[GRASS-SVN] r53908 - in grass-addons/grass6/raster: . r.mcda.roughset

svn_grass at osgeo.org svn_grass at osgeo.org
Mon Nov 19 05:34:38 PST 2012


Author: gianluca
Date: 2012-11-19 05:34:37 -0800 (Mon, 19 Nov 2012)
New Revision: 53908

Added:
   grass-addons/grass6/raster/r.mcda.roughset/
   grass-addons/grass6/raster/r.mcda.roughset/Makefile
   grass-addons/grass6/raster/r.mcda.roughset/description.html
   grass-addons/grass6/raster/r.mcda.roughset/r.mcda.roughset.py
Log:


Added: grass-addons/grass6/raster/r.mcda.roughset/Makefile
===================================================================
--- grass-addons/grass6/raster/r.mcda.roughset/Makefile	                        (rev 0)
+++ grass-addons/grass6/raster/r.mcda.roughset/Makefile	2012-11-19 13:34:37 UTC (rev 53908)
@@ -0,0 +1,7 @@
+#MODULE_TOPDIR = ../..
+
+PGM = r.mcda.roughset
+
+include $(MODULE_TOPDIR)/include/Make/Script.make
+
+default: script

Added: grass-addons/grass6/raster/r.mcda.roughset/description.html
===================================================================
--- grass-addons/grass6/raster/r.mcda.roughset/description.html	                        (rev 0)
+++ grass-addons/grass6/raster/r.mcda.roughset/description.html	2012-11-19 13:34:37 UTC (rev 53908)
@@ -0,0 +1,31 @@
+<h2>DESCRIPTION</h2>
+
+<em>r.mcda.roughset</em> is the python implementation of the dominance rough set approach (Domlem algorithm) in GRASS GIS environment. It requires the following input:
+<br>1. the geographical criteria constituting the information system for the rough set analysis; they have to describe environmental, economic or social issues(<b>criteria</b>=<em>name[,name,...]</em>);<br> 2. the preference (<b>preferences</b>=<em>character</em>)for each criteria used in analysis (gain or cost with comma separator)<br>3. the theme in which areas with the issues to be studied are classified (with crescent preference values) (<b>decision</b>=<em>string</em>).
+
+<p>An information system is generated and Domlem algorithm is applied for extraction a minimal set of rules.</P>  The algorithm builds two text  files (<b>outputTxt</b>=<em>name</em>): the first with isf extension for more deep  analysis with non geographic software like 4emka and  JAMM ; the second file with rls extension hold all the set of rules generate. An output map (<b>outputMap</b>=<em>string</em>)is generated for  region  classification with the rules finded and the criteria stored in GRASS geodb.
+
+<h2>NOTES</h2>
+<p> The module can work very slowly with high number of criteria and sample. For bug please contact Gianluca Massei (g_mass at libero.it)</P>
+
+
+<h2>REFERENCE</h2>
+<ol>
+	<li><p>Greco S., Matarazzo B., Slowinski R.: <i>Rough sets theory for multicriteria decision analysis</i>. European Journal of Operational Research, 129, 1 (2001) 1-47.</P>
+	<li><p>Greco S., Matarazzo B., Slowinski R.:<i> Multicriteria classification by dominance-based rough set approach</i>. In: W.Kloesgen and J.Zytkow (eds.), Handbook of Data Mining and Knowledge Discovery, Oxford University Press, New York, 2002.</P>
+	<li><p>Greco S., Matarazzo B., Slowinski, R., Stefanowski, J.: <i>An Algorithm for Induction of Decision Rules Consistent with the Dominance Principle</i>. In W. Ziarko, Y. Yao (eds.): Rough Sets and Current Trends in Computing. Lecture Notes in Artificial Intelligence 2005 (2001) 304 - 313. Springer-Verlag</P>
