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# pylint: disable=C0302
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# pylint: disable=unused-argument
"""Namespace for numpy operators used in Gluon dispatched by F=ndarray."""
import numpy as _np
from ...base import numeric_types, integer_types
from ...util import _sanity_check_params, set_module
from ...util import wrap_np_unary_func, wrap_np_binary_func
from ...util import is_np_default_dtype, dtype_from_number
from ...device import current_device
from . import _internal as _npi
from . import _api_internal
from ..ndarray import NDArray, get_dtype_name
__all__ = ['shape', 'zeros', 'zeros_like', 'ones', 'ones_like', 'full', 'full_like', 'empty_like', 'invert', 'delete',
'add', 'broadcast_to', 'subtract', 'multiply', 'divide', 'mod', 'remainder', 'fmod',
'power', 'bitwise_not', 'trace', 'transpose', 'copy', 'moveaxis', 'reshape', 'dot',
'arctan2', 'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'log10', 'sqrt', 'cbrt', 'abs', 'insert', 'fabs',
'absolute', 'exp', 'expm1', 'arcsin', 'arccos', 'arctan', 'sign', 'log', 'degrees', 'log2', 'matmul',
'log1p', 'rint', 'radians', 'reciprocal', 'square', 'negative', 'fix', 'ceil', 'floor', 'histogram',
'trunc', 'logical_not', 'arcsinh', 'arccosh', 'arctanh', 'argsort', 'all', 'any', 'sort',
'tensordot', 'eye', 'linspace', 'median', 'tril_indices', 'triu_indices_from', 'triu_indices',
'logspace', 'expand_dims', 'tile', 'arange', 'array_split', 'split', 'hsplit', 'vsplit', 'dsplit',
'concatenate', 'append', 'stack', 'vstack', 'row_stack', 'column_stack', 'hstack', 'dstack',
'average', 'mean', 'maximum', 'fmax', 'minimum', 'fmin', 'around', 'round', 'round_', 'flatnonzero',
'max', 'min', 'amax', 'amin', 'logical_and', 'logical_or', 'logical_xor',
'swapaxes', 'clip', 'argmax', 'argmin', 'std', 'var', 'indices', 'copysign', 'ravel', 'unravel_index',
'diag_indices_from', 'hanning', 'hamming', 'blackman', 'flip', 'flipud', 'fliplr',
'hypot', 'bitwise_and', 'bitwise_xor', 'bitwise_or', 'rad2deg', 'deg2rad', 'unique', 'lcm', 'gcd',
'tril', 'triu', 'tri', 'identity', 'take', 'ldexp', 'vdot', 'inner', 'outer', 'cross', 'kron',
'equal', 'not_equal', 'greater', 'less', 'greater_equal', 'less_equal', 'roll', 'rot90', 'einsum',
'true_divide', 'nonzero', 'quantile', 'percentile', 'shares_memory', 'may_share_memory', 'interp',
'diff', 'ediff1d', 'resize', 'polyval', 'nan_to_num', 'isnan', 'isinf', 'isposinf', 'isneginf', 'isfinite',
'atleast_1d', 'atleast_2d', 'atleast_3d', 'fill_diagonal', 'squeeze',
'where', 'bincount', 'rollaxis', 'diagflat', 'repeat', 'prod', 'pad', 'cumsum', 'sum', 'diag', 'diagonal',
'positive', 'logaddexp', 'floor_divide', 'bitwise_left_shift', 'bitwise_right_shift']
@set_module('mxnet.ndarray.numpy')
def shape(a):
"""
Return the shape of an array.
Parameters
----------
a : array_like
Input array.
Returns
-------
shape : tuple of ints
The elements of the shape tuple give the lengths of the
corresponding array dimensions.
See Also
--------
ndarray.shape : Equivalent array method.
Examples
--------
>>> np.shape(np.eye(3))
(3, 3)
>>> np.shape([[1, 2]])
(1, 2)
>>> np.shape([0])
(1,)
>>> np.shape(0)
()
"""
return a.shape
@set_module('mxnet.ndarray.numpy')
def zeros(shape, dtype=None, order='C', device=None): # pylint: disable=redefined-outer-name
"""Return a new array of given shape and type, filled with zeros.
This function currently only supports storing multi-dimensional data
in row-major (C-style).
Parameters
----------
shape : int or tuple of int
The shape of the empty array.
dtype : str or numpy.dtype, optional
An optional value type.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
Note that this behavior is different from NumPy's `zeros` function where `float64`
is the default value, here we can set 'float32' or 'float64' as your default dtype,
because `float32` is considered as the default data type in deep learning.
order : {'C'}, optional, default: 'C'
How to store multi-dimensional data in memory, currently only row-major
(C-style) is supported.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
out : ndarray
Array of zeros with the given shape, dtype, and device.
"""
if order != 'C':
raise NotImplementedError
# If the following code (4 lines) regarding device is removed
# np.zeros((3, 4)) can be as fast as 4.96 us
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.zeros(shape, dtype, device)
@set_module('mxnet.ndarray.numpy')
def ones(shape, dtype=None, order='C', device=None): # pylint: disable=redefined-outer-name
"""Return a new array of given shape and type, filled with ones.
This function currently only supports storing multi-dimensional data
in row-major (C-style).
Parameters
----------
shape : int or tuple of int
The shape of the empty array.
dtype : str or numpy.dtype, optional
An optional value type.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
Note that this behavior is different from NumPy's `ones` function where
`float64` is the default value.
order : {'C'}, optional, default: 'C'
How to store multi-dimensional data in memory, currently only row-major
(C-style) is supported.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
out : ndarray
Array of ones with the given shape, dtype, and device.
"""
if order != 'C':
raise NotImplementedError
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.ones(shape, dtype, device)
# pylint: disable=too-many-arguments, redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def zeros_like(a, dtype=None, order='C', device=None, out=None):
"""
Return an array of zeros with the same shape and type as a given array.
Parameters
----------
a : ndarray
The shape and data-type of `a` define these same attributes of
the returned array.
dtype : data-type, optional
Overrides the data type of the result.
Temporarily do not support boolean type.
order : {'C'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. Currently only supports C order.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
out : ndarray
Array of zeros with the same shape and type as a.
See Also
--------
empty_like : Return an empty array with shape and type of input.
ones_like : Return an array of ones with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
full : Return a new array of given shape filled with value.
Examples
--------
>>> x = np.arange(6)
>>> x = x.reshape((2, 3))
>>> x
array([[0., 1., 2.],
[3., 4., 5.]])
>>> np.zeros_like(x)
array([[0., 0., 0.],
[0., 0., 0.]])
>>> np.zeros_like(x, int)
array([[0, 0, 0],
[0, 0, 0]], dtype=int64)
>>> y = np.arange(3, dtype=float)
>>> y
array([0., 1., 2.], dtype=float64)
>>> np.zeros_like(y)
array([0., 0., 0.], dtype=float64)
"""
if order != 'C':
raise NotImplementedError
return full_like(a, 0, dtype=dtype, order=order, device=device, out=out)
@set_module('mxnet.ndarray.numpy')
def ones_like(a, dtype=None, order='C', device=None, out=None):
"""
Return an array of ones with the same shape and type as a given array.
Parameters
----------
a : ndarray
The shape and data-type of `a` define these same attributes of
the returned array.
dtype : data-type, optional
Overrides the data type of the result.
Temporarily do not support boolean type.
order : {'C'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. Currently only supports C order.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
out : ndarray
Array of ones with the same shape and type as a.
See Also
--------
empty_like : Return an empty array with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
full_like : Return a new array with shape of input filled with value.
ones : Return a new array setting values to one.
Examples
--------
>>> x = np.arange(6)
>>> x = x.reshape((2, 3))
>>> x
array([[0., 1., 2.],
[3., 4., 5.]])
>>> np.ones_like(x)
array([[1., 1., 1.],
[1., 1., 1.]])
>>> np.ones_like(x, int)
array([[1, 1, 1],
[1, 1, 1]], dtype=int64)
>>> y = np.arange(3, dtype=float)
>>> y
array([0., 1., 2.], dtype=float64)
>>> np.ones_like(y)
array([1., 1., 1.], dtype=float64)
"""
return full_like(a, 1, dtype=dtype, order=order, device=device, out=out)
@set_module('mxnet.ndarray.numpy')
def broadcast_to(array, shape):
"""
Broadcast an array to a new shape.
Parameters
----------
array : ndarray or scalar
The array to broadcast.
shape : tuple
The shape of the desired array.
Returns
-------
broadcast : array
A readonly view on the original array with the given shape. It is
typically not contiguous. Furthermore, more than one element of a
broadcasted array may refer to a single memory location.
Raises
------
MXNetError
If the array is not compatible with the new shape according to NumPy's
broadcasting rules.
"""
if _np.isscalar(array):
return full(shape, array)
return _api_internal.broadcast_to(array, shape)
@set_module('mxnet.ndarray.numpy')
def full(shape, fill_value, dtype=None, order='C', device=None, out=None): # pylint: disable=too-many-arguments
"""
Return a new array of given shape and type, filled with `fill_value`.
Parameters
----------
shape : int or sequence of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
fill_value : scalar or ndarray
Fill value.
dtype : data-type, optional
If dtype is None, the output array data type must be inferred from fill_value.
If it’s an int, the output array dtype must be the default integer dtype;
If it’s a float, then the output array dtype must be the default floating-point data type;
If it’s a bool then the output array must have boolean dtype. Default: None.
order : {'C'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. Currently only supports C order.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
out : ndarray
Array of `fill_value` with the given shape, dtype, and order.
If `fill_value` is an ndarray, out will have the same device as `fill_value`
regardless of the provided `device`.
Notes
-----
This function differs from the original `numpy.full
https://docs.scipy.org/doc/numpy/reference/generated/numpy.full.html`_ in
the following way(s):
- Have an additional `device` argument to specify the device
- Have an additional `out` argument
- Currently does not support `order` selection
See Also
--------
empty : Return a new uninitialized array.
ones : Return a new array setting values to one.
zeros : Return a new array setting values to zero.
Examples
--------
>>> np.full((2, 2), 10)
array([[10., 10.],
[10., 10.]])
>>> np.full((2, 2), 2, dtype=np.int32, device=mx.cpu(0))
array([[2, 2],
[2, 2]], dtype=int32)
"""
if order != 'C':
raise NotImplementedError
if isinstance(fill_value, NDArray):
if dtype is None:
ret = broadcast_to(fill_value, shape)
else:
ret = broadcast_to(fill_value, shape).astype(dtype)
return ret
if device is None:
device = str(current_device())
else:
device = str(device)
if isinstance(fill_value, bool):
fill_value = int(fill_value)
dtype = _np.bool if dtype is None else dtype
elif isinstance(fill_value, numeric_types):
if dtype is None or dtype is float:
dtype = dtype_from_number(fill_value)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.full(shape, dtype, fill_value, device, out)
# pylint: enable=too-many-arguments, redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def full_like(a, fill_value, dtype=None, order='C', device=None, out=None): # pylint: disable=too-many-arguments
"""
Return a full array with the same shape and type as a given array.
Parameters
----------
a : ndarray
The shape and data-type of `a` define these same attributes of
the returned array.
fill_value : scalar
Fill value.
dtype : data-type, optional
Overrides the data type of the result.
Temporarily do not support boolean type.
order : {'C'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. Currently only supports C order.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
out : ndarray
Array of `fill_value` with the same shape and type as `a`.
See Also
--------
empty_like : Return an empty array with shape and type of input.
ones_like : Return an array of ones with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
full : Return a new array of given shape filled with value.
Examples
--------
>>> x = np.arange(6, dtype=int)
>>> np.full_like(x, 1)
array([1, 1, 1, 1, 1, 1], dtype=int64)
>>> np.full_like(x, 0.1)
array([0, 0, 0, 0, 0, 0], dtype=int64)
>>> np.full_like(x, 0.1, dtype=np.float64)
array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1], dtype=float64)
>>> np.full_like(x, np.nan, dtype=np.double)
array([nan, nan, nan, nan, nan, nan], dtype=float64)
>>> y = np.arange(6, dtype=np.float32)
>>> np.full_like(y, 0.1)
array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
"""
if order != 'C':
raise NotImplementedError
if isinstance(fill_value, bool):
fill_value = int(fill_value)
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.full_like(a, fill_value, dtype, device, out)
@set_module('mxnet.ndarray.numpy')
def empty_like(prototype, dtype=None, order='C', subok=False, shape=None): # pylint: disable=W0621
"""
Return a new array with the same shape and type as a given array.
Parameters
----------
prototype : ndarray
The shape and data-type of `prototype` define these same attributes
of the returned array.
dtype : data-type, optional
Overrides the data type of the result.
order : {'C'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. Currently only supports C order.
subok : {False}, optional
If True, then the newly created array will use the sub-class
type of 'a', otherwise it will be a base-class array. Defaults
to False.
(Only support False at this moment)
shape : int or sequence of ints, optional.
Overrides the shape of the result. If order='K' and the number of
dimensions is unchanged, will try to keep order, otherwise,
order='C' is implied.
(Not supported at this moment)
Returns
-------
out : ndarray
Array of uninitialized (arbitrary) data with the same
shape and type as `prototype`.
See Also
--------
ones_like : Return an array of ones with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
full_like : Return a new array with shape of input filled with value.
empty : Return a new uninitialized array.
Notes
-----
This function does *not* initialize the returned array; to do that use
`zeros_like` or `ones_like` instead. It may be marginally faster than
the functions that do set the array values.
Examples
--------
>>> a = np.array([[1,2,3], [4,5,6]])
>>> np.empty_like(a)
array([[-5764607523034234880, -2305834244544065442, 4563075075], # uninitialized
[ 4567052944, -5764607523034234880, 844424930131968]])
>>> a = np.array([[1., 2., 3.],[4.,5.,6.]])
>>> np.empty_like(a)
array([[4.9e-324, 9.9e-324, 1.5e-323], # uninitialized
[2.0e-323, 2.5e-323, 3.0e-323]])
"""
dtype_list = {_np.float16: 'float16', _np.float32: 'float32', _np.float64: 'float64',
float: 'float64', _np.int8: 'int8', _np.int16: 'int16', _np.int32: 'int32',
_np.int64: 'int64', int:'int64', _np.uint8: 'uint8', _np.uint16: 'uint16',
_np.uint32: 'uint32', _np.uint64: 'uint64', _np.bool: 'bool',
_np.bool_: 'bool_', bool: 'bool', None: 'None'}
if order != 'C':
raise NotImplementedError("Only support C-order at this moment")
if subok:
raise NotImplementedError("Creating array by using sub-class is not supported at this moment")
if shape is not None:
raise NotImplementedError("Assigning new shape is not supported at this moment")
try:
dtype = dtype if isinstance(dtype, str) else dtype_list[dtype]
except:
raise NotImplementedError("Do not support this dtype at this moment")
return _npi.empty_like_fallback(prototype, dtype=dtype, order=order, subok=subok, shape=shape)
@set_module('mxnet.ndarray.numpy')
def arange(start, stop=None, step=1, dtype=None, device=None):
"""Return evenly spaced values within a given interval.
Values are generated within the half-open interval ``[start, stop)``
(in other words, the interval including `start` but excluding `stop`).
For integer arguments the function is equivalent to the Python built-in
`range` function, but returns an ndarray rather than a list.
Parameters
----------
start : number, optional
Start of interval. The interval includes this value. The default
start value is 0.
stop : number
End of interval. The interval does not include this value, except
in some cases where `step` is not an integer and floating point
round-off affects the length of `out`.
step : number, optional
Spacing between values. For any output `out`, this is the distance
between two adjacent values, ``out[i+1] - out[i]``. The default
step size is 1. If `step` is specified as a position argument,
`start` must also be given.
dtype : dtype
The type of the output array.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
Returns
-------
arange : ndarray
Array of evenly spaced values.
For floating point arguments, the length of the result is
``ceil((stop - start)/step)``. Because of floating point overflow,
this rule may result in the last element of `out` being greater
than `stop`.
"""
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
if device is None:
device = str(current_device())
else:
device = str(device)
if stop is None:
stop = start
start = 0
if step is None:
step = 1
if start is None and stop is None:
raise ValueError('start and stop cannot be both None')
if step == 0:
raise ZeroDivisionError('step cannot be 0')
return _api_internal.arange(start, stop, step, dtype, device)
@set_module('mxnet.ndarray.numpy')
def identity(n, dtype=None, device=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.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
out : ndarray
`n` x `n` array with its main diagonal set to one,
and all other elements 0.
Examples
--------
>>> 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 device is None:
device = str(current_device())
else:
device = str(device)
shape = (n, n) # pylint: disable=redefined-outer-name
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.identity(shape, dtype, device)
# 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 is None:
return _api_internal.take(reshape(a, -1), indices, 0, mode, out)
else:
return _api_internal.take(a, indices, axis, mode, out)
# pylint: enable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def insert(arr, obj, values, axis=None):
"""
Insert values along the given axis before the given indices.
Parameters
----------
arr : ndarray
Input array.
obj : int, slice or ndarray of int64
Object that defines the index or indices before which `values` is
inserted.
Support for multiple insertions when `obj` is a single scalar or a
sequence with one element (only support int32 and int64 element).
values : ndarray
Values to insert into `arr`.
If the type of values is different from that of arr, values is converted
to the type of arr.
axis : int, optional
Axis along which to insert `values`. If `axis` is None then `arr`
is flattened first.
Returns
-------
out : ndarray
A copy of `arr` with `values` inserted. Note that `insert`
does not occur in-place: a new array is returned. If
`axis` is None, `out` is a flattened array.
Notes
-----
- Note that for higher dimensional inserts `obj=0` behaves very different
from `obj=[0]` just like `arr[:,0,:] = values` is different from
`arr[:,[0],:] = values`.
- If obj is a ndarray, it's dtype only supports int64
Examples
--------
>>> a = np.array([[1, 1], [2, 2], [3, 3]])
>>> a
array([[1., 1.],
[2., 2.],
[3., 3.]])
>>> np.insert(a, 1, np.array(5))
array([1., 5., 1., 2., 2., 3., 3.])
>>> np.insert(a, 1, np.array(5), axis=1)
array([[1., 5., 1.],
[2., 5., 2.],
[3., 5., 3.]])
Difference between sequence and scalars:
>>> np.insert(a, np.array([1], dtype=np.int64), np.array([[1],[2],[3]]), axis=1)
array([[1., 1., 1.],
[2., 2., 2.],
[3., 3., 3.]])
>>> np.insert(a, 1, np.array([1, 2, 3]), axis=1)
array([[1., 1., 1.],
[2., 2., 2.],
[3., 3., 3.]])
>>> b = a.flatten()
>>> b
array([1., 1., 2., 2., 3., 3.])
>>> np.insert(b, np.array([2, 2], dtype=np.int64), np.array([5, 6]))
array([1., 1., 5., 6., 2., 2., 3., 3.])
>>> np.insert(b, slice(2, 4), np.array([5, 6]))
array([1., 1., 5., 2., 6., 2., 3., 3.])
# type casting
>>> np.insert(b.astype(np.int32), np.array([2, 2],dtype='int64'), np.array([7.13, False]))
array([1, 1, 7, 0, 2, 2, 3, 3], dtype=int32)
>>> x = np.arange(8).reshape(2, 4)
>>> idx = np.array([1, 3], dtype=np.int64)
>>> np.insert(x, idx, np.array([999]), axis=1)
array([[ 0., 999., 1., 2., 999., 3.],
[ 4., 999., 5., 6., 999., 7.]])
"""
if isinstance(values, numeric_types):
if isinstance(obj, slice):
start = obj.start
stop = obj.stop
step = 1 if obj.step is None else obj.step
return _api_internal.insert_slice(arr, values, start, stop, step, axis)
elif isinstance(obj, integer_types):
return _api_internal.insert_scalar(arr, values, obj, axis)
elif isinstance(obj, NDArray):
return _api_internal.insert_tensor(arr, obj, values, axis)
if not isinstance(arr, NDArray):
raise TypeError("'arr' can not support type {}".format(str(type(arr))))
if not isinstance(values, NDArray):
raise TypeError("'values' can not support type {}".format(str(type(values))))
if isinstance(obj, slice):
start = obj.start
stop = obj.stop
step = 1 if obj.step is None else obj.step
return _api_internal.insert_slice(arr, values, start, stop, step, axis)
elif isinstance(obj, integer_types):
return _api_internal.insert_scalar(arr, values, obj, axis)
elif isinstance(obj, NDArray):
return _api_internal.insert_tensor(arr, values, obj, axis)
else:
raise TypeError("'obj' can not support type {}".format(str(type(obj))))
#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.
The function will perform numpy-like broadcasting if needed and call different functions.
Parameters
--------
lhs : ndarray or numeric value
Left-hand side operand.
rhs : ndarray or numeric value
Right-hand operand,
fn_array : function
Function to be called if both lhs and rhs are of ``ndarray`` type.
fn_scalar : function
Function to be called if both lhs and rhs are numeric values.
lfn_scalar : function
Function to be called if lhs is ``ndarray`` while rhs is numeric value
rfn_scalar : function
Function to be called if lhs is numeric value while rhs is ``ndarray``;
if none is provided, then the function is commutative, so rfn_scalar is equal to lfn_scalar
Returns
--------
mxnet.numpy.ndarray or scalar
result array or scalar
"""
from ...numpy import ndarray
from ...numpy_extension import from_numpy # pylint: disable=unused-import
if isinstance(lhs, numeric_types):
if isinstance(rhs, numeric_types):
return fn_scalar(lhs, rhs, out=out)
else:
if rfn_scalar is None:
# commutative function
return lfn_scalar(rhs, float(lhs), out=out)
else:
return rfn_scalar(rhs, float(lhs), out=out)
elif isinstance(rhs, numeric_types):
return lfn_scalar(lhs, float(rhs), out=out)
elif isinstance(lhs, ndarray) and isinstance(rhs, ndarray):
return fn_array(lhs, rhs, out=out)
else:
raise TypeError('type {} not supported'.format(str(type(rhs))))
#pylint: enable= too-many-arguments, no-member, protected-access
@set_module('mxnet.ndarray.numpy')
def unique(ar, return_index=False, return_inverse=False, return_counts=False, axis=None):
"""
Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional
outputs in addition to the unique elements:
* the indices of the input array that give the unique values
* the indices of the unique array that reconstruct the input array
* the number of times each unique value comes up in the input array
Parameters
----------
ar : ndarray
Input array. Unless `axis` is specified, this will be flattened if it
is not already 1-D.
return_index : bool, optional
If True, also return the indices of `ar` (along the specified axis,
if provided, or in the flattened array) that result in the unique array.
return_inverse : bool, optional
If True, also return the indices of the unique array (for the specified
axis, if provided) that can be used to reconstruct `ar`.
return_counts : bool, optional
If True, also return the number of times each unique item appears
in `ar`.
axis : int or None, optional
The axis to operate on. If None, `ar` will be flattened. If an integer,
the subarrays indexed by the given axis will be flattened and treated
as the elements of a 1-D array with the dimension of the given axis,
see the notes for more details. The default is None.
Returns
-------
unique : ndarray
The sorted unique values.
unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the
original array. Only provided if `return_index` is True.
unique_inverse : ndarray, optional
The indices to reconstruct the original array from the
unique array. Only provided if `return_inverse` is True.
unique_counts : ndarray, optional
The number of times each of the unique values comes up in the
original array. Only provided if `return_counts` is True.
Notes
-----
When an axis is specified the subarrays indexed by the axis are sorted.
This is done by making the specified axis the first dimension of the array
and then flattening the subarrays in C order. The flattened subarrays are
then viewed as a structured type with each element given a label, with the
effect that we end up with a 1-D array of structured types that can be
treated in the same way as any other 1-D array. The result is that the
flattened subarrays are sorted in lexicographic order starting with the
first element.
This function differs from the original `numpy.unique
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.unique.html>`_ in
the following aspects:
- Only support ndarray as input.
- Object arrays or structured arrays are not supported.
Examples
--------
>>> np.unique(np.array([1, 1, 2, 2, 3, 3]))
array([1., 2., 3.])
>>> a = np.array([[1, 1], [2, 3]])
>>> np.unique(a)
array([1., 2., 3.])
Return the unique rows of a 2D array
>>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
>>> np.unique(a, axis=0)
array([[1., 0., 0.],
[2., 3., 4.]])
Return the indices of the original array that give the unique values:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> u, indices = np.unique(a, return_index=True)
>>> u
array([1., 2., 3., 4., 6.])
>>> indices
array([0, 1, 5, 3, 2], dtype=int64)
>>> a[indices]
array([1., 2., 3., 4., 6.])
Reconstruct the input array from the unique values:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> u, indices = np.unique(a, return_inverse=True)
>>> u
array([1., 2., 3., 4., 6.])
>>> indices
array([0, 1, 4, 3, 1, 2, 1], dtype=int64)
>>> u[indices]
array([1., 2., 6., 4., 2., 3., 2.])
"""
ret = list(_api_internal.unique(ar, return_index, return_inverse, return_counts, axis))
return ret[0] if len(ret) == 1 else tuple(ret)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def add(x1, x2, out=None, **kwargs):
"""
Add arguments element-wise.
Parameters
----------
x1, x2 : ndarrays or scalar values
The arrays to be added. 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
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
-------
add : ndarray or scalar
The sum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.
Notes
-----
This operator now supports automatic type promotion. The resulting type will be determined
according to the following rules:
* If both inputs are of floating number types, the output is the more precise type.
* If only one of the inputs is floating number type, the result is that type.
* If both inputs are of integer types (including boolean), not supported yet.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.add(x1, x2, out=out)
return _api_internal.add(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def subtract(x1, x2, out=None, **kwargs):
"""
Subtract arguments element-wise.
Parameters
----------
x1, x2 : ndarrays or scalar values
The arrays to be subtracted from each other. 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
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
-------
subtract : ndarray or scalar
The difference of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.
Notes
-----
This operator now supports automatic type promotion. The resulting type will be determined
according to the following rules:
* If both inputs are of floating number types, the output is the more precise type.
* If only one of the inputs is floating number type, the result is that type.
* If both inputs are of integer types (including boolean), not supported yet.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.subtract(x1, x2, out=out)
return _api_internal.subtract(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def multiply(x1, x2, out=None, **kwargs):
"""
Multiply arguments element-wise.
Parameters
----------
x1, x2 : ndarrays or scalar values
The arrays to be multiplied. 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
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
-------
out : ndarray or scalar
The multiplication of x1 and x2, element-wise. This is a scalar if both x1 and x2
are scalars.
Notes
-----
This operator now supports automatic type promotion. The resulting type will be determined
according to the following rules:
* If both inputs are of floating number types, the output is the more precise type.
* If only one of the inputs is floating number type, the result is that type.
* If both inputs are of integer types (including boolean), not supported yet.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.multiply(x1, x2, out=out)
return _api_internal.multiply(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def divide(x1, x2, out=None, **kwargs):
"""
Returns a true division of the inputs, element-wise.
Parameters
----------
x1 : ndarray or scalar
Dividend array.
x2 : ndarray or scalar
Divisor array.
out : ndarray
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
-------
out : ndarray or scalar
This is a scalar if both x1 and x2 are scalars.
Notes
-----
This operator now supports automatic type promotion. The resulting type will be determined
according to the following rules:
* If both inputs are of floating number types, the output is the more precise type.
* If only one of the inputs is floating number type, the result is that type.
* If both inputs are of integer types (including boolean), the output is of default dtype.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.divide(x1, x2, out=out)
return _api_internal.true_divide(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def true_divide(x1, x2, out=None):
"""Returns a true division of the inputs, element-wise.
Instead of the Python traditional 'floor division', this returns a true
division. True division adjusts the output type to present the best
answer, regardless of input types.
Parameters
----------
x1 : ndarray or scalar
Dividend array.
x2 : ndarray or scalar
Divisor array.
out : ndarray
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
-------
out : ndarray or scalar
This is a scalar if both x1 and x2 are scalars.
Notes
-----
This operator now supports automatic type promotion. The resulting type will be determined
according to the following rules:
* If both inputs are of floating number types, the output is the more precise type.
* If only one of the inputs is floating number type, the result is that type.
* If both inputs are of integer types (including boolean), the output is of default dtype.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.true_divide(x1, x2, out=out)
return _api_internal.true_divide(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def floor_divide(x1, x2, out=None):
"""Return the largest integer smaller or equal to the division of the inputs.
It is equivalent to the Python // operator and pairs with the Python % (remainder),
function so that a = a % b + b * (a // b) up to roundoff.
Parameters
----------
x1 : ndarray or scalar
Dividend array.
x2 : ndarray or scalar
Divisor array.
out : ndarray
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
-------
out : ndarray or scalar
This is a scalar if both x1 and x2 are scalars.
.. note::
This operator now supports automatic type promotion. The resulting type will be determined
according to the following rules:
* If both inputs are of floating number types, the output is the more precise type.
* If only one of the inputs is floating number type, the result is that type.
* If both inputs are of integer types (including boolean), the output is the more
precise type
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.floor_divide(x1, x2, out=out)
return _api_internal.floor_divide(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def mod(x1, x2, out=None, **kwargs):
"""
Return element-wise remainder of division.
Parameters
----------
x1 : ndarray or scalar
Dividend array.
x2 : ndarray or scalar
Divisor array.
out : ndarray
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
-------
out : ndarray or scalar
This is a scalar if both x1 and x2 are scalars.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.mod(x1, x2, out=out)
return _api_internal.mod(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def fmod(x1, x2, out=None, **kwargs):
"""
Return element-wise remainder of division.
Parameters
----------
x1 : ndarray or scalar
Dividend array.
x2 : ndarray or scalar
Divisor array.
out : ndarray
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
-------
out : ndarray or scalar
This is a scalar if both x1 and x2 are scalars.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
_np.fmod(x1, x2, out=out)
return _api_internal.fmod(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def delete(arr, obj, axis=None):
"""
Return a new array with sub-arrays along an axis deleted. For a one
dimensional array, this returns those entries not returned by
`arr[obj]`.
