3 #---------------------------------------------------------------------------------------------------
5 # % ./regress.py griffon_skampi_pt2pt.ski.dat 65536 120832
8 # Given two vectors of same length n: message size S(.. s_i ..), and communication time T( .. t_i .. )
9 # where t_i is the time associated to a mesage size s_i, computes the segmentation of the vectors
10 # in 3 segments such that linear regressions on the 3 segments maximize correlation.
11 # The metric for correlation is now the cumulative, log error of the estimated time value given
12 # by regression, to the real time value.
14 # Call r(X[i:j],Y[i:j]) = ax + b the regression line for data of X,Y between indices i and j
15 # Call E[i:j] = E( e_i, .., e_j) the vector of estimates from the regression, where e_i = a*S[i] + b
16 # 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.
17 # i.e mean_logerr( T,T' ) = 1/n * Sum_i^n ( exp(| ln(t_i)-ln(t'_i)|) - 1 )
19 # The script computes indices k and l, s.t.
20 # mean_logerr( r(S[0:k],T[0:k]) , E[0,k] ) +
21 # mean_logerr( r(S[k:l],T[k:l]) , E[k,l] ) +
22 # mean_logerr( r(S[l:n],T[l:n]) , E[l,n] )
24 #---------------------------------------------------------------------------------------------------
27 from math import sqrt,log,exp
30 if len(sys.argv) != 2 and len(sys.argv) != 4:
31 print("Usage : {} datafile".format(sys.argv[0]))
32 print("or : {0} datafile p1 p2".format(sys.argv[0]))
33 print("where : p1 < p2 belongs to sizes in datafiles")
36 if len(sys.argv) == 4:
40 ##-----------------------------------------
41 ## avg : return average of a list of values
42 ## param l list of values
43 ##-----------------------------------------
50 ##-------------------------------------------------
52 ## param X first data vector (..x_i..)
53 ## param Y second data vector (..y_i..)
54 ## = 1/n \Sum_{i=1}^n (x_i - avg(x)) * (y_i - avg(y))
55 ##--------------------------------------------------
57 assert(len(X)==len(Y))
58 n=len(X) # n=len(X)=len(Y)
63 S_XY = S_XY + ((X[i]-avg_X)*(Y[i]-avg_Y))
68 ##----------------------------------
69 ## variance : variance
70 ## param X data vector ( ..x_i.. )
71 ## (S_X)^2 = (Sum ( x_i - avg(X) )^2 ) / n
72 ##----------------------------------
78 S_X2 = S_X2 + ((X[i] - avg_X)**2)
82 ##----------------------------------
84 ## param X data vector ( ..x_i.. ), length n
85 ## param Y data vector ( ..y_i.. ), length n
86 ## return mean( 1/n * Sum_i^n ( exp(| ln(x_i)-ln(y_i)|) - 1 )
87 ##----------------------------------
88 def mean_logerr( X,Y ):
89 assert( len(X) == len(Y) )
90 E = list(); # the list of errors
91 for i in range(len(X)):
92 E.append( exp(abs(log(X[i])-log(Y[i])))-1 )
96 ##-----------------------------------------------------------------------------------------------
97 ## correl_split_weighted_logerr : compute regression on each segment and
98 ## return the weigthed sum of correlation coefficients
99 ## param X first data vector (..x_i..)
100 ## param Y second data vector (..x_i..)
101 ## param segments list of pairs (i,j) where i refers to the ith value in X, and jth value in X
102 ## return (C,[(i1,j1,X[i1],X[j1]), (i2,j2,X[i2],X[j2]), ....]
103 ## where i1,j1 is the first segment, c1 the correlation coef on this segment, n1 the number of values
104 ## i2,j2 is the second segment, c2 the correlation coef on this segment, n2 the number of values
106 ## and C=c1/n1+c2/n2+...
107 ##-----------------------------------------------------------------------------------------------
108 def correl_split_weighted_logerr( X , Y , segments ):
109 # expects segments = [(0,i1-1),(i1-1,i2-1),(i2,len-1)]
111 interv = list() # regr. line coeffs and range
113 for (start,stop) in segments:
116 S_XY= cov( X [start:stop+1], Y [start:stop+1] )
117 S_X2 = variance( X [start:stop+1] )
118 a = S_XY/S_X2 # regr line coeffs
119 b = avg ( Y[start:stop+1] ) - a * avg( X[start:stop+1] )
120 # fill a vector (Z) with predicted values from regression
122 for i in range(start,stop+1):
123 Z.append( a * X[i] + b )
124 # compare real values and computed values
125 e = mean_logerr( Y[start:stop+1] , Z )
126 correl.append( (e, stop-start+1) ); # store correl. coef + number of values (segment length)
127 interv.append( (a,b, X[start],X[stop],e) );
130 glob_err = glob_err + (e*l/len( X )) # the average log err for this segment (e) is
131 # weighted by the number of values of the segment (l) out of the total number of values
133 #print("-> glob_corr={}\n".format(glob_corr))
134 return (glob_err,interv);
136 ##-----------------------------------------------------------------------------------------------
137 ## correl_split_weighted : compute regression on each segment and
138 ## return the weigthed sum of correlation coefficients
139 ## param X first data vector (..x_i..)