+	<li><p>Greco, S., B. Matarazzo, R. Slowinski and J. Stefanowski:<i> Variable consistency model of dominance-based rough set approach.</i> In W.Ziarko, Y.Yao (eds.): Rough Sets and Current Trends in Computing. Lecture Notes in Artificial Intelligence 2005 (2001) 170 - 181. Springer-Verlag</P>
+	<li><p><a href="http://en.wikipedia.org/wiki/Dominance-based_rough_set_approach">http://en.wikipedia.org/wiki/Dominance-based_rough_set_approach</a> - “Dominance-based rough set approach”</P>
+	<li><p><a href="http://idss.cs.put.poznan.pl/site/software.html">http://idss.cs.put.poznan.pl/site/software.html</a> - Software from Laboratory of intelligent decision support system in Poznam University of Technology
+	</P>
+</ol>
+
+<h2>SEE ALSO</h2>
+<p><em>r.mcda.fuzzy, r.mcda.electre, r.mcda.regime, r.to.drsa, r.in.drsa</em></P>
+
+<h2>AUTHORS</h2>
+Antonio Boggia - Gianluca Massei<br>
+Department of Economics and Appraisal - University of Perugia - Italy 
+
+<p>
+<i>Last changed: $Date: 2011-11-08 22:56:45 +0100 (mar, 08 nov 2011) $</i>

Added: grass-addons/grass6/raster/r.mcda.roughset/r.mcda.roughset.py
===================================================================
--- grass-addons/grass6/raster/r.mcda.roughset/r.mcda.roughset.py	                        (rev 0)
+++ grass-addons/grass6/raster/r.mcda.roughset/r.mcda.roughset.py	2012-11-19 13:34:37 UTC (rev 53908)
@@ -0,0 +1,611 @@
+#!/usr/bin/env python
+############################################################################
+#
+# MODULE:	   r.mcda.roughset
+# AUTHOR:	   Gianluca Massei - Antonio Boggia
+# PURPOSE:	  Generate a MCDA map from several criteria maps using Dominance Rough Set Approach - DRSA 
+#					   (DOMLEM algorithm proposed by  (S. Greco, B. Matarazzo, R. Slowinski)	 
+# COPYRIGHT:  c) 2010 Gianluca Massei, Antonio Boggia  and the GRASS 
+#					   Development Team. This program is free software under the 
+#					   GNU General PublicLicense (>=v2). Read the file COPYING 
+#					   that comes with GRASS for details.
+#
+#############################################################################
+
+#%Module
+#% description: Generate a MCDA map from several criteria maps using Dominance Rough Set Approach.
+#% keywords: raster, Dominance Rough Set Approach 
+#% keywords: Multi Criteria Decision Analysis (MCDA)
+#%End
+#%option
+#% key: criteria
+#% type: string
+#% multiple: yes
+#% gisprompt: old,cell,raster
+#% key_desc: name
+#% description: Name of criteria raster maps 
+#% required: yes
+#%end
+#%option
+#% key: preferences
+#% type: string
+#% key_desc: character
+#% description: gain,cost
+#% required: yes
+#%end
+#%option
+#% key: decision
+#% type: string
+#% gisprompt: old,cell,raster
+#% key_desc: name
+#% description: Name of decision raster map 
+#% required: yes
+#%end
+#%option
+#% key: outputMap
+#% type: string
+#% gisprompt: new_file,cell,output
+#% description: Output classified raster map
+#% required: yes
+#%end
+#%option
+#% key: outputTxt
+#% type: string
+#% gisprompt: new_file,file,output
+#% key_desc: name
+#% description: Name for output files (base for *.isf  and *.rls files)
+#% answer:infosys
+#% required: yes
+#%end
+#%flag
+#% key: l
+#% description: do not remove single rules in vector format
+#% answer:false
+#%end
+#%flag
+#% key: n
+#% description: compute null value as zero
+#% answer:true
+#%end
+
+import sys
+import copy
+import numpy as np
+from time import time, ctime  
