jax.numpy.arccosh — JAX documentation (original) (raw)

jax.numpy.arccosh#

jax.numpy.arccosh(x, /)[source]#

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.arccoshfor 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)