diff --git a/packages/cplint/doc/manual.html b/packages/cplint/doc/manual.html index 5bbf13c0e..4c8816cb3 100644 --- a/packages/cplint/doc/manual.html +++ b/packages/cplint/doc/manual.html @@ -7,7 +7,7 @@ - + @@ -21,7 +21,7 @@ class="cmr-12">Fabrizio Riguzzi
fabrizio.riguzzi@unife.it
September 4, 2013
+class="cmr-12">September 17, 2013

1 Introduction

@@ -1339,69 +1339,138 @@ class="cmtt-10">background_clauses (values: integer, d
  • maxdepth_var (values: integer, default value: 2, valid for SLIPCOVER): maximum depth of variables in clauses (as defined in [10]).
  • -

    +href="#XDBLP:journals/ai/Cohen95">10]). + +

  • score (values: ll, aucpr, default value ll, valid for SLIPCOVER): + determines the score function for refinement: if set to ll, log likelihood is + used, if set to aucpr, the area under the Precision-Recall curve is used.
  • + +

    5.3 Commands

    -

    To execute CEM, load

    To execute CEM, load em.pl with

    ?:- use_module(library(’cplint/em’)).
    -

    and call: +

    and call:

    ?:- em(stem).
    -

    To execute RIB, load

    To execute RIB, load rib.pl with

    ?:- use_module(library(’cplint/rib’)).
    -

    and call: +

    and call:

    ?:- ib_par(stem).
    -

    To execute EMBLEM, load

    To execute EMBLEM, load slipcase.pl with

    ?:- use_module(library(’cplint/slipcase’)).
    -

    and call +

    and call

    ?:- em(stem).
    -

    To execute SLIPCASE, load

    To execute SLIPCASE, load slipcase.pl with

    ?:- use_module(library(’cplint/slipcase’)).
    -

    and call +

    and call

    ?:- sl(stem).
    -

    To execute SLIPCOVER, load

    To execute SLIPCOVER, load slipcover.pl with

    ?:- use_module(library(’cplint/slipcover’)).
    -

    and call +

    and call

    ?:- sl(stem).
    -

    +

    +

    5.4 Learning Examples

    -

    The subfolders Testing +

    To test the theories learned, load test.pl with + +

    +?:- use_module(library(’cplint/test’)). +
    +

    and call + +

    +?:- main([<stem_fold1>,...,<stem_foldn>],[<testing_set_fold1>,..., + 
      <testing_set_foldn>]). +
    +

    For example, if you want to test the theory in ai_train.rules on the set ai.kb, +you can call + +

    +?:- main([ai_train],[ai]). +
    +

    The testing program has the following parameter: +

    +

    The testing program produces the following output in the current folder: +

    +

    +

    5.5 Learning Examples

    +

    The subfolders em, rib, slipcase and slipcover of the class="cmtt-10">packages/cplint folder in Yap git distribution contain examples of input and output files for the learning algorithms. -

    +

    6 License

    -

    License +

    cplint, as Yap, follows the Artistic License 2.0 that you can find in Yap CVS root dir. The copyright is by Fabrizio Riguzzi. -

    The modules in the approx subdirectory use SimplecuddLPADs, a modification of + +

    The modules in the approx subdirectory use SimplecuddLPADs, a modification of the Simplecudd library whose copyright is by Katholieke Universiteit Leuven and that follows the Artistic License 2.0. -

    Some modules use the library

    Some modules use the library CUDD for manipulating BDDs that is included in glu. For the use of CUDD, the following license must be accepted: -

    Copyright (c) 1995-2004, Regents of the University of Colorado -

    All rights reserved. -

    Redistribution and use in source and binary forms, with or without modification, +

    Copyright (c) 1995-2004, Regents of the University of Colorado +

    All rights reserved. +

    Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

    - -

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS
    AND CONTRIBUTORS ”AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR @@ -1452,7 +1521,7 @@ class="newline" />AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -

    lpad.pl, semlpad.pl and cpl.pl are based on the SLG system by Weidong @@ -1460,9 +1529,10 @@ Chen and David Scott Warren , Copyright (C) 1993 Southern Methodist University, 1993 SUNY at Stony Brook, see the file COYPRIGHT_SLG for detailed information on this copyright. +

    References

    + id="x1-170006">References

    @@ -1490,7 +1560,6 @@ class="cmti-10">31-2 September, 2011, 2011.