Parameters
----------
arr : ndarray
Input array.
obj : slice, int or ndarray of ints
Indicate indices of sub-arrays to remove along the specified axis.
axis : int, optional
The axis along which to delete the subarray defined by `obj`.
If `axis` is None, `obj` is applied to the flattened array.
Returns
-------
out : ndarray
A copy of `arr` with the elements specified by `obj` removed. Note
that `delete` does not occur in-place. If `axis` is None, `out` is
a flattened array.
Examples
--------
>>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
>>> arr
array([[ 1., 2., 3., 4.],
[ 5., 6., 7., 8.],
[ 9., 10., 11., 12.]])
>>> np.delete(arr, 1, 0)
array([[ 1., 2., 3., 4.],
[ 9., 10., 11., 12.]])
>>> np.delete(arr, slice(None, None, 2), 1)
array([[ 2., 4.],
[ 6., 8.],
[10., 12.]])
>>> np.delete(arr, np.array([1,3,5]), None)
array([ 1., 3., 5., 7., 8., 9., 10., 11., 12.])
>>> np.delete(arr, np.array([1,1,5]), None)
array([ 1., 3., 4., 5., 7., 8., 9., 10., 11., 12.])
"""
if not isinstance(arr, NDArray):
raise TypeError("'arr' can not support type {}".format(str(type(arr))))
if isinstance(obj, slice):
start = obj.start
stop = obj.stop
step = 1 if obj.step is None else obj.step
return _api_internal.delete(arr, start, stop, step, axis)
elif isinstance(obj, integer_types):
return _api_internal.delete(arr, obj, axis)
elif isinstance(obj, NDArray):
return _api_internal.delete(arr, obj, axis)
else:
raise TypeError("'obj' can not support type {}".format(str(type(obj))))
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def matmul(a, b, out=None):
"""
Matrix product of two arrays.
Parameters
----------
a, b : ndarray
Input arrays, scalars not allowed.
out : ndarray, optional
A location into which the result is stored.
If provided, it must have a shape that matches the signature (n,k),(k,m)->(n,m).
If not provided or None, a freshly-allocated array is returned.
Returns
-------
y : ndarray
The matrix product of the inputs.
This is a scalar only when both x1, x2 are 1-d vectors.
Raises
------
MXNetError
If the last dimension of a is not the same size as the second-to-last dimension of b.
If a scalar value is passed in.
See Also
--------
tensordot :
Sum products over arbitrary axes.
dot :
alternative matrix product with different broadcasting rules.
einsum :
Einstein summation convention.
Notes
-----
The behavior depends on the arguments in the following way.
- If both arguments are 2-D they are multiplied like conventional matrices.
- If either argument is N-D, N > 2, it is treated as a stack of matrices
residing in the last two indexes and broadcast accordingly.
- If the first argument is 1-D, it is promoted to a matrix by prepending
a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
- If the second argument is 1-D, it is promoted to a matrix by appending a 1
to its dimensions. After matrix multiplication the appended 1 is removed.
matmul differs from dot in two important ways:
- Multiplication by scalars is not allowed, use multiply instead.
- Stacks of matrices are broadcast together as if the matrices were elements,
respecting the signature (n,k),(k,m)->(n,m):
>>> a = np.ones([9, 5, 7, 4])
>>> c = np.ones([9, 5, 4, 3])
>>> np.dot(a, c).shape
(9, 5, 7, 9, 5, 3)
>>> np.matmul(a, c).shape
(9, 5, 7, 3)
>>> # n is 7, k is 4, m is 3
Examples
--------
For 2-D arrays it is the matrix product:
>>> a = np.array([[1, 0],
... [0, 1]])
>>> b = np.array([[4, 1],
... [2, 2]])
>>> np.matmul(a, b)
array([[4., 1.],
[2., 2.]])
For 2-D mixed with 1-D, the result is the usual.
>>> a = np.array([[1, 0],
... [0, 1]])
>>> b = np.array([1, 2])
>>> np.matmul(a, b)
array([1., 2.])
>>> np.matmul(b, a)
array([1., 2.])
Broadcasting is conventional for stacks of arrays
>>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4))
>>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2))
>>> np.matmul(a, b).shape
(2, 2, 2)
>>> np.matmul(a, b)[0, 1, 1]
array(98.)
>>> sum(a[0, 1, :] * b[0, :, 1])
array(98.)
Scalar multiplication raises an error.
>>> np.matmul([1, 2], 3)
Traceback (most recent call last):
...
mxnet.base.MXNetError: ... : Multiplication by scalars is not allowed.
"""
return _api_internal.matmul(a, b, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def remainder(x1, x2, out=None):
"""
Return element-wise remainder of division.
Parameters
----------
x1 : ndarray or scalar
Dividend array.
x2 : ndarray or scalar
Divisor array.
out : ndarray
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
-------
out : ndarray or scalar
This is a scalar if both x1 and x2 are scalars.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
_np.mod(x1, x2, out=out)
return _api_internal.mod(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def power(x1, x2, out=None, **kwargs):
"""
First array elements raised to powers from second array, element-wise.
Parameters
----------
x1 : ndarray or scalar
The bases.
x2 : ndarray or scalar
The exponent.
out : ndarray
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
-------
out : ndarray or scalar
The bases in x1 raised to the exponents in x2.
This is a scalar if both x1 and x2 are scalars.
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.power(x1, x2, out=out)
return _api_internal.power(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def all(a, axis=None, out=None, keepdims=False):
"""
Test whether all array elements along a given axis evaluate to True.
Parameters
----------
a : ndarray
Input array or object that can be converted to an array.
axis : None or int or tuple of ints, optional
Axis or axes along which a logical AND reduction is performed.
The default (axis = None) is to perform a logical AND over
all the dimensions of the input array.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in
the result as dimensions with size one. With this option,
the result will broadcast correctly against the input array.
out : ndarray, optional
Alternate output array in which to place the result. It must have
the same shape as the expected output and its type is preserved
Returns
--------
all : ndarray, bool
A new boolean or array is returned unless out is specified,
in which case a reference to out is returned.
Examples:
---------
>>> np.all([[True,False],[True,True]])
False
>>> np.all([[True,False],[True,True]], axis=0)
array([ True, False])
>>> np.all([-1, 4, 5])
True
>>> np.all([1.0, np.nan])
True
>>> o=np.array(False)
>>> z=np.all([-1, 4, 5], out=o)
>>> id(z), id(o), z
(28293632, 28293632, array(True)) # may vary
"""
return _api_internal.all(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def any(a, axis=None, out=None, keepdims=False):
"""
Test whether any array element along a given axis evaluates to True.
Returns single boolean unless axis is not None
Parameters
----------
a : ndarray
Input array or object that can be converted to an array.
axis : None or int or tuple of ints, optional
Axis or axes along which a logical AND reduction is performed.
The default (axis = None) is to perform a logical AND over
all the dimensions of the input array.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in
the result as dimensions with size one. With this option,
the result will broadcast correctly against the input array.
out : ndarray, optional
Alternate output array in which to place the result. It must have
the same shape as the expected output and its type is preserved
Returns
--------
any : bool or ndarray
A new boolean or ndarray is returned unless out is specified,
in which case a reference to out is returned.
Examples:
---------
>>> np.any([[True, False], [True, True]])
True
>>> np.any([[True, False], [False, False]], axis=0)
array([ True, False])
>>> np.any([-1, 0, 5])
True
>>> np.any(np.nan)
True
>>> o=np.array(False)
>>> z=np.any([-1, 4, 5], out=o)
>>> z, o
(array(True), array(True))
>>> # Check now that z is a reference to o
>>> z is o
True
>>> id(z), id(o) # identity of z and o # doctest: +SKIP
(191614240, 191614240)
"""
return _api_internal.any(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def argsort(a, axis=-1, descending=False, stable=True):
"""
Returns the indices that sort an array `x` along a specified axis.
Notes
-----
`argsort` is a standard API in
https://data-apis.org/array-api/latest/API_specification/generated/signatures.sorting_functions.argsort.html
instead of an official NumPy operator.
Parameters
----------
a : ndarray
Array to sort.
axis : int or None, optional
Axis along which to sort. The default is -1 (the last axis). If None,
the flattened array is used.
descending : bool, optional
sort order. If `True`, the returned indices sort x in descending order (by value).
If `False`, the returned indices sort x in ascending order (by value).Default: False.
stable : bool, optional
sort stability. If `True`, the returned indices must maintain the relative order
of x values which compare as equal. If `False`, the returned indices may or may not
maintain the relative order of x values which compare as equal. Default: True.
Returns
-------
index_array : ndarray, int
Array of indices that sort `a` along the specified `axis`.
If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`.
More generally, ``np.take_along_axis(a, index_array, axis=axis)``
always yields the sorted `a`, irrespective of dimensionality.
Notes
-----
This operator does not support different sorting algorithms.
Examples
--------
One dimensional array:
>>> x = np.array([3, 1, 2])
>>> np.argsort(x)
array([1, 2, 0])
Two-dimensional array:
>>> x = np.array([[0, 3], [2, 2]])
>>> x
array([[0, 3],
[2, 2]])
>>> ind = np.argsort(x, axis=0) # sorts along first axis (down)
>>> ind
array([[0, 1],
[1, 0]])
>>> np.take_along_axis(x, ind, axis=0) # same as np.sort(x, axis=0)
array([[0, 2],
[2, 3]])
>>> ind = np.argsort(x, axis=1) # sorts along last axis (across)
>>> ind
array([[0, 1],
[0, 1]])
>>> np.take_along_axis(x, ind, axis=1) # same as np.sort(x, axis=1)
array([[0, 3],
[2, 2]])
Indices of the sorted elements of a N-dimensional array:
>>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
>>> ind
(array([0, 1, 1, 0]), array([0, 0, 1, 1]))
>>> x[ind] # same as np.sort(x, axis=None)
array([0, 2, 2, 3])
"""
return _api_internal.argsort(a, axis, not descending, 'int64')
@set_module('mxnet.ndarray.numpy')
def sort(a, axis=-1, descending=False, stable=True):
"""
Return a sorted copy of an array.
Notes
-----
`sort` is a standard API in
https://data-apis.org/array-api/latest/API_specification/generated/signatures.sorting_functions.sort.html
instead of an official NumPy operator.
Parameters
----------
a : ndarray
Array to sort.
axis : int or None, optional
Axis along which to sort. The default is -1 (the last axis). If None,
the flattened array is used.
descending : bool, optional
sort order. If `True`, the returned indices sort x in descending order (by value).
If `False`, the returned indices sort x in ascending order (by value).Default: False.
stable : bool, optional
sort stability. If `True`, the returned indices must maintain the relative order
of x values which compare as equal. If `False`, the returned indices may or may not
maintain the relative order of x values which compare as equal. Default: True.
Returns
-------
sorted_array : ndarray
Array of the same type and shape as `a`.
Notes
-----
This operator does not support different sorting algorithms.
Examples
--------
>>> a = np.array([[1,4],[3,1]])
>>> np.sort(a) # sort along the last axis
array([[1, 4],
[1, 3]])
>>> np.sort(a, axis=None) # sort the flattened array
array([1, 1, 3, 4])
>>> np.sort(a, axis=0) # sort along the first axis
array([[1, 1],
[3, 4]])
"""
return _api_internal.sort(a, axis, not descending)
@set_module('mxnet.ndarray.numpy')
def dot(a, b, out=None):
"""
Dot product of two arrays. Specifically,
- If both `a` and `b` are 1-D arrays, it is inner product of vectors
- If both `a` and `b` are 2-D arrays, it is matrix multiplication,
- If either `a` or `b` is 0-D (scalar), it is equivalent to :func:`multiply`
and using ``np.multiply(a, b)`` or ``a * b`` is preferred.
- If `a` is an N-D array and `b` is a 1-D array, it is a sum product over
the last axis of `a` and `b`.
- If `a` is an N-D array and `b` is a 2-D array, it is a
sum product over the last axis of `a` and the second-to-last axis of `b`::
dot(a, b)[i,j,k] = sum(a[i,j,:] * b[:,k])
Parameters
----------
a : ndarray
First argument.
b : ndarray
Second argument.
out : ndarray, optional
Output argument. It must have the same shape and type as the expected output.
Returns
-------
output : ndarray
Returns the dot product of `a` and `b`. If `a` and `b` are both
scalars or both 1-D arrays then a scalar is returned; otherwise
an array is returned.
If `out` is given, then it is returned
Examples
--------
>>> a = np.array(3)
>>> b = np.array(4)
>>> np.dot(a, b)
array(12.)
For 2-D arrays it is the matrix product:
>>> a = np.array([[1, 0], [0, 1]])
>>> b = np.array([[4, 1], [2, 2]])
>>> np.dot(a, b)
array([[4., 1.],
[2., 2.]])
>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(5*6)[::-1].reshape((6,5))
>>> np.dot(a, b)[2,3,2,2]
array(29884.)
>>> np.sum(a[2,3,2,:] * b[:,2])
array(29884.)
"""
return _api_internal.dot(a, b, out)
@set_module('mxnet.ndarray.numpy')
def tensordot(a, b, axes=2):
r"""
tensordot(a, b, axes=2)
Compute tensor dot product along specified axes for arrays >= 1-D.
Given two tensors (arrays of dimension greater than or equal to one),
`a` and `b`, and an ndarray object containing two ndarray
objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s
elements (components) over the axes specified by ``a_axes`` and
``b_axes``. The third argument can be a single non-negative
integer_like scalar, ``N``; if it is such, then the last ``N``
dimensions of `a` and the first ``N`` dimensions of `b` are summed
over.
Parameters
----------
a, b : ndarray, len(shape) >= 1
Tensors to "dot".
axes : int or (2,) ndarray
* integer_like
If an int N, sum over the last N axes of `a` and the first N axes
of `b` in order. The sizes of the corresponding axes must match.
* (2,) ndarray
Or, a list of axes to be summed over, first sequence applying to `a`,
second to `b`. Both elements ndarray must be of the same length.
See Also
--------
dot, einsum
Notes
-----
Three common use cases are:
* ``axes = 0`` : tensor product :math:`a\otimes b`
* ``axes = 1`` : tensor dot product :math:`a\cdot b`
* ``axes = 2`` : (default) tensor double contraction :math:`a:b`
When `axes` is integer_like, the sequence for evaluation will be: first
the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and
Nth axis in `b` last.
When there is more than one axis to sum over - and they are not the last
(first) axes of `a` (`b`) - the argument `axes` should consist of
two sequences of the same length, with the first axis to sum over given
first in both sequences, the second axis second, and so forth.
Examples
--------
>>> a = np.arange(60.).reshape(3,4,5)
>>> b = np.arange(24.).reshape(4,3,2)
>>> c = np.tensordot(a,b, axes=([1,0],[0,1]))
>>> c.shape
(5, 2)
>>> c
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
[ 4796., 5162.],
[ 4928., 5306.]])
"""
return _api_internal.tensordot(a, b, axes)
@set_module('mxnet.ndarray.numpy')
def histogram(a, bins=10, range=None, normed=None, weights=None, density=None): # pylint: disable=too-many-arguments
"""
Compute the histogram of a set of data.
Parameters
----------
a : ndarray
Input data. The histogram is computed over the flattened array.
bins : int or NDArray
If `bins` is an int, it defines the number of equal-width
bins in the given range (10, by default). If `bins` is a
sequence, it defines a monotonically increasing array of bin edges,
including the rightmost edge, allowing for non-uniform bin widths.
.. versionadded:: 1.11.0
If `bins` is a string, it defines the method used to calculate the
optimal bin width, as defined by `histogram_bin_edges`.
range : (float, float)
The lower and upper range of the bins. Required when `bins` is an integer.
Values outside the range are ignored. The first element of the range must
be less than or equal to the second.
normed : bool, optional
Not supported yet, coming soon.
weights : array_like, optional
Not supported yet, coming soon.
density : bool, optional
Not supported yet, coming soon.
"""
if normed is True:
raise NotImplementedError("normed is not supported yet...")
if weights is not None:
raise NotImplementedError("weights is not supported yet...")
if density is True:
raise NotImplementedError("density is not supported yet...")
if isinstance(bins, numeric_types):
if range is None:
raise NotImplementedError("automatic range is not supported yet...")
return tuple(_api_internal.histogram(a, None, bins, range))
if isinstance(bins, (list, tuple)):
raise NotImplementedError("array_like bins is not supported yet...")
if isinstance(bins, str):
raise NotImplementedError("string bins is not supported yet...")
if isinstance(bins, NDArray):
return tuple(_api_internal.histogram(a, bins, None, None))
raise ValueError("np.histogram fails with", locals())
@set_module('mxnet.ndarray.numpy')
def eye(N, M=None, k=0, dtype=float, **kwargs):
"""
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.
- When npx.is_np_default_dtype() returns False, default dtype is float32;
- When npx.is_np_default_dtype() returns True, default dtype is float64.
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.
"""
_sanity_check_params('eye', ['order'], kwargs)
device = kwargs.pop('device', current_device())
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is None or dtype is float:
dtype = _np.float64 if is_np_default_dtype() else _np.float32
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
# To avoid overflow errors, map large positive k values to the just-out-of-range "num_columns" value
k = minimum(k, M if M is not None else N)
# Similarly, map large negative k values to the just-out-of-range "-num_rows" value
k = maximum(k, -N)
return _api_internal.eye(N, M, int(k), device, dtype)
@set_module('mxnet.ndarray.numpy')
def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0, device=None): # pylint: disable=too-many-arguments
r"""
Return evenly spaced numbers over a specified interval.
Returns num evenly spaced samples, calculated over the interval [start, stop].
The endpoint of the interval can optionally be excluded.
Parameters
----------
start : int or float
The starting value of the sequence.
stop : int or float
The end value of the sequence, unless endpoint is set to False. In
that case, the sequence consists of all but the last of num + 1
evenly spaced samples, so that stop is excluded. Note that the step
size changes when endpoint is False.
num : int, optional
Number of samples to generate. Default is 50. Must be non-negative.
endpoint : bool, optional
If True, stop is the last sample. Otherwise, it is not included.
Default is True.
retstep : bool, optional
If True, return (samples, step), where step is the spacing between samples.
dtype : dtype, optional
The type of the output array. If dtype is not given, infer the data
type from the other input arguments.
axis : int, optional
The axis in the result to store the samples. Relevant only if start or
stop are array-like. By default (0), the samples will be along a new
axis inserted at the beginning. Use -1 to get an axis at the end.
Returns
-------
samples : ndarray
There are num equally spaced samples in the closed interval
`[start, stop]` or the half-open interval `[start, stop)`
(depending on whether endpoint is True or False).
step : float, optional
Only returned if retstep is True
Size of spacing between samples.
See Also
--------
arange : Similar to `linspace`, but uses a step size (instead of the
number of samples).
Examples
--------
>>> np.linspace(2.0, 3.0, num=5)
array([2. , 2.25, 2.5 , 2.75, 3. ])
>>> np.linspace(2.0, 3.0, num=5, endpoint=False)
array([2. , 2.2, 2.4, 2.6, 2.8])
>>> np.linspace(2.0, 3.0, num=5, retstep=True)
(array([2. , 2.25, 2.5 , 2.75, 3. ]), 0.25)
Graphical illustration:
>>> import matplotlib.pyplot as plt
>>> N = 8
>>> y = np.zeros(N)
>>> x1 = np.linspace(0, 10, N, endpoint=True)
>>> x2 = np.linspace(0, 10, N, endpoint=False)
>>> plt.plot(x1.asnumpy(), y.asnumpy(), 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.plot(x2.asnumpy(), (y + 0.5).asnumpy(), 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.ylim([-0.5, 1])
(-0.5, 1)
>>> plt.show()
Notes
-----
This function differs from the original `numpy.linspace
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html>`_ in
the following aspects:
- `start` and `stop` do not support list, numpy ndarray and mxnet ndarray
- axis could only be 0
- There could be an additional `device` argument to specify the device, e.g. the i-th
GPU.
"""
if isinstance(start, (list, _np.ndarray, NDArray)) or \
isinstance(stop, (list, _np.ndarray, NDArray)):
raise NotImplementedError('start and stop only support int')
if axis != 0:
raise NotImplementedError("the function only support axis 0")
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
if dtype is None:
dtype = _np.float64 if is_np_default_dtype() else _np.float32
if retstep:
step = (stop - start) / (num - int(endpoint))
return _api_internal.linspace(start, stop, num, endpoint, device, dtype), step
else:
return _api_internal.linspace(start, stop, num, endpoint, device, dtype)
@set_module('mxnet.ndarray.numpy')
def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0, device=None): # pylint: disable=too-many-arguments
r"""Return numbers spaced evenly on a log scale.
In linear space, the sequence starts at ``base ** start``
(`base` to the power of `start`) and ends with ``base ** stop``
(see `endpoint` below).
Non-scalar `start` and `stop` are now supported.
Parameters
----------
start : int or float
``base ** start`` is the starting value of the sequence.
stop : int or float
``base ** stop`` is the final value of the sequence, unless `endpoint`
is False. In that case, ``num + 1`` values are spaced over the
interval in log-space, of which all but the last (a sequence of
length `num`) are returned.
num : integer, optional
Number of samples to generate. Default is 50.
endpoint : boolean, optional
If true, `stop` is the last sample. Otherwise, it is not included.
Default is True.
base : float, optional
The base of the log space. The step size between the elements in
``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.
Default is 10.0.
dtype : dtype
The type of the output array. If `dtype` is not given, infer the data
type from the other input arguments.
axis : int, optional
The axis in the result to store the samples. Relevant only if start
or stop are array-like. By default (0), the samples will be along a
new axis inserted at the beginning. Now, axis only support axis = 0.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
samples : ndarray
`num` samples, equally spaced on a log scale.
See Also
--------
arange : Similar to linspace, with the step size specified instead of the
number of samples. Note that, when used with a float endpoint, the
endpoint may or may not be included.
linspace : Similar to logspace, but with the samples uniformly distributed
in linear space, instead of log space.
Notes
-----
Logspace is equivalent to the code. Now wo only support axis = 0.
>>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
...
>>> power(base, y).astype(dtype)
...
Examples
--------
>>> np.logspace(2.0, 3.0, num=4)
array([ 100. , 215.44347, 464.15887, 1000. ])
>>> np.logspace(2.0, 3.0, num=4, endpoint=False)
array([100. , 177.82794, 316.22775, 562.3413 ])
>>> np.logspace(2.0, 3.0, num=4, base=2.0)
array([4. , 5.0396843, 6.349604 , 8. ])
>>> np.logspace(2.0, 3.0, num=4, base=2.0, dtype=np.int32)
array([4, 5, 6, 8], dtype=int32)
>>> np.logspace(2.0, 3.0, num=4, device=npx.gpu(0))
array([ 100. , 215.44347, 464.15887, 1000. ], device=gpu(0))
"""
if isinstance(start, (list, tuple, _np.ndarray, NDArray)) or \
isinstance(stop, (list, tuple, _np.ndarray, NDArray)):
raise NotImplementedError('start and stop only support int and float')
if axis != 0:
raise NotImplementedError("the function only support axis 0")
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.logspace(start, stop, num, endpoint, base, device, dtype)
@set_module('mxnet.ndarray.numpy')
def expand_dims(a, axis):
"""Expand the shape of an array.
Insert a new axis that will appear at the `axis` position in the expanded
Parameters
----------
a : ndarray
Input array.
axis : int
Position in the expanded axes where the new axis is placed.
Returns
-------
res : ndarray
Output array. The number of dimensions is one greater than that of
the input array.
"""
return _api_internal.expand_dims(a, axis)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def gcd(x1, x2, out=None, **kwargs):
"""
Returns the greatest common divisor of ``|x1|`` and ``|x2|``
Parameters
----------
x1, x2 : ndarrays or scalar values
The arrays for computing greatest common divisor. 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 greatest common divisor of the absolute value of the inputs
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
lcm : The lowest common multiple
Examples
--------
>>> np.gcd(12, 20)
4
>>> np.gcd(np.arange(6, dtype=int), 20)
array([20, 1, 2, 1, 4, 5], dtype=int64)
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.gcd(x1, x2, out=out)
return _api_internal.gcd(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def lcm(x1, x2, out=None, **kwargs):
"""
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)
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.lcm(x1, x2, out=out)
return _api_internal.lcm(x1, x2, 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 _api_internal.tril(m, k)
@set_module('mxnet.ndarray.numpy')
def triu(m, k=0):
r"""
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(np.array([[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 _api_internal.triu(m, k)
@set_module('mxnet.ndarray.numpy')
def trace(a, offset=0, axis1=0, axis2=1, out=None):
"""
Return the sum along diagonals of the array.
If `a` is 2-D, the sum along its diagonal with the given offset
is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.
If `a` has more than two dimensions, then the axes specified by axis1 and
axis2 are used to determine the 2-D sub-arrays whose traces are returned.
The shape of the resulting array is the same as that of `a` with `axis1`
and `axis2` removed.
Parameters
----------
a : ndarray
Input array, from which the diagonals are taken.
offset : int, optional
Offset of the diagonal from the main diagonal. Can be both positive
and negative. Defaults to 0.
axis1, axis2 : int, optional
Axes to be used as the first and second axis of the 2-D sub-arrays
from which the diagonals should be taken. Defaults are the first two
axes of `a`.
out : ndarray, optional
Array into which the output is placed. It must be of the right shape
and right type to hold the output.
Returns
-------
sum_along_diagonals : ndarray
If `a` is 2-D, the sum along the diagonal is returned. If `a` has
larger dimensions, then an array of sums along diagonals is returned.
Examples
--------
>>> a = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> np.trace(a)
array(3.)
>>> a = np.arange(8).reshape((2, 2, 2))
>>> np.trace(a)
array([6., 8.])
>>> a = np.arange(24).reshape((2, 2, 2, 3))
>>> np.trace(a).shape
(2, 3)
"""
return _api_internal.trace(a, offset, axis1, axis2, out)
@set_module('mxnet.ndarray.numpy')
def tri(N, M=None, k=0, dtype=None, device=None):
r"""
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 device is None:
device = str(current_device())
return _api_internal.tri(N, M, k, dtype, device)
@set_module('mxnet.ndarray.numpy')
def triu_indices(n, k=0, m=None, device=None):
r"""
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
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]])
"""
return nonzero(~tri(N=n, M=m, k=k-1, dtype=bool, device=device))
@set_module('mxnet.ndarray.numpy')
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
"""
if arr.ndim != 2:
raise ValueError("input array must be 2-d")
return triu_indices(arr.shape[-2], k=k, m=arr.shape[-1])
def _unary_func_helper(x, fn_array, fn_scalar, out=None, **kwargs):
"""Helper function for unary operators with kwargs.
Parameters
----------
x : ndarray or scalar
Input of the unary operator.
fn_array : function
Function to be called if x is of ``ndarray`` type.
fn_scalar : function
Function to be called if x is a Python scalar.
out : ndarray
The buffer ndarray for storing the result of the unary function.
Returns
-------
out : mxnet.numpy.ndarray or scalar
Result array or scalar.
"""
if isinstance(x, numeric_types):
return fn_scalar(x, **kwargs)
elif isinstance(x, NDArray):
return fn_array(x, out=out, **kwargs)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
def _pure_unary_func_helper(x, fn_array, fn_scalar, out=None, **kwargs):
"""Helper function for unary operators without support for kwargs.
Parameters
----------
x : ndarray or scalar
Input of the unary operator.
fn_array : function
Function to be called if x is of ``ndarray`` type.
fn_scalar : function
Function to be called if x is a Python scalar.
out : ndarray
The buffer ndarray for storing the result of the unary function.
Returns
-------
out : mxnet.numpy.ndarray or scalar
Result array or scalar.
"""
if isinstance(x, numeric_types):
return fn_scalar(x, **kwargs)
elif isinstance(x, NDArray):
return fn_array(x, out)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def sin(x, out=None, **kwargs):
r"""
Trigonometric sine, element-wise.
Parameters
----------
x : ndarray or scalar
Angle, in radians (:math:`2 \pi` rad equals 360 degrees).
out : ndarray or None
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. The dtype of the
output is the same as that of the input if the input is an ndarray.
Returns
-------
y : ndarray or scalar
The sine of each element of x. This is a scalar if `x` is a scalar.
Notes
----
This function only supports input type of float.
Examples
--------
>>> np.sin(np.pi/2.)
1.0
>>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180.)
array([0. , 0.5 , 0.70710677, 0.86602545, 1. ])
"""
return _pure_unary_func_helper(x, _api_internal.sin, _np.sin, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def cos(x, out=None, **kwargs):
r"""
Cosine, element-wise.
Parameters
----------
x : ndarray or scalar
Angle, in radians (:math:`2 \pi` rad equals 360 degrees).
out : ndarray or None
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. The dtype of the
output is the same as that of the input if the input is an ndarray.
Returns
-------
y : ndarray or scalar
The corresponding cosine values. This is a scalar if x is a scalar.
Notes
----
This function only supports input type of float.
Examples
--------
>>> np.cos(np.array([0, np.pi/2, np.pi]))
array([ 1.000000e+00, -4.371139e-08, -1.000000e+00])
>>> # Example of providing the optional output parameter
>>> out1 = np.array([0], dtype='f')
>>> out2 = np.cos(np.array([0.1]), out1)
>>> out2 is out1
True
"""
return _pure_unary_func_helper(x, _api_internal.cos, _np.cos, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def sinh(x, out=None, **kwargs):
"""
Hyperbolic sine, element-wise.
Equivalent to ``1/2 * (np.exp(x) - np.exp(-x))`` or ``-1j * np.sin(1j*x)``.
Parameters
----------
x : ndarray or scalar
Input array or scalar.
out : ndarray or None
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. The dtype of the
output is the same as that of the input if the input is an ndarray.
Returns
-------
y : ndarray or scalar
The corresponding hyperbolic sine values. This is a scalar if `x` is a scalar.
Notes
----
This function only supports input type of float.
Examples
--------
>>> np.sinh(0)
0.0
>>> # Example of providing the optional output parameter
>>> out1 = np.array([0], dtype='f')
>>> out2 = np.sinh(np.array([0.1]), out1)
>>> out2 is out1
True
"""
return _pure_unary_func_helper(x, _api_internal.sinh, _np.sinh, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def cosh(x, out=None, **kwargs):
"""
Hyperbolic cosine, element-wise.
