mygrad.arccosh

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

Inverse hyperbolic cosine, element-wise.

This docstring was adapted from that of numpy.arccosh [3]

Parameters:

xArrayLike

Input tensor.

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:

arccoshTensor

Tensor of the same shape as x.

See also

cosh, arcsinh, sinh, arctanh, tanh

Notes

arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [-pi, pi] and the real part in [0, inf].

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.

References

[1]

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

[2]

Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arccosh

[3]

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

Examples

>>> import mygrad as mg
>>> mg.arccosh([mg.e, 10.0])
Tensor([ 1.65745445,  2.99322285])
>>> mg.arccosh(1)
Tensor(0.0)

(Source code, png, hires.png, pdf)

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