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File Content: `twodim_base.py`

""" Basic functions for manipulating 2d arrays

"""
from __future__ import division, absolute_import, print_function

from numpy.core.numeric import (
    asanyarray, arange, zeros, greater_equal, multiply, ones, asarray,
    where, int8, int16, int32, int64, empty, promote_types, diagonal,
    )
from numpy.core import iinfo


__all__ = [
    'diag', 'diagflat', 'eye', 'fliplr', 'flipud', 'rot90', 'tri', 'triu',
    'tril', 'vander', 'histogram2d', 'mask_indices', 'tril_indices',
    'tril_indices_from', 'triu_indices', 'triu_indices_from', ]


i1 = iinfo(int8)
i2 = iinfo(int16)
i4 = iinfo(int32)


def _min_int(low, high):
    """ get small int that fits the range """
    if high <= i1.max and low >= i1.min:
        return int8
    if high <= i2.max and low >= i2.min:
        return int16
    if high <= i4.max and low >= i4.min:
        return int32
    return int64


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 A[:,::-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

    """
    m = asanyarray(m)
    if m.ndim < 2:
        raise ValueError("Input must be >= 2-d.")
    return m[:, ::-1]


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 ``A[::-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, ...]


def rot90(m, k=1):
    """
    Rotate an array by 90 degrees in the counter-clockwise direction.

    The first two dimensions are rotated; therefore, the array must be at
    least 2-D.

    Parameters
    ----------
    m : array_like
        Array of two or more dimensions.
    k : integer
        Number of times the array is rotated by 90 degrees.

    Returns
    -------
    y : ndarray
        Rotated array.

    See Also
    --------
    fliplr : Flip an array horizontally.
    flipud : Flip an array vertically.

    Examples
    --------
    >>> m = np.array([[1,2],[3,4]], int)
    >>> m
    array([[1, 2],
           [3, 4]])
    >>> np.rot90(m)
    array([[2, 4],
           [1, 3]])
    >>> np.rot90(m, 2)
    array([[4, 3],
           [2, 1]])

    """
    m = asanyarray(m)
    if m.ndim < 2:
        raise ValueError("Input must >= 2-d.")
    k = k % 4
    if k == 0:
        return m
    elif k == 1:
        return fliplr(m).swapaxes(0, 1)
    elif k == 2:
        return fliplr(flipud(m))
    else:
        # k == 3
        return fliplr(m.swapaxes(0, 1))


def eye(N, M=None, k=0, dtype=float):
    """
    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.]])

    """
    if M is None:
        M = N
    m = zeros((N, M), dtype=dtype)
    if k >= M:
        return m
    if k >= 0:
        i = k
    else:
        i = (-k) * M
    m[:M-k].flat[i::M+1] = 1
    return m


def diag(v, k=0):
    """
    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]])

    """
    v = asanyarray(v)
    s = v.shape
    if len(s) == 1:
        n = s[0]+abs(k)
        res = zeros((n, n), v.dtype)
        if k >= 0:
            i = k
        else:
            i = (-k) * n
        res[:n-k].flat[i::n+1] = v
        return res
    elif len(s) == 2:
        return diagonal(v, k)
    else:
        raise ValueError("Input must be 1- or 2-d.")


def diagflat(v, k=0):
    """
    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)


def tri(N, M=None, k=0, dtype=float):
    """
    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.]])

    """
    if M is None:
        M = N

    m = greater_equal.outer(arange(N, dtype=_min_int(0, N)),
                            arange(-k, M-k, dtype=_min_int(-k, M - k)))

    # Avoid making a copy if the requested type is already bool
    m = m.astype(dtype, copy=False)

    return m


def tril(m, k=0):
    """
    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))


def triu(m, k=0):
    """
    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]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k-1, dtype=bool)

    return where(mask, zeros(1, m.dtype), m)


# Originally borrowed from John Hunter and matplotlib
def vander(x, N=None, increasing=False):
    """
    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


def histogram2d(x, y, bins=10, range=None, normed=False, weights=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.
    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,)
        The bin edges along the first dimension.
    yedges : ndarray, shape(ny,)
        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 2D-histogram with variable bin width. First define the bin
    edges:

    >>> xedges = [0, 1, 1.5, 3, 5]
    >>> yedges = [0, 2, 3, 4, 6]

    Next we create a histogram H with random bin content:

    >>> x = np.random.normal(3, 1, 100)
    >>> y = np.random.normal(1, 1, 100)
    >>> H, xedges, yedges = np.histogram2d(y, x, bins=(xedges, yedges))

    Or we fill the histogram H with a determined bin content:

    >>> H = np.ones((4, 4)).cumsum().reshape(4, 4)
    >>> print(H[::-1])  # This shows the bin content in the order as plotted
    [[ 13.  14.  15.  16.]
     [  9.  10.  11.  12.]
     [  5.   6.   7.   8.]
     [  1.   2.   3.   4.]]

