mxnet.ndarray.numpy

Module for numpy ops under mxnet.ndarray.

Functions

abs(x[, out])	Calculate the absolute value element-wise.
absolute(x[, out])	Calculate the absolute value element-wise.
add(x1, x2[, out])	Add arguments element-wise.
all(a[, axis, out, keepdims])	Test whether all array elements along a given axis evaluate to True.
amax(a[, axis, out, keepdims])	Return the maximum of an array or maximum along an axis.
amin(a[, axis, out, keepdims])	Return the minimum of an array or minimum along an axis.
any(a[, axis, out, keepdims])	Test whether any array element along a given axis evaluates to True.
append(arr, values[, axis])	Append values to the end of an array.
arange(start[, stop, step, dtype, device])	Return evenly spaced values within a given interval.
arccos(x[, out])	Trigonometric inverse cosine, element-wise.
arccosh(x[, out])	Inverse hyperbolic cosine, element-wise.
arcsin(x[, out])	Inverse sine, element-wise.
arcsinh(x[, out])	Inverse hyperbolic sine, element-wise.
arctan(x[, out])	Trigonometric inverse tangent, element-wise.
arctan2(x1, x2[, out])	Element-wise arc tangent of x1/x2 choosing the quadrant correctly.
arctanh(x[, out])	Inverse hyperbolic tangent, element-wise.
argmax(a[, axis, out, keepdims])	Returns the indices of the maximum values along an axis.
argmin(a[, axis, out, keepdims])	Returns the indices of the maximum values along an axis.
argsort(a[, axis, descending, stable])	Returns the indices that sort an array x along a specified axis.
around(x[, decimals, out])	Evenly round to the given number of decimals.
array_split(ary, indices_or_sections[, axis])	Split an array into multiple sub-arrays.
atleast_1d(*arys)	Convert inputs to arrays with at least one dimension.
atleast_2d(*arys)	Convert inputs to arrays with at least two dimensions.
atleast_3d(*arys)	Convert inputs to arrays with at least three dimension.
average(a[, axis, weights, returned, out])	Compute the weighted average along the specified axis.
bincount(x[, weights, minlength])	Count number of occurrences of each value in array of non-negative ints.
bitwise_and(x1, x2[, out])	Compute the bit-wise XOR of two arrays element-wise.
bitwise_left_shift(x1, x2[, out])	Shift the bits of and integer to the left.
bitwise_not(x[, out])	Compute bit-wise inversion, or bit-wise NOT, element-wise.
bitwise_or(x1, x2[, out])	Compute the bit-wise OR of two arrays element-wise.
bitwise_right_shift(x1, x2[, out])	Shift the bits of and integer to the right.
bitwise_xor(x1, x2[, out])	Compute the bit-wise XOR of two arrays element-wise.
blackman(M[, dtype, device])	Return the Blackman window.
broadcast_to(array, shape)	Broadcast an array to a new shape.
cbrt(x[, out])	Return the cube-root of an array, element-wise.
ceil(x[, out])	Return the ceiling of the input, element-wise.
clip(a, a_min, a_max[, out])	Clip (limit) the values in an array.
column_stack(tup)	Stack 1-D arrays as columns into a 2-D array.
concatenate(seq[, axis, out])	Join a sequence of arrays along an existing axis.
copy(a)	Return an array copy of the given object.
copysign(x1, x2[, out])	Change the sign of x1 to that of x2, element-wise.
cos(x[, out])	Cosine, element-wise.
cosh(x[, out])	Hyperbolic cosine, element-wise.
cross(a, b[, axisa, axisb, axisc, axis])	Return the cross product of two (arrays of) vectors.
cumsum(a[, axis, dtype, out])	Return the cumulative sum of the elements along a given axis.
deg2rad(x[, out])	Convert angles from degrees to radians.
degrees(x[, out])	Convert angles from radians to degrees.
delete(arr, obj[, axis])	Return a new array with sub-arrays along an axis deleted.
diag(v[, k])	Extracts a diagonal or constructs a diagonal array.
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).
diagflat(v[, k])	Create a two-dimensional array with the flattened input as a diagonal.
diagonal(a[, offset, axis1, axis2])	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].
diff(a[, n, axis, prepend, append])	Calculate the n-th discrete difference along the given axis.
divide(x1, x2[, out])	Returns a true division of the inputs, element-wise.
dot(a, b[, out])	Dot product of two arrays.
dsplit(ary, indices_or_sections)	Split array into multiple sub-arrays along the 3rd axis (depth).
dstack(arrays)	Stack arrays in sequence depth wise (along third axis).
ediff1d(ary[, to_end, to_begin])	The differences between consecutive elements of an array.
einsum(subscripts, *operands[, out, optimize])	Evaluates the Einstein summation convention on the operands.
empty_like(prototype[, dtype, order, subok, ...])	Return a new array with the same shape and type as a given array.
equal(x1, x2[, out])	Return (x1 == x2) element-wise.
exp(x[, out])	Calculate the exponential of all elements in the input array.
expand_dims(a, axis)	Expand the shape of an array.
expm1(x[, out])	Calculate exp(x) - 1 of all elements in the input array.
eye(N[, M, k, dtype])	Return a 2-D array with ones on the diagonal and zeros elsewhere.
fabs(x[, out])	Calculate the absolute value element-wise.
fill_diagonal(a, val[, wrap])	Fill the main diagonal of the given array of any dimensionality.
fix(x[, out])	Round an array of floats element-wise to nearest integer towards zero.
flip(m[, axis, out])	Reverse the order of elements in an array along the given axis.
fliplr(*args, **kwargs)	Flip array in the left/right direction.
flipud(*args, **kwargs)	Flip array in the up/down direction.
floor(x[, out])	Return the floor of the input, element-wise.
floor_divide(x1, x2[, out])	Return the largest integer smaller or equal to the division of the inputs.
fmax(x1, x2[, out])	Returns element-wise maximum of the input arrays with broadcasting.
fmin(x1, x2[, out])	Returns element-wise minimum of the input arrays with broadcasting.
fmod(x1, x2[, out])	Return element-wise remainder of division.
full(shape, fill_value[, dtype, order, ...])	Return a new array of given shape and type, filled with fill_value.
full_like(a, fill_value[, dtype, order, ...])	Return a full array with the same shape and type as a given array.
gcd(x1, x2[, out])	Returns the greatest common divisor of |x1| and |x2|
greater(x1, x2[, out])	Return the truth value of (x1 > x2) element-wise.
greater_equal(x1, x2[, out])	Return the truth value of (x1 >= x2) element-wise.
hamming(M[, dtype, device])	Return the hamming window.
hanning(M[, dtype, device])	Return the Hanning window.
histogram(a[, bins, range, normed, weights, ...])	Compute the histogram of a set of data.
hsplit(ary, indices_or_sections)	Split an array into multiple sub-arrays horizontally (column-wise).
hstack(arrays)	Stack arrays in sequence horizontally (column wise).
hypot(x1, x2[, out])	Given the "legs" of a right triangle, return its hypotenuse.
identity(n[, dtype, device])	Return the identity array.
indices(dimensions[, dtype, device])	Return an array representing the indices of a grid.
inner(a, b)	Inner product of two arrays.
insert(arr, obj, values[, axis])	Insert values along the given axis before the given indices.
interp(x, xp, fp[, left, right, period])	One-dimensional linear interpolation.
invert(x[, out])	Compute bit-wise inversion, or bit-wise NOT, element-wise.
isfinite(x[, out])	Test element-wise for finiteness (not infinity or not Not a Number).
isinf(x[, out])	Test element-wise for positive or negative infinity.
isnan(x[, out])	Test element-wise for NaN and return result as a boolean array.
