Numpy operators: lcm, tril, identity and take (apache#16264)

* numpy op lcm

* numpy op tril

* numpy op identity & fix some typo

* numpy op take

python/mxnet/ndarray/numpy/_op.py

@@ -35,7 +35,7 @@
            'linspace', 'expand_dims', 'tile', 'arange', 'split', 'concatenate', 'stack', 'vstack', 'mean',
            'maximum', 'minimum', 'swapaxes', 'clip', 'argmax', 'std', 'var', 'indices', 'copysign',
            'ravel', 'hanning', 'hamming', 'blackman', 'flip', 'around', 'hypot', 'rad2deg', 'deg2rad',
-           'unique']
+           'unique', 'lcm', 'tril', 'identity', 'take']
 
 
 @set_module('mxnet.ndarray.numpy')
@@ -50,7 +50,7 @@ def zeros(shape, dtype=_np.float32, order='C', ctx=None):
         The shape of the empty array.
     dtype : str or numpy.dtype, optional
         An optional value type. Default is `numpy.float32`. Note that this
-        behavior is different from NumPy's `ones` function where `float64`
+        behavior is different from NumPy's `zeros` function where `float64`
         is the default value, because `float32` is considered as the default
         data type in deep learning.
     order : {'C'}, optional, default: 'C'
@@ -96,7 +96,7 @@ def ones(shape, dtype=_np.float32, order='C', ctx=None):
     Returns
     -------
     out : ndarray
-        Array of zeros with the given shape, dtype, and ctx.
+        Array of ones with the given shape, dtype, and ctx.
     """
     if order != 'C':
         raise NotImplementedError
@@ -213,6 +213,134 @@ def arange(start, stop=None, step=1, dtype=None, ctx=None):
     return _npi.arange(start=start, stop=stop, step=step, dtype=dtype, ctx=ctx)
 
 
+@set_module('mxnet.ndarray.numpy')
+def identity(n, dtype=None, ctx=None):
+    """
+    Return the identity array.
+
+    The identity array is a square array with ones on
+    the main diagonal.
+
+    Parameters
+    ----------
+    n : int
+        Number of rows (and columns) in `n` x `n` output.
+    dtype : data-type, optional
+        Data-type of the output.  Defaults to ``numpy.float32``.
+    ctx : Context, optional
+        An optional device context (default is the current default context).
+
+    Returns
+    -------
+    out : ndarray
+        `n` x `n` array with its main diagonal set to one,
+        and all other elements 0.
+
+    Examples
+    --------
+    >>> np.identity(3)
+    >>> np.identity(3)
+    array([[1., 0., 0.],
+           [0., 1., 0.],
+           [0., 0., 1.]])
+    """
+    if not isinstance(n, int):
+        raise TypeError("Input 'n' should be an integer")
+    if n < 0:
+        raise ValueError("Input 'n' cannot be negative")
+    if ctx is None:
+        ctx = current_context()
+    dtype = _np.float32 if dtype is None else dtype
+    return _npi.identity(shape=(n, n), ctx=ctx, dtype=dtype)
+
+
+# pylint: disable=redefined-outer-name
+@set_module('mxnet.ndarray.numpy')
+def take(a, indices, axis=None, mode='raise', out=None):
+    r"""
+    Take elements from an array along an axis.
+
+    When axis is not None, this function does the same thing as "fancy"
+    indexing (indexing arrays using arrays); however, it can be easier to use
+    if you need elements along a given axis. A call such as
+    ``np.take(arr, indices, axis=3)`` is equivalent to
+    ``arr[:,:,:,indices,...]``.
+
+    Explained without fancy indexing, this is equivalent to the following use
+    of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of
+    indices::
+
+        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
+        Nj = indices.shape
+        for ii in ndindex(Ni):
+            for jj in ndindex(Nj):
+                for kk in ndindex(Nk):
+                    out[ii + jj + kk] = a[ii + (indices[jj],) + kk]
+
+    Parameters
+    ----------
+    a : ndarray
+        The source array.
+    indices : ndarray
+        The indices of the values to extract. Also allow scalars for indices.
+    axis : int, optional
+        The axis over which to select values. By default, the flattened
+        input array is used.
+    out : ndarray, optional
+        If provided, the result will be placed in this array. It should
+        be of the appropriate shape and dtype.
+    mode : {'clip', 'wrap'}, optional
+        Specifies how out-of-bounds indices will behave.
+
+        * 'clip' -- clip to the range (default)
+        * 'wrap' -- wrap around
+
+        'clip' mode means that all indices that are too large are replaced
+        by the index that addresses the last element along that axis. Note
+        that this disables indexing with negative numbers.
+
+    Returns
+    -------
+    out : ndarray
+        The returned array has the same type as `a`.
+
+    Notes
+    -----
+
+    This function differs from the original `numpy.take
+    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.take.html>`_ in
+    the following way(s):
+
+    - Only ndarray or scalar ndarray is accepted as valid input.
+
+    Examples
+    --------
+    >>> a = np.array([4, 3, 5, 7, 6, 8])
+    >>> indices = np.array([0, 1, 4])
+    >>> np.take(a, indices)
+    array([4., 3., 6.])
+
+    In this example for `a` is an ndarray, "fancy" indexing can be used.
+
+    >>> a[indices]
+    array([4., 3., 6.])
+
+    If `indices` is not one dimensional, the output also has these dimensions.
+
+    >>> np.take(a, np.array([[0, 1], [2, 3]]))
+    array([[4., 3.],
+           [5., 7.]])
+    """
+    if mode not in ('wrap', 'clip', 'raise'):
+        raise NotImplementedError(
+            "function take does not support mode '{}'".format(mode))
+    if axis:
+        return _npi.take(a, indices, axis, mode, out)
+    else:
+        return _npi.take(_npi.reshape(a, -1), indices, 0, mode, out)
+# pylint: enable=redefined-outer-name
+
+
 #pylint: disable= too-many-arguments, no-member, protected-access
 def _ufunc_helper(lhs, rhs, fn_array, fn_scalar, lfn_scalar, rfn_scalar=None, out=None):
     """ Helper function for element-wise operation.
@@ -732,6 +860,79 @@ def expand_dims(a, axis):
     return _npi.expand_dims(a, axis)
 
