function v = testNN( w )
%
%    v = testNN( w )
%
% returns the falue of the empirical error of the NN (or, in fact,
% whatever function is encoded in 'roughNN()') with the weights contained
% in w.
%
% The empirical error is estimated over a 288-strong input/output pair
% ( X , y ), with X containing only one feature, that is hard-coded into
% the function so that its gradient can be easily computed by ADiGator.
%
% Input:
%
% - w is the real vector containing the weights of the NN, see roughNN
%   for details
%
% Output:
%
% - the MSE of the error done by roughNN() on the given test set
%
%{
% =======================================
% Author: Antonio Frangioni
% Date: 28-08-22
% Version 1.00
% Copyright Antonio Frangioni
% =======================================
%}

N = 288;  % size

% inputs
X = [
0.0000000000000000
0.0034843205574913
0.0069686411149826
0.0104529616724739
0.0139372822299652
0.0174216027874564
0.0209059233449477
0.0243902439024390
0.0278745644599303
0.0313588850174216
0.0348432055749129
0.0383275261324042
0.0418118466898955
0.0452961672473868
0.0487804878048781
0.0522648083623693
0.0557491289198606
0.0592334494773519
0.0627177700348432
0.0662020905923345
0.0696864111498258
0.0731707317073171
0.0766550522648084
0.0801393728222996
0.0836236933797909
0.0871080139372822
0.0905923344947735
0.0940766550522648
0.0975609756097561
0.1010452961672474
0.1045296167247387
0.1080139372822300
0.1114982578397213
0.1149825783972125
0.1184668989547038
0.1219512195121951
0.1254355400696864
0.1289198606271777
0.1324041811846690
0.1358885017421603
0.1393728222996516
0.1428571428571428
0.1463414634146341
0.1498257839721254
0.1533101045296167
0.1567944250871080
0.1602787456445993
0.1637630662020906
0.1672473867595819
0.1707317073170732
0.1742160278745645
0.1777003484320558
0.1811846689895470
0.1846689895470383
0.1881533101045296
0.1916376306620209
0.1951219512195122
0.1986062717770035
0.2020905923344948
0.2055749128919861
0.2090592334494774
0.2125435540069686
0.2160278745644599
0.2195121951219512
0.2229965156794425
0.2264808362369338
0.2299651567944251
0.2334494773519164
0.2369337979094077
0.2404181184668990
0.2439024390243902
0.2473867595818815
0.2508710801393728
0.2543554006968641
0.2578397212543554
0.2613240418118467
0.2648083623693380
0.2682926829268293
0.2717770034843205
0.2752613240418119
0.2787456445993031
0.2822299651567944
0.2857142857142857
0.2891986062717770
0.2926829268292683
0.2961672473867596
0.2996515679442509
0.3031358885017422
0.3066202090592334
0.3101045296167247
0.3135888501742160
0.3170731707317073
0.3205574912891986
0.3240418118466899
0.3275261324041812
0.3310104529616725
0.3344947735191638
0.3379790940766551
0.3414634146341464
0.3449477351916376
0.3484320557491289
0.3519163763066202
0.3554006968641115
0.3588850174216028
0.3623693379790941
0.3658536585365854
0.3693379790940767
0.3728222996515679
0.3763066202090593
0.3797909407665505
0.3832752613240418
0.3867595818815331
0.3902439024390244
0.3937282229965157
0.3972125435540070
0.4006968641114982
0.4041811846689896
0.4076655052264808
0.4111498257839721
0.4146341463414634
0.4181184668989547
0.4216027874564460
0.4250871080139373
