rectilinear_nonlinear_stats_non_constant_variance.m

clear

% % C6
% 
% T = [360 360 360 400 400 400 440 440 440 460 460 460];
% pv = [0.007100 0.008316 0.008153 0.018849 0.019010 0.018165 0.038615 0.039760 0.041636664 0.057443062 0.05398867 0.0572793];
% pL = [0.597439 0.598927 0.599733 0.552854 0.553790 0.551556 0.496253 0.498060 0.496882192 0.461768983 0.462319412 0.462637091];
% 
% % Best fit parameters
% 
% A_fit = 4.3843204*10^-4;
% b_fit = 0.1203741;
% pc_fit = 0.2398562;
% TC_fit = 504.7126613;
% 
% % Ranges used
% 
% A_range = 0.0004:0.000002:0.000478;
% b_range = 0.1194:0.0002:0.1214;
% pc_range = 0.236:0.0001:0.2437;
% TC_range = 503.1:0.05:506.4;

% % % C8
% % 
% T = [390 390 390 440 440 440 490 490 490 515 515 515];
% pv = [0.004456 0.003813 0.004219 0.013343 0.011971 0.012818 0.032864 0.031561 0.031015949 0.052363289 0.053323735 0.05073475];
% pL = [0.625403 0.624078 0.625876 0.573911 0.572892 0.574369 0.511936 0.512849 0.5114893 0.47685196 0.476022927 0.475198579];
% 
% % Best fit parameters
% 
% A_fit = 4.096851*10^-4;
% b_fit = 0.1181472;
% pc_fit = 0.2405976;
% TC_fit = 569.5065255;
% 
% % Ranges used
% 
% A_range = 0.000376:0.000002:0.000444;
% b_range = 0.1173:0.00005:0.1191;
% pc_range = 0.2364:0.0002:0.2448;
% TC_range = 567.4:0.1:571.7;

% C8 all exact

T = [390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,390,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,440,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,490,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515,515];
pv = [0.00432793900000000,0.00418456400000000,0.00391715900000000,0.00410154300000000,0.00447783400000000,0.00350739400000000,0.00437038600000000,0.00429504900000000,0.00390946500000000,0.00409517200000000,0.00396118600000000,0.00362800700000000,0.00369628500000000,0.00372563000000000,0.00453825800000000,0.00379149500000000,0.00402554100000000,0.00389273500000000,0.00368230600000000,0.00445552400000000,0.00381255200000000,0.00421901200000000,0.0125714790000000,0.0123311450000000,0.0122856790000000,0.0121264380000000,0.0128754040000000,0.0126838350000000,0.0126793340000000,0.0129770490000000,0.0120622840000000,0.0126521160000000,0.0125107960000000,0.0119132010000000,0.0115167190000000,0.0121300970000000,0.0132708890000000,0.0125979480000000,0.0128119750000000,0.0118827490000000,0.0122814560000000,0.0133434330000000,0.0119709810000000,0.0128175990000000,0.0320723040000000,0.0311026970000000,0.0331766570000000,0.0313079720000000,0.0324732930000000,0.0325431630000000,0.0331805460000000,0.0307968800000000,0.0324056740000000,0.0310623450000000,0.0334263930000000,0.0336777840000000,0.0328874300000000,0.0328262100000000,0.0306754480000000,0.0308364960000000,0.0317688030000000,0.0307508770000000,0.0336924750000000,0.0328635450000000,0.0315605560000000,0.0310159490000000,0.0505107300000000,0.0508302460000000,0.0489921300000000,0.0571107520000000,0.0526511010000000,0.0523392840000000,0.0495526930000000,0.0533079640000000,0.0502355710000000,0.0523632890000000,0.0526168450000000,0.0544538520000000,0.0538710970000000,0.0499890630000000,0.0521845070000000,0.0489267740000000,0.0499996520000000,0.0497650020000000,0.0499555620000000,0.0523632890000000,0.0533237350000000,0.0507347500000000];
pL = [0.625888790000000,0.624029464000000,0.624803710000000,0.624295007000000,0.626001224000000,0.623824273000000,0.624325807000000,0.625056439000000,0.624467903000000,0.625360839000000,0.624593780000000,0.624175523000000,0.624014819000000,0.624714229000000,0.626538872000000,0.624632971000000,0.624956424000000,0.625354585000000,0.624977206000000,0.625403293000000,0.624078045000000,0.625875774000000,0.573141775000000,0.573362883000000,0.573233316000000,0.572219544000000,0.574339626000000,0.574855147000000,0.575721706000000,0.573172940000000,0.573599977000000,0.572957209000000,0.573499894000000,0.572745119000000,0.573631613000000,0.572926795000000,0.573486909000000,0.574746432000000,0.574074923000000,0.572385450000000,0.573332909000000,0.573911377000000,0.572891604000000,0.574369315000000,0.514984100000000,0.511010445000000,0.512082774000000,0.512010323000000,0.511868857000000,0.515346328000000,0.511909917000000,0.511482209000000,0.513196845000000,0.511338411000000,0.513673407000000,0.514005980000000,0.513282354000000,0.512709949000000,0.511393191000000,0.511791603000000,0.511763086000000,0.513327369000000,0.512734432000000,0.511936205000000,0.512849102000000,0.511489300000000,0.475287289000000,0.474352627000000,0.470077928000000,0.476141671000000,0.473799760000000,0.473303127000000,0.475469186000000,0.475587343000000,0.477135568000000,0.476851960000000,0.475542761000000,0.474066296000000,0.477039424000000,0.476481347000000,0.476874839000000,0.474308630000000,0.475447446000000,0.469115182000000,0.473508210000000,0.476851960000000,0.476022927000000,0.475198579000000];
sigmay = [0.000484676 0.000567086 0.000946223 0.001716146];
sigmaz = [0.000581324 0.00075617 0.001167651 0.002302394];

sy = zeros(1,length(T));
sz = sy;

for i=1:length(T)
    
    if T(i) == 390
    
        sy(i) = sigmay(1);
        sz(i) = sigmaz(1);
        
    elseif T(i) == 440
        
        sy(i) = sigmay(2);
        sz(i) = sigmaz(2);
        
    elseif T(i) == 490

        sy(i) = sigmay(3);
        sz(i) = sigmaz(3);
        
    else
        
        sy(i) = sigmay(4);
        sz(i) = sigmaz(4);
        
    end
    
end

% Best fit parameters
% 
A_fit = 4.191675*10^-4;
b_fit = 0.1177868;
pc_fit = 0.2385685;
TC_fit = 570.6878129;

% Ranges used

A_range = 0.00041:0.0000005:0.000428;
b_range = 0.1174:0.00002:0.1181;
pc_range = 0.2372:0.00003:0.2399;
TC_range = 569.75:0.025:571.6;

% This is using their approach but not with propagation of error

% sy =[0.000577915000000000,0.000734327000000000,0.000510877000000000,0.000596985000000000,0.000228341000000000,0.000754748000000000,0.000273816000000000,0.000160871000000000,0.000561697000000000,0.00108009400000000,0.000709366000000000,0.000399882000000000,0.000431566000000000,0.000735747000000000,0.00117645700000000,0.000640649000000000,0.000861004000000000,0.000567776000000000,0.000236754000000000,0.00139877600000000,0.000734748000000000,0.000986106000000000,0.00116441600000000,0.00126205800000000,0.000922291000000000,0.000959928000000000,0.00122770900000000,0.000776217000000000,0.000931699000000000,0.000787201000000000,0.00123571600000000,0.00125723100000000,0.00149922300000000,0.000581767000000000,0.00153886100000000,0.000620891000000000,0.000386564000000000,0.00208801600000000,0.000806021000000000,0.00133578200000000,0.000484106000000000,0.00118573200000000,0.000647795000000000,0.00143746100000000,0.00130539700000000,0.000936855000000000,0.00116433500000000,0.00248617400000000,0.00157059800000000,0.00124337600000000,0.00124460500000000,0.000650728000000000,0.00356785000000000,0.00243456200000000,0.00337505600000000,0.00325343500000000,0.00119200500000000,0.00108900300000000,0.00227519100000000,0.00142212200000000,0.00326209100000000,0.00196769000000000,0.00250989600000000,0.00210758300000000,0.000373476000000000,0.000861117000000000,0.00374582300000000,0.00502718700000000,0.00627597700000000,0.00443683500000000,0.00410907800000000,0.00358659200000000,0.00290526500000000,0.00676342300000000,0.00285107900000000,0.00395310200000000,0.00698173100000000,0.00564116900000000,0.00277590400000000,0.00250363000000000,0.00488567600000000,0.00101409400000000,0.00303648600000000,0.00396660500000000,0.00280575300000000,0.00395310200000000,0.00460668400000000,0.00314966300000000];
% sz =[0.000756305000000000,0.000862643000000000,0.000390278000000000,0.000846981000000000,0.00148801100000000,0.00154112900000000,0.000694066000000000,0.000796412000000000,0.00115314900000000,0.00129349600000000,0.00171882200000000,0.00107526600000000,0.000608354000000000,0.00125305400000000,0.000818067000000000,0.000793339000000000,0.00125963900000000,0.00121896800000000,0.000982815000000000,0.00181001500000000,0.00100568600000000,0.00193655400000000,0.00120656400000000,0.00145981800000000,0.00148945400000000,0.000875485000000000,0.00111808200000000,0.00134337900000000,0.00124241500000000,0.00153875900000000,0.00179380500000000,0.00151685800000000,0.000908812000000000,0.00150282700000000,0.00179861400000000,0.000656115000000000,0.00150085700000000,0.00231757900000000,0.00122778000000000,0.00132053200000000,0.000943832000000000,0.00171875500000000,0.00189893100000000,0.00103501800000000,0.00234597100000000,0.00339628700000000,0.00457571400000000,0.000980116000000000,0.00120431300000000,0.00335384600000000,0.000735784000000000,0.00297161100000000,0.00294152500000000,0.00238524300000000,0.000883999000000000,0.00124523800000000,0.00173527000000000,0.00394891200000000,0.00293221400000000,0.00290566400000000,0.00280544900000000,0.000527150000000000,0.00335393500000000,0.00165089100000000,0.00182618100000000,0.00101412100000000,0.00190628700000000,0.00454340900000000,0.00250992500000000,0.00675657300000000,0.00410955500000000,0.00502037300000000,0.00194643500000000,0.00681035800000000,0.00342757000000000,0.00288467000000000,0.00234247200000000,0.00329850400000000,0.00253847100000000,0.00282742000000000,0.00373989900000000,0.00146376600000000,0.00354988700000000,0.00618770200000000,0.00212816800000000,0.00288467000000000,0.00247348200000000,0.00195021200000000];
% 
% % Best fit parameters
% 
% A_fit = 4.2453056*10^-4;
% b_fit = 0.1177291;
% pc_fit = 0.2377114;
% TC_fit = 570.8769823;
% 
% % Ranges used
% 
% A_range = 0.000417:0.0000005:0.000432;
% b_range = 0.1174:0.00002:0.1181;
% pc_range = 0.2364:0.00003:0.2391;
% TC_range = 570.05:0.025:571.7;
% 
% % This is using their approach and using propagation of error
% 
% sy =[0.00129383700000000,0.00127862900000000,0.00105253300000000,0.00156361500000000,0.00127265300000000,0.00170275100000000,0.000932244000000000,0.00104313900000000,0.000956158000000000,0.00157541300000000,0.00115890400000000,0.00107815800000000,0.000953368000000000,0.00109452200000000,0.00158653200000000,0.00127899600000000,0.00123095300000000,0.00116692500000000,0.00117715000000000,0.00150406400000000,0.00108884700000000,0.00174810300000000,0.00189309000000000,0.00207112100000000,0.00200769200000000,0.00148338200000000,0.00285457000000000,0.00203606200000000,0.00227724500000000,0.00140021900000000,0.00198968500000000,0.00207949300000000,0.00209887700000000,0.00218303400000000,0.00196377800000000,0.00235141200000000,0.00143762800000000,0.00276703400000000,0.00186932300000000,0.00198422100000000,0.00193872600000000,0.00225915900000000,0.00186273900000000,0.00168898000000000,0.00350711300000000,0.00412591500000000,0.00473025900000000,0.00372025900000000,0.00378858500000000,0.00314433400000000,0.00361515700000000,0.00416172100000000,0.00431086200000000,0.00322760200000000,0.00424426400000000,0.00396090300000000,0.00337988900000000,0.00462493900000000,0.00463958600000000,0.00375513100000000,0.00482159300000000,0.00376435200000000,0.00405744400000000,0.00359565300000000,0.00310617100000000,0.00277155000000000,0.00552430400000000,0.00766658500000000,0.00620224600000000,0.00839710200000000,0.00705126100000000,0.00649494100000000,0.00534790900000000,0.00672558200000000,0.00494717900000000,0.00577556900000000,0.00728237700000000,0.00795926100000000,0.00621032200000000,0.00474442700000000,0.00717931200000000,0.00395233800000000,0.00521869100000000,0.00688156000000000,0.00517315700000000,0.00577556900000000,0.00621809200000000,0.00643866900000000];
% sz = 2*sy;
% 
% % Best fit parameters
% 
% A_fit = 4.1987381*10^-4;
% b_fit = 0.1176799;
% pc_fit = 0.2383262;
% TC_fit = 570.9659889;
% 
% % Ranges used
% 
% A_range = 0.0004134:0.0000004:0.0004266;
% b_range = 0.11736:0.00002:0.11794;
% pc_range = 0.2371:0.00003:0.2396;
% TC_range = 569.85:0.025:572.1;

