Fisher matrix calculation

The Fisher matrix associated with the signal model and its inversion is calculated using this code.

Prerequisites

The code is written in standard C and it's mostly based on functions used in search. Arbitrary-precision interval arithmetic Arb library is used to invert the (usually) not-very-well posed Fisher matrix, so it has to be installed beforehand. Arb requires FLINT, MPFR, and either MPIR or GMP.

Compilation

Run make fisher in search/network/src-cpu - resulting binary is called fisher. Modify the Makefile (especially the variable ARB_DIR) to fit your system.

Full list of switches

For the full list of options, type

% ./fisher --help

Switch	Description
-data	Data directory (default is `.`)
-ident	Frame number
-band	Band number
-fpo	Reference band frequency `fpo` value
-dt	Data sampling time dt (default value: `0.5`)
-usedet	Use only detectors from string (default is `use all available`)
-addsig	Add signal with parameters from `<file>`

Also:


--help	This help

Example

Minimal call to fisher is as follows:

% ./fisher -data 2d_0.25 -ident 001 -band 1234 -usedet H1 -dt 2 -nod 2 -addsig sigfile

where

data is the base directory of input data files (e.g., this Gaussian data),
Sampling time dt is $2 s$ ,
ident is the number of time frame to be analyzed ( $001$ ),
nod number of days is $2$ ,
band is the number of the frequency band (see the input data structure for details).
usedet switch to chose a detector (here $H1$ )
addsig switch to chose a file with signal data

The sigfile file consists of 8 numbers:

frequency [radians, between 0 and $\pi$ ] above fpo
spindown (frequency time derivative) [ $\mathrm{Hz/s}$ ]
declination [radians, between $\pi$ and $-\pi$ ]
right ascension [radians, between 0 and $2\pi$ ]
4 amplitudes $a_1, a_2, a_3, a_4$

e.g.,

1.431318175386891
-7.9539e-9
0.6363615896875658
4.396884357060633
7.764354801848407e-3
-1.422468474545797e-2
-1.559826840666228e-2
-8.623005535014139e-3

The amplitudes $a_1, a_2, a_3, a_4$ correspond to the signal amplitude model

$h = a_1 h_1 + a_2 h_2 + a_3 h_3 + a_4 h_4,$

where

$h(t) = \left(a_1 a(t) + a_2 b(t)\right)\cos(\psi) + \left(a_3 a(t) + a_4 b(t)\right)sin(\psi),$

with $\psi(f, \dot{f}, \delta, \alpha, t)$ being the phase of the signal, and $a$ and $b$ the amplitude modulation functions (calculated in the modvir function).

Example output

Number of days is 2
Input data directory is 2d_0.25
Frame and band numbers are 1 and 1234
The reference frequency fpo is 308.859375
The data sampling time dt is 2.000000
Adding signal from 'sigfile'
Settings - number of detectors: 1
Using H1 IFO as detector #0... 2d_0.25/001/H1/xdatc_001_1234.bin as input time series data
Using 2d_0.25/001/H1/DetSSB.bin as detector H1 ephemerids...
The Fisher matrix:
1.4602194451385117e+10 9.6224528459395950e+14 1.0472943290223141e+10 1.9109038902196317e+11 -5.6465717962684985e+06 -4.1172082782989331e+06 -2.9517981884375727e+06 7.0470722915177587e+06 
9.6224528459395950e+14 6.7134859540063060e+19 6.5156368686556762e+14 1.1289208033400466e+16 -3.3340781322676825e+11 -2.4401458951787103e+11 -1.7381344007331134e+11 4.1673668536337537e+11 
1.0472943290223141e+10 6.5156368686556762e+14 8.0545511145922174e+09 1.5540065972734366e+11 -4.6112260504154256e+06 -3.4059196396034071e+06 -2.3414307185722976e+06 5.7018637665277841e+06 
1.9109038902196317e+11 1.1289208033400466e+16 1.5540065972734366e+11 3.1204237328935298e+12 -9.2852217833914995e+07 -6.9173973293523684e+07 -4.6213130625602841e+07 1.1410003283718885e+08 
-5.6465717962684985e+06 -3.3340781322676825e+11 -4.6112260504154256e+06 -9.2852217833914995e+07 7.6814199126393523e+03 -1.6833193661163169e-03 0.0000000000000000e+00 0.0000000000000000e+00 
-4.1172082782989331e+06 -2.4401458951787103e+11 -3.4059196396034071e+06 -6.9173973293523684e+07 -1.6833193661163169e-03 1.0351065428550139e+04 0.0000000000000000e+00 0.0000000000000000e+00 
-2.9517981884375727e+06 -1.7381344007331134e+11 -2.3414307185722976e+06 -4.6213130625602841e+07 0.0000000000000000e+00 0.0000000000000000e+00 7.6814199126393523e+03 -1.6833193661163169e-03 
7.0470722915177587e+06 4.1673668536337537e+11 5.7018637665277841e+06 1.1410003283718885e+08 0.0000000000000000e+00 0.0000000000000000e+00 -1.6833193661163169e-03 1.0351065428550139e+04 
Inverting the Fisher matrix...
Diagonal elements of the covariance matrix:
2.561275e-04 3.867944e-18 2.363103e-03 9.137957e-04 1.343874e+05 4.107046e+04 3.329715e+04 1.117611e+05