    [4]   Elena Bellodi and Fabrizio Riguzzi. Learning the structure of - probabilistic logic programs. In Inductive Logic Programming, 21th Programming, 2013. class="cmti-10">Inductive Logic Programming (ILP 2004), Work in Progress Track, 2004. +

    [8]   Intell., 79(1):1–38, 1995. class="cmti-10">International Joint Conference on Artificial Intelligence, pages 2462–2467, 2007. -

    [12]   Research, 3:679–707, December 2002. id="XDBLP:journals/ai/Poole97">David Poole. The independent choice logic for modelling multiple agents under uncertainty. Artificial Intelligence, 94(1-2):7–56, 1997. +

    [16]   Proceedings of the 26th Italian class="cmti-10">Conference on Computational Logic (CILC2011), Pescara, Italy, 31 August-2 September, 2011, 2011. -

    [20]   Proceedings of the 10th class="cmti-10">European Conference on Logics in Artificial Intelligence, LNAI. Springer, September 2006.

    +

    [23]   J. Vennekens, Marc Denecker, and Maurice Bruynooghe. CP-logic: diff --git a/packages/cplint/doc/manual.pdf b/packages/cplint/doc/manual.pdf index 216e2ef4d..5771d7bcc 100644 Binary files a/packages/cplint/doc/manual.pdf and b/packages/cplint/doc/manual.pdf differ diff --git a/packages/cplint/doc/manual.tex b/packages/cplint/doc/manual.tex index bcf914e76..1b6bc9295 100644 --- a/packages/cplint/doc/manual.tex +++ b/packages/cplint/doc/manual.tex @@ -629,6 +629,8 @@ maximum number of theory search iterations maximum numbers of background clauses \item \verb|maxdepth_var| (values: integer, default value: 2, valid for SLIPCOVER): maximum depth of variables in clauses (as defined in \cite{DBLP:journals/ai/Cohen95}). +\item \verb|score| (values: \verb|ll|, \verb|aucpr|, default value \verb|ll|, valid for SLIPCOVER): determines the score function for refinement: if set to \verb|ll|, log likelihood is used, if set to \verb|aucpr|, the area under the +Precision-Recall curve is used. \end{itemize} \subsection{Commands} To execute CEM, load \texttt{em.pl} with @@ -671,6 +673,36 @@ and call \begin{verbatim} ?:- sl(stem). \end{verbatim} + + +\subsection{Testing} +To test the theories learned, load \texttt{test.pl} with +\begin{verbatim} +?:- use_module(library('cplint/test')). +\end{verbatim} +and call +\begin{verbatim} +?:- main([,...,],[,..., + ]). +\end{verbatim} +For example, if you want to test the theory in \verb|ai_train.rules| on the set \verb|ai.kb|, you can call +\begin{verbatim} +?:- main([ai_train],[ai]). +\end{verbatim} +The testing program has the following parameter: +\begin{itemize} +\item \verb|neg_ex| (values: \verb|given|, \verb|cw|, default value: \verb|cw|): if set to \verb|given|, the negative examples +are taken from \verb|.kb|, i.e., those example \verb|ex| stored as \verb|neg(ex)|; if set to \verb|cw|, the negative examples are generated according to the closed world assumption, i.e., all atoms for target predicates that are not positive examples. The set of all atoms is obtained by collecting the set of constants for each type of the arguments of the target predicate. +\end{itemize} +The testing program produces the following output in the current folder: +\begin{itemize} +\item \verb|cll.pl|: for each fold, the list of examples orderd by their probability of being true +\item \verb|areas.csv|: the areas under the Precision-Recall curve and the Receiver Operating Characteristic curve +\item \verb|curve_roc.m|: a Matlab file for plotting the Receiver Operating Characteristic curve +\item \verb|curve_pr.m|: a Matlab file for plotting the Precision-Recall curve +\end{itemize} + + \subsection{Learning Examples} The subfolders \verb|em|, \verb|rib|, \verb|slipcase| and \verb|slipcover| of the \verb|packages/cplint| folder in Yap git distribution contain examples of input and output files for the learning algorithms. diff --git a/packages/cplint/slipcover/test.pl b/packages/cplint/slipcover/test.pl new file mode 100644 index 000000000..42a7bc9eb --- /dev/null +++ b/packages/cplint/slipcover/test.pl @@ -0,0 +1,469 @@ +:-multifile setting/2. +:-source. +:-use_module(library('cplint/slipcover')). + +setting(neg_ex,cw). +/* allowed values: given, cw */ + +main(TrainP,TestSets):- + system('rm -f areas.csv'), + system('rm -f curve_roc.m'), + system('rm -f curve_pr.m'), + open('cll1.pl',write,S), + open('areas.csv',append,SA), + format(SA,"Fold;\tCLL;\t AUCROC;\t AUCPR~n",[]), + close(SA), + test(TrainP,TestSets,S,[],LG,0,Pos,0,Neg,0,CLL), + keysort(LG,LG1), + format(S,"cll(all,post,~d,~d,[",[Pos,Neg]), + writes(LG1,S), + reverse(LG1,LGR1), + compute_areas(LGR1,Pos,Neg,AUCROC,AUCPR), + open('areas.csv',append,SA1), + format(SA1,"~a;\t ~f;\t ~f;\t ~f~n",[all,CLL,AUCROC,AUCPR]), + close(SA1), + close(S). + +test([],[],_S,LG,LG,Pos,Pos,Neg,Neg,CLL,CLL). + +test([HP|TP],[HT|TT],S,LG0,LG,Pos0,Pos,Neg0,Neg,CLL0,CLL):- + test_fold(HP,HT,S,LG1,Pos1,Neg1,CLL1), + append(LG0,LG1,LG2), + Pos2 is Pos0+Pos1, + Neg2 is Neg0+Neg1, + CLL2 is CLL0+CLL1, + test(TP,TT,S,LG2,LG,Pos2,Pos,Neg2,Neg,CLL2,CLL). + +test_fold(P,F,S,LGOrd,Pos,Neg,CLL1):- + atom_concat([P,'.rules'],PR), + atom_concat([P,'.bg'],PBG), + atom_concat([P,'.l'],FL), + atom_concat([F,'.kb'],TKB), + reconsult(FL), + (file_exists(PBG)-> + set(compiling,on), + load(PBG,_ThBG,RBG), + set(compiling,off), + generate_clauses(RBG,_RBG1,0,[],ThBG), + assert_all(ThBG) + ; + true + ), + format("~a~n",[TKB]), + load_models(TKB,DB), + set(compiling,on), + load(PR,Th1,R1), + set(compiling,off), + assert_all(Th1), + assert_all(R1), + find_ex(DB,LG,Pos,Neg), + compute_CLL_atoms(LG,0,0,CLL1,LG1), + (file_exists(PBG)-> + retract_all(ThBG) + ; + true + ), + retract_all(Th1), + retract_all(R1), + keysort(LG1,LGOrd), + reverse(LGOrd,LGROrd), + compute_areas(LGROrd,Pos,Neg,AUCROC,AUCPR), + format(S,"cll(~a,post,~d,~d,[",[F,Pos,Neg]), + writes(LGOrd,S), + open('areas.csv',append,SA), + format(SA,"~a;\t ~f;\t ~f;\t ~f~n",[F,CLL1,AUCROC,AUCPR]), + close(SA). + +compute_areas(LG,Pos,Neg,AUCROC,AUCPR):- + compute_pointsroc(LG,+inf,0,0,Pos,Neg,[],ROC), + hull(ROC,0,0,0,AUCROC), + open('curve_roc.m',append,SC), + write_p(ROC,SC), + close(SC), + compute_aucpr(LG,Pos,Neg,AUCPR,PR), + open('curve_pr.m',append,SPR), + write_ppr(PR,SPR), + close(SPR). + +compute_pointsroc([],_P0,_TP,_FP,_FN,_TN,P0,P1):-!, + append(P0,[1.0-1.0],P1). + +compute_pointsroc([P- (\+ _)|T],P0,TP,FP,FN,TN,Po0,Po1):-!, + (P + FPR is FP/(FP+TN), + TPR is TP/(TP+FN), + append(Po0,[(FPR-TPR)],Po2), + P1=P + ; + Po2=Po0, + P1=P0 + ), + FP1 is FP+1, + TN1 is TN-1, + compute_pointsroc(T,P1,TP,FP1,FN,TN1,Po2,Po1). + +compute_pointsroc([P- _|T],P0,TP,FP,FN,TN,Po0,Po1):-!, + (P + FPR is FP/(FP+TN), + TPR is TP/(TP+FN), + append(Po0,[FPR-TPR],Po2), + P1=P + ; + Po2=Po0, + P1=P0 + ), + TP1 is TP+1, + FN1 is FN-1, + compute_pointsroc(T,P1,TP1,FP,FN1,TN,Po2,Po1). + + +hull([],FPR,TPR,AUC0,AUC1):- + AUC1 is AUC0+(1-FPR)*(1+TPR)/2. + + +hull([FPR1-TPR1|T],FPR,TPR,AUC0,AUC1):- + AUC2 is AUC0+(FPR1-FPR)*(TPR1+TPR)/2, + hull(T,FPR1,TPR1,AUC2,AUC1). + +compute_aucpr(L,Pos,Neg,A,PR):- + L=[P_0-E|TL], + (E= (\+ _ )-> + FP=1, + TP=0, + FN=Pos, + TN is Neg -1 + ; + FP=0, + TP=1, + FN is Pos -1, + TN=Neg + ), + compute_curve_points(TL,P_0,TP,FP,FN,TN,Points), + Points=[R0-P0|_TPoints], + (R0=:=0,P0=:=0-> + Flag=true + ; + Flag=false + ), + area(Points,Flag,Pos,0,0,0,A,[],PR). + +compute_curve_points([],_P0,TP,FP,_FN,_TN,[1.0-Prec]):-!, + Prec is TP/(TP+FP). + +compute_curve_points([P- (\+ _)|T],P0,TP,FP,FN,TN,Pr):-!, + (P + Prec is TP/(TP+FP), + Rec is TP/(TP+FN), + Pr=[Rec-Prec|Pr1], + P1=P + ; + Pr=Pr1, + P1=P0 + ), + FP1 is FP+1, + TN1 is TN-1, + compute_curve_points(T,P1,TP,FP1,FN,TN1,Pr1). + +compute_curve_points([P- _|T],P0,TP,FP,FN,TN,Pr):-!, + (P + Prec is TP/(TP+FP), + Rec is TP/(TP+FN), + Pr=[Rec-Prec|Pr1], + P1=P + ; + Pr=Pr1, + P1=P0 + ), + TP1 is TP+1, + FN1 is FN-1, + compute_curve_points(T,P1,TP1,FP,FN1,TN,Pr1). + +area([],_Flag,_Pos,_TPA,_FPA,A,A,PR,PR). + +area([R0-P0|T],Flag,Pos,TPA,FPA,A0,A,PR0,PR):- + TPB is R0*Pos, + (TPB=:=0-> + A1=A0, + FPB=0, + PR2=PR0, + PR=[R0-P0|PR3] + ; + R_1 is TPA/Pos, + (TPA=:=0-> + (Flag=false-> + P_1=P0, + PR=[0.0-P0|PR3] + ; + P_1=0.0, + PR=[0.0-0.0|PR3] + ) + ; + P_1 