(* ========================================================================== *) (* FLYSPECK - BOOK FORMALIZATION *) (* *) (* Lemma: OXLZLEZ *) (* Chapter: Packing *) (* Author: Thomas C. Hales *) (* Date: 2010-02-09 *) (* ========================================================================== *) (* This file contains the inequalities for the hard case of the cluster inequality, consisting of 4 blades, 3 quarters, and one half-weight. *) type irecord = { caseno : int; coef1 : term * term * term * term; coef2 : term*term*term*term; coef3 : term*term*term*term; coef4 : term*term*term*term; branch1 : int list; branch2 : int list; branch3 : int list; branch4 : int list; branch5 : int list; eps : float; numerical1 : float list; numerical2 : float list; numerical3 : float list; numerical4 : float list; };; module Ineqdata3q1h : sig val records : irecord list val mk_ineq : int -> irecord -> term val domain_cover_calculation: bool val combine : (int list*int list*int list*int list*int list)* (int list*int list*int list*int list*int list) -> (bool*int)*(int list*int list*int list*int list*int list) end = struct (* FOUR BLADE INEQUALITIES Each record corresponds to 5 different formal inequalities obtained by mk_ineq i, for i=0,1,2,3,4. Data nonlindata automatically generated by Mathematica sphereBook.nb, *process* function . There is a nonlinear optimization problem of 4blades, 3quarters, 1halfwt along a common spine. This is a 13-dimensional problem. A Mathematica calculation has broken it into a collection of 6-dimensional nonlinear optimizations. The data describing these 6-dimensional problems appears below. Each list entry corresponds to four nonlinear optimization problems (for the four different simplices around the spine. Each list entry has the following format. [[caseno];lindata;b1;b2;b3;b4;b5;d1;d2;d3;d4] caseno : 1, 2,3,4 This gives information about what the lengths of the spine and edge#4 on the 1halfwt are: case spine edge#4 1 2h0 to 2hplus 2hminus to 2h0 2 2h0 to 2hplus 2h0 to 2hplus 3 2hminus to 2h0 2hminus to 2h0 4 2hminus to 2h0 2h0 to 2hplus **** lindata is a list of length 14. [eps,a, b1,c1,d1, b2,c2,d2, b3,c3,d3, b4,c4,d4] These are the inequalities: gamma + a dih + bi y1 + ci (y2+y3+y5+y6) + di >= 0. -eps gives the margin by which it holds. The first group is for the 4-cell of wt 0.5. The indices 2,3,4 are for the quarters. **** b1,b2,b3,b4,b5 branch data each of these is a sequence of 0s and 1s. b1 <-> domain of y1 (the spine) b2 <-> domain of y4 (on the (halfwt) b3 <-> domain of the y4 variable on quarter 2 b4 <-> domain of the y4 variable on quarter 3 b5 <-> domain of the y4 variable on quarter 4 each entry in bi cuts the domain in half, 0 takes the LHS, 1 takes the RHS. The first in the sequence is the first subdivision performed. **** d1,d2,d3,d4 data on the numerical optimization of the 4 nonlinear inequalities di = [value;y1,y2,y3,y4,y5,y6] minimizer(numerical) and optimal point. *) (* produced from /tmp/ineqdata3q1h.ml (from Mathematica) with the following edits: s/{/[ /g s/}/ ]/g s/,/ ;/g s/. /.0 /g The formal version has the additional edits s/-/-- /g \([0-9]\)-> #\1 s/ //g *) open Sphere;; let do_betas x = all_forall (snd(dest_eq(concl(BETAS_CONV x))));; let dest_decimal x = match strip_comb x with | (dec,[a;b]) -> div_num (dest_numeral a) (dest_numeral b) | _ -> failwith ("dest_decimal: '" ^ string_of_term x ^ "'");; let dest_signed_decimal x = match strip_comb x with | (dec,[a;b]) -> dest_decimal x | (neg,[a]) -> Num.minus_num(dest_decimal a) | _ -> failwith ("dest_decimal: '" ^ string_of_term x ^ "'");; let int_of_dec u = Num.int_of_num (dest_signed_decimal u);; let float_of_dec u = Num.float_of_num (dest_signed_decimal u);; let mk_irecord oni = let fd t = map float_of_dec t in let i t = map int_of_dec t in let g = function [eps;a;b1;c1;d1;b2;c2;d2;b3;c3;d3;b4;c4;d4] -> (float_of_dec eps,(a,b1,c1,d1),(a,b2,c2,d2),(a,b3,c3,d3),(a,b4,c4,d4)) | _ -> failwith "parse error g" in let f = function [[case];lindata;b1;b2;b3;b4;b5;d1;d2;d3;d4] -> (int_of_dec case,g lindata,i b1,i b2, i b3,i b4,i b5,fd d1,fd d2,fd d3,fd d4) | _ -> failwith "parse error f" in let (i,(e,c1,c2,c3,c4),b1,b2,b3,b4,b5,n1,n2,n3,n4) = f oni in { caseno = i; coef1 = c1; coef2 = c2; coef3 = c3; coef4 = c4; branch1 = b1; branch2 = b2; branch3 = b3; branch4 = b4; branch5 = b5; eps = e; numerical1 = n1; numerical2 = n2; numerical3 = n3; numerical4 = n4; };; let y1domain d = List.nth [`&2 * h0,&2 * hplus`;`&2 * h0,&2 * hplus`; `&2 * hminus,&2 * h0`; `&2 * hminus,&2 * h0`] (d.caseno -1);; let y4domain d = List.nth [`&2 * hminus,&2 * h0`; `&2 * h0,&2 * hplus`; `&2 * hminus,&2 * h0`; `&2 * h0,&2 * hplus` ] (d.caseno-1);; (* in sphere.hl: let pathL = new_definition `pathL (a,b) = (a,(a+b)/ &2)`;; let pathR = new_definition `pathR (a,b) = ((a+b)/ &2,b)`;; *) let rec mkpath r = function [] -> r | x::xs -> let t = if (x=0) then `pathL` else `pathR` in mkpath (mk_comb (t,r)) xs;; let template = `\ y1d y2d y3d y4d y5d y6d a b c d w m. ineq [(FST y1d, y1, SND y1d); (FST y2d ,y2, SND y2d); (FST y3d,y3,SND y3d); (FST y4d,y4,SND y4d); (FST y5d,y5,SND y5d); (FST y6d,y6,SND y6d)] (gamma4fgcy y1 y2 y3 y4 y5 y6 lmfun / &w + &m *beta_bump_force_y y1 y2 y3 y4 y5 y6 + a * dih_y y1 y2 y3 y4 y5 y6 + b * y1 + c * (y2 + y3 + y5 + y6) + d > &0)`;; let mk_ineq1 i d = (* i=1,2,3,4, d reconstructs the formal statement of the ineq *) let nth = List.nth in let halfwt i = (i=1) in let mk = mk_small_numeral in let y1d = (y1domain d) in let yd = `(&2, &2 * hminus)` in let y4d = if halfwt i then (y4domain d) else yd in let y j = nth [y1d;yd;yd;y4d;yd;yd] (j-1) in let w = if halfwt i then 2 else 1 in let m = w - 1 in let (a,b,c,e) = nth [d.coef1;d.coef2;d.coef3;d.coef4] (i-1) in let p1 = d.branch1 in let p4 = nth [d.branch2;d.branch3;d.branch4;d.branch5] (i-1) in let p j = nth [p1;[];[];p4;[];[]] (j-1) in let x j = mkpath (y j) (p j) in do_betas(list_mk_comb (template, [x 1;x 2;x 3;x 4;x 5;x 6;a;b;c;e;mk