140 ## param Y second data vector (..x_i..)
141 ## param segments list of pairs (i,j) where i refers to the ith value in X, and jth value in X
142 ## return (C,[(i1,j1,X[i1],X[j1]), (i2,j2,X[i2],X[j2]), ....]
143 ## where i1,j1 is the first segment, c1 the correlation coef on this segment, n1 the number of values
144 ## i2,j2 is the second segment, c2 the correlation coef on this segment, n2 the number of values
146 ## and C=c1/n1+c2/n2+...
147 ##-----------------------------------------------------------------------------------------------
148 def correl_split_weighted( X , Y , segments ):
149 # expects segments = [(0,i1-1),(i1-1,i2-1),(i2,len-1)]
151 interv = list(); # regr. line coeffs and range
154 for (start,stop) in segments:
155 sum_nb_val = sum_nb_val + stop - start;
158 S_XY= cov( X [start:stop+1], Y [start:stop+1] )
159 S_X2 = variance( X [start:stop+1] )
160 S_Y2 = variance( Y [start:stop+1] ) # to compute correlation
163 c = S_XY/(sqrt(S_X2)*sqrt(S_Y2))
164 a = S_XY/S_X2 # regr line coeffs
165 b= avg ( Y[start:stop+1] ) - a * avg( X[start:stop+1] )
166 #print(" range [%d,%d] corr=%f, coeff det=%f [a=%f, b=%f]" % (X[start],X[stop],c,c**2,a, b))
167 correl.append( (c, stop-start) ); # store correl. coef + number of values (segment length)
168 interv.append( (a,b, X[start],X[stop]) );
171 glob_corr = glob_corr + (l/sum_nb_val)*c # weighted product of correlation
172 #print('-- %f * %f' % (c,l/sum_nb_val))
174 #print("-> glob_corr={}\n".format(glob_corr))
175 return (glob_corr,interv);
180 ##-----------------------------------------------------------------------------------------------
181 ## correl_split : compute regression on each segment and
182 ## return the product of correlation coefficient
183 ## param X first data vector (..x_i..)
184 ## param Y second data vector (..x_i..)
185 ## param segments list of pairs (i,j) where i refers to the ith value in X, and jth value in X
186 ## return (C,[(i1,j1,X[i1],X[j1]), (i2,j2,X[i2],X[j2]), ....]
187 ## where i1,j1 is the first segment, c1 the correlation coef on this segment,
188 ## i2,j2 is the second segment, c2 the correlation coef on this segment,
191 ##-----------------------------------------------------------------------------------------------
192 def correl_split( X , Y , segments ):
193 # expects segments = [(0,i1-1),(i1-1,i2-1),(i2,len-1)]
195 interv = list(); # regr. line coeffs and range
197 for (start,stop) in segments:
200 S_XY= cov( X [start:stop+1], Y [start:stop+1] )
201 S_X2 = variance( X [start:stop+1] )
202 S_Y2 = variance( Y [start:stop+1] ) # to compute correlation
205 c = S_XY/(sqrt(S_X2)*sqrt(S_Y2))
206 a = S_XY/S_X2 # regr line coeffs
207 b= avg ( Y[start:stop+1] ) - a * avg( X[start:stop+1] )
208 #print(" range [%d,%d] corr=%f, coeff det=%f [a=%f, b=%f]" % (X[start],X[stop],c,c**2,a, b))
209 correl.append( (c, stop-start) ); # store correl. coef + number of values (segment length)
210 interv.append( (a,b, X[start],X[stop]) );
213 glob_corr = glob_corr * c # product of correlation coeffs
214 return (glob_corr,interv);
218 ##-----------------------------------------------------------------------------------------------
220 ##-----------------------------------------------------------------------------------------------
223 skampidat = open(sys.argv[1], "r")
226 ## read data from skampi logs.
230 for line in skampidat:
232 if line[0] != '#' and len(l) >= 3: # is it a comment ?