isneginf(x[, out])	Test element-wise for negative infinity, return result as bool array.
kron(a, b)	Kronecker product of two arrays.
lcm(x1, x2[, out])	Returns the lowest common multiple of |x1| and |x2|
ldexp(x1, x2[, out])	Returns x1 * 2**x2, element-wise.
less(x1, x2[, out])	Return the truth value of (x1 < x2) element-wise.
less_equal(x1, x2[, out])	Return the truth value of (x1 <= x2) element-wise.
linspace(start, stop[, num, endpoint, ...])	Return evenly spaced numbers over a specified interval.
log(x[, out])	Natural logarithm, element-wise.
log10(x[, out])	Return the base 10 logarithm of the input array, element-wise.
log1p(x[, out])	Return the natural logarithm of one plus the input array, element-wise.
log2(x[, out])	Base-2 logarithm of x.
logaddexp(x1, x2[, out])	Logarithm of the sum of exponentiations of the inputs.
logical_not(x[, out])	Compute the truth value of NOT x element-wise.
logical_or(x1, x2[, out])	Compute the truth value of x1 OR x2 element-wise.
logical_xor(x1, x2[, out])	Compute the truth value of x1 XOR x2 element-wise.
logspace(start, stop[, num, endpoint, base, ...])	Return numbers spaced evenly on a log scale.
matmul(a, b[, out])	Matrix product of two arrays.
max(a[, axis, out, keepdims])	Return the maximum of an array or maximum along an axis.
maximum(x1, x2[, out])	Returns element-wise maximum of the input arrays with broadcasting.
may_share_memory(a, b[, max_work])	Determine if two arrays might share memory
mean(a[, axis, dtype, out, keepdims])	Compute the arithmetic mean along the specified axis.
median(a[, axis, out, overwrite_input, keepdims])	Compute the median along the specified axis.
min(a[, axis, out, keepdims])	Return the minimum of an array or minimum along an axis.
minimum(x1, x2[, out])	Returns element-wise minimum of the input arrays with broadcasting.
mod(x1, x2[, out])	Return element-wise remainder of division.
moveaxis(a, source, destination)	Move axes of an array to new positions.
multiply(x1, x2[, out])	Multiply arguments element-wise.
nan_to_num(x[, copy, nan, posinf, neginf])	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.
negative(x[, out])	Numerical negative, element-wise.
nonzero(a)	Return the indices of the elements that are non-zero.
not_equal(x1, x2[, out])	Return (x1 != x2) element-wise.
ones(shape[, dtype, order, device])	Return a new array of given shape and type, filled with ones.
ones_like(a[, dtype, order, device, out])	Return an array of ones with the same shape and type as a given array.
outer(a, b)	Compute the outer product of two vectors.
pad(x, pad_width[, mode])	Pad an array.
percentile(a, q[, axis, out, ...])	Compute the q-th percentile of the data along the specified axis.
polyval(p, x)	Evaluate a polynomial at specific values.
positive(x[, out])	Computes the numerical positive of each element x_i (i.e.,`y_i = +x_i`) of the input array x .
power(x1, x2[, out])	First array elements raised to powers from second array, element-wise.
prod(a[, axis, dtype, out, keepdims, initial])	Return the product of array elements over a given axis.
product([a, axis, dtype, keepdims, initial, ...])	Return the product of array elements over a given axis.
quantile(a, q[, axis, out, overwrite_input, ...])	Compute the q-th quantile of the data along the specified axis.
rad2deg(x[, out])	Convert angles from radians to degrees.
radians(x[, out])	Convert angles from degrees to radians.
ravel(x)	Return a contiguous flattened array.
reciprocal(x[, out])	Return the reciprocal of the argument, element-wise.
remainder(x1, x2[, out])	Return element-wise remainder of division.
repeat(a, repeats[, axis])	Repeat elements of an array.
reshape(a, newshape[, order])	Gives a new shape to an array without changing its data.
resize(a, new_shape)	Return a new array with the specified shape.
rint(x[, out])	Round elements of the array to the nearest integer.
roll(a, shift[, axis])	Roll array elements along a given axis.
rollaxis(a, axis[, start])	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.
rot90(m[, k, axes])	Rotate an array by 90 degrees in the plane specified by axes.
round(a[, decimals, out])	Round an array to the given number of decimals.
round_(a[, decimals, out])	Round an array to the given number of decimals.
row_stack(arrays)	Stack arrays in sequence vertically (row wise).
shape(a)	Return the shape of an array.
shares_memory(a, b[, max_work])	Determine if two arrays share memory
sign(x[, out])	Returns an element-wise indication of the sign of a number.
sin(x[, out])	Trigonometric sine, element-wise.
sinh(x[, out])	Hyperbolic sine, element-wise.
sometrue([data, axis, keepdims, out, name])	Check whether some values are true.
sort(a[, axis, descending, stable])	Return a sorted copy of an array.
split(ary, indices_or_sections[, axis])	Split an array into multiple sub-arrays.
sqrt(x[, out])	Return the non-negative square-root of an array, element-wise.
square(x[, out])	Return the element-wise square of the input.
squeeze(x[, axis])	Remove single-dimensional entries from the shape of an array.
stack(arrays[, axis, out])	Join a sequence of arrays along a new axis.
std(a[, axis, dtype, out, ddof, keepdims])	Compute the standard deviation along the specified axis.
subtract(x1, x2[, out])	Subtract arguments element-wise.
sum(a[, axis, dtype, out, keepdims, ...])	Sum of array elements over a given axis.
swapaxes(a, axis1, axis2)	Interchange two axes of an array.
take(a, indices[, axis, mode, out])	Take elements from an array along an axis.
tan(x[, out])	Compute tangent element-wise.
tanh(x[, out])	Compute hyperbolic tangent element-wise.
tensordot(a, b[, axes])	Compute tensor dot product along specified axes for arrays >= 1-D.
tile(A, reps)	Construct an array by repeating A the number of times given by reps.
trace(a[, offset, axis1, axis2, out])	Return the sum along diagonals of the array.
transpose(a[, axes])	Permute the dimensions of an array.
tri(N[, M, k, dtype, device])	An array with ones at and below the given diagonal and zeros elsewhere.
tril(m[, k])	Lower triangle of an array.
tril_indices(n[, k, m])	Return the indices for the lower-triangle of an (n, m) array.
triu(m[, k])	Upper triangle of an array.
triu_indices(n[, k, m, device])	Return the indices for the upper-triangle of an (n, m) array.
triu_indices_from(arr[, k])	Return the indices for the upper-triangle of arr.
true_divide(x1, x2[, out])	Returns a true division of the inputs, element-wise.
trunc(x[, out])	Return the truncated value of the input, element-wise.
unique(ar[, return_index, return_inverse, ...])	Find the unique elements of an array.
unravel_index(indices, shape[, order])	Converts a flat index or array of flat indices into a tuple of coordinate arrays.
var(a[, axis, dtype, out, ddof, keepdims])	Compute the variance along the specified axis.
vdot(a, b)	Return the dot product of two vectors.
vsplit(ary, indices_or_sections)	Split an array into multiple sub-arrays vertically (row-wise).
vstack(arrays[, out])	Stack arrays in sequence vertically (row wise).
where(condition, [x, y])	Return elements chosen from x or y depending on condition.
zeros(shape[, dtype, order, device])	Return a new array of given shape and type, filled with zeros.
zeros_like(a[, dtype, order, device, out])	Return an array of zeros with the same shape and type as a given array.

