function experiment
%determination of reaction rate for crystal growth from aqeous solutions
%save this file as mfile to run in matlab 
% inputs are dc, rpm, dp, temp, rg
%normalized inputs are given by Dc/20,rpm/400,dp,rg*1000
input = [0.900045311	0.850043781	0.800087421	0.750019169	0.700028638	0.65003094	0.600051464	0.550052882	0.500032868	0.450031839	0.400017616	0.900078827	0.850052872	0.800097926	0.750014569	0.700040523	0.65000618	0.600035508	0.550030326	0.500053633	0.450021568	0.950058968	0.900036807	0.850016683	0.800046281	0.750041401	0.700027348	0.650073741	0.600015053	0.550058262	0.500005224	0.450003183	0.40004627	0.900041798	0.850029311	0.800061212	0.750004561	0.700025224	0.650072004	0.600005722	0.550076663	0.500031258	0.450037471	0.400004301	0.900085361	0.850054436	0.800075273	0.750024407	0.70011423	0.650111898	0.600084301	0.550021222	0.500065785	0.450017353	0.400022541	0.95009469	0.900075766	0.850015329	0.800048421	0.750080179	0.700031782	0.650038196	0.600010359	0.550060478	0.500009399	0.450042121	0.900033144	0.850029334	0.800089605	0.750028696	0.700013352	0.650000447	0.600049071	0.550088123	0.500066065	0.450057211	0.400056284	0.90003767	0.850075555	0.800044227	0.750056071	0.700047086	0.650039756	0.600045823	0.550064365	0.500043599	0.450001693	0.400007761	0.947136219	0.900039341	0.850039942	0.800043483	0.750027387	0.700008659	0.650035049	0.600008549	0.55001934	0.500007395	0.450018292	0.400011997	0.350001561	0.92398626	0.900152198	0.850015434	0.800035162	0.750011096	0.700048794	0.650119072	0.600041123	0.550043248	0.500022476	0.45000688	0.400018521	0.373641323; 
0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75	1	1	1	1	1	1	1	1	1	1	1	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625; 
0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.07088	0.07088	0.07088	0.07088	0.07088	0.07088	0.07088	0.07088	0.07088	0.07088	0.07088	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184; 
0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	1	1	1	1	1	1	1	1	1	1	1	1	1]; 
%normalized target is given by rg*1000
target=[0.586881752132946	0.497724675211997	0.441969563072223	0.390702562868991	0.342290431189180	0.301507430040278	0.261605279420230	0.219681638780439	0.177525083407579	0.137221988837990	0.091453974856195	0.674192282188662	0.568609242084542	0.488669609489998	0.434624306685732	0.377177381035452	0.334348219330841	0.295432968105673	0.250784513255421	0.206663920225938	0.157218235654358	0.898021426814809	0.688709176139550	0.593660389913298	0.518273050268273	0.467584398276636	0.422386548962463	0.368635259704099	0.332146987729259	0.285447225127710	0.242281788755245	0.184410609576556	0.131029385547087	0.630490640566574	0.520768840170616	0.483185467327212	0.462453397861048	0.440445905055517	0.381949221810470	0.337402144745992	0.291922979810380	0.243272779600021	0.191063588180464	0.141627150231091	0.804228880950062	0.675413130353109	0.584724002966957	0.532139237999268	0.485630200853976	0.432489055263579	0.394891733007953	0.341802909118604	0.287362804767845	0.229750610910781	0.175499216722282	0.310866018786595	0.234810404055919	0.199783720800070	0.174245758676327	0.156761056745877	0.136935989376632	0.120301369902926	0.107815344040041	0.091935016527195	0.076815896545410	0.060556710316550	0.740764736158475	0.629399231509792	0.539097229965586	0.472078996783694	0.431267582926293	0.374235214668404	0.329876748615853	0.282840890494955	0.238631690731717	0.187700647682211	0.142297850834563	1.015163312694240	0.866043026725307	0.747991230014243	0.656015000567104	