    Imshow can only do an equidistant representation of bins:

    >>> fig = plt.figure(figsize=(7, 3))
    >>> ax = fig.add_subplot(131)
    >>> ax.set_title('imshow: equidistant')
    >>> im = plt.imshow(H, interpolation='nearest', origin='low',
                    extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])

    pcolormesh can display exact bin edges:

    >>> ax = fig.add_subplot(132)
    >>> ax.set_title('pcolormesh: exact bin edges')
    >>> X, Y = np.meshgrid(xedges, yedges)
    >>> ax.pcolormesh(X, Y, H)
    >>> ax.set_aspect('equal')

    NonUniformImage displays exact bin edges with interpolation:

    >>> ax = fig.add_subplot(133)
    >>> ax.set_title('NonUniformImage: interpolated')
    >>> im = mpl.image.NonUniformImage(ax, interpolation='bilinear')
    >>> xcenters = xedges[:-1] + 0.5 * (xedges[1:] - xedges[:-1])
    >>> ycenters = yedges[:-1] + 0.5 * (yedges[1:] - yedges[:-1])
    >>> im.set_data(xcenters, ycenters, H)
    >>> ax.images.append(im)
    >>> ax.set_xlim(xedges[0], xedges[-1])
    >>> ax.set_ylim(yedges[0], yedges[-1])
    >>> ax.set_aspect('equal')
    >>> plt.show()

    """
    from numpy import histogramdd

    try:
        N = len(bins)
    except TypeError:
        N = 1

    if N != 1 and N != 2:
        xedges = yedges = asarray(bins, float)
        bins = [xedges, yedges]
    hist, edges = histogramdd([x, y], bins, range, normed, weights)
    return hist, edges[0], edges[1]


def mask_indices(n, mask_func, k=0):
    """
    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 where(a != 0)


def tril_indices(n, k=0, m=None):
    """
    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 where(tri(n, m, k=k, dtype=bool))


def tril_indices_from(arr, k=0):
    """
    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

    """
    if arr.ndim != 2:
        raise ValueError("input array must be 2-d")
    return tril_indices(arr.shape[-2], k=k, m=arr.shape[-1])


def triu_indices(n, k=0, m=None):
    """
    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 where(~tri(n, m, k=k-1, dtype=bool))


def triu_indices_from(arr, k=0):
    """
    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

    """
    if arr.ndim != 2:
        raise ValueError("input array must be 2-d")
    return triu_indices(arr.shape[-2], k=k, m=arr.shape[-1])
Name	Size	Permission
__pycache__	---	0755
tests	---	0755
__init__.py	1189 bytes	0644
_datasource.py	21266 bytes	0644
_iotools.py	32062 bytes	0644
_version.py	4867 bytes	0644
arraypad.py	52079 bytes	0644
arraysetops.py	13815 bytes	0644
arrayterator.py	7203 bytes	0644
financial.py	23843 bytes	0644
format.py	28234 bytes	0644
function_base.py	150516 bytes	0644
index_tricks.py	26204 bytes	0644
info.py	6501 bytes	0644
nanfunctions.py	46486 bytes	0644
npyio.py	71412 bytes	0644
polynomial.py	38012 bytes	0644
recfunctions.py	35012 bytes	0644
scimath.py	14085 bytes	0644
setup.py	379 bytes	0644
shape_base.py	25574 bytes	0644
stride_tricks.py	6827 bytes	0644
twodim_base.py	26904 bytes	0644
type_check.py	15799 bytes	0644
ufunclike.py	4844 bytes	0644
user_array.py	8000 bytes	0644
utils.py	34996 bytes	0644
File Content: twodim_base.py

File Content: `twodim_base.py`