+import grass.script as grass
+import grass.script.array as garray
+
+
+def BuildFileISF(attributes, preferences, decision, outputMap, outputTxt):
+	outputTxt=outputTxt+".isf"
+	outf = file(outputTxt,"w")
+	outf.write("**ATTRIBUTES\n")
+	for i in range(len(attributes)):
+		outf.write("+ %s: (continuous)\n" % attributes[i])
+	outf.write("+ %s: [" % decision)
+	value=[]
+	value=grass.read_command("r.describe", flags = "1n", map = decision)
+	v=value.split()
+
+	for i in range(len(v)-1):
+		outf.write("%s, " % str(v[i]))
+	outf.write("%s]\n" % str(v[len(v)-1]))
+	outf.write("decision: %s\n" % decision)
+
+	outf.write("\n**PREFERENCES\n")
+	for i in range(len(attributes)):
+		if(preferences[i]==""):
+			preferences[i]="none"
+		outf.write("%s: %s\n" % (attributes[i], preferences[i]))
+	outf.write("%s: gain\n" % decision)
+	
+	if flags['n']:
+		for i in range(len(attributes)):
+			print "%s - convert null to 0" % str(attributes[i])
+			grass.run_command("r.null", map=attributes[i], null=0)
+			
+	outf.write("\n**EXAMPLES\n")
+	examples=[]
+	MATRIX=[]
+
+	for i in range(len(attributes)):
+		grass.mapcalc("rast=if(isnull(${decision})==0,${attribute},null())",
+						 rast="rast",
+						 decision=decision,
+						 attribute=attributes[i])
+		tmp=grass.read_command("r.stats", flags = "1n", nv="?", input = "rast")
+		example=tmp.split()
+		examples.append(example)
+	tmp=grass.read_command("r.stats", flags = "1n", nv="?", input = decision)
+	example=tmp.split()
+	examples.append(example)
+
+	MATRIX=map(list,zip(*examples))
+	MATRIX=[r for r in MATRIX if not '?' in r] #remove all rows with almost one "?"
+	MATRIX=[list(i) for i in set(tuple(j) for j in MATRIX)] #remove duplicate example 
+	
+	for r in range(len(MATRIX)):
+		for c in range(len(MATRIX[0])):
+			outf.write("%s " % (MATRIX[r][c]))
+#			outf.write("%s " % round(float(MATRIX[r][c]), 2))
+		outf.write("\n")
+	   
+	outf.write("**END")
+	outf.close()
+	return outputTxt
+	
+	
+
+def collect_attributes (data):
+	"Collects the values of header files isf, puts them in an array of dictionaries"
+	header=[]
+	attribute=dict()
+	j=0
+	start=(data.index(['**ATTRIBUTES'])+1)
+	end=(data.index(['**PREFERENCES'])-1)
+	for r in range(start, end):
+		attribute={'name':data[r][1].strip('+:')}
+		header.append(attribute)
+	decision=data[end-1][1]
+	end=(data.index(['**EXAMPLES']))
+	
+	start=(data.index(['**PREFERENCES'])+1)
+	for r in header:
+		r['preference']=data[start+j][1]
+		j=j+1
+	return header	
+
+
+def collect_examples (data):
+	"Collect examples values and put them in a matrix (list of lists) "
+	
+	matrix=[]
+	data=[r for r in data if not '?' in r] #filter objects with " ?"
+#	data=[data.remove(r) for r in data if data.count(r)>1] 
+	start=(data.index(['**EXAMPLES'])+1)
+	end=data.index(['**END'])
+	for i in range(start, end):
+		data[i]=(map(float, data[i]))
+		matrix.append(data[i])
+	i=1
+	for r in matrix:
+		r.insert(0, str(i))
+		i=i+1
+##	matrix=[list(i) for i in set(tuple(j) for j in matrix)] #remove duplicate example   
+	return matrix
+
+
+def FileToInfoSystem(isf):
+	"Read *.isf file and copy it's values in Infosystem dictionary"
+	data=[]
+	try:
+		infile=open(isf,"r")
+		rows=infile.readlines()
+		for line in rows:
+			line=(line.split())
+			if (len(line)>0 ):
+				data.append(line)
+		infile.close()	   
+		infosystem={'attributes':collect_attributes(data),'examples':collect_examples(data)}