is TPA/(TPA+FPA), + PR=PR3 + ), + FPB is TPB*(1-P0)/P0, + N is TPB-TPA+0.5, + (N<1.0-> + append(PR0,[R0-P0],PR2), + A1=A0 + ; + interpolate(1,N,Pos,R_1,P_1,TPA,FPA,TPB,FPB,A0,A1,[],PR1), + append(PR0,PR1,PR2) + ) + ), + area(T,Flag,Pos,TPB,FPB,A1,A,PR2,PR3). + +interpolate(I,N,_Pos,_R0,_P0,_TPA,_FPA,_TPB,_FPB,A,A,PR,PR):-I>N,!. + +interpolate(I,N,Pos,R0,P0,TPA,FPA,TPB,FPB,A0,A,PR0,[R-P|PR]):- + R is (TPA+I)/Pos, + P is (TPA+I)/(TPA+I+FPA+(FPB-FPA)/(TPB-TPA)*I), + A1 is A0+(R-R0)*(P+P0)/2, + I1 is I+1, + interpolate(I1,N,Pos,R,P,TPA,FPA,TPB,FPB,A1,A,PR0,PR). + + +find_ex(DB,LG,Pos,Neg):- + findall(P/A,output(P/A),LP), + setting(neg_ex,given),!, + find_ex_pred(LP,DB,[],LG,0,Pos,0,Neg). + +find_ex(DB,LG,Pos,Neg):- + findall(P/A,output(P/A),LP), + setting(neg_ex,cw), + find_ex_pred_cw(LP,DB,[],LG,0,Pos,0,Neg). + + +find_ex_pred([],_DB,LG,LG,Pos,Pos,Neg,Neg). + +find_ex_pred([P/A|T],DB,LG0,LG,Pos0,Pos,Neg0,Neg):- + functor(At,P,A), + find_ex_db(DB,At,LG0,LG1,Pos0,Pos1,Neg0,Neg1), + find_ex_pred(T,DB,LG1,LG,Pos1,Pos,Neg1,Neg). + +find_ex_db([],_At,LG,LG,Pos,Pos,Neg,Neg). + +find_ex_db([H|T],At,LG0,LG,Pos0,Pos,Neg0,Neg):- + At=..[P|L], + At1=..[P,H|L], + findall(At1,At1,LP), + findall(\+ At1,neg(At1),LN), + length(LP,NP), + length(LN,NN), + append([LG0,LP,LN],LG1), + Pos1 is Pos0+NP, + Neg1 is Neg0+NN, + find_ex_db(T,At,LG1,LG,Pos1,Pos,Neg1,Neg). + + +find_ex_pred_cw([],_DB,LG,LG,Pos,Pos,Neg,Neg). + +find_ex_pred_cw([P/A|T],DB,LG0,LG,Pos0,Pos,Neg0,Neg):- + functor(At,P,A), + get_types(At,Types), + remove_duplicates(Types,Types1), + find_ex_db_cw(DB,At,Types1,LG0,LG1,Pos0,Pos1,Neg0,Neg1), + find_ex_pred_cw(T,DB,LG1,LG,Pos1,Pos,Neg1,Neg). + +get_types(At,Types):- + modeh(_,At), + At=..[_|Args], + get_args(Args,Types). + +get_args([],[]). + +get_args([+H|T],[H|T1]):-!, + get_args(T,T1). + +get_args([-H|T],[H|T1]):-!, + get_args(T,T1). + +get_args([#H|T],[H|T1]):-!, + get_args(T,T1). + +get_args([-#H|T],[H|T1]):-!, + get_args(T,T1). + +get_args([H|T],[H|T1]):- + get_args(T,T1). + + + + +get_constants([],_M,[]). + +get_constants([Type|T],M,[(Type,Co)|C]):- + find_pred_using_type(Type,LP), + find_constants(LP,M,[],Co), + get_constants(T,M,C). + +find_pred_using_type(T,L):- + setof((P,Ar,A),pred_type(T,P,Ar,A),L). + +pred_type(T,P,Ar,A):- + modeh(_,S), + S=..[P|Args], + length(Args,Ar), + scan_args(Args,T,1,A). + +pred_type(T,P,Ar,A):- + modeb(_,S), + S=..[P|Args], + length(Args,Ar), + scan_args(Args,T,1,A). + +scan_args([+T|_],T,A,A):-!. + +scan_args([-T|_],T,A,A):-!. + +scan_args([#T|_],T,A,A):-!. + +scan_args([-#T|_],T,A,A):-!. + +scan_args([_|Tail],T,A0,A):- + A1 is A0+1, + scan_args(Tail,T,A1,A). + +find_constants([],_M,C,C). + +find_constants([(P,Ar,A)|T],M,C0,C):- + gen_goal(1,Ar,A,Args,ArgsNoV,V), + G=..