*** Fisher matrix calculation ***
October 25, 2008: E.Komatsu
Ref: Shoji, Jeong & Komatsu, arXiv:0805.4238v2 (ApJ in press)

Here we provide a program for computing the Fisher matrix
of the 1-dimensional distance scale, R, from the galaxy power spectrum
in REAL SPACE. The details of the code are also described in Appendix of 
Shoji, Jeong & Komatsu, arXiv:0805.4238v2.
http://arxiv.org/abs/0805.4238

Users may choose to use any of the following elements:

- Linear spectrum, or non-linear spectrum in real space
- Whether to include the Kaiser boost for the amplitude
- Marginalize over the amplitude, tilt (ns), and/or running index (alpha)
- Arbitrary number of redshift bins
- Time-dependent linear galaxy bias, and the maximum wavenumber used in 
the analysis (kmax)

The effects that are NOT included in this program (yet) are:

- Marginalization over neutrino masses
- Marginalization over non-linear galaxy bias parameters
- Primordial non-Gaussianity parameter (f_NL)

For the computation with the linear spectrum, we provide the data for 
the linear power spectrum at z=30, 
"wmap5baosn_max_likelihood_matterpower_at_z=30.dat," which was
generated using CAMB code for the maximum likelihood parameters
given in Table I of Komatsu et al.(2008) [WMAP 5-year interpretation paper] 
with "WMAP5+BAO+SN". The input file for CAMB is also provided 
(wmap5baosn_max_likelihood_params.ini). 

We also provide the data for the non-linear power spectrum,
"wavenumber_wavenumber_pkd11_pkd22_pkd13_at_z=30.txt", computed from
the 3rd-order perturbation theory.

The program reports on the errors in ln(R) in percent, with some other 
parameters marginalized over: ln(amplitude), ns, and/or running index.

- To compile and use the program, edit Makefile
and simply "./make"
- It will generate executables called "fisher_distance_realspace"

For convenience, we provide a sample script, "sample.cmd", which would generate
the output like this:

 Use:
 1) Linear power spectrum in real space
 2) Non-linear power spectrum (3PT)  in real space
 Include the Kaiser boost for the amplitude?
 1) Yes
 0) No
 How many parameters (out of 3: amplitude,ns,running)
    do you wish to marginalize over?
 Select the parameters to marginalize over from:
 1) ln(amplitude)
 2) tilt (ns)
 3) running index (alpha)
 For the area, the redshift range and the number of galaxies:
 1) Read in "number.txt"
 2) Read in your favorite file
 0) Enter your choice of area (in deg^2), zmin, zmax, # of galaxies in millions
    (A new file called "number.txt" will be created.)
 read in wmap5baosn_max_likelihood_matterpower_at_z=30.dat
 Enter area (in deg^2), zmin, zmax, # of galaxies (in millions)
 in the redshift bin#=( 1 )
 (Enter 0,0,0,0 when you are done.)
 Enter the values of
 bias and kmax [h Mpc^-1] in 
 1.500 < z < 3.500
 read in wavenumber_pkd11_pkd22_pkd13_at_z=30.txt
 === redshift bin#=( 1 ) ===
 1.500 < z < 3.500
 Vsur = 3.48185 h^-3 Gpc^3
 Ngal = 1.00000 millions
 ngal = 0.28720 10^-3 h^3 Mpc^-3
 bias = 2.00000
 beta = 0.48413
 kmax = 0.43000 h Mpc^-1
 Err[lnR](%)  =  0.99638
 *** marginalized over ln(amplitude) ***
 Err[ln(A)][%]=  3.94688
 *** marginalized over tilt (ns) ***
 Err[ns]      =  0.01292
 *** marginalized over running index (alpha) ***
 Err[alpha]   =  0.01398
 
 Enter area (in deg^2), zmin, zmax, # of galaxies (in millions)
 in the redshift bin#=( 2 )
 (Enter 0,0,0,0 when you are done.)
 Enter the values of
 bias and kmax [h Mpc^-1] in 
 3.500 < z < 6.500
 read in wavenumber_pkd11_pkd22_pkd13_at_z=30.txt
 === redshift bin#=( 2 ) ===
 3.500 < z < 6.500
 Vsur =11.01239 h^-3 Gpc^3
 Ngal =10.00000 millions
 ngal = 0.90807 10^-3 h^3 Mpc^-3
 bias = 4.00000
 beta = 0.24837
 kmax = 1.00000 h Mpc^-1
 Err[lnR](%)  =  0.27386
 *** marginalized over ln(amplitude) ***
 Err[ln(A)][%]=  1.06127
 *** marginalized over tilt (ns) ***
 Err[ns]      =  0.00390
 *** marginalized over running index (alpha) ***
 Err[alpha]   =  0.00237
 
 Enter area (in deg^2), zmin, zmax, # of galaxies (in millions)
 in the redshift bin#=( 3 )
 (Enter 0,0,0,0 when you are done.)
 === combined ===
 Vsur =14.49424 h^-3 Gpc^3
 Ngal =11.00000 millions
 ngal = 0.75892 10^-3 h^3 Mpc^-3
 Err[lnR](%)  =  0.26499
 *** marginalized over ln(amplitude) ***
 Err[ln(A)][%]=  1.00694
 *** marginalized over tilt (ns) ***
 Err[ns]      =  0.00365
 *** marginalized over running index (alpha) ***
 Err[alpha]   =  0.00224