pro kstwo, data1, data2, D, prob ;+ ; NAME: ; KSTWO ; PURPOSE: ; Return the two-sided Kolmogorov-Smirnov statistic ; EXPLANATION: ; Returns the Kolmogorov-Smirnov statistic and associated probability ; that two arrays of data values are drawn from the same distribution ; Algorithm taken from procedure of the same name in "Numerical ; Recipes" by Press et al., 2nd edition (1992), Chapter 14 ; ; CALLING SEQUENCE: ; kstwo, data1, data2, D, prob ; ; INPUT PARAMETERS: ; data1 - vector of data values, at least 4 data values must be included ; for the K-S statistic to be meaningful ; data2 - second set of data values, does not need to have the same ; number of elements as data1 ; ; OUTPUT PARAMETERS: ; D - floating scalar giving the Kolmogorov-Smirnov statistic. It ; specifies the maximum deviation between the cumulative ; distribution of the data and the supplied function ; prob - floating scalar between 0 and 1 giving the significance level of ; the K-S statistic. Small values of PROB show that the ; cumulative distribution function of DATA1 is significantly ; different from DATA2 ; ; EXAMPLE: ; Test whether two vectors created by the RANDOMN function likely came ; from the same distribution ; ; IDL> data1 = randomn(seed,40) ;Create data vectors to be ; IDL> data2 = randomn(seed,70) ;compared ; IDL> kstwo, data1, data2, D, prob & print,D,prob ; ; PROCEDURE CALLS ; procedure PROB_KS - computes significance of K-S distribution ; ; REVISION HISTORY: ; Written W. Landsman August, 1992 ; FP computation of N_eff H. Ebeling/W. Landsman March 1996 ; Fix for arrays containing equal values J. Ballet/W. Landsman Oct. 2001 ; Fix index when maximum difference is at array end Renbin Yan Dec 2008 ; Handle large number when computing N_err D. Schnitzeler/WL Sep 2010 ;- On_error, 2 compile_opt idl2 if ( N_params() LT 4 ) then begin print,'Syntax - KSTWO, data1, data2, d, prob' return endif n1 = N_elements( data1 ) if ( N1 LE 3 ) then message, \$ 'ERROR - Input data values (first param) must contain at least 4 values' n2 = N_elements( data2 ) if ( n2 LE 3 ) then message, \$ 'ERROR - Input data values (second param) must contain at least 4 values' sortdata1 = data1[ sort( data1 ) ] ;Sort input arrays into sortdata2 = data2[ sort( data2 ) ] ;ascending order fn1 = ( findgen( n1 +1 ) ) / n1 ;updated Dec 2008 fn2 = ( findgen( n2 +1) ) / n2 j1 = 0l & j2 = 0l id1 = lonarr(n1+n2) & id2 = id1 i = 0l ; Form the two cumulative distribution functions, marking points where one ; must test their difference while ( j1 LT N1 ) and ( j2 LT n2 ) do begin d1 = sortdata1[j1] d2 = sortdata2[j2] if d1 LE d2 then j1 = j1 +1 if d2 LE d1 then j2 = j2 +1 id1[i] = j1 & id2[i] = j2 i = i+1 endwhile id1 = id1[0:i-1] & id2 = id2[0:i-1] ; The K-S statistic D is the maximum difference between the two distribution ; functions D = max( abs( fn1[id1] - fn2[id2] ) ) N_eff = long64(n1)*n2/ float(n1 + n2) ;Effective # of data points PROB_KS, D, N_eff, prob ;Compute significance of statistic return end