% % C10
% 
% T = [435 435 435 485 485 485 535 535 535 560 560 560];
% pv = [0.004295 0.004261 0.004211 0.012505 0.012221 0.011700 0.031815 0.028807 0.031028531 0.051708648 0.045894317 0.048360928];
% pL = [0.622251 0.623121 0.621574 0.572349 0.574318 0.572322 0.514071 0.514585 0.513628661 0.481939724 0.474247655 0.475425097];
% 
% % Best fit parameters
% 
% A_fit = 4.0409358*10^-4;
% b_fit = 0.1168491;
% pc_fit = 0.2388512;
% TC_fit = 618.6369737;
% 
% % Ranges used
% 
% A_range = 0.000352:0.000002:0.000456;
% b_range = 0.1155:0.0001:0.1182;
% pc_range = 0.232:0.0004:0.2456;
% TC_range = 615:0.2:622.5;

% % C12
% 
% T = [465 465 465 515 515 515 575 575 575 600 600 600];
% pv = [0.003580 0.003552 0.003339 0.010001 0.009599 0.010041 0.030038 0.029929 0.028757277 0.044420097 0.0498691 0.045674285];
% pL = [0.623247 0.623791 0.622866 0.574519 0.573699 0.575558 0.507140 0.508380 0.507617368 0.473982013 0.473380267 0.472424309];
% 
% % Best fit parameters
% 
% A_fit = 3.9687675*10^-4;
% b_fit = 0.1145123;
% pc_fit = 0.2349135;
% TC_fit = 661.3181029;
% 
% % Ranges used
% 
% A_range = 0.00036:0.000002:0.000432;
% b_range = 0.1134:0.0001:0.1156;
% pc_range = 0.23:0.0002:0.24;
% TC_range = 658.6:0.1:664;

% % % C16
% % 
% T = [510 510 510 565 565 565 625 625 625 655 655 655]; 
% pv = [0.002506 0.002280 0.002327 0.007297 0.006940 0.008036 0.023236 0.022384 0.020300153 0.032705779 0.035817672 0.036051192];
% pL = [0.625422 0.624818 0.623635 0.574335 0.573793 0.576441 0.511448 0.510382 0.506862842 0.465499537 0.472704048 0.472517505];
% 
% % Best fit parameters
% 
% A_fit = 4.200469*10^-4;
% b_fit = 0.1116021;
% pc_fit = 0.2233379;
% TC_fit = 725.4052262;
% 
% % Ranges used
% 
% A_range = 0.000384:0.000002:0.000456;
% b_range = 0.1105:0.00005:0.1127;
% pc_range = 0.2175:0.0005:0.229;
% TC_range = 722:0.25:729;

% D_optimal

% C8

% 1 replica evenly spaced /Can't use the F parameter with only 4 points

% T = [390 432 473 515];
% pL = [0.625403293 0.584015542 0.536099011 0.47685196];
% pv = [0.004455524 0.011077102 0.024725339 0.052363289];
% 
% % Best fit parameters
% 
% A_fit = 4.041669*10^-4;
% b_fit = 0.1182516;
% pc_fit = 0.2420708;
% TC_fit = 569.5396808;
% 
% % Ranges used
% 
% A_range = 0.0004:0.0000002:0.00041; 
% b_range = 0.118:0.00002:0.119;
% pc_range = 0.24:0.0001:0.245;
% TC_range = 569:0.02:570;

% 2 replica evenly spaced

% T = [390 407.9 425.7 443.6 461.4 479.3 497.1 515];
% pL = [0.625403293 0.607700 0.589924405 0.568803543 0.550001442 0.525968268 0.503678108 0.47685196]; 
% pv = [0.004455524 0.006481 0.009262596 0.012929947 0.019705356 0.025792423 0.037406377 0.052363289];
% 
% % Best fit parameters
% 
% A_fit = 4.2307752*10^-4;
% b_fit = 0.1177996;
% pc_fit = 0.2380486;
% TC_fit = 571.0186623;
% 
% % Ranges used
% 
% A_range = 0.00037:0.000005:0.000475; 
% b_range = 0.1164:0.0001:0.1192;
% pc_range = 0.23:0.0005:0.246;
% TC_range = 566.5:0.25:576;

% 2 replica D-optimal

% T = [390 390 440 440 490 490 515 515];
% pL = [0.625403293 0.624078 0.573911 0.572892 0.511936 0.512849 0.476022927 0.47685196];  
% pv = [0.004455524 0.003813 0.013343 0.011971 0.032864 0.031561  0.053323735 0.052363289];
% 
% % Best fit parameters
% 
% A_fit = 4.1641649*10^-4;
% b_fit = 0.1177363;
% pc_fit = 0.2390204;
% TC_fit = 570.6866463;
% 
% % Ranges used
% 
% A_range = 0.000365:0.000005:0.00047; 
% b_range = 0.1165:0.0001:0.1189;
% pc_range = 0.231:0.0005:0.247;
% TC_range = 566.5:0.25:575;

% 3 replica evenly spaced

% T = [390 401.4 412.7 424.1 435.5 446.8 458.2 469.5 480.9 492.3 503.6 515];
% pL = [0.625403293 0.614761 0.603990 0.591236 0.578668 0.565855174 0.554183804 0.539091228 0.525532815 0.507080109 0.492467243 0.47685196];  
% pv = [0.004455524 0.005481 0.007298 0.008515 0.012045 0.013393087 0.018613249 0.023314203 0.027956202 0.034286962 0.040200772 0.052363289]; 
% 
% % Best fit parameters
% 
% A_fit = 4.1664922*10^-4;
% b_fit = 0.1183365;
% pc_fit = 0.2398046;
% TC_fit = 569.2779861;
% 
% % Ranges used
% 
% A_range = 0.00038:0.0000025:0.000455; 
% b_range = 0.11745:0.00005:0.1192;
% pc_range = 0.23525:0.000125:0.2445;
% TC_range = 566.75:0.125:571.75;

% 3 replica D-optimal

% T = [390 390 390 440 440 440 490 490 490 515 515 515];
% pv = [0.004456 0.003813 0.004219 0.013343 0.011971 0.012818 0.032864 0.031561 0.031015949 0.052363289 0.053323735 0.05073475];
% pL = [0.625403 0.624078 0.625876 0.573911 0.572892 0.574369 0.511936 0.512849 0.5114893 0.47685196 0.476022927 0.475198579];
% 
% % Best fit parameters
% 
% A_fit = 4.096851*10^-4;
% b_fit = 0.1181472;
% pc_fit = 0.2405976;
% TC_fit = 569.5065255;
% 
% % Ranges used
% 
% A_range = 0.000376:0.000002:0.000444;
% b_range = 0.1173:0.00005:0.1191;
% pc_range = 0.2364:0.0002:0.2448;
% TC_range = 567.4:0.1:571.7;

% C24

% T = [580 580 610 610 700 700 750 750];
% pv = [0.001335 0.001367 0.002629 0.003020 0.016575 0.014621 0.037178 0.034133];
% pL = [0.612410 0.612435 0.588341 0.589391 0.503411 0.502576 0.438590 0.438502]; 
% 
% % Best fit parameters
% 
% A_fit = 4.1042904*10^-4;
% b_fit = 0.1068806;
% pc_fit = 0.2117532;
% TC_fit = 813.5752419;
% 
% % Ranges used
% 
% A_range = 0.000372:0.000002:0.000448; 
% b_range = 0.1058:0.0001:0.108;
% pc_range = 0.2052:0.0002:0.2182;
% TC_range = 809.5:0.25:817.5;

% Comparison with normal and 8 data points (subtracted 590)

% T = [580 600 610 625 675 700 725 750];
% pv = [0.0010309 0.0021023 0.0025044 0.003415 0.009588 0.016419 0.026868 0.032001];
% pL = [0.611756 0.5909036 0.5878981 0.57159 0.52602 0.50403 0.47456 0.43912];
% 
% % Best fit parameters
% 
% A_fit = 3.9773024*10^-4;
% b_fit = 0.1058519;
% pc_fit = 0.2118309;
% TC_fit = 816.9198185;
% 
% % Ranges used
% 
% A_range = 0.000328:0.000004:0.000468; 
% b_range = 0.1038:0.0001:0.1078;
% pc_range = 0.1994:0.0004:0.2238;
% TC_range = 809.5:0.25:825.5;


% C24
% T = [580 590 600 610 625 675 700 725 750 580 580 610 610 700 700 750 750];
% pv = [0.0010309 0.0015445 0.0021023 0.0025044 0.003415 0.009588 0.016419 0.026868 0.032001 0.001335 0.001367 0.002629 0.003020 0.016575 0.014621 0.037178 0.034133];
% pL = [0.611756 0.6060484 0.5909036 0.5878981 0.57159 0.52602 0.50403 0.47456 0.43912 0.612410 0.612435 0.588341 0.589391 0.503411 0.502576 0.438590 0.438502];
% 
% % Best fit parameters
% 
% A_fit = 4.0693673*10^-4;
% b_fit = 0.1065858;
% pc_fit = 0.211668;
% TC_fit = 814.7195529;
% 
% % Ranges used
% 
% A_range = 0.000376:0.000002:0.000436; 
% b_range = 0.1056:0.00005:0.1074;
% pc_range = 0.2064:0.0002:0.217;
% TC_range = 811.5:0.125:818.25;
 
% C25
% T = [580 590 600 615 610 650 690 730 750 580 580 610 610 700 700 750 750]; 
% pv = [0.001064 0.001586 0.001359 0.002745 0.002614 0.005403 0.012151 0.023300 0.029873 0.000904 0.001055 0.002179 0.002059 0.013796 0.012328 0.028189 0.032565];
% pL = [0.616612 0.608685 0.598211 0.587222 0.590739 0.559048 0.524589 0.476545 0.451116 0.616773 0.617805 0.590005 0.592117 0.508013 0.508888 0.447092 0.455939];
% 
% % Best fit parameters
% 
% A_fit = 3.9702334*10^-4;
% b_fit = 0.1057551;
% pc_fit = 0.2115999;
% TC_fit = 825.1198415;
% 
% % Ranges used
% 
% A_range = 0.00037:0.000002:0.000424; 
% b_range = 0.1049:0.00005:0.1066;
% pc_range = 0.2064:0.0002:0.2166;
% TC_range = 821.75:0.25:828.5;

% C26
% T = [610 610 700 700 750 750 610 615 655 700 740 760];  
% pv = [0.001528935 0.001459271 0.011283077 0.011035822 0.02711579 0.024839302 0.001410743 0.002145831 0.004527904 0.010563924 0.023272831 0.030291144];
% pL = [0.593680527 0.595483838 0.517748319 0.517497756 0.46280141 0.461840465 0.594709241 0.590855063 0.55869304 0.513824039 0.474420931 0.450737686];
% 
% % Best fit parameters
% 
% A_fit = 3.8433457*10^-4;
% b_fit = 0.1045803;
% pc_fit = 0.2110033;
% TC_fit = 837.0296931;
% 
% % Ranges used
% 
% A_range = 0.000362:0.000002:0.000408; 
% b_range = 0.1039:0.0001:0.1053;
% pc_range = 0.2072:0.0002:0.2148;
% TC_range = 834:0.125:840;

% % C27
% T = [580 610 620 660 700 745 765 580 580 610 610 700 700 750 750];  
% pv = [0.000349 0.001231 0.001637 0.004996 0.009306 0.019798 0.027616456 0.000357766 0.000382407  0.001249904 0.001207952 0.008496211 0.009638921 0.02102701 0.020568281];
% pL = [0.620569 0.599969 0.589006 0.561226 0.520605  0.474628056 0.443361733 0.616267576 0.618256609 0.602201177 0.599266388 0.519436747 0.522455617 0.466660959  0.464093241];
% 
% % Best fit parameters
% 
% A_fit = 3.9510738*10^-4;
% b_fit = 0.1044592;
% pc_fit = 0.2076862;
% TC_fit = 842.4407698;
% 
% % Ranges used
% 
% A_range = 0.000356:0.000002:0.000434; 
% b_range = 0.1032:0.0001:0.1057;
% pc_range = 0.1995:0.00025:0.2155;
% TC_range = 837:0.25:848.5;

