+++ /dev/null
-#!/usr/bin/env python
-
-# Copyright (c) 2010-2011, 2014. The SimGrid Team.
-# All rights reserved.
-
-# This program is free software; you can redistribute it and/or modify it
-# under the terms of the license (GNU LGPL) which comes with this package.
-
-#---------------------------------------------------------------------------------------------------
-# Example invokation:
-# % ./regress.py griffon_skampi_pt2pt.ski.dat 65536 120832
-#
-#
-# Given two vectors of same length n: message size S(.. s_i ..), and communication time T( .. t_i .. )
-# where t_i is the time associated to a mesage size s_i, computes the segmentation of the vectors
-# in 3 segments such that linear regressions on the 3 segments maximize correlation.
-# The metric for correlation is now the cumulative, log error of the estimated time value given
-# by regression, to the real time value.
-#
-# Call r(X[i:j],Y[i:j]) = ax + b the regression line for data of X,Y between indices i and j
-# Call E[i:j] = E( e_i, .., e_j) the vector of estimates from the regression, where e_i = a*S[i] + b
-# Call mean_logerr( T,T' ) the average log error of paired elements t_i and t'_i, of vectors len n T and T' resp.
-# i.e mean_logerr( T,T' ) = 1/n * Sum_i^n ( exp(| ln(t_i)-ln(t'_i)|) - 1 )
-#
-# The script computes indices k and l, s.t.
-# mean_logerr( r(S[0:k],T[0:k]) , E[0,k] ) +
-# mean_logerr( r(S[k:l],T[k:l]) , E[k,l] ) +
-# mean_logerr( r(S[l:n],T[l:n]) , E[l,n] )
-# is minimum.
-#---------------------------------------------------------------------------------------------------
-
-import sys
-from math import sqrt,log,exp
-
-
-if len(sys.argv) != 2 and len(sys.argv) != 4:
- print("Usage : {} datafile".format(sys.argv[0]))
- print("or : {0} datafile p1 p2".format(sys.argv[0]))
- print("where : p1 < p2 belongs to sizes in datafiles")
- sys.exit(-1)
-
-if len(sys.argv) == 4:
- p1=int(sys.argv[2])
- p2=int(sys.argv[3])
-
-##-----------------------------------------
-## avg : return average of a list of values
-## param l list of values
-##-----------------------------------------
-def avg (l):
- sum=0
- for e in l:
- sum=sum+e;
- return sum/len(l)
-
-##-------------------------------------------------
-## cov : covariance
-## param X first data vector (..x_i..)
-## param Y second data vector (..y_i..)
-## = 1/n \Sum_{i=1}^n (x_i - avg(x)) * (y_i - avg(y))
-##--------------------------------------------------
-def cov(X,Y):
- assert(len(X)==len(Y))
- n=len(X) # n=len(X)=len(Y)
- avg_X = avg( X )
- avg_Y = avg( Y )
- S_XY=0
- for i in range(n):
- S_XY = S_XY + ((X[i]-avg_X)*(Y[i]-avg_Y))
-
- return (S_XY/n)
-
-
-##----------------------------------
-## variance : variance
-## param X data vector ( ..x_i.. )
-## (S_X)^2 = (Sum ( x_i - avg(X) )^2 ) / n
-##----------------------------------
-def variance( X ):
- S_X2 = 0
- n = len( X )
- avg_X = avg ( X )
- for i in range(n):
- S_X2 = S_X2 + ((X[i] - avg_X)**2)
-
- return (S_X2/n)
-
-##----------------------------------
-## mean log_error
-## param X data vector ( ..x_i.. ), length n
-## param Y data vector ( ..y_i.. ), length n
-## return mean( 1/n * Sum_i^n ( exp(| ln(x_i)-ln(y_i)|) - 1 )
-##----------------------------------
-def mean_logerr( X,Y ):
- assert( len(X) == len(Y) )
- E = list(); # the list of errors
- for i in range(len(X)):
- E.append( exp(abs(log(X[i])-log(Y[i])))-1 )
- return (avg( E ))
-
-
-##-----------------------------------------------------------------------------------------------
-## correl_split_weighted_logerr : compute regression on each segment and
-## return the weigthed sum of correlation coefficients
-## param X first data vector (..x_i..)