w; mk m]));; (* NB: In each simplex ineq, there are four products ci * yj. When we sum, we get 16 products, each (ci + ci') is paired with y(i,i') and z(i,i'), where y is the edge at the origin and z is the edge on top. We combine y(i,i')+z(i,i') into a single variable &2 *y... *) let templateB = `\ a b1 b2 b3 b4 c1 c2 c3 c4 d1 d2 d3 d4 y1d. ineq [(FST y1d, y1, SND y1d); (&2 ,y12, &2 * hminus); (&2,y23, &2 * hminus); (&2,y34, &2 * hminus); (&2,y41, &2 * hminus)] (&2 * pi * a + (b1+b2+b3+b4)* y1 + &2 * (c1+c2) * y12 + &2 *(c2 + c3) * y23 + &2 *(c3 + c4) * y34 + &2 * (c4+c1)* y41 + d1 + d2 + d3 + d4 < &0)`;; let mk_ineq0 d = (* test constant compatibility for the 4 simplices around the spine *) let (a,b1,c1,d1) = d.coef1 in let (_,b2,c2,d2) = d.coef2 in let (_,b3,c3,d3) = d.coef3 in let (_,b4,c4,d4) = d.coef4 in let y1d = mkpath (y1domain d) d.branch1 in do_betas(list_mk_comb(templateB, [a; b1; b2; b3; b4; c1; c2; c3; c4; d1; d2; d3; d4; y1d]));; let mk_ineq case d = let _ = (case >= 0) or failwith "mk_ineq domain error" in let _ = (case <= 4) or failwith "mk_ineq domain error" in if (case=0) then mk_ineq0 d else mk_ineq1 case d;; (* formal version. We take the floating point numbers to be exact rational numbers given by their decimal expansions: *) let raw_nonlindatah = [ [ [ `#4.0` ] ; [ `-- #0.00289` ; `#0.129913` ; `-- #0.060416` ; `#0.002372` ; `-- #0.113134` ; `#0.01764` ; `-- #0.002372` ; `-- #0.198777` ; `#0.045166` ; `#0.002372` ; `-- #0.306092` ; `#0.021777` ; `-- #0.002372` ; `-- #0.259166` ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.003326` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.463514` ; `#2.0` ; `#2.463508` ; `#2.0` ; `#2.000001` ; `#2.000001` ] ; [ `#0.003534` ; `#2.463509` ; `#2.000001` ; `#2.463508` ; `#2.0` ; `#2.0` ; `#2.000001` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ] ; [ [ `#4.0` ] ; [ `-- #0.002889` ; `#0.129699` ; `-- #0.060316` ; `#0.002264` ; `-- #0.112116` ; `#0.019214` ; `-- #0.002264` ; `-- #0.203309` ; `#0.021887` ; `#0.002264` ; `-- #0.29619` ; `#0.019214` ; `-- #0.002264` ; `-- #0.203309` ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.003328` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.463513` ; `#2.0` ; `#2.463508` ; `#2.0` ; `#2.000001` ; `#2.0` ] ; [ `#0.002889` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ; [ `#0.002998` ; `#2.519915` ; `#2.000025` ; `#2.000038` ; `#2.000022` ; `#2.463485` ; `#2.000022` ] ] ; [ [ `#4.0` ] ; [ `-- #0.00289` ; `#0.129913` ; `-- #0.060416` ; `#0.002372` ; `-- #0.113134` ; `#0.021777` ; `-- #0.002372` ; `-- #0.259166` ; `#0.045166` ; `#0.002372` ; `-- #0.306092` ; `#0.01764` ; `-- #0.002372` ; `-- #0.198777` ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.003326` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ; [ `#0.003534` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463508` ; `#2.0` ] ; [ `#0.002915` ; `#2.519935` ; `#2.000027` ; `#2.00004` ; `#2.000024` ; `#2.463484` ; `#2.000025` ] ] ; [ [ `#4.0` ] ; [ `-- #0.000426` ; `-- #0.114872` ; `#0.133539` ; `-- #0.080919` ; `#0.532524` ; `#0.148605` ; `#0.080919` ; `-- #0.855148` ; `#0.08743` ; `-- #0.080919` ; `#0.593722` ; `#0.148605` ; `#0.080919` ; `-- #0.855148` ] ; [ ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.000426` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.6508` ; `#2.0` ; `#2.0` ] ; [ `#0.000435` ; `#2.463511` ; `#2.000001` ; `#2.000001` ; `#2.000002` ; `#2.000002` ; `#2.000002` ] ; [ `#0.004824` ; `#2.46351` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.000435` ; `#2.463511` ; `#2.000001` ; `#2.000001` ; `#2.000002` ; `#2.000002` ; `#2.000002` ] ] ; [ [ `#3.0` ] ; [ `-- #0.00272` ; `#0.065103` ; `-- #0.008732` ; `-- #0.024884` ; `#0.097156` ; `#0.072591` ; `#0.024884` ; `-- #0.464803` ; `#0.042651` ; `-- #0.024884` ; `#0.008797` ; `#0.055356` ; `#0.024884` ; `-- #0.458108` ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.002594` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.491729` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.463509` ; `#2.0` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ] ; [ [ `#3.0` ] ; [ `-- #0.00272` ; `#0.065103` ; `-- #0.029778` ; `-- #0.027449` ; `#0.170713` ; `#0.072591` ; `#0.027449` ; `-- #0.485323` ; `#0.055356` ; `-- #0.027449` ; `-- #0.039438` ; `#0.072591` ; `#0.027449` ; `-- #0.485323` ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.002594` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.491998` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#3.0` ] ; [ `-- #0.00272` ; `#0.065103` ; `-- #0.008732` ; `#0.025458` ; `-- #0.30558` ; `#0.055356` ; `-- #0.025458` ; `-- #0.055371` ; `#0.072591` ; `#0.025458` ; `-- #0.469389` ; `#0.037947` ; `-- #0.025458` ; `#0.025236` ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.002612` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.489061` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#3.0` ] ; [ `-- #0.00225` ; `-- #0.114872` ; `#0.116669` ; `#0.080919` ; `-- #0.7251449999999999` ; `#0.08743` ; `-- #0.080919` ; `#0.595546` ; `#0.148605` ; `#0.080919` ; `-- #0.853324` ; `#0.08743` ; `-- #0.080919` ; `#0.595546` ] ; [ ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.00225` ; `#2.519989` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.006648` ; `#2.46351` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.002259` ; `#2.463511` ; `#2.000001` ; `#2.000001` ; `#2.000002` ; `#2.000002` ; `#2.000002` ] ; [ `#0.006648` ; `#2.46351` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.00289` ; `#0.129913` ; `-- #0.09152` ; `#0.002372` ; `-- #0.034749` ; `#0.347659` ; `-- #0.002372` ; `-- #1.030425` ; `-- #0.105208` ; `#0.002372` ; `#0.072849` ; `-- #0.150931` ; `-- #0.002372` ; `#0.176057` ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.005089` ; `#2.52` ; `#2.0` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.00289` ; `#0.129913` ; `#0.340765` ; `#0.002372` ; `-- #1.124108` ; `-- #0.094917` ; `-- #0.002372` ; `#0.084866` ; `-- #0.150931` ; `#0.002372` ; `#0.138108` ; `-- #0.094917` ; `-- #0.002372` ; `#0.084866` ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.520001` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.00289` ; `#0.129913` ; `-- #0.09152` ; `#0.002372` ; `-- #0.034749` ; `#0.291645` ; `-- #0.002372` ; `-- #0.939234` ; `-- #0.105208` ; `#0.002372` ; `#0.072849` ; `-- #0.094917` ; `-- #0.002372` ; `#0.084866` ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.00289` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.231754` ; `#2.0` ; `#2.0` ] ; [ `#0.005089` ; `#2.520002` ; `#2.000001` ; `#2.000001` ; `#2.000001` ; `#2.463507` ; `#2.000001` ] ; [ `#0.00289` ; `#2.520001` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.005361` ; `#0.128506` ; `#0.290371` ; `#0.003287` ; `-- #1.026581` ; `-- #0.070878` ; `-- #0.003287` ; `#0.033394` ; `-- #0.097658` ; `#0.003287` ; `#0.050047` ; `-- #0.121835` ; `-- #0.003287` ; `#0.13571` ] ; [ `#1.0` ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.005361` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.005361` ; `#2.585401` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.008408` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.005361` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.005361` ; `#0.128506` ; `#0.263591` ; `#0.003287` ; `-- #0.957343` ; `-- #0.070878` ; `-- #0.003287` ; `#0.033394` ; `-- #0.121835` ; `#0.003287` ; `#0.083125` ; `-- #0.070878` ; `-- #0.003287` ; `#0.033394` ] ; [ `#1.0` ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.005361` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.005361` ; `#2.585401` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.005361` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ; [ `#0.005362` ; `#2.585403` ; `#2.0` ; `#2.000001` ; `#2.0` ; `#2.463508` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.005361` ; `#0.128506` ; `-- #0.066254` ; `#0.003287` ; `-- #0.104563` ; `#0.234791` ; `-- #0.003287` ; `-- #0.786309` ; `-- #0.097658` ; `#0.003287` ; `#0.050047` ; `-- #0.070878` ; `-- #0.003287` ; `#0.033394` ] ; [ `#1.0` ] ; [ ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.005361` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.005361` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ; [ `#0.008409` ; `#2.585403` ; `#2.000001` ; `#2.000001` ; `#2.000001` ; `#2.463508` ; `#2.000001` ] ; [ `#0.005362` ; `#2.585403` ; `#2.0` ; `#2.000001` ; `#2.0` ; `#2.463508` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001637` ; `#0.127166` ; `-- #0.07331` ; `#0.003788` ; `-- #0.105909` ; `#0.23984` ; `-- #0.003788` ; `-- #0.767737` ; `-- #0.096981` ; `#0.003788` ; `#0.04248` ; `-- #0.069548` ; `-- #0.003788` ; `#0.032155` ] ; [ `#1.0` ] ; [ `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.001637` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.5854` ; `#2.0` ; `#2.0` ] ; [ `#0.001637` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.005148` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001637` ; `#2.585403` ; `#2.0` ; `#2.000001` ; `#2.0` ; `#2.463508` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.00125` ; `#0.126777` ; `-- #0.053069` ; `#0.003525` ; `-- #0.142652` ; `#0.196466` ; `-- #0.003525` ; `-- #0.667227` ; `-- #0.093532` ; `#0.003525` ; `#0.035622` ; `-- #0.049865` ; `-- #0.003525` ; `-- #0.022307` ] ; [ `#1.0` ; `#1.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.00125` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.463509` ; `#2.0` ] ; [ `#0.001388` ; `#2.6181` ; `#2.000001` ; `#2.000001` ; `#2.0` ; `#2.463508` ; `#2.0` ] ; [ `#0.004482` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001388` ; `#2.618101` ; `#2.000001` ; `#2.000002` ; `#2.0` ; `#2.463508` ; `#2.000001` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001974` ; `-- #0.0469` ; `#0.051237` ; `#0.060747` ; `-- #0.530637` ; `-- #0.014413` ; `-- #0.060747` ; `#0.594377` ; `-- #0.014413` ; `#0.060747` ; `-- #0.377571` ; `-- #0.02241` ; `-- #0.060747` ; `#0.608509` ] ; [ `#1.0` ; `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.001974` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.520037` ; `#2.0` ; `#2.0` ] ; [ `#0.005733` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001976` ; `#2.618027` ; `#2.000001` ; `#2.000001` ; `#2.000002` ; `#2.000001` ; `#2.000001` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.057939` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001974` ; `-- #0.0469` ; `#0.051237` ; `#0.060747` ; `-- #0.530636` ; `-- #0.014413` ; `-- #0.060747` ; `#0.594377` ; `-- #0.02241` ; `#0.060747` ; `-- #0.36344` ; `-- #0.014413` ; `-- #0.060747` ; `#0.594377` ] ; [ `#1.0` ; `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.001974` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.520037` ; `#2.0` ; `#2.0` ] ; [ `#0.005733` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001975` ; `#2.585404` ; `#2.000001` ; `#2.000001` ; `#2.05794` ; `#2.000001` ; `#2.000001` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001974` ; `-- #0.0469` ; `#0.051237` ; `#0.060747` ; `-- #0.530637` ; `-- #0.02241` ; `-- #0.060747` ; `#0.608509` ; `-- #0.014413` ; `#0.060747` ; `-- #0.377571` ; `-- #0.014413` ; `-- #0.060747` ; `#0.594377` ] ; [ `#1.0` ; `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.001974` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.520037` ; `#2.0` ; `#2.0` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.057939` ; `#2.0` ; `#2.0` ] ; [ `#0.001975` ; `#2.585402` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.00033` ; `-- #0.036939` ; `#0.050064` ; `-- #0.057593` ; `#0.397884` ; `-- #0.016688` ; `#0.057593` ; `-- #0.362427` ; `-- #0.016688` ; `-- #0.057593` ; `#0.559062` ; `-- #0.016688` ; `-- #0.057593` ; `#0.559062` ] ; [ `#1.