n-pcf

C++ code for FFT-based estimation of 2- and 3-points correlation functions of 2D signals sampled on structured grids.

Author: Nicolas Venkovic.

email: venkovic@gmail.com.

Supporting document:

• Jupyter notebook (npcf.ipynb).

Compiler and dependencies:

• g++, FFTW3, Eigen.
• Enable g++ to link FFTW3 shared libraries with the option -lfftw3.
• Download Eigen header and source files. Copy the Eigen folder as is in the current directory.

Installation:

$ make -f Makefile CONF=Release

Usage:

$ ./dist/GNU-Linux/npcf nx ny x0 y0 verb data.in

data.in: 2D csv data file.

nx, ny: Size of the 2D sub-slice of data to analyze.

x0, y0: upper left starting point of sub-slice in data file.

verb: Controls display settings.

• 0: No output.
• 1: Error messages only.
• 2: Error messages / 2D slice of data / Comparison of S2 and S3 results.

Example:

$ ./dist/GNU-Linux/npcf 30 30 0 0 2 im00.csv

s2(0,0) = 0.668750, s2(1,0) = 0.626250, s2(2,0) = 0.590625
s2(0,0) = 0.668750, s2(0,1) = 0.631250, s2(0,2) = 0.602500
s3(0,0,0,0) = 0.668750, s3(1,0,0,0) = 0.626250, s3(2,0,0,0) = 0.590625
s3(0,0,0,0) = 0.668750, s3(0,1,0,0) = 0.631250, s3(0,2,0,0) = 0.602500
s3(0,0,0,0) = 0.668750, s3(0,0,1,0) = 0.626250, s3(0,0,2,0) = 0.590625
s3(0,0,0,0) = 0.668750, s3(0,0,0,1) = 0.631250, s3(0,0,0,2) = 0.602500


s2(0,0) = 0.668750, s2(-1,0) = 0.626250, s2(-2,0) = 0.590625
s2(0,0) = 0.668750, s2(0,-1) = 0.631250, s2(0,-2) = 0.602500
s3(0,0,0,0) = 0.668750, s3(-1,0,0,0) = 0.626250, s3(-2,0,0,0) = 0.590625
s3(0,0,0,0) = 0.668750, s3(0,-1,0,0) = 0.631250, s3(0,-2,0,0) = 0.602500
s3(0,0,0,0) = 0.668750, s3(0,0,-1,0) = 0.626250, s3(0,0,-2,0) = 0.590625
s3(0,0,0,0) = 0.668750, s3(0,0,0,-1) = 0.631250, s3(0,0,0,-2) = 0.602500

Public functions of NpcfTools:

• void get_anisotropic_map_s2(int nx, int ny, string fname="")

• void get_anisotropic_map_s3(int nx, int ny, int dx1, int dy1, int dx2, int dy2, string fname="")

Example:

#include "NpcfTools.h"

NpcfTools npcf("im00.csv");
npcf.get_anisotropic_map_s2(60,60,"im00.s2");
npcf.get_anisotropic_map_s3(60,60,0,1,1,0,"im00.s3");

Formats of output files

Anisotropic estimators:

• foo.s2 : Complete anisotropic 2-pcf estimator.

  nx,ny
  s2(-nx,0)  , s2(-nx,1)  , ...., s2(-nx,ny-1)  , s2(-nx,ny)
  s2(-nx+1,0), s2(-nx+1,1), ...., s2(-nx+1,ny-1), s2(-nx+1,ny)
  s2(-nx+2,0), s2(-nx+2,1), ...., s2(-nx+2,ny-1), s2(-nx+2,ny)
     :             :                  :               :
     :             :                  :               :
  s2(-1,0)   , s2(-1,1)   , ...., s2(-1,ny-1)   , s2(-1,ny)
  s2(0,0)    , s2(0,1)    , ...., s2(0,ny-1)    , s2(0,ny)
  s2(1,0)    , s2(1,1)    , ...., s2(1,ny-1)    , s2(1,ny)
     :             :                  :               :
     :             :                  :               :
  s2(nx-1,0) , s2(nx-1,1) , ...., s2(nx-1,ny-1) , s2(nx-1,ny)
  s2(nx,0)   , s2(nx,1)   , ...., s2(nx,ny-1)   , s2(nx,ny)
  

• foo.s3 : Anisotropic 3-pcf estimator of point configurations with fixed opening and rotation angles.

  nx,ny
  dx1,dy1,dx2,dyy
  s3(0,0,0,0)          , s3(0,0,dx2,dy2)          , ...., s3(0,0,ny*dx2,ny*dy2)
  s3(dx1,dy1,0,0)      , s3(dx1,dy1,dx2,dy2)      , ...., s3(dx,dy,ny*dx2,ny*dy2)
  s3(2*dx1,2*dy1,0,0)  , s3(2*dx1,2*dy1,dx2,dy2)  , ...., s3(2*dx,2*dy,ny*dx2,ny*dy2)
        :                          :                                   :
        :                          :                                   :
  s3(nx*dx1,nx*dy1,0,0), s3(nx*dx1,nx*dy1,dx2,dy2), ...., s3(nx*dx1,nx*dy1,ny*dx2,ny*dy2)
  

Pending tasks:

• Error to fix when almost all data entries are equal. For example, try

  $ ./dist/GNU-Linux/npcf 12 11 0 0 im00.csv

• Compute hs3 on minimum domain and copy values to other components instead of repeating calculations.

• Write subroutines to write output files.

• Complete implementation of S4(dx1,dy1,dx2,dy2,dx3,dy3).

• Verify implementation for odd nx and ny.

• Add inference subroutines.