+	except TypeError:
+		print "\n\n Computing error or input file %s is not readeable. Exiting gracefully" % isf
+		sys.exit(0)
+		
+	return infosystem
+
+
+def UnionOfClasses (infosystem):
+	"Find upward and downward union for all classes and put it in a dictionary"
+	DecisionClass=[]
+	AllClasses=[]
+	matrix=infosystem['examples']
+	for r in matrix:
+		DecisionClass.append(int(r[-1]))
+	DecisionClass=list(set(DecisionClass))
+	for c in range(len(DecisionClass)):
+		tmplist=[r for r in matrix if int(r[-1])==DecisionClass[c]]
+		AllClasses.append(tmplist)  
+	
+	return AllClasses
+	
+	
+def DownwardUnionsOfClasses (infosystem):
+	"For each decision class, downward union corresponding to a decision class\
+	is composed of this class and all worse classes (<=)"
+
+	DownwardUnionClass=[]
+	DecisionClass=[]
+	matrix=infosystem['examples']
+	for r in matrix:
+		DecisionClass.append(int(r[-1]))
+	DecisionClass=list(set(DecisionClass))
+	for c in DecisionClass:
+		tmplist=[r for r in matrix if int(r[-1])<=c]
+		DownwardUnionClass.append(tmplist)
+		#label=[row[0] for row in tmplist]
+	return DownwardUnionClass
+
+
+def UpwardUnionsOfClasses (infosystem):
+	"For each decision class, upward union corresponding to a decision class \
+	is composed of this class and all better classes.(>=)"
+
+	UpwardUnionClass=[]
+	DecisionClass=[]
+	matrix=infosystem['examples']
+	for r in matrix:
+		DecisionClass.append(int(r[-1]))
+	DecisionClass=list(set(DecisionClass))
+	for c in DecisionClass:
+		tmplist=[r for r in matrix if int(r[-1])>=c]
+		UpwardUnionClass.append(tmplist)
+		#label=[row[0] for row in tmplist]
+	return UpwardUnionClass
+  
+	
+###############################
+def is_better (r1,r2, preference):
+	"Check if r1 is better than r2"
+	return all((( x >=y and p=='gain') or (x<=y and p=='cost')) for x,y, p in zip(r1,r2, preference) ) 
+	
+
+def is_worst (r1,r2, preference): 
+	"Check if r1 is worst than r2"
+	return all((( x <=y and p=='gain') or (x>=y and p=='cost')) for x,y, p in zip(r1,r2, preference) ) 
+ #################################
+
+
+def DominatingSet (infosystem):
+	"Find P-dominating set"
+	matrix=infosystem['examples']
+	preference=[s['preference'] for s in infosystem['attributes'] ]
+	Dominating=[]
+	for row in matrix:
+		examples=[r  for r in matrix if  is_better(r[1:-1], row[1:-1], preference) ] 
+		Dominating.append({'object':row[0], 'dominance':[i[0] for i in examples], 'examples':examples})
+##	for dom in Dominating:
+##		print  dom['dominance'] ,' dominating ', dom['object'] 
+	return Dominating
+
+def DominatedSet (infosystem):
+	"Find P-Dominated set"
+	matrix=infosystem['examples']
+	preference=[s['preference'] for s in infosystem['attributes'] ]
+	Dominated=[]
+	for row in matrix:
+		examples=[r  for r in matrix if  is_worst(r[1:-1], row[1:-1], preference[:-1]) ] 
+		Dominated.append({'object':row[0], 'dominance':[i[0] for i in examples], 'examples':examples})
+##	for dom in Dominated:
+##		print  dom['dominance'] ,' is dominated by ', dom['object'] 
+	return Dominated
+
+
+def LowerApproximation (UnionClasses,  Dom):
+	"Find Lower approximation and return a dictionaries list"
+	c=1
+	LowApprox=[]
+	single=dict()
+	for union in UnionClasses:
+		tmp=[]
+		UClass=set([row[0] for row in union] )
+		for d in Dom:
+			if (UClass.issuperset(set(d['dominance']))): #if Union class is a superse of dominating/dominated set, =>single Loer approx.