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.00033` ; `#2.618094` ; `#2.000003` ; `#2.000003` ; `#2.520014` ; `#2.000003` ; `#2.000003` ] ; [ `#0.00033` ; `#2.601753` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00033` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00033` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000417` ; `-- #0.049823` ; `#0.047052` ; `-- #0.061687` ; `#0.463622` ; `-- #0.015684` ; `#0.061687` ; `-- #0.379191` ; `-- #0.015684` ; `-- #0.061687` ; `#0.607807` ; `-- #0.015684` ; `#0.061687` ; `-- #0.379191` ] ; [ `#1.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000417` ; `#2.60175` ; `#2.0` ; `#2.0` ; `#2.5527` ; `#2.0` ; `#2.0` ] ; [ `#0.000418` ; `#2.601748` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000417` ; `#2.60175` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000418` ; `#2.601748` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000396` ; `-- #0.053582` ; `#0.049452` ; `-- #0.06302` ; `#0.475514` ; `-- #0.013853` ; `#0.06302` ; `-- #0.389234` ; `-- #0.020791` ; `-- #0.06302` ; `#0.637132` ; `-- #0.013853` ; `-- #0.062897` ; `#0.618101` ] ; [ `#1.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000359` ; `#2.601749` ; `#2.0` ; `#2.0` ; `#2.536279` ; `#2.0` ; `#2.0` ] ; [ `#0.000396` ; `#2.601748` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000396` ; `#2.60175` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000396` ; `#2.60175` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.002012` ; `-- #0.066935` ; `#0.079693` ; `#0.066241` ; `-- #0.605497` ; `-- #0.021495` ; `-- #0.066241` ; `#0.685308` ; `-- #0.021495` ; `#0.066241` ; `-- #0.374549` ; `-- #0.036704` ; `-- #0.066241` ; `#0.715304` ] ; [ `#0.0` ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.00141` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.584895` ; `#2.0` ; `#2.0` ] ; [ `#0.004908` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.002012` ; `#2.585399` ; `#2.000001` ; `#2.000001` ; `#2.000001` ; `#2.000001` ; `#2.0` ] ; [ `#0.002012` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.002012` ; `-- #0.066935` ; `#0.028887` ; `#0.066241` ; `-- #0.477466` ; `-- #0.021495` ; `-- #0.066241` ; `#0.685308` ; `#0.014102` ; `#0.066241` ; `-- #0.472584` ; `-- #0.021495` ; `-- #0.066241` ; `#0.685308` ] ; [ `#0.0` ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.001651` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.596115` ; `#2.0` ; `#2.0` ] ; [ `#0.004908` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.002012` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.115878` ; `#2.0` ; `#2.0` ] ; [ `#0.004908` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.002012` ; `-- #0.066935` ; `#0.028887` ; `-- #0.066241` ; `#0.582391` ; `#0.014102` ; `#0.066241` ; `-- #0.472584` ; `-- #0.021495` ; `-- #0.066241` ; `#0.685308` ; `-- #0.021495` ; `#0.066241` ; `-- #0.374549` ] ; [ `#0.0` ] ; [ ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.00141` ; `#2.520001` ; `#2.000001` ; `#2.000001` ; `#2.58489` ; `#2.000001` ; `#2.000001` ] ; [ `#0.002012` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.115878` ; `#2.0` ; `#2.0` ] ; [ `#0.004908` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.002012` ; `#2.520001` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000405` ; `-- #0.070081` ; `#0.043025` ; `#0.06775` ; `-- #0.520998` ; `-- #0.014342` ; `-- #0.06775` ; `#0.681778` ; `-- #0.014342` ; `#0.06775` ; `-- #0.402228` ; `-- #0.014342` ; `-- #0.06775` ; `#0.681778` ] ; [ `#0.0` ; `#1.0` ] ; [ `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.000317` ; `#2.585399` ; `#2.0` ; `#2.0` ; `#2.612413` ; `#2.0` ; `#2.0` ] ; [ `#0.004048` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.000405` ; `#2.585391` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.004048` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001161` ; `-- #0.074623` ; `#0.079355` ; `#0.068595` ; `-- #0.608613` ; `-- #0.023711` ; `-- #0.068595` ; `#0.719631` ; `-- #0.023711` ; `#0.068595` ; `-- #0.37789` ; `-- #0.031932` ; `-- #0.068595` ; `#0.735738` ] ; [ `#0.0` ; `#0.0` ] ; [ `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.001019` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.61793` ; `#2.0` ; `#2.0` ] ; [ `#0.004236` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001162` ; `#2.520001` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.001161` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.057939` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001161` ; `-- #0.074623` ; `#0.019702` ; `-- #0.081204` ; `#0.740105` ; `-- #0.023711` ; `#0.081204` ; `-- #0.47876` ; `-- #0.031932` ; `-- #0.081204` ; `#0.836608` ; `#0.035942` ; `#0.081204` ; `-- #0.629086` ] ; [ `#0.0` ; `#0.0` ] ; [ `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.001084` ; `#2.552699` ; `#2.000001` ; `#2.000001` ; `#2.625659` ; `#2.000001` ; `#2.000001` ] ; [ `#0.001161` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.002657` ; `#2.52` ; `#2.0` ; `#2.463509` ; `#2.057939` ; `#2.0` ; `#2.0` ] ; [ `#0.001162` ; `#2.52` ; `#2.000001` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.001161` ; `-- #0.074623` ; `#0.019702` ; `-- #0.068595` ; `#0.639237` ; `-- #0.031932` ; `#0.068595` ; `-- #0.361784` ; `-- #0.023711` ; `-- #0.068595` ; `#0.719631` ; `#0.035942` ; `#0.068595` ; `-- #0.528217` ] ; [ `#0.0` ; `#0.0` ] ; [ `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.001084` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.625659` ; `#2.0` ; `#2.0` ] ; [ `#0.001161` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.057939` ; `#2.0` ; `#2.0` ] ; [ `#0.004236` ; `#2.52` ; `#2.0` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.001161` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000308` ; `-- #0.090009` ; `#0.04151` ; `#0.073665` ; `-- #0.523458` ; `-- #0.013837` ; `-- #0.073665` ; `#0.755879` ; `-- #0.013837` ; `#0.073665` ; `-- #0.422755` ; `-- #0.013837` ; `-- #0.073665` ; `#0.755879` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#1.