0.4285714285714285
0.4320557491289199
0.4355400696864111
0.4390243902439024
0.4425087108013937
0.4459930313588850
0.4494773519163763
0.4529616724738676
0.4564459930313589
0.4599303135888502
0.4634146341463415
0.4668989547038327
0.4703832752613241
0.4738675958188153
0.4773519163763066
0.4808362369337979
0.4843205574912892
0.4878048780487805
0.4912891986062718
0.4947735191637631
0.4982578397212544
0.5017421602787456
0.5052264808362370
0.5087108013937283
0.5121951219512195
0.5156794425087108
0.5191637630662020
0.5226480836236933
0.5261324041811847
0.5296167247386759
0.5331010452961673
0.5365853658536586
0.5400696864111498
0.5435540069686411
0.5470383275261324
0.5505226480836236
0.5540069686411150
0.5574912891986064
0.5609756097560976
0.5644599303135889
0.5679442508710801
0.5714285714285714
0.5749128919860627
0.5783972125435540
0.5818815331010453
0.5853658536585367
0.5888501742160279
0.5923344947735192
0.5958188153310104
0.5993031358885017
0.6027874564459930
0.6062717770034843
0.6097560975609756
0.6132404181184670
0.6167247386759582
0.6202090592334495
0.6236933797909407
0.6271777003484320
0.6306620209059233
0.6341463414634146
0.6376306620209059
0.6411149825783973
0.6445993031358885
0.6480836236933798
0.6515679442508711
0.6550522648083623
0.6585365853658536
0.6620209059233449
0.6655052264808362
0.6689895470383276
0.6724738675958188
0.6759581881533101
0.6794425087108014
0.6829268292682926
0.6864111498257840
0.6898954703832753
0.6933797909407666
0.6968641114982579
0.7003484320557491
0.7038327526132404
0.7073170731707317
0.7108013937282229
0.7142857142857143
0.7177700348432056
0.7212543554006969
0.7247386759581882
0.7282229965156795
0.7317073170731707
0.7351916376306620
0.7386759581881532
0.7421602787456446
0.7456445993031359
0.7491289198606272
0.7526132404181185
0.7560975609756098
0.7595818815331010
0.7630662020905923
0.7665505226480837
0.7700348432055749
0.7735191637630662
0.7770034843205575
0.7804878048780488
0.7839721254355401
0.7874564459930313
0.7909407665505226
0.7944250871080140
0.7979094076655052
0.8013937282229965
0.8048780487804879
0.8083623693379791
0.8118466898954704
0.8153310104529616
0.8188153310104529
0.8222996515679443
0.8257839721254355
0.8292682926829268
0.8327526132404182
0.8362369337979094
0.8397212543554007
0.8432055749128919
0.8466898954703833
0.8501742160278746
0.8536585365853658
0.8571428571428572
0.8606271777003485
0.8641114982578397
0.8675958188153310
0.8710801393728222
0.8745644599303136
0.8780487804878049
0.8815331010452961
0.8850174216027875
0.8885017421602788
0.8919860627177700
0.8954703832752613
0.8989547038327526
0.9024390243902439
0.9059233449477352
0.9094076655052264
0.9128919860627178
0.9163763066202091
0.9198606271777003
0.9233449477351916
0.9268292682926830
0.9303135888501742
0.9337979094076655
0.9372822299651568
0.9407665505226481
0.9442508710801394
0.9477351916376306
0.9512195121951219
0.9547038327526133
0.9581881533101045
0.9616724738675958
0.9651567944250871
0.9686411149825784
0.9721254355400697
0.9756097560975610
0.9790940766550522
0.9825783972125436
0.9860627177700348
0.9895470383275261
0.9930313588850174
0.9965156794425087
1.0000000000000000 ];

