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Structure: struct cubic_grid

This structure is used to store precomputed coefficients of the cubic fit to the match function, generated by match_cubic() on an equally spaced grid in the $m_1,m_2$ parameter space. The stucture stores the coefficients as well as all the information required to generate, retrieve, and interpolate among them. The fields of this structure are:

struct cubic_grid {

int n; The number of points along the side of the grid.

float m_mn; The minimum mass of an object in the parameter space covered by the grid (solar masses).

float m_mx; The minimum mass of an object in the parameter space covered by the grid (solar masses).

float dm; The spacing between grid points (solar masses); equal to $(\hbox{\tt m\_mx}-\hbox{\tt m\_mn})/(\hbox{\tt n}-1)$.

float match; The match level (between 0 and 1) out to which the cubic fit was made.

float angle; The angle (radians) counterclockwise from the $\tau_0$ axis to the $x$ axis (see below).

int order; Twice the post-Newtonian order of the chirp templates used to compute the match function.

float srate; The sampling rate of the chirp templates used to compute the match function.

float flo; The initial frequency of the chirp templates used to compute the match function.

float ftau; The reference frequency used to define the $\tau_0,\tau_1$ coordinates.

int detector; The index of the detector site in the data file detectors.dat, used to identify a noise curve for computing the match function.

float ***coef; A pointer to the array of coefficients.

};

The cubic_grid.coef field points to an array of the form coef[0..n-1][0..n-1][0..9]. The first two indecies [i][j] identify a point in the mass parameter space: $m_1=\hbox{\tt m\_mn}+\hbox{\tt i}\times\hbox{\tt dm}$ and $m_2=\hbox{\tt m\_mn}+\hbox{\tt j}\times\hbox{\tt dm}$. The third index identifies a particular coefficient computed at that point. The individual coefficients are defined as follows: The first 7 entries [0..6] are the actual coefficients of the cubic fit to the match function $\mu$:

\begin{displaymath}
\mu = 1 + {\hbox{\tt [0]}}x^2 + {\hbox{\tt [1]}}xy
+ {\hbo...
...t [4]}}y^3 + {\hbox{\tt [5]}}x^2y
+ {\hbox{\tt [6]}}xy^2 \; ,
\end{displaymath} (9.12.215)

where $x,y$ are small displacements in directions at an angle cubic_grid.angle counterclockwise from the $\tau_0,\tau_1$ directions, respectively. If one considers only the quadratic part of this fit, the equation $\mu=\hbox{\tt cubic\_grid.match}$ defines an ellipse in the $x,y$ plane. Entries [7] and [8] are then the semimajor and semiminor axes of this ellipse, respectively (in units of seconds), and entry [9] is the angle (in radians) counterclockwise from the $x$ axis to the semimajor axis. The entries [7..9] can be computed without too much difficulty from the entries [0..2] and the value of match, but it can be useful to have them precomputed.


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