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000308` ; `#2.53635` ; `#2.0` ; `#2.0` ; `#2.650799` ; `#2.0` ; `#2.0` ] ; [ `#0.000308` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000308` ; `#2.536357` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000308` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000418` ; `-- #0.17025` ; `#0.094709` ; `#0.098535` ; `-- #0.692034` ; `-- #0.021455` ; `-- #0.098535` ; `#1.087114` ; `#0.009749` ; `#0.098535` ; `-- #0.568591` ; `-- #0.021455` ; `-- #0.098535` ; `#1.087114` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#1.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000418` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.6508` ; `#2.0` ; `#2.0` ] ; [ `#0.000418` ; `#2.53635` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000418` ; `#2.536343` ; `#2.0` ; `#2.0` ; `#2.000004` ; `#2.0` ; `#2.0` ] ; [ `#0.000418` ; `#2.53635` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000644` ; `-- #0.172166` ; `#0.09973` ; `-- #0.099785` ; `#0.882284` ; `#0.014169` ; `#0.099785` ; `-- #0.586728` ; `-- #0.017353` ; `-- #0.099785` ; `#1.0903` ; `#0.014169` ; `#0.099785` ; `-- #0.586728` ] ; [ `#0.0` ; `#0.0` ] ; [ `#1.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000644` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.6181` ; `#2.0` ; `#2.0` ] ; [ `#0.000644` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000644` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.000644` ; `#2.5527` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#2.0` ] ; [ `-- #0.000313` ; `-- #0.084789` ; `#0.039845` ; `-- #0.071708` ; `#0.632521` ; `-- #0.013282` ; `-- #0.071708` ; `#0.731624` ; `-- #0.013282` ; `-- #0.071708` ; `#0.731624` ; `-- #0.013282` ; `#0.071708` ; `-- #0.415701` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.000313` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.5854` ; `#2.0` ; `#2.0` ] ; [ `#0.003624` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.003624` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.000314` ; `#2.520002` ; `#2.000002` ; `#2.000001` ; `#2.000001` ; `#2.000001` ; `#2.000001` ] ] ; [ [ `#1.0` ] ; [ `-- #0.00272` ; `#0.065103` ; `-- #0.052337` ; `-- #0.02292` ; `#0.191326` ; `#0.23854` ; `#0.02292` ; `-- #0.867278` ; `-- #0.073933` ; `-- #0.02292` ; `#0.286871` ; `-- #0.11227` ; `#0.02292` ; `-- #0.019974` ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.002703` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.474335` ; `#2.0` ; `#2.0` ] ; [ `#0.00272` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.004959` ; `#2.6508` ; `#2.0` ; `#2.463509` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.002721` ; `#2.650799` ; `#2.0` ; `#2.0` ; `#2.231755` ; `#2.0` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.00272` ; `#0.065103` ; `-- #0.052337` ; `#0.02292` ; `-- #0.17539` ; `#0.23854` ; `-- #0.02292` ; `-- #0.500562` ; `-- #0.11227` ; `#0.02292` ; `-- #0.019974` ; `-- #0.073933` ; `-- #0.02292` ; `#0.286871` ] ; [ ] ; [ ] ; [ ] ; [ `#1.0` ] ; [ `#0.0` ] ; [ `#0.002703` ; `#2.650799` ; `#2.0` ; `#2.000001` ; `#2.474442` ; `#2.000001` ; `#2.0` ] ; [ `#0.00272` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.002721` ; `#2.650799` ; `#2.0` ; `#2.0` ; `#2.231755` ; `#2.0` ; `#2.0` ] ; [ `#0.003897` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.00272` ; `#0.065103` ; `-- #0.052337` ; `#0.02292` ; `-- 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; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.004545` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.004545` ; `#0.062681` ; `-- #0.026929` ; `#0.023742` ; `-- #0.242815` ; `#0.176245` ; `-- #0.023742` ; `-- #0.348621` ; `-- #0.084906` ; `#0.023742` ; `-- #0.075969` ; `-- #0.06441` ; `-- #0.023742` ; `#0.273568` ] ; [ `#1.0` ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.004424` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.491903` ; `#2.0` ; `#2.0` ] ; [ `#0.004545` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.004545` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ; [ `#0.006469` ; `#2.585401` ; `#2.0` ; `#2.000001` ; `#2.0` ; `#2.463508` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.004545` ; `#0.062681` ; `-- #0.026929` ; `#0.023742` ; `-- #0.242815` ; `-- #0.084906` ; `-- #0.023742` ; `#0.3039` ; `#0.176245` ; `#0.023742` ; `-- #0.72849` ; `-- #0.06441` ; `-- #0.023742` ; `#0.273568` ] ; [ `#1.0` ] ; [ ] ; [ `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.004424` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.491903` ; `#2.0` ; `#2.0` ] ; [ `#0.004545` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.115877` ; `#2.0` ; `#2.0` ] ; [ `#0.004545` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.006469` ; `#2.585401` ; `#2.0` ; `#2.000001` ; `#2.0` ; `#2.463508` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.000884` ; `#0.061714` ; `-- #0.014502` ; `-- #0.02407` ; `#0.104941` ; `#0.134266` ; `#0.02407` ; `-- #0.631477` ; `-- #0.059882` ; `-- #0.02407` ; `#0.261947` ; `-- #0.059882` ; `-- #0.02407` ; `#0.261947` ] ; [ `#1.0` ; `#1.0` ] ; [ ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.000796` ; `#2.6508` ; `#2.0` ; `#2.0` ; `#2.488246` ; `#2.0` ; `#2.0` ] ; [ `#0.000884` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.003066` ; `#2.618101` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.003066` ; `#2.618101` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.001974` ; `-- #0.0469` ; `#0.051237` ; `#0.060747` ; `-- #0.530637` ; `-- #0.014413` ; `-- #0.060747` ; `#0.594377` ; `-- #0.014413` ; `#0.060747` ; `-- #0.377571` ; `-- #0.02241` ; `-- #0.060747` ; `#0.608509` ] ; [ `#1.0` ; `#0.0` ] ; [ ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.002084` ; `#2.585663` ; `#2.000116` ; `#2.000116` ; `#2.519822` ; `#2.000113` ; `#2.000116` ] ; [ `#0.005733` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001976` ; `#2.618027` ; `#2.000001` ; `#2.000001` ; `#2.000002` ; `#2.000001` ; `#2.000001` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.057939` ; `#2.0` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.001974` ; `-- #0.0469` ; `#0.051237` ; `-- #0.073427` ; `#0.542756` ; `-- #0.014413` ; `#0.073427` ; `-- #0.479016` ; `-- #0.02241` ; `-- #0.073427` ; `#0.709954` ; `-- #0.014413` ; `#0.073427` ; `-- #0.479016` ] ; [ `#1.0` ; `#0.0` ] ; [ ] ; [ `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.001974` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.004138` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.057939` ; `#2.463509` ; `#2.0` ] ; [ `#0.001974` ; `#2.585401` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.001974` ; `-- #0.0469` ; `#0.051237` ; `-- #0.060747` ; `#0.44131200000000004` ; `-- #0.02241` ; `#0.060747` ; `-- #0.36344` ; `-- #0.014413` ; `-- #0.060747` ; `#0.594377` ; `-- #0.014413` ; `#0.060747` ; `-- #0.377571` ] ; [ `#1.0` ; `#0.0` ] ; [ ] ; [ `#0.0` ; `#0.0` ; `#1.