#reads in lambdalist.txt then calculates bm for each lambda
#bm is the ratio of the actual integral of your eigenfunction to its approximate (discrete) integral at the specified level. 
#bm is calculated using the formula to get <f,f>_m+1 from <f,f>_m for an eigenfunction f.


read "itall.txt":

lvl:=1:
path:=cat("../data/level",lvl,"/"):
#lambdatol: tolerance for deleting repeated lambdas
lambdatol:=.0000000001:
#bmtol: tolerance for covergence of bm
bmtol:=.0000000001:

numvertices:=(3^(lvl+1)-3)/2:

lambdalist:=[];

fd:=fopen(cat(path,lvl,"lambdalist.txt"),READ):

for i from 1 to numvertices do
	lambdalist:=[op(lambdalist),fscanf(fd,"%g\n")[1]];
end do;

fclose(fd);

l:=nops(lambdalist);

i:=1;

while (i < l) do
	badlist:=[];
	for j from (i+1) to nops(lambdalist) do
		if (abs(lambdalist[j]-lambdalist[i]) < lambdatol) then
			badlist:=[op(badlist),j=NULL];
		end if;
	end do;
	lambdalist:=subsop(op(badlist),lambdalist);
	l:=nops(lambdalist);
	i:=i+1;
end do;

fd:=fopen(cat(path,lvl,"bm.txt"),WRITE);

fprintf(fd,"lambda,\t\t\t\tbm\t(level %d)\n",lvl);

for i from 1 to nops(lambdalist) do
	fprintf(fd,"%20.20g\t\t%20.20g\n",lambdalist[i],calcbm(lambdalist[i],[],bmtol));
end do;

fclose(fd);