mygrad.arcsin

class mygrad.arcsin(x: ArrayLike, out: Optional[Union[Tensor, ndarray]] = None, *, where: Mask = True, dtype: DTypeLikeReals = None, constant: Optional[bool] = None)

Inverse sine, element-wise.

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

Parameters

xArrayLike

y-coordinate on the unit circle.

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

angleTensor

The inverse sine of each element in x, in radians and in the closed interval [-pi/2, pi/2].

See also

sin, cos, arccos, tan, arctan, arctan2

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.

For complex-valued input, arcsin is a complex analytic function that has, by convention, the branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter.

The inverse sine is also known as asin or sin^{-1}.

References

1

Retrieved from https://numpy.org/doc/stable/reference/generated/numpy.arcsin.html

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/

Examples

>>> import mygrad as mg
>>> mg.arcsin(1)     # pi/2
Tensor(1.5707963267948966)
>>> mg.arcsin(-1)    # -pi/2
Tensor(-1.5707963267948966)
>>> mg.arcsin(0)
Tensor(0.0)

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

__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

Attributes

identity
nargs
nin
nout
ntypes
signature
types