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.002165` ; `#2.585453` ; `#2.000636` ; `#2.000639` ; `#2.51972` ; `#2.000635` ; `#2.000606` ] ; [ `#0.001975` ; `#2.585404` ; `#2.000001` ; `#2.000001` ; `#2.05794` ; `#2.000001` ; `#2.000001` ] ; [ `#0.001974` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.001975` ; `#2.585402` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.00033` ; `-- #0.036939` ; `#0.050064` ; `#0.057593` ; `-- #0.523604` ; `-- #0.016688` ; `-- #0.057593` ; `#0.559062` ; `-- #0.016688` ; `#0.057593` ; `-- #0.362427` ; `-- #0.016688` ; `-- #0.057593` ; `#0.559062` ] ; [ `#1.0` ; `#0.0` ; `#1.0` ] ; [ ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000403` ; `#2.609586` ; `#2.000023` ; `#2.00002` ; `#2.519733` ; `#2.000019` ; `#2.000024` ] ; [ `#0.00033` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00033` ; `#2.601753` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.00033` ; `#2.6181` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ; [ [ `#1.0` ] ; [ `-- #0.000886` ; `-- #0.177145` ; `#0.151334` ; `-- #0.103308` ; `#0.774954` ; `#0.041584` ; `#0.103308` ; `-- #0.677721` ; `#0.00995` ; `-- #0.103308` ; `#1.057518` ; `#0.041584` ; `#0.103308` ; `-- #0.677721` ] ; [ `#1.0` ; `#0.0` ; `#0.0` ] ; [ ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.0` ; `#0.0` ; `#0.0` ] ; [ `#0.000886` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.000887` ; `#2.601712` ; `#2.000001` ; `#2.000001` ; `#2.000015` ; `#2.000001` ; `#2.000001` ] ; [ `#0.000886` ; `#2.601749` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.000001` ; `#2.0` ] ; [ `#0.000887` ; `#2.601712` ; `#2.000001` ; `#2.000001` ; `#2.000015` ; `#2.000001` ; `#2.000001` ] ] ; [ [ `#1.0` ] ; [ `-- #0.001328` ; `-- #0.121189` ; `#0.06473` ; `-- #0.084657` ; `#0.741383` ; `-- #0.016252` ; `#0.084657` ; `-- #0.45858` ; `-- #0.022099` ; `-- #0.084657` ; `#0.911046` ; `-- #0.016252` ; `#0.084657` ; `-- #0.45858` ] ; [ `#0.0` ] ; [ ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.0` ] ; [ `#0.001328` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.52` ; `#2.0` ; `#2.0` ] ; [ `#0.001328` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ; [ `#0.006318` ; `#2.52` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.463509` ; `#2.0` ] ; [ `#0.001328` ; `#2.5854` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ; `#2.0` ] ] ];; let records = map mk_irecord raw_nonlindatah;; (* let nonlindata = [ [ [ 4.0 ] ; [ -0.00289 ; 0.129913 ; -0.060416 ; 0.002372 ; -0.113134 ; 0.01764 ; -0.002372 ; -0.198777 ; 0.045166 ; 0.002372 ; -0.306092 ; 0.021777 ; -0.002372 ; -0.259166 ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.003326 ; 2.463509 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.463514 ; 2.0 ; 2.463508 ; 2.0 ; 2.000001 ; 2.000001 ] ; [ 0.003534 ; 2.463509 ; 2.000001 ; 2.463508 ; 2.0 ; 2.0 ; 2.000001 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ] ; [ [ 4.0 ] ; [ -0.002889 ; 0.129699 ; -0.060316 ; 0.002264 ; -0.112116 ; 0.019214 ; -0.002264 ; -0.203309 ; 0.021887 ; 0.002264 ; -0.29619 ; 0.019214 ; -0.002264 ; -0.203309 ] ; [ ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.0 ] ; [ 0.003328 ; 2.463509 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.463513 ; 2.0 ; 2.463508 ; 2.0 ; 2.000001 ; 2.0 ] ; [ 0.002889 ; 2.463509 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ; [ 0.002998 ; 2.519915 ; 2.000025 ; 2.000038 ; 2.000022 ; 2.463485 ; 2.000022 ] ] ; [ [ 4.0 ] ; [ -0.00289 ; 0.129913 ; -0.060416 ; 0.002372 ; -0.113134 ; 0.021777 ; -0.002372 ; -0.259166 ; 0.045166 ; 0.002372 ; -0.306092 ; 0.01764 ; -0.002372 ; -0.198777 ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.003326 ; 2.463509 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ; [ 0.003534 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ; 2.463508 ; 2.0 ] ; [ 0.002915 ; 2.519935 ; 2.000027 ; 2.00004 ; 2.000024 ; 2.463484 ; 2.000025 ] ] ; [ [ 4.0 ] ; [ -0.000426 ; -0.114872 ; 0.133539 ; -0.080919 ; 0.532524 ; 0.148605 ; 0.080919 ; -0.855148 ; 0.08743 ; -0.080919 ; 0.593722 ; 0.148605 ; 0.080919 ; -0.855148 ] ; [ ] ; [ ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.000426 ; 2.463509 ; 2.0 ; 2.0 ; 2.6508 ; 2.0 ; 2.0 ] ; [ 0.000435 ; 2.463511 ; 2.000001 ; 2.000001 ; 2.000002 ; 2.000002 ; 2.000002 ] ; [ 0.004824 ; 2.46351 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.000435 ; 2.463511 ; 2.000001 ; 2.000001 ; 2.000002 ; 2.000002 ; 2.000002 ] ] ; [ [ 3.0 ] ; [ -0.00272 ; 0.065103 ; -0.008732 ; -0.024884 ; 0.097156 ; 0.072591 ; 0.024884 ; -0.464803 ; 0.042651 ; -0.024884 ; 0.008797 ; 0.055356 ; 0.024884 ; -0.458108 ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.002594 ; 2.52 ; 2.0 ; 2.0 ; 2.491729 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.463509 ; 2.0 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.52 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ] ; [ [ 3.0 ] ; [ -0.00272 ; 0.065103 ; -0.029778 ; -0.027449 ; 0.170713 ; 0.072591 ; 0.027449 ; -0.485323 ; 0.055356 ; -0.027449 ; -0.039438 ; 0.072591 ; 0.027449 ; -0.485323 ] ; [ ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.0 ] ; [ 0.002594 ; 2.52 ; 2.0 ; 2.0 ; 2.491998 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.463509 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ] ; [ [ 3.0 ] ; [ -0.00272 ; 0.065103 ; -0.008732 ; 0.025458 ; -0.30558 ; 0.055356 ; -0.025458 ; -0.055371 ; 0.072591 ; 0.025458 ; -0.469389 ; 0.037947 ; -0.025458 ; 0.025236 ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.002612 ; 2.463509 ; 2.0 ; 2.0 ; 2.489061 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.52 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.52 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00272 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ] ; [ [ 3.0 ] ; [ -0.00225 ; -0.114872 ; 0.116669 ; 0.080919 ; -0.7251449999999999 ; 0.08743 ; -0.080919 ; 0.595546 ; 0.148605 ; 0.080919 ; -0.853324 ; 0.08743 ; -0.080919 ; 0.595546 ] ; [ ] ; [ ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.00225 ; 2.519989 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.006648 ; 2.46351 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.002259 ; 2.463511 ; 2.000001 ; 2.000001 ; 2.000002 ; 2.000002 ; 2.000002 ] ; [ 0.006648 ; 2.46351 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.00289 ; 0.129913 ; -0.09152 ; 0.002372 ; -0.034749 ; 0.347659 ; -0.002372 ; -1.030425 ; -0.105208 ; 0.002372 ; 0.072849 ; -0.150931 ; -0.002372 ; 0.176057 ] ; [ ] ; [ ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.005089 ; 2.52 ; 2.0 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.6508 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.00289 ; 0.129913 ; 0.340765 ; 0.002372 ; -1.124108 ; -0.094917 ; -0.002372 ; 0.084866 ; -0.150931 ; 0.002372 ; 0.138108 ; -0.094917 ; -0.002372 ; 0.084866 ] ; [ ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.463509 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.6508 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.520001 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.00289 ; 0.129913 ; -0.09152 ; 0.002372 ; -0.034749 ; 0.291645 ; -0.002372 ; -0.939234 ; -0.105208 ; 0.002372 ; 0.072849 ; -0.094917 ; -0.002372 ; 0.084866 ] ; [ ] ; [ ] ; [ 1.0 ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.00289 ; 2.52 ; 2.0 ; 2.0 ; 2.231754 ; 2.0 ; 2.0 ] ; [ 0.005089 ; 2.520002 ; 2.000001 ; 2.000001 ; 2.000001 ; 2.463507 ; 2.000001 ] ; [ 0.00289 ; 2.520001 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.005361 ; 0.128506 ; 0.290371 ; 0.003287 ; -1.026581 ; -0.070878 ; -0.003287 ; 0.033394 ; -0.097658 ; 0.003287 ; 0.050047 ; -0.121835 ; -0.003287 ; 0.13571 ] ; [ 1.0 ] ; [ ] ; [ 0.0 ] ; [ 0.0 ] ; [ 0.0 ; 1.0 ] ; [ 0.005361 ; 2.5854 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.005361 ; 2.585401 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.008408 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.005361 ; 2.6508 ; 2.0 ; 2.0 ; 2.115877 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.005361 ; 0.128506 ; 0.263591 ; 0.003287 ; -0.957343 ; -0.070878 ; -0.003287 ; 0.033394 ; -0.121835 ; 0.003287 ; 0.083125 ; -0.070878 ; -0.003287 ; 0.033394 ] ; [ 1.0 ] ; [ ] ; [ 0.0 ] ; [ 0.0 ; 1.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.005361 ; 2.5854 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.005361 ; 2.585401 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.005361 ; 2.6508 ; 2.0 ; 2.0 ; 2.115877 ; 2.0 ; 2.0 ] ; [ 0.005362 ; 2.585403 ; 2.0 ; 2.000001 ; 2.0 ; 2.463508 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.005361 ; 0.128506 ; -0.066254 ; 0.003287 ; -0.104563 ; 0.234791 ; -0.003287 ; -0.786309 ; -0.097658 ; 0.003287 ; 0.050047 ; -0.070878 ; -0.003287 ; 0.033394 ] ; [ 1.0 ] ; [ ] ; [ 0.0 ; 1.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.005361 ; 2.5854 ; 2.0 ; 2.0 ; 2.52 ; 2.0 ; 2.0 ] ; [ 0.005361 ; 2.5854 ; 2.0 ; 2.0 ; 2.115877 ; 2.0 ; 2.0 ] ; [ 0.008409 ; 2.585403 ; 2.000001 ; 2.000001 ; 2.000001 ; 2.463508 ; 2.000001 ] ; [ 0.005362 ; 2.585403 ; 2.0 ; 2.000001 ; 2.0 ; 2.463508 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.001637 ; 0.127166 ; -0.07331 ; 0.003788 ; -0.105909 ; 0.23984 ; -0.003788 ; -0.767737 ; -0.096981 ; 0.003788 ; 0.04248 ; -0.069548 ; -0.003788 ; 0.032155 ] ; [ 1.0 ] ; [ 1.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.001637 ; 2.5854 ; 2.0 ; 2.0 ; 2.5854 ; 2.0 ; 2.0 ] ; [ 0.001637 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.005148 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.001637 ; 2.585403 ; 2.0 ; 2.000001 ; 2.0 ; 2.463508 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.00125 ; 0.126777 ; -0.053069 ; 0.003525 ; -0.142652 ; 0.196466 ; -0.003525 ; -0.667227 ; -0.093532 ; 0.003525 ; 0.035622 ; -0.049865 ; -0.003525 ; -0.022307 ] ; [ 1.0 ; 1.0 ] ; [ 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.00125 ; 2.6181 ; 2.0 ; 2.0 ; 2.52 ; 2.463509 ; 2.0 ] ; [ 0.001388 ; 2.6181 ; 2.000001 ; 2.000001 ; 2.0 ; 2.463508 ; 2.0 ] ; [ 0.004482 ; 2.6508 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.001388 ; 2.618101 ; 2.000001 ; 2.000002 ; 2.0 ; 2.463508 ; 2.000001 ] ] ; [ [ 2.0 ] ; [ -0.001974 ; -0.0469 ; 0.051237 ; 0.060747 ; -0.530637 ; -0.014413 ; -0.060747 ; 0.594377 ; -0.014413 ; 0.060747 ; -0.377571 ; -0.02241 ; -0.060747 ; 0.608509 ] ; [ 1.0 ; 0.0 ] ; [ 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 1.0 ] ; [ 0.001974 ; 2.5854 ; 2.0 ; 2.0 ; 2.520037 ; 2.0 ; 2.0 ] ; [ 0.005733 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.001976 ; 2.618027 ; 2.000001 ; 2.000001 ; 2.000002 ; 2.000001 ; 2.000001 ] ; [ 0.001974 ; 2.6181 ; 2.0 ; 2.0 ; 2.057939 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.001974 ; -0.0469 ; 0.051237 ; 0.060747 ; -0.530636 ; -0.014413 ; -0.060747 ; 0.594377 ; -0.02241 ; 0.060747 ; -0.36344 ; -0.014413 ; -0.060747 ; 0.594377 ] ; [ 1.0 ; 0.0 ] ; [ 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 1.