% % C28
% T = [580 600 610 625 665 710 750 770 580 580 610 610 700 700 750 750];  
% pv = [0.000298 0.000631 0.001106 0.001405 0.004707 0.010290 0.019214 0.026309459 0.00029182 0.00027203 0.000967441 0.001018792 0.009694453 0.008461965 0.019446644 0.02028996];
% pL = [0.624490 0.608165 0.603661 0.590478 0.560705 0.515192 0.471939007  0.443930466 0.625790733 0.623418891 0.603743905 0.603731412 0.528199675 0.525271634 0.474261152 0.475542704];
% 
% % Best fit parameters
% 
% A_fit = 3.9300499*10^-4;
% b_fit = 0.1044713;
% pc_fit = 0.2081894;
% TC_fit = 848.0099344;
% 
% % Ranges used
% 
% A_range = 0.000364:0.000002:0.00042; 
% b_range = 0.1036:0.00005:0.1053;
% pc_range = 0.202:0.00025:0.2136;
% TC_range = 844:0.25:852.5;

% 
% % pentacosane C25
%  T2 = [580 590 600 610 615 650 690 730 750];
%  pv2 = [0.00109 0.001412 0.001406 0.002087415 0.00265 0.004574594 0.010672267 0.018401342 0.031339834];
%  pL2 = [0.616996 0.608843 0.59835 0.592602248 0.587282 0.555748238 0.519263592 0.471308627 0.45664106];
% 
% % hexacosane C26
%  T3 = [610 655 700 740 760];
%  pv3 = [ 0.001423	0.00429041	0.010017451	0.023451055	0.026356036];
%  pL3  = [ 0.592659	0.557560998	0.516726592	0.477174855	0.441255922];
% % 615 0.001808302 0.59482208 data excluded b/c inconsistent with new data
% 
% % heptacosane C27
%  T4 = [580 610 620 660 700 745 765];
%  pv4 = [0.00036 0.001345 0.15333E-02 0.45482E-02  0.91630E-02 0.19332E-01 0.24939E-01];
%  pL4 = [0.620732 0.602083 0.58842 0.55523 0.52438 0.47300 0.44285];
% % The 580 data is questionable b/c not equil, but it improved regression
% 
% % octacosane C28
%  T5 = [580 600 610 625 665 710 750 770];
%  pv5 = [0.000304 0.000655 0.001123 0.17462E-02 0.48022E-02 0.11550E-01 0.17752E-01 0.25336E-01];
%  pL5 = [0.624137 0.612879 0.602442 0.59089 0.56211 0.51428 0.46550 0.45160];

% Best fit parameters for C24-28 
% A1 = 4.01007 * 10^-4;
% b1 = 0.106082;
% pc1 = 0.2117255;
% TC1 = 816.29647;
% 
% A2 = 4.00359 * 10^-4;
% b2 = 0.105439;
% pc2 = 0.2099192;
% TC2 = 826.79941;
% 
% A3 = 4.01609 * 10^-4;
% b3 = 0.104866;
% pc3 = 0.2079285;
% TC3 = 835.3348;
% 
% A4 = 4.07269 * 10^-4;
% b4 = 0.10461;
% pc4 = 0.2056181;
% TC4 = 841.6028;
% 
% A5 = 4.04998 * 10^-4;
% b5 = 0.1043;
% pc5 = 0.2057137;
% TC5 = 848.7852;

% C33-37

% T = [650 670 690 700 720 740 760 780];

% C33
% 
% pv = [0.001073 0.001966 0.002971 0.003732 0.005607 0.008941 0.011962 0.015912];
% pL = [0.5854 0.570751 0.552497 0.545686 0.529824 0.509445 0.487610 0.466331];
% 
% % C34
% 
% pv = [0.001050 0.001720 0.002901 0.003180 0.005365 0.006861 0.010403 0.015635];
% pL = [0.591568 0.572263 0.558647 0.546515 0.531991 0.512897 0.493274 0.471725];
% 
% % C35
% 
% pv = [0.001041 0.001817 0.002313 0.002877 0.004391 0.005698 0.008517 0.014334];
% pL = [0.587856 0.565179 0.561448 0.541005 0.531668 0.509027 0.496020 0.484413];
% 
% % C36
% 
% pv = [0.000552 0.001281 0.001954 0.002775 0.003899 0.005903 0.008470 0.010884];
% pL = [0.591362 0.577485 0.563171 0.555280 0.537394 0.521031 0.502703 0.481827];
%   
% % C37
% 
% pv = [0.000594 0.001053 0.001612 0.002157 0.003430 0.004820 0.007200 0.010791];
% pL = [0.595985 0.580918 0.563758 0.556302 0.540153 0.523064 0.504754 0.487191];

% C46

% T = [730 735 740 745 750 755 760 765 770 775 780 785 790 795 800];
% pv = [0.0014 0.0017 0.0018 0.0023 0.0027 0.0023 0.0035 0.0032 0.0048 0.0035 0.0051 0.0045 0.0048 0.0053 0.007];
% pL = [0.5545 0.549 0.5482 0.5414 0.5421 0.5291 0.5285 0.5241 0.5212 0.5127 0.5129 0.506 0.5066 0.493 0.4919];

% C47

% T = [730 735 740 745 750 755 760 765 770 775 780 785 790 795 800];
% pv = [0.0011 0.0026 0.0014 0.0028 0.0016 0.0019 0.0026 0.0028 0.0026 0.0035 0.0035 0.004 0.0059 0.005 0.0058];
% pL = [0.5496 0.5553 0.5438 0.5424 0.5333 0.5338 0.5326 0.522 0.5217 0.516 0.5102 0.5045 0.5034 0.4992 0.4938];

% C48

% T = [730 735 740 745 750 755 760 765 770 775 780 785 790 795 800];
% pv = [0.0012 0.0014 0.0022 0.0015 0.002 0.0017 0.0028 0.0033 0.0024 0.0033 0.0026 0.0048 0.0047 0.0049 0.0052];
% pL = [0.5521 0.5538 0.5468 0.5402 0.5351 0.5315 0.5329 0.5336 0.5183 0.5221 0.5102 0.5137 0.5022 0.499 0.4912];

% C49

% T = [730 740 745 755 760 765 770 775 785 790 795 800];
% pv = [0.0013 0.0015 0.0009 0.002 0.0017 0.0024 0.0033 0.0025 0.0026 0.0035 0.0036 0.0055];
% pL = [0.556 0.5488 0.5422 0.5336 0.5287 0.5335 0.5217 0.5215 0.4993 0.5021 0.5052 0.5013];

% C50

% T = [720 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800];
% pv = [0.0005  0.0011 0.0006 0.0011 0.0019 0.0023 0.0017 0.002 0.0029 0.0027 0.0023 0.0025 0.0024 0.0028 0.0036 0.0045];
% pL = [0.5624 0.5619 0.5533 0.5467 0.5476 0.5449 0.5301 0.5307 0.531 0.527 0.519 0.5169 0.5123 0.5076 0.5093 0.5006];

% NERD results

% C6

% T = [360 360 360 400 400 400 440 440 440 460 460 460];
% pv = [0.005757 0.005808 0.005683 0.013249 0.012586 0.014501 0.030337 0.031102 0.031705025 0.044821483 0.045372356 0.044413538];
% pL = [0.582023 0.582101 0.581954 0.539911 0.540029 0.541567 0.491526 0.490267 0.492136898 0.461476596 0.460660596 0.461322963];
% 
% % Best fit parameters
% 
% A_fit = 4.0744651*10^-4;
% b_fit = 0.1146151;
% pc_fit = 0.2298442;
% TC_fit = 516.6540937;
% 
% % Ranges used
% 
% A_range = 0.00037:0.000002:0.000444;
% b_range = 0.1137:0.00005:0.1156;
% pc_range = 0.2258:0.0001:0.2339;
% TC_range = 514.6:0.05:518.8;

% % C8
% 
% T = [390 390 390 440 440 440 490 490 490 515 515 515];
% pv = [0.003241 0.003413 0.003242 0.010886 0.010174 0.010268 0.027002 0.026314 0.028841329 0.045625972 0.044027079 0.044742652];
% pL = [0.611275 0.612258 0.610583 0.563404 0.563799 0.562474 0.506009 0.503972 0.505561593 0.472323048 0.472227824 0.46938894];
% 
% % Best fit parameters
% 
% A_fit = 3.9824602*10^-4;
% b_fit = 0.1143298;
% pc_fit = 0.2326731;
% TC_fit = 576.6514026;
% 
% % Ranges used
% 
% A_range = 0.00036:0.000002:0.000436;
% b_range = 0.1133:0.00005:0.1153;
% pc_range = 0.2275:0.0002:0.2375;
% TC_range = 574:0.25:579.5;

% % C10
% 
% T = [435 435 435 485 485 485 535 535 535 560 560 560];
% pv = [0.003368 0.003589 0.003592 0.011799 0.010227 0.010427 0.030406 0.026074 0.026484149 0.041913696 0.039958104 0.041566625]; 
% pL = [0.609275 0.610087 0.609962 0.565079 0.561401 0.562010 0.508393 0.506088 0.501838198 0.468182095 0.468544115 0.470179046];
% 
% % Best fit parameters
% 
% A_fit = 4.1049813*10^-4;
% b_fit = 0.1136805;
% pc_fit = 0.2296828;
% TC_fit = 623.3247469;
% 
% % Ranges used
% 
% A_range = 0.000364:0.000002:0.000456;
% b_range = 0.1124:0.00005:0.115;
% pc_range = 0.2236:0.0002:0.2358;
% TC_range = 619.6:0.2:628;

% % C12
% 
% T = [465 465 465 515 515 515 575 575 575];
% pv = [0.003170 0.003149 0.003086 0.009480 0.008823 0.009666 0.026868 0.026901 0.028098426];
% pL = [0.613298 0.611823 0.613342 0.566183 0.565398 0.566691 0.497933 0.498380 0.500184631];
% 
% % Best fit parameters
% 
% A_fit = 4.0847418*10^-4;
% b_fit = 0.1121094;
% pc_fit = 0.226682;
% TC_fit = 664.1601327;
% 
% % Ranges used
% 
% A_range = 0.000382:0.000002:0.000436;
% b_range = 0.1113:0.00005:0.1129;
% pc_range = 0.2224:0.0002:0.231;
% TC_range = 661.4:0.1:667;

% % C16
% 
% T = [510 510 510 565 565 565 625 625 625 655 655 655]; 
% pv = [0.002182 0.002027 0.002604 0.007151 0.007071 0.006751 0.020692 0.022353 0.023460931 0.036327665 0.036577224 0.039021581];
% pL = [0.615588 0.614011 0.615127 0.566946 0.564920 0.565313 0.500943 0.499603 0.503899311 0.46228747 0.464771013 0.463362443];
% 
% % Best fit parameters
% 
% A_fit = 4.028671*10^-4;
% b_fit = 0.1102368;
% pc_fit = 0.2224605;
% TC_fit = 723.6077322;
% 
% % Ranges used
% 
% A_range = 0.000372:0.000002:0.000432;
% b_range = 0.1094:0.00005:0.1111;
% pc_range = 0.218:0.00025:0.227;
% TC_range = 720.75:0.125:726.5;

% D_optimal

% C24

% T = [580 580 610 610 700 700 750 750];
% pv = [0.001680 0.001591 0.003191 0.003197 0.015927 0.018041 0.041546 0.038739];
% pL = [0.605773 0.605160 0.579052 0.580196 0.496101 0.495883 0.438059 0.427755]; 
% 
% % Best fit parameters
% 
% A_fit = 3.9298293*10^-4;
% b_fit = 0.1058859;
% pc_fit = 0.2128536;
% TC_fit = 810.4907503;
% 
% % Ranges used
% 
% A_range = 0.000324:0.000004:0.00046; 
% b_range = 0.1039:0.0001:0.1078;
% pc_range = 0.2012:0.0004:0.2244;
% TC_range = 804:0.25:818;

% % C24
% T = [580 590 600 610 625 675 700 725 750 580 580 610 610 700 700 750 750];  
% pv = [0.001619 0.001667 0.002398 0.002976 0.003789 0.010386 0.018751 0.025737 0.037634 0.00167959 0.001591341 0.003191456 0.003196898 0.015927365  0.018041253 0.041546128 0.038739384];
% pL = [0.604481 0.596667 0.588530 0.581371 0.567082 0.516721 0.498091 0.466649 0.428144 0.605772962 0.605159567 0.579052094 0.580196333 0.496101193 0.495882876 0.438058885 0.427755428]; 
% 
% % Best fit parameters
% 
% A_fit = 3.9711274*10^-4;
% b_fit = 0.1059186;
% pc_fit = 0.2120307;
% TC_fit = 810.2073147;
% 
% % Ranges used
% 
% A_range = 0.000364:0.000002:0.000428; 
% b_range = 0.105:0.00005:0.1068;
% pc_range = 0.2065:0.00025:0.2175;
% TC_range = 807.25:0.125:813.5;