mxnet.ndarray.numpy.abs(x, out=None, **kwargs)

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 – An ndarray containing the absolute value of each element in x. This is a scalar if x is a scalar.

Return type:

ndarray

Examples

>>> x = np.array([-1.2, 1.2])
>>> np.abs(x)
array([1.2, 1.2])

mxnet.ndarray.numpy.absolute(x, out=None, **kwargs)

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 – An ndarray containing the absolute value of each element in x.

Return type:

ndarray

Examples

>>> x = np.array([-1.2, 1.2])
>>> np.absolute(x)
array([ 1.2,  1.2])

mxnet.ndarray.numpy.add(x1, x2, out=None, **kwargs)

Add arguments element-wise.

Parameters:

• x1 (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).

• 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 – The sum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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.

mxnet.ndarray.numpy.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

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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.)

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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

mxnet.ndarray.numpy.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)

mxnet.ndarray.numpy.append(arr, values, axis=None)

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 – 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.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

mxnet.ndarray.numpy.arccos(x, out=None, **kwargs)

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 – 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.

Return type:

ndarray

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])

mxnet.ndarray.numpy.arccosh(x, out=None, **kwargs)

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 – Array of the same shape as x. This is a scalar if x is a scalar.

Return type:

ndarray

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

mxnet.ndarray.numpy.arcsin(x, out=None, **kwargs)

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 – 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].

Return type:

ndarray or scalar

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 \(sin(z) = x\). 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 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/

mxnet.ndarray.numpy.arcsinh(x, out=None, **kwargs)

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 – Array of the same shape as x. This is a scalar if x is a scalar.

Return type:

ndarray

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

mxnet.ndarray.numpy.arctan(x, out=None, **kwargs)

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 – 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.

Return type:

ndarray or 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

mxnet.ndarray.numpy.arctan2(x1, x2, out=None, **kwargs)

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 – Array of angles in radians, in the range [-pi, pi]. This is a scalar if x1 and x2 are scalars.

Return type:

ndarray or scalar

Notes

arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: [1]_

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])

mxnet.ndarray.numpy.arctanh(x, out=None, **kwargs)

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 – Array of the same shape as x. This is a scalar if x is a scalar.

Return type:

ndarray

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

mxnet.ndarray.numpy.argmax(a, axis=None, out=None, keepdims=False)

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 – Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.

Return type:

ndarray of indices whose dtype is same as the input ndarray.

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 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.])

mxnet.ndarray.numpy.argmin(a, axis=None, out=None, keepdims=False)

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 – Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.

Return type:

ndarray of indices whose dtype is same as the input ndarray.

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 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.])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray, int

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])

mxnet.ndarray.numpy.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 – An array of the same type as x, containing the rounded values. A reference to the result is returned.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.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 – A list of sub-arrays.

Return type:

list of ndarrays

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.])]

mxnet.ndarray.numpy.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 (ndarray) – One or more input arrays.

• arys2 (ndarray) – One or more input arrays.

• ... (ndarray) – One or more input arrays.

Returns:

ret – An array, or list of arrays, each with a.ndim >= 1. Copies are made only if necessary.

