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""" Basic functions for manipulating 2d arrays
"""
absolute, asanyarray, arange, zeros, greater_equal, multiply, ones, asarray, where, int8, int16, int32, int64, empty, promote_types, diagonal, nonzero )
'diag', 'diagflat', 'eye', 'fliplr', 'flipud', 'tri', 'triu', 'tril', 'vander', 'histogram2d', 'mask_indices', 'tril_indices', 'tril_indices_from', 'triu_indices', 'triu_indices_from', ]
overrides.array_function_dispatch, module='numpy')
""" get small int that fits the range """ if high <= i4.max and low >= i4.min: return int32 return int64
return (m,)
def fliplr(m): """ 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
""" raise ValueError("Input must be >= 2-d.")
def flipud(m): """ 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])
""" m = asanyarray(m) if m.ndim < 1: raise ValueError("Input must be >= 1-d.") return m[::-1, ...]
""" 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
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.]])
""" return m else: i = (-k) * M
return (v,)
""" 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]])
""" else: i = (-k) * n else: raise ValueError("Input must be 1- or 2-d.")
""" 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]])
""" try: wrap = v.__array_wrap__ except AttributeError: wrap = None v = asarray(v).ravel() s = len(v) n = s + abs(k) res = zeros((n, n), v.dtype) if (k >= 0): i = arange(0, n-k) fi = i+k+i*n else: i = arange(0, n+k) fi = i+(i-k)*n res.flat[fi] = v if not wrap: return res return wrap(res)
""" 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.]])
""" M = N
arange(-k, M-k, dtype=_min_int(-k, M - k)))
# Avoid making a copy if the requested type is already bool
return (m,)
""" 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]])
""" m = asanyarray(m) mask = tri(*m.shape[-2:], k=k, dtype=bool)
return where(mask, m, zeros(1, m.dtype))
""" 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]])
"""
return (x,)
# Originally borrowed from John Hunter and matplotlib """ 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
""" x = asarray(x) if x.ndim != 1: raise ValueError("x must be a one-dimensional array or sequence.") if N is None: N = len(x)
v = empty((len(x), N), dtype=promote_types(x.dtype, int)) tmp = v[:, ::-1] if not increasing else v
if N > 0: tmp[:, 0] = 1 if N > 1: tmp[:, 1:] = x[:, None] multiply.accumulate(tmp[:, 1:], out=tmp[:, 1:], axis=1)
return v
weights=None, density=None): return (x, y, bins, weights)
density=None): """ 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``. normed : bool, optional An alias for the density argument that behaves identically. To avoid confusion with the broken normed argument to `histogram`, `density` should be preferred. 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 -------- >>> 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)) >>> 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 = 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()
""" from numpy import histogramdd
try: N = len(bins) except TypeError: N = 1
if N != 1 and N != 2: xedges = yedges = asarray(bins) bins = [xedges, yedges] hist, edges = histogramdd([x, y], bins, range, normed, weights, density) return hist, edges[0], edges[1]
""" 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])
""" m = ones((n, n), int) a = mask_func(m, k) return nonzero(a != 0)
""" 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]])
"""
return (arr,)
""" 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
""" raise ValueError("input array must be 2-d")
""" 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]])
"""
""" 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
""" raise ValueError("input array must be 2-d") |