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.001974 ; 2.5854 ; 2.0 ; 2.0 ; 2.520037 ; 2.0 ; 2.0 ] ; [ 0.005733 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.001975 ; 2.585404 ; 2.000001 ; 2.000001 ; 2.05794 ; 2.000001 ; 2.000001 ] ; [ 0.001974 ; 2.6181 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.001974 ; -0.0469 ; 0.051237 ; 0.060747 ; -0.530637 ; -0.02241 ; -0.060747 ; 0.608509 ; -0.014413 ; 0.060747 ; -0.377571 ; -0.014413 ; -0.060747 ; 0.594377 ] ; [ 1.0 ; 0.0 ] ; [ 0.0 ] ; [ 0.0 ; 0.0 ; 1.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.001974 ; 2.5854 ; 2.0 ; 2.0 ; 2.520037 ; 2.0 ; 2.0 ] ; [ 0.001974 ; 2.6181 ; 2.0 ; 2.0 ; 2.057939 ; 2.0 ; 2.0 ] ; [ 0.001975 ; 2.585402 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.001974 ; 2.6181 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.00033 ; -0.036939 ; 0.050064 ; -0.057593 ; 0.397884 ; -0.016688 ; 0.057593 ; -0.362427 ; -0.016688 ; -0.057593 ; 0.559062 ; -0.016688 ; -0.057593 ; 0.559062 ] ; [ 1.0 ; 0.0 ; 1.0 ] ; [ 0.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.00033 ; 2.618094 ; 2.000003 ; 2.000003 ; 2.520014 ; 2.000003 ; 2.000003 ] ; [ 0.00033 ; 2.601753 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00033 ; 2.6181 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.00033 ; 2.6181 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.000417 ; -0.049823 ; 0.047052 ; -0.061687 ; 0.463622 ; -0.015684 ; 0.061687 ; -0.379191 ; 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; -0.068595 ; 0.735738 ] ; [ 0.0 ; 0.0 ] ; [ 1.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 1.0 ] ; [ 0.001019 ; 2.52 ; 2.0 ; 2.0 ; 2.61793 ; 2.0 ; 2.0 ] ; [ 0.004236 ; 2.52 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.001162 ; 2.520001 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.001161 ; 2.5527 ; 2.0 ; 2.0 ; 2.057939 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.001161 ; -0.074623 ; 0.019702 ; -0.081204 ; 0.740105 ; -0.023711 ; 0.081204 ; -0.47876 ; -0.031932 ; -0.081204 ; 0.836608 ; 0.035942 ; 0.081204 ; -0.629086 ] ; [ 0.0 ; 0.0 ] ; [ 1.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 1.0 ] ; [ 0.0 ; 0.0 ; 0.0 ] ; [ 0.001084 ; 2.552699 ; 2.000001 ; 2.000001 ; 2.625659 ; 2.000001 ; 2.000001 ] ; [ 0.001161 ; 2.52 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.002657 ; 2.52 ; 2.0 ; 2.463509 ; 2.057939 ; 2.0 ; 2.0 ] ; [ 0.001162 ; 2.52 ; 2.000001 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ] ; [ [ 2.0 ] ; [ -0.001161 ; -0.074623 ; 0.019702 ; -0.068595 ; 0.639237 ; -0.031932 ; 0.068595 ; -0.361784 ; -0.023711 ; -0.068595 ; 0.719631 ; 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] ; [ 0.004545 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.006469 ; 2.585401 ; 2.0 ; 2.000001 ; 2.0 ; 2.463508 ; 2.0 ] ] ; [ [ 1.0 ] ; [ -0.000884 ; 0.061714 ; -0.014502 ; -0.02407 ; 0.104941 ; 0.134266 ; 0.02407 ; -0.631477 ; -0.059882 ; -0.02407 ; 0.261947 ; -0.059882 ; -0.02407 ; 0.261947 ] ; [ 1.0 ; 1.0 ] ; [ ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.000796 ; 2.6508 ; 2.0 ; 2.0 ; 2.488246 ; 2.0 ; 2.0 ] ; [ 0.000884 ; 2.6181 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ; 2.0 ] ; [ 0.003066 ; 2.618101 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 0.003066 ; 2.618101 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ] ; [ [ 1.0 ] ; [ -0.001974 ; -0.0469 ; 0.051237 ; 0.060747 ; -0.530637 ; -0.014413 ; -0.060747 ; 0.594377 ; -0.014413 ; 0.060747 ; -0.377571 ; -0.02241 ; -0.060747 ; 0.608509 ] ; [ 1.0 ; 0.0 ] ; [ ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ] ; [ 0.0 ; 0.0 ; 1.0 ] ; [ 0.002084 ; 2.585663 ; 2.000116 ; 2.000116 ; 2.519822 ; 2.000113 ; 2.000116 ] ; [ 0.005733 ; 2.5854 ; 2.0 ; 2.0 ; 2.0 ; 2.463509 ; 2.0 ] ; [ 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0.041584, 0.103308, -0.677721, 0.00995, -0.103308, 1.057518, 0.041584, 0.103308, -0.677721}, {1., 0., 0.}, {}, {0., 0., 0.}, {0., 0., 0.}, {0., 0., 0.}, {0.000886, 2.5854, 2., 2., 2.52, 2., 2.}, {0.000887, 2.601712, 2.000001, 2.000001, 2.000015, 2.000001, 2.000001}, {0.000886, 2.601749, 2., 2., 2., 2.000001, 2.}, {0.000887, 2.601712, 2.000001, 2.000001, 2.000015, 2.000001, 2.000001}}, {{1.}, {-0.001328, -0.121189, 0.06473, -0.084657, 0.741383, -0.016252, 0.084657, -0.45858, -0.022099, -0.084657, 0.911046, -0.016252, 0.084657, -0.45858}, {0.}, {}, {0.}, {0.}, {0.}, {0.001328, 2.52, 2., 2., 2.52, 2., 2.}, {0.001328, 2.5854, 2., 2., 2., 2., 2.}, {0.006318, 2.52, 2., 2., 2., 2.463509, 2.}, {0.001328, 2.5854, 2., 2., 2., 2., 2.}}} *) (* test that the data covers the entire 13-dimensional domain of octahedra *) let get_cover i = let v = List.rev in let r = map (fun t -> (v t.branch1,v t.branch2,v t.branch3,v t.branch4,v t.branch5)) (filter (fun t -> t.caseno =i ) records) in r;; let check ((r1,r2,r3,r4,r5),(s1,s2,s3,s4,s5)) = not(r1=[]) && not(s1=[]) && not(hd r1 = hd s1) && (tl r1 = tl s1) && (r2 = s2) && (r3 = s3) && (r4=s4) &&(r5=s5);; let combine ((r1,r2,r3,r4,r5),(s1,s2,s3,s4,s5))= if check((r1,r2,r3,r4,r5),(s1,s2,s3,s4,s5)) then (hd r1 < hd s1,0),(tl r1,r2,r3,r4,r5) else if check((r2,r1,r3,r4,r5),(s2,s1,s3,s4,s5)) then (hd r2 < hd s2,1),(r1,tl r2,r3,r4,r5) else if check((r3,r1,r2,r4,r5),(s3,s1,s2,s4,s5)) then (hd r3 < hd s3,2),(r1,r2,tl r3,r4,r5) else if check((r4,r1,r2,r3,r5),(s4,s1,s2,s3,s5)) then (hd r4 < hd s4,3),(r1,r2,r3,tl r4,r5) else if check((r5,r1,r2,r3,r4),(s5,s1,s2,s3,s4)) then (hd r5 < hd s5,4),(r1,r2,r3,r4,tl r5) else failwith "combine";; let rec combine_l = function [] -> [] | [a] -> [a] | a::b::cs -> try (snd(combine (a,b))) :: cs with Failure _ -> a:: (combine_l (b::cs));; let rec combine_r x= let y = combine_l x in if (y = x) then x else combine_r y;; let rec nub = function (* from lpproc *) | [] -> [] | x::xs -> x::filter ((<>) x) (nub xs);; let domain_cover_calculation = ([[([],[],[],[],[])]] = nub(map (fun t -> combine_r (get_cover t)) ( 1 -- 4) ));; (* for testing in cfsqp: let exec case r = let d = List.nth records r in let f = mk_ineq case d in execute_cfsqp { ineq = f; id = "TEST"; tags = []; doc = ""; };; *) end;;