def theta_calc(x): """ helper for hadamard decomp. """ return jnp.real(2 * jnp.arccos(1 / in_the_arc(x)))
def b_calc(x): """ helper for hadamard decomp. """ return jnp.real((-1j * (jnp.arcsinh(1) + log_b(x))))
def a_calc(x): """ helper for hadamard decomp. """ return jnp.real((-(0.5) * 1j * (2 * jnp.arcsinh(1) + first_log_a(x) + second_log_a(x))))
def theta_calc(x): return jnp.real(2 * jnp.arccos(1 / in_the_arc(x)))
def b_calc(x): return jnp.real((-1j * (jnp.arcsinh(1) + log_b(x))))
def a_calc(x): return jnp.real((-(0.5) * 1j * (2 * jnp.arcsinh(1) + first_log_a(x) + second_log_a(x))))