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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
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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�
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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 )�likec � � |fS r7 r8 )�N�M�k�dtype�orderrE s r3 �_eye_dispatcherrL � � � � �7�Nr5 �Cc � � |�t | |||||�� � S |�| }t | |f||�� � }||k r|S t j |� � }t j |� � }|dk r|}n| |z }d|d||z
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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.]])
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� 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 rS r rB )rV rI �s�n�resrT s r3 r r � s� � �n �1�
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� �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
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|< |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 �ravelrZ r[ r rJ r r rS )rV rI �wrapr\ r] r^ rT �fis r3 r r 8 s� � �P�� ���� � � � �����������
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� �c � � |fS r7 r8 )rG rH rI rJ rE s r3 �_tri_dispatcherrg t rM r5 c � � |�t | ||||�� � S |�| }t j t | t d| � � �� � t | ||z
t | ||z
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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.
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
tri : ndarray of shape (N, M)
Array with its lower triangle filled with ones and zero elsewhere;
in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise.
Examples
--------
>>> np.tri(3, 5, 2, dtype=int)
array([[1, 1, 1, 0, 0],
[1, 1, 1, 1, 0],
[1, 1, 1, 1, 1]])
>>> np.tri(3, 5, -1)
array([[0., 0., 0., 0., 0.],
[1., 0., 0., 0., 0.],
[1., 1., 0., 0., 0.]])
N)rH rI rJ rE r r` F)�copy)�_tri_with_liker �outerr r4 �astype)rG rH rI rJ rE r: s r3 r r x s� � �T �� �a�1���T�B�B�B�B��y�
����F�1�H�Q��N�N� ;� ;� ;� "�A�2�q��s�(�A�2�q�1�u�2E�2E� F� F� F� H� H�A�
����U��#�#�A� �Hr5 c � � | fS r7 r8 )r: rI s r3 �_trilu_dispatcherrn � r< r5 c � � t | � � } t | j dd� |t d��}t || t d| j � � � � S )a$
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 rY �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]]])
rp NrD rq rr rt s r3 r r � sP � �L �1�
�
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increasings r3 �_vander_dispatcherrz 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 rZ r r rJ �intr �
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-�!�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> )rZ � TypeError)rx �y�bins�range�density�weightsrG s r3 �_histogram2d_dispatcherr� } s� � � � �
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} |
| 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.images.append(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()
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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 r~ r )r] � mask_funcrI r: �as r3 r$ r$ 8 s7 � �D
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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]])
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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
r> �input array must be 2-drp r? �rI r: )rA rB r% rY r� s r3 r& r& � s? � �0 �x�1�}�}��2�3�3�3� �� �"�
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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 rq c 3 �N �K � | ] }t |�j � � � V � � d S r7 r� r� s �r3 r� z triu_indices.<locals>.<genexpr>F 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`.
See Also
--------
triu_indices, triu
Notes
-----
.. versionadded:: 1.4.0
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