This function integrates Lai and Shapiro's frequency and phase evolution equations, () and (), for a hung-up collapsed core. We use numerical recipes odeint, an adaptive step size 4th order Runge-Kutta integrator for the frequency integration and a simple trapezoidal integration for the phase.

The arguments are:

`Phi[]`: Output. An array which holds the phase of the gravitational wave in radians at equally spaced time intervals.`Phi[]`must be allocated sufficient memory before being passed to`LS_phas_and_freq()`.`u[]`: Output. An array which holds the reduced frequency (frequency divided by ) of the gravitational wave at equally spaced time intervals.`u[]`must be allocated sufficient memory before being passed to`LS_phas_and_freq()`.`A`: Input. The Amplitude as calculated in ()`fmax`: Input. The maximum frequency, . Usually taken from the appropriate field of a`LS_physical_constants`structure.`dt`: Input. The time interval (in seconds) at which the phase and frequency values should be output.`n_samples`: Input. The number of phase and frequency values to be output (i.e. the number of elements in the arrays`Phi[]`and`u[]`).

- Authors: Warren G. Anderson, warren@ricci.phys.uwm.edu and Patrick Brady, patrick@tapir.caltech.edu