-## param Y second data vector (..x_i..)
-## param segments list of pairs (i,j) where i refers to the ith value in X, and jth value in X
-## return (C,[(i1,j1,X[i1],X[j1]), (i2,j2,X[i2],X[j2]), ....]
-## where i1,j1 is the first segment, c1 the correlation coef on this segment, n1 the number of values
-## i2,j2 is the second segment, c2 the correlation coef on this segment, n2 the number of values
-## ...
-## and C=c1/n1+c2/n2+...
-##-----------------------------------------------------------------------------------------------
-def correl_split_weighted_logerr( X , Y , segments ):
- # expects segments = [(0,i1-1),(i1-1,i2-1),(i2,len-1)]
- correl = list()
- interv = list() # regr. line coeffs and range
- glob_err=0
- for (start,stop) in segments:
- #if start==stop :
- # return 0
- S_XY= cov( X [start:stop+1], Y [start:stop+1] )
- S_X2 = variance( X [start:stop+1] )
- a = S_XY/S_X2 # regr line coeffs
- b = avg ( Y[start:stop+1] ) - a * avg( X[start:stop+1] )
- # fill a vector (Z) with predicted values from regression
- Z=list()
- for i in range(start,stop+1):
- Z.append( a * X[i] + b )
- # compare real values and computed values
- e = mean_logerr( Y[start:stop+1] , Z )
- correl.append( (e, stop-start+1) ); # store correl. coef + number of values (segment length)
- interv.append( (a,b, X[start],X[stop],e) );
-
- for (e,l) in correl:
- glob_err = glob_err + (e*l/len( X )) # the average log err for this segment (e) is
- # weighted by the number of values of the segment (l) out of the total number of values
-
- #print("-> glob_corr={}\n".format(glob_corr))
- return (glob_err,interv);
-
-##-----------------------------------------------------------------------------------------------
-## correl_split_weighted : compute regression on each segment and
-## return the weigthed sum of correlation coefficients
-## param X first data vector (..x_i..)
-## param Y second data vector (..x_i..)
-## param segments list of pairs (i,j) where i refers to the ith value in X, and jth value in X
-## return (C,[(i1,j1,X[i1],X[j1]), (i2,j2,X[i2],X[j2]), ....]
-## where i1,j1 is the first segment, c1 the correlation coef on this segment, n1 the number of values
-## i2,j2 is the second segment, c2 the correlation coef on this segment, n2 the number of values
-## ...
-## and C=c1/n1+c2/n2+...
-##-----------------------------------------------------------------------------------------------
-def correl_split_weighted( X , Y , segments ):
- # expects segments = [(0,i1-1),(i1-1,i2-1),(i2,len-1)]
- correl = list();
- interv = list(); # regr. line coeffs and range
- glob_corr=0
- sum_nb_val=0
- for (start,stop) in segments:
- sum_nb_val = sum_nb_val + stop - start;
- #if start==stop :
- # return 0
- S_XY= cov( X [start:stop+1], Y [start:stop+1] )
- S_X2 = variance( X [start:stop+1] )
- S_Y2 = variance( Y [start:stop+1] ) # to compute correlation
- if S_X2*S_Y2 == 0:
- return (0,[])
- c = S_XY/(sqrt(S_X2)*sqrt(S_Y2))
- a = S_XY/S_X2 # regr line coeffs
- b= avg ( Y[start:stop+1] ) - a * avg( X[start:stop+1] )
- #print(" range [%d,%d] corr=%f, coeff det=%f [a=%f, b=%f]" % (X[start],X[stop],c,c**2,a, b))
- correl.append( (c, stop-start) ); # store correl. coef + number of values (segment length)
- interv.append( (a,b, X[start],X[stop]) );
-
- for (c,l) in correl:
- glob_corr = glob_corr + (l/sum_nb_val)*c # weighted product of correlation
- #print('-- %f * %f' % (c,l/sum_nb_val))
-
- #print("-> glob_corr={}\n".format(glob_corr))
- return (glob_corr,interv);
-
-
-
-
-##-----------------------------------------------------------------------------------------------
-## correl_split : compute regression on each segment and
-## return the product of correlation coefficient
-## param X first data vector (..x_i..)
