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

The sigfile file consists of 8 numbers:

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 correspond to the signal amplitude model

where

with being the phase of the signal, and and 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