Equivalent to ``1/2 * (np.exp(x) + np.exp(-x))`` and ``np.cos(1j*x)``.
Parameters
----------
x : ndarray or scalar
Input array or scalar.
out : ndarray or None
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. The dtype of the
output is the same as that of the input if the input is an ndarray.
Returns
-------
y : ndarray or scalar
The corresponding hyperbolic cosine values. This is a scalar if `x` is a scalar.
Notes
----
This function only supports input type of float.
Examples
--------
>>> np.cosh(0)
1.0
"""
return _pure_unary_func_helper(x, _api_internal.cosh, _np.cosh, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def tanh(x, out=None, **kwargs):
"""
Compute hyperbolic tangent element-wise.
Equivalent to ``np.sinh(x)/np.cosh(x)``.
Parameters
----------
x : ndarray or scalar.
Input array.
out : ndarray or None
A location into which the result is stored. If provided, it
must have a shape that the inputs fill into. If not provided
or None, a freshly-allocated array is returned. The dtype of the
output and input must be the same.
Returns
-------
y : ndarray or scalar
The corresponding hyperbolic tangent values.
Notes
-----
If `out` is provided, the function writes the result into it,
and returns a reference to `out`. (See Examples)
- input x does not support complex computation (like imaginary number)
>>> np.tanh(np.pi*1j)
TypeError: type <type 'complex'> not supported
Examples
--------
>>> np.tanh(np.array[0, np.pi]))
array([0. , 0.9962721])
>>> np.tanh(np.pi)
0.99627207622075
>>> # Example of providing the optional output parameter illustrating
>>> # that what is returned is a reference to said parameter
>>> out1 = np.array(1)
>>> out2 = np.tanh(np.array(0.1), out1)
>>> out2 is out1
True
"""
return _pure_unary_func_helper(x, _api_internal.tanh, _np.tanh, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def log10(x, out=None, **kwargs):
"""
Return the base 10 logarithm of the input array, element-wise.
Parameters
----------
x : ndarray or scalar
Input array or scalar.
out : ndarray or None
A location into which t'absolute', he 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. The dtype of the
output is the same as that of the input if the input is an ndarray.
Returns
-------
y : ndarray or scalar
The logarithm to the base 10 of `x`, element-wise. NaNs are
returned where x is negative. This is a scalar if `x` is a scalar.
Notes
----
This function only supports input type of float.
Examples
--------
>>> np.log10(np.array([1e-15, -3.]))
array([-15., nan])
"""
return _pure_unary_func_helper(x, _api_internal.log10, _np.log10, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def sqrt(x, out=None, **kwargs):
"""
Return the non-negative square-root of an array, element-wise.
Parameters
----------
x : ndarray or scalar
The values whose square-roots are required.
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
An array of the same shape as `x`, containing the positive
square-root of each element in `x`. This is a scalar if `x` is a scalar.
Notes
----
This function only supports input type of float.
Examples
--------
>>> np.sqrt(np.array([1,4,9]))
array([1., 2., 3.])
>>> np.sqrt(np.array([4, -1, _np.inf]))
array([ 2., nan, inf])
"""
return _pure_unary_func_helper(x, _api_internal.sqrt, _np.sqrt, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def cbrt(x, out=None, **kwargs):
r"""
Return the cube-root of an array, element-wise.
Parameters
----------
x : ndarray
The values whose cube-roots are required.
out : ndarray, 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.
A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
Returns
----------
y : ndarray
An array of the same shape as x, containing the cube cube-root of each element in x.
If out was provided, y is a reference to it. This is a scalar if x is a scalar.
Examples
----------
>>> np.cbrt([1,8,27])
array([ 1., 2., 3.])
"""
return _pure_unary_func_helper(x, _api_internal.cbrt, _np.cbrt, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def abs(x, out=None, **kwargs):
r"""
Calculate the absolute value element-wise.
Parameters
----------
x : ndarray or scalar
Input array.
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
-------
absolute : ndarray
An ndarray containing the absolute value of
each element in `x`. This is a scalar if `x` is a scalar.
Examples
--------
>>> x = np.array([-1.2, 1.2])
>>> np.abs(x)
array([1.2, 1.2])
"""
return _pure_unary_func_helper(x, _api_internal.abs, _np.abs, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def fabs(x, out=None, **kwargs):
r"""
Calculate the absolute value element-wise.
This function returns the absolute values (positive magnitude) of the
data in `x`. Complex values are not handled, use `absolute` to find the
absolute values of complex data.
Parameters
----------
x : ndarray or scalar
Input array.
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
-------
absolute : ndarray
An ndarray containing the absolute value of
each element in `x`. This is a scalar if `x` is a scalar.
Examples
--------
>>> np.fabs(-1)
1.0
>>> np.fabs(np.array([-1.2, 1.2]))s
array([ 1.2, 1.2])
"""
return _pure_unary_func_helper(x, _api_internal.abs, _np.abs, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def absolute(x, out=None, **kwargs):
r"""
Calculate the absolute value element-wise.
np.abs is a shorthand for this function.
Parameters
----------
x : ndarray
Input array.
out : ndarray, 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.
A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
Returns
----------
absolute : ndarray
An ndarray containing the absolute value of each element in x.
Examples
----------
>>> x = np.array([-1.2, 1.2])
>>> np.absolute(x)
array([ 1.2, 1.2])
"""
return _pure_unary_func_helper(x, _api_internal.abs, _np.abs, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def sign(x, out=None, **kwargs):
r"""
Returns an element-wise indication of the sign of a number.
The `sign` function returns ``-1 if x < 0, 0 if x==0, 1 if x > 0``. Only supports real number.
Parameters
----------
x : ndarray or a scalar
Input values.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray
The sign of `x`.
This is a scalar if `x` is a scalar.
Note
-------
- Only supports real number as input elements.
- Input type does not support Python native iterables(list, tuple, ...).
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> a = np.array([-5., 4.5])
>>> np.sign(a)
array([-1., 1.])
>>> # Use scalars as inputs:
>>> np.sign(4.0)
1.0
>>> np.sign(0)
0
>>> # Use ``out`` parameter:
>>> b = np.zeros((2, ))
>>> np.sign(a, out=b)
array([-1., 1.])
>>> b
array([-1., 1.])
"""
return _pure_unary_func_helper(x, _api_internal.sign, _np.sign, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def exp(x, out=None, **kwargs):
r"""
Calculate the exponential of all elements in the input array.
Parameters
----------
x : ndarray or scalar
Input values.
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
-------
out : ndarray or scalar
Output array, element-wise exponential of `x`.
This is a scalar if `x` is a scalar.
Examples
--------
>>> np.exp(1)
2.718281828459045
>>> x = np.array([-1, 1, -2, 2])
>>> np.exp(x)
array([0.36787945, 2.7182817 , 0.13533528, 7.389056 ])
"""
return _pure_unary_func_helper(x, _api_internal.exp, _np.exp, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def expm1(x, out=None, **kwargs):
r"""
Calculate `exp(x) - 1` of all elements in the input array.
Parameters
----------
x : ndarray or scalar
Input values.
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
-------
out : ndarray or scalar
Output array, element-wise exponential minus one: `out = exp(x) - 1`.
This is a scalar if `x` is a scalar.
Examples
--------
>>> np.expm1(1)
1.718281828459045
>>> x = np.array([-1, 1, -2, 2])
>>> np.expm1(x)
array([-0.63212056, 1.71828183, -0.86466472, 6.3890561])
"""
return _pure_unary_func_helper(x, _api_internal.expm1, _np.expm1, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def arcsin(x, out=None, **kwargs):
r"""
Inverse sine, element-wise.
Parameters
----------
x : ndarray or scalar
`y`-coordinate on the unit circle.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape as the input.
If not provided or None, a freshly-allocated array is returned.
Returns
-------
angle : ndarray or scalar
Output array is same shape and type as x. This is a scalar if x is a scalar.
The inverse sine of each element in `x`, in radians and in the
closed interval ``[-pi/2, pi/2]``.
Examples
--------
>>> np.arcsin(1) # pi/2
1.5707963267948966
>>> np.arcsin(-1) # -pi/2
-1.5707963267948966
>>> np.arcsin(0)
0.0
Notes
-----
`arcsin` is a multivalued function: for each `x` there are infinitely
many numbers `z` such that :math:`sin(z) = x`. The convention is to
return the angle `z` whose real part lies in [-pi/2, pi/2].
For real-valued input data types, *arcsin* always returns real output.
For each value that cannot be expressed as a real number or infinity,
it yields ``nan`` and sets the `invalid` floating point error flag.
The inverse sine is also known as `asin` or sin^{-1}.
The output `ndarray` has the same `device` as the input `ndarray`.
This function differs from the original `numpy.arcsin
<https://numpy.org/doc/stable/reference/generated/numpy.arcsin.html>`_ in
the following aspects:
- Only support ndarray or scalar now.
- `where` argument is not supported.
- Complex input is not supported.
References
----------
Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
10th printing, New York: Dover, 1964, pp. 79ff.
http://www.math.sfu.ca/~cbm/aands/
"""
return _pure_unary_func_helper(x, _api_internal.arcsin, _np.arcsin, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def arccos(x, out=None, **kwargs):
r"""
Trigonometric inverse cosine, element-wise.
The inverse of cos so that, if y = cos(x), then x = arccos(y).
Parameters
----------
x : ndarray
x-coordinate on the unit circle. For real arguments, the domain is [-1, 1].
out : ndarray, 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.
A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
Returns
----------
angle : ndarray
The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi].
This is a scalar if x is a scalar.
See also
----------
cos, arctan, arcsin
Notes
----------
arccos is a multivalued function: for each x there are infinitely many numbers z such that
cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi].
For real-valued input data types, arccos always returns real output.
For each value that cannot be expressed as a real number or infinity, it yields nan and sets
the invalid floating point error flag.
The inverse cos is also known as acos or cos^-1.
Examples
----------
>>> np.arccos([1, -1])
array([ 0. , 3.14159265])
"""
return _pure_unary_func_helper(x, _api_internal.arccos, _np.arccos, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def arctan(x, out=None, **kwargs):
r"""
Trigonometric inverse tangent, element-wise.
The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``.
Parameters
----------
x : ndarray or scalar
Input values.
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
-------
out : ndarray or scalar
Out has the same shape as `x`. It lies is in
``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``).
This is a scalar if `x` is a scalar.
Notes
-----
`arctan` is a multi-valued function: for each `x` there are infinitely
many numbers `z` such that tan(`z`) = `x`. The convention is to return
the angle `z` whose real part lies in [-pi/2, pi/2].
For real-valued input data types, `arctan` always returns real output.
For each value that cannot be expressed as a real number or infinity,
it yields ``nan`` and sets the `invalid` floating point error flag.
For complex-valued input, we do not have support for them yet.
The inverse tangent is also known as `atan` or tan^{-1}.
Examples
--------
>>> x = np.array([0, 1])
>>> np.arctan(x)
array([0. , 0.7853982])
>>> np.pi/4
0.7853981633974483
"""
return _pure_unary_func_helper(x, _api_internal.arctan, _np.arctan, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def log(x, out=None, **kwargs):
"""
Natural logarithm, element-wise.
The natural logarithm `log` is the inverse of the exponential function,
so that `log(exp(x)) = x`. The natural logarithm is logarithm in base
`e`.
Parameters
----------
x : ndarray
Input value. Elements must be of real value.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray
The natural logarithm of `x`, element-wise.
This is a scalar if `x` is a scalar.
Notes
-----
Currently only supports data of real values and ``inf`` as input. Returns data of real value, ``inf``, ``-inf`` and
``nan`` according to the input.
This function differs from the original `numpy.log
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html>`_ in
the following aspects:
- Does not support complex number for now
- Input type does not support Python native iterables(list, tuple, ...).
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> a = np.array([1, np.exp(1), np.exp(2), 0], dtype=np.float64)
>>> np.log(a)
array([ 0., 1., 2., -inf], dtype=float64)
>>> # Using default float32 dtype may lead to slightly different behavior:
>>> a = np.array([1, np.exp(1), np.exp(2), 0], dtype=np.float32)
>>> np.log(a)
array([ 0., 0.99999994, 2., -inf])
>>> np.log(1)
0.0
"""
return _pure_unary_func_helper(x, _api_internal.log, _np.log, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def degrees(x, out=None, **kwargs):
"""
Convert angles from radians to degrees.
Parameters
----------
x : ndarray
Input value. Elements must be of real value.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray
The corresponding degree values; if `out` was supplied this is a
reference to it.
This is a scalar if `x` is a scalar.
Notes
-------
This function differs from the original `numpy.degrees
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.degrees.html>`_ in
the following aspects:
- Input type does not support Python native iterables(list, tuple, ...). Only ndarray is supported.
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> rad = np.arange(12.) * np.pi / 6
>>> np.degrees(rad)
array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.])
>>> # Use specified ``out`` ndarray:
>>> out = np.zeros((rad.shape))
>>> np.degrees(rad, out)
array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.])
>>> out
array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.])
"""
return _pure_unary_func_helper(x, _api_internal.degrees, _np.degrees, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def rad2deg(x, out=None, **kwargs):
r"""
Convert angles from radians to degrees.
Parameters
----------
x : ndarray or scalar
Angles in degrees.
out : ndarray or None, optional
A location into which the result is stored. If not provided or `None`,
a freshly-allocated array is returned.
Returns
-------
y : ndarray or scalar
The corresponding angle in radians.
This is a scalar if `x` is a scalar.
Notes
-----
"rad2deg(x)" is "x *180 / pi".
This function differs from the original numpy.arange in the following aspects:
- Only support float32 and float64.
- `out` must be in the same size of input.
Examples
--------
>>> np.rad2deg(np.pi/2)
90.0
"""
return _pure_unary_func_helper(x, _api_internal.rad2deg, _np.rad2deg, out=out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def rint(x, out=None, **kwargs):
"""
Round elements of the array to the nearest integer.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None
A location into which the result is stored.
If provided, it must have the same shape and type as the input.
If not provided or None, a freshly-allocated array is returned.
Returns
-------
out : ndarray or scalar
Output array is same shape and type as x. This is a scalar if x is a scalar.
Notes
-----
This function differs from the original `numpy.rint
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.rint.html>`_ in
the following way(s):
- only ndarray or scalar is accpted as valid input, tuple of ndarray is not supported
- broadcasting to `out` of different shape is currently not supported
- when input is plain python numerics, the result will not be stored in the `out` param
Examples
--------
>>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
>>> np.rint(a)
array([-2., -2., -0., 0., 1., 2., 2.])
"""
return _pure_unary_func_helper(x, _api_internal.rint, _np.rint, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def log2(x, out=None, **kwargs):
"""
Base-2 logarithm of x.
Parameters
----------
x : ndarray or scalar
Input values.
out : ndarray or None
A location into which the result is stored.
If provided, it must have the same shape and type as the input.
If not provided or None, a freshly-allocated array is returned.
Returns
-------
y : ndarray
The logarithm base two of `x`, element-wise.
This is a scalar if `x` is a scalar.
Notes
-----
This function differs from the original `numpy.log2
<https://www.google.com/search?q=numpy+log2>`_ in
the following way(s):
- only ndarray or scalar is accpted as valid input, tuple of ndarray is not supported
- broadcasting to `out` of different shape is currently not supported
- when input is plain python numerics, the result will not be stored in the `out` param
Examples
--------
>>> x = np.array([0, 1, 2, 2**4])
>>> np.log2(x)
array([-inf, 0., 1., 4.])
"""
return _pure_unary_func_helper(x, _api_internal.log2, _np.log2, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def log1p(x, out=None, **kwargs):
"""
Return the natural logarithm of one plus the input array, element-wise.
Calculates ``log(1 + x)``.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None
A location into which the result is stored. If provided, it
must have a shape that the inputs fill into. If not provided
or None, a freshly-allocated array is returned. The dtype of the
output and input must be the same.
Returns
-------
y : ndarray or scalar
Natural logarithm of 1 + x, element-wise. This is a scalar
if x is a scalar.
Notes
-----
For real-valued input, `log1p` is accurate also for `x` so small
that `1 + x == 1` in floating-point accuracy.
Logarithm is a multivalued function: for each `x` there is an infinite
number of `z` such that `exp(z) = 1 + x`. The convention is to return
the `z` whose imaginary part lies in `[-pi, pi]`.
For real-valued input data types, `log1p` always returns real output.
For each value that cannot be expressed as a real number or infinity,
it yields ``nan`` and sets the `invalid` floating point error flag.
cannot support complex-valued input.
Examples
--------
>>> np.log1p(1e-99)
1e-99
>>> a = np.array([3, 4, 5])
>>> np.log1p(a)
array([1.3862944, 1.609438 , 1.7917595])
"""
return _pure_unary_func_helper(x, _api_internal.log1p, _np.log1p, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def radians(x, out=None, **kwargs):
"""
Convert angles from degrees to radians.
Parameters
----------
x : ndarray or scalar
Input array in degrees.
out : ndarray or None
A location into which the result is stored.
If provided, it must have the same shape and type as the input.
If not provided or None, a freshly-allocated array is returned.
Returns
-------
y : ndarray
The corresponding radian values. This is a scalar if x is a scalar.
Notes
-----
This function differs from the original `numpy.radians
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.radians.html>`_ in
the following way(s):
- only ndarray or scalar is accpted as valid input, tuple of ndarray is not supported
- broadcasting to `out` of different shape is currently not supported
- when input is plain python numerics, the result will not be stored in the `out` param
Examples
--------
>>> deg = np.arange(12.) * 30.
>>> np.radians(deg)
array([0. , 0.5235988, 1.0471976, 1.5707964, 2.0943952, 2.6179938,
3.1415927, 3.6651914, 4.1887903, 4.712389 , 5.2359877, 5.7595863],
dtype=float32)
"""
return _pure_unary_func_helper(x, _api_internal.radians, _np.radians, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def deg2rad(x, out=None, **kwargs):
r"""
Convert angles from degrees to radians.
Parameters
----------
x : ndarray or scalar
Angles in degrees.
out : ndarray or None, optional
A location into which the result is stored. If not provided or `None`,
a freshly-allocated array is returned.
Returns
-------
y : ndarray or scalar
The corresponding angle in radians.
This is a scalar if `x` is a scalar.
Notes
-----
"deg2rad(x)" is "x * pi / 180".
This function differs from the original numpy.arange in the following aspects:
- Only support float32 and float64.
- `out` must be in the same size of input.
Examples
--------
>>> np.deg2rad(180)
3.1415927
"""
return _pure_unary_func_helper(x, _api_internal.deg2rad, _np.deg2rad, out=out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def reciprocal(x, out=None, **kwargs):
r"""
Return the reciprocal of the argument, element-wise.
Calculates ``1/x``.
Parameters
----------
x : ndarray or scalar
The values whose reciprocals are required.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape as the input.
If not provided or None, a freshly-allocated array is returned.
Returns
-------
y : ndarray or scalar
Output array is same shape and type as x. This is a scalar if x is a scalar.
Examples
--------
>>> np.reciprocal(2.)
0.5
>>> x = np.array([1, 2., 3.33])
>>> np.reciprocal(x)
array([1. , 0.5 , 0.3003003])
Notes
-----
.. note::
This function is not designed to work with integers.
For integer arguments with absolute value larger than 1 the result is
always zero because of the way Python handles integer division. For
integer zero the result is an overflow.
The output `ndarray` has the same `device` as the input `ndarray`.
This function differs from the original `numpy.reciprocal
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.reciprocal.html>`_ in
the following aspects:
- Only support ndarray and scalar now.
- `where` argument is not supported.
"""
return _pure_unary_func_helper(x, _api_internal.reciprocal, _np.reciprocal, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def square(x, out=None, **kwargs):
r"""
Return the element-wise square of the input.
Parameters
----------
x : ndarray or scalar
The values whose squares are required.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape as the input.
If not provided or None, a freshly-allocated array is returned.
Returns
-------
y : ndarray or scalar
Output array is same shape and type as x. This is a scalar if x is a scalar.
Examples
--------
>>> np.square(2.)
4.0
>>> x = np.array([1, 2., -1])
>>> np.square(x)
array([1., 4., 1.])
Notes
-----
The output `ndarray` has the same `device` as the input `ndarray`.
This function differs from the original `numpy.square
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.square.html>`_ in
the following aspects:
- Only support ndarray and scalar now.
- `where` argument is not supported.
- Complex input is not supported.
"""
return _pure_unary_func_helper(x, _api_internal.square, _np.square, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def negative(x, out=None, **kwargs):
r"""
Numerical negative, element-wise.
Parameters:
------------
x : ndarray or scalar
Input array.
out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored.
Returns:
---------
y : ndarray or scalar
Returned array or scalar: y = -x. This is a scalar if x is a scalar.
Examples:
---------
>>> np.negative(1)
-1
"""
return _pure_unary_func_helper(x, _api_internal.negative, _np.negative, out=out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def positive(x, out=None, **kwargs):
r"""
Computes the numerical positive of each element `x_i` (i.e.,`y_i = +x_i`)
of the input array x .
Parameters
----------
x : ndarray or scalar
Input array.
Returns
-------
y : ndarray or scalar
Returned array or scalar: y = +x. This is a scalar if x is a scalar.
Notes
-----
Equivalent to `x.copy()`, but only defined for types that support arithmetic.
Examples
--------
>>> x1 = np.array(([1., -1.]))
>>> np.positive(x1)
array([ 1., -1.])
>>> +x1
array([ 1., -1.])
"""
if out is x:
return x
return _pure_unary_func_helper(x, _api_internal.copy, _np.positive, out=out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def fix(x, out=None, **kwargs):
r"""
Round an array of floats element-wise to nearest integer towards zero.
The rounded values are returned as floats.
Parameters:
----------
x : ndarray
An array of floats to be rounded
out : ndarray, optional
Output array
Returns:
-------
y : ndarray of floats
Examples
---------
>>> np.fix(3.14)
3
"""
return _pure_unary_func_helper(x, _api_internal.fix, _np.fix, out=out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def tan(x, out=None, **kwargs):
r"""
Compute tangent element-wise.
Equivalent to np.sin(x)/np.cos(x) element-wise.
Parameters:
----------
x : ndarray
Input array.
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a keyword argument)
must have length equal to the number of outputs.
where : ndarray, optional
Values of True indicate to calculate the ufunc at that position,
values of False indicate to leave the value in the output alone.
Returns:
-------
y : ndarray
The corresponding tangent values. This is a scalar if x is a scalar.
Examples:
---------
>>> np.tan(0.5)
0.5463024898437905
"""
return _pure_unary_func_helper(x, _api_internal.tan, _np.tan, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def ceil(x, out=None, **kwargs):
r"""
Return the ceiling of the input, element-wise.
The ceil of the ndarray `x` is the smallest integer `i`, such that
`i >= x`. It is often denoted as :math:`\lceil x \rceil`.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None
A location into which the result is stored. If provided, it
must have a same shape that the inputs fill into. If not provided
or None, a freshly-allocated array is returned. The dtype of the
output and input must be the same.
Returns
-------
y : ndarray or scalar
The ceiling of each element in `x`, with `float` dtype.
This is a scalar if `x` is a scalar.
Examples
--------
>>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
>>> np.ceil(a)
array([-1., -1., -0., 1., 2., 2., 2.])
>>> #if you use parameter out, x and out must be ndarray.
>>> a = np.array(1)
>>> np.ceil(np.array(3.5), a)
array(4.)
>>> a
array(4.)
"""
if isinstance(x, NDArray) and _np.issubdtype(x.dtype, _np.integer):
return x
return _pure_unary_func_helper(x, _api_internal.ceil, _np.ceil, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def floor(x, out=None, **kwargs):
r"""
Return the floor of the input, element-wise.
The floor of the ndarray `x` is the largest integer `i`, such that
`i <= x`. It is often denoted as :math:`\lfloor x \rfloor`.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None
A location into which the result is stored. If provided, it
must have a same shape that the inputs fill into. If not provided
or None, a freshly-allocated array is returned. The dtype of the
output and input must be the same.
Returns
-------
y : ndarray or scalar
The floor of each element in `x`, with `float` dtype.
This is a scalar if `x` is a scalar.
Examples
--------
>>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
>>> np.floor(a)
array([-2., -2., -1., 0., 1., 1., 2.])
>>> #if you use parameter out, x and out must be ndarray.
>>> a = np.array(1)
>>> np.floor(np.array(3.5), a)
array(3.)
>>> a
array(3.)
"""
if isinstance(x, NDArray) and _np.issubdtype(x.dtype, _np.integer):
return x
return _pure_unary_func_helper(x, _api_internal.floor, _np.floor, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def bitwise_not(x, out=None, **kwargs):
r"""
Compute bit-wise inversion, or bit-wise NOT, element-wise.
Computes the bit-wise NOT of the underlying binary representation of
the integers in the input arrays. This ufunc implements the C/Python
operator ``~``.
Parameters
----------
x : array_like
Only integer and boolean types are handled.
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
Returns
-------
out : ndarray or scalar
Result.
This is a scalar if `x` is a scalar.
See Also
--------
bitwise_and, bitwise_or, bitwise_xor
logical_not
binary_repr :
Return the binary representation of the input number as a string.
Examples
--------
We've seen that 13 is represented by ``00001101``.
The invert or bit-wise NOT of 13 is then:
>>> x = np.invert(np.array(13, dtype=np.uint8))
>>> x
242
>>> np.binary_repr(x, width=8)
'11110010'
Notes
-----
`bitwise_not` is an alias for `invert`:
>>> np.bitwise_not is np.invert
True
"""
return _pure_unary_func_helper(x, _api_internal.bitwise_not, _np.bitwise_not, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def invert(x, out=None, **kwargs):
r"""
Compute bit-wise inversion, or bit-wise NOT, element-wise.
Computes the bit-wise NOT of the underlying binary representation of
the integers in the input arrays. This ufunc implements the C/Python
operator ``~``.
Parameters
----------
x : array_like
Only integer and boolean types are handled.
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
Returns
-------
out : ndarray or scalar
Result.
This is a scalar if `x` is a scalar.
See Also
--------
bitwise_and, bitwise_or, bitwise_xor
logical_not
binary_repr :
Return the binary representation of the input number as a string.
Examples
--------
We've seen that 13 is represented by ``00001101``.
The invert or bit-wise NOT of 13 is then:
>>> x = np.invert(np.array(13, dtype=np.uint8))
>>> x
242
>>> np.binary_repr(x, width=8)
'11110010'
Notes
-----
`bitwise_not` is an alias for `invert`:
>>> np.bitwise_not is np.invert
True
"""
return _pure_unary_func_helper(x, _api_internal.bitwise_not, _np.bitwise_not, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def trunc(x, out=None, **kwargs):
r"""
Return the truncated value of the input, element-wise.
The truncated value of the scalar `x` is the nearest integer `i` which
is closer to zero than `x` is. In short, the fractional part of the
signed number `x` is discarded.
Parameters
----------
x : ndarray or scalar
Input data.
out : ndarray or None, optional
A location into which the result is stored.
Returns
-------
y : ndarray or scalar
The truncated value of each element in `x`.
This is a scalar if `x` is a scalar.
Notes
-----
This function differs from the original numpy.trunc in the following aspects:
- Do not support `where`, a parameter in numpy which indicates where to calculate.
- Cannot cast type automatically. Dtype of `out` must be same as the expected one.
- Cannot broadcast automatically. Shape of `out` must be same as the expected one.
- If `x` is plain python numeric, the result won't be stored in out.
Examples
--------
>>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
>>> np.trunc(a)
array([-1., -1., -0., 0., 1., 1., 2.])
"""
if isinstance(x, NDArray) and _np.issubdtype(x.dtype, _np.integer):
return x
return _pure_unary_func_helper(x, _api_internal.trunc, _np.trunc, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def logical_not(x, out=None, **kwargs):
r"""
Compute the truth value of NOT x element-wise.
Parameters
----------
x : ndarray or scalar
Logical NOT is applied to the elements of `x`.
out : ndarray or None, optional
A location into which the result is stored.
Returns
-------
y : bool or ndarray of bool
Boolean result with the same shape as `x` of the NOT operation
on elements of `x`.
This is a scalar if `x` is a scalar.
Notes
-----
This function differs from the original numpy.logical_not in the following aspects:
- Do not support `where`, a parameter in numpy which indicates where to calculate.
- Cannot cast type automatically. Dtype of `out` must be same as the expected one.
- Cannot broadcast automatically. Shape of `out` must be same as the expected one.
- If `x` is plain python numeric, the result won't be stored in out.
Examples
--------
>>> x= np.array([True, False, 0, 1])
>>> np.logical_not(x)
array([False, True, True, False])
>>> x = np.arange(5)
>>> np.logical_not(x<3)
array([False, False, False, True, True])
"""
return _pure_unary_func_helper(x, _api_internal.logical_not, _np.logical_not, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def arcsinh(x, out=None, **kwargs):
r"""
Inverse hyperbolic sine, element-wise.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None, optional
A location into which the result is stored.
Returns
-------
arcsinh : ndarray
Array of the same shape as `x`.
This is a scalar if `x` is a scalar.
Notes
-----
`arcsinh` is a multivalued function: for each `x` there are infinitely
many numbers `z` such that `sinh(z) = x`.
For real-valued input data types, `arcsinh` always returns real output.
For each value that cannot be expressed as a real number or infinity, it
yields ``nan`` and sets the `invalid` floating point error flag.
This function differs from the original numpy.arcsinh in the following aspects:
- Do not support `where`, a parameter in numpy which indicates where to calculate.
- Do not support complex-valued input.
- Cannot cast type automatically. DType of `out` must be same as the expected one.
- Cannot broadcast automatically. Shape of `out` must be same as the expected one.
- If `x` is plain python numeric, the result won't be stored in out.
Examples
--------
>>> a = np.array([3.2, 5.0])
>>> np.arcsinh(a)
array([1.8309381, 2.2924316])
>>> np.arcsinh(1)
0.0
"""
return _pure_unary_func_helper(x, _api_internal.arcsinh, _np.arcsinh, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def arccosh(x, out=None, **kwargs):
r"""
Inverse hyperbolic cosine, element-wise.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None, optional
A location into which the result is stored.