% C25
% T = [580 590 600 610 615 650 690 730 750 580 580 610 610 700 700 750 750];  
% pv = [0.001029 0.001662 0.001882 0.002377 0.003016 0.006104 0.011976 0.024035 0.035363 0.001074382  0.00138886 0.002426445  0.00201612 0.013619834 0.014328696 0.034080248 0.032407971];
% pL = [0.608930 0.602443 0.594064 0.584965 0.581729 0.549812 0.507892 0.466597 0.437719 0.60844285 0.610485852 0.585372808  0.583287997 0.499475161 0.503780523 0.439947067 0.435394226]; 
% 
% % Best fit parameters
% 
% A_fit = 4.0805556*10^-4;
% b_fit = 0.1059558;
% pc_fit = 0.2095253;
% TC_fit = 815.9270657;
% 
% % Ranges used
% 
% A_range = 0.000384:0.000002:0.000432; 
% b_range = 0.1053:0.00005:0.1066;
% pc_range = 0.205:0.00025:0.214;
% TC_range = 813.5:0.125:818.5;

% % C26
% T = [610 615 655 700 740 760 610 610 700 700 750 750];  
% pv = [0.001730 0.002511 0.005567 0.011576 0.025610 0.033160 0.001727449 0.001646569 0.0120155 0.011678769 0.026384856 0.031271232];
% pL = [0.589418 0.582305 0.550872 0.504893 0.462788 0.434283 0.583430354 0.58864492 0.502071348 0.505357365 0.443386146 0.448300598];  
% 
% % Best fit parameters
% 
% A_fit = 4.0434889*10^-4;
% b_fit = 0.1049229;
% pc_fit = 0.207561;
% TC_fit = 825.4514265;
% 
% % Ranges used
% 
% A_range = 0.00036:0.000004:0.000448; 
% b_range = 0.1036:0.0001:0.1062;
% pc_range = 0.20075:0.00025:0.2145;
% TC_range = 821:0.25:830.25;

% C27
% T = [610 620 660 700 745 765 610 610 700 700 750 750];  
% pv = [0.001322 0.002026 0.004474 0.010121 0.025276 0.030342 0.001656261 0.001715668 0.010126828 0.009271811 0.021935796 0.023349075];
% pL = [0.589559 0.583809 0.549077 0.511672 0.464210 0.433615 0.593270744 0.592975846 0.509905005 0.508225119 0.454802484 0.452330328];    
% 
% % Best fit parameters
% 
% A_fit = 4.1215071*10^-4;
% b_fit = 0.1046005;
% pc_fit = 0.2049728;
% TC_fit = 833.1781206;
% 
% % Ranges used
% 
% A_range = 0.00038:0.000002:0.000444; 
% b_range = 0.1036:0.00005:0.1056;
% pc_range = 0.1995:0.00025:0.2105;
% TC_range = 829:0.25:837;

% C28
% T = [580 600 610 625 665 710 750 770 580 580 610 610 700 700 750 750];  
% pv = [0.000397 0.000712 0.001411 0.002181 0.004945 0.010761 0.020755 0.030654 0.000405969 0.000385136 0.001344139 0.001246781 0.00852292 0.00875679 0.02133648 0.021405128];
% pL = [0.613736 0.593789 0.597085 0.585475 0.548103 0.506095 0.462064 0.438617 0.611914045 0.614107042 0.597043421 0.596345057 0.515412213 0.517807587 0.463462361 0.462063357];     
% 
% % Best fit parameters
% 
% A_fit = 3.8734342*10^-4;
% b_fit = 0.1033782;
% pc_fit = 0.2064371;
% TC_fit = 843.5788019;
% 
% % Ranges used
% 
% A_range = 0.000348:0.000002:0.000428; 
% b_range = 0.1021:0.00005:0.1047;
% pc_range = 0.1985:0.00025:0.2145;
% TC_range = 838:0.25:849.5;

% C24

% T = [580 590 600 610 625 675 700 725 750];
% pv = [0.001619 0.001667 0.002398 0.002976 0.003789 0.010386 0.018751 0.025737 0.037634];
% pL = [0.604481 0.596667 0.588530 0.581371  0.567082 0.516721 0.498091 0.466649 0.428144];

% C25

% T = [580 590 600 610 615 650 690 730 750];
% pv = [0.001029 0.001662 0.001882 0.002377 0.003016 0.006104 0.011976 0.024035 0.035363];
% pL = [0.608930 0.602443 0.594064 0.584965  0.581729 0.549812 0.507892 0.466597 0.437719];

% C26

% T = [580 610 615 655 700 740 760];
% pv = [0.000387 0.001730 0.002511 0.005567 0.011576 0.025610 0.033160];
% pL = [0.588771 0.589418  0.582305 0.550872 0.504893 0.462788 0.434283];

% C27

% T = [580 610 620 660 700 745 765];
% pv = [0.000404 0.001322 0.002026 0.004474 0.010121 0.025276 0.030342];
% pL = [0.595680 0.589559 0.583809 0.549077 0.511672 0.464210 0.433615];

% C28

% T = [580 600 610 625 665 710 750 770];
% pv = [0.000397 0.000712 0.001411 0.002181 0.004945 0.010761 0.020755 0.030654];
% pL = [0.613736 0.593789 0.597085 0.585475 0.548103 0.506095 0.462064 0.438617];

% C33

% T = [650 670 690 700 720 740 760 780];
% pv = [0.0014800412 0.0021160377 0.0035441113 0.0044979045 0.0067590477  0.0098662242 0.0133931944 0.0179835768];
% pL = [0.5773043270 0.5603416398 0.5459020510 0.5372950448 0.5212976420 0.4977019063 0.4735290995 0.4510251965];

% C34

% T = [650 670 690 700 720 740 760 780];
% pv = [0.0012521636 0.0021723554 0.0033243425 0.0037879623 0.0059354507 0.0083442310 0.0121785344 0.0162190970];
% pL = [0.5833375425 0.5670695785 0.5497589948 0.5403452950 0.5212394608 0.5029797910 0.4822209300 0.4597585211];

% C35

% T = [650 670 690 700 720 740 760 780];
% pv = [0.0010718106 0.0017104674 0.0025408439 0.0030748106 0.0047977756 0.0070315364 0.0119786238 0.0158614664];
% pL = [0.5844917423 0.5691310355 0.5515296346 0.5410115205 0.5258032285 0.5056431808 0.4908145479 0.4633789476];

% C36

% T = [650 670 690 700 720 740 760 780];
% pv = [0.0008094989 0.0016877892 0.0021551963  0.0030767817 0.0045551961 0.0065043031 0.0100443799 0.0133588035];
% pL = [0.5874779169 0.5685943216 0.5517865471 0.5468477034 0.5296205544 0.5098528430 0.4906453011 0.4690504700];

% C37

% T = [650 670 690 700 720 740 760 780];
% pv = [0.0007475237 0.0010473105 0.0019404346 0.0024709094 0.0036606407 0.0058179911 0.0085930769 0.0129597539];
% pL = [0.5873992644 0.5727134112 0.5590986411 0.5477730905 0.5312507349 0.5102144945 0.4955879363 0.4752972941];

% C46

% T = [710 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 820 845];
% pv = [0.000744 0.001445 0.001602 0.002576 0.002194 0.002799 0.003309 0.004740 0.0035362 0.0043959 0.0041746 0.0043175 0.0052654 0.0062563 0.0102269 0.0071172 0.0123651 0.0146600];
% pL = [0.561729 0.539370 0.539264 0.536076 0.532207 0.522725 0.518926 0.524981 0.5137009 0.5043426 0.5032184 0.4970508 0.4900569 0.4915564 0.4910791 0.4827681 0.4680001 0.4327650];

% C47

% T = [710 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 820 850];
% pv = [0.001226 0.002809 0.001184 0.002413 0.003055 0.002142 0.002955 0.003502 0.003590 0.004027 0.004382 0.004268 0.005309 0.005006 0.006936 0.006539 0.012098 0.019229];
% pL = [0.565879 0.544808 0.544519 0.537427 0.537344 0.527980 0.523959 0.517472 0.514650 0.513739 0.506369 0.493476 0.494618 0.489753 0.489019 0.484933 0.461813 0.430493];

% C48

% T = [730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 825 850 875];
% pv = [0.000747 0.001040 0.001877 0.002031 0.002842 0.001885 0.002627 0.004205 0.002975 0.005018 0.004623 0.005681 0.004681 0.005886 0.006463 0.008845 0.018972 0.022225];
% pL = [0.546940 0.534897 0.531829 0.534222 0.528077 0.518782 0.519876 0.517968 0.511938 0.505700 0.500951 0.503801 0.491146 0.487153 0.483035 0.464160 0.442747 0.400302];

% C49

% T = [715 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 825 850];
% pv = [0.000509 0.001075 0.001742 0.001759 0.001530 0.001756 0.003216 0.002735 0.003091 0.003684 0.003711 0.004023 0.003477 0.005287 0.004936 0.005786 0.010652 0.016770];
% pL = [0.559873 0.543286 0.544892 0.544456 0.531902 0.532107 0.528428  0.521845 0.521441 0.513786 0.511387 0.499918 0.499908 0.497415 0.494825 0.488954 0.463589 0.440130];

% C50

% T = [720 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 830 855];
% pv = [0.000987 0.001384 0.001295 0.001000 0.001930 0.001813 0.001425 0.002193 0.003256 0.003650 0.002215 0.003014 0.003747 0.004753 0.004325 0.003738 0.008249 0.014170];
% pL = [0.556244 0.550830 0.546407 0.539321 0.538955 0.537231 0.522057 0.524627 0.522931 0.518481 0.506345 0.506311 0.501106 0.501922 0.489626 0.485847 0.458353 0.432481]; 

                        %%%%% Alkene Family %%%%%%
                            % TraPPE model

% C24

% T = [580 590 600 610 625 675 700 725 750];
% pv = [0.001063 0.001764 0.002670 0.003239 0.003823 0.009470 0.014679 0.024323 0.037461]; 
% pL = [0.614552 0.609385 0.600372 0.591711 0.578116 0.530210 0.506419 0.476406 0.450192];
% 
% % Best fit parameters
% 
% A_fit = 3.9409602*10^-4;
% b_fit = 0.1066752;
% pc_fit = 0.2149813;
% TC_fit = 817.7758097;
% 
% % Ranges used
% 
% A_range = 0.000355:0.0000025:0.000435;
% b_range = 0.1055:0.00005:0.1078;
% pc_range = 0.2075:0.00025:0.2225;
% TC_range = 813.2:0.2:822.6;

% C25

% T = [580 590 600 610 615 650 690 730 750];
% pv = [0.000885 0.001267 0.001746 0.002269 0.002626 0.004825 0.010509 0.022075 0.030916]; 
% pL = [0.619452 0.612555 0.604131 0.597284 0.593239 0.562304 0.522013 0.480500 0.449839];
% 
% % Best fit parameters
% 
% A_fit = 4.0872936*10^-4;
% b_fit = 0.106978;
% pc_fit = 0.2122096;
% TC_fit = 822.6197283;
% 
% % Ranges used
% 
% A_range = 0.0003675:0.0000025:0.00045;
% b_range = 0.1058:0.00005:0.1082;
% pc_range = 0.20425:0.00025:0.22025;
% TC_range = 817.75:0.25:828;

% C26

% T = [580 590 600 610 615 655 700 740 760];
% pv = [0.000713 0.001081 0.001456 0.001515 0.002224 0.004918 0.011271 0.021102 0.033367]; 
% pL = [0.623549 0.616260 0.606206 0.597883 0.595993 0.560654 0.517225 0.475955 0.448742]; 
% 
% % Best fit parameters
% 
% A_fit = 3.9696659*10^-4;
% b_fit = 0.1059591;
% pc_fit = 0.2119295;
% TC_fit = 832.6889807;
% 
% % Ranges used
% 
% A_range = 0.00036:0.0000025:0.000435;
% b_range = 0.1049:0.00005:0.107;
% pc_range = 0.20475:0.00025:0.219;
% TC_range = 828.25:0.25:837.5;

% C27

% T = [580 590 600 610 620 660 700 745 765];
% pv = [0.000569 0.000818 0.001075 0.001280 0.002029 0.004296 0.009808 0.019631 0.028717]; 
% pL = [0.626848 0.617375 0.612789 0.601710 0.595619 0.561297 0.524794 0.477901 0.452059];  
% 
% % Best fit parameters
% 
% A_fit = 3.9462326*10^-4;
% b_fit = 0.1051186;
% pc_fit = 0.2100199;
% TC_fit = 843.4394887;
% 
% % Ranges used
% 
% A_range = 0.000365:0.0000025:0.000425;
% b_range = 0.1043:0.00005:0.106;
% pc_range = 0.204:0.00025:0.216;
% TC_range = 839.5:0.25:847.5;