+				tmp.append(d['object'])
+		single={'class':c, 'objects':tmp} #dictionary for lower approximation  -- 
+		LowApprox.append(single) #insert all Lower approximation in a list
+		c+=1
+	return LowApprox
+
+
+def UpperApproximation (UnionClasses,  Dom):
+	"Find Upper approximation and return a dictionaries list"
+	c=1
+	UppApprox=[]
+	single=dict()
+	for union in UnionClasses:
+		UnClass=[row[0] for row in union]  #single union class
+		s=[]
+		for d in Dom:
+		   if len(set(d['dominance']) & set(UnClass)) >0:
+			   s.append(d['object'])
+#			   print set(s)
+		single={'class':c,'objects':list(set(s))}
+		UppApprox.append(single)
+		c+=1
+
+	return UppApprox
+
+
+def Boundaries (UppApprox, LowApprox):
+	"Find Boundaries like doubtful regions"
+	Boundary=[]
+	single=dict()
+
+	for i in range(len(UppApprox)):
+		single={'class':i, 'objects':list (set(UppApprox[i]['objects'])-set(LowApprox[i]['objects']) )}
+		Boundary.append(single)
+		
+	return Boundary
+	
+
+def AccuracyOfApproximation(UppApprox, LowApprox):
+	"Define the accuracy of approximation of Upward and downward approximation class"
+	return len(LowApprox)/len(UppApprox)
+	
+	
+def QualityOfQpproximation(DownwardBoundary,  infosystem):
+	"Defines the quality of approximation of the partition Cl or, briefly, the quality of sorting"
+	UnionBoundary=set()
+	U=set([i[0] for i in infosystem['examples']])
+	for b in DownwardBoundary:
+		UnionBoundary=set(UnionBoundary) | set(b['objects'])
+	return float(len(U-UnionBoundary)) / float(len(U))
+	
+	
+def FindObjectCovered (rules, selected):
+	"Find objects covered by a single rule and return\
+	all related examples covered"
+	obj=[]
+	examples=[]
+	
+	for rule in rules:
+		examples.append(rule['objectsCovered']) 
+
+	if len(examples)>0:
+		examples = reduce(set.intersection,map(set,examples))  #functional approach: intersect all lists if example is not empty
+		examples = list(set(examples) & set([r[0] for r in selected]))
+	return examples #all examples covered from a single rule
+	
+		
+def Evaluate (elem,rules,G,selected,infosystem):
+	"Calcolate first and second evaluate index, according with original DOMLEM Algorithm"
+	tmpRules=copy.deepcopy(rules)
+	tmpElem=copy.deepcopy(elem)
+	tmpRules.append(tmpElem)
+	Object=[]
+	Object=FindObjectCovered(tmpRules,selected)
+	if(float(len(Object)))>0:
+			 firstEvaluate=float(len(set(G) & set(Object))) / float(len(Object))
+			 secondEvaluate=float(len(set(G) & set(Object)))
+	else:
+			 firstEvaluate=0
+			 secondEvaluate=0
+			 
+	return firstEvaluate,secondEvaluate
+	
+	
+  
+def FindBestCondition (best, elem, rules, selected, G, infosystem):
+	"Choose the best condition"
+
+	firstElem,secondElem=Evaluate(elem,rules,G,selected,infosystem)
+	firstBest,secondBest=Evaluate(best,rules,G,selected,infosystem)
+	
+	if (firstElem>firstBest) or (firstElem==firstBest and secondElem>=secondBest):
+		best=copy.deepcopy(elem)
+	else:
+		best=best
+
+	return best
+
+	
+def Type_one_rule (c,  e,  preference,  matrix):
+	elem={'criterion':c,'condition':e, 'sign':preference[c-1],'class':'', \
+	'objectsCovered':[r[0] for r in matrix if (((r[c] >= e ) and (preference[c-1] == 'gain')) \
+																			  or ((r[c] <= e ) and (preference[c-1] == 'cost' )))],'label':''}
+	return elem
+	
+def Type_three_rule (c,  e,  preference,  matrix):
+	elem={'criterion':c,'condition':e, 'sign':preference[c-1],'class':'', \
+	'objectsCovered':[r[0] for r in matrix if (((r[c] <= e ) and (preference[c-1] == 'gain')) \
+														or ((r[c] >= e ) and (preference[c-1] == 'cost' )))],'label':''}
+	return elem
+
+
+def Find_rules (B, infosystem, type_rule):
+	"Search rule from a family of lower approximation of upward unions \
+	of decision classes"
+	start=time()