Returns
-------
arccosh : ndarray
Array of the same shape as `x`.
This is a scalar if `x` is a scalar.
Notes
-----
`arccosh` is a multivalued function: for each `x` there are infinitely
many numbers `z` such that `cosh(z) = x`.
For real-valued input data types, `arccosh` always returns real output.
For each value that cannot be expressed as a real number or infinity, it
yields ``nan`` and sets the `invalid` floating point error flag.
This function differs from the original numpy.arccosh in the following aspects:
- Do not support `where`, a parameter in numpy which indicates where to calculate.
- Do not support complex-valued input.
- Cannot cast type automatically. Dtype of `out` must be same as the expected one.
- Cannot broadcast automatically. Shape of `out` must be same as the expected one.
- If `x` is plain python numeric, the result won't be stored in out.
Examples
--------
>>> a = np.array([3.2, 5.0])
>>> np.arccosh(a)
array([1.8309381, 2.2924316])
>>> np.arccosh(1)
0.0
"""
return _pure_unary_func_helper(x, _api_internal.arccosh, _np.arccosh, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def arctanh(x, out=None, **kwargs):
r"""
Inverse hyperbolic tangent, element-wise.
Parameters
----------
x : ndarray or scalar
Input array.
out : ndarray or None, optional
A location into which the result is stored.
Returns
-------
arctanh : ndarray
Array of the same shape as `x`.
This is a scalar if `x` is a scalar.
Notes
-----
`arctanh` is a multivalued function: for each `x` there are infinitely
many numbers `z` such that `tanh(z) = x`.
For real-valued input data types, `arctanh` always returns real output.
For each value that cannot be expressed as a real number or infinity, it
yields ``nan`` and sets the `invalid` floating point error flag.
This function differs from the original numpy.arctanh in the following aspects:
- Do not support `where`, a parameter in numpy which indicates where to calculate.
- Do not support complex-valued input.
- Cannot cast type automatically. Dtype of `out` must be same as the expected one.
- Cannot broadcast automatically. Shape of `out` must be same as the expected one.
- If `x` is plain python numeric, the result won't be stored in out.
Examples
--------
>>> a = np.array([0.0, -0.5])
>>> np.arctanh(a)
array([0., -0.54930615])
>>> np.arctanh(0.0)
0.0
"""
return _pure_unary_func_helper(x, _api_internal.arctanh, _np.arctanh, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
def tile(A, reps):
r"""
Construct an array by repeating A the number of times given by reps.
If `reps` has length ``d``, the result will have dimension of
``max(d, A.ndim)``.
If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new
axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,
or shape (1, 1, 3) for 3-D replication. If this is not the desired
behavior, promote `A` to d-dimensions manually before calling this
function.
If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it.
Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as
(1, 1, 2, 2).
Parameters
----------
A : ndarray or scalar
An input array or a scalar to repeat.
reps : a single integer or tuple of integers
The number of repetitions of `A` along each axis.
Returns
-------
c : ndarray
The tiled output array.
Examples
--------
>>> a = np.array([0, 1, 2])
>>> np.tile(a, 2)
array([0., 1., 2., 0., 1., 2.])
>>> np.tile(a, (2, 2))
array([[0., 1., 2., 0., 1., 2.],
[0., 1., 2., 0., 1., 2.]])
>>> np.tile(a, (2, 1, 2))
array([[[0., 1., 2., 0., 1., 2.]],
[[0., 1., 2., 0., 1., 2.]]])
>>> b = np.array([[1, 2], [3, 4]])
>>> np.tile(b, 2)
array([[1., 2., 1., 2.],
[3., 4., 3., 4.]])
>>> np.tile(b, (2, 1))
array([[1., 2.],
[3., 4.],
[1., 2.],
[3., 4.]])
>>> c = np.array([1,2,3,4])
>>> np.tile(c,(4,1))
array([[1., 2., 3., 4.],
[1., 2., 3., 4.],
[1., 2., 3., 4.],
[1., 2., 3., 4.]])
Scalar as input:
>>> np.tile(2, 3)
array([2, 2, 2]) # repeating integer `2`
"""
if isinstance(A, numeric_types):
return _np.tile(A, reps)
elif isinstance(A, NDArray):
return _api_internal.tile(A, reps)
else:
raise TypeError('type {} not supported'.format(str(type(A))))
@set_module('mxnet.ndarray.numpy')
def transpose(a, axes=None):
"""
Permute the dimensions of an array.
Parameters
----------
a : ndarray
Input array.
axes : list of ints, optional
By default, reverse the dimensions,
otherwise permute the axes according to the values given.
Returns
-------
p : ndarray
a with its axes permuted.
Notes
-----
This function differs from the original `numpy.transpose
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html>`_ in
the following way(s):
- only ndarray is accepted as valid input, python iterables are not supported
- the operator always returns an `ndarray` that does not share the memory with the input
Examples
--------
>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0., 1.],
[2., 3.]])
>>> np.transpose(x)
array([[0., 2.],
[1., 3.]])
>>> x = np.ones((1, 2, 3))
>>> np.transpose(x, (1, 0, 2)).shape
(2, 1, 3)
"""
return _api_internal.transpose(a, axes)
@set_module('mxnet.ndarray.numpy')
def repeat(a, repeats, axis=None):
"""
Repeat elements of an array.
Parameters
----------
a : array_like
Input array.
repeats : int
The number of repetitions for each element.
axis : int, optional
The axis along which to repeat values. By default, use the
flattened input array, and return a flat output array.
Returns
-------
repeated_array : ndarray
Output array which has the same shape as `a`, except along
the given axis.
See Also
--------
tile : Tile an array.
Examples
--------
>>> np.repeat(3, 4)
array([3, 3, 3, 3])
>>> x = np.array([[1,2],[3,4]])
>>> np.repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
>>> np.repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 4, 4, 4]])
>>> np.repeat(x, [1, 2], axis=0)
array([[1, 2],
[3, 4],
[3, 4]])
"""
if isinstance(repeats, numeric_types):
repeats = [repeats]
return _api_internal.repeats(a, repeats, axis)
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def split(ary, indices_or_sections, axis=0):
"""
Split an array into multiple sub-arrays.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int or 1-D python tuple, list or set.
If `indices_or_sections` is an integer, N, the array will be divided
into N equal arrays along `axis`. If such a split is not possible,
an error is raised.
If `indices_or_sections` is a 1-D array of sorted integers, the entries
indicate where along `axis` the array is split. For example,
``[2, 3]`` would, for ``axis=0``, result in
- ary[:2]
- ary[2:3]
- ary[3:]
If an index exceeds the dimension of the array along `axis`,
an empty sub-array is returned correspondingly.
axis : int, optional
The axis along which to split, default is 0.
Returns
-------
sub-arrays : list of ndarrays
A list of sub-arrays.
Raises
------
ValueError
If `indices_or_sections` is given as an integer, but
a split does not result in equal division.
"""
if isinstance(indices_or_sections, set):
indices_or_sections = list(indices_or_sections)
return list(_api_internal.split(ary, indices_or_sections, axis))
# pylint: enable=redefined-outer-name
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def array_split(ary, indices_or_sections, axis=0):
"""Split an array into multiple sub-arrays.
If `indices_or_sections` is an integer, N, the array will be divided
into N equal arrays along `axis`. If such a split is not possible,
an array of length l that should be split into n sections, it returns
l % n sub-arrays of size l//n + 1 and the rest of size l//n.
If `indices_or_sections` is a 1-D array of sorted integers, the entries
indicate where along `axis` the array is split. For example,
``[2, 3]`` would, for ``axis=0``, result in
- ary[:2]
- ary[2:3]
- ary[3:]
If an index exceeds the dimension of the array along `axis`,
an empty sub-array is returned correspondingly.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int or 1-D Python tuple, list or set.
Param used to determine the number and size of the subarray.
axis : int, optional
The axis along which to split, default is 0.
Returns
-------
sub-arrays : list of ndarrays
A list of sub-arrays.
Examples
--------
>>> x = np.arange(9.0)
>>> np.array_split(x, 3)
[array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7., 8.])]
>>> np.array_split(x, [3, 5, 6, 8])
[array([0., 1., 2.]), array([3., 4.]), array([5.]), array([6., 7.]), array([])]
>>> x = np.arange(8.0)
>>> np.array_split(x, 3)
[array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7.])]
>>> x = np.arange(7.0)
>>> np.array_split(x, 3)
[array([0., 1., 2.]), array([3., 4.]), array([5., 6.])]
"""
if isinstance(indices_or_sections, set):
indices_or_sections = list(indices_or_sections)
return list(_api_internal.array_split(ary, indices_or_sections, axis))
# pylint: enable=redefined-outer-name
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def hsplit(ary, indices_or_sections):
"""Split an array into multiple sub-arrays horizontally (column-wise).
This is equivalent to ``split`` with ``axis=0`` if ``ary`` has one
dimension, and otherwise that with ``axis=1``.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int, list of ints or tuple of ints.
If `indices_or_sections` is an integer, N, the array will be divided
into N equal arrays along `axis`. If such a split is not possible,
an error is raised.
If `indices_or_sections` is a list of sorted integers, the entries
indicate where along `axis` the array is split.
If an index exceeds the dimension of the array along `axis`,
it will raises errors. so index must less than or euqal to
the dimension of the array along axis.
Returns
-------
sub-arrays : list of ndarrays
A list of sub-arrays.
Notes
------
- If `indices_or_sections` is given as an integer, but a split
does not result in equal division.It will raises ValueErrors.
- If indices_or_sections is an integer, and the number is 1, it will
raises an error. Because single output from split is not supported yet...
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
>>> x = np.arange(16.0).reshape(4, 4)
>>> x
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[12., 13., 14., 15.]])
>>> np.hsplit(x, 2)
[array([[ 0., 1.],
[ 4., 5.],
[ 8., 9.],
[12., 13.]]),
array([[ 2., 3.],
[ 6., 7.],
[10., 11.],
[14., 15.]])]
>>> np.hsplit(x, [3, 6])
[array([[ 0., 1., 2.],
[ 4., 5., 6.],
[ 8., 9., 10.],
[12., 13., 14.]]),
array([[ 3.],
[ 7.],
[11.],
[15.]]),
array([], shape=(4, 0), dtype=float32)]
With a higher dimensional array the split is still along the second axis.
>>> x = np.arange(8.0).reshape(2, 2, 2)
>>> x
array([[[ 0., 1.],
[ 2., 3.]],
[[ 4., 5.],
[ 6., 7.]]])
>>> np.hsplit(x, 2)
[array([[[ 0., 1.]],
[[ 4., 5.]]]),
array([[[ 2., 3.]],
[[ 6., 7.]]])]
If ``ary`` has one dimension, 'axis' = 0.
>>> x = np.arange(4)
array([0., 1., 2., 3.])
>>> np.hsplit(x, 2)
[array([0., 1.]), array([2., 3.])]
If you want to produce an empty sub-array, you can see an example.
>>> np.hsplit(x, [2, 2])
[array([0., 1.]), array([], dtype=float32), array([2., 3.])]
"""
if isinstance(indices_or_sections, set):
indices_or_sections = list(indices_or_sections)
return list(_api_internal.hsplit(ary, indices_or_sections))
# pylint: enable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def vsplit(ary, indices_or_sections):
r"""
vsplit(ary, indices_or_sections)
Split an array into multiple sub-arrays vertically (row-wise).
``vsplit`` is equivalent to ``split`` with `axis=0` (default): the array is always split
along the first axis regardless of the array dimension.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int or 1 - D Python tuple, list or set.
If `indices_or_sections` is an integer, N, the array will be divided into N equal arrays
along axis 0. If such a split is not possible, an error is raised.
If `indices_or_sections` is a 1-D array of sorted integers, the entries indicate where
along axis 0 the array is split. For example, ``[2, 3]`` would result in
- ary[:2]
- ary[2:3]
- ary[3:]
If an index exceeds the dimension of the array along axis 0, an error will be thrown.
Returns
-------
sub-arrays : list of ndarrays
A list of sub-arrays.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Notes
-------
This function differs from the original `numpy.degrees
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.degrees.html>`_ in
the following aspects:
- Currently parameter ``indices_or_sections`` does not support ndarray, but supports scalar,
tuple and list.
- In ``indices_or_sections``, if an index exceeds the dimension of the array along axis 0,
an error will be thrown.
Examples
--------
>>> x = np.arange(16.0).reshape(4, 4)
>>> x
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])
>>> np.vsplit(x, 2)
[array([[0., 1., 2., 3.],
[4., 5., 6., 7.]]), array([[ 8., 9., 10., 11.],
[12., 13., 14., 15.]])]
With a higher dimensional array the split is still along the first axis.
>>> x = np.arange(8.0).reshape(2, 2, 2)
>>> x
array([[[ 0., 1.],
[ 2., 3.]],
[[ 4., 5.],
[ 6., 7.]]])
>>> np.vsplit(x, 2)
[array([[[0., 1.],
[2., 3.]]]), array([[[4., 5.],
[6., 7.]]])]
"""
if isinstance(indices_or_sections, set):
indices_or_sections = list(indices_or_sections)
return list(_api_internal.vsplit(ary, indices_or_sections))
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def dsplit(ary, indices_or_sections):
"""
Split array into multiple sub-arrays along the 3rd axis (depth).
Please refer to the `split` documentation. `dsplit` is equivalent
to `split` with ``axis=2``, the array is always split along the third
axis provided the array dimension is greater than or equal to 3.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int or 1 - D Python tuple, list or set.
If `indices_or_sections` is an integer, N, the array will be divided into N equal arrays
along axis 2. If such a split is not possible, an error is raised.
If `indices_or_sections` is a 1-D array of sorted integers, the entries indicate where
along axis 2 the array is split. For example, ``[2, 3]`` would result in
- ary[:, :, :2]
- ary[:, :, 2:3]
- ary[:, :, 3:]
If an index exceeds the dimension of the array along axis 2, an error will be thrown.
Examples
--------
>>> x = np.arange(16.0).reshape(2, 2, 4)
>>> x
array([[[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.]],
[[ 8., 9., 10., 11.],
[12., 13., 14., 15.]]])
>>> np.dsplit(x, 2)
[array([[[ 0., 1.],
[ 4., 5.]],
[[ 8., 9.],
[12., 13.]]]), array([[[ 2., 3.],
[ 6., 7.]],
[[10., 11.],
[14., 15.]]])]
>>> np.dsplit(x, np.array([3, 6]))
[array([[[ 0., 1., 2.],
[ 4., 5., 6.]],
[[ 8., 9., 10.],
[12., 13., 14.]]]),
array([[[ 3.],
[ 7.]],
[[11.],
[15.]]]),
array([], shape=(2, 2, 0), dtype=float64)]
"""
if isinstance(indices_or_sections, set):
indices_or_sections = list(indices_or_sections)
return list(_api_internal.dsplit(ary, indices_or_sections))
# pylint: enable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def concatenate(seq, axis=0, out=None):
"""
Join a sequence of arrays along an existing axis.
Parameters
----------
a1, a2, ... : sequence of ndarray
The arrays must have the same shape, except in the dimension
corresponding to `axis` (the first, by default).
axis : int, optional
The axis along which the arrays will be joined. If axis is None,
arrays are flattened before use. Default is 0.
out : ndarray, optional
If provided, the destination to place the result. The shape must be
correct, matching that of what concatenate would have returned if no
out argument were specified.
Returns
-------
res : ndarray
The concatenated array.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> b = np.array([[5, 6]])
>>> np.concatenate((a, b), axis=0)
array([[1., 2.],
[3., 4.],
[5., 6.]])
>>> np.concatenate((a, b), axis=None)
array([1., 2., 3., 4., 5., 6.])
>>> np.concatenate((a, b.T), axis=1)
array([[1., 2., 5.],
[3., 4., 6.]])
"""
return _api_internal.concatenate(*seq, axis, out)
@set_module('mxnet.ndarray.numpy')
def append(arr, values, axis=None): # pylint: disable=redefined-outer-name
"""
Append values to the end of an array.
Parameters
----------
arr : ndarray
Values are appended to a copy of this array.
values : ndarray
These values are appended to a copy of `arr`. It must be of the
correct shape (the same shape as `arr`, excluding `axis`). If
`axis` is not specified, `values` can be any shape and will be
flattened before use.
axis : int, optional
The axis along which `values` are appended. If `axis` is not
given, both `arr` and `values` are flattened before use.
Returns
-------
append : ndarray
A copy of `arr` with `values` appended to `axis`. Note that
`append` does not occur in-place: a new array is allocated and
filled. If `axis` is None, `out` is a flattened array.
Examples
--------
>>> np.append(np.array([1, 2, 3]), np.array([[4, 5, 6],[7, 8, 9]]))
array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
When `axis` is specified, `values` must have the correct shape.
>>> np.append(np.array([[1, 2, 3], [4, 5, 6]]), np.array([[7, 8, 9]]), axis=0)
array([[1., 2., 3.],
[4., 5., 6.],
[7., 8., 9.]])
"""
out = None
return _api_internal.concatenate(arr, values, axis, out)
@set_module('mxnet.ndarray.numpy')
def stack(arrays, axis=0, out=None):
"""Join a sequence of arrays along a new axis.
The axis parameter specifies the index of the new axis in the dimensions of the result.
For example, if `axis=0` it will be the first dimension and if `axis=-1` it will be the last dimension.
Parameters
----------
arrays : sequence of ndarray
Each array must have the same shape.
axis : int, optional
The axis in the result array along which the input arrays are stacked.
out : ndarray, optional
If provided, the destination to place the result. The shape must be correct,
matching that of what stack would have returned if no out argument were specified.
Returns
-------
stacked : ndarray
The stacked array has one more dimension than the input arrays."""
def get_list(arrays):
if not hasattr(arrays, '__getitem__') and hasattr(arrays, '__iter__'):
raise ValueError("expected iterable for arrays but got {}".format(type(arrays)))
return [arr for arr in arrays]
arrays = get_list(arrays)
return _api_internal.stack(*arrays, axis, out)
@set_module('mxnet.ndarray.numpy')
def vstack(arrays, out=None):
r"""Stack arrays in sequence vertically (row wise).
This is equivalent to concatenation along the first axis after 1-D arrays
of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by
`vsplit`.
This function makes most sense for arrays with up to 3 dimensions. For
instance, for pixel-data with a height (first axis), width (second axis),
and r/g/b channels (third axis). The functions `concatenate` and `stack`
provide more general stacking and concatenation operations.
Parameters
----------
tup : sequence of ndarrays
The arrays must have the same shape along all but the first axis.
1-D arrays must have the same length.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays, will be at least 2-D.
Examples
--------
>>> a = np.array([1, 2, 3])
>>> b = np.array([2, 3, 4])
>>> np.vstack((a, b))
array([[1., 2., 3.],
[2., 3., 4.]])
>>> a = np.array([[1], [2], [3]])
>>> b = np.array([[2], [3], [4]])
>>> np.vstack((a, b))
array([[1.],
[2.],
[3.],
[2.],
[3.],
[4.]])
"""
def get_list(arrays):
if not hasattr(arrays, '__getitem__') and hasattr(arrays, '__iter__'):
raise ValueError("expected iterable for arrays but got {}".format(type(arrays)))
return [arr for arr in arrays]
arrays = get_list(arrays)
return _api_internal.vstack(*arrays)
@set_module('mxnet.ndarray.numpy')
def row_stack(arrays):
r"""Stack arrays in sequence vertically (row wise).
This is equivalent to concatenation along the first axis after 1-D arrays
of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by
`vsplit`.
This function makes most sense for arrays with up to 3 dimensions. For
instance, for pixel-data with a height (first axis), width (second axis),
and r/g/b channels (third axis). The functions `concatenate` and `stack`
provide more general stacking and concatenation operations.
Parameters
----------
tup : sequence of ndarrays
The arrays must have the same shape along all but the first axis.
1-D arrays must have the same length.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays, will be at least 2-D.
Examples
--------
>>> a = np.array([1, 2, 3])
>>> b = np.array([2, 3, 4])
>>> np.vstack((a, b))
array([[1., 2., 3.],
[2., 3., 4.]])
>>> a = np.array([[1], [2], [3]])
>>> b = np.array([[2], [3], [4]])
>>> np.vstack((a, b))
array([[1.],
[2.],
[3.],
[2.],
[3.],
[4.]])
"""
def get_list(arrays):
if not hasattr(arrays, '__getitem__') and hasattr(arrays, '__iter__'):
raise ValueError("expected iterable for arrays but got {}".format(type(arrays)))
return [arr for arr in arrays]
arrays = get_list(arrays)
return _api_internal.vstack(*arrays)
@set_module('mxnet.ndarray.numpy')
def column_stack(tup):
"""
Stack 1-D arrays as columns into a 2-D array.
Take a sequence of 1-D arrays and stack them as columns
to make a single 2-D array. 2-D arrays are stacked as-is,
just like with `hstack`. 1-D arrays are turned into 2-D columns
first.
Returns
--------
stacked : 2-D array
The array formed by stacking the given arrays.
See Also
--------
stack, hstack, vstack, concatenate
Examples
--------
>>> a = np.array((1,2,3))
>>> b = np.array((2,3,4))
>>> np.column_stack((a,b))
array([[1., 2.],
[2., 3.],
[3., 4.]])
"""
return _api_internal.column_stack(*tup)
@set_module('mxnet.ndarray.numpy')
def hstack(arrays):
"""
Stack arrays in sequence horizontally (column wise).
This is equivalent to concatenation along the second axis,
except for 1-D arrays where it concatenates along the first axis.
Rebuilds arrays divided by hsplit.
This function makes most sense for arrays with up to 3 dimensions.
For instance, for pixel-data with a height (first axis), width (second axis),
and r/g/b channels (third axis). The functions concatenate,
stack and block provide more general stacking and concatenation operations.
Parameters
----------
tup : sequence of ndarrays
The arrays must have the same shape along all but the second axis, except 1-D arrays which can be any length.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
Examples
--------
>>> from mxnet import np,npx
>>> a = np.array((1,2,3))
>>> b = np.array((2,3,4))
>>> np.hstack((a,b))
array([1., 2., 3., 2., 3., 4.])
>>> a = np.array([[1],[2],[3]])
>>> b = np.array([[2],[3],[4]])
>>> np.hstack((a,b))
array([[1., 2.],
[2., 3.],
[3., 4.]])
"""
return _api_internal.hstack(*arrays)
@set_module('mxnet.ndarray.numpy')
def dstack(arrays):
"""
Stack arrays in sequence depth wise (along third axis).
This is equivalent to concatenation along the third axis after 2-D arrays
of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape
`(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by
`dsplit`.
This function makes most sense for arrays with up to 3 dimensions. For
instance, for pixel-data with a height (first axis), width (second axis),
and r/g/b channels (third axis). The functions `concatenate`, `stack` and
`block` provide more general stacking and concatenation operations.
Parameters
----------
tup : sequence of arrays
The arrays must have the same shape along all but the third axis.
1-D or 2-D arrays must have the same shape.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays, will be at least 3-D.
Examples
--------
>>> a = np.array((1,2,3))
>>> b = np.array((2,3,4))
>>> np.dstack((a,b))
array([[[1, 2],
[2, 3],
[3, 4]]])
>>> a = np.array([[1],[2],[3]])
>>> b = np.array([[2],[3],[4]])
>>> np.dstack((a,b))
array([[[1, 2]],
[[2, 3]],
[[3, 4]]])
"""
return _api_internal.dstack(*arrays)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def maximum(x1, x2, out=None, **kwargs):
"""
Returns element-wise maximum of the input arrays with broadcasting.
Parameters
----------
x1, x2 : scalar or mxnet.numpy.ndarray
The arrays holding the elements to be compared. They must have the same shape,
or shapes that can be broadcast to a single shape.
Returns
-------
out : mxnet.numpy.ndarray or scalar
The maximum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars."""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.maximum(x1, x2, out=out)
return _api_internal.maximum(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def fmax(x1, x2, out=None, **kwargs):
"""
Returns element-wise maximum of the input arrays with broadcasting. (Ignores NaNs)
Parameters
----------
x1, x2 : scalar or mxnet.numpy.ndarray
The arrays holding the elements to be compared. They must have the same shape,
or shapes that can be broadcast to a single shape.
Returns
-------
out : mxnet.numpy.ndarray or scalar
The maximum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars."""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
_np.fmax(x1, x2, out=out)
return _api_internal.fmax(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def minimum(x1, x2, out=None, **kwargs):
"""
Returns element-wise minimum of the input arrays with broadcasting.
Parameters
----------
x1, x2 : scalar or mxnet.numpy.ndarray
The arrays holding the elements to be compared. They must have the same shape,
or shapes that can be broadcast to a single shape.
Returns
-------
out : mxnet.numpy.ndarray or scalar
The minimum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars."""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.minimum(x1, x2, out=out)
return _api_internal.minimum(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def fmin(x1, x2, out=None, **kwargs):
"""
Returns element-wise minimum of the input arrays with broadcasting. (Ignores NaNs)
Parameters
----------
x1, x2 : scalar or mxnet.numpy.ndarray
The arrays holding the elements to be compared. They must have the same shape,
or shapes that can be broadcast to a single shape.
Returns
-------
out : mxnet.numpy.ndarray or scalar
The minimum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars."""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
_np.fmin(x1, x2, out=out)
return _api_internal.fmin(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def max(a, axis=None, out=None, keepdims=False):
"""
Return the maximum of an array or maximum along an axis.
Parameters
----------
a : ndarray
Input data.
axis : int, optional
Axis along which to operate. By default, flattened input is used.
out : ndarray, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
See `doc.ufuncs` (Section "Output arguments") for more details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
max : ndarray
Maximum of `a`. If `axis` is None, the result is an array of dimension 1.
If `axis` is given, the result is an array of dimension
``a.ndim - 1``.
See Also
--------
min :
The minimum value of an array along a given axis, ignoring any nan.
maximum :
Element-wise maximum of two arrays, ignoring any nan.
argmax :
Return the indices of the maximum values.
Notes
-----
NaN in the orginal `numpy` is denoted as nan and will be ignored.
Don't use `max` for element-wise comparison of 2 arrays; when
``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
``max(a, axis=0)``.
Examples
--------
>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0., 1.],
[2., 3.]])
>>> np.max(a) # Maximum of the flattened array
array(3.)
>>> np.max(a, axis=0) # Maxima along the first axis
array([2., 3.])
>>> np.max(a, axis=1) # Maxima along the second axis
array([1., 3.])
>>> b = np.arange(5, dtype=np.float32)
>>> b[2] = np.nan
>>> np.max(b)
array(4.)
"""
return _api_internal.max(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def min(a, axis=None, out=None, keepdims=False):
"""
Return the minimum of an array or minimum along an axis.
Parameters
----------
a : ndarray
Input data.
axis : int, optional
Axis along which to operate. By default, flattened input is used.
out : ndarray, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
See `doc.ufuncs` (Section "Output arguments") for more details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
min : ndarray
Minimum of `a`. If `axis` is None, the result is an array of dimension 1.
If `axis` is given, the result is an array of dimension
``a.ndim - 1``.
See Also
--------
max :
The maximum value of an array along a given axis, ignoring any nan.
minimum :
Element-wise minimum of two arrays, ignoring any nan.
Notes
-----
NaN in the orginal `numpy` is denoted as nan and will be ignored.
Don't use `min` for element-wise comparison of 2 arrays; when
``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
``min(a, axis=0)``.
Examples
--------
>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0., 1.],
[2., 3.]])
>>> np.min(a) # Minimum of the flattened array
array(0.)
>>> np.min(a, axis=0) # Minima along the first axis
array([0., 1.])
>>> np.min(a, axis=1) # Minima along the second axis
array([0., 2.])
>>> b = np.arange(5, dtype=np.float32)
>>> b[2] = np.nan
>>> np.min(b)
array(0.) # nan will be ignored
"""
return _api_internal.min(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def amax(a, axis=None, out=None, keepdims=False):
"""
Return the maximum of an array or maximum along an axis.
Parameters
----------
a : ndarray
Input data.
axis : int, optional
Axis along which to operate. By default, flattened input is used.
out : ndarray, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
See `doc.ufuncs` (Section "Output arguments") for more details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
max : ndarray
Maximum of `a`. If `axis` is None, the result is an array of dimension 1.
If `axis` is given, the result is an array of dimension
``a.ndim - 1``.
See Also
--------
min :
The minimum value of an array along a given axis, ignoring any nan.
maximum :
Element-wise maximum of two arrays, ignoring any nan.
argmax :
Return the indices of the maximum values.
Notes
-----
NaN in the orginal `numpy` is denoted as nan and will be ignored.
Don't use `max` for element-wise comparison of 2 arrays; when
``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
``max(a, axis=0)``.
Examples
--------
>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0., 1.],
[2., 3.]])
>>> np.max(a) # Maximum of the flattened array
array(3.)
>>> np.max(a, axis=0) # Maxima along the first axis
array([2., 3.])
>>> np.max(a, axis=1) # Maxima along the second axis
array([1., 3.])
>>> b = np.arange(5, dtype=np.float32)
>>> b[2] = np.nan
>>> np.max(b)
array(4.)
"""
return _api_internal.amax(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def amin(a, axis=None, out=None, keepdims=False):
"""
Return the minimum of an array or minimum along an axis.
Parameters
----------
a : ndarray
Input data.
axis : int, optional
Axis along which to operate. By default, flattened input is used.
out : ndarray, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
See `doc.ufuncs` (Section "Output arguments") for more details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
min : ndarray
Minimum of `a`. If `axis` is None, the result is an array of dimension 1.
If `axis` is given, the result is an array of dimension
``a.ndim - 1``.
See Also
--------
max :
The maximum value of an array along a given axis, ignoring any nan.
minimum :
Element-wise minimum of two arrays, ignoring any nan.
Notes
-----
NaN in the orginal `numpy` is denoted as nan and will be ignored.
Don't use `min` for element-wise comparison of 2 arrays; when
``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
``min(a, axis=0)``.
Examples
--------
>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0., 1.],
[2., 3.]])