% C28

% T = [580 590 600 610 625 665 710 750 770];
% pv = [0.000493 0.000690 0.000836 0.001096 0.001790 0.003921 0.009813 0.017584 0.027553]; 
% pL = [0.630163 0.620923 0.611692 0.603612 0.596406 0.561120 0.516765 0.470276 0.452479];   
% 
% % Best fit parameters
% 
% A_fit = 4.0359257*10^-4;
% b_fit = 0.1049567;
% pc_fit = 0.2071992;
% TC_fit = 847.9440506;
% 
% % Ranges used
% 
% A_range = 0.000355:0.0000025:0.00045;
% b_range = 0.1035:0.00005:0.1063;
% pc_range = 0.197:0.00025:0.217;
% TC_range = 841.5:0.25:855;

% C33

% T = [650 670 690 700 720 740 760 780];
% pv = [0.001147 0.001939 0.003002 0.003880 0.005875 0.008500 0.011575 0.015960];
% pL = [0.588784 0.575032 0.553289 0.548779 0.528303 0.510573 0.490233 0.471032];
% 
% % Best fit parameters
% 
% A_fit = 4.0115726*10^-4;
% b_fit = 0.1023732;
% pc_fit = 0.2013276;
% TC_fit = 884.6054919;
% 
% % Ranges used
% 
% A_range = 0.00033:0.000005:0.00048;
% b_range = 0.1:0.0001:0.1046;
% pc_range = 0.188:0.0005:0.214;
% TC_range = 874:0.5:898;

% C34

% T = [650 670 690 700 720 740 760 780];
% pv = [0.000950 0.001608 0.003136 0.003901 0.004751 0.007499 0.010120 0.015295]; 
% pL = [0.589304 0.574464 0.561557 0.550474 0.531088 0.517002 0.496593 0.475550];
% 
% % Best fit parameters
% 
% A_fit = 3.8587507*10^-4;
% b_fit = 0.1015666;
% pc_fit = 0.2022742;
% TC_fit = 893.0348463;
% 
% % Ranges used
% 
% A_range = 0.00032:0.0000025:0.00045;
% b_range = 0.0994:0.0001:0.1036;
% pc_range = 0.19:0.0005:0.215;
% TC_range = 883:0.5:905;

% C35

% T = [650 670 690 700 720 740 760 780];
% pv = [0.000985 0.001540 0.002086 0.002854 0.004752 0.007401 0.009725 0.012975]; 
% pL = [0.595457 0.576242 0.562586 0.555626 0.535180 0.521200 0.502846 0.479113];
% 
% % Best fit parameters
% 
% A_fit = 3.8721682*10^-4;
% b_fit = 0.101589;
% pc_fit = 0.2019441;
% TC_fit = 897.6686294;
% 
% % Ranges used
% 
% A_range = 0.00031:0.000005:0.000465;
% b_range = 0.099:0.0001:0.104;
% pc_range = 0.186:0.0005:0.217;
% TC_range = 885:0.5:912.5;

% C36

% T = [650 670 690 700 720 740 760 780];
% pv = [0.000647 0.001265 0.002430 0.002620 0.004120 0.005454 0.008240 0.011993];  
% pL = [0.596812 0.581091 0.565395 0.559796 0.541654 0.524009 0.505712 0.487695];
% 
% % Best fit parameters
% 
% A_fit = 3.7888578*10^-4;
% b_fit = 0.1008809;
% pc_fit = 0.2017706;
% TC_fit = 906.8496415;
% 
% % Ranges used
% 
% A_range = 0.00034:0.0000025:0.000415;
% b_range = 0.0996:0.0001:0.1021;
% pc_range = 0.194:0.00025:0.21;
% TC_range = 900:0.25:914.5;

% C37

% T = [650 670 690 700 720 740 760 780];
% pv = [0.000521 0.000927 0.001553 0.002166 0.003279 0.004589 0.007201 0.011356];  
% pL = [0.597346 0.582459  0.564702 0.557580 0.540910 0.524784 0.503997 0.489562];
% 
% % Best fit parameters
% 
% A_fit = 3.8092139*10^-4;
% b_fit = 0.100677;
% pc_fit = 0.2003252;
% TC_fit = 908.6275932;
% 
% % Ranges used
% 
% A_range = 0.00032:0.0000025:0.00044;
% b_range = 0.0986:0.0001:0.1028;
% pc_range = 0.1875:0.0005:0.2125;
% TC_range = 897:0.5:921;

% C46

% T = [710 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 820 845];
% pv = [0.001031 0.001310 0.001697 0.001904 0.002258 0.002126 0.002817 0.002399 0.0032308 0.0031746 0.0041398 0.0037728 0.0046403 0.0040069 0.0063944 0.0066535 0.0102105 0.0148167];  
% pL = [0.568852  0.548048 0.548334 0.546159 0.543636 0.541821 0.529037  0.529188 0.5237609 0.5178099 0.5184448 0.5145962 0.4971586 0.5002300 0.5028423 0.4947494 0.4756602 0.4509375];
% 
% % Best fit parameters
% 
% A_fit = 3.8401042*10^-4;
% b_fit = 0.0979972;
% pc_fit = 0.1923692;
% TC_fit = 950.4701068;
% 
% % Ranges used
% 
% A_range = 0.00029:0.000005:0.00047;
% b_range = 0.0952:0.0001:0.1006;
% pc_range = 0.175:0.0005:0.209;
% TC_range = 936.5:0.5:967;

% C47

% T = [710 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 820 850];
% pv = [0.000677 0.000956 0.001305 0.001449 0.001175 0.002290 0.002512 0.002090 0.0028587 0.0027397 0.0030574 0.0032223 0.0042963 0.0050575 0.0051929 0.0049225 0.0075997 0.0144437];  
% pL = [0.571248 0.549250 0.546881 0.554519 0.542676 0.540919 0.536159 0.531260 0.5216808 0.5211159 0.5152588 0.5091881 0.5109595 0.5010020 0.4978122 0.4966143 0.4797654 0.4408262];
% 
% % Best fit parameters
% 
% A_fit = 4.0479648*10^-4;
% b_fit = 0.0987725;
% pc_fit = 0.1898111;
% TC_fit = 948.1234851;
% 
% % Ranges used
% 
% A_range = 0.00032:0.000005:0.00049;
% b_range = 0.0962:0.0001:0.1012;
% pc_range = 0.173:0.0005:0.206;
% TC_range = 935:0.5:963;

% C48

% T = [730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 825 850 875];
% pv = [0.001082 0.001977 0.001320 0.002051 0.001789 0.002159 0.002123 0.001954 0.0023458  0.0025069 0.0044756 0.0029043 0.0051212 0.0037721  0.0045951 0.0070845 0.0135579 0.0175367];  
% pL = [0.558202 0.558706 0.543807 0.542072 0.543216 0.538703 0.533410 0.530433 0.5231345 0.5209282 0.5171288 0.5105599  0.5086141 0.5048533 0.4935874 0.4674230 0.4505435 0.4217981];  
% 
% % Best fit parameters
% 
% A_fit = 4.1412326*10^-4;
% b_fit = 0.0978467;
% pc_fit = 0.1859051;
% TC_fit = 957.1091515;
% 
% % Ranges used
% 
% A_range = 0.00035:0.000005:0.00048;
% b_range = 0.096:0.0001:0.0996;
% pc_range = 0.173:0.0005:0.198;
% TC_range = 948:0.5:968;

% C49

% T = [715 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 825 850];
% pv = [0.000585 0.001913 0.001777 0.001011 0.001379 0.001467 0.001793 0.001806 0.0025682 0.0023653 0.0024709 0.0034744 0.0044282 0.0037516 0.0033566 0.0068532 0.0070671 0.0118375];  
% pL = [0.573358 0.562748 0.553145 0.551587 0.542701 0.543038 0.539197 0.527376 0.5283437 0.5235963 0.5179991 0.5202390 0.5190576 0.5068002 0.5022426 0.5040868 0.4736001 0.4428524];   
% 
% % Best fit parameters
% 
% A_fit = 4.2022139*10^-4;
% b_fit = 0.0993326;
% pc_fit = 0.1882498;
% TC_fit = 949.7384719;
% 
% % Ranges used
% 
% A_range = 0.00034:0.000005:0.0005;
% b_range = 0.096:0.00025:0.102;
% pc_range = 0.172:0.0005:0.204;
% TC_range = 937:0.5:964;

% C50

% T = [720 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 830 855];
% pv = [0.000739 0.000829 0.000462 0.001331 0.001170 0.000866 0.001910 0.001656 0.0024995 0.0021676 0.0025376 0.0044518  0.0033200 0.0045820 0.0028688 0.0046048 0.0079197 0.0153023];   
% pL = [0.569064 0.556329 0.555610 0.557046 0.552488 0.542526 0.540768  0.538999 0.5357303 0.5246897 0.5239249 0.5256202  0.5174700 0.5203213 0.5025580 0.5068485 0.4715451 0.4573043];    
% 
% % Best fit parameters
% 
% A_fit = 3.722803*10^-4;
% b_fit = 0.0974817;
% pc_fit = 0.193134;
% TC_fit = 965.5013046;
% 
% % Ranges used
% 
% A_range = 0.00029:0.000005:0.00046;
% b_range = 0.094:0.0002:0.0999;
% pc_range = 0.175:0.0005:0.211;
% TC_range = 951:0.5:983;

                            %%%%% End of Alkenes %%%%
                            
                            %%%%% Alcohol Family %%%%%%
                            % TraPPE model

% C24

% T = [580 590 600 610 625 675 700 725 750];
% pv = [0.001871 0.002758 0.003247 0.003363 0.004863 0.013079 0.021154 0.028737 0.041020]; 
% pL = [0.626759 0.619196 0.609262 0.601683 0.588232 0.538290 0.513674 0.479007 0.440888]; 
% % 
% % % Best fit parameters
% % 
% A_fit = 4.2282177*10^-4;
% b_fit = 0.1103707;
% pc_fit = 0.2196296;
% TC_fit = 806.0937264;
% % 
% % % Ranges used
% % 
% A_range = 0.000385:0.0000025:0.00046;
% b_range = 0.1094:0.00005:0.1113;
% pc_range = 0.213:0.00025:0.226;
% TC_range = 802:0.2:810;

% C25

% T = [580 590 600 610 615 650 690 730 750];
% pv = [0.001280 0.001854 0.001985 0.002970 0.003459 0.006401 0.014139 0.026282 0.034937]; 
% pL = [0.631111 0.623071 0.613065 0.607631 0.602276 0.566816 0.527910 0.479116 0.450825];
% 
% % Best fit parameters
% 
% A_fit = 4.2986848*10^-4;
% b_fit = 0.1100042;
% pc_fit = 0.216645;
% TC_fit = 813.5425548;
% 
% % Ranges used
% 
% A_range = 0.0004:0.000002:0.00046;
% b_range = 0.109:0.00005:0.111;
% pc_range = 0.211:0.0002:0.2222;
% TC_range = 810:0.2:817;

% C26

% T = [580 590 600 610 615 655 700 740 760];
% pv = [0.000968 0.001302 0.001759 0.001761 0.002561 0.005784 0.013202 0.026353 0.037279]; 
% pL = [0.633539 0.625622 0.617504 0.598577 0.602939 0.569012 0.524132 0.480082 0.453379];  
% 
% % Best fit parameters
% 
% A_fit = 3.9542784*10^-4;
% b_fit = 0.1079821;
% pc_fit = 0.2182063;
% TC_fit = 828.154204;
% 
% % Ranges used
% 
% A_range = 0.00032:0.000005:0.00047;
% b_range = 0.105:0.0001:0.11;
% pc_range = 0.203:0.0005:0.233;
% TC_range = 819:0.5:838;

% C27

% T = [580 590 600 610 620 660 700 745 765];
% pv = [0.000864 0.001100 0.001448 0.001667 0.002449 0.005139 0.012134 0.025709 0.031991]; 
% pL = [0.637265 0.629412 0.620968 0.608452 0.605167 0.571147 0.533029 0.480972 0.452956];   
% 
% % Best fit parameters
% 
% A_fit = 4.0377924*10^-4;
% b_fit = 0.1078891;
% pc_fit = 0.2160778;
% TC_fit = 835.5574702;
% 
% % Ranges used
% 
% A_range = 0.00035:0.0000025:0.00045;
% b_range = 0.1066:0.00005:0.1092;
% pc_range = 0.206:0.0005:0.226;
% TC_range = 830:0.25:842;

