mygrad.arctan#

class mygrad.arctan(x: ArrayLike, out: Tensor | ndarray | None = None, *, where: Mask = True, dtype: DTypeLikeReals = None, constant: bool | None = None)#

Inverse tangent, element-wise.

This docstring was adapted from that of numpy.arctan [1]

Parameters:
xArrayLike
outOptional[Union[Tensor, 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 tensor is returned.

constantOptional[bool]

If True, this tensor is treated as a constant, and thus does not facilitate back propagation (i.e. constant.grad will always return None).

Defaults to False for float-type data. Defaults to True for integer-type data.

Integer-type tensors must be constant.

whereMask

This condition is broadcast over the input. At locations where the condition is True, the out tensor will be set to the ufunc result. Elsewhere, the out tensor will retain its original value. Note that if an uninitialized out tensor is created via the default out=None, locations within it where the condition is False will remain uninitialized.

dtypeOptional[DTypeLikeReals]

The dtype of the resulting tensor.

Returns:
outTensor

See also

arctan2

The “four quadrant” arctan of the angle formed by (x, y) and the positive x-axis.

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, arctan is a complex analytic function that has [1j, infj] and [-1j, -infj] as branch cuts, and is continuous from the left on the former and from the right on the latter.

The inverse tangent is also known as atan or tan^{-1}.

References

Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

Examples

We expect the arctan of 0 to be 0, and of 1 to be pi/4:

>>> import mygrad as mg
>>> mg.arctan([0, 1])
Tensor([ 0.        ,  0.78539816])

>>> mg.pi / 4
0.78539816339744828
Attributes:
identity
signature

Methods

accumulate([axis, dtype, out, constant])

Not implemented

at(indices[, b, constant])

Not implemented

outer(b, *[, dtype, out])

Not Implemented

reduce([axis, dtype, out, keepdims, ...])

Not Implemented

reduceat(indices[, axis, dtype, out])

Not Implemented

resolve_dtypes(dtypes, *[, signature, ...])

Find the dtypes NumPy will use for the operation.
__init__(*args, **kwargs)#

Methods

__init__(*args, **kwargs)

accumulate([axis, dtype, out, constant])

Not implemented

at(indices[, b, constant])

Not implemented

outer(b, *[, dtype, out])

Not Implemented

reduce([axis, dtype, out, keepdims, ...])

Not Implemented

reduceat(indices[, axis, dtype, out])

Not Implemented

resolve_dtypes(dtypes, *[, signature, ...])

Find the dtypes NumPy will use for the operation.

Attributes

identity

nargs

nin

nout

ntypes

signature

types