 
+@set_module('mxnet.ndarray.numpy')
+def lcm(x1, x2, out=None):
+    """
+    Returns the lowest common multiple of ``|x1|`` and ``|x2|``
+
+    Parameters
+    ----------
+    x1, x2 : ndarrays or scalar values
+        The arrays for computing lowest common multiple. If x1.shape != x2.shape,
+        they must be broadcastable to a common shape (which may be the shape of
+        one or the other).
+
+    out : ndarray or None, optional
+        A location into which the result is stored. If provided, it must have a shape
+        that the inputs broadcast to. If not provided or None, a freshly-allocated array
+        is returned.
+
+    Returns
+    -------
+    y : ndarray or scalar
+        The lowest common multiple of the absolute value of the inputs
+        This is a scalar if both `x1` and `x2` are scalars.
+
+    See Also
+    --------
+    gcd : The greatest common divisor
+
+    Examples
+    --------
+    >>> np.lcm(12, 20)
+    60
+    >>> np.lcm(np.arange(6, dtype=int), 20)
+    array([ 0, 20, 20, 60, 20, 20], dtype=int64)
+    """
+    return _ufunc_helper(x1, x2, _npi.lcm, _np.lcm, _npi.lcm_scalar, None, out)
+
+
+@set_module('mxnet.ndarray.numpy')
+def tril(m, k=0):
+    r"""
+    Lower triangle of an array.
+
+    Return a copy of an array with elements above the `k`-th diagonal zeroed.
+
+    Parameters
+    ----------
+    m : ndarray, 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
+    --------
+    >>> a = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
+    >>> np.tril(a, -1)
+    array([[ 0.,  0.,  0.],
+           [ 4.,  0.,  0.],
+           [ 7.,  8.,  0.],
+           [10., 11., 12.]])
+    """
+    return _npi.tril(m, k)
+
+
 def _unary_func_helper(x, fn_array, fn_scalar, out=None, **kwargs):
     """Helper function for unary operators.