[P,M|Args], + setof(V,ArgsNoV^G,LC), + append(C0,LC,C1), + remove_duplicates(C1,C2), + find_constants(T,M,C2,C). + + +gen_goal(Arg,Ar,_A,[],[],_):- + Arg =:= Ar+1,!. + +gen_goal(A,Ar,A,[V|Args],ArgsNoV,V):-!, + Arg1 is A+1, + gen_goal(Arg1,Ar,A,Args,ArgsNoV,V). + +gen_goal(Arg,Ar,A,[ArgV|Args],[ArgV|ArgsNoV],V):- + Arg1 is Arg+1, + gen_goal(Arg1,Ar,A,Args,ArgsNoV,V). + + + +find_ex_db_cw([],_At,_Ty,LG,LG,Pos,Pos,Neg,Neg). + +find_ex_db_cw([H|T],At,Types,LG0,LG,Pos0,Pos,Neg0,Neg):- + get_constants(Types,H,C), + At=..[P|L], + get_types(At,TypesA), + length(L,N), + length(LN,N), + At1=..[P,H|LN], + findall(At1,At1,LP), + setof(\+ At1,neg_ex(LN,TypesA,At1,C),LNeg), + length(LP,NP), + length(LNeg,NN), + append([LG0,LP,LNeg],LG1), + Pos1 is Pos0+NP, + Neg1 is Neg0+NN, + find_ex_db_cw(T,At,Types,LG1,LG,Pos1,Pos,Neg1,Neg). + +neg_ex([],[],At1,_C):- + \+ At1. + +neg_ex([H|T],[HT|TT],At1,C):- + member((HT,Co),C), + member(H,Co), + neg_ex(T,TT,At1,C). + +compute_CLL_atoms([],_N,CLL,CLL,[]):-!. + +compute_CLL_atoms([\+ H|T],N,CLL0,CLL1,[PG- (\+ H)|T1]):-!, + rule_n(NR), + init_test(NR), +% write(\+ H), + get_node(H,BDD),!, + ret_prob(BDD,PG), +% write(PG),nl, + end_test,!, + PG1 is 1-PG, + (PG1=:=0.0-> + CLL2 is CLL0-10 + ; + CLL2 is CLL0+ log(PG1) + ), + N1 is N+1, + compute_CLL_atoms(T,N1,CLL2,CLL1,T1). + +compute_CLL_atoms([H|T],N,CLL0,CLL1,[PG-H|T1]):- + rule_n(NR), + init_test(NR), +% write(H), + get_node(H,BDD),!, + ret_prob(BDD,PG), +% write(PG),nl, + end_test,!, + (PG=:=0.0-> + CLL2 is CLL0-10 + ; + CLL2 is CLL0+ log(PG) + ), + N1 is N+1, + compute_CLL_atoms(T,N1,CLL2,CLL1,T1). + + +writes([H-H1],S):- + format(S,"~f - (~p)]).~n~n",[H,H1]). + +writes([H-H1|T],S):- + format(S,"~f - (~p),~n",[H,H1]), + writes(T,S). + +write_p(P,S):- + get_xy(P,PX,PY), + format(S,"x=[",[]), + writesf(PX,S), + format(S,"y=[",[]), + writesf(PY,S), + format(S," +figure('Name','roc','NumberTitle','off') +set(gca,'XLim',[0.0 1.0]) +set(gca,'YLim',[0.0 1.0]) +x=[x 1.0] +y=[y 0.0] +k=convhull(x,y) +plot(x(k),y(k),'r-',x,y,'--b+') +%A = polyarea(x,y)~n~n +%save area_roc.csv A -ascii -append +", + []). + +get_xy([],[],[]). + +get_xy([X-Y|T],[X|TX],[Y|TY]):- + get_xy(T,TX,TY). + + +writesf([H],S):- + format(S,"~f]~n",[H]). + +writesf([H|T],S):- + format(S,"~f ",[H]), + writesf(T,S). + +write_ppr(P,S):- + get_xy(P,PX,PY), + format(S,"rec=[",[A]), + writesf(PX,S), + format(S,"prec=[",[A]), + writesf(PY,S), + format(S," +figure('Name','pr','NumberTitle','off') +set(gca,'XLim',[0.0 1.0]) +set(gca,'YLim',[0.0 1.0]) +rec=[0.0 rec 1.0]; +prec=[0.0 prec 0.0]; +plot(rec,prec,'--*k') +%A=polyarea(rec,prec) +%save area_pr.csv A -ascii -append +~n~n", + []). +