235 #count= 8388608 8388608 144916.1 7.6 32 144916.1 143262.0
236 #("%s %d %d %f %f %d %f %f\n" % (countlbl, count, countn, time, stddev, iter, mini, maxi)
237 readdata.append( (int(l[1]),float(l[3])) );
240 ## These may not be sorted so sort it by message size before processing.
241 sorteddata = sorted( readdata, key=lambda pair: pair[0])
242 sizes,timings = zip(*sorteddata);
244 # zip makes tuples; cast to lists for backward compatibility with python2.X
246 timings = list(timings)
248 ##----------------------- search for best break points-----------------
250 ## p1=2048 -> p1inx=11 delta=3 -> [8;14]
251 ## 8 : segments[(0,7),(8,13),(13,..)]
253 ## p2=65536 -> p2inx=16 delta=3 -> [13;19]
255 if len(sys.argv) == 4:
257 p1inx = sizes.index( p1 );
258 p2inx = sizes.index( p2 );
259 max_glob_corr = 999990;
263 ## tweak parameters here to extend/reduce search
264 search_p1 = 70 # number of values to search +/- around p1
265 search_p2 = 70 # number of values to search +/- around p2
267 if (search_p2 + min_seg_size > len(sizes)): # reduce min segment sizes when points close to data extrema
268 min_seg_size = len(sizes)-search_p2
269 if (search_p1 - min_seg_size < 0):
270 min_seg_size = search_p1
272 lb1 = max( 1, p1inx-search_p1 )
273 ub1 = min( p1inx+search_p1, p2inx);
274 lb2 = max( p1inx, p2inx-search_p2) # breakpoint +/- delta
275 ub2 = min( p2inx+search_p2, len(sizes)-1);
277 print("** evaluating over \n");
278 print("interv1:\t %d <--- %d ---> %d" % (sizes[lb1],p1,sizes[ub1]))
279 print("rank: \t (%d)<---(%d)--->(%d)\n" % (lb1,p1inx,ub1))
280 print("interv2:\t\t %d <--- %d ---> %d" % (sizes[lb2],p2,sizes[ub2]))
281 print("rank: \t\t(%d)<---(%d)--->(%d)\n" % (lb2,p2inx,ub2))
284 for i in range(lb1,ub1+1):
285 for j in range(lb2,ub2+1):
286 if i<j: # segments must not overlap
287 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
288 #print("** i=%d,j=%d" % (i,j))
289 segments = [(0,i),(i,j),(j,len(sizes)-1)]
290 result.append( correl_split_weighted_logerr( sizes, timings, segments) ) # add pair (metric,interval)
292 # sort results on ascending metric: ok for logerr. Add "reverse=true" for desc sort if you use a correlation metric
293 result = sorted( result, key=lambda pair: pair[0])
296 top_n_sol=5; # tweak to display top best n solution
298 print("#-------------------- result summary ---------------------------------------------------------------------\n");
300 for k in range(top_n_sol):
301 (err,interval) = result[k]
303 print("\n RANK {0}\n-------".format(k))
304 print("** overall metric = {0}".format(err))
305 for (a,b,i,j,e) in interval:
306 print("** OPT: [{0} .. {1}] segment_metric={2} slope: {3} x + {4}".format(i,j,e,a,b))
311 print("#-------------------- Best Solution : cut here the gnuplot code -----------------------------------------------------------\n");
312 preamble='set output "regr.eps"\n\
313 set terminal postscript eps color\n\
315 set xlabel "Each message size in bytes"\n\
316 set ylabel "Time in us"\n\
322 print('plot "%s" u 3:4:($5) with errorbars title "skampi traces %s",\\' % (sys.argv[1],sys.argv[1]));
323 (err,interval) = result[0]
324 for (a,b,i,j,e) in interval:
325 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))
327 print("#-------------------- /cut here the gnuplot code -----------------------------------------------------------\n");
331 print('\n** Linear regression on %d values **\n' % (nblines))
332 print('\n sizes=',sizes,'\n\n')
333 avg_sizes = avg( sizes )
334 avg_timings = avg( timings )
335 print("avg_timings=%f, avg_sizes=%f, nblines=%d\n" % (avg_timings,avg_sizes,nblines))
337 S_XY= cov( sizes, timings )
338 S_X2 = variance( sizes )
339 S_Y2 = variance( timings ) # to compute correlation
342 correl = S_XY/(sqrt(S_X2)*sqrt(S_Y2)) # corealation coeff (Bravais-Pearson)
345 b= avg_timings - a * avg_sizes
346 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))