-## param Y second data vector (..x_i..)
-## param segments list of pairs (i,j) where i refers to the ith value in X, and jth value in X
-## return (C,[(i1,j1,X[i1],X[j1]), (i2,j2,X[i2],X[j2]), ....]
-## where i1,j1 is the first segment, c1 the correlation coef on this segment,
-## i2,j2 is the second segment, c2 the correlation coef on this segment,
-## ...
-## and C=c1*c2*...
-##-----------------------------------------------------------------------------------------------
-def correl_split( X , Y , segments ):
- # expects segments = [(0,i1-1),(i1-1,i2-1),(i2,len-1)]
- correl = list();
- interv = list(); # regr. line coeffs and range
- glob_corr=1
- for (start,stop) in segments:
- #if start==stop :
- # return 0
- S_XY= cov( X [start:stop+1], Y [start:stop+1] )
- S_X2 = variance( X [start:stop+1] )
- S_Y2 = variance( Y [start:stop+1] ) # to compute correlation
- if S_X2*S_Y2 == 0:
- return (0,[])
- c = S_XY/(sqrt(S_X2)*sqrt(S_Y2))
- a = S_XY/S_X2 # regr line coeffs
- b= avg ( Y[start:stop+1] ) - a * avg( X[start:stop+1] )
- #print(" range [%d,%d] corr=%f, coeff det=%f [a=%f, b=%f]" % (X[start],X[stop],c,c**2,a, b))
- correl.append( (c, stop-start) ); # store correl. coef + number of values (segment length)
- interv.append( (a,b, X[start],X[stop]) );
-
- for (c,l) in correl:
- glob_corr = glob_corr * c # product of correlation coeffs
- return (glob_corr,interv);
-
-
-
-##-----------------------------------------------------------------------------------------------
-## main
-##-----------------------------------------------------------------------------------------------
-sum=0
-nblines=0
-skampidat = open(sys.argv[1], "r")
-
-
-## read data from skampi logs.
-timings = []
-sizes = []
-readdata =[]
-for line in skampidat:
- l = line.split();
- if line[0] != '#' and len(l) >= 3: # is it a comment ?
- ## expected format
- ## ---------------
- #count= 8388608 8388608 144916.1 7.6 32 144916.1 143262.0
- #("%s %d %d %f %f %d %f %f\n" % (countlbl, count, countn, time, stddev, iter, mini, maxi)
- readdata.append( (int(l[1]),float(l[3])) );
- nblines=nblines+1
-
-## These may not be sorted so sort it by message size before processing.
-sorteddata = sorted( readdata, key=lambda pair: pair[0])
-sizes,timings = zip(*sorteddata);
-
-# zip makes tuples; cast to lists for backward compatibility with python2.X
-sizes = list(sizes)
-timings = list(timings)
-
-##----------------------- search for best break points-----------------
-## example
-## p1=2048 -> p1inx=11 delta=3 -> [8;14]
-## 8 : segments[(0,7),(8,13),(13,..)]
-## ....