% C28

% T = [580 590 600 610 625 665 710 750 770];
% pv = [0.000544 0.000726 0.001070 0.001353 0.002402 0.005159 0.011405 0.022274 0.031508]; 
% pL = [0.641631 0.631697 0.624222 0.615801 0.605592 0.570015 0.525948 0.477756 0.449177];   
% 
% % Best fit parameters
% 
% A_fit = 4.1878593*10^-4;
% b_fit = 0.1082;
% pc_fit = 0.2131128;
% TC_fit = 838.9229347;
% 
% % Ranges used
% 
% A_range = 0.00038:0.0000025:0.00046;
% b_range = 0.1072:0.00005:0.1092;
% pc_range = 0.206:0.00025:0.22;
% TC_range = 834:0.25:844;

% C33

% T = [650 670 690 700 720 740 760 780];
% pv = [0.001178 0.002392 0.003059 0.004758 0.005753 0.009624 0.014472 0.019449];
% pL = [0.597384 0.583763 0.556875 0.559437 0.527846 0.515582 0.495402 0.470737];
% 
% % Best fit parameters
% 
% A_fit = 4.1734978*10^-4;
% b_fit = 0.1054758;
% pc_fit = 0.2062457;
% TC_fit = 873.6520544;
% 
% % Ranges used
% 
% A_range = 0.00025:0.00001:0.00059;
% b_range = 0.1:0.00025:0.111;
% pc_range = 0.175:0.001:0.235;
% TC_range = 854:1:900;

% C34

% T = [650 670 690 700 720 740 760 780];
% pv = [0.001104 0.002175 0.002644 0.003701 0.006264 0.007691 0.011571 0.017386]; 
% pL = [0.597827 0.582919 0.565554 0.557073 0.545395 0.519109 0.500540 0.479281]; 
% 
% % Best fit parameters
% 
% A_fit = 3.9747516*10^-4;
% b_fit = 0.1040582;
% pc_fit = 0.2065544;
% TC_fit = 885.9877395;
% 
% % Ranges used
% 
% A_range = 0.0003:0.000005:0.00049;
% b_range = 0.101:0.0002:0.107;
% pc_range = 0.189:0.001:0.223;
% TC_range = 873:0.5:902;

% C35

% T = [650 670 690 700 720 740 760 780];
% pv = [0.001078 0.001712 0.002602 0.003151 0.004735 0.007731 0.011377 0.013882]; 
% pL = [0.601742 0.584619 0.568054 0.560481 0.541755 0.525137 0.505677 0.480637];
% 
% % Best fit parameters
% 
% A_fit = 4.0413932*10^-4;
% b_fit = 0.1038497;
% pc_fit = 0.204559;
% TC_fit = 890.2711053;
% 
% % Ranges used
% 
% A_range = 0.00035:0.0000025:0.00046;
% b_range = 0.102:0.0001:0.106;
% pc_range = 0.195:0.00025:0.214;
% TC_range = 883:0.25:899;

% C36

% T = [650 670 690 700 720 740 760 780];
% pv = [0.000832 0.001416 0.002314 0.002969 0.004942 0.007526 0.009913 0.014947];  
% pL = [0.604059 0.591235 0.570929 0.562616 0.545386 0.527977 0.508277 0.488136];
% 
% % Best fit parameters
% 
% A_fit = 3.9640956*10^-4;
% b_fit = 0.1039633;
% pc_fit = 0.2064128;
% TC_fit = 893.6252714;
% 
% % Ranges used
% 
% A_range = 0.00034:0.0000025:0.00045;
% b_range = 0.102:0.0002:0.106;
% pc_range = 0.196:0.00025:0.217;
% TC_range = 885:0.5:903;

% C37

% T = [650 670 690 700 720 740 760 780];
% pv = [0.000663 0.001298 0.002418 0.002517 0.004422 0.005246 0.007557 0.013907];  
% pL = [0.605641 0.588546 0.572807 0.568120 0.549641 0.526462 0.504405 0.494860];
% 
% % Best fit parameters
% 
% A_fit = 3.9896774*10^-4;
% b_fit = 0.1033698;
% pc_fit = 0.2040743;
% TC_fit = 899.1223475;
% 
% % Ranges used
% 
% A_range = 0.00027:0.000005:0.00053;
% b_range = 0.098:0.0002:0.108;
% pc_range = 0.175:0.001:0.23;
% TC_range = 879:1:926;

                            %%%%% End of Alcohols %%%%%
  
                            %%%% Muller's Simulations %%%%%
% n_c = 10;                            
% MW_10 = 12.0107*n_c+1.00794*(2*n_c+2);
% n_c = 20;                            
% MW_20 = 12.0107*n_c+1.00794*(2*n_c+2);
% n_c = 60;                            
% MW_60 = 12.0107*n_c+1.00794*(2*n_c+2);
% n_c = 100;                            
% MW_100 = 12.0107*n_c+1.00794*(2*n_c+2);
% 
% beta = 0.325;

% SKS Results

% C10
                          
% T = [350 375 400 425 450 475 500 525 550];
% pv = [0.002 0.008 0.013 0.023 0.038 0.061 0.096 0.169 0.259];
% pL = [4.766 4.628 4.503 4.317 4.147 3.969 3.758 3.524 3.252]; 
% 
% pv = pv*MW_10/1000;
% pL = pL*MW_10/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.5064788*10^-4;
% b_fit = 0.1113842;
% pc_fit = 0.2231025;
% TC_fit = 613.2596194;
% 
% % Ranges used
% 
% A_range = 0.000388:0.000004:0.000512; 
% b_range = 0.1094:0.0002:0.1134;
% pc_range = 0.212:0.0005:0.2345;
% TC_range = 607:0.25:620.5;

% C20
                          
% T = [350 400 450 500 550 600 625 650 675 700];
% pv = [0.002 0.002 0.003 0.005  0.009 0.019 0.029  0.045 0.063 0.087]; 
% pL = [2.6717 2.5438 2.4154 2.2703 2.1193 1.9414 1.8468 1.726 1.6059 1.4809]; 
% 
% pv = pv*MW_20/1000;
% pL = pL*MW_20/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.4412439*10^-4;
% b_fit = 0.1064343;
% pc_fit = 0.2049017;
% TC_fit = 752.9960676;
% 
% % Ranges used
% 
% A_range = 0.00038:0.000004:0.000508; 
% b_range = 0.1042:0.0001:0.1086;
% pc_range = 0.1895:0.0005:0.22;
% TC_range = 744.5:0.5:763;

% C60
                          
% T = [500 550 600 650 700 750 800 850];
% pv = [0.00001 0.0001 0.0001 0.0001 0.0002 0.0008 0.0023 0.0061]; 
% pL = [0.8486 0.8072 0.7639 0.7203 0.6717 0.6193 0.5643 0.5053]; 
% 
% pv = pv*MW_60/1000;
% pL = pL*MW_60/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.0615488*10^-4;
% b_fit = 0.097829;
% pc_fit = 0.1858866;
% TC_fit = 932.6557591;
% 
% % Ranges used
% 
% A_range = 0.000288:0.000008:0.000528; 
% b_range = 0.0932:0.0002:0.1022;
% pc_range = 0.148:0.002:0.222;
% TC_range = 908:2:966;

% C100
                          
% T = [600 650 700 750 803 850 900]; 
% pv = [0.0001 0.0001 0.0001 0.0002 0.0003 0.0007 0.0022]; 
% pL = [0.4723 0.447 0.4208 0.3921 0.3589 0.3275 0.2898]; 
% 
% pv = pv*MW_100/1000;
% pL = pL*MW_100/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.2075436*10^-4;
% b_fit = 0.0947642;
% pc_fit = 0.1746967;
% TC_fit = 981.9621325;
% 
% % Ranges used
% 
% A_range = 0.00028:0.00001:0.00056; 
% b_range = 0.0896:0.0004:0.0996;
% pc_range = 0.136:0.001:0.21;
% TC_range = 957.5:1.5:1017.5;

% NERD Results

% C10
                          
% T = [350 375 400 425 450 475 500 525 550];
% pv = [0.01 0.013 0.017 0.027 0.044 0.067 0.103 0.17 0.284];
% pL = [4.756 4.612 4.455 4.3 4.132 3.937 3.742 3.505 3.135]; 
% 
% pv = pv*MW_10/1000;
% pL = pL*MW_10/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.6667841*10^-4;
% b_fit = 0.1121028;
% pc_fit = 0.2219972;
% TC_fit = 606.2222515;
% 
% % Ranges used
% 
% A_range = 0.00034:0.000008:0.000588; 
% b_range = 0.1086:0.0002:0.1154;
% pc_range = 0.2:0.001:0.244;
% TC_range = 595.5:0.5:619.5;

% C20
                          
% T = [350 400 450 500 550 600 625 650 675];
% pv = [0.0011 0.0012 0.0013 0.0024 0.0065 0.0179 0.0284 0.0418 0.0611]; 
% pL = [2.6656 2.5384 2.4053 2.2675 2.1119 1.9544 1.86 1.7459 1.6305];  
% 
% pv = pv*MW_20/1000;
% pL = pL*MW_20/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.1965509*10^-4;
% b_fit = 0.1061712;
% pc_fit = 0.2105112;
% TC_fit = 755.1564581;
% 
% % Ranges used
% 
% A_range = 0.000368:0.000004:0.000472; 
% b_range = 0.1041:0.0001:0.1081;
% pc_range = 0.197:0.0005:0.224;
% TC_range = 745.5:0.5:766;

% C60
                          
% T = [500 550 600 650 700 750 800 850 875];
% pv = [0.0001 0.0001 0.0001 0.0001 0.0002 0.0007 0.003 0.0085 0.0192]; 
% pL = [0.8417 0.8024 0.76 0.7179 0.6648 0.6203 0.5613 0.4964 0.441];  
% 
% pv = pv*MW_60/1000;
% pL = pL*MW_60/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.2134241*10^-4;
% b_fit = 0.0976977;
% pc_fit = 0.1807567;
% TC_fit = 928.7008414;
% 
% % Ranges used
% 
% A_range = 0.000336:0.000004:0.000512; 
% b_range = 0.0946:0.0002:0.1006;
% pc_range = 0.157:0.001:0.204;
% TC_range = 915:1:946;

% C100
                          
% T = [600 650 700 750 803 850 900 925];  
% pv = [0.0001 0.0001 0.0001 0.0002 0.0003 0.0007 0.0022 0.0044]; 
% pL = [0.4697 0.445 0.42 0.3917 0.3606 0.3327 0.2947 0.2709]; 
% 
% pv = pv*MW_100/1000;
% pL = pL*MW_100/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.1578179*10^-4;
% b_fit = 0.0931347;
% pc_fit = 0.1702054;
% TC_fit = 994.9425215;
% 
% % Ranges used
% 
% A_range = 0.00032:0.000005:0.000515; 
% b_range = 0.0896:0.0002:0.0966;
% pc_range = 0.144:0.001:0.195;
% TC_range = 978:1:1017;

% TraPPE Results

% C10
                          
% T = [350 375 400 425 450 475 500 525 550 575];
% pv = [0.016 0.019 0.023 0.033 0.048 0.088 0.138 0.217 0.341 0.479];
% pL = [4.85 4.71 4.554 4.406 4.231 4.056 3.845 3.623 3.355 2.997]; 
% 
% pv = pv*MW_10/1000;
% pL = pL*MW_10/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.3042439*10^-4;
% b_fit = 0.1137395;
% pc_fit = 0.2355154;
% TC_fit = 609.9670651;
% 
% % Ranges used
% 
% A_range = 0.000368:0.000004:0.000492; 
% b_range = 0.1122:0.0001:0.1152;
% pc_range = 0.225:0.0005:0.246;
% TC_range = 605.5:0.25:614.5;

% C20
                          
% T = [350 400 450 500 550 600 625 650 675 700];
% pv = [0.0032 0.0039 0.0043 0.0069 0.011 0.0198 0.0296 0.0454 0.0651 0.0924]; 
% pL = [2.6774 2.5694 2.4401 2.303 2.1567 1.9955 1.9145 1.807 1.7055 1.5712];  
% 
% pv = pv*MW_20/1000;
% pL = pL*MW_20/1000;
% 
% % Best fit parameters
% 
% A_fit = 4.0834574*10^-4;
% b_fit = 0.1058951;
% pc_fit = 0.2136513;
% TC_fit = 767.9130991;
% 
% % Ranges used
% 
% A_range = 0.000364:0.000004:0.000452; 
% b_range = 0.1042:0.0001:0.1075;
% pc_range = 0.2025:0.0005:0.2245;
% TC_range = 760.5:0.25:776;

% C60
                          
% T = [500 550 600 650 700 750 800 850 875 900];
% pv = [0.0001 0.0001 0.0001 0.0002 0.0002 0.0008 0.0027 0.0088 0.012 0.018]; 
% pL = [0.8495 0.811 0.7742 0.7332 0.6903 0.6437 0.5954 0.5431 0.5067 0.4671];  
% 
% pv = pv*MW_60/1000;
% pL = pL*MW_60/1000;
% 
% % Best fit parameters
% 
% A_fit = 3.7907247*10^-4;
% b_fit = 0.0957958;
% pc_fit = 0.1863986;
% TC_fit = 966.5437885;
% 
% % Ranges used
% 
% A_range = 0.00032:0.000004:0.00044; 
% b_range = 0.0934:0.0002:0.0982;
% pc_range = 0.1685:0.0005:0.204;
% TC_range = 954:0.5:981;