Return type:

ndarray

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.])]

mxnet.ndarray.numpy.atleast_2d(*arys)

Convert inputs to arrays with at least two dimensions.

Parameters:

• arys1 (ndarray) – One or more input arrays.

• arys2 (ndarray) – One or more input arrays.

• ... (ndarray) – One or more input arrays.

Returns:

ret – An array, or list of arrays, each with a.ndim >= 2. Copies are made only if necessary.

Return type:

ndarray

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.]])]

mxnet.ndarray.numpy.atleast_3d(*arys)

Convert inputs to arrays with at least three dimension.

Parameters:

• arys1 (ndarray) – One or more input arrays.

• arys2 (ndarray) – One or more input arrays.

• ... (ndarray) – One or more input arrays.

Returns:

ret – 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).

Return type:

ndarray

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)

mxnet.ndarray.numpy.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] – 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.)

Return type:

ndarray

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. –

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])

mxnet.ndarray.numpy.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 – the result of binning the input array. The length of out is equal to amax(x)+1.

Return type:

ndarray

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])

mxnet.ndarray.numpy.bitwise_and(x1, x2, out=None, **kwargs)

Compute the bit-wise XOR of two arrays element-wise.

Parameters:

• x1 (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).

• 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 – Result.

Return type:

ndarray

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])

mxnet.ndarray.numpy.bitwise_left_shift(x1, x2, out=None)

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 – Result.

Return type:

ndarray

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])

mxnet.ndarray.numpy.bitwise_not(x, out=None, **kwargs)

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 – Result. This is a scalar if x is a scalar.

Return type:

ndarray or 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

mxnet.ndarray.numpy.bitwise_or(x1, x2, out=None, **kwargs)

Compute the bit-wise OR of two arrays element-wise.

Parameters:

• x1 (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).

• 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 – Result.

Return type:

ndarray

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])

mxnet.ndarray.numpy.bitwise_right_shift(x1, x2, out=None)

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 – 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 – Result.

Return type:

ndarray

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])

mxnet.ndarray.numpy.bitwise_xor(x1, x2, out=None, **kwargs)

Compute the bit-wise XOR of two arrays element-wise.

Parameters:

• x1 (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).

• 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 – Result.

Return type:

ndarray

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])

mxnet.ndarray.numpy.blackman(M, dtype=None, device=None)

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 – 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.

Return type:

ndarray

See also

hamming, hanning

Notes

The Blackman window is defined as

\[w(n) = 0.42 - 0.5 \cos(2\pi n/{M-1}) + 0.08 \cos(4\pi n/{M-1})\]

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()

mxnet.ndarray.numpy.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 – 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.

Return type:

array

Raises:

MXNetError – If the array is not compatible with the new shape according to NumPy’s broadcasting rules.

mxnet.ndarray.numpy.cbrt(x, out=None, **kwargs)

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 – 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.

Return type:

ndarray

Examples

>>> np.cbrt([1,8,27])
array([ 1.,  2.,  3.])

mxnet.ndarray.numpy.ceil(x, out=None, **kwargs)

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 \(\lceil x \rceil\).

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 – The ceiling of each element in x, with float dtype. This is a scalar if x is a scalar.

Return type:

ndarray or 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.)

mxnet.ndarray.numpy.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 – An array with the elements of a, but where values < a_min are replaced with a_min, and those > a_max with a_max.

Return type:

ndarray

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.])

mxnet.ndarray.numpy.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 – The array formed by stacking the given arrays.

Return type:

2-D array

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.]])

mxnet.ndarray.numpy.concatenate(seq, axis=0, out=None)

Join a sequence of arrays along an existing axis.

Parameters:

• a1 (sequence of ndarray) – The arrays must have the same shape, except in the dimension corresponding to axis (the first, by default).

• a2 (sequence of ndarray) – The arrays must have the same shape, except in the dimension corresponding to axis (the first, by default).

• ... (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 – The concatenated array.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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

mxnet.ndarray.numpy.copysign(x1, x2, out=None, **kwargs)

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 – The values of x1 with the sign of x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

Notes

This function differs from the original numpy.copysign 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.])

mxnet.ndarray.numpy.cos(x, out=None, **kwargs)

Cosine, element-wise.

Parameters:

• x (ndarray or scalar) – Angle, in radians (\(2 \pi\) 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 – The corresponding cosine values. This is a scalar if x is a scalar.

Return type:

ndarray or 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

mxnet.ndarray.numpy.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 – The corresponding hyperbolic cosine values. This is a scalar if x is a scalar.

Return type:

ndarray or scalar

Notes

This function only supports input type of float.

Examples

>>> np.cosh(0)
1.0

mxnet.ndarray.numpy.cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None)

Return the cross product of two (arrays of) vectors.

The cross product of a and b in \(R^3\) 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 – Vector cross product(s).

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray.

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]])

mxnet.ndarray.numpy.deg2rad(x, out=None, **kwargs)

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 – The corresponding angle in radians. This is a scalar if x is a scalar.

Return type:

ndarray or 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

mxnet.ndarray.numpy.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 – The corresponding degree values; if out was supplied this is a reference to it. This is a scalar if x is a scalar.

Return type:

ndarray

Notes

This function differs from the original numpy.degrees 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.])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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.])

mxnet.ndarray.numpy.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]])

mxnet.ndarray.numpy.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:

arrndarray

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]])

mxnet.ndarray.numpy.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 – The 2-D output array.

Return type:

ndarray

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]])

mxnet.ndarray.numpy.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 – Output result

Return type:

ndarray

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]])

mxnet.ndarray.numpy.diff(a, n=1, axis=-1, prepend=None, append=None)

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 (ndarray, optional) – Not supported yet

• append (ndarray, optional) – Not supported yet

Returns:

diff – 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.

Return type:

ndarray

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

mxnet.ndarray.numpy.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 – This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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.

mxnet.ndarray.numpy.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 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 – 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

Return type:

ndarray

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.)

mxnet.ndarray.numpy.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)]

mxnet.ndarray.numpy.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 – The array formed by stacking the given arrays, will be at least 3-D.

