Calculate element-wise inverse of hyperbolic cosine of input.
JAX implementation of numpy.arccosh.
The inverse of hyperbolic cosine is defined by:
\[arccosh(x) = \ln(x + \sqrt{x^2 - 1})\]
x (ArrayLike) – input array or scalar.
An array of same shape as x containing the inverse of hyperbolic cosine of each element of x, promoting to inexact dtype.
Note
jnp.arccosh returns nan for real-values in the range [-inf, 1).
jnp.arccosh follows the branch cut convention of numpy.arccosh for complex inputs.
Examples
>>> x = jnp.array([[1, 3, -4],
... [-5, 2, 7]])
>>> with jnp.printoptions(precision=3, suppress=True):
... jnp.arccosh(x)
Array([[0. , 1.763, nan],
[ nan, 1.317, 2.634]], dtype=float32)
For complex-valued input:
>>> x1 = jnp.array([-jnp.inf+0j, 1+2j, -5+0j]) >>> with jnp.printoptions(precision=3, suppress=True): ... jnp.arccosh(x1) Array([ inf+3.142j, 1.529+1.144j, 2.292+3.142j], dtype=complex64)
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