DŽgvdZddlZddlZddlmZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZddlmZmZddlmZddlmZddlmZgd Z ejBejDd Z"eeZ#eeZ$eeZ%d Z&d Z'e"e'dZ(e"e'dZ)eed dde*dfddddZ+e"e+Z,d%dZ-e"e-d&dZ.e"e-d&dZ/eed dde*fdddZ0e"e0Z1d%dZ2e"e2d&dZ3e"e2d&dZ4d'dZ5e"e5d(dZ6 d)dZ7e"e7d*dZ8ed d&dZ9ed d+d Z:d%d!Z;e"e;d&d"Z<ed d+d#Z=e"e;d&d$Z>y),z- Basic functions for manipulating 2d arrays N)_array_converter) asanyarrayarangezeros greater_equalmultiplyonesasarraywhereint8int16int32int64intpempty promote_typesdiagonalnonzeroindices)set_array_function_like_doc set_module) overrides)iinfo) broadcast_to)diagdiagflateyefliplrflipudtritriutrilvander histogram2d mask_indices tril_indicestril_indices_from triu_indicestriu_indices_fromnumpy)modulec|tjkr|tjk\rtS|tjkr|tjk\rt S|t jkr|t jk\rtStS)z# get small int that fits the range ) i1maxminr i2r i4rr)lowhighs c/home/mcse/projects/flask_80/flask-venv/lib/python3.12/site-packages/numpy/lib/_twodim_base_impl.py_min_intr5"sU rvv~#-  rvv~#-  rvv~#- Lc|fSNms r4_flip_dispatcherr<- 4Kr6cdt|}|jdkr td|dddddfS)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.Nrndim ValueErrorr:s r4rr1s7` 1 Avvz011 Q"W:r6c`t|}|jdkr td|ddddfS)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@.rAr:s r4rrgs7d 1 Avvz011 TrT3Y<r6C)devicelikec  |t|||||||S||}t||f|||}||k\r|Stj|}tj|}|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 device : str, optional The device on which to place the created array. Default: None. For Array-API interoperability only, so must be ``"cpu"`` if passed. .. versionadded:: 2.0.0 ${ARRAY_FUNCTION_LIKE} .. versionadded:: 1.20.0 Returns ------- I : ndarray of shape (N,M) An array where all elements are equal to zero, except for the `k`-th diagonal, whose values are equal to one. See Also -------- identity : (almost) equivalent function diag : diagonal 2-D array from a 1-D array specified by the user. Examples -------- >>> np.eye(2, dtype=int) array([[1, 0], [0, 1]]) >>> np.eye(3, k=1) array([[0., 1., 0.], [0., 0., 1.], [0., 0., 0.]]) N)MkdtypeorderrG)rLrMrGrrE)_eye_with_likeroperatorindexflat) NrJrKrLrMrGrHr;is r4rrsl  !qAU%   y  q!fEv>AAv qAqAAv R1HAdqsGLLAaC Hr6c|fSr8r9)vrKs r4_diag_dispatcherrVr=r6c>t|}|j}t|dk(rT|dt|z}t ||f|j }|dk\r|}n| |z}||d||z j |d|dz<|St|dk(r t||Std)a Extract a diagonal or construct a diagonal array. See the more detailed documentation for ``numpy.diagonal`` if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using. Parameters ---------- v : array_like If `v` is a 2-D array, return a copy of its `k`-th diagonal. If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th diagonal. k : int, optional Diagonal in question. The default is 0. Use `k>0` for diagonals above the main diagonal, and `k<0` for diagonals below the main diagonal. Returns ------- out : ndarray The extracted diagonal or constructed diagonal array. See Also -------- diagonal : Return specified diagonals. diagflat : Create a 2-D array with the flattened input as a diagonal. trace : Sum along diagonals. triu : Upper triangle of an array. tril : Lower triangle of an array. Examples -------- >>> x = np.arange(9).reshape((3,3)) >>> x array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> np.diag(x) array([0, 4, 8]) >>> np.diag(x, k=1) array([1, 5]) >>> np.diag(x, k=-1) array([3, 7]) >>> np.diag(np.diag(x)) array([[0, 0, 0], [0, 4, 0], [0, 0, 8]]) rErNr?zInput must be 1- or 2-d.) rshapelenabsrrLrQrrC)rUrKsnresrSs r4rrsn 1 A A 1v{ aDQKQFAGG$ 6AqA!"DQqS qv!A#v Q11~344r6ct|}|jd\}|j}t|}|t |z}t ||f|j }|dk\r!td||z t}||z||zz}n td||zt}|||z |zz}||j|<|j|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]]) F)subokrrL) r as_arraysravelrYrZrrLrrrQwrap)rUrKconvr[r\r]rSfis r4rr:sP A D e $BA  A AA CF A A C Q 1ac & qS1W 1ac & !QwYCHHRL 99S>r6)rHc |t|||||S||}tjt|t d|t| ||z t | ||z }|j |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. ${ARRAY_FUNCTION_LIKE} .. versionadded:: 1.20.0 Returns ------- tri : ndarray of shape (N, M) Array with its lower triangle filled with ones and zero elsewhere; in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise. Examples -------- >>> np.tri(3, 5, 