Return type:

ndarray

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]]])

mxnet.ndarray.numpy.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 – The differences. Loosely, this is ary.flat[1:] - ary.flat[:-1].

Return type:

ndarray

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.])

mxnet.ndarray.numpy.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 – The calculation based on the Einstein summation convention.

Return type:

ndarray

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, np.trace().

• Return a diagonal, np.diag().

• Array axis summations, np.sum().

• Transpositions and permutations, np.transpose().

• Matrix multiplication and dot product, np.matmul() np.dot().

• Vector inner and outer products, np.inner() np.outer().

• Broadcasting, element-wise and scalar multiplication, np.multiply().

• Tensor contractions, 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 np.inner(a,b). 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 np.matmul(a,b). Repeated subscript labels in one operand take the diagonal. For example, np.einsum('ii', a) is equivalent to np.trace(a).

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 np.sum(a, axis=-1), and np.einsum('ii->i', a) is like np.diag(a). 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 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)

mxnet.ndarray.numpy.empty_like(prototype, dtype=None, order='C', subok=False, shape=None)

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 – Array of uninitialized (arbitrary) data with the same shape and type as prototype.

Return type:

ndarray

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]])

mxnet.ndarray.numpy.equal(x1, x2, out=None)

Return (x1 == x2) element-wise.

Parameters:

• x1 (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).

• 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 – Output array of type bool, element-wise comparison of x1 and x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.exp(x, out=None, **kwargs)

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 – Output array, element-wise exponential of x. This is a scalar if x is a scalar.

Return type:

ndarray or 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  ])

mxnet.ndarray.numpy.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 – Output array. The number of dimensions is one greater than that of the input array.

Return type:

ndarray

mxnet.ndarray.numpy.expm1(x, out=None, **kwargs)

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 – Output array, element-wise exponential minus one: out = exp(x) - 1. This is a scalar if x is a scalar.

Return type:

ndarray or 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])

mxnet.ndarray.numpy.eye(N, M=None, k=0, dtype=<class '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 – An array where all elements are equal to zero, except for the k-th diagonal, whose values are equal to one.

Return type:

ndarray of shape (N,M)

mxnet.ndarray.numpy.fabs(x, out=None, **kwargs)

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 – An ndarray containing the absolute value of each element in x. This is a scalar if x is a scalar.

Return type:

ndarray

Examples

>>> np.fabs(-1)
1.0
>>> np.fabs(np.array([-1.2, 1.2]))s
array([ 1.2,  1.2])

mxnet.ndarray.numpy.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.

mxnet.ndarray.numpy.fix(x, out=None, **kwargs)

Round an array of floats element-wise to nearest integer towards zero. The rounded values are returned as floats.

Parameters:

xndarray

An array of floats to be rounded

outndarray, optional

Output array

Returns:

: y : ndarray of floats

Examples

>>> np.fix(3.14)
3

mxnet.ndarray.numpy.flatnonzero(a)

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 – Output array, containing the indices of the elements of a.ravel() that are non-zero.

Return type:

ndarray

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])

mxnet.ndarray.numpy.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 – A view of m with the entries of axis reversed. Since a view is returned, this operation is done in constant time.

Return type:

ndarray or scalar

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]]])

mxnet.ndarray.numpy.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 – A view of m with the columns reversed. Since a view is returned, this operation is \(\mathcal O(1)\).

Return type:

ndarray

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)

mxnet.ndarray.numpy.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 – A view of m with the rows reversed. Since a view is returned, this operation is \(\mathcal O(1)\).

Return type:

array_like

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.])

mxnet.ndarray.numpy.floor(x, out=None, **kwargs)

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 \(\lfloor x \rfloor\).

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 – The floor of each element in x, with float dtype. This is a scalar if x is a scalar.

Return type:

ndarray or 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.)

mxnet.ndarray.numpy.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

mxnet.ndarray.numpy.fmax(x1, x2, out=None, **kwargs)

Returns element-wise maximum of the input arrays with broadcasting. (Ignores NaNs)

Parameters:

• x1 (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.

• 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 – The maximum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

mxnet.numpy.ndarray or scalar

mxnet.ndarray.numpy.fmin(x1, x2, out=None, **kwargs)

Returns element-wise minimum of the input arrays with broadcasting. (Ignores NaNs)

Parameters:

• x1 (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.

• 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 – The minimum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

mxnet.numpy.ndarray or scalar

mxnet.ndarray.numpy.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 – This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

mxnet.ndarray.numpy.full(shape, fill_value, dtype=None, order='C', device=None, out=None)

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 – 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.

Return type:

ndarray

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)

mxnet.ndarray.numpy.full_like(a, fill_value, dtype=None, order='C', device=None, out=None)

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 – Array of fill_value with the same shape and type as a.

Return type:

ndarray

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])

mxnet.ndarray.numpy.gcd(x1, x2, out=None, **kwargs)

Returns the greatest common divisor of |x1| and |x2|

Parameters:

• x1 (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).

• 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 – The greatest common divisor of the absolute value of the inputs This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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)

mxnet.ndarray.numpy.greater(x1, x2, out=None)

Return the truth value of (x1 > x2) element-wise.

Parameters:

• x1 (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).

• 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 – Output array of type bool, element-wise comparison of x1 and x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.greater_equal(x1, x2, out=None)

Return the truth value of (x1 >= x2) element-wise.

Parameters:

• x1 (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).

• 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 – Output array of type bool, element-wise comparison of x1 and x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.hamming(M, dtype=None, device=None)

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 – 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.

Return type:

ndarray, shape(M,)

See also

blackman, hanning

Notes

The Hamming window is defined as

\[w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1\]

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()

mxnet.ndarray.numpy.hanning(M, dtype=None, device=None)

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 – 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.

Return type:

ndarray, shape(M,)

See also

blackman, hamming

Notes

The Hanning window is defined as

\[w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1\]

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()

mxnet.ndarray.numpy.histogram(a, bins=10, range=None, normed=None, weights=None, density=None)

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.

mxnet.ndarray.numpy.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 – A list of sub-arrays.

Return type:

list of ndarrays

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.])]

mxnet.ndarray.numpy.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 – The array formed by stacking the given arrays.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.hypot(x1, x2, out=None, **kwargs)

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 (ndarray) – Leg of the triangle(s).