% C100
                          
% T = [600 650 700 750 803 850 900 925 950 975];  
% pv = [0.0001 0.0001 0.0001 0.0002 0.0003 0.0007 0.0023 0.0042 0.0052 0.0082]; 
% pL = [0.4746 0.4532 0.4286 0.4052 0.3778  0.3519 0.3217 0.3039 0.2849 0.2642]; 
% 
% pv = pv*MW_100/1000;
% pL = pL*MW_100/1000;
% 
% % Best fit parameters
% 
% A_fit = 3.764856*10^-4;
% b_fit = 0.0907643;
% pc_fit = 0.1724739;
% TC_fit = 1040.0719;
% 
% % Ranges used
% 
% A_range = 0.00031:0.000005:0.00044; 
% b_range = 0.0882:0.0002:0.0932;
% pc_range = 0.155:0.0005:0.1895;
% TC_range = 1027.5:0.5:1055.5;


% Best fit parameters for C33-37

% C33
% A_fit = 4.01742*10^-4;
% b_fit = 0.10225;
% pc_fit = 0.20075;
% TC_fit = 882.93986;

% C34

% A_fit = 4.03063*10^-4;
% b_fit = 0.10227;
% pc_fit = 0.20043;
% TC_fit = 887.27725;

% C35

% A_fit = 3.5922207*10^-4;
% b_fit = 0.0985483;
% pc_fit = 0.1999684;
% TC_fit = 908.3013977;

% C36

% A_fit = 3.8075253*10^-4;
% b_fit = 0.1003832;
% pc_fit = 0.199841;
% TC_fit = 905.5600979;

% C37

% A_fit = 3.8499003*10^-4;
% b_fit = 0.1003855;
% pc_fit = 0.1987953;
% TC_fit = 909.0754594;

% C46

% A_fit = 4.1285525*10^-4;
% b_fit = 0.0999612;
% pc_fit = 0.1918263;
% TC_fit = 939.4204673;

% C47

% A_fit = 3.9753534*10^-4;
% b_fit = 0.0984275;
% pc_fit = 0.1906801;
% TC_fit = 948.4887806;

% C48

% A_fit = 3.974647*10^-4;
% b_fit = 0.0985471;
% pc_fit = 0.1908685;
% TC_fit = 949.5568175;

% C49

% A_fit = 3.9459647*10^-4;
% b_fit = 0.0976654;
% pc_fit = 0.1889417;
% TC_fit = 956.5220833;

% C50

% A_fit = 3.7910815*10^-4;
% b_fit = 0.0966692;
% pc_fit = 0.1895036;
% TC_fit = 965.9621628;

% NERD best fits

% C24

% A_fit = 4.0260516*10^-4;
% b_fit = 0.1059854;
% pc_fit = 0.2110485;
% TC_fit = 809.7729414;

% C25
 
% A_fit = 4.0739026*10^-4;
% b_fit = 0.1060784;
% pc_fit = 0.210107;
% TC_fit = 815.1642174;

% C26

% A_fit = 3.6546438*10^-4;
% b_fit = 0.103009;
% pc_fit = 0.2103295;
% TC_fit = 831.6979337;

% C27

% A_fit = 3.6961889*10^-4;
% b_fit = 0.1028549;
% pc_fit = 0.2088123;
% TC_fit = 838.2854731;

% C28

% A_fit = 3.8774466*10^-4;
% b_fit = 0.1033183;
% pc_fit = 0.2063438;
% TC_fit = 843.5102329;

% C33

% A_fit = 4.2147853*10^-4;
% b_fit = 0.1028812;
% pc_fit = 0.1983849;
% TC_fit = 869.4285578;

% C34

% A_fit = 4.1726179*10^-4;
% b_fit = 0.1024687;
% pc_fit = 0.19816;
% TC_fit = 876.9216223;

% C35

% A_fit = 3.9916082*10^-4;
% b_fit = 0.1018949;
% pc_fit = 0.1998156;
% TC_fit = 883.2964736;

% C36

% A_fit = 3.9897256*10^-4;
% b_fit = 0.1012107;
% pc_fit = 0.1980929;
% TC_fit = 890.2317023;

% C37

% A_fit = 3.9079436*10^-4;
% b_fit = 0.1008164;
% pc_fit = 0.1984803;
% TC_fit = 896.2130141;


% Best fit C46-50

% C46

% A_fit = 3.9714658*10^-4;
% b_fit = 0.0978159;
% pc_fit = 0.1894215;
% TC_fit = 938.8720153;

% C47

% A_fit = 4.2013432*10^-4;
% b_fit = 0.0993863;
% pc_fit = 0.1889086;
% TC_fit = 932.9106273;

% C48

% A_fit = 3.8973532*10^-4;
% b_fit = 0.0966332;
% pc_fit = 0.1876118;
% TC_fit = 948.2327662;

% C49

% A_fit = 3.8744021*10^-4;
% b_fit = 0.0975184;
% pc_fit = 0.1900679;
% TC_fit = 947.4713087;

% C50

% A_fit = 4.2024238*10^-4;
% b_fit = 0.0978166;
% pc_fit = 0.1842185;
% TC_fit = 947.6199178;


% NERD literature

% C2

% T = [175.4 213.8 252.2 271 280.8];
% pv = [0.005 0.009 0.023 0.041 0.049];
% pL = [0.543 0.496 0.438 0.405 0.381];

% C3

% T = [250 281 312 340 344];
% pv = [0.005 0.012 0.027 0.055 0.058];
% pL = [0.546 0.516 0.474 0.428 0.418];

% C4

% T = [295 327 360 380 392];
% pv = [0.005 0.014 0.024 0.040 0.051];
% pL = [0.566 0.533 0.487 0.460 0.438];

% C6

% T = [370 400 430 450 470];
% pv = [0.0065 0.013 0.023 0.037 0.051];
% pL = [0.577 0.546 0.506 0.480 0.439];

% C8 Doesn't work because only have four data points.

% T = [400 440 490 540];
% pv = [0.003 0.009 0.026 0.063];
% pL = [0.61 0.567 0.508 0.424];

% C10

% T = [450 480 520 565 580];
% pv = [0.005 0.011 0.023 0.050 0.060];
% pL = [0.602 0.570 0.525 0.469 0.439];

% C12

% T = [525 550 575 600 625];
% pv = [0.009 0.013 0.023 0.034 0.053];
% pL = [0.558 0.532 0.5 0.461 0.415];

% C16 remember this isn't the best data b/c I had to steal it from graph

% T = [520 600 650 680 690];
% pv = [0.001 0.012 0.038 0.05 0.055];
% pL = [0.61 0.53 0.45 0.42 0.41];

% C48

% T = [780 810 840 860 870];
% pv = [0.004 0.007 0.012 0.015 0.018];
% pL = [0.538 0.490 0.442 0.404 0.382];

% SKS 48

% T = [800 825 850 875 890 900];
% pv = [0.005 0.011 0.020 0.036 0.055 0.06];
% pL = [0.465 0.453 0.419 0.393 0.35 0.32];

% sv = [0.003 0.005 0.010 0.010 0.020 0.03];
% sL = [0.010 0.010 0.010 0.015 0.03 0.03];
% 
% sz = (sv.^2 + sL.^2).^(1/2);
% sy = sz/2;

% C2

% A_fit = 5.490906*10^-4;
% b_fit = 0.1123837;
% pc_fit = 0.1995258;
% TC_fit = 310.5379519;

% C3

% A_fit = 3.9267596*10^-4;
% b_fit = 0.11505;
% pc_fit = 0.2247002;
% TC_fit = 379.76146;

% C4

% A_fit = 4.4232568*10^-4;
% b_fit = 0.115308;
% pc_fit = 0.223915;
% TC_fit = 436.4179388;

% C6

% A_fit = 4.5330597*10^-4;
% b_fit = 0.1171386;
% pc_fit = 0.2275365;
% TC_fit = 512.920314;

% C8

% A_fit = 4.4314063*10^-4;
% b_fit = 0.1163945;
% pc_fit = 0.2288834;
% TC_fit = 574.4125461;

% C10

% A_fit = 3.9983775*10^-4;
% b_fit = 0.1146628;
% pc_fit = 0.2342275;
% TC_fit = 621.969428;

% C12

% A_fit = 4.9089056*10^-4;
% b_fit = 0.1141985;
% pc_fit = 0.2171601;
% TC_fit = 661.8522929;

% C16

% A_fit = 4.389749*10^-4;
% b_fit = 0.1092501;
% pc_fit = 0.2146496;
% TC_fit = 725.8481916;

% C48

% A_fit = 7.66822*10^-4;
% b_fit = 0.11161;
% pc_fit = 0.17214;
% TC_fit = 909.41618;

% SKS C48

% A_fit = 4.2099964*10^-4;
% b_fit = 0.1020903;
% pc_fit = 0.1892379;
% TC_fit = 919.2410694;

% With uncertainties

% A_fit = 3.3593792*10^-4;
% b_fit = 0.0995759;
% pc_fit = 0.1950357;
% TC_fit = 925.2405065;

% n1 = length(T1);
% n2 = length(T2);
% n3 = length(T3);
% n4 = length(T4);
% n5 = length(T5);

n = length(T);

beta = 0.32;

p = 4;

% y1 = (pv1 + pL1)/2;
% z1 = pL1 - pv1;
% 
% y2 = (pv2 + pL2)/2;
% z2 = pL2 - pv2;
% 
% y3 = (pv3 + pL3)/2;
% z3 = pL3 - pv3;
% 
% y4 = (pv4 + pL4)/2;
% z4 = pL4 - pv4;
% 
% y5 = (pv5 + pL5)/2;
% z5 = pL5 - pv5;

y = (pv + pL)/2;
z = pL - pv;

% SE_fit1 = (y1 - (pc1 + A1*(TC1-T1))).^2 + (z1 - (b1*(TC1-T1).^beta)).^2;
% SE_fit2 = (y2 - (pc2 + A2*(TC2-T2))).^2 + (z2 - (b2*(TC2-T2).^beta)).^2;
% SE_fit3 = (y3 - (pc3 + A3*(TC3-T3))).^2 + (z3 - (b3*(TC3-T3).^beta)).^2;
% SE_fit4 = (y4 - (pc4 + A4*(TC4-T4))).^2 + (z4 - (b4*(TC4-T4).^beta)).^2;
% SE_fit5 = (y5 - (pc5 + A5*(TC5-T5))).^2 + (z5 - (b5*(TC5-T5).^beta)).^2;

% SE_fit = (y - (pc_fit + A_fit*(TC_fit-T))).^2 + (z - (b_fit*(TC_fit-T).^beta)).^2;
SE_fit = ((y - (pc_fit + A_fit*(TC_fit-T)))./sy).^2 + ((z - (b_fit*(TC_fit-T).^beta))./sz).^2; % This includes uncertainties

% Include the estimate of the uncertainties

% SE_fit = SE_fit./((sigma_spline(T).^2)');

% SSE_fit1 = sum(SE_fit1);
% SSE_fit2 = sum(SE_fit2);
% SSE_fit3 = sum(SE_fit3);
% SSE_fit4 = sum(SE_fit4);
% SSE_fit5 = sum(SE_fit5);

SSE_fit = sum(SE_fit);

% sigma1 = SSE_fit1/(n1-p);
% sigma2 = SSE_fit2/(n2-p);
% sigma3 = SSE_fit3/(n3-p);
% sigma4 = SSE_fit4/(n4-p);
% sigma5 = SSE_fit5/(n5-p);

sigma = SSE_fit/(n-p);

% RHS1 = sigma1 * (n1 + p * (finv(0.95^p,p,n1-p)-1));
% RHS2 = sigma2 * (n2 + p * (finv(0.95^p,p,n2-p)-1));
% RHS3 = sigma3 * (n3 + p * (finv(0.95^p,p,n3-p)-1));
% RHS4 = sigma4 * (n4 + p * (finv(0.95^p,p,n4-p)-1));
% RHS5 = sigma5 * (n5 + p * (finv(0.95^p,p,n5-p)-1));

RHS = sigma * (n + p * (finv(0.95^p,p,n-p)-1));

% These are supposed to be slightly larger than the extrema found below, just so that you can verify this range.
% Be careful, for the b_range I realized that the displayed number is
% rounded off, so make sure it really found the min or max

% Ranges used for 24
% A_range = 0.000338:0.000002:0.000468; 
% b_range = 0.10432:0.00004:0.10774;
% pc_range = 0.2:0.0002:0.225;
% TC_range = 808:0.2:825;