0.587711949208396	0.520373300383549	0.460945138774777	0.403519680994158	0.328187488280960	0.268431033653582	0.195513056044595	0.446951973515169	0.281784547678459	0.234176576884461	0.214809344834097	0.183491219945897	0.170999932274366	0.148755157679827	0.120433801721394	0.096594749426642	0.069452052793637	0.057546388301159	0.041907427766188	0.040808551660468	1.155579123505110	1.047271558585880	0.869501770853259	0.724108849197606	0.606950572825248	0.507675201543773	0.422585400491946	0.345687528100719	0.255053099360127	0.175507006943277	0.094504709316731	0.038165881857560	0.024731324877138]
%target1=1000*target
%net = newff( minmax(input), [10 1], {'tansig', 'purelin', 'trainbr', 'trainlm'} )
%above command train network using a leverberg marquardt strategy;%refer to command in line 15; % remove the percentage in line 15 to activate the command
%alternatively a bayesian regularization in combination with levenberg marquardt algorithm can be used as follows; %both trainbr and trainlm are tried initially; %trainlm was used with early stopping to avoid overfitting
net = newff( minmax(input), [10 1], {'tansig', 'purelin'}, 'trainbr')
net.trainParam.epochs=3000;%(number of epochs)
%net.trainParam.lr=0.3;%(learning rate)
%net.trainParam.mc=0.6;%(momentum)
net=train(net,input,target)
output = sim(net, input)
[target1,output]
plot(target1, 'o')
hold on
plot(output, '+r')
[output]'
validationset1=[0.947136219	0.894562956	0.837895473	0.780051308	0.722078824	0.664903669	0.63908421	0.569320886	0.517574646	0.478792805	0.413454477	0.357348907	0.332760288	0.283211443	0.913242002	0.889185144	0.839002081	0.789330139	0.739922305	0.690640155	0.641516423	0.592461499	0.543885331	0.495457321	0.447212149	0.398496493	0.960365624	0.925100595	0.875008899	0.825010349	0.775106244	0.725102144	0.675069857	0.625013753	0.575033716	0.525082952	0.475072979	0.904135974	0.902008285	0.851064924	0.800048421	0.749112056	0.699509448	0.650739887	0.603219762	0.555245048	0.509690165	0.464622834	0.420297146	0.951386619	0.895336367	0.845189655	0.795297662	0.745246551	0.695165714	0.645381077	0.595643216	0.546083521	0.496471452	0.447027815	0.397647179	0.945117954	0.914436635	0.871343803	0.828675856	0.785939326	0.744032491	0.702841568	0.66146318	0.620374284	0.577878625	0.534014139; 
0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375	0.375; 
0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.01885	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05498	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362	0.05362; 
0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	1	1	1	1	1	1	1	1	1	1	1	1	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8]
validationset2=[0.942520227	0.942470787	0.94242135	0.942371913	0.841963099	0.84180187	0.841640648	0.841479434	0.841318226	0.927055934	0.926935476	0.926814957	0.926694439	0.926573859	0.926453219	0.926332518	0.716537671	0.716444857	0.716352045	0.716259233	0.716166422	0.716073551	0.585355539	0.585263637	0.585171796	0.585080016	0.584988237	0.584896459	0.871066347	0.870963494	0.870860641	0.870757789	0.870654938; 0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	0.625	1	1	1	1	1	1	1	0.375	0.375	0.375	0.375	0.375	0.375	0.5	0.5	0.5	0.5	0.5	0.5	0.625	0.625	0.625	0.625	0.625; 0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.0536184	0.01885	0.01885	0.01885	0.01885	0.01885; 0.6	0.6	0.6	0.6	1	1	1	1	1	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8];
y=sim(net,validationset1)
rgvalidationset1=[y]'/1000
z=sim(net,validationset1)
rgvalidationset2=[z]'/1000