• 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 – The hypotenuse of the triangle(s). This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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 – n x n array with its main diagonal set to one, and all other elements 0.

Return type:

ndarray

Examples

>>> np.identity(3)
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])

mxnet.ndarray.numpy.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 – The array of grid indices, grid.shape = (len(dimensions),) + tuple(dimensions).

Return type:

ndarray

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].

mxnet.ndarray.numpy.inner(a, b)

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 (ndarray) – If a and b are nonscalar, their last dimensions must match.

• b (ndarray) – If a and b are nonscalar, their last dimensions must match.

Returns:

out – out.shape = a.shape[:-1] + b.shape[:-1]

Return type:

ndarray

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]])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.interp(x, xp, fp, left=None, right=None, period=None)

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 – The interpolated values, same shape as x.

Return type:

float (corresponding to fp) or ndarray

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])

mxnet.ndarray.numpy.invert(x, out=None, **kwargs)

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 – Result. This is a scalar if x is a scalar.

Return type:

ndarray or 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

mxnet.ndarray.numpy.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 – True where x is negative infinity, false otherwise. This is a scalar if x is a scalar.

Return type:

ndarray or bool

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])

mxnet.ndarray.numpy.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 – True where x is positive or negative infinity, false otherwise. This is a scalar if x is a scalar.

Return type:

ndarray or bool

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 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])

mxnet.ndarray.numpy.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 – True where x is NaN, false otherwise. This is a scalar if x is a scalar.

Return type:

ndarray or bool

Notes

NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).

This function differs from the original numpy.isinf 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])

mxnet.ndarray.numpy.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 – True where x is negative infinity, false otherwise. This is a scalar if x is a scalar.

Return type:

ndarray or bool

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])

mxnet.ndarray.numpy.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 – True where x is positive infinity, false otherwise. This is a scalar if x is a scalar.

Return type:

ndarray or bool

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])

mxnet.ndarray.numpy.kron(a, b)

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 (ndarray)

• b (ndarray)

Returns:

out

Return type:

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])

mxnet.ndarray.numpy.lcm(x1, x2, out=None, **kwargs)

Returns the lowest common multiple of |x1| and |x2|

Parameters:

• x1 (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).

• 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 – The lowest common multiple of the absolute value of the inputs This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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)

mxnet.ndarray.numpy.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 – The result of x1 * 2**x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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.])

mxnet.ndarray.numpy.less(x1, x2, out=None)

Return the truth value of (x1 < x2) element-wise.

Parameters:

• x1 (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).

• 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 – Output array of type bool, element-wise comparison of x1 and x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.less_equal(x1, x2, out=None)

Return the truth value of (x1 <= x2) element-wise.

Parameters:

• x1 (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).

• 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 – Output array of type bool, element-wise comparison of x1 and x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0, device=None)

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 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.

mxnet.ndarray.numpy.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 – The natural logarithm of x, element-wise. This is a scalar if x is a scalar.

Return type:

ndarray

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 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

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray or scalar

Notes

This function only supports input type of float.

Examples

>>> np.log10(np.array([1e-15, -3.]))
array([-15.,  nan])

mxnet.ndarray.numpy.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 – Natural logarithm of 1 + x, element-wise. This is a scalar if x is a scalar.

Return type:

ndarray or 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])

mxnet.ndarray.numpy.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 – The logarithm base two of x, element-wise. This is a scalar if x is a scalar.

Return type:

ndarray

Notes

This function differs from the original 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.])

mxnet.ndarray.numpy.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 – Logarithm of exp(x1) + exp(x2). This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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

mxnet.ndarray.numpy.logical_and(x1, x2, out=None)

Compute the truth value of x1 AND x2 element-wise.

Parameters:

• x1 (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).

• 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 – 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.

Return type:

ndarray or bool

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])

mxnet.ndarray.numpy.logical_not(x, out=None, **kwargs)

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 – 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.

Return type:

bool or ndarray of bool

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])

mxnet.ndarray.numpy.logical_or(x1, x2, out=None)

Compute the truth value of x1 OR x2 element-wise.

Parameters:

• x1 (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).

• 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 – 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.

Return type:

ndarray or bool

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])

mxnet.ndarray.numpy.logical_xor(x1, x2, out=None)

Compute the truth value of x1 XOR x2 element-wise.

Parameters:

• x1 (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).

• 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 – 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.

Return type:

ndarray or bool

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])

mxnet.ndarray.numpy.logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0, device=None)

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 – num samples, equally spaced on a log scale.

Return type:

ndarray

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))

mxnet.ndarray.numpy.matmul(a, b, out=None)

Matrix product of two arrays.

Parameters:

• a (ndarray) – Input arrays, scalars not allowed.

• 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 – The matrix product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors.

Return type:

ndarray

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.

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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.)

mxnet.ndarray.numpy.maximum(x1, x2, out=None, **kwargs)

Returns element-wise maximum of the input arrays with broadcasting.

Parameters:

• x1 (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.

• 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 – The maximum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

mxnet.numpy.ndarray or scalar

mxnet.ndarray.numpy.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 (ndarray) – Input arrays

• b (ndarray) – Input arrays

Returns:

out

Return type:

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 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

mxnet.ndarray.numpy.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 – If out=None, returns a new array containing the mean values, otherwise a reference to the output array is returned.

Return type:

ndarray, see dtype parameter above

Notes

This function differs from the original numpy.mean 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)

mxnet.ndarray.numpy.median(a, axis=None, out=None, overwrite_input=None, keepdims=False)

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 – 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.

Return type:

ndarray

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.])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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

mxnet.ndarray.numpy.minimum(x1, x2, out=None, **kwargs)

Returns element-wise minimum of the input arrays with broadcasting.

Parameters:

• x1 (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.

• 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 – The minimum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

mxnet.numpy.ndarray or scalar

mxnet.ndarray.numpy.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 – This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

mxnet.ndarray.numpy.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 – Array with moved axes. This array is a view of the input array.

