You had a misunderstanding. The A variable should be a scalar, not a vector. All issues stemmed from that one misunderstanding.
rng default
A = 2; % Was [2,3]
a = [-0.9,-2.9];
tdata = 3*rand(200,1);
tdata = sort(tdata); % Increasing times for easier plotting
noisydata=0.07*randn(size(tdata));
ydata = A.*exp(a(1).*tdata).*cos(a(2).*tdata) + noisydata ;
plot(tdata,ydata,'b*')
xlabel 't'
ylabel 'Response'
A = optimvar('A'); % used to be of size 2
a = optimvar('a',2);
objfunction =@(A,a)A.*exp(a(1).*tdata).*cos(a(2).*tdata);
response = fcn2optimexpr(objfunction,A,a,"ReuseEvaluation",true) % 200-by-1, not 200-by-2
response =
200×1 Nonlinear OptimizationExpression array with properties:
IndexNames: {{} {}}
Variables: [1×1 struct] containing 2 OptimizationVariables
See expression formulation with show.
obj = sum((response - ydata).^2);
%%%%%%%%error appear when run the optimproblem
lsqprob = optimproblem;
lsqprob.Objective=obj;
x0.A = 1/2; % was [1/2 3/2]
x0.a = [-1/2,-3/2];
show(lsqprob)
OptimizationProblem :
Solve for:
A, a
minimize :
sum((((A .* exp((a(1) .* extraParams{1}))) .* cos((a(2) .* extraParams{2}))) - extraParams{3}).^2)
extraParams{1}:
0.0139
0.0357
0.0462
0.0955
0.1033
0.1071
0.1291
0.1385
0.1490
0.1619
0.1793
0.2276
0.2279
0.2345
0.2434
0.2515
0.2533
0.2894
0.2914
0.2926
0.3200
0.3336
0.3570
0.3700
0.3810
0.3897
0.3959
0.4082
0.4159
0.4257
0.4349
0.4366
0.4479
0.4571
0.4728
0.4865
0.4878
0.4969
0.5070
0.5136
0.5455
0.5505
0.5517
0.5606
0.5669
0.5898
0.6714
0.6869
0.7043
0.7197
0.7199
0.7251
0.7306
0.7533
0.7628
0.7653
0.7725
0.7796
0.7889
0.7914
0.8281
0.8308
0.8355
0.8575
0.8890
0.9190
0.9336
0.9513
1.0114
1.0132
1.0212
1.0500
1.0529
1.0550
1.0595
1.1055
1.1077
1.1413
1.1447
1.1692
1.1767
1.1993
1.2054
1.2117
1.2518
1.2653
1.2942
1.3076
1.3162
1.3280
1.3368
1.3404
1.3516
1.3528
1.4082
1.4199
1.4561
1.4604
1.4678
1.4693
1.4726
1.4951
1.5179
1.5255
1.5323
1.5397
1.5856
1.5924
1.6150
1.6406
1.6410
1.6416
1.6492
1.6496
1.7035
1.7065
1.7256
1.7391
1.7558
1.7558
1.8059
1.8481
1.8662
1.8769
1.8971
1.9389
1.9432
1.9473
1.9622
1.9653
1.9664
1.9672
2.0362
2.0391
2.0603
2.0676
2.0845
2.0972
2.1181
2.1281
2.1952
2.2294
2.2341
2.2445
2.2538
2.2612
2.2641
2.2716
2.2732
2.2966
2.3247
2.3271
2.3375
2.3407
2.3408
2.3766
2.3829
2.3845
2.3856
2.4002
2.4008
2.4429
2.4442
2.4519
2.4529
2.4636
2.4704
2.4775
2.4925
2.5222
2.5474
2.5591
2.6061
2.6079
2.6727
2.7002
2.7081
2.7174
2.7319
2.7400
2.7401
2.7472
2.7516
2.7878
2.7882
2.8020
2.8020
2.8262
2.8344
2.8507
2.8684
2.8715
2.8725
2.8779
2.8785
2.8792
2.8857
2.8947
2.9118
2.9884
extraParams{2}:
0.0139
0.0357
0.0462
0.0955
0.1033
0.1071
0.1291
0.1385
