Function:

`int match_cubic(float m1ref, float m2ref, float matchcont, int order, float srate,
float flo, float ftau, char *noisefile, float *semimajor,
float *semiminor, float *theta, float mcoef[])
`

This function is almost identical to `match_parab()`, except
that it attempts to fit the match to a cubic form:

(9.10.214) |

The arguments to the function are:

`m1ref`: Input. Mass of body 1 for the reference chirp (solar masses).`m2ref`: Input. Mass of body 2 for the reference chirp (solar masses).`matchcont`: Input. The value of the match contour.`order`: Input. Twice the post-Newtonian order to be used in computing the templates;*i.e.*, the power of used in the post-Newtonian expansion.`srate`: Input. The sample rate, in Hz. Used to determine the spacing of frequency bins for the templates.`flo`: Input. The low-frequency cutoff to impose, in Hz. Within the code, this is used as the starting frequency of the templates; see`make_filters()`.`ftau`: Input. The frequency used to find and ; see Eqs. () and (). Different authors use different conventions for this frequency--for example, Sathyaprakash uses the seismic wall frequency, whereas Owen uses the frequency at which the noise power is minimum.`ftau`is arbitrary, but should be used consistently: pick a value and stick with it.`noisefile`: Input. A character string that specifies the name of a data file containing information about the noise power spectrum of a dectector. See`noise_power()`for extended discussion.`semimajor`: Output. The semimajor axis of the ellipse along which the match has the value`matchcont`.`semiminor`: Output. The semiminor axis of the ellipse.`theta`: Output. The counterclockwise angle, in radians, between`semimajor`and the axis.`mcoef`: Output. The array`mcoef[0..6]`contains the coefficients of the parabolic fit to the match: .

The function works in almost exactly the same manner as `match_parab()`. In particular, it constructs an ellipse using
the parabolic piece of the cubic fit, and checks the goodness
of the fit along that ellipse. Because the ellipse is not made
from the full functional form of the fit, the fit does not have
constant value along the ellipse. Thus, `match_cubic()`
does not really find contours with constant match value
`matchcont`. The ellipses it finds, however, generally
have match values fairly close to `matchcont`; and, more
importantly, the match values along the ellipse are never less
than `matchcont`.

- Author: Scott Hughes, hughes@tapir.caltech.edu