Return type:

ndarray

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)

mxnet.ndarray.numpy.multiply(x1, x2, out=None, **kwargs)

Multiply arguments element-wise.

Parameters:

• x1 (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).

• 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 – The multiplication of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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.

mxnet.ndarray.numpy.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.

  Added in version 1.13.

Returns:

out – x, with the non-finite values replaced. If copy is False, this may be x itself.

Return type:

ndarray

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)

mxnet.ndarray.numpy.negative(x, out=None, **kwargs)

Numerical negative, element-wise.

Parameters:

xndarray or scalar

Input array.

outndarray, 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

mxnet.ndarray.numpy.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 – Indices of elements that are non-zero.

Return type:

tuple

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))

mxnet.ndarray.numpy.not_equal(x1, x2, out=None)

Return (x1 != x2) element-wise.

Parameters:

• x1 (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).

• 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 – Output array of type bool, element-wise comparison of x1 and x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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])

mxnet.ndarray.numpy.ones(shape, dtype=None, order='C', device=None)

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 – Array of ones with the given shape, dtype, and device.

Return type:

ndarray

mxnet.ndarray.numpy.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 – Array of ones with the same shape and type as a.

Return type:

ndarray

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)

mxnet.ndarray.numpy.outer(a, b)

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 – out[i, j] = a[i] * b[j]

Return type:

(M, N) ndarray

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.]])

mxnet.ndarray.numpy.pad(x, pad_width, mode='constant', **kwargs)

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 – Padded array of rank equal to array with shape increased according to pad_width.

Return type:

ndarray

mxnet.ndarray.numpy.percentile(a, q, axis=None, out=None, overwrite_input=None, interpolation='linear', keepdims=False)

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 – Output array.

Return type:

scalar or ndarray

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])

mxnet.ndarray.numpy.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 – Result array of polynomials

Return type:

ndarray

Notes

This function differs from the original numpy.polyval 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.])

mxnet.ndarray.numpy.positive(x, out=None, **kwargs)

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 – Returned array or scalar: y = +x. This is a scalar if x is a scalar.

Return type:

ndarray or 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.])

mxnet.ndarray.numpy.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 – The bases in x1 raised to the exponents in x2. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

mxnet.ndarray.numpy.prod(a, axis=None, dtype=None, out=None, keepdims=False, initial=None)

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 – An array shaped as a but with the specified axis removed. Returns a reference to out if specified.

Return type:

ndarray, see dtype parameter above.

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

mxnet.ndarray.numpy.product(a=None, axis=_Null, dtype=_Null, keepdims=_Null, initial=_Null, out=None, name=None, **kwargs)

Return the product of array elements over a given axis.

See also

prod

equivalent function; see for details.

mxnet.ndarray.numpy.quantile(a, q, axis=None, out=None, overwrite_input=None, interpolation='linear', keepdims=False)

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 – 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.

Return type:

ndarray

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 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])

mxnet.ndarray.numpy.rad2deg(x, out=None, **kwargs)

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 – The corresponding angle in radians. This is a scalar if x is a scalar.

Return type:

ndarray or 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

mxnet.ndarray.numpy.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 – The corresponding radian values. This is a scalar if x is a scalar.

Return type:

ndarray

Notes

This function differs from the original numpy.radians 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)

mxnet.ndarray.numpy.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 – 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.

Return type:

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.]

mxnet.ndarray.numpy.reciprocal(x, out=None, **kwargs)

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 – Output array is same shape and type as x. This is a scalar if x is a scalar.

Return type:

ndarray or 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 in the following aspects: - Only support ndarray and scalar now. - where argument is not supported.

mxnet.ndarray.numpy.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 – This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

mxnet.ndarray.numpy.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 – Output array which has the same shape as a, except along the given axis.

Return type:

ndarray

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]])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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 – Output array is same shape and type as x. This is a scalar if x is a scalar.

Return type:

ndarray or scalar

Notes

This function differs from the original numpy.rint 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.])

mxnet.ndarray.numpy.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 – Output array, with the same shape as a.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.rollaxis(a, axis, start=0)

Roll the specified axis backwards, until it lies in a given position. a

Input array.

axisinteger

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)

mxnet.ndarray.numpy.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.]]])

mxnet.ndarray.numpy.round(a, decimals=0, out=None)

Round an array to the given number of decimals.

See also

around

equivalent function; see for details.

mxnet.ndarray.numpy.round_(a, decimals=0, out=None)

Round an array to the given number of decimals.

See also

around

equivalent function; see for details.

mxnet.ndarray.numpy.row_stack(arrays)

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 – The array formed by stacking the given arrays, will be at least 2-D.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.shape(a)

Return the shape of an array.

Parameters:

a (array_like) – Input array.

Returns:

shape – The elements of the shape tuple give the lengths of the corresponding array dimensions.

Return type:

tuple of ints

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)
()

mxnet.ndarray.numpy.shares_memory(a, b, max_work=None)

Determine if two arrays share memory

Parameters:

• a (ndarray) – Input arrays

• b (ndarray) – Input arrays

Returns:

out

Return type:

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 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

mxnet.ndarray.numpy.sign(x, out=None, **kwargs)

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 – The sign of x. This is a scalar if x is a scalar.

Return type:

ndarray

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.])

mxnet.ndarray.numpy.sin(x, out=None, **kwargs)

Trigonometric sine, element-wise.

Parameters:

• x (ndarray or scalar) – Angle, in radians (\(2 \pi\) 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 – The sine of each element of x. This is a scalar if x is a scalar.

Return type:

ndarray or 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.        ])

mxnet.ndarray.numpy.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 – The corresponding hyperbolic sine values. This is a scalar if x is a scalar.

Return type:

ndarray or 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

mxnet.ndarray.numpy.sometrue(data=None, axis=_Null, keepdims=_Null, out=None, name=None, **kwargs)

Check whether some values are true.

Refer to any for full documentation.

See also

any

equivalent function; see for details.

mxnet.ndarray.numpy.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 – Array of the same type and shape as a.

Return type:

ndarray

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]])

mxnet.ndarray.numpy.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 – A list of sub-arrays.