>>> np.min(a) # Minimum of the flattened array
array(0.)
>>> np.min(a, axis=0) # Minima along the first axis
array([0., 1.])
>>> np.min(a, axis=1) # Minima along the second axis
array([0., 2.])
>>> b = np.arange(5, dtype=np.float32)
>>> b[2] = np.nan
>>> np.min(b)
array(0.) # nan will be ignored
"""
return _api_internal.amin(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def swapaxes(a, axis1, axis2):
"""Interchange two axes of an array.
Parameters
----------
a : ndarray
Input array.
axis1 : int
First axis.
axis2 : int
Second axis.
Returns
-------
a_swapped : ndarray
Swapped array. This is always a copy of the input array.
"""
return _npi.swapaxes(a, dim1=axis1, dim2=axis2)
@set_module('mxnet.ndarray.numpy')
def clip(a, a_min, a_max, out=None):
"""clip(a, a_min, a_max, out=None)
Clip (limit) the values in an array.
Given an interval, values outside the interval are clipped to
the interval edges. For example, if an interval of ``[0, 1]``
is specified, values smaller than 0 become 0, and values larger
than 1 become 1.
Parameters
----------
a : ndarray
Array containing elements to clip.
a_min : scalar or `None`
Minimum value. If `None`, clipping is not performed on lower
interval edge. Not more than one of `a_min` and `a_max` may be
`None`.
a_max : scalar or `None`
Maximum value. If `None`, clipping is not performed on upper
interval edge. Not more than one of `a_min` and `a_max` may be
`None`.
out : ndarray, optional
The results will be placed in this array. It may be the input
array for in-place clipping. `out` must be of the right shape
to hold the output. Its type is preserved.
Returns
-------
clipped_array : ndarray
An array with the elements of `a`, but where values
< `a_min` are replaced with `a_min`, and those > `a_max`
with `a_max`.
Notes
-----
ndarray `a_min` and `a_max` are not supported.
Examples
--------
>>> a = np.arange(10)
>>> np.clip(a, 1, 8)
array([1., 1., 2., 3., 4., 5., 6., 7., 8., 8.])
>>> a
array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])
>>> np.clip(a, 3, 6, out=a)
array([3., 3., 3., 3., 4., 5., 6., 6., 6., 6.])
"""
if a_min is None and a_max is None:
raise ValueError('array_clip: must set either max or min')
return _api_internal.clip(a, a_min, a_max, out)
@set_module('mxnet.ndarray.numpy')
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]])
"""
if m is None:
m = n
return tuple(_api_internal.tril_indices(n, k, m))
@set_module('mxnet.ndarray.numpy')
def argmax(a, axis=None, out=None, keepdims=False):
r"""
Returns the indices of the maximum values along an axis.
Parameters
----------
a : ndarray
Input array. Only support ndarrays of dtype `float16`, `float32`, and `float64`.
axis : int, optional
By default, the index is into the flattened array, otherwise
along the specified axis.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
keepdims : bool
If True, the reduced axes (dimensions) must be included in the result as
singleton dimensions, and, accordingly, the result must be compatible with
the input array. Otherwise, if False, the reduced axes (dimensions) must
not be included in the result. Default: False .
Returns
-------
index_array : ndarray of indices whose dtype is same as the input ndarray.
Array of indices into the array. It has the same shape as `a.shape`
with the dimension along `axis` removed.
Notes
-----
``keepdims`` param is part of request in data-api-standard
<https://data-apis.org/array-api/latest/API_specification/generated/signatures.searching_functions.argmax.html>`_,
which is not the parameter in official NumPy
In case of multiple occurrences of the maximum values, the indices
corresponding to the first occurrence are returned.
This function differs from the original `numpy.argmax
<https://numpy.org/doc/stable/reference/generated/numpy.argmax.html>`_ in
the following aspects:
- Input type does not support Python native iterables(list, tuple, ...).
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> a = np.arange(6).reshape(2,3) + 10
>>> a
array([[10., 11., 12.],
[13., 14., 15.]])
>>> np.argmax(a)
array(5.)
>>> np.argmax(a, axis=0)
array([1., 1., 1.])
>>> np.argmax(a, axis=1)
array([2., 2.])
>>> b = np.arange(6)
>>> b[1] = 5
>>> b
array([0., 5., 2., 3., 4., 5.])
>>> np.argmax(b) # Only the first occurrence is returned.
array(1.)
Specify ``out`` ndarray:
>>> a = np.arange(6).reshape(2,3) + 10
>>> b = np.zeros((2,))
>>> np.argmax(a, axis=1, out=b)
array([2., 2.])
>>> b
array([2., 2.])
"""
return _api_internal.argmax(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def argmin(a, axis=None, out=None, keepdims=False):
r"""
Returns the indices of the maximum values along an axis.
Parameters
----------
a : ndarray
Input array. Only support ndarrays of dtype `float16`, `float32`, and `float64`.
axis : int, optional
By default, the index is into the flattened array, otherwise
along the specified axis.
out : ndarray or None, optional
If provided, the result will be inserted into this array. It should
be of the appropriate shape and dtype.
keepdims : bool
If True, the reduced axes (dimensions) must be included in the result as
singleton dimensions, and, accordingly, the result must be compatible with
the input array. Otherwise, if False, the reduced axes (dimensions) must
not be included in the result. Default: False .
Returns
-------
index_array : ndarray of indices whose dtype is same as the input ndarray.
Array of indices into the array. It has the same shape as `a.shape`
with the dimension along `axis` removed.
Notes
-----
``keepdims`` param is part of request in data-api-standard
<https://data-apis.org/array-api/latest/API_specification/generated/signatures.searching_functions.argmin.html>`_,
which is not the parameter in official NumPy
In case of multiple occurrences of the maximum values, the indices
corresponding to the first occurrence are returned.
This function differs from the original `numpy.argmax
<https://numpy.org/doc/stable/reference/generated/numpy.argmax.html>`_ in
the following aspects:
- Input type does not support Python native iterables(list, tuple, ...).
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> a = np.arange(6).reshape(2,3) + 10
>>> a
array([[10., 11., 12.],
[13., 14., 15.]])
>>> np.argmin(a)
array(0.)
>>> np.argmin(a, axis=0)
array([0., 0., 0.])
>>> np.argmin(a, axis=1)
array([0., 0.])
>>> b = np.arange(6)
>>> b[2] = 0
>>> b
array([0., 1., 0., 3., 4., 5.])
>>> np.argmax(b) # Only the first occurrence is returned.
array(0.)
Specify ``out`` ndarray:
>>> a = np.arange(6).reshape(2,3) + 10
>>> b = np.zeros((2,))
>>> np.argmin(a, axis=1, out=b)
array([0., 0.])
>>> b
array([0., 0.])
"""
return _api_internal.argmin(a, axis, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def average(a, axis=None, weights=None, returned=False, out=None):
"""
Compute the weighted average along the specified axis.
Parameters
--------
a : ndarray
Array containing data to be averaged.
axis : None or int or tuple of ints, optional
Axis or axes along which to average a.
The default, axis=None, will average over
all of the elements of the input array.
If axis is negative it counts from the last to the first axis.
New in version 1.7.0.
If axis is a tuple of ints, averaging is
performed on all of the axes specified in the tuple
instead of a single axis or all the axes as before.
weights : ndarray, optional
An array of weights associated with the values in a, must be the same dtype with a.
Each value in a contributes to the average according to its associated weight.
The weights array can either be 1-D (in which case its length must be
the size of a along the given axis) or of the same shape as a.
If weights=None, then all data in a are assumed to have a weight equal to one.
The 1-D calculation is: avg = sum(a * weights) / sum(weights)
The only constraint on weights is that sum(weights) must not be 0.
returned : bool, optional
Default is False.
If True, the tuple (average, sum_of_weights) is returned,
otherwise only the average is returned.
If weights=None, sum_of_weights is equivalent to
the number of elements over which the average is taken.
out : ndarray, optional
If provided, the calculation is done into this array.
Returns
--------
retval, [sum_of_weights] : ndarray
Return the average along the specified axis.
When returned is True, return a tuple with the average as the first element
and the sum of the weights as the second element. sum_of_weights is of the same type as retval.
If a is integral, the result dtype will be current default dtype, otherwise it will be the same
as dtype of a. (i.e. When npx.is_np_default_dtype() returns False, default dtype is float32; When
npx.is_np_default_dtype() returns True, default dtype is float64.)
Raises
--------
MXNetError
- When all weights along axis sum to zero.
- When the length of 1D weights is not the same as the shape of a along axis.
- When given 1D weights, the axis is not specified or is not int.
- When the shape of weights and a differ, but weights are not 1D.
See also
--------
mean
Notes
--------
This function differs from the original `numpy.average`
<https://numpy.org/devdocs/reference/generated/numpy.average.html>`_ in
the following way(s):
- Does not guarantee the same behavior with numpy when given float16 dtype and overflow happens
- Does not support complex dtype
- The dtypes of a and weights must be the same
- Integral a results in default dtype.
i.e. When npx.is_np_default_dtype() returns False, default dtype is float32;
When npx.is_np_default_dtype() returns True, default dtype is float64.
Examples
--------
>>> data = np.arange(1, 5)
>>> data
array([1., 2., 3., 4.])
>>> np.average(data)
array(2.5)
>>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1))
array(4.)
>>> data = np.arange(6).reshape((3,2))
>>> data
array([[0., 1.],
[2., 3.],
[4., 5.]])
>>> weights = np.array([0.25, 0.75])
array([0.25, 0.75])
>>> np.average(data, axis=1, weights=weights)
array([0.75, 2.75, 4.75])
"""
out = _api_internal.average(a, weights, axis, returned, weights is not None, out)
if isinstance(out, NDArray):
return out
else:
return list(out)
@set_module('mxnet.ndarray.numpy')
def mean(a, axis=None, dtype=None, out=None, keepdims=False): # pylint: disable=arguments-differ
"""
mean(a, axis=None, dtype=None, out=None, keepdims=None)
Compute the arithmetic mean along the specified axis.
Returns the average of the array elements.
The average is taken over the flattened array by default, otherwise over the specified axis.
Parameters
----------
a : ndarray
ndarray containing numbers whose mean is desired.
axis : None or int or tuple of ints, optional
Axis or axes along which the means are computed. The default is to compute the mean of the flattened array.
If this is a tuple of ints, a mean is performed over multiple axes,
instead of a single axis or all the axes as before.
dtype : data-type, optional
Type to use in computing the mean.
For integer inputs, the default is your current default dtype (i.e. When npx.is_np_default_dtype() returns
False, default dtype is float32; When npx.is_np_default_dtype() returns True, default dtype is float64.);
For floating point inputs, it is the same as the input dtype.
out : ndarray, optional
Alternate output array in which to place the result. The default is None; if provided,
it must have the same shape and type as the expected output
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result
as dimensions with size one. With this option, the result will broadcast correctly
against the input array.
If the default value is passed, then keepdims will not be passed through to the mean
method of sub-classes of ndarray, however any non-default value will be. If the sub-class
method does not implement keepdims any exceptions will be raised.
Returns
-------
m : ndarray, see dtype parameter above
If out=None, returns a new array containing the mean values,
otherwise a reference to the output array is returned.
Notes
-----
This function differs from the original `numpy.mean
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html>`_ in
the following way(s):
- only ndarray is accepted as valid input, python iterables or scalar is not supported
- default data type for integer input is float32 or float64, which depends on your current default dtype.
When npx.is_np_default_dtype() returns False, default dtype is float32;
When npx.is_np_default_dtype() returns True, default dtype is float64.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> np.mean(a)
array(2.5)
>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0,:] = 1.0
>>> a[1,:] = 0.1
>>> np.mean(a)
array(0.55)
>>> np.mean(a, dtype=np.float64)
array(0.55)
"""
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.mean(a, axis, dtype, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False): # pylint: disable=too-many-arguments
"""
Compute the standard deviation along the specified axis.
Returns the standard deviation, a measure of the spread of a distribution,
of the array elements. The standard deviation is computed for the
flattened array by default, otherwise over the specified axis.
Parameters
----------
a : ndarray
Calculate the standard deviation of these values.
axis : None or int or tuple of ints, optional
Axis or axes along which the standard deviation is computed. The
default is to compute the standard deviation of the flattened array.
.. versionadded:: 1.7.0
If this is a tuple of ints, a standard deviation is performed over
multiple axes, instead of a single axis or all the axes as before.
dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of
integer type the default is float64, for arrays of float types it is
the same as the array type.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type (of the calculated
values) will be cast if necessary.
ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations
is ``N - ddof``, where ``N`` represents the number of elements.
By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the input array.
If the default value is passed, then `keepdims` will not be
passed through to the `std` method of sub-classes of
`ndarray`, however any non-default value will be. If the
sub-class' method does not implement `keepdims` any
exceptions will be raised.
Returns
-------
standard_deviation : ndarray, see dtype parameter above.
If `out` is None, return a new array containing the standard deviation,
otherwise return a reference to the output array.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> np.std(a)
1.1180339887498949 # may vary
>>> np.std(a, axis=0)
array([1., 1.])
>>> np.std(a, axis=1)
array([0.5, 0.5])
In single precision, std() can be inaccurate:
>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> np.std(a)
array(0.45)
>>> np.std(a, dtype=np.float64)
array(0.45, dtype=float64)
"""
return _api_internal.std(a, axis, dtype, ddof, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False): # pylint: disable=too-many-arguments
"""
Compute the variance along the specified axis.
Returns the variance of the array elements, a measure of the spread of a
distribution. The variance is computed for the flattened array by
default, otherwise over the specified axis.
Parameters
----------
a : ndarray
Array containing numbers whose variance is desired. If `a` is not an
array, a conversion is attempted.
axis : None or int or tuple of ints, optional
Axis or axes along which the variance is computed. The default is to
compute the variance of the flattened array.
.. versionadded:: 1.7.0
If this is a tuple of ints, a variance is performed over multiple axes,
instead of a single axis or all the axes as before.
dtype : data-type, optional
Type to use in computing the variance.
For arrays of integer type the default is `float32` or 'float64',
When npx.is_np_default_dtype() returns False, default dtype is float32,
When npx.is_np_default_dtype() returns True, default dtype is float64;
For arrays of float types it is the same as the array type.
out : ndarray, optional
Alternate output array in which to place the result. It must have
the same shape as the expected output, but the type is cast if
necessary.
ddof : int, optional
"Delta Degrees of Freedom": the divisor used in the calculation is
``N - ddof``, where ``N`` represents the number of elements. By
default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the input array.
If the default value is passed, then `keepdims` will not be
passed through to the `var` method of sub-classes of
`ndarray`, however any non-default value will be. If the
sub-class' method does not implement `keepdims` any
exceptions will be raised.
Returns
-------
variance : ndarray, see dtype parameter above
If ``out=None``, returns a new array containing the variance;
otherwise, a reference to the output array is returned.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> np.var(a)
array(1.25)
>>> np.var(a, axis=0)
array([1., 1.])
>>> np.var(a, axis=1)
array([0.25, 0.25])
>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> np.var(a)
array(0.2025)
>>> np.var(a, dtype=np.float64)
array(0.2025, dtype=float64)
>>> ((1-0.55)**2 + (0.1-0.55)**2)/2
0.2025
"""
return _api_internal.var(a, axis, dtype, ddof, keepdims, out)
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def indices(dimensions, dtype=None, device=None):
"""Return an array representing the indices of a grid.
Compute an array where the subarrays contain index values 0,1,...
varying only along the corresponding axis.
Parameters
----------
dimensions : sequence of ints
The shape of the grid.
dtype : data-type, optional
The desired data-type for the array. Default is `int64`.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
grid : ndarray
The array of grid indices,
``grid.shape = (len(dimensions),) + tuple(dimensions)``.
Notes
-----
The output shape is obtained by prepending the number of dimensions
in front of the tuple of dimensions, i.e. if `dimensions` is a tuple
``(r0, ..., rN-1)`` of length ``N``, the output shape is
``(N,r0,...,rN-1)``.
The subarrays ``grid[k]`` contains the N-D array of indices along the
``k-th`` axis. Explicitly::
grid[k,i0,i1,...,iN-1] = ik
Examples
--------
>>> grid = np.indices((2, 3))
>>> grid.shape
(2, 2, 3)
>>> grid[0] # row indices
array([[0, 0, 0],
[1, 1, 1]], dtype=int64)
>>> grid[1] # column indices
array([[0, 0, 0],
[1, 1, 1]], dtype=int64)
The indices can be used as an index into an array.
>>> x = np.arange(20).reshape(5, 4)
>>> row, col = np.indices((2, 3))
>>> x[row, col]
array([[0., 1., 2.],
[4., 5., 6.]])
Note that it would be more straightforward in the above example to
extract the required elements directly with ``x[:2, :3]``.
"""
if isinstance(dimensions, (tuple, list)):
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.indices(dimensions, dtype, device)
else:
raise ValueError("The dimensions must be sequence of ints")
# pylint: enable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def copysign(x1, x2, out=None, **kwargs):
r"""
Change the sign of x1 to that of x2, element-wise.
If `x2` is a scalar, its sign will be copied to all elements of `x1`.
Parameters
----------
x1 : ndarray or scalar
Values to change the sign of.
x2 : ndarray or scalar
The sign of `x2` is copied to `x1`.
out : ndarray or None, optional
A location into which the result is stored. It must be of the
right shape and right type to hold the output. If not provided
or `None`,a freshly-allocated array is returned.
Returns
-------
out : ndarray or scalar
The values of `x1` with the sign of `x2`.
This is a scalar if both `x1` and `x2` are scalars.
Notes
-------
This function differs from the original `numpy.copysign
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.copysign.html>`_ in
the following aspects:
- ``where`` param is not supported.
Examples
--------
>>> np.copysign(1.3, -1)
-1.3
>>> 1/np.copysign(0, 1)
inf
>>> 1/np.copysign(0, -1)
-inf
>>> a = np.array([-1, 0, 1])
>>> np.copysign(a, -1.1)
array([-1., -0., -1.])
>>> np.copysign(a, np.arange(3)-1)
array([-1., 0., 1.])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.copysign(x1, x2, out=out)
return _api_internal.copysign(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def ravel(x, order='C'):
r"""
ravel(x)
Return a contiguous flattened array.
A 1-D array, containing the elements of the input, is returned. A copy is
made only if needed.
Parameters
----------
x : ndarray
Input array. The elements in `x` are read in row-major, C-style order and
packed as a 1-D array.
order : `C`, optional
Only support row-major, C-style order.
Returns
-------
y : ndarray
y is an array of the same subtype as `x`, with shape ``(x.size,)``.
Note that matrices are special cased for backward compatibility, if `x`
is a matrix, then y is a 1-D ndarray.
Notes
-----
This function differs from the original numpy.arange in the following aspects:
- Only support row-major, C-style order.
Examples
--------
It is equivalent to ``reshape(x, -1)``.
>>> x = np.array([[1, 2, 3], [4, 5, 6]])
>>> print(np.ravel(x))
[1. 2. 3. 4. 5. 6.]
>>> print(x.reshape(-1))
[1. 2. 3. 4. 5. 6.]
>>> print(np.ravel(x.T))
[1. 4. 2. 5. 3. 6.]
"""
if order == 'F':
raise NotImplementedError('order {} is not supported'.format(order))
if isinstance(x, numeric_types):
return _np.reshape(x, -1)
elif isinstance(x, NDArray):
return reshape(x, -1)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
@set_module('mxnet.ndarray.numpy')
def unravel_index(indices, shape, order='C'): # pylint: disable=redefined-outer-name
"""
Converts a flat index or array of flat indices into a tuple of coordinate arrays.
Parameters:
-------------
indices : array_like
An integer array whose elements are indices into the flattened version of an array of dimensions shape.
Before version 1.6.0, this function accepted just one index value.
shape : tuple of ints
The shape of the array to use for unraveling indices.
Returns:
-------------
unraveled_coords : ndarray
Each row in the ndarray has the same shape as the indices array.
Each column in the ndarray represents the unravelled index
Examples:
-------------
>>> np.unravel_index([22, 41, 37], (7,6))
([3. 6. 6.]
[4. 5. 1.])
>>> np.unravel_index(1621, (6,7,8,9))
(3, 1, 4, 1)
"""
if order == 'C':
if isinstance(indices, numeric_types):
return _np.unravel_index(indices, shape)
if isinstance(indices, NDArray):
return tuple(_api_internal.unravel_index(indices, shape))
raise TypeError('Do not support type {} as indices.'.format(str(type(indices))))
raise NotImplementedError('Do not support column-major (Fortran-style) order at this moment')
def flatnonzero(a):
r"""
Return indices that are non-zero in the flattened version of a.
This is equivalent to np.nonzero(np.ravel(a))[0].
Parameters
----------
a : array_like
Input data.
Returns
-------
res : ndarray
Output array, containing the indices of the elements of `a.ravel()`
that are non-zero.
See Also
--------
nonzero : Return the indices of the non-zero elements of the input array.
ravel : Return a 1-D array containing the elements of the input array.
Examples
--------
>>> x = np.arange(-2, 3)
>>> x
array([-2, -1, 0, 1, 2])
>>> np.flatnonzero(x)
array([0, 1, 3, 4])
Use the indices of the non-zero elements as an index array to extract
these elements:
>>> x.ravel()[np.flatnonzero(x)]
array([-2, -1, 1, 2])
"""
return nonzero(ravel(a))[0]
@set_module('mxnet.ndarray.numpy')
def diag_indices_from(arr):
"""
This returns a tuple of indices that can be used to access the main diagonal of an array
a with a.ndim >= 2 dimensions and shape (n, n, ..., n). For a.ndim = 2 this is
the usual diagonal, for a.ndim > 2 this is the set of indices to access
a[i, i, ..., i] for i = [0..n-1].
Parameters:
-------------
arr : ndarray
Input array for acessing the main diagonal. All dimensions
should have equal length.
Return:
-------------
diag: tuple of ndarray
indices of the main diagonal.
Examples:
-------------
>>> 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]])
>>> idx = np.diag_indices_from(a)
>>> idx
(array([0, 1, 2, 3]), array([0, 1, 2, 3]))
>>> a[idx] = 100
>>> a
array([[100, 1, 2, 3],
[ 4, 100, 6, 7],
[ 8, 9, 100, 11],
[ 12, 13, 14, 100]])
"""
return tuple(_api_internal.diag_indices_from(arr))
@set_module('mxnet.ndarray.numpy')
def hanning(M, dtype=None, device=None):
r"""Return the Hanning window.
The Hanning window is a taper formed by using a weighted cosine.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an
empty array is returned.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
out : ndarray, shape(M,)
The window, with the maximum value normalized to one (the value
one appears only if `M` is odd).
When npx.is_np_default_dtype() returns False, default dtype is float32;
When npx.is_np_default_dtype() returns True, default dtype is float64.
Note that you need select numpy.float32 or float64 in this operator.
See Also
--------
blackman, hamming
Notes
-----
The Hanning window is defined as
.. math:: w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right)
\qquad 0 \leq n \leq M-1
The Hanning was named for Julius von Hann, an Austrian meteorologist.
It is also known as the Cosine Bell. Some authors prefer that it be
called a Hann window, to help avoid confusion with the very similar
Hamming window.
Most references to the Hanning window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.
References
----------
.. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
spectra, Dover Publications, New York.
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
The University of Alberta Press, 1975, pp. 106-108.
.. [3] Wikipedia, "Window function",
http://en.wikipedia.org/wiki/Window_function
.. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
"Numerical Recipes", Cambridge University Press, 1986, page 425.
Examples
--------
>>> np.hanning(12)
array([0. , 0.07937324, 0.29229254, 0.5711574 , 0.8274304 ,
0.9797465 , 0.97974646, 0.82743025, 0.5711573 , 0.29229245,
0.07937312, 0. ])
Plot the window and its frequency response:
>>> import matplotlib.pyplot as plt
>>> window = np.hanning(51)
>>> plt.plot(window.asnumpy())
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Hann window")
Text(0.5, 1.0, 'Hann window')
>>> plt.ylabel("Amplitude")
Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("Sample")
Text(0.5, 0, 'Sample')
>>> plt.show()
"""
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.hanning(M, dtype, device)
@set_module('mxnet.ndarray.numpy')
def hamming(M, dtype=None, device=None):
r"""Return the hamming window.
The hamming window is a taper formed by using a weighted cosine.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an
empty array is returned.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
out : ndarray, shape(M,)
The window, with the maximum value normalized to one (the value
one appears only if `M` is odd).
When npx.is_np_default_dtype() returns False, default dtype is float32;
When npx.is_np_default_dtype() returns True, default dtype is float64.
Note that you need select numpy.float32 or float64 in this operator.
See Also
--------
blackman, hanning
Notes
-----
The Hamming window is defined as
.. math:: w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right)
\qquad 0 \leq n \leq M-1
The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
and is described in Blackman and Tukey. It was recommended for
smoothing the truncated autocovariance function in the time domain.
Most references to the Hamming window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.
References
----------
.. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
spectra, Dover Publications, New York.
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
University of Alberta Press, 1975, pp. 109-110.
.. [3] Wikipedia, "Window function",
https://en.wikipedia.org/wiki/Window_function
.. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
"Numerical Recipes", Cambridge University Press, 1986, page 425.
Examples
--------
>>> np.hamming(12)
array([0.08000001, 0.15302339, 0.34890914, 0.6054648 , 0.841236 ,
0.9813669 , 0.9813668 , 0.8412359 , 0.6054647 , 0.34890908,
0.15302327, 0.08000001])
Plot the window and its frequency response:
>>> import matplotlib.pyplot as plt
>>> window = np.hamming(51)
>>> plt.plot(window.asnumpy())
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("hamming window")
Text(0.5, 1.0, 'hamming window')
>>> plt.ylabel("Amplitude")
Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("Sample")
Text(0.5, 0, 'Sample')
>>> plt.show()
"""
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.hamming(M, dtype, device)
@set_module('mxnet.ndarray.numpy')
def blackman(M, dtype=None, device=None):
r"""Return the Blackman window.
The Blackman window is a taper formed by using the first three
terms of a summation of cosines. It was designed to have close to the
minimal leakage possible. It is close to optimal, only slightly worse
than a Kaiser window.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an
empty array is returned.
device : Device, optional
Device context on which the memory is allocated. Default is
`mxnet.device.current_device()`.
Returns
-------
out : ndarray
The window, with the maximum value normalized to one (the value one
appears only if the number of samples is odd).
When npx.is_np_default_dtype() returns False, default dtype is float32;
When npx.is_np_default_dtype() returns True, default dtype is float64.
Note that you need select numpy.float32 or float64 in this operator.
See Also
--------
hamming, hanning
Notes
-----
The Blackman window is defined as
.. math:: w(n) = 0.42 - 0.5 \cos(2\pi n/{M-1}) + 0.08 \cos(4\pi n/{M-1})
Most references to the Blackman window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function. It is known as a
"near optimal" tapering function, almost as good (by some measures)
as the kaiser window.
References
----------
Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
Dover Publications, New York.
Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.
Examples
--------
>>> np.blackman(12)
array([-1.4901161e-08, 3.2606423e-02, 1.5990365e-01, 4.1439798e-01,
7.3604530e-01, 9.6704686e-01, 9.6704674e-01, 7.3604506e-01,
4.1439781e-01, 1.5990359e-01, 3.2606363e-02, -1.4901161e-08])
Plot the window and its frequency response:
>>> import matplotlib.pyplot as plt
>>> window = np.blackman(51)
>>> plt.plot(window.asnumpy())
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("blackman window")
Text(0.5, 1.0, 'blackman window')
>>> plt.ylabel("Amplitude")
Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("Sample")
Text(0.5, 0, 'Sample')
>>> plt.show()
"""
if device is None:
device = str(current_device())
else:
device = str(device)
if dtype is not None and not isinstance(dtype, str):
dtype = get_dtype_name(dtype)
return _api_internal.blackman(M, dtype, device)
@set_module('mxnet.ndarray.numpy')
def flip(m, axis=None, out=None):
r"""
flip(m, axis=None, out=None)
Reverse the order of elements in an array along the given axis.
The shape of the array is preserved, but the elements are reordered.
Parameters
----------
m : ndarray or scalar
Input array.
axis : None or int or tuple of ints, optional
Axis or axes along which to flip over. The default,
axis=None, will flip over all of the axes of the input array.
If axis is negative it counts from the last to the first axis.
If axis is a tuple of ints, flipping is performed on all of the axes
specified in the tuple.
out : ndarray or scalar, optional
Alternative output array in which to place the result. It must have
the same shape and type as the expected output.
Returns
-------
out : ndarray or scalar
A view of `m` with the entries of axis reversed. Since a view is
returned, this operation is done in constant time.
Examples
--------
>>> A = np.arange(8).reshape((2,2,2))
>>> A
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> np.flip(A, 0)
array([[[4, 5],
[6, 7]],
[[0, 1],
[2, 3]]])
>>> np.flip(A, 1)
array([[[2, 3],
[0, 1]],
[[6, 7],
[4, 5]]])
>>> np.flip(A)
array([[[7, 6],
[5, 4]],
[[3, 2],
[1, 0]]])
>>> np.flip(A, (0, 2))
array([[[5, 4],
[7, 6]],
[[1, 0],
[3, 2]]])
"""
from ...numpy import ndarray
if isinstance(m, numeric_types):
return _np.flip(m, axis)
elif isinstance(m, ndarray):
return _api_internal.flip(m, axis, out)
else:
raise TypeError('type {} not supported'.format(str(type(m))))
@set_module('mxnet.ndarray.numpy')
def flipud(m):
r"""
flipud(*args, **kwargs)
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(np.array([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,...])
array(True)
>>> np.flipud(np.array([1,2]))
array([2., 1.])
"""
return flip(m, 0)
@set_module('mxnet.ndarray.numpy')
def fliplr(m):
r"""
fliplr(*args, **kwargs)
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(np.array([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,...])
array(True)
"""
return flip(m, 1)
@set_module('mxnet.ndarray.numpy')
def around(x, decimals=0, out=None, **kwargs):
r"""
around(x, decimals=0, out=None)
Evenly round to the given number of decimals.
