jax.numpy.arccosh

jax.numpy.arccosh(x, /)

Calculate element-wise inverse of hyperbolic cosine of input.

JAX implementation of numpy.arccosh.

The inverse of hyperbolic cosine is defined by:

\[arccosh(x) = \ln(x + \sqrt{x^2 - 1})\]

Parameters:

x (ArrayLike) – input array or scalar.

Returns:

An array of same shape as x containing the inverse of hyperbolic cosine of each element of x, promoting to inexact dtype.

Return type:

Array

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.

See also

• jax.numpy.cosh(): Computes the element-wise hyperbolic cosine of the input.

• jax.numpy.arcsinh(): Computes the element-wise inverse of hyperbolic sine of the input.

• jax.numpy.arctanh(): Computes the element-wise inverse of hyperbolic tangent of the input.

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)