% Ranges used for 25
% A_range = 0.000346:0.000002:0.000454; 
% b_range = 0.10392:0.00004:0.10694;
% pc_range = 0.197:0.0003:0.221;
% TC_range = 820:0.2:835;

% Ranges used for 26 (these data are worthless) Essentially you must have
% more data points to lock down pc-TC at all

% A_range = -0.0002:0.00002:0.001; 
% b_range = 0.08:0.0005:0.12;
% pc_range = 0.08:0.004:0.31;
% TC_range = 780:2:960;

% Ranges used for 27

%  A_range = 0.0003:0.000004:0.00052; 
%  b_range = 0.101:0.0001:0.108;
%  pc_range = 0.18:0.0005:0.23;
%  TC_range = 825:0.5:860;
 
% Ranges used for 28

% A_range = 0.00031:0.000004:0.0005; 
% b_range = 0.101:0.0001:0.11;
% pc_range = 0.184:0.0005:0.226;
% TC_range = 835:0.4:865;

% Ranges used for 33

% A_range = 0.000344:0.000001:0.000454;
% b_range = 0.1:0.00005:0.1045;
% pc_range = 0.19:0.00025:0.212;
% TC_range = 874:0.2:892;

% Ranges used for 34

% A_range = 0.00034:0.0000015:0.00046;
% b_range = 0.1:0.00005:0.1045;
% pc_range = 0.189:0.00025:0.212;
% TC_range = 878:0.2:897;

% Ranges used for 35

% A_range = 0.00015:0.000005:0.00056;
% b_range = 0.09:0.00025:0.105;
% pc_range = 0.15:0.001:0.245;
% TC_range = 876:1:964;

% Ranges used for 36

% A_range = 0.000342:0.000001:0.000419;
% b_range = 0.099:0.00005:0.102;
% pc_range = 0.191:0.00025:0.209;
% TC_range = 898.4:0.2:914;

% Ranges used for 37

% A_range = 0.000347:0.000001:0.000417;
% b_range = 0.0992:0.00005:0.102;
% pc_range = 0.192:0.0002:0.207;
% TC_range = 902:0.2:916;

% 46

% A_range = 0.000297:0.000005:0.000527;
% b_range = 0.0962:0.0002:0.1034;
% pc_range = 0.17:0.001:0.212;
% TC_range = 922:1:961;

% 47

% A_range = 0.000287:0.000005:0.000507;
% b_range = 0.0946:0.0002:0.1020;
% pc_range = 0.168:0.001:0.212;
% TC_range = 925:1:975;

% 48

% A_range = 0.000247:0.00001:0.000547;
% b_range = 0.0932:0.0002:0.1034;
% pc_range = 0.159:0.001:0.219;
% TC_range = 924:1:984;

% 49

% A_range = 0.000167:0.00001:0.000617;
% b_range = 0.089:0.0002:0.105;
% pc_range = 0.136:0.002:0.232;
% TC_range = 915:2:1020;

% 50

% A_range = 0.000267:0.000005:0.000497;
% b_range = 0.0922:0.0002:0.1002;
% pc_range = 0.162:0.001:0.214;
% TC_range = 943:1:998;

% Ranges used for NERD simulations

% C24

% A_range = 0.00035:0.000002:0.000454; 
% b_range = 0.1045:0.00006:0.1074;
% pc_range = 0.202:0.0004:0.220;
% TC_range = 804:0.5:816;

% C25

% A_range = 0.000374:0.000002:0.000442; 
% b_range = 0.105:0.00004:0.107;
% pc_range = 0.2036:0.0002:0.2164;
% TC_range = 811:0.25:819;

% C26

% A_range = 0.0001:0.00001:0.00064; 
% b_range = 0.0942:0.0004:0.1104;
% pc_range = 0.158:0.002:0.26;
% TC_range = 804:1:876;

% C27

% A_range = 0.00015:0.00001:0.00059; 
% b_range = 0.095:0.0002:0.109;
% pc_range = 0.166:0.001:0.249;
% TC_range = 815:1:874;

% C28

% A_range = 0.00029:0.000005:0.00048; 
% b_range = 0.1006:0.0001:0.106;
% pc_range = 0.188:0.001:0.224;
% TC_range = 832:0.5:857;

% Ranges used for 33

% A_range = 0.000328:0.000004:0.00052;
% b_range = 0.1:0.0002:0.1056;
% pc_range = 0.182:0.0005:0.214;
% TC_range = 858:0.5:883;

% Ranges used for 34

% A_range = 0.000385:0.0000025:0.00045;
% b_range = 0.1016:0.00005:0.1034;
% pc_range = 0.193:0.00025:0.2035;
% TC_range = 873:0.2:881;

% Ranges used for 35

% A_range = 0.000325:0.000005:0.000475;
% b_range = 0.0994:0.0002:0.1042;
% pc_range = 0.1855:0.0005:0.214;
% TC_range = 872:0.5:896;

% Ranges used for 36

% A_range = 0.000335:0.0000025:0.00046;
% b_range = 0.0992:0.0001:0.1032;
% pc_range = 0.186:0.0005:0.210;
% TC_range = 880:0.5:901;

% Ranges used for 37

% A_range = 0.00032:0.000005:0.00046;
% b_range = 0.0984:0.0001:0.103;
% pc_range = 0.184:0.0005:0.212;
% TC_range = 885:0.5:909;

% Ranges used for 46

% A_range = 0.000307:0.000005:0.000487;
% b_range = 0.095:0.0001:0.1002;
% pc_range = 0.173:0.0006:0.210;
% TC_range = 927:0.5:953;

% Ranges used for 47

% A_range = 0.000332:0.000005:0.000512;
% b_range = 0.0974:0.0001:0.1013;
% pc_range = 0.176:0.0005:0.201;
% TC_range = 924:0.5:943;

% Ranges used for 48

% A_range = 0.000312:0.000005:0.000462;
% b_range = 0.0947:0.0001:0.0985;
% pc_range = 0.1745:0.0005:0.2005;
% TC_range = 939:0.5:959;

% Ranges used for 49

% A_range = 0.000322:0.000005:0.000452;
% b_range = 0.0955:0.0001:0.0993;
% pc_range = 0.1775:0.0005:0.2015;
% TC_range = 938:0.5:959;

% Ranges used for 50

% A_range = 0.000352:0.0000025:0.000487;
% b_range = 0.0959:0.0001:0.0997;
% pc_range = 0.171:0.0005:0.197;
% TC_range = 938:0.5:959;

% Ranges used for NERD literature

% C2

% A_range = 0.000155:0.00001:0.000945;
% b_range = 0.104:0.00025:0.120;
% pc_range = 0.164:0.001:0.232;
% TC_range = 300.2:0.4:327;

% C3

% A_range = -0.00036:0.00002:0.00120;
% b_range = 0.098:0.0005:0.129;
% pc_range = 0.152:0.002:0.288;
% TC_range = 362:0.5:421;

% C4

% A_range = 0:0.00001:0.00084;
% b_range = 0.105:0.00025:0.124;
% pc_range = 0.184:0.001:0.264;
% TC_range = 422:0.5:459;

% C6

% A_range = -0.00012:0.00002:0.00110;
% b_range = 0.1035:0.0005:0.1285;
% pc_range = 0.166:0.0015:0.285;
% TC_range = 490:1:550;

% C8 Didn't work because of F statistic

% A_range = 0.00044314:0.00000000002:0.000443141;
% b_range = 0.116394:0.00000005:0.116395;
% pc_range = 0.22888:0.0000001:0.228885;
% TC_range = 574.412:0.00002:574.413;

% C10

% A_range = 0.000096:0.00001:0.000716;
% b_range = 0.107:0.00025:0.1215;
% pc_range = 0.1975:0.00075:0.2695;
% TC_range = 609:0.5:641;

% C12

% A_range = 0.000086:0.00001:0.000906;
% b_range = 0.1055:0.00025:0.1215;
% pc_range = 0.175:0.00125:0.255;
% TC_range = 649:0.5:682;

% C16 I guess because the data was so poor this range is uncontrollable. I
% know that the SSE was an order of magnitude greater than usual, but this
% still surprised me. TC is the problem, because the ranges for A and b are
% typical of poor data, but the range for TC is so large that pc is able to
% cross the axis and become negative.

% A_range = -0.002:0.0005:0.04;
% b_range = 0:0.004:0.13;
% pc_range = -10:0.2:1;
% TC_range = 690:100:10000;

% C48

% A_range = -0.00004:0.00002:0.0017;
% b_range = 0.091:0.0005:0.129;
% pc_range = 0.07:0.002:0.242;
% TC_range = 888:1:970;

% SKS C48

% A_range = -0.0004:0.00004:0.0017;
% b_range = 0.061:0.001:0.129;
% pc_range = 0.126:0.002:0.25;
% TC_range = 906:1:952;

% With uncertainties

% A_range = -0.00008:0.00001:0.00075;
% b_range = 0.0805:0.0005:0.1115;
% pc_range = 0.139:0.001:0.236;
% TC_range = 903:1:1006;

confidence_region = ones(length(pc_range),length(TC_range));

Ext = zeros(1,(length(A_range)*length(b_range)*length(pc_range)*length(TC_range)));
A_ext = Ext;
b_ext = Ext;
pc_ext = Ext;
TC_ext = Ext;

s=1;

for g=1:length(A_range)
    
    for h=1:length(b_range)

        for i=1:length(pc_range)
    
            for j=1:length(TC_range)
      
%        SE = (y - (pc_range(i) + A_range(g)*(TC_range(j)-T))).^2 + (z - (b_range(h)*(TC_range(j)-T).^beta)).^2;
       SE = ((y - (pc_range(i) + A_range(g)*(TC_range(j)-T)))./sy).^2 + ((z - (b_range(h)*(TC_range(j)-T).^beta))./sz).^2;
 
%        SE = SE./((sigma_spline(T).^2)');

       SSE = sum(SE);
       
       if SSE < RHS 
                     
           %We start confidence_region at one value and change it only if
           %the SSE is less than the RHS.  This is because we want to plot
           %any pc-TC that is acceptable. Otherwise we would be
           %overwritting accepted points whenever one is rejected.
           
           confidence_region(i,j) = 0; % We only want to plot pc vs TC
           
           A_ext(s) = A_range(g);
           b_ext(s) = b_range(h);
           pc_ext(s) = pc_range(i);
           TC_ext(s) = TC_range(j);
           
           s=s+1;
           
           if SSE < SSE_fit % This is to make sure that we actually have the global minimum. If not, rerun the analysis with the new optimum (after plugging in as a new Mathcad guess)
               
              new_best_fit = [A_range(g) b_range(h) pc_range(i) TC_range(j)]; 
              SSE_fit = SSE;
              
           end
           
       end
       
            end
            
       end
       
   end
    
end

% This eliminates the superfluous zero elements
A_ext = A_ext(:,1:(s-1));
b_ext = b_ext(:,1:(s-1));
pc_ext = pc_ext(:,1:(s-1));
TC_ext = TC_ext(:,1:(s-1));

% AbpcTC = [A_ext; b_ext; pc_ext; TC_ext]';

A_low = min(A_ext);
A_high = max(A_ext);
b_low = min(b_ext);
b_high = max(b_ext);
pc_low = min(pc_ext);
pc_high = max(pc_ext);
TC_low = min(TC_ext);
TC_high = max(TC_ext);

subplot(3,2,1)
plot(A_ext,b_ext)
subplot(3,2,2)
plot(pc_ext,b_ext)
subplot(3,2,3)
plot(A_ext,TC_ext)
subplot(3,2,4)
plot(pc_ext,TC_ext)
subplot(3,2,5)
plot(A_ext,pc_ext)
subplot(3,2,6)
plot(b_ext,TC_ext)

(pc_high-pc_low)/pc_fit
TC_high-TC_low

% hold
% 
% contour(TC_range,pc_range,confidence_region)
% 
% hold

% % To plot just the pc and TC region

pc_space = 0.00003;

pc_scan=min(pc_range):pc_space:max(pc_range);

k=1;

for h=1:length(pc_scan)
    
j=1;

    for i=1:length(pc_ext)
    
	if pc_ext(i) == pc_scan(h)
   
    TC_scan(j) = TC_ext(i);

    j=j+1;

        end

    end

% I did it this way because, for some reason, not every pc in the range of 
% pc_scan actually has an accepted point.  Somehow I missed the A,B and TC 
% combinations that were required.

    if j>1
       
    TC_upper(k) = max(TC_scan);
    TC_lower(k) = min(TC_scan);
    pc_plot(k) = pc_scan(h);
    
    k=k+1;
    
    end
    
TC_scan=TC_fit;

end

figure
hold

plot(pc_ext,TC_ext)
plot(pc_plot,TC_upper);
plot(pc_plot,TC_lower);

hold