Parameters
----------
x : ndarray or scalar
Input data.
decimals : int, optional
Number of decimal places to round to (default: 0). If
decimals is negative, it specifies the number of positions to
the left of the decimal point.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape and type as the expected output.
Returns
-------
rounded_array : ndarray or scalar
An array of the same type as `x`, containing the rounded values.
A reference to the result is returned.
Notes
-----
For values exactly halfway between rounded decimal values, NumPy
rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
-0.5 and 0.5 round to 0.0, etc.
This function differs from the original numpy.prod in the following aspects:
- Cannot cast type automatically. Dtype of `out` must be same as the expected one.
- Cannot support complex-valued number.
Examples
--------
>>> np.around([0.37, 1.64])
array([ 0., 2.])
>>> np.around([0.37, 1.64], decimals=1)
array([ 0.4, 1.6])
>>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
array([ 0., 2., 2., 4., 4.])
>>> np.around([1, 2, 3, 11], decimals=1) # ndarray of ints is returned
array([ 1, 2, 3, 11])
>>> np.around([1, 2, 3, 11], decimals=-1)
array([ 0, 0, 0, 10])
"""
from ...numpy import ndarray
if isinstance(x, numeric_types):
return _np.around(x, decimals, **kwargs)
elif isinstance(x, ndarray):
return _api_internal.around(x, decimals, out, **kwargs)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
@set_module('mxnet.ndarray.numpy')
def round(x, decimals=0, out=None, **kwargs):
r"""
round(a, decimals=0, out=None)
Round an array to the given number of decimals.
See Also
--------
around : equivalent function; see for details.
"""
from ...numpy import ndarray
if isinstance(x, numeric_types):
return _np.around(x, decimals, **kwargs)
elif isinstance(x, ndarray):
return _api_internal.around(x, decimals, out, **kwargs)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
@set_module('mxnet.ndarray.numpy')
def round_(x, decimals=0, out=None, **kwargs):
r"""
round_(a, decimals=0, out=None)
Round an array to the given number of decimals.
See Also
--------
around : equivalent function; see for details.
"""
from ...numpy import ndarray
if isinstance(x, numeric_types):
return _np.around(x, decimals, **kwargs)
elif isinstance(x, ndarray):
return _npi.around(x, decimals, out=out, **kwargs)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def arctan2(x1, x2, out=None, **kwargs):
r"""
Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly.
The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is
the signed angle in radians between the ray ending at the origin and
passing through the point (1,0), and the ray ending at the origin and
passing through the point (`x2`, `x1`). (Note the role reversal: the
"`y`-coordinate" is the first function parameter, the "`x`-coordinate"
is the second.) By IEEE convention, this function is defined for
`x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see
Notes for specific values).
This function is not defined for complex-valued arguments; for the
so-called argument of complex values, use `angle`.
Parameters
----------
x1 : ndarray or scalar
`y`-coordinates.
x2 : ndarray or scalar
`x`-coordinates. `x2` must be broadcastable to match the shape of
`x1` or vice versa.
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
-------
out : ndarray or scalar
Array of angles in radians, in the range ``[-pi, pi]``. This is a scalar if
`x1` and `x2` are scalars.
Notes
-----
*arctan2* is identical to the `atan2` function of the underlying
C library. The following special values are defined in the C
standard: [1]_
====== ====== ================
`x1` `x2` `arctan2(x1,x2)`
====== ====== ================
+/- 0 +0 +/- 0
+/- 0 -0 +/- pi
> 0 +/-inf +0 / +pi
< 0 +/-inf -0 / -pi
+/-inf +inf +/- (pi/4)
+/-inf -inf +/- (3*pi/4)
====== ====== ================
Note that +0 and -0 are distinct floating point numbers, as are +inf
and -inf.
This function differs from the original numpy.arange in the following aspects:
- Only support float16, float32 and float64.
References
----------
.. [1] ISO/IEC standard 9899:1999, "Programming language C."
Examples
--------
Consider four points in different quadrants:
>>> x = np.array([-1, +1, +1, -1])
>>> y = np.array([-1, -1, +1, +1])
>>> np.arctan2(y, x) * 180 / np.pi
array([-135., -45., 45., 135.])
Note the order of the parameters. `arctan2` is defined also when `x2` = 0
and at several other special points, obtaining values in
the range ``[-pi, pi]``:
>>> x = np.array([1, -1])
>>> y = np.array([0, 0])
>>> np.arctan2(x, y)
array([ 1.5707964, -1.5707964])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.arctan2(x1, x2, out=out)
return _api_internal.arctan2(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def hypot(x1, x2, out=None, **kwargs):
r"""
Given the "legs" of a right triangle, return its hypotenuse.
Equivalent to ``sqrt(x1**2 + x2**2)``, element-wise. If `x1` or
`x2` is scalar_like (i.e., unambiguously cast-able to a scalar type),
it is broadcast for use with each element of the other argument.
Parameters
----------
x1, x2 : ndarray
Leg of the triangle(s).
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
Returns
-------
z : ndarray
The hypotenuse of the triangle(s).
This is a scalar if both `x1` and `x2` are scalars.
Notes
-----
This function differs from the original numpy.arange in the following aspects:
- Only support float16, float32 and float64.
Examples
--------
>>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3)))
array([[ 5., 5., 5.],
[ 5., 5., 5.],
[ 5., 5., 5.]])
Example showing broadcast of scalar_like argument:
>>> np.hypot(3*np.ones((3, 3)), [4])
array([[ 5., 5., 5.],
[ 5., 5., 5.],
[ 5., 5., 5.]])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.hypot(x1, x2, out=out)
return _api_internal.hypot(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def bitwise_and(x1, x2, out=None, **kwargs):
r"""
Compute the bit-wise XOR of two arrays element-wise.
Parameters
----------
x1, x2 : ndarray or scalar
Only integer and boolean types are handled. If x1.shape != x2.shape,
they must be broadcastable to a common shape (which becomes the shape of the output).
out : ndarray, 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
-------
out : ndarray
Result.
Examples
--------
>>> np.bitwise_and(13, 17)
1
>>> np.bitwise_and(14, 13)
12
>>> np.bitwise_and(np.array([14,3], dtype='int32'), 13)
array([12, 1], dtype=int32)
>>> np.bitwise_and(np.array([11,7], dtype='int32'), np.array([4,25], dtype='int32'))
array([0, 1], dtype=int32)
>>> np.bitwise_and(np.array([2,5,255], dtype='int32'), np.array([3,14,16], dtype='int32'))
array([ 2, 4, 16], dtype=int32)
>>> np.bitwise_and(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
array([False, True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.bitwise_and(x1, x2, out=out)
return _api_internal.bitwise_and(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def bitwise_xor(x1, x2, out=None, **kwargs):
r"""
Compute the bit-wise XOR of two arrays element-wise.
Parameters
----------
x1, x2 : ndarray or scalar
Only integer and boolean types are handled. If x1.shape != x2.shape,
they must be broadcastable to a common shape (which becomes the shape of the output).
out : ndarray, 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
-------
out : ndarray
Result.
Examples
--------
>>> np.bitwise_xor(13, 17)
28
>>> np.bitwise_xor(31, 5)
26
>>> np.bitwise_xor(np.array([31,3], dtype='int32'), 5)
array([26, 6])
>>> np.bitwise_xor(np.array([31,3], dtype='int32'), np.array([5,6], dtype='int32'))
array([26, 5])
>>> np.bitwise_xor(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
array([ True, False])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.bitwise_xor(x1, x2, out=out)
return _api_internal.bitwise_xor(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def bitwise_or(x1, x2, out=None, **kwargs):
r"""
Compute the bit-wise OR of two arrays element-wise.
Parameters
----------
x1, x2 : ndarray or scalar
Only integer and boolean types are handled. If x1.shape != x2.shape,
they must be broadcastable to a common shape (which becomes the shape of the output).
out : ndarray, 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
-------
out : ndarray
Result.
Examples
--------
>>> np.bitwise_or(13, 17)
29
>>> np.bitwise_or(31, 5)
31
>>> np.bitwise_or(np.array([31,3], dtype='int32'), 5)
array([31, 7])
>>> np.bitwise_or(np.array([31,3], dtype='int32'), np.array([5,6], dtype='int32'))
array([31, 7])
>>> np.bitwise_or(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
array([ True, True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.bitwise_or(x1, x2, out=out)
return _api_internal.bitwise_or(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def ldexp(x1, x2, out=None, **kwargs):
"""
Returns x1 * 2**x2, element-wise.
The mantissas `x1` and twos exponents `x2` are used to construct
floating point numbers ``x1 * 2**x2``.
Parameters
----------
x1 : ndarray or scalar
Array of multipliers.
x2 : ndarray or scalar, int
Array of twos exponents.
out : ndarray, optional
A location into which the result is stored. If provided, it must have
a shape that the inputs broadcast to. If not, a freshly-allocated array is returned.
Returns
-------
y : ndarray or scalar
The result of ``x1 * 2**x2``.
This is a scalar if both `x1` and `x2` are scalars.
Notes
-----
Complex dtypes are not supported, they will raise a TypeError.
Different from numpy, we allow x2 to be float besides int.
`ldexp` is useful as the inverse of `frexp`, if used by itself it is
more clear to simply use the expression ``x1 * 2**x2``.
Examples
--------
>>> np.ldexp(5, np.arange(4))
array([ 5., 10., 20., 40.])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.ldexp(x1, x2, out=out)
return _api_internal.ldexp(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def logaddexp(x1, x2, out=None, **kwargs):
"""
Logarithm of the sum of exponentiations of the inputs.
Calculates log(exp(x1) + exp(x2)). This function is useful in statistics where
the calculated probabilities of events may be so small as to exceed the range of
normal floating point numbers. In such cases the logarithm of the calculate
probability is stored. This function allows adding probabilities stored
in such a fashion.
Parameters
----------
x1 : ndarray or scalar
Array of multipliers.
x2 : ndarray or scalar, int
Array of twos exponents.
out : ndarray, optional
A location into which the result is stored. If provided, it must have
a shape that the inputs broadcast to. If not, a freshly-allocated array is returned.
Returns
-------
y : ndarray or scalar
Logarithm of exp(x1) + exp(x2). This is a scalar if both x1 and x2 are scalars.
Examples
--------
>>> prob1 = np.log(1e-50)
>>> prob2 = np.log(2.5e-50)
>>> prob12 = np.logaddexp(prob1, prob2)
>>> prob12
-113.87649168120691
>>> np.exp(prob12)
3.5000000000000057e-50
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.logaddexp(x1, x2, out=out)
return _api_internal.logaddexp(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def vdot(a, b):
r"""
Return the dot product of two vectors.
Note that `vdot` handles multidimensional arrays differently than `dot`:
it does *not* perform a matrix product, but flattens input arguments
to 1-D vectors first. Consequently, it should only be used for vectors.
Parameters
----------
a : ndarray
First argument to the dot product.
b : ndarray
Second argument to the dot product.
Returns
-------
output : ndarray
Dot product of `a` and `b`.
See Also
--------
dot : Return the dot product without using the complex conjugate of the
first argument.
Examples
--------
Note that higher-dimensional arrays are flattened!
>>> a = np.array([[1, 4], [5, 6]])
>>> b = np.array([[4, 1], [2, 2]])
>>> np.vdot(a, b)
30
>>> np.vdot(b, a)
30
>>> 1*4 + 4*1 + 5*2 + 6*2
30
"""
return tensordot(a.flatten(), b.flatten(), 1)
@set_module('mxnet.ndarray.numpy')
def inner(a, b):
r"""
Inner product of two arrays.
Ordinary inner product of vectors for 1-D arrays (without complex
conjugation), in higher dimensions a sum product over the last axes.
Parameters
----------
a, b : ndarray
If `a` and `b` are nonscalar, their last dimensions must match.
Returns
-------
out : ndarray
`out.shape = a.shape[:-1] + b.shape[:-1]`
Raises
------
ValueError
If the last dimension of `a` and `b` has different size.
See Also
--------
tensordot : Sum products over arbitrary axes.
dot : Generalised matrix product, using second last dimension of `b`.
einsum : Einstein summation convention.
Notes
-----
For vectors (1-D arrays) it computes the ordinary inner-product::
np.inner(a, b) = sum(a[:]*b[:])
More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`::
np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))
or explicitly::
np.inner(a, b)[i0,...,ir-1,j0,...,js-1]
= sum(a[i0,...,ir-1,:]*b[j0,...,js-1,:])
In addition `a` or `b` may be scalars, in which case::
np.inner(a,b) = a*b
Examples
--------
Ordinary inner product for vectors:
>>> a = np.array([1,2,3])
>>> b = np.array([0,1,0])
>>> np.inner(a, b)
2
A multidimensional example:
>>> a = np.arange(24).reshape((2,3,4))
>>> b = np.arange(4)
>>> np.inner(a, b)
array([[ 14, 38, 62],
[ 86, 110, 134]])
"""
return tensordot(a, b, [-1, -1])
@set_module('mxnet.ndarray.numpy')
def outer(a, b):
r"""
Compute the outer product of two vectors.
Given two vectors, ``a = [a0, a1, ..., aM]`` and
``b = [b0, b1, ..., bN]``,
the outer product [1]_ is::
[[a0*b0 a0*b1 ... a0*bN ]
[a1*b0 .
[ ... .
[aM*b0 aM*bN ]]
Parameters
----------
a : (M,) ndarray
First input vector. Input is flattened if
not already 1-dimensional.
b : (N,) ndarray
Second input vector. Input is flattened if
not already 1-dimensional.
Returns
-------
out : (M, N) ndarray
``out[i, j] = a[i] * b[j]``
See also
--------
inner
einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.
ufunc.outer : A generalization to N dimensions and other operations.
``np.multiply.outer(a.ravel(), b.ravel())`` is the equivalent.
References
----------
.. [1] : G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd
ed., Baltimore, MD, Johns Hopkins University Press, 1996,
pg. 8.
Examples
--------
Make a (*very* coarse) grid for computing a Mandelbrot set:
>>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
>>> rl
array([[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.]])
"""
return tensordot(a.reshape_view((-1, )), b.reshape_view((-1, )), 0)
@set_module('mxnet.ndarray.numpy')
def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None): # pylint: disable=too-many-arguments
"""
Return the cross product of two (arrays of) vectors.
The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular
to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors
are defined by the last axis of `a` and `b` by default, and these axis
can have dimensions 2 or 3. Where the dimension of either `a` or `b` is
2, the third component of the input vector is assumed to be zero and the
cross product calculated accordingly. In cases where both input vectors
have dimension 2, the z-component of the cross product is returned.
Parameters
----------
a : ndarray
Components of the first vector(s).
b : ndarray
Components of the second vector(s).
axisa : int, optional
Axis of `a` that defines the vector(s). By default, the last axis.
axisb : int, optional
Axis of `b` that defines the vector(s). By default, the last axis.
axisc : int, optional
Axis of `c` containing the cross product vector(s). Ignored if
both input vectors have dimension 2, as the return is scalar.
By default, the last axis.
axis : int, optional
If defined, the axis of `a`, `b` and `c` that defines the vector(s)
and cross product(s). Overrides `axisa`, `axisb` and `axisc`.
Returns
-------
c : ndarray
Vector cross product(s).
Raises
------
ValueError
When the dimension of the vector(s) in `a` and/or `b` does not
equal 2 or 3.
Notes
-----
Supports full broadcasting of the inputs.
Examples
--------
Vector cross-product.
>>> x = np.array([1., 2., 3.])
>>> y = np.array([4., 5., 6.])
>>> np.cross(x, y)
array([-3., 6., -3.])
One vector with dimension 2.
>>> x = np.array([1., 2.])
>>> y = np.array([4., 5., 6.])
>>> np.cross(x, y)
array([12., -6., -3.])
Equivalently:
>>> x = np.array([1., 2., 0.])
>>> y = np.array([4., 5., 6.])
>>> np.cross(x, y)
array([12., -6., -3.])
Both vectors with dimension 2.
>>> x = np.array([1., 2.])
>>> y = np.array([4., 5.])
>>> np.cross(x, y)
array(-3.)
Multiple vector cross-products. Note that the direction of the cross
product vector is defined by the `right-hand rule`.
>>> x = np.array([[1., 2., 3.], [4., 5., 6.]])
>>> y = np.array([[4., 5., 6.], [1., 2., 3.]])
>>> np.cross(x, y)
array([[-3., 6., -3.],
[ 3., -6., 3.]])
The orientation of `c` can be changed using the `axisc` keyword.
>>> np.cross(x, y, axisc=0)
array([[-3., 3.],
[ 6., -6.],
[-3., 3.]])
Change the vector definition of `x` and `y` using `axisa` and `axisb`.
>>> x = np.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])
>>> y = np.array([[7., 8., 9.], [4., 5., 6.], [1., 2., 3.]])
>>> np.cross(x, y)
array([[ -6., 12., -6.],
[ 0., 0., 0.],
[ 6., -12., 6.]])
>>> np.cross(x, y, axisa=0, axisb=0)
array([[-24., 48., -24.],
[-30., 60., -30.],
[-36., 72., -36.]])
"""
if axis is not None:
axisa, axisb, axisc = (axis,) * 3
if isinstance(a, NDArray) and isinstance(b, NDArray):
return _api_internal.cross(a, b, axisa, axisb, axisc)
else:
raise TypeError("Input data should be NDarray")
@set_module('mxnet.ndarray.numpy')
def kron(a, b):
r"""
Kronecker product of two arrays.
Computes the Kronecker product, a composite array made of blocks of the
second array scaled by the first.
Parameters
----------
a, b : ndarray
Returns
-------
out : ndarray
See Also
--------
outer : The outer product
Notes
-----
The function assumes that the number of dimensions of `a` and `b`
are the same, if necessary prepending the smallest with ones.
If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`,
the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`.
The elements are products of elements from `a` and `b`, organized
explicitly by::
kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
where::
kt = it * st + jt, t = 0,...,N
In the common 2-D case (N=1), the block structure can be visualized::
[[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ],
[ ... ... ],
[ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]]
Examples
--------
>>> np.kron([1,10,100], [5,6,7])
array([ 5, 6, 7, 50, 60, 70, 500, 600, 700])
>>> np.kron([5,6,7], [1,10,100])
array([ 5, 50, 500, 6, 60, 600, 7, 70, 700])
"""
return _api_internal.kron(a, b)
@set_module('mxnet.ndarray.numpy')
def equal(x1, x2, out=None):
"""
Return (x1 == x2) element-wise.
Parameters
----------
x1, x2 : ndarrays or scalars
Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
a common shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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
-------
out : ndarray or scalar
Output array of type bool, element-wise comparison of `x1` and `x2`.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
not_equal, greater_equal, less_equal, greater, less
Examples
--------
>>> np.equal(np.ones(2, 1)), np.zeros(1, 3))
array([[False, False, False],
[False, False, False]])
>>> np.equal(1, np.ones(1))
array([ True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.equal(x1, x2, out=out)
return _api_internal.equal(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def not_equal(x1, x2, out=None):
"""
Return (x1 != x2) element-wise.
Parameters
----------
x1, x2 : ndarrays or scalars
Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
a common shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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
-------
out : ndarray or scalar
Output array of type bool, element-wise comparison of `x1` and `x2`.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
equal, greater, greater_equal, less, less_equal
Examples
--------
>>> np.not_equal(np.ones(2, 1)), np.zeros(1, 3))
array([[ True, True, True],
[ True, True, True]])
>>> np.not_equal(1, np.ones(1))
array([False])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.not_equal(x1, x2, out=out)
return _api_internal.not_equal(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def greater(x1, x2, out=None):
"""
Return the truth value of (x1 > x2) element-wise.
Parameters
----------
x1, x2 : ndarrays or scalars
Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
a common shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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
-------
out : ndarray or scalar
Output array of type bool, element-wise comparison of `x1` and `x2`.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
equal, greater, greater_equal, less, less_equal
Examples
--------
>>> np.greater(np.ones(2, 1)), np.zeros(1, 3))
array([[ True, True, True],
[ True, True, True]])
>>> np.greater(1, np.ones(1))
array([False])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.greater(x1, x2, out=out)
return _api_internal.greater(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def less(x1, x2, out=None):
"""
Return the truth value of (x1 < x2) element-wise.
Parameters
----------
x1, x2 : ndarrays or scalars
Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
a common shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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
-------
out : ndarray or scalar
Output array of type bool, element-wise comparison of `x1` and `x2`.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
equal, greater, greater_equal, less, less_equal
Examples
--------
>>> np.less(np.ones(2, 1)), np.zeros(1, 3))
array([[ True, True, True],
[ True, True, True]])
>>> np.less(1, np.ones(1))
array([False])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.less(x1, x2, out=out)
return _api_internal.less(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def greater_equal(x1, x2, out=None):
"""
Return the truth value of (x1 >= x2) element-wise.
Parameters
----------
x1, x2 : ndarrays or scalars
Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
a common shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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
-------
out : ndarray or scalar
Output array of type bool, element-wise comparison of `x1` and `x2`.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
equal, greater, greater_equal, less, less_equal
Examples
--------
>>> np.greater_equal(np.ones(2, 1)), np.zeros(1, 3))
array([[ True, True, True],
[ True, True, True]])
>>> np.greater_equal(1, np.ones(1))
array([True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.greater_equal(x1, x2, out=out)
return _api_internal.greater_equal(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def less_equal(x1, x2, out=None):
"""
Return the truth value of (x1 <= x2) element-wise.
Parameters
----------
x1, x2 : ndarrays or scalars
Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
a common shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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
-------
out : ndarray or scalar
Output array of type bool, element-wise comparison of `x1` and `x2`.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
equal, greater, greater_equal, less, less_equal
Examples
--------
>>> np.less_equal(np.ones(2, 1)), np.zeros(1, 3))
array([[False, False, False],
[False, False, False]])
>>> np.less_equal(1, np.ones(1))
array([True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.less_equal(x1, x2, out=out)
return _api_internal.less_equal(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def roll(a, shift, axis=None):
"""
Roll array elements along a given axis.
Elements that roll beyond the last position are re-introduced at
the first.
Parameters
----------
a : ndarray
Input array.
shift : int or tuple of ints
The number of places by which elements are shifted. If a tuple,
then `axis` must be a tuple of the same size, and each of the
given axes is shifted by the corresponding number. If an int
while `axis` is a tuple of ints, then the same value is used for
all given axes.
axis : int or tuple of ints, optional
Axis or axes along which elements are shifted. By default, the
array is flattened before shifting, after which the original
shape is restored.
Returns
-------
res : ndarray
Output array, with the same shape as `a`.
Notes
-----
Supports rolling over multiple dimensions simultaneously.
Examples
--------
>>> x = np.arange(10)
>>> np.roll(x, 2)
array([8., 9., 0., 1., 2., 3., 4., 5., 6., 7.])
>>> np.roll(x, -2)
array([2., 3., 4., 5., 6., 7., 8., 9., 0., 1.])
>>> x2 = np.reshape(x, (2,5))
>>> x2
array([[0., 1., 2., 3., 4.],
[5., 6., 7., 8., 9.]])
>>> np.roll(x2, 1)
array([[9., 0., 1., 2., 3.],
[4., 5., 6., 7., 8.]])
>>> np.roll(x2, -1)
array([[1., 2., 3., 4., 5.],
[6., 7., 8., 9., 0.]])
>>> np.roll(x2, 1, axis=0)
array([[5., 6., 7., 8., 9.],
[0., 1., 2., 3., 4.]])
>>> np.roll(x2, -1, axis=0)
array([[5., 6., 7., 8., 9.],
[0., 1., 2., 3., 4.]])
>>> np.roll(x2, 1, axis=1)
array([[4., 0., 1., 2., 3.],
[9., 5., 6., 7., 8.]])
>>> np.roll(x2, -1, axis=1)
array([[1., 2., 3., 4., 0.],
[6., 7., 8., 9., 5.]])
"""
return _api_internal.roll(a, shift, axis)
@wrap_np_binary_func
def logical_and(x1, x2, out=None):
r"""
Compute the truth value of x1 AND x2 element-wise.
Parameters
----------
x1, x2 : array_like
Logical AND is applied to the elements of `x1` and `x2`.
If ``x1.shape != x2.shape``, they must be broadcastable to a common
shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
Returns
-------
y : ndarray or bool
Boolean result of the logical AND operation applied to the elements
of `x1` and `x2`; the shape is determined by broadcasting.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
logical_or, logical_not, logical_xor, bitwise_or
Examples
--------
>>> np.logical_and(True, False)
False
>>> np.logical_and(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
array([False, True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.logical_and(x1, x2, out=out)
return _api_internal.logical_and(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def logical_or(x1, x2, out=None):
"""
Compute the truth value of x1 OR x2 element-wise.
Parameters
----------
x1, x2 : array_like
Logical OR is applied to the elements of `x1` and `x2`.
If ``x1.shape != x2.shape``, they must be broadcastable to a common
shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
Returns
-------
y : ndarray or bool
Boolean result of the logical OR operation applied to the elements
of `x1` and `x2`; the shape is determined by broadcasting.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
logical_and, logical_not, logical_xor, bitwise_or
Examples
--------
>>> np.logical_or(True, False)
True
>>> np.logical_or(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
array([True, True])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.logical_or(x1, x2, out=out)
return _api_internal.logical_or(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
@wrap_np_binary_func
def logical_xor(x1, x2, out=None):
"""
Compute the truth value of x1 XOR x2 element-wise.
Parameters
----------
x1, x2 : array_like
Logical XOR is applied to the elements of `x1` and `x2`.
If ``x1.shape != x2.shape``, they must be broadcastable to a common
shape (which becomes the shape of the output).
out : ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
Returns
-------
y : ndarray or bool
Boolean result of the logical XOR operation applied to the elements
of `x1` and `x2`; the shape is determined by broadcasting.
This is a scalar if both `x1` and `x2` are scalars.
See Also
--------
logical_and, logical_not, logical_or, bitwise_or
Examples
--------
>>> np.logical_xor(True, False)
True
>>> np.logical_xor(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
array([ True, False])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.logical_xor(x1, x2, out=out)
return _api_internal.logical_xor(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def rot90(m, k=1, axes=(0, 1)):
"""
Rotate an array by 90 degrees in the plane specified by axes.
Rotation direction is from the first towards the second axis.
Parameters
----------
m : ndarray
Array of two or more dimensions.
k : integer
Number of times the array is rotated by 90 degrees.
axes: (2,) array_like
The array is rotated in the plane defined by the axes.
Axes must be different.
Returns
-------
y : ndarray
A rotated view of `m`.
-----
rot90(m, k=1, axes=(1,0)) is the reverse of rot90(m, k=1, axes=(0,1))
rot90(m, k=1, axes=(1,0)) is equivalent to rot90(m, k=-1, axes=(0,1))
Examples
--------
>>> m = np.array([[1,2],[3,4]], 'int')
>>> m
array([[1, 2],
[3, 4]], dtype=int64)
>>> np.rot90(m)
array([[2, 4],
[1, 3]], dtype=int64)
>>> np.rot90(m, 2)
array([[4, 3],
[2, 1]], dtype=int64)
>>> m = np.arange(8).reshape((2,2,2))
>>> np.rot90(m, 1, (1,2))
array([[[1., 3.],
[0., 2.]],
[[5., 7.],
[4., 6.]]])
"""
return _api_internal.rot90(m, k, axes)
@set_module('mxnet.ndarray.numpy')
def einsum(*operands, **kwargs):
r"""
einsum(subscripts, *operands, out=None, optimize=False)
Evaluates the Einstein summation convention on the operands.
Using the Einstein summation convention, many common multi-dimensional,
linear algebraic array operations can be represented in a simple fashion.
In *implicit* mode `einsum` computes these values.
In *explicit* mode, `einsum` provides further flexibility to compute
other array operations that might not be considered classical Einstein
summation operations, by disabling, or forcing summation over specified
subscript labels.
See the notes and examples for clarification.
Parameters
----------
subscripts : str
Specifies the subscripts for summation as comma separated list of
subscript labels. An implicit (classical Einstein summation)
calculation is performed unless the explicit indicator '->' is
included as well as subscript labels of the precise output form.
operands : list of ndarray
These are the arrays for the operation.
out : ndarray, optional
If provided, the calculation is done into this array.
optimize : {False, True}, optional
Controls if intermediate optimization should occur. No optimization
will occur if False. Defaults to False.
Returns
-------
output : ndarray
The calculation based on the Einstein summation convention.
Notes
-----
The Einstein summation convention can be used to compute
many multi-dimensional, linear algebraic array operations. `einsum`
provides a succinct way of representing these.
A non-exhaustive list of these operations,
which can be computed by `einsum`, is shown below along with examples:
* Trace of an array, :py:func:`np.trace`.
* Return a diagonal, :py:func:`np.diag`.
* Array axis summations, :py:func:`np.sum`.
* Transpositions and permutations, :py:func:`np.transpose`.
* Matrix multiplication and dot product, :py:func:`np.matmul` :py:func:`np.dot`.
* Vector inner and outer products, :py:func:`np.inner` :py:func:`np.outer`.
* Broadcasting, element-wise and scalar multiplication, :py:func:`np.multiply`.
* Tensor contractions, :py:func:`np.tensordot`.
The subscripts string is a comma-separated list of subscript labels,
where each label refers to a dimension of the corresponding operand.
Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
is equivalent to :py:func:`np.inner(a,b) <np.inner>`. If a label
appears only once, it is not summed, so ``np.einsum('i', a)`` produces a
view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)``
describes traditional matrix multiplication and is equivalent to
:py:func:`np.matmul(a,b) <np.matmul>`. Repeated subscript labels in one
operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent
to :py:func:`np.trace(a) <np.trace>`.
In *implicit mode*, the chosen subscripts are important
since the axes of the output are reordered alphabetically. This
means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
``np.einsum('ji', a)`` takes its transpose. Additionally,
``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
``np.einsum('ij,jh', a, b)`` returns the transpose of the
multiplication since subscript 'h' precedes subscript 'i'.
In *explicit mode* the output can be directly controlled by
specifying output subscript labels. This requires the
identifier '->' as well as the list of output subscript labels.