Return type:

list of ndarrays

Raises:

ValueError – If indices_or_sections is given as an integer, but a split does not result in equal division.

mxnet.ndarray.numpy.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 – 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.

Return type:

ndarray or 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])

mxnet.ndarray.numpy.square(x, out=None, **kwargs)

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 – Output array is same shape and type as x. This is a scalar if x is a scalar.

Return type:

ndarray or 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 in the following aspects: - Only support ndarray and scalar now. - where argument is not supported. - Complex input is not supported.

mxnet.ndarray.numpy.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) –

  Added in version 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 – 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.

Return type:

ndarray

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)

mxnet.ndarray.numpy.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 – The stacked array has one more dimension than the input arrays.

Return type:

ndarray

mxnet.ndarray.numpy.std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)

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 – If out is None, return a new array containing the standard deviation, otherwise return a reference to the output array.

Return type:

ndarray, see dtype parameter above.

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)

mxnet.ndarray.numpy.subtract(x1, x2, out=None, **kwargs)

Subtract arguments element-wise.

Parameters:

• x1 (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).

• 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 – The difference of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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.

mxnet.ndarray.numpy.sum(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None)

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 – 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.

Return type:

ndarray

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 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)

mxnet.ndarray.numpy.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 – Swapped array. This is always a copy of the input array.

Return type:

ndarray

mxnet.ndarray.numpy.take(a, indices, axis=None, mode='raise', out=None)

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 – The returned array has the same type as a.

Return type:

ndarray

Notes

This function differs from the original numpy.take 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.]])

mxnet.ndarray.numpy.tan(x, out=None, **kwargs)

Compute tangent element-wise. Equivalent to np.sin(x)/np.cos(x) element-wise.

Parameters:

xndarray

Input array.

outndarray, 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.

wherendarray, 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

mxnet.ndarray.numpy.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 – The corresponding hyperbolic tangent values.

Return type:

ndarray or scalar

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

mxnet.ndarray.numpy.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 (ndarray, len(shape) >= 1) – Tensors to “dot”.

• 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 \(a\otimes b\)

• axes = 1 : tensor dot product \(a\cdot b\)

• axes = 2 : (default) tensor double contraction \(a:b\)

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.]])

mxnet.ndarray.numpy.tile(A, reps)

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 – The tiled output array.

Return type:

ndarray

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`

mxnet.ndarray.numpy.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 (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.

• 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 – 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.

Return type:

ndarray

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)

mxnet.ndarray.numpy.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 – a with its axes permuted.

Return type:

ndarray

Notes

This function differs from the original numpy.transpose 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)

mxnet.ndarray.numpy.tri(N, M=None, k=0, dtype=None, device=None)

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 – Array with its lower triangle filled with ones and zero elsewhere; in other words T[i,j] == 1 for i <= j + k, 0 otherwise.

Return type:

ndarray of shape (N, M)

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.]])

mxnet.ndarray.numpy.tril(m, k=0)

Lower triangle of an array.

Return a copy of an array with elements above the k-th diagonal zeroed.

Parameters:

• m (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 – Lower triangle of m, of same shape and data-type as m.

Return type:

ndarray, shape (M, N)

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.]])

mxnet.ndarray.numpy.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) –

  Added in version 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 – The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array.

Return type:

tuple of arrays

See also

triu_indices

similar function, for upper-triangular.

mask_indices

generic function accepting an arbitrary mask function.

tril, triu

Notes

Added in version 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]])

mxnet.ndarray.numpy.triu(m, k=0)

Upper triangle of an array.

Return a copy of a matrix with the elements below the k-th diagonal zeroed.

Please refer to the documentation for tril for further details.

See also

tril

lower triangle of an array

Examples

>>> np.triu(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]])

mxnet.ndarray.numpy.triu_indices(n, k=0, m=None, device=None)

Return the indices for the upper-triangle of an (n, m) array.

Parameters:

• n (int) – The size of the arrays for which the returned indices will be valid.

• k (int, optional) – Diagonal offset (see triu for details).

• m (int, optional) –

  Added in version 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 – 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).

Return type:

tuple, shape(2) of ndarrays, shape(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]])

mxnet.ndarray.numpy.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 – Indices for the upper-triangle of arr.

Return type:

tuple, shape(2) of ndarray, shape(N)

See also

triu_indices, triu

mxnet.ndarray.numpy.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 – This is a scalar if both x1 and x2 are scalars.

Return type:

ndarray or scalar

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.

mxnet.ndarray.numpy.trunc(x, out=None, **kwargs)

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 – The truncated value of each element in x. This is a scalar if x is a scalar.

Return type:

ndarray or 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.])

mxnet.ndarray.numpy.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 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.])

mxnet.ndarray.numpy.unravel_index(indices, shape, order='C')

Converts a flat index or array of flat indices into a tuple of coordinate arrays.

Parameters:

indicesarray_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.

shapetuple 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)

mxnet.ndarray.numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)

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 – If out=None, returns a new array containing the variance; otherwise, a reference to the output array is returned.

Return type:

ndarray, see dtype parameter above

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

mxnet.ndarray.numpy.vdot(a, b)

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 – Dot product of a and b.

Return type:

ndarray

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

mxnet.ndarray.numpy.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 – A list of sub-arrays.

Return type:

list of ndarrays

See also

split

Split an array into multiple sub-arrays of equal size.

Notes

This function differs from the original numpy.degrees 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.]]])]

mxnet.ndarray.numpy.vstack(arrays, out=None)

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 – The array formed by stacking the given arrays, will be at least 2-D.

Return type:

ndarray

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.]])

mxnet.ndarray.numpy.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 (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.

• 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 – An array with elements from x where condition is True, and elements from y elsewhere.

Return type:

ndarray

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 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.]])

mxnet.ndarray.numpy.zeros(shape, dtype=None, order='C', device=None)

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 – Array of zeros with the given shape, dtype, and device.

Return type:

ndarray

mxnet.ndarray.numpy.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 – Array of zeros with the same shape and type as a.

Return type:

ndarray

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)

Modules

linalg	Namespace for operators used in Gluon dispatched by F=ndarray.
random	Namespace for operators used in Gluon dispatched by F=ndarray.