jax.numpy.arcsinh

jax.numpy.arcsinh(x, /)

Calculate element-wise inverse of hyperbolic sine of input.

JAX implementation of numpy.arcsinh.

The inverse of hyperbolic sine is defined by:

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

Parameters:

x (ArrayLike) – input array or scalar.

Returns:

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

Return type:

Array

Note

• jnp.arcsinh returns nan for values outside the range (-inf, inf).

• jnp.arcsinh follows the branch cut convention of numpy.arcsinh for complex inputs.

See also

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

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

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

Examples

>>> x = jnp.array([[-2, 3, 1],
...                [4, 9, -5]])
>>> with jnp.printoptions(precision=3, suppress=True):
...   jnp.arcsinh(x)
Array([[-1.444,  1.818,  0.881],
       [ 2.095,  2.893, -2.312]], dtype=float32)

For complex-valued inputs:

>>> x1 = jnp.array([4-3j, 2j])
>>> with jnp.printoptions(precision=3, suppress=True):
...   jnp.arcsinh(x1)
Array([2.306-0.634j, 1.317+1.571j], dtype=complex64)