This feature increases the flexibility of the function since
summing can be disabled or forced when required. The call
``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) <np.sum>`,
and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) <np.diag>`.
The difference is that `einsum` does not allow broadcasting by default.
Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
order of the output subscript labels and therefore returns matrix
multiplication, unlike the example above in implicit mode.
To enable and control broadcasting, use an ellipsis. Default
NumPy-style broadcasting is done by adding an ellipsis
to the left of each term, like ``np.einsum('...ii->...i', a)``.
To take the trace along the first and last axes,
you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
product with the left-most indices instead of rightmost, one can do
``np.einsum('ij...,jk...->ik...', a, b)``.
When there is only one operand, no axes are summed, and no output
parameter is provided, a view into the operand is returned instead
of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)``
produces a view.
The ``optimize`` argument which will optimize the contraction order
of an einsum expression. For a contraction with three or more operands this
can greatly increase the computational efficiency at the cost of a larger
memory footprint during computation.
Typically a 'greedy' algorithm is applied which empirical tests have shown
returns the optimal path in the majority of cases. 'optimal' is not supported
for now.
This function differs from the original `numpy.einsum
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html>`_ in
the following way(s):
- Does not support 'optimal' strategy
- Does not support the alternative subscript like
`einsum(op0, sublist0, op1, sublist1, ..., [sublistout])`
- Does not produce view in any cases
Examples
--------
>>> a = np.arange(25).reshape(5,5)
>>> b = np.arange(5)
>>> c = np.arange(6).reshape(2,3)
Trace of a matrix:
>>> np.einsum('ii', a)
array(60.)
Extract the diagonal (requires explicit form):
>>> np.einsum('ii->i', a)
array([ 0., 6., 12., 18., 24.])
Sum over an axis (requires explicit form):
>>> np.einsum('ij->i', a)
array([ 10., 35., 60., 85., 110.])
>>> np.sum(a, axis=1)
array([ 10., 35., 60., 85., 110.])
For higher dimensional arrays summing a single axis can be done with ellipsis:
>>> np.einsum('...j->...', a)
array([ 10., 35., 60., 85., 110.])
Compute a matrix transpose, or reorder any number of axes:
>>> np.einsum('ji', c)
array([[0., 3.],
[1., 4.],
[2., 5.]])
>>> np.einsum('ij->ji', c)
array([[0., 3.],
[1., 4.],
[2., 5.]])
>>> np.transpose(c)
array([[0., 3.],
[1., 4.],
[2., 5.]])
Vector inner products:
>>> np.einsum('i,i', b, b)
array(30.)
Matrix vector multiplication:
>>> np.einsum('ij,j', a, b)
array([ 30., 80., 130., 180., 230.])
>>> np.dot(a, b)
array([ 30., 80., 130., 180., 230.])
>>> np.einsum('...j,j', a, b)
array([ 30., 80., 130., 180., 230.])
Broadcasting and scalar multiplication:
>>> np.einsum('..., ...', np.array(3), c)
array([[ 0., 3., 6.],
[ 9., 12., 15.]])
>>> np.einsum(',ij', np.array(3), c)
array([[ 0., 3., 6.],
[ 9., 12., 15.]])
>>> np.multiply(3, c)
array([[ 0., 3., 6.],
[ 9., 12., 15.]])
Vector outer product:
>>> np.einsum('i,j', np.arange(2)+1, b)
array([[0., 1., 2., 3., 4.],
[0., 2., 4., 6., 8.]])
Tensor contraction:
>>> a = np.arange(60.).reshape(3,4,5)
>>> b = np.arange(24.).reshape(4,3,2)
>>> np.einsum('ijk,jil->kl', a, b)
array([[4400., 4730.],
[4532., 4874.],
[4664., 5018.],
[4796., 5162.],
[4928., 5306.]])
Example of ellipsis use:
>>> a = np.arange(6).reshape((3,2))
>>> b = np.arange(12).reshape((4,3))
>>> np.einsum('ki,jk->ij', a, b)
array([[10., 28., 46., 64.],
[13., 40., 67., 94.]])
>>> np.einsum('ki,...k->i...', a, b)
array([[10., 28., 46., 64.],
[13., 40., 67., 94.]])
>>> np.einsum('k...,jk', a, b)
array([[10., 28., 46., 64.],
[13., 40., 67., 94.]])
Chained array operations. For more complicated contractions, speed ups
might be achieved by repeatedly computing a 'greedy' path. Performance
improvements can be particularly significant with larger arrays:
>>> a = np.ones(64).reshape(2,4,8)
# Basic `einsum`: ~42.22ms (benchmarked on 3.4GHz Intel Xeon.)
>>> for iteration in range(500):
... np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)
# Greedy `einsum` (faster optimal path approximation): ~0.117ms
>>> for iteration in range(500):
... np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=True)
"""
# Grab non-einsum kwargs; do not optimize by default.
optimize_arg = kwargs.pop('optimize', False)
out = kwargs.pop('out', None)
subscripts = operands[0]
operands = operands[1:]
return _api_internal.einsum(*operands, subscripts, out, int(optimize_arg))
@set_module('mxnet.ndarray.numpy')
def nonzero(a):
"""
Return the indices of the elements that are non-zero.
Returns a tuple of arrays, one for each dimension of `a`,
containing the indices of the non-zero elements in that
dimension. The values in `a` are always returned in
row-major, C-style order.
To group the indices by element, rather than dimension, use `argwhere`,
which returns a row for each non-zero element.
Parameters
----------
a : ndarray
Input array.
Returns
-------
tuple_of_arrays : tuple
Indices of elements that are non-zero.
See Also
--------
ndarray.nonzero :
Equivalent ndarray method.
Notes
-----
While the nonzero values can be obtained with ``a[nonzero(a)]``, it is
recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which
will correctly handle 0-d arrays.
Examples
--------
>>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
>>> x
array([[3, 0, 0],
[0, 4, 0],
[5, 6, 0]], dtype=int32)
>>> np.nonzero(x)
(array([0, 1, 2, 2], dtype=int64), array([0, 1, 0, 1], dtype=int64))
>>> x[np.nonzero(x)]
array([3, 4, 5, 6])
>>> np.transpose(np.stack(np.nonzero(x)))
array([[0, 0],
[1, 1],
[2, 0],
[2, 1]], dtype=int64)
A common use for ``nonzero`` is to find the indices of an array, where
a condition is True. Given an array `a`, the condition `a` > 3 is a
boolean array and since False is interpreted as 0, np.nonzero(a > 3)
yields the indices of the `a` where the condition is true.
>>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.int32)
>>> a > 3
array([[False, False, False],
[ True, True, True],
[ True, True, True]])
>>> np.nonzero(a > 3)
(array([1, 1, 1, 2, 2, 2], dtype=int64), array([0, 1, 2, 0, 1, 2], dtype=int64))
Using this result to index `a` is equivalent to using the mask directly:
>>> a[np.nonzero(a > 3)]
array([4, 5, 6, 7, 8, 9], dtype=int32)
>>> a[a > 3]
array([4, 5, 6, 7, 8, 9], dtype=int32)
``nonzero`` can also be called as a method of the array.
>>> (a > 3).nonzero()
(array([1, 1, 1, 2, 2, 2], dtype=int64), array([0, 1, 2, 0, 1, 2], dtype=int64))
"""
out = _api_internal.nonzero(a).transpose()
return tuple([out[i] for i in range(len(out))])
@set_module('mxnet.ndarray.numpy')
def percentile(a, q, axis=None, out=None, overwrite_input=None, interpolation='linear', keepdims=False): # pylint: disable=too-many-arguments
"""
Compute the q-th percentile of the data along the specified axis.
Returns the q-th percentile(s) of the array elements.
Parameters
----------
a : ndarray
Input array
q : ndarray
Percentile or sequence of percentiles to compute.
axis : {int, tuple of int, None}, optional
Axis or axes along which the percentiles are computed. The default is to
compute the percentile(s) along a flattened version of the array.
out : ndarray, optional
Alternative output array in which to place the result. It must have the same
shape and buffer length as the expected output, but the type (of the output)
will be cast if necessary.
overwrite_input : bool, optional (Not supported yet)
If True, then allow the input array a to be modified by intermediate calculations,
to save memory. In this case, the contents of the input a after this function
completes is undefined.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to use when the
desired percentile lies between two data points i < j:
'linear': i + (j - i) * fraction, where fraction is the fractional part of the
index surrounded by i and j.
'lower': i.
'higher': j.
'nearest': i or j, whichever is nearest.
'midpoint': (i + j) / 2.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as
dimensions with size one. With this option, the result will broadcast
correctly against the original array a.
Returns
-------
percentile : scalar or ndarray
Output array.
Examples
--------
>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> a
array([[10, 7, 4],
[ 3, 2, 1]])
>>> np.percentile(a, np.array(50))
array(3.5)
>>> np.percentile(a, np.array(50), axis=0)
array([6.5, 4.5, 2.5])
>>> np.percentile(a, np.array(50), axis=1)
array([7., 2.])
>>> np.percentile(a, np.array(50), axis=1, keepdims=True)
array([[7.],
[2.]])
>>> m = np.percentile(a, np.array(50), axis=0)
>>> out = np.zeros_like(m)
>>> np.percentile(a, np.array(50), axis=0, out=out)
array([6.5, 4.5, 2.5])
>>> m
array([6.5, 4.5, 2.5])
"""
if overwrite_input is not None:
raise NotImplementedError('overwrite_input is not supported yet')
return _api_internal.percentile(a, q, axis, interpolation, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def median(a, axis=None, out=None, overwrite_input=None, keepdims=False):
r"""
Compute the median along the specified axis.
Returns the median of the array elements.
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
axis : {int, sequence of int, None}, optional
Axis or axes along which the medians are computed. The default
is to compute the median along a flattened version of the array.
A sequence of axes is supported since version 1.9.0.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
median : ndarray
A new array holding the result. If the input contains integers
or floats smaller than ``float32``, then the output data-type is
``np.float32``. Otherwise, the data-type of the output is the
same as that of the input. If `out` is specified, that array is
returned instead.
See Also
--------
mean, percentile
Examples
--------
>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> a
array([[10, 7, 4],
[ 3, 2, 1]])
>>> np.median(a)
3.5
>>> np.median(a, axis=0)
array([6.5, 4.5, 2.5])
>>> np.median(a, axis=1)
array([7., 2.])
"""
return quantile(a=a, q=0.5, axis=axis, out=out, overwrite_input=overwrite_input,
interpolation='midpoint', keepdims=keepdims)
@set_module('mxnet.ndarray.numpy')
def quantile(a, q, axis=None, out=None, overwrite_input=None, interpolation='linear', keepdims=False): # pylint: disable=too-many-arguments
"""
Compute the q-th quantile of the data along the specified axis.
New in version 1.15.0.
Parameters
----------
a : ndarray
Input array or object that can be converted to an array.
q : ndarray
Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.
axis : {int, tuple of int, None}, optional
Axis or axes along which the quantiles are computed.
The default is to compute the quantile(s) along a flattened version of the array.
out : ndarray, optional
Alternative output array in which to place the result.
It must have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to use
when the desired quantile lies between two data points i < j:
linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.
lower: i.
higher: j.
nearest: i or j, whichever is nearest.
midpoint: (i + j) / 2.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one.
With this option, the result will broadcast correctly against the original array a.
Returns
-------
quantile : ndarray
If q is a single quantile and axis=None, then the result is a scalar.
If multiple quantiles are given, first axis of the result corresponds to the quantiles.
The other axes are the axes that remain after the reduction of a.
If out is specified, that array is returned instead.
See also
--------
mean
Notes
-----
Given a vector V of length N, the q-th quantile of V is the value q of the way from the minimum
to the maximum in a sorted copy of V. The values and distances of the two nearest neighbors
as well as the interpolation parameter will determine the quantile if the normalized ranking
does not match the location of q exactly. This function is the same as the median if q=0.5,
the same as the minimum if q=0.0 and the same as the maximum if q=1.0.
This function differs from the original `numpy.quantile
<https://numpy.org/devdocs/reference/generated/numpy.quantile.html>`_ in
the following aspects:
- q must be ndarray type even if it is a scalar
- do not support overwrite_input
Examples
--------
>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> a
array([[10., 7., 4.],
[3., 2., 1.]])
>>> q = np.array(0.5)
>>> q
array(0.5)
>>> np.quantile(a, q)
array(3.5)
>>> np.quantile(a, q, axis=0)
array([6.5, 4.5, 2.5])
>>> np.quantile(a, q, axis=1)
array([7., 2.])
>>> np.quantile(a, q, axis=1, keepdims=True)
array([[7.],
[2.]])
>>> m = np.quantile(a, q, axis=0)
>>> out = np.zeros_like(m)
>>> np.quantile(a, q, axis=0, out=out)
array([6.5, 4.5, 2.5])
>>> out
array([6.5, 4.5, 2.5])
"""
if overwrite_input is not None:
raise NotImplementedError('overwrite_input is not supported yet')
return _api_internal.percentile(a, q * 100, axis, interpolation, keepdims, out)
@set_module('mxnet.ndarray.numpy')
def shares_memory(a, b, max_work=None):
"""
Determine if two arrays share memory
Parameters
----------
a, b : ndarray
Input arrays
Returns
-------
out : bool
See Also
--------
may_share_memory
Examples
--------
>>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
False
This function differs from the original `numpy.shares_memory
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.shares_memory.html>`_ in
the following way(s):
- Does not support `max_work`, it is a dummy argument
- Actually it is same as `may_share_memory` in MXNet np
"""
return _api_internal.share_memory(a, b).item()
@set_module('mxnet.ndarray.numpy')
def may_share_memory(a, b, max_work=None):
"""
Determine if two arrays might share memory
A return of True does not necessarily mean that the two arrays
share any element. It just means that they *might*.
Only the memory bounds of a and b are checked by default.
Parameters
----------
a, b : ndarray
Input arrays
Returns
-------
out : bool
See Also
--------
shares_memory
Examples
--------
>>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
False
>>> x = np.zeros([3, 4])
>>> np.may_share_memory(x[:,0], x[:,1])
True
This function differs from the original `numpy.may_share_memory
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.may_share_memory.html>`_ in
the following way(s):
- Does not support `max_work`, it is a dummy argument
- Actually it is same as `shares_memory` in MXNet np
"""
return _api_internal.share_memory(a, b).item()
@set_module('mxnet.ndarray.numpy')
def interp(x, xp, fp, left=None, right=None, period=None): # pylint: disable=too-many-arguments
"""
One-dimensional linear interpolation.
Returns the one-dimensional piecewise linear interpolant to a function
with given values at discrete data-points.
Parameters
----------
x : ndarray
The x-coordinates of the interpolated values.
xp : 1-D array of floats
The x-coordinates of the data points, must be increasing if argument
`period` is not specified. Otherwise, `xp` is internally sorted after
normalizing the periodic boundaries with ``xp = xp % period``.
fp : 1-D array of floats
The y-coordinates of the data points, same length as `xp`.
left : optional float corresponding to fp
Value to return for `x < xp[0]`, default is `fp[0]`.
right : optional float corresponding to fp
Value to return for `x > xp[-1]`, default is `fp[-1]`.
period : None or float, optional
A period for the x-coordinates. This parameter allows the proper
interpolation of angular x-coordinates. Parameters `left` and `right`
are ignored if `period` is specified.
.. versionadded:: 1.10.0
Returns
-------
y : float (corresponding to fp) or ndarray
The interpolated values, same shape as `x`.
Raises
------
ValueError
If `xp` and `fp` have different length
If `xp` or `fp` are not 1-D sequences
If `period == 0`
Notes
-----
Does not check that the x-coordinate sequence `xp` is increasing.
If `xp` is not increasing, the results are nonsense.
A simple check for increasing is::
np.all(np.diff(xp) > 0)
Examples
--------
>>> xp = [1, 2, 3]
>>> fp = [3, 2, 0]
>>> np.interp(2.5, xp, fp)
1.0
>>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)
array([ 3. , 3. , 2.5 , 0.56, 0. ])
>>> UNDEF = -99.0
>>> np.interp(3.14, xp, fp, right=UNDEF)
-99.0
Plot an interpolant to the sine function:
>>> x = np.linspace(0, 2*np.pi, 10)
>>> y = np.sin(x)
>>> xvals = np.linspace(0, 2*np.pi, 50)
>>> yinterp = np.interp(xvals, x, y)
>>> import matplotlib.pyplot as plt
>>> plt.plot(x, y, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.plot(xvals, yinterp, '-x')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.show()
Interpolation with periodic x-coordinates:
>>> x = [-180, -170, -185, 185, -10, -5, 0, 365]
>>> xp = [190, -190, 350, -350]
>>> fp = [5, 10, 3, 4]
>>> np.interp(x, xp, fp, period=360)
array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75])
"""
if not isinstance(x, numeric_types):
x = x.astype(float)
return _api_internal.interp(xp.astype(float), fp.astype(float), x, left,
right, period)
@set_module('mxnet.ndarray.numpy')
def diff(a, n=1, axis=-1, prepend=None, append=None): # pylint: disable=redefined-outer-name
r"""
Calculate the n-th discrete difference along the given axis.
Parameters
----------
a : ndarray
Input array
n : int, optional
The number of times values are differenced. If zero, the input is returned as-is.
axis : int, optional
The axis along which the difference is taken, default is the last axis.
prepend, append : ndarray, optional
Not supported yet
Returns
-------
diff : ndarray
The n-th differences.
The shape of the output is the same as a except along axis where the dimension is smaller by n.
The type of the output is the same as the type of the difference between any two elements of a.
Examples
--------
>>> x = np.array([1, 2, 4, 7, 0])
>>> np.diff(x)
array([ 1, 2, 3, -7])
>>> np.diff(x, n=2)
array([ 1, 1, -10])
>>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])
>>> np.diff(x)
array([[2, 3, 4],
[5, 1, 2]])
>>> np.diff(x, axis=0)
array([[-1, 2, 0, -2]])
Notes
-----
Optional inputs `prepend` and `append` are not supported yet
"""
if (prepend or append):
raise NotImplementedError('prepend and append options are not supported yet')
return _api_internal.diff(a, n, axis)
@set_module('mxnet.ndarray.numpy')
def ediff1d(ary, to_end=None, to_begin=None):
"""
The differences between consecutive elements of an array.
Parameters
----------
ary : ndarray
If necessary, will be flattened before the differences are taken.
to_end : ndarray or scalar, optional
Number(s) to append at the end of the returned differences.
to_begin : ndarray or scalar, optional
Number(s) to prepend at the beginning of the returned differences.
Returns
-------
ediff1d : ndarray
The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.
Examples
--------
>>> x = np.array([1, 2, 4, 7, 0])
>>> np.ediff1d(x)
array([ 1., 2., 3., -7.])
>>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
rray([-99., 1., 2., 3., -7., 88., 99.])
The returned array is always 1D.
>>> y = np.array([[1, 2, 4], [1, 6, 24]])
>>> np.ediff1d(y)
array([ 1., 2., -3., 5., 18.])
>>> np.ediff1d(x, to_begin=y)
array([ 1., 2., 4., 1., 6., 24., 1., 2., 3., -7.])
"""
return _api_internal.ediff1d(ary, to_end, to_begin)
@set_module('mxnet.ndarray.numpy')
def resize(a, new_shape):
"""
Return a new array with the specified shape.
If the new array is larger than the original array, then the new
array is filled with repeated copies of `a`. Note that this behavior
is different from a.resize(new_shape) which fills with zeros instead
of repeated copies of `a`.
Parameters
----------
a : ndarray
Array to be resized.
new_shape : int or tuple of int
Shape of resized array.
Returns
-------
reshaped_array : ndarray
The new array is formed from the data in the old array, repeated
if necessary to fill out the required number of elements. The
data are repeated in the order that they are stored in memory.
See Also
--------
ndarray.resize : resize an array in-place.
Notes
-----
Warning: This functionality does **not** consider axes separately,
i.e. it does not apply interpolation/extrapolation.
It fills the return array with the required number of elements, taken
from `a` as they are laid out in memory, disregarding strides and axes.
(This is in case the new shape is smaller. For larger, see above.)
This functionality is therefore not suitable to resize images,
or data where each axis represents a separate and distinct entity.
Examples
--------
>>> a = np.array([[0, 1], [2, 3]])
>>> np.resize(a, (2, 3))
array([[0., 1., 2.],
[3., 0., 1.]])
>>> np.resize(a, (1, 4))
array([[0., 1., 2., 3.]])
>>> np.resize(a,(2, 4))
array([[0., 1., 2., 3.],
[0., 1., 2., 3.]])
"""
return _npi.resize_fallback(a, new_shape=new_shape)
@set_module('mxnet.ndarray.numpy')
def fill_diagonal(a, val, wrap=False):
"""
Fill the main diagonal of the given array of any dimensionality.
For an array `a` with ``a.ndim >= 2``, the diagonal is the list of
locations with indices ``a[i, ..., i]`` all identical. This function
modifies the input array in-place, it does not return a value.
Parameters
----------
a : array, at least 2-D.
Array whose diagonal is to be filled, it gets modified in-place.
val : scalar
Value to be written on the diagonal, its type must be compatible with
that of the array a.
wrap : bool
For tall matrices in NumPy version up to 1.6.2, the
diagonal "wrapped" after N columns. You can have this behavior
with this option. This affects only tall matrices.
Examples
--------
>>> a = np.zeros((3, 3), int)
>>> np.fill_diagonal(a, 5)
>>> a
array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5]])
The same function can operate on a 4-D array:
>>> a = np.zeros((3, 3, 3, 3), int)
>>> np.fill_diagonal(a, 4)
We only show a few blocks for clarity:
>>> a[0, 0]
array([[4, 0, 0],
[0, 0, 0],
[0, 0, 0]])
>>> a[1, 1]
array([[0, 0, 0],
[0, 4, 0],
[0, 0, 0]])
>>> a[2, 2]
array([[0, 0, 0],
[0, 0, 0],
[0, 0, 4]])
The wrap option affects only tall matrices:
>>> # tall matrices no wrap
>>> a = np.zeros((5, 3), int)
>>> np.fill_diagonal(a, 4)
>>> a
array([[4, 0, 0],
[0, 4, 0],
[0, 0, 4],
[0, 0, 0],
[0, 0, 0]])
>>> # tall matrices wrap
>>> a = np.zeros((5, 3), int)
>>> np.fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0],
[0, 4, 0],
[0, 0, 4],
[0, 0, 0],
[4, 0, 0]])
>>> # wide matrices
>>> a = np.zeros((3, 5), int)
>>> np.fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0, 0, 0],
[0, 4, 0, 0, 0],
[0, 0, 4, 0, 0]])
The anti-diagonal can be filled by reversing the order of elements
using either `numpy.flipud` or `numpy.fliplr`.
>>> a = np.zeros((3, 3), int);
>>> np.fill_diagonal(np.fliplr(a), [1,2,3]) # Horizontal flip
>>> a
array([[0, 0, 1],
[0, 2, 0],
[3, 0, 0]])
>>> np.fill_diagonal(np.flipud(a), [1,2,3]) # Vertical flip
>>> a
array([[0, 0, 3],
[0, 2, 0],
[1, 0, 0]])
Note that the order in which the diagonal is filled varies depending
on the flip function.
"""
if isinstance(val, list):
val = [float(v) for v in val]
else:
val = [float(val)]
_api_internal.fill_diagonal(a, val, wrap, a)
@set_module('mxnet.ndarray.numpy')
def squeeze(x, axis=None):
"""
Remove single-dimensional entries from the shape of an array.
Parameters
----------
a : array_like
Input data.
axis : None or int or tuple of ints, optional
.. versionadded:: 1.7.0
Selects a subset of the single-dimensional entries in the
shape. If an axis is selected with shape entry greater than
one, an error is raised.
Returns
-------
squeezed : ndarray
The input array, but with all or a subset of the
dimensions of length 1 removed. This is always `a` itself
or a view into `a`.
Raises
------
ValueError
If `axis` is not `None`, and an axis being squeezed is not of length 1
See Also
--------
expand_dims : The inverse operation, adding singleton dimensions
reshape : Insert, remove, and combine dimensions, and resize existing ones
Examples
--------
>>> x = np.array([[[0], [1], [2]]])
>>> x.shape
(1, 3, 1)
>>> np.squeeze(x).shape
(3,)
>>> np.squeeze(x, axis=0).shape
(3, 1)
>>> np.squeeze(x, axis=1).shape
Traceback (most recent call last):
...
ValueError: cannot select an axis to squeeze out which has size not equal to one
>>> np.squeeze(x, axis=2).shape
(1, 3)
"""
return _api_internal.squeeze(x, axis)
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def nan_to_num(x, copy=True, nan=0.0, posinf=None, neginf=None, **kwargs):
"""
Replace NaN with zero and infinity with large finite numbers (default
behaviour) or with the numbers defined by the user using the `nan`,
`posinf` and/or `neginf` keywords.
If `x` is inexact, NaN is replaced by zero or by the user defined value in
`nan` keyword, infinity is replaced by the largest finite floating point
values representable by ``x.dtype`` or by the user defined value in
`posinf` keyword and -infinity is replaced by the most negative finite
floating point values representable by ``x.dtype`` or by the user defined
value in `neginf` keyword.
For complex dtypes, the above is applied to each of the real and
imaginary components of `x` separately.
If `x` is not inexact, then no replacements are made.
Parameters
----------
x : ndarray
Input data.
copy : bool, optional
Whether to create a copy of `x` (True) or to replace values
in-place (False). The in-place operation only occurs if
casting to an array does not require a copy.
Default is True.
nan : int, float, optional
Value to be used to fill NaN values. If no value is passed
then NaN values will be replaced with 0.0.
posinf : int, float, optional
Value to be used to fill positive infinity values. If no value is
passed then positive infinity values will be replaced with a very
large number.
neginf : int, float, optional
Value to be used to fill negative infinity values. If no value is
passed then negative infinity values will be replaced with a very
small (or negative) number.
.. versionadded:: 1.13
Returns
-------
out : ndarray
`x`, with the non-finite values replaced. If `copy` is False, this may
be `x` itself.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
Examples
--------
>>> np.nan_to_num(np.inf)
1.7976931348623157e+308
>>> np.nan_to_num(-np.inf)
-1.7976931348623157e+308
>>> np.nan_to_num(np.nan)
0.0
>>> x = np.array([np.inf, -np.inf, np.nan, -128, 128])
>>> np.nan_to_num(x)
array([ 3.4028235e+38, -3.4028235e+38, 0.0000000e+00, -1.2800000e+02,
1.2800000e+02])
>>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333)
array([ 3.3333332e+07, 3.3333332e+07, -9.9990000e+03, -1.2800000e+02,
1.2800000e+02])
>>> y = np.array([[-1, 0, 1],[9999,234,-14222]],dtype="float64")/0
array([[-inf, nan, inf],
[ inf, inf, -inf]], dtype=float64)
>>> np.nan_to_num(y)
array([[-1.79769313e+308, 0.00000000e+000, 1.79769313e+308],
[ 1.79769313e+308, 1.79769313e+308, -1.79769313e+308]], dtype=float64)
>>> np.nan_to_num(y, nan=111111, posinf=222222)
array([[-1.79769313e+308, 1.11111000e+005, 2.22222000e+005],
[ 2.22222000e+005, 2.22222000e+005, -1.79769313e+308]], dtype=float64)
>>> y
array([[-inf, nan, inf],
[ inf, inf, -inf]], dtype=float64)
>>> np.nan_to_num(y, copy=False, nan=111111, posinf=222222)
array([[-1.79769313e+308, 1.11111000e+005, 2.22222000e+005],
[ 2.22222000e+005, 2.22222000e+005, -1.79769313e+308]], dtype=float64)
>>> y
array([[-1.79769313e+308, 1.11111000e+005, 2.22222000e+005],
[ 2.22222000e+005, 2.22222000e+005, -1.79769313e+308]], dtype=float64)
"""
if isinstance(x, numeric_types):
return _np.nan_to_num(x, copy, nan, posinf, neginf)
elif isinstance(x, NDArray):
if x.dtype in ['int8', 'uint8', 'int32', 'int64']:
return x
if not copy:
return _api_internal.nan_to_num(x, copy, nan, posinf, neginf, x)
return _api_internal.nan_to_num(x, copy, nan, posinf, neginf, None)
else:
raise TypeError('type {} not supported'.format(str(type(x))))
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def isnan(x, out=None, **kwargs):
"""
Test element-wise for NaN and return result as a boolean array.
Parameters
----------
x : ndarray
Input array.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray or bool
True where x is NaN, false otherwise.
This is a scalar if x is a scalar.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
This function differs from the original `numpy.isinf
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.isnan.html>`_ in
the following aspects:
- Does not support complex number for now
- Input type does not support Python native iterables(list, tuple, ...).
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> np.isnan(np.nan)
True
>>> np.isnan(np.inf)
False
>>> np.isnan(np.array([np.log(-1.),1.,np.log(0)]))
array([ True, False, False])
"""
return _pure_unary_func_helper(x, _api_internal.isnan, _np.isnan, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def isinf(x, out=None, **kwargs):
"""
Test element-wise for positive or negative infinity.
Parameters
----------
x : ndarray
Input array.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray or bool
True where x is positive or negative infinity, false otherwise.
This is a scalar if x is a scalar.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
This means that Not a Number is not equivalent to infinity.
This function differs from the original `numpy.isnan
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.isnan.html>`_ in
the following aspects:
- Does not support complex number for now
- Input type does not support Python native iterables(list, tuple, ...).
- ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
- ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
- ``out`` param does not support scalar input case.
Examples
--------
>>> np.isinf(np.inf)
True
>>> np.isinf(np.nan)
False
>>> np.isinf(np.array([np.inf, -np.inf, 1.0, np.nan]))
array([ True, True, False, False])
>>> x = np.array([-np.inf, 0., np.inf])
>>> y = np.array([True, True, True], dtype=np.bool_)
>>> np.isinf(x, y)
array([ True, False, True])
>>> y
array([ True, False, True])
"""
return _pure_unary_func_helper(x, _api_internal.isinf, _np.isinf, out=out, **kwargs)
@wrap_np_unary_func
def isposinf(x, out=None, **kwargs):
"""
Test element-wise for positive infinity, return result as bool array.