-## p2=65536 -> p2inx=16 delta=3 -> [13;19]
-
-if len(sys.argv) == 4:
-
- p1inx = sizes.index( p1 );
- p2inx = sizes.index( p2 );
- max_glob_corr = 999990;
- max_p1inx = p1inx
- max_p2inx = p2inx
-
- ## tweak parameters here to extend/reduce search
- search_p1 = 70 # number of values to search +/- around p1
- search_p2 = 70 # number of values to search +/- around p2
- min_seg_size = 3
- if (search_p2 + min_seg_size > len(sizes)): # reduce min segment sizes when points close to data extrema
- min_seg_size = len(sizes)-search_p2
- if (search_p1 - min_seg_size < 0):
- min_seg_size = search_p1
-
- lb1 = max( 1, p1inx-search_p1 )
- ub1 = min( p1inx+search_p1, p2inx);
- lb2 = max( p1inx, p2inx-search_p2) # breakpoint +/- delta
- ub2 = min( p2inx+search_p2, len(sizes)-1);
-
- print("** evaluating over \n");
- print("interv1:\t %d <--- %d ---> %d" % (sizes[lb1],p1,sizes[ub1]))
- print("rank: \t (%d)<---(%d)--->(%d)\n" % (lb1,p1inx,ub1))
- print("interv2:\t\t %d <--- %d ---> %d" % (sizes[lb2],p2,sizes[ub2]))
- print("rank: \t\t(%d)<---(%d)--->(%d)\n" % (lb2,p2inx,ub2))
-
- result = list()
- for i in range(lb1,ub1+1):
- for j in range(lb2,ub2+1):
- if i<j: # segments must not overlap
- if i+1 >=min_seg_size and j-i+1 >= min_seg_size and len(sizes)-1-j >= min_seg_size : # not too small segments
- #print("** i=%d,j=%d" % (i,j))
- segments = [(0,i),(i,j),(j,len(sizes)-1)]
- result.append( correl_split_weighted_logerr( sizes, timings, segments) ) # add pair (metric,interval)
-
- # sort results on ascending metric: ok for logerr. Add "reverse=true" for desc sort if you use a correlation metric
- result = sorted( result, key=lambda pair: pair[0])
-
-
- top_n_sol=5; # tweak to display top best n solution
-
- print("#-------------------- result summary ---------------------------------------------------------------------\n");
-
- for k in range(top_n_sol):
- (err,interval) = result[k]
- print(k)
- print("\n RANK {0}\n-------".format(k))
- print("** overall metric = {0}".format(err))
- for (a,b,i,j,e) in interval:
- print("** OPT: [{0} .. {1}] segment_metric={2} slope: {3} x + {4}".format(i,j,e,a,b))
-
-
- print("\n\n\n")
-
- print("#-------------------- Best Solution : cut here the gnuplot code -----------------------------------------------------------\n");
- preamble='set output "regr.eps"\n\
-set terminal postscript eps color\n\
-set key left\n\
-set xlabel "Each message size in bytes"\n\
-set ylabel "Time in us"\n\
-set logscale x\n\
-set logscale y\n\
-set grid'
-
- print(preamble);
- print('plot "%s" u 3:4:($5) with errorbars title "skampi traces %s",\\' % (sys.argv[1],sys.argv[1]));
- (err,interval) = result[0]
- for (a,b,i,j,e) in interval:
- print('"%s" u (%d<=$3 && $3<=%d? $3:0/0):(%f*($3)+%f) w linespoints title "regress. %s-%s bytes",\\' % (sys.argv[1],i,j,a,b,i,j))
-
- print("#-------------------- /cut here the gnuplot code -----------------------------------------------------------\n");
-
-
-else:
- print('\n** Linear regression on %d values **\n' % (nblines))
- print('\n sizes=',sizes,'\n\n')
- avg_sizes = avg( sizes )
- avg_timings = avg( timings )
- print("avg_timings=%f, avg_sizes=%f, nblines=%d\n" % (avg_timings,avg_sizes,nblines))
-
- S_XY= cov( sizes, timings )
- S_X2 = variance( sizes )
- S_Y2 = variance( timings ) # to compute correlation
-
- a = S_XY/S_X2
- correl = S_XY/(sqrt(S_X2)*sqrt(S_Y2)) # corealation coeff (Bravais-Pearson)
-
-
- b= avg_timings - a * avg_sizes
- print("[S_XY=%f, S_X2=%f]\n[correlation=%f, coeff det=%f]\n[a=%f, b=%f]\n" % (S_XY, S_X2, correl,correl**2,a, b))
-
-