+	matrix=copy.deepcopy(infosystem['examples'])
+	criteria_num=len(infosystem['attributes'])
+	criteria=[r[1:-1] for r in matrix]
+	preference=[s['preference'] for s in infosystem['attributes'] ] #extract preference label
+	num_rules=0 #total rules number for each lower approximation
+	G=copy.deepcopy(B)		#a set of objects from the given approximation
+	E=[]		#a set  of rules covering set B (is a list of dictionary)
+	all_obj_cov_by_rules=[] #all objects covered by all rules in E
+	selected=copy.deepcopy(matrix) #storage reduct matrix by single elementary condition
+	while (len(G)!=0 ):
+		rules=[]	 #starting comples (single rule built from elementary conditions  )
+		S=copy.deepcopy(G)		 #set of objects currently covered by rule
+		control=0
+		while (len(rules)==0 or set(obj_cov_by_rules).issubset(B)==False):
+			obj_cov_by_rules=[] #set covered by rules
+			best={'criterion':'','condition':'','sign':'','class':'','objectsCovered':'','label':'', 'type':''} #best candidate for elementary condition - start as empty
+			for c in range(1, criteria_num):
+				Cond=[r[c] for r in selected if  r[0] in S] #for each positive object from S create an elementary condition
+				for e in Cond:
+					if type_rule=='one':
+						elem= Type_one_rule (c,  e,  preference,  matrix)
+					elif type_rule=='three':
+						elem= Type_three_rule (c,  e,  preference,  matrix)
+					else:
+						elem={'criterion':'','condition':'','sign':'','class':'','objectsCovered':'','label':'', 'type':''}
+					best=FindBestCondition(best, elem, rules, selected, G, infosystem)
+			if best not in rules:
+				rules.append(best)   #add the best condition to the complex 
+
+			for r in rules:
+				obj_cov_by_rules.append(r['objectsCovered'])
+			obj_cov_by_rules=list((reduce(set.intersection,map(set,obj_cov_by_rules)))) #reduce():Apply function of two arguments cumulatively to the items of iterable, from left to right, so as to reduce the iterable to a single value.
+
+			S=list(set(S) & set(best['objectsCovered'] ))
+			control+=1
+
+#		rules=CheckMinimalCondition (rules,B,matrix)
+		
+		if rules not in E:
+			E.append(rules) #add the induced rule
+			num_rules+=1
+		all_obj_cov_by_rules=list(set(all_obj_cov_by_rules) | set(obj_cov_by_rules))
+		
+		G=list(set(B)-set(all_obj_cov_by_rules)) #remove example coverred by all finded rule -- this operation is a set difference
+		selected=[o  for o in selected if  not  o[0]  in all_obj_cov_by_rules] #reduct matrix, remove object coverred by all finded rule
+		num_rules+=1
+		
+	return E
+	
+	
+  
+def Domlem(Lu,Ld, infosystem):
+	"DOMLEM algoritm \
+	(An algorithm for induction of decision rules consistent with the dominance\
+	principle - Greco S., Matarazzo, B., Slowinski R., Stefanowski J.)"
+	attributes=infosystem['attributes']
+	
+	RULES=[]
+
+##  *** AT MOST {<= Class} - Type 3 rules ***"		
+	for b in Ld[:-1]:
+		B=b['objects']
+		E=Find_rules(B, infosystem, 'three')
+		for e in E:
+			for i in e:
+				i['class']=b['class']
+				i['label']=attributes[i['criterion']-1]['name']
+				i['type']='at_most'
+				if (attributes[i['criterion']-1]['preference']=='gain'):
+					i['sign']='<='
+				else:
+					i['sign']='>='
+			RULES.append(e)
+			
+## *** AT LEAST {>= Class} - Type 1 rules *** "
+	for a in Lu[1:]:
+		B=a['objects']
+		E=Find_rules (B, infosystem, 'one')
+		for e in E:
+			for i in e:
+				i['class']=a['class']
+				i['label']=attributes[i['criterion']-1]['name']
+				i['type']='at_least'
+				if (attributes[i['criterion']-1]['preference']=='gain'):
+					i['sign']='>='
+				else:
+					i['sign']='<='
+			RULES.append(e)	   
+
+	return RULES
+	
+	
+def Print_rules(RULES, outputTxt):
+	"Print rls output file"
+	i=1
+	outfile=open(outputTxt+".rls","w")
+	outfile.write('[RULES]\n')
+	
+	for R in RULES:
+		outfile.write("%d: " % i, )
+		for e in R:
+				outfile.write("( %s %s %.3f )" % (e['label'], e['sign'],e['condition'] ))
+		outfile.write("=> ( class %s , %s )\n" % ( e['type'], e['class'] ))
+		i+=1
+	outfile.close()
+	return 0
+
+def Parser_mapcalc(RULES, outputMap):
+	"Parser to build a formula to be included  in mapcalc command"
+	i=1
+	category=[]
+	maps=[]
+	stringa=[]
+	
+	for R in RULES: 
+		formula="if("
+		for e in R[:-1]: #build a mapcalc formula
+			formula+= "(%s %s %.4f ) && " % (e['label'],  e['sign'] ,  e['condition'] )
+		formula+= "(%s %s %.4f ),%d,null())" % (R[-1]['label'],R[-1]['sign'], R[-1]['condition'] ,i )
+		mappa="r%d_%s_%d" % ( i, R[0]['type'], R[0]['class'] ) #build map name for mapcalc output
+		category.append({'id':i, 'type': R[0]['type'], 'class':R[0]['class']}) #extract category name
+		maps.append(mappa) #extract maps name
+		grass.mapcalc(mappa +"=" +formula)
+		i+=1
+	mapstring=",".join(maps)
+
+	
+	#make one layer for each label rule
+	labels=["_".join(m.split('_')[1:]) for m in maps] 
+	labels=list(set(labels))
+	for l in labels:
+		print "mapping %s rule" % str(l)
+		map_synth=[]
+		for m in maps:
+			if l == "_".join(m.split('_')[1:]):
+				map_synth.append(m)
+		if len(map_synth)>1:
+			grass.run_command("r.patch", overwrite='True', input=(",".join(map_synth)), output=l )
+		else:
+			grass.run_command("g.copy",rast=(str(map_synth),l))
+		print "__",str(map_synth),l
+		grass.run_command("r.to.vect", overwrite='True', flags='s', input=l, output=l, feature='area')
+		grass.run_command("v.db.addcol", map=l, columns='rule varchar(25)')
+		grass.run_command("v.db.update", map=l, column='rule', value=l)
+		grass.run_command("v.db.update", map=l, column='label', value=l)
+	mapslabels=",".join(labels)
+
+	if len(maps)>1:
+		grass.run_command("v.patch", overwrite='True', flags='e', input=mapslabels, output=outputMap)
+	else:
+		grass.run_command("g.copy",vect=(mapslabels,outputMap))
+			
+	if not flags['l']:
+		grass.run_command("g.remove",  rast=mapstring)
+		grass.run_command("g.remove",  vect=mapstring)
+		
+	return 0
+	  
+	
+def main():
+	"main function for DOMLEM algorithm"
+	#try:
+	start=time()
+	attributes = options['criteria'].split(',')
+	preferences=options['preferences'].split(',')
+	decision=options['decision']
+	outputMap= options['outputMap']
+	outputTxt= options['outputTxt']
+	out=BuildFileISF(attributes, preferences, decision, outputMap, outputTxt)
+	infosystem=FileToInfoSystem(out)
+	
+	UnionOfClasses(infosystem)
+	DownwardUnionClass=DownwardUnionsOfClasses(infosystem)
+	UpwardUnionClass=UpwardUnionsOfClasses(infosystem)
+	Dominating=DominatingSet(infosystem)
+	Dominated=DominatedSet(infosystem)
+##	upward union class
+	print "elaborate upward union"
+	Lu=LowerApproximation(UpwardUnionClass, Dominating) #lower approximation of upward union for type 1 rules
+	Uu=UpperApproximation(UpwardUnionClass,Dominated ) #upper approximation of upward union
+	UpwardBoundary=Boundaries(Uu, Lu)
+##	downward union class
+	print "elaborate downward union"
+	Ld=LowerApproximation(DownwardUnionClass, Dominated) # lower approximation of  downward union for type 3 rules
+	Ud=UpperApproximation(DownwardUnionClass,Dominating ) # upper approximation of  downward union 
+	DownwardBoundary=Boundaries(Ud, Ld)
+	QualityOfQpproximation(DownwardBoundary,  infosystem)
+	print "RULES extraction (*)" 
+	RULES=Domlem(Lu,Ld, infosystem)
+	Parser_mapcalc(RULES, outputMap)		   
+	Print_rules(RULES, outputTxt)
+	end=time()
+	print "Time computing-> %.4f s" % (end-start)
+	return 0
+	#except:
+		#print "ERROR! Rules does not generated!"
+		#sys.exit()
+
+if __name__ == "__main__":
+	options, flags = grass.parser()
+	sys.exit(main())
+
+



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