Edit File: twodim_base.cpython-37.pyc
B ��Fd�c � @ sT d Z ddlmZmZmZ ddlmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZ ddlmZmZ ddddd d d d d ddddddgZee�Zee�Zee�Z dd� Z dd� Z dd � Z dde fdd�Z!d(dd�Z"d)dd�Z#dde fd d �Z$d*d d �Z%d+d d �Z&d,d d �Z'd-d"d�Z(d.d#d�Z)d/d$d�Z*d0d%d�Z+d1d&d�Z,d2d'd�Z-dS )3z- Basic functions for manipulating 2d arrays � )�division�absolute_import�print_function)�absolute� asanyarray�arange�zeros� greater_equal�multiply�ones�asarray�where�int8�int16�int32�int64�empty� promote_types�diagonal)�iinfo� transpose�diag�diagflat�eye�fliplr�flipud�tri�triu�tril�vander� histogram2d� mask_indices� tril_indices�tril_indices_from� triu_indices�triu_indices_fromc C sL |t jkr| t jkrtS |tjkr0| tjkr0tS |tjkrH| tjkrHtS tS )z# get small int that fits the range ) �i1�max�minr �i2r �i4r r )�low�high� r- �H/opt/alt/python37/lib64/python3.7/site-packages/numpy/lib/twodim_base.py�_min_int s r/ c C s0 t | �} | jdk rtd��| dd�ddd�f S )a� Flip array in the left/right direction. Flip 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. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to m[:,::-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� ValueError)�mr- r- r. r # s , c C s, t | �} | jdk rtd��| ddd�df S )a Flip array in the up/down direction. Flip 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. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[::-1,...]``. Does not require the array to be two-dimensional. 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.Nr1 .)r r2 r3 )r4 r- r- r. r U s 0 Nc C sd |dkr | }t | |f|d�}||kr(|S |dkr6|}n | | }d|d|| � j|d|d �< |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. 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)�dtyper r5 )r �flat)�N�M�kr6 r4 �ir- r- r. r � s ' c C s� t | �} | j}t|�dkrv|d t|� }t||f| j�}|dkrH|}n | | }| |d|| � j|d|d �< |S t|�dkr�t| |�S td��dS )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]]) r5 r Nr0 zInput must be 1- or 2-d.) r �shape�len�absr r6 r7 r r3 )�vr: �s�n�resr; r- r- r. r � s 6 c C s� y | j }W n tk r" d}Y nX t| ��� } t| �}|t|� }t||f| j�}|dkr|td|| �}|| || }n td|| �}||| | }| |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 ) Z__array_wrap__�AttributeErrorr Zravelr= r> r r6 r r7 )r? r: �wrapr@ rA rB r; �fir- r- r. r s" ' c C sT |dkr | }t �t| td| �d�t| || t| || �d��}|j|dd�}|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. 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 ``i <= j + 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.]]) Nr )r6 F)�copy)r Zouterr r/ �astype)r8 r9 r: r6 r4 r- r- r. r A s %"c C s6 t | �} t| jdd� |td��}t|| td| j��S )a� Lower triangle of an array. Return a copy of an array with elements above the `k`-th diagonal zeroed. 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]]) ���N)r: r6 r5 )r r r< �boolr r r6 )r4 r: �maskr- r- r. r r s c C s: t | �} t| jdd� |d td��}t|td| j�| �S )a� Upper triangle of an array. Return a copy of a matrix with the elements below the `k`-th diagonal zeroed. 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]]) rH Nr5 )r: r6 )r r r< rI r r r6 )r4 r: rJ r- r- r. r � s Fc C s� t | �} | jdkrtd��|dkr*t| �}tt| �|ft| jt�d�}|s`|dd�ddd�f n|}|dkr|d|dd�df< |dkr�| dd�df |dd�dd�f< tj |dd�dd�f |dd�dd�f dd� |S )ag 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 >>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1) 48 r5 z.x must be a one-dimensional array or sequence.N)r6 r1 r )�outZaxis) r r2 r3 r= r r r6 �intr � accumulate)�xr8 Z increasingr? �tmpr- r- r. r � s H 0� c C s� ddl m} y t|�}W n tk r0 d}Y nX |dkrX|dkrXt|t� }} || 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. normed : bool, optional If False, returns the number of samples in each bin. If True, returns the bin density ``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 `normed` is True. If `normed` 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 `normed` 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 -------- >>> import matplotlib as mpl >>> 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)) >>> H = H.T # Let each row list bins with common y range. :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='low', ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) :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) :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 = mpl.image.NonUniformImage(ax, interpolation='bilinear') >>> xcenters = (xedges[:-1] + xedges[1:]) / 2 >>> ycenters = (yedges[:-1] + yedges[1:]) / 2 >>> im.set_data(xcenters, ycenters, H) >>> ax.images.append(im) >>> plt.show() r )� histogramddr5 r0 )�numpyrQ r= � TypeErrorr �float) rN �yZbins�range�normed�weightsrQ r8 ZxedgesZyedgesZhistZedgesr- r- r. r s p c C s$ 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 rL r )rA Z mask_funcr: r4 �ar- r- r. r! � s A c C s t t| ||td��S )a{ 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, 8, 9, 10, 12, 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]]) )r: r6 )r r rI )rA r: r4 r- r- r. r" � s Mc C s, | j dkrtd��t| jd || jd d�S )a� 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). See Also -------- tril_indices, tril Notes ----- .. versionadded:: 1.4.0 r0 zinput array must be 2-drH r1 )r: r4 )r2 r3 r" r< )�arrr: r- r- r. r# # s c C s t t| ||d td� �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, 3, 5, 6, 7, 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]]) r5 )r: r6 )r r rI )rA r: r4 r- r- r. r$ ? s Oc C s, | j dkrtd��t| jd || jd 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`. See Also -------- triu_indices, triu Notes ----- .. versionadded:: 1.4.0 r0 zinput array must be 2-drH r1 )r: r4 )r2 r3 r$ r< )rZ r: r- r- r. r% � s )r )r )r )r )NF)rP NFN)r )r N)r )r N)r ).�__doc__� __future__r r r Znumpy.core.numericr r r r r r r r r r r r r r r r Z numpy.corer r �__all__r& r) r* r/ r r rT r r r r r r r r r! r" r# r$ r% r- r- r- r. �<module> s2 H 264 G ;1 & Z ~ F P R