Parameters
----------
x : ndarray
Input array.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray or bool
True where x is positive infinity, false otherwise.
This is a scalar if x is a scalar.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
This means that Not a Number is not equivalent to infinity.
Examples
--------
>>> np.isposinf(np.inf)
True
>>> np.isposinf(-np.inf)
False
>>> np.isposinf(np.nan)
False
>>> np.isposinf(np.array([-np.inf, 0., np.inf]))
array([False, False, True])
>>> x = np.array([-np.inf, 0., np.inf])
>>> y = np.array([True, True, True], dtype=np.bool)
>>> np.isposinf(x, y)
array([False, False, True])
>>> y
array([False, False, True])
"""
return _pure_unary_func_helper(x, _api_internal.isposinf, _np.isposinf, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def isneginf(x, out=None, **kwargs):
"""
Test element-wise for negative infinity, return result as bool array.
Parameters
----------
x : ndarray
Input array.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray or bool
True where x is negative infinity, false otherwise.
This is a scalar if x is a scalar.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
This means that Not a Number is not equivalent to infinity.
Examples
--------
>>> np.isneginf(-np.inf)
True
>>> np.isneginf(np.inf)
False
>>> np.isneginf(float('-inf'))
True
>>> np.isneginf(np.array([-np.inf, 0., np.inf]))
array([ True, False, False])
>>> x = np.array([-np.inf, 0., np.inf])
>>> y = np.array([True, True, True], dtype=np.bool)
>>> np.isneginf(x, y)
array([ True, False, False])
>>> y
array([ True, False, False])
"""
return _pure_unary_func_helper(x, _api_internal.isneginf, _np.isneginf, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def isfinite(x, out=None, **kwargs):
"""
Test element-wise for finiteness (not infinity or not Not a Number).
Parameters
----------
x : ndarray
Input array.
out : ndarray or None, optional
A location into which the result is stored.
If provided, it must have the same shape and dtype as input ndarray.
If not provided or `None`, a freshly-allocated array is returned.
Returns
-------
y : ndarray or bool
True where x is negative infinity, false otherwise.
This is a scalar if x is a scalar.
Notes
-----
Not a Number, positive infinity and negative infinity are considered to be non-finite.
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
This means that Not a Number is not equivalent to infinity.
Also that positive infinity is not equivalent to negative infinity.
But infinity is equivalent to positive infinity. Errors result if the second argument
is also supplied when x is a scalar input, or if first and second arguments have different shapes.
Examples
--------
>>> np.isfinite(1)
True
>>> np.isfinite(0)
True
>>> np.isfinite(np.nan)
False
>>> np.isfinite(np.inf)
False
>>> np.isfinite(-np.inf)
False
>>> np.isfinite(np.array([np.log(-1.),1.,np.log(0)]))
array([False, True, False])
>>> x = np.array([-np.inf, 0., np.inf])
>>> y = np.array([True, True, True], dtype=np.bool)
>>> np.isfinite(x, y)
array([False, True, False])
>>> y
array([False, True, False])
"""
return _pure_unary_func_helper(x, _api_internal.isfinite, _np.isfinite, out=out, **kwargs)
@set_module('mxnet.ndarray.numpy')
def atleast_1d(*arys):
"""
Convert inputs to arrays with at least one dimension.
Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved.
Parameters
----------
arys1, arys2, ... : ndarray
One or more input arrays.
Returns
-------
ret : ndarray
An array, or list of arrays, each with a.ndim >= 1. Copies are made only if necessary.
See also
--------
atleast_2d, atleast_3d
Examples
--------
>>> np.atleast_1d(1.0)
array([1.])
>>> x = np.arange(9.0).reshape(3,3)
>>> np.atleast_1d(x)
array([[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]])
>>> np.atleast_1d(np.array(1), np.array([3, 4]))
[array([1.]), array([3., 4.])]
"""
if len(arys) == 1:
return _api_internal.atleast_1d(*arys)[0]
return list(_api_internal.atleast_1d(*arys))
@set_module('mxnet.ndarray.numpy')
def atleast_2d(*arys):
"""
Convert inputs to arrays with at least two dimensions.
Parameters
----------
arys1, arys2, ... : ndarray
One or more input arrays.
Returns
-------
ret : ndarray
An array, or list of arrays, each with a.ndim >= 2. Copies are made only if necessary.
See also
--------
atleast_1d, atleast_3d
Examples
--------
>>> np.atleast_2d(3.0)
array([[3.]])
>>> x = np.arange(3.0)
>>> np.atleast_2d(x)
array([[0., 1., 2.]])
>>> np.atleast_2d(np.array(1), np.array([1, 2]), np.array([[1, 2]]))
[array([[1.]]), array([[1., 2.]]), array([[1., 2.]])]
"""
if len(arys) == 1:
return _api_internal.atleast_2d(*arys)[0]
return list(_api_internal.atleast_2d(*arys))
@set_module('mxnet.ndarray.numpy')
def atleast_3d(*arys):
"""
Convert inputs to arrays with at least three dimension.
Parameters
----------
arys1, arys2, ... : ndarray
One or more input arrays.
Returns
-------
ret : ndarray
An array, or list of arrays, each with a.ndim >= 3.
For example, a 1-D array of shape (N,) becomes a view of shape (1, N, 1),
and a 2-D array of shape (M, N) becomes a view of shape (M, N, 1).
See also
--------
atleast_1d, atleast_2d
Examples
--------
>>> np.atleast_3d(3.0)
array([[[3.]]])
>>> x = np.arange(3.0)
>>> np.atleast_3d(x).shape
(1, 3, 1)
>>> x = np.arange(12.0).reshape(4,3)
>>> np.atleast_3d(x).shape
(4, 3, 1)
>>> for arr in np.atleast_3d(np.array([1, 2]), np.array([[1, 2]]), np.array([[[1, 2]]])):
... print(arr, arr.shape)
...
[[[1.]
[2.]]] (1, 2, 1)
[[[1.]
[2.]]] (1, 2, 1)
[[[1. 2.]]] (1, 1, 2)
"""
if len(arys) == 1:
return _api_internal.atleast_3d(*arys)[0]
return list(_api_internal.atleast_3d(*arys))
@set_module('mxnet.ndarray.numpy')
def where(condition, x=None, y=None): # pylint: disable=too-many-return-statements
"""where(condition, [x, y])
Return elements chosen from `x` or `y` depending on `condition`.
.. note::
When only `condition` is provided, this function is a shorthand for
``np.asarray(condition).nonzero()``. The rest of this documentation
covers only the case where all three arguments are provided.
Parameters
----------
condition : ndarray
Where True, yield `x`, otherwise yield `y`.
x, y : ndarray
Values from which to choose. `x`, `y` and `condition` need to be
broadcastable to some shape. `x` and `y` must have the same dtype.
Returns
-------
out : ndarray
An array with elements from `x` where `condition` is True, and elements
from `y` elsewhere.
Notes
-----
If all the arrays are 1-D, `where` is equivalent to::
[xv if c else yv
for c, xv, yv in zip(condition, x, y)]
This function differs from the original `numpy.where
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html>`_ in
the following way(s):
- If `condition` is a scalar, this operator returns x or y directly without broadcasting.
- If `condition` is ndarray, while both `x` and `y` are scalars,
the output dtype will be `float32`.
Examples
--------
>>> a = np.arange(10)
>>> a
array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])
>>> np.where(a < 5, a, 10*a)
array([ 0., 1., 2., 3., 4., 50., 60., 70., 80., 90.])
This can be used on multidimensional arrays too:
>>> cond = np.array([[True, False], [True, True]])
>>> x = np.array([[1, 2], [3, 4]])
>>> y = np.array([[9, 8], [7, 6]])
>>> np.where(cond, x, y)
array([[1., 8.],
[3., 4.]])
The shapes of x, y, and the condition are broadcast together:
>>> x, y = onp.ogrid[:3, :4]
>>> x = np.array(x)
>>> y = np.array(y)
>>> np.where(x < y, x, 10 + y) # both x and 10+y are broadcast
array([[10, 0, 0, 0],
[10, 11, 1, 1],
[10, 11, 12, 2]], dtype=int64)
>>> a = np.array([[0, 1, 2],
... [0, 2, 4],
... [0, 3, 6]])
>>> np.where(a < 4, a, -1) # -1 is broadcast
array([[ 0., 1., 2.],
[ 0., 2., -1.],
[ 0., 3., -1.]])
"""
if x is None and y is None:
return nonzero(condition)
else:
if isinstance(condition, numeric_types):
if condition != 0:
return x
else:
return y
else:
return _api_internal.where(condition, x, y)
@set_module('mxnet.ndarray.numpy')
def polyval(p, x):
"""
Evaluate a polynomial at specific values.
If p is of length N, this function returns the value:
p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]
If x is a sequence, then p(x) is returned for each element of x.
If x is another polynomial then the composite polynomial p(x(t)) is returned.
Parameters
----------
p : ndarray
1D array of polynomial coefficients (including coefficients equal to zero)
from highest degree to the constant term.
x : ndarray
An array of numbers, at which to evaluate p.
Returns
-------
values : ndarray
Result array of polynomials
Notes
-----
This function differs from the original `numpy.polyval
<https://numpy.org/devdocs/reference/generated/numpy.polyval.html>`_ in
the following way(s):
- Does not support poly1d.
- X should be ndarray type even if it contains only one element.
Examples
--------
>>> p = np.array([3, 0, 1])
array([3., 0., 1.])
>>> x = np.array([5])
array([5.])
>>> np.polyval(p, x) # 3 * 5**2 + 0 * 5**1 + 1
array([76.])
>>> x = np.array([5, 4])
array([5., 4.])
>>> np.polyval(p, x)
array([76., 49.])
"""
from ...numpy import ndarray
if isinstance(p, numeric_types) and isinstance(x, numeric_types):
return _np.polyval(p, x)
elif isinstance(p, ndarray) and isinstance(x, ndarray):
return _api_internal.polyval(p, x)
else:
raise TypeError('type not supported')
@set_module('mxnet.ndarray.numpy')
def bincount(x, weights=None, minlength=0):
"""
Count number of occurrences of each value in array of non-negative ints.
Parameters
----------
x : ndarray
input array, 1 dimension, nonnegative ints.
weights: ndarray
input weigths same shape as x. (Optional)
minlength: int
A minimum number of bins for the output. (Optional)
Returns
--------
out : ndarray
the result of binning the input array. The length of out is equal to amax(x)+1.
Raises
--------
Value Error
If the input is not 1-dimensional, or contains elements with negative values,
or if minlength is negative
TypeError
If the type of the input is float or complex.
Examples
--------
>>> np.bincount(np.arange(5))
array([1, 1, 1, 1, 1])
>>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7]))
array([1, 3, 1, 1, 0, 0, 0, 1])
>>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])
>>> np.bincount(x).size == np.amax(x)+1
True
>>> np.bincount(np.arange(5, dtype=float))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: array cannot be safely cast to required type
>>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights
>>> x = np.array([0, 1, 1, 2, 2, 2])
>>> np.bincount(x, weights=w)
array([ 0.3, 0.7, 1.1])
"""
if minlength < 0:
raise ValueError("Minlength value should greater than 0")
return _api_internal.bincount(x, weights, minlength)
@set_module('mxnet.ndarray.numpy')
def pad(x, pad_width, mode='constant', **kwargs): # pylint: disable=too-many-arguments
"""
Pad an array.
Parameters
----------
array : array_like of rank N
The array to pad.
pad_width : {sequence, array_like, int}
Number of values padded to the edges of each axis.
((before_1, after_1), ... (before_N, after_N)) unique pad widths
for each axis.
((before, after),) yields same before and after pad for each axis.
(pad,) or int is a shortcut for before = after = pad width for all
axes.
mode : str or function, optional
One of the following string values or a user supplied function.
'constant' (default)
Pads with a constant value.
'edge'
Pads with the edge values of array.
'linear_ramp'
not supported yet
'maximum'
Pads with the maximum value of all of the
vector along each axis.
'mean'
not supported yet
'median'
not supported yet
'minimum'
Pads with the minimum value of all of the
vector along each axis.
'reflect'
Pads with the reflection of the vector mirrored on
the first and last values of the vector along each
axis.
'symmetric'
Pads with the reflection of the vector mirrored
along the edge of the array.
'wrap'
not supported yet.
'empty'
not supported yet.
<function>
not supported yet.
stat_length : not supported yet
constant_values : scalar, optional
Used in 'constant'. The values to set the padded values for each
axis.
Default is 0.
end_values : not supported yet
reflect_type : {'even', 'odd'}, optional
only support even now
Returns
-------
pad : ndarray
Padded array of rank equal to `array` with shape increased
according to `pad_width`.
"""
# pylint: disable = too-many-return-statements, inconsistent-return-statements
if not _np.asarray(pad_width).dtype.kind == 'i':
raise TypeError('`pad_width` must be of integral type.')
if not isinstance(pad_width, tuple):
raise TypeError("`pad_width` must be tuple.")
if mode == "linear_ramp":
raise ValueError("mode {'linear_ramp'} is not supported.")
if mode == "wrap":
raise ValueError("mode {'wrap'} is not supported.")
if mode == "median":
raise ValueError("mode {'median'} is not supported.")
if mode == "mean":
raise ValueError("mode {'mean'} is not supported.")
if mode == "empty":
raise ValueError("mode {'empty'} is not supported.")
if callable(mode):
raise ValueError("mode {'<function>'} is not supported.")
allowedkwargs = {
'constant': ['constant_values'],
'edge': [],
'linear_ramp': ['end_values'],
'maximum': ['stat_length'],
'mean': ['stat_length'],
'median': ['stat_length'],
'minimum': ['stat_length'],
'reflect': ['reflect_type'],
'symmetric': ['reflect_type'],
'wrap': [],
}
if isinstance(mode, _np.compat.basestring):
# Make sure have allowed kwargs appropriate for mode
for key in kwargs:
if key not in allowedkwargs[mode]:
raise ValueError(f'{key} keyword not in allowed keywords {allowedkwargs[mode]}')
unsupported_kwargs = set(kwargs) - set(allowedkwargs[mode])
if unsupported_kwargs:
raise ValueError("unsupported keyword arguments for mode '{}': {}"
.format(mode, unsupported_kwargs))
if mode == "constant":
values = kwargs.get("constant_values", 0)
if isinstance(values, tuple):
raise TypeError("unsupported constant_values type: {'tuple'}.")
return _api_internal.pad(x, pad_width, 'constant', values, "even")
elif mode == "symmetric":
values = kwargs.get("reflect_type", "even")
if values != "even" and values is not None:
raise ValueError("unsupported reflect_type '{}'".format(values))
return _api_internal.pad(x, pad_width, 'symmetric', 0, "even")
elif mode == "edge":
return _api_internal.pad(x, pad_width, 'edge', 0, "even")
elif mode == "reflect":
values = kwargs.get("reflect_type", "even")
if values != "even" and values is not None:
raise ValueError("unsupported reflect_type '{}'".format(values))
return _api_internal.pad(x, pad_width, 'reflect', 0, "even")
elif mode == "maximum":
values = kwargs.get("stat_length", None)
if values is not None:
raise ValueError("unsupported stat_length '{}'".format(values))
return _api_internal.pad(x, pad_width, 'maximum', 0, "even")
elif mode == "minimum":
values = kwargs.get("stat_length", None)
if values is not None:
raise ValueError("unsupported stat_length '{}'".format(values))
return _api_internal.pad(x, pad_width, 'minimum', 0, "even")
return _api_internal.pad(x, pad_width, 'constant', 0, "even")
@set_module('mxnet.ndarray.numpy')
def prod(a, axis=None, dtype=None, out=None, keepdims=False, initial=None): # pylint: disable=too-many-arguments
"""
Return the product of array elements over a given axis.
Parameters
----------
a : array_like
Input data.
axis : None or int or tuple of ints, optional
Axis or axes along which a product is performed. The default,
axis=None, will calculate the product of all the elements in the
input array. If axis is negative it counts from the last to the
first axis.
.. versionadded:: 1.7.0
If axis is a tuple of ints, a product is performed on all of the
axes specified in the tuple instead of a single axis or all the
axes as before.
dtype : dtype, optional
The type of the returned array, as well as of the accumulator in
which the elements are multiplied. The dtype of `a` is used by
default unless `a` has an integer dtype of less precision than the
default platform integer. In that case, if `a` is signed then the
platform integer is used while if `a` is unsigned then an unsigned
integer of the same precision as the platform integer is used.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output, but the type of the output
values will be cast if necessary.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the
result as dimensions with size one. With this option, the result
will broadcast correctly against the input array.
If the default value is passed, then `keepdims` will not be
passed through to the `prod` method of sub-classes of
`ndarray`, however any non-default value will be. If the
sub-class' method does not implement `keepdims` any
exceptions will be raised.
initial : scalar, optional
The starting value for this product. See `~numpy.ufunc.reduce` for details.
where : not supported
Returns
-------
product_along_axis : ndarray, see `dtype` parameter above.
An array shaped as `a` but with the specified axis removed.
Returns a reference to `out` if specified.
Examples
--------
By default, calculate the product of all elements:
>>> np.prod([1.,2.])
2.0
Even when the input array is two-dimensional:
>>> np.prod([[1.,2.],[3.,4.]])
24.0
But we can also specify the axis over which to multiply:
>>> np.prod([[1.,2.],[3.,4.]], axis=1)
array([ 2., 12.])
Or select specific elements to include:
>>> np.prod([1., np.nan, 3.], where=[True, False, True])
3.0
If the type of `x` is unsigned, then the output type is
the unsigned platform integer:
>>> x = np.array([1, 2, 3], dtype=np.uint8)
>>> np.prod(x).dtype == np.uint
True
If `x` is of a signed integer type, then the output type
is the default platform integer:
>>> x = np.array([1, 2, 3], dtype=np.int8)
>>> np.prod(x).dtype == int
True
You can also start the product with a value other than one:
>>> np.prod([1, 2], initial=5)
10
"""
return _api_internal.prod(a, axis, dtype, keepdims, initial, out)
@set_module('mxnet.ndarray.numpy')
def cumsum(a, axis=None, dtype=None, out=None):
"""
Return the cumulative sum of the elements along a given axis.
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative sum is computed. The default
(None) is to compute the cumsum over the flattened array.
dtype : dtype, optional
Type of the returned array and of the accumulator in which the
elements are summed. If `dtype` is not specified, it defaults
to the dtype of `a`, unless `a` has an integer dtype with a
precision less than that of the default platform integer. In
that case, the default platform integer is used.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type will be cast if necessary. See `doc.ufuncs`
(Section "Output arguments") for more details.
Returns
-------
cumsum_along_axis : ndarray.
A new array holding the result is returned unless `out` is
specified, in which case a reference to `out` is returned. The
result has the same size as `a`, and the same shape as `a` if
`axis` is not None or `a` is a 1-d array.
Examples
--------
>>> a = np.array([[1,2,3], [4,5,6]])
>>> a
array([[1, 2, 3],
[4, 5, 6]])
>>> np.cumsum(a)
array([ 1, 3, 6, 10, 15, 21])
>>> np.cumsum(a, dtype=float) # specifies type of output value(s)
array([ 1., 3., 6., 10., 15., 21.])
>>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns
array([[1, 2, 3],
[5, 7, 9]])
>>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows
array([[ 1, 3, 6],
[ 4, 9, 15]])
"""
return _api_internal.cumsum(a, axis, dtype, out)
@set_module('mxnet.ndarray.numpy')
def reshape(a, newshape, order='C'):
"""
Gives a new shape to an array without changing its data.
This function always returns a copy of the input array if
``out`` is not provided.
Parameters
----------
a : ndarray
Array to be reshaped.
newshape : int or tuple of ints
The new shape should be compatible with the original shape. If
an integer, then the result will be a 1-D array of that length.
One shape dimension can be -1. In this case, the value is
inferred from the length of the array and remaining dimensions.
order : {'C'}, optional
Read the elements of `a` using this index order, and place the
elements into the reshaped array using this index order. 'C'
means to read / write the elements using C-like index order,
with the last axis index changing fastest, back to the first
axis index changing slowest. Other order types such as 'F'/'A'
may be added in the future.
Returns
-------
reshaped_array : ndarray
It will be always a copy of the original array. This behavior is different
from the official NumPy ``reshape`` operator where views of the original array may be
generated.
See Also
--------
ndarray.reshape : Equivalent method.
Examples
--------
>>> a = np.arange(6).reshape((3, 2))
>>> a
array([[0., 1.],
[2., 3.],
[4., 5.]])
>>> np.reshape(a, (2, 3)) # C-like index ordering
array([[0., 1., 2.],
[3., 4., 5.]])
>>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
array([[0., 1., 2.],
[3., 4., 5.]])
>>> a = np.array([[1,2,3], [4,5,6]])
>>> np.reshape(a, 6)
array([1., 2., 3., 4., 5., 6.])
>>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2
array([[1., 2.],
[3., 4.],
[5., 6.]])
"""
return _api_internal.reshape(a, newshape, False, order)
@set_module('mxnet.ndarray.numpy')
def moveaxis(a, source, destination):
"""Move axes of an array to new positions.
Other axes remain in their original order.
Parameters
----------
a : ndarray
The array whose axes should be reordered.
source : int or sequence of int
Original positions of the axes to move. These must be unique.
destination : int or sequence of int
Destination positions for each of the original axes. These must also be
unique.
Returns
-------
result : ndarray
Array with moved axes. This array is a view of the input array.
See Also
--------
transpose: Permute the dimensions of an array.
swapaxes: Interchange two axes of an array.
Examples
--------
>>> x = np.zeros((3, 4, 5))
>>> np.moveaxis(x, 0, -1).shape
(4, 5, 3)
>>> np.moveaxis(x, -1, 0).shape
(5, 3, 4)
These all achieve the same result:
>>> np.transpose(x).shape
(5, 4, 3)
>>> np.swapaxes(x, 0, -1).shape
(5, 4, 3)
>>> np.moveaxis(x, [0, 1], [-1, -2]).shape
(5, 4, 3)
>>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape
(5, 4, 3)
"""
return _api_internal.moveaxis(a, source, destination)
# pylint: disable=redefined-outer-name
@set_module('mxnet.ndarray.numpy')
def copy(a):
"""
Return an array copy of the given object.
Parameters
----------
a :
Input array.
Returns
-------
arr : ndarray
Array interpretation of a.
-----
Examples
--------
>>> x = np.array([1, 2, 3])
>>> y = x
>>> z = np.copy(x)
>>> x[0] = 10
>>> x[0] == y[0]
True
>>> x[0] == z[0]
False
"""
return _api_internal.copy(a)
@set_module('mxnet.ndarray.numpy')
def rollaxis(a, axis, start=0):
"""
Roll the specified axis backwards, until it lies in a given position.
a
Input array.
axis : integer
The axis to roll backwards. The positions of the other axes do not
change relative to one another.
start: int, optional
The axis is rolled until it lies before this position.
The default, 0, results in a “complete” roll.
Returns
-------
res : ndarray
A view after applying rollaxis to `a` is returned.
-----
Examples
--------
>>> a = np.ones((3,4,5,6))
>>> np.rollaxis(a, 3, 1).shape
(3, 6, 4, 5)
>>> np.rollaxis(a, 2).shape
(5, 3, 4, 6)
>>> np.rollaxis(a, 1, 4).shape
(3, 5, 6, 4)
"""
return _api_internal.rollaxis(a, axis, start)
@set_module('mxnet.ndarray.numpy')
def diag(v, k=0):
"""
Extracts a diagonal or constructs a diagonal array.
- 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
- 2-D arrays: extracts the k-th Diagonal
Parameters
----------
array : ndarray
The array to apply diag method.
k : offset
extracts or constructs kth diagonal given input array
Returns
----------
out : ndarray
The extracted diagonal or constructed diagonal 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]])
"""
return _api_internal.diag(v, k)
@set_module('mxnet.ndarray.numpy')
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]])
"""
return _api_internal.diagflat(v, k)
@set_module('mxnet.ndarray.numpy')
def diagonal(a, offset=0, axis1=0, axis2=1):
"""
If a is 2-D, returns the diagonal of a with the given offset, i.e., the collection of elements of
the form a[i, i+offset]. If a has more than two dimensions, then the axes specified by axis1 and
axis2 are used to determine the 2-D sub-array whose diagonal is returned. The shape of the
resulting array can be determined by removing axis1 and axis2 and appending an index to the
right equal to the size of the resulting diagonals.
Parameters
----------
a : ndarray
Input data from which diagonal are taken.
offset: int, Optional
Offset of the diagonal from the main diagonal
axis1: int, Optional
Axis to be used as the first axis of the 2-D sub-arrays
axis2: int, Optional
Axis to be used as the second axis of the 2-D sub-arrays
Returns
-------
out : ndarray
Output result
Raises
-------
ValueError: If the dimension of a is less than 2.
Examples
--------
>>> a = np.arange(4).reshape(2,2)
>>> a
array([[0, 1],
[2, 3]])
>>> np.diagonal(a)
array([0, 3])
>>> np.diagonal(a, 1)
array([1])
>>> a = np.arange(8).reshape(2,2,2)
>>>a
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> np.diagonal(a, 0, 0, 1)
array([[0, 6],
[1, 7]])
"""
return _api_internal.diagonal(a, offset, axis1, axis2)
# pylint:disable=redefined-outer-name, too-many-arguments
@set_module('mxnet.ndarray.numpy')
def sum(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None):
r"""
Sum of array elements over a given axis.
Parameters
----------
a : ndarray
Input data.
axis : None or int, optional
Axis or axes along which a sum is performed. The default,
axis=None, will sum all of the elements of the input array. If
axis is negative it counts from the last to the first axis.
dtype : dtype, optional
The type of the returned array and of the accumulator in which the
elements are summed. The default type is float32.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the input array.
If the default value is passed, then `keepdims` will not be
passed through to the `sum` method of sub-classes of
`ndarray`, however any non-default value will be. If the
sub-classes `sum` method does not implement `keepdims` any
exceptions will be raised.
initial: Currently only supports None as input, optional
Starting value for the sum.
Currently not implemented. Please use ``None`` as input or skip this argument.
out : ndarray or None, optional
Alternative output array in which to place the result. It must have
the same shape and dtype as the expected output.
Returns
-------
sum_along_axis : ndarray
An ndarray with the same shape as `a`, with the specified
axis removed. If an output array is specified, a reference to
`out` is returned.
Notes
-----
- Input type does not support Python native iterables.
- "out" param: cannot perform auto type change. out ndarray's dtype must be the same as the expected output.
- "initial" param is not supported yet. Please use None as input.
- Arithmetic is modular when using integer types, and no error is raised on overflow.
- The sum of an empty array is the neutral element 0:
>>> a = np.empty(1)
>>> np.sum(a)
array(0.)
This function differs from the original `numpy.sum
<https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html>`_ in
the following aspects:
- Input type does not support Python native iterables(list, tuple, ...).
- "out" param: cannot perform auto type cast. out ndarray's dtype must be the same as the expected output.
- "initial" param is not supported yet. Please use ``None`` as input or skip it.
- The default type is float32.
Examples
--------
>>> a = np.array([0.5, 1.5])
>>> np.sum(a)
array(2.)
>>> a = np.array([0.5, 0.7, 0.2, 1.5])
>>> np.sum(a, dtype=np.int32)
array(2, dtype=int32)
>>> a = np.array([[0, 1], [0, 5]])
>>> np.sum(a)
array(6.)
>>> np.sum(a, axis=0)
array([0., 6.])
>>> np.sum(a, axis=1)
array([1., 5.])
With output ndarray:
>>> a = np.array([[0, 1], [0, 5]])
>>> b = np.ones((2,), dtype=np.float32)
>>> np.sum(a, axis=0, out=b)
array([0., 6.])
>>> b
array([0., 6.])
If the accumulator is too small, overflow occurs:
>>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
array(-128, dtype=int8)
"""
if where is not None and where is not True:
raise ValueError("only where=None or where=True cases are supported for now")
return _api_internal.sum(a, axis, dtype, keepdims, initial, out)
# pylint:enable=redefined-outer-name, too-many-arguments
@set_module('mxnet.ndarray.numpy')
def bitwise_left_shift(x1, x2, out=None):
r"""
Shift the bits of and integer to the left. Bits are shifted to the left by
appending x2 0s at the right of x1. Since the internal representation of numbers
is in binary format, this operation is equivalent to ``x1 * 2**x2``
Parameters
----------
x1 : ndarray or scalar
Input values.
x2 : ndarray or scalar
Number of zeros to append to x1. Has to be non-negative. If x1.shape != x2.shape,
they must be broadcastable to a common shape (which becomes the shape of the output).
out : ndarray, 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
-------
out : ndarray
Result.
Examples
--------
>>> np.binary_repr(5)
'101'
>>> np.left_shift(5, 2)
20
>>> np.binary_repr(20)
'10100'
>>> np.left_shift(5, np.array([1,2,3]))
array([10, 20, 40])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.left_shift(x1, x2, out=out)
return _api_internal.bitwise_left_shift(x1, x2, out)
@set_module('mxnet.ndarray.numpy')
def bitwise_right_shift(x1, x2, out=None):
r"""
Shift the bits of and integer to the right. Bits are shifted to the right by
x2. Because the internal representation of numbers is in binary format,
this operation is equivalent to ``x1 / 2**x2``
Parameters
----------
x1 : ndarray or scalar
Input values.
x1 : ndarray or scalar
Number of bits to remove at the right of x1. If x1.shape != x2.shape,
they must be broadcastable to a common shape (which becomes the shape of the output).
out : ndarray, 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
-------
out : ndarray
Result.
Examples
--------
>>> np.binary_repr(10)
'1010'
>>> np.right_shift(10, 1)
5
>>> np.binary_repr(5)
'101'
>>> np.right_shift(10, np.array([1,2,3]))
array([5, 2, 1])
"""
if isinstance(x1, numeric_types) and isinstance(x2, numeric_types):
return _np.right_shift(x1, x2, out=out)
return _api_internal.bitwise_right_shift(x1, x2, out)