% outputs
y = [
0.096798166000
0.143459740000
0.208317990000
-0.038018393000
0.148793230000
0.512799550000
-0.120798510000
0.177158750000
0.083816932000
0.000756494710
0.006887211700
0.213572840000
0.493783350000
0.035274935000
0.243769090000
0.087417919000
0.476797600000
0.271438160000
0.178877000000
0.302770820000
0.219586200000
0.397548740000
0.215089090000
0.086588415000
0.304056660000
0.513946170000
0.113409000000
0.270068060000
0.471061630000
0.046628439000
0.443157150000
0.477349380000
0.411852220000
0.280063680000
0.410626170000
0.442082230000
0.585090200000
0.561297160000
0.426446760000
0.739395540000
0.506414480000
0.409925250000
0.483992110000
0.696575460000
0.615166110000
0.737349800000
0.632542540000
1.013287300000
0.408451860000
0.613835270000
0.681370910000
0.724988310000
0.947395900000
0.779004190000
0.745667780000
0.789666080000
0.908202240000
0.707755840000
0.894037990000
0.606428220000
0.843615470000
0.727874550000
0.784348430000
0.937189250000
0.737952220000
0.769620390000
0.701166820000
0.604155740000
0.924881630000
1.130475900000
0.936493470000
0.935667120000
0.819976810000
1.219958800000
0.949769640000
1.185254200000
1.048672000000
0.957402250000
1.160938800000
1.147023700000
0.983283410000
1.194051400000
1.265849000000
0.987167510000
0.956395550000
1.052589900000
1.041239900000
1.105649800000
0.941725790000
1.082398200000
1.127045200000
0.990602660000
0.980803460000
0.763155870000
0.768571290000
0.718186990000
0.743430540000
0.899271220000
0.672586160000
1.243876900000
1.009891400000
0.580803050000
0.709665650000
0.858643730000
0.609667610000
0.789520360000
1.014111700000
0.817911210000
0.824534040000
0.676622590000
0.735885580000
0.609022520000
0.859070820000
0.729465540000
0.907844320000
0.969161960000
0.938595000000
0.765435590000
0.688922170000
0.574990840000
0.770659830000
0.891310740000
0.690971710000
0.711048000000
0.824634750000
0.857126400000
0.510549630000
0.748820900000
0.744129450000
0.688191070000
0.841053850000
0.648943870000
0.576231820000
0.738291460000
0.762720980000
0.658108930000
0.807248650000
0.457323660000
0.521077750000
0.218860160000
0.755337450000
0.525976310000
0.634217410000
0.821176590000
0.675074910000
0.599022390000
0.535501720000
0.624415250000
0.748616920000
0.428448630000
0.643341520000
0.768654000000
0.435878620000
0.747073780000
0.746823840000
0.509674810000
0.413964070000
0.702246380000
0.756141550000
0.719368010000
0.744580020000
0.450466060000
0.713008860000
0.536099090000
0.536595750000
0.385158420000
0.781369420000
0.640457830000
0.762680940000
0.836824400000
0.437730550000
0.703038130000
0.603083350000
0.740709380000
0.768477480000
0.724346000000
0.477804350000
0.580883120000
0.639146320000
1.073252500000
0.783713950000
0.948384040000
0.663369380000
0.634232460000
0.696070360000
0.526957260000
0.794798220000
0.587766610000
0.408654360000
0.749043110000
0.387306230000
0.350567280000
0.675537030000
0.495158740000
0.507149810000
0.625867220000
0.583647850000
0.630796900000
0.712643020000
0.504536230000
0.504499780000
0.381836730000
0.647114640000
0.814415180000
0.618741310000
0.808727320000
0.824111580000
0.901249190000
0.910594790000
0.668334220000
0.652467030000
0.797380800000
0.699257390000
1.025428600000
1.022629700000
0.837597600000
0.766407010000
0.913657810000
0.744506570000
0.829397600000
0.773018020000
0.872046570000
1.028215500000
0.972177970000
1.033239200000
0.724398150000
0.887466840000
0.710846670000
0.912868530000
0.899725750000
1.039970600000
1.003988400000
0.929601600000
0.747319110000
0.742110530000
0.495198080000
0.724133980000
0.546209190000
0.904975290000
0.886555800000
0.756973180000
0.663691170000
0.725449860000
0.927661000000
0.871628610000
0.583857660000
0.657822350000
0.445564610000
0.654537190000
0.685853290000
0.690412010000
0.306045040000
0.591718740000
0.366728870000
0.420310670000
0.575582700000
0.482907520000
0.394669790000
0.491601190000
0.627475460000
0.270874460000
0.144405290000
0.155561360000
0.171715630000
0.196642150000
0.368318080000
-0.046015957000
0.287831380000
0.121822920000
0.390236930000
0.084253654000
0.201575720000
0.048222309000
0.075602342000
0.128340910000
0.123106810000
0.069294711000
0.308367180000
0.213239800000
0.401070710000
0.073746174000
0.268322470000
-0.213145400000
0.191332180000
0.145485930000
0.028213679000
0.183566020000
0.206160990000 ];

% compute MSE of prediction on all ( X( i ) , y( i ) )

v = 0;  % return value

for i = 1 : N  % for all input / output pairs

    v = v + ( y( i ) - roughNN( w , X( i ) ) )^2;

end

v = v / 2;

end