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Function: match_cubic()

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:


\begin{displaymath}
m = 1 + a x^2 + 2b xy + c y^2 + dx^3 + e y^3 + fx^2y + g xy^2
\end{displaymath} (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 $(v/c)$ 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 $\tau_0$ and $\tau_1$; 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 $P(f)$ 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 $\tau_0$ axis.
mcoef: Output. The array mcoef[0..6] contains the coefficients of the parabolic fit to the match: $\mu_{\rm fit} = 1 + {\hbox{\tt mcoef[0]}} x^2 + {\hbox{\tt mcoef[1]}} xy +
{\hb...
...ox{\tt mcoef[4]}} y^3 + {\hbox{\tt mcoef[5]}} x^2y +
{\hbox{\tt mcoef[6]}} xy^2$.

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


next up previous contents
Next: Example: match_fit program Up: GRASP Routines: Template Bank Previous: Function: match_parab()   Contents
Bruce Allen 2000-11-19