ��arrrI s r3 � _trilu_indices_form_dispatcherr� � s � � �6�Mr5 c � � | j dk rt d� � �t | j d || j d �� � S )aI Return the indices for the lower-triangle of arr. See `tril_indices` for full details. Parameters ---------- arr : array_like The indices will be valid for square arrays whose dimensions are the same as arr. k : int, optional Diagonal offset (see `tril` for details). Examples -------- Create a 4 by 4 array. >>> 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]]) Pass the array to get the indices of the lower triangular elements. >>> trili = np.tril_indices_from(a) >>> trili (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3])) >>> a[trili] array([ 0, 4, 5, 8, 9, 10, 12, 13, 14, 15]) This is syntactic sugar for tril_indices(). >>> np.tril_indices(a.shape[0]) (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3])) Use the `k` parameter to return the indices for the lower triangular array up to the k-th diagonal. >>> trili1 = np.tril_indices_from(a, k=1) >>> a[trili1] array([ 0, 1, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15]) See Also -------- tril_indices, tril, triu_indices_from Notes ----- .. versionadded:: 1.4.0 r> �input array must be 2-drk r? �rI r: )rA rB r% rV r� s r3 r& r& � s@ � �r �x�1�}�}��2�3�3�3� �� �"� ��c�i��m� <� <� <�<r5 c � �� t | ||dz t �� � �t �fd�t �j d�� � D � � � � S )a� Return the indices for the upper-triangle of an (n, m) array. Parameters ---------- n : int The size of the arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `triu` for details). m : int, optional .. versionadded:: 1.9.0 The column dimension of the arrays for which the returned arrays will be valid. By default `m` is taken equal to `n`. Returns ------- inds : tuple, shape(2) of ndarrays, shape(`n`) The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array. Can be used to slice a ndarray of shape(`n`, `n`). See also -------- tril_indices : similar function, for lower-triangular. mask_indices : generic function accepting an arbitrary mask function. triu, tril Notes ----- .. versionadded:: 1.4.0 Examples -------- Compute two different sets of indices to access 4x4 arrays, one for the upper triangular part starting at the main diagonal, and one starting two diagonals further right: >>> iu1 = np.triu_indices(4) >>> iu2 = np.triu_indices(4, 2) Here is how they can be used with a sample array: >>> 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]]) Both for indexing: >>> a[iu1] array([ 0, 1, 2, ..., 10, 11, 15]) And for assigning values: >>> a[iu1] = -1 >>> a array([[-1, -1, -1, -1], [ 4, -1, -1, -1], [ 8, 9, -1, -1], [12, 13, 14, -1]]) These cover only a small part of the whole array (two diagonals right of the main one): >>> a[iu2] = -10 >>> a array([[ -1, -1, -10, -10], [ 4, -1, -1, -10], [ 8, 9, -1, -1], [ 12, 13, 14, -1]]) rD rl c 3 �N �K � | ] }t |�j � � � V � � d S r7 r� r� s �r3 r� z triu_indices.<locals>.<genexpr>[ r� r5 Tr� r� r� s @r3 r' r' sj �� �` ��1��A��T� *� *� *� *�D� � ?� ?� ?� ?� $�T�Z�� =� =� =�?� ?� ?� ?� ?� ?r5 c � � | j dk rt d� � �t | j d || j d �� � S )a� Return the indices for the upper-triangle of arr. See `triu_indices` for full details. Parameters ---------- arr : ndarray, shape(N, N) The indices will be valid for square arrays. k : int, optional Diagonal offset (see `triu` for details). Returns ------- triu_indices_from : tuple, shape(2) of ndarray, shape(N) Indices for the upper-triangle of `arr`. Examples -------- Create a 4 by 4 array. >>> a = np.arange(16).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Pass the array to get the indices of the upper triangular elements. >>> triui = np.triu_indices_from(a) >>> triui (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3])) >>> a[triui] array([ 0, 1, 2, 3, 5, 6, 7, 10, 11, 15]) This is syntactic sugar for triu_indices(). >>> np.triu_indices(a.shape[0]) (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3])) Use the `k` parameter to return the indices for the upper triangular array from the k-th diagonal. >>> triuim1 = np.triu_indices_from(a, k=1) >>> a[triuim1] array([ 1, 2, 3, 6, 7, 11]) See Also -------- triu_indices, triu, tril_indices_from Notes ----- .. versionadded:: 1.4.0 r> r� rk r? r� )rA rB r' rV r� s r3 r( r( _ s@ � �| �x�1�}�}��2�3�3�3� �� �"� ��c�i��m� <� <� <�<r5 r7 )r )NN)NF)NNNN)r� NNN)r N)=�__doc__� functoolsrM �numpy.core.numericr r r r r r r r r r r r r r r r r r �numpy.core.overridesr r � numpy.corer r �numpy.lib.stride_tricksr �__all__�partial�array_function_dispatchr, r/ r0 r4 r; r r �floatr rL rT r r r re ri r! r ru r" r� r# r$ r% r� r& r' r( r8 r5 r3 �<module>r� se ��� � � � � � ����� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � I� H� H� H� H� H� H� H� � � � � � � � � � � � � 0� 0� 0� 0� 0� 0� @� @� @�� ,�)�+� �%�g�7� 7� 7� � �U�4�[�[�� �U�5�\�\�� �U�5�\�\��� � �� � � ��)�*�*�2� 2� +�*�2�j ��)�*�*�4� 4� +�*�4�n � ��G��� �Q�e�3� @ �� @ � @ � @ � @ � �� � �@ �F +�(�(�*�*�3�/�/��� � � � ��)�*�*�D5� D5� D5� +�*�D5�N ��)�*�*�8� 8� 8� +�*�8�v � ��G��� �Q�e� 4 �T� 4 � 4 � 4 � 4 � �� � �4 �n +�(�(�*�*�3�/�/��� � � � ��*�+�+�3-� 3-� 3-� ,�+�3-�l ��*�+�+�(-� (-� (-� ,�+�(-�V� � � � ��+�,�,�W � W � W � -�,�W �t BF�$(�� � � �$ ��0�1�1�e$� e$� e$� 2�1�e$�P ��G���C� C� C� ��C�L ��G���P?� P?� P?� ��P?�f� � � � ��7�8�8�:=� :=� :=� 9�8�:=�z ��G���R?� R?� R?� ��R?�j ��7�8�8�?=� ?=� ?=� 9�8�?=� ?=� ?=r5