2, dtype=int) array([[1, 1, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 1, 1]]) >>> np.tri(3, 5, -1) array([[0., 0., 0., 0., 0.], [1., 0., 0., 0., 0.], [1., 1., 0., 0., 0.]]) )rJrKrLrr`F)copy)_tri_with_likerouterrr5astype)rRrJrKrLrHr;s r4r r ssT dAau==y F1HQN;"A2qs(A2q1u2EF HA U#A Hr6c|fSr8r9)r;rKs r4_trilu_dispatcherrlr=r6ct|}t|jdd|td}t ||t d|j S)a$ 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]]]) NrKrLrErr rXboolr rrLr;rKmasks r4r"r"s@b 1 A   .D q%177+ ,,r6ct|}t|jdd|dz td}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]]]) rnNrErorprrs r4r!r!sDL 1 A  !4 0D uQ(! ,,r6c|fSr8r9)xrR increasings r4_vander_dispatcherrxr=r6ct|}|jdk7r td| t|}t t||ft |j t}|s |dddddfn|}|dkDr d|dddf<|dkDr<|dddf|ddddf<tj|ddddf|ddddfd|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 rEz.x must be a one-dimensional array or sequence.Nr`r@r)outaxis) r rBrCrYrrrLintr accumulate)rvrRrwrUtmps r4r#r#sR  Avv{IJJy F s1vqkqww!<=A&!AttG*AC1uAqD 1uq$wZAqrE C12JC12JQ? Hr6c#K|| t|}|dk(r |Ed{n||y#t$rd}Y&wxYw7w)NrEr?)rY TypeError)rvybinsrangedensityweightsrRs r4_histogram2d_dispatcherrvsS G G I Av M   s* A 0 AAA >A>Acddlm}t|t|k7r td t|}|dk7r|dk7rt |x}} || g}|||g||||\} } | | d| dfS#t$rd}YDwxYw)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 ` 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]]) :func:`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 ` 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 `, and a :func:`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.rEr?)r*rrYrCrr ) rvrrrrrrrRxedgesyedgeshistedgess r4r$r$sp" 1vQ=>> I Av!q&!$-'q!fdE7GDKD% q58 ##  s A,, A:9A:cTt||ft}|||}t|dk7S)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 r|r)r\ mask_funcrKr;as r4r%r%1s.D aVSA!QA 16?r6c|t|||ttfdtjdDS)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]]) roc3PK|]}t|jywr8rrX.0indstri_s r4 ztril_indices..)?dDJJ/5?#&Tsparser rqtuplerrXr\rKr;rs @r4r&r&xs;\ q!q %D ?$TZZ=? ??r6c|fSr8r9arrrKs r4_trilu_indices_form_dispatcherrs 6Mr6c|jdk7r tdt|jd||jdS)aI Return the indices for the lower-triangle of arr. See `tril_indices` for full details. Parameters ---------- arr : array_like The indices will be valid for square arrays whose dimensions are the same as arr. k : int, optional Diagonal offset (see `tril` for details). Examples -------- Create a 4 by 4 array. >>> a = np.arange(16).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Pass the array to get the indices of the lower triangular elements. >>> trili = np.tril_indices_from(a) >>> trili (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3])) >>> a[trili] array([ 0, 4, 5, 8, 9, 10, 12, 13, 14, 15]) This is syntactic sugar for tril_indices(). >>> np.tril_indices(a.shape[0]) (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3])) Use the `k` parameter to return the indices for the lower triangular array up to the k-th diagonal. >>> trili1 = np.tril_indices_from(a, k=1) >>> a[trili1] array([ 0, 1, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15]) See Also -------- tril_indices, tril, triu_indices_from Notes ----- .. versionadded:: 1.4.0 r?input array must be 2-drnr@rKr;)rBrCr&rXrs r4r'r's;r xx1}233  " ciim <>> iu1 = np.triu_indices(4) >>> iu2 = np.triu_indices(4, 2) Here is how they can be used with a sample array: >>> a = np.arange(16).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Both for indexing: >>> a[iu1] array([ 0, 1, 2, ..., 10, 11, 15]) And for assigning values: >>> a[iu1] = -1 >>> a array([[-1, -1, -1, -1], [ 4, -1, -1, -1], [ 8, 9, -1, -1], [12, 13, 14, -1]]) These cover only a small part of the whole array (two diagonals right of the main one): >>> a[iu2] = -10 >>> a array([[ -1, -1, -10, -10], [ 4, -1, -1, -10], [ 8, 9, -1, -1], [ 12, 13, 14, -1]]) rEroc3PK|]}t|jywr8rrs r4rztriu_indices..`rrTrrrs @r4r(r(sB` 1AT * *D ?$TZZ=? ??r6c|jdk7r tdt|jd||jdS)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?rrnr@r)rBrCr(rXrs r4r)r)ds;| xx1}233  " ciim <rs: J!6 @ ,)++ %%g7 4[ 5\ 5\)*2+2j)*4+4n G Qe3G $TG G T+(*3/)*D5+D5N)*5+5p G Qe4 T4 4 n+(*3/*+3-,3-l*+(-,(-V +,W -W tBF$($01e$2e$P GCCL GP?P?f78:=9:=z GR?R?j78?=9?=r6