0.1490
0.1619
0.1793
0.2276
0.2279
0.2345
0.2434
0.2515
0.2533
0.2894
0.2914
0.2926
0.3200
0.3336
0.3570
0.3700
0.3810
0.3897
0.3959
0.4082
0.4159
0.4257
0.4349
0.4366
0.4479
0.4571
0.4728
0.4865
0.4878
0.4969
0.5070
0.5136
0.5455
0.5505
0.5517
0.5606
0.5669
0.5898
0.6714
0.6869
0.7043
0.7197
0.7199
0.7251
0.7306
0.7533
0.7628
0.7653
0.7725
0.7796
0.7889
0.7914
0.8281
0.8308
0.8355
0.8575
0.8890
0.9190
0.9336
0.9513
1.0114
1.0132
1.0212
1.0500
1.0529
1.0550
1.0595
1.1055
1.1077
1.1413
1.1447
1.1692
1.1767
1.1993
1.2054
1.2117
1.2518
1.2653
1.2942
1.3076
1.3162
1.3280
1.3368
1.3404
1.3516
1.3528
1.4082
1.4199
1.4561
1.4604
1.4678
1.4693
1.4726
1.4951
1.5179
1.5255
1.5323
1.5397
1.5856
1.5924
1.6150
1.6406
1.6410
1.6416
1.6492
1.6496
1.7035
1.7065
1.7256
1.7391
1.7558
1.7558
1.8059
1.8481
1.8662
1.8769
1.8971
1.9389
1.9432
1.9473
1.9622
1.9653
1.9664
1.9672
2.0362
2.0391
2.0603
2.0676
2.0845
2.0972
2.1181
2.1281
2.1952
2.2294
2.2341
2.2445
2.2538
2.2612
2.2641
2.2716
2.2732
2.2966
2.3247
2.3271
2.3375
2.3407
2.3408
2.3766
2.3829
2.3845
2.3856
2.4002
2.4008
2.4429
2.4442
2.4519
2.4529
2.4636
2.4704
2.4775
2.4925
2.5222
2.5474
2.5591
2.6061
2.6079
2.6727
2.7002
2.7081
2.7174
2.7319
2.7400
2.7401
2.7472
2.7516
2.7878
2.7882
2.8020
2.8020
2.8262
2.8344
2.8507
2.8684
2.8715
2.8725
2.8779
2.8785
2.8792
2.8857
2.8947
2.9118
2.9884
extraParams{3}:
2.0062
1.9117
1.9451
1.7782
1.6691
1.7957
1.6789
1.6345
1.6244
1.5602
1.4110
1.2761
1.2759
1.2219
1.3405
1.1280
1.1478
0.9800
0.9390
1.0025
0.8799
0.9476
0.7227
0.6102
0.7500
0.6871
0.5583
0.4173
0.4596
0.4391
0.4314
0.3866
0.3900
0.3491
0.1715
0.1390
0.1485
0.1298
0.1048
0.1034
-0.2258
-0.0634
0.0514
-0.1410
-0.0224
-0.1391
-0.4037
-0.4280
-0.5918
-0.5227
-0.4047
-0.5213
-0.5369
-0.6361
-0.6045
-0.5904
-0.5894
-0.6573
-0.6627
-0.5084
-0.8589
-0.5481
-0.6861
-0.6632
-0.8761
-0.8185
-0.8026
-0.7585
-0.9043
-0.7540
-0.8698
-0.7691
-0.7267
-0.7484
-0.6931
-0.6676
-0.7817
-0.6879
-0.7687
-0.7692
-0.6036
-0.6415
-0.6378
-0.5622
-0.5308
-0.5288
-0.4233
-0.4256
-0.4606
-0.5075
-0.4911
-0.3564
-0.5349
-0.4219
-0.4676
-0.2408
-0.1933
-0.2467
-0.2399
-0.4066
-0.1866
-0.3450
-0.3183
-0.1385
-0.2001
-0.0936
-0.0073
0.0150
-0.0618
0.0522
0.0283
0.0799
0.0693
0.0952
0.0882
0.0905
0.1923
-0.0128
0.1172
0.0636
0.1705
0.2739
0.2979
0.1754
0.2244
0.2855
0.2570
0.3000
0.3117
0.2195
0.2725
0.1359
0.3776
0.2536
0.2141
0.2806
0.1977
0.2953
0.2551
0.4452
0.3561
0.0897
0.2936
0.1607
0.2369
0.2631
0.3027
0.2279
0.3566
0.2017
0.2442
0.2666
0.2206
0.2746
0.2355
0.1383
0.0633
0.3188
0.1458
0.1869
0.2187
0.1624
0.0903
0.1162
0.1397
0.2454
0.0775
0.1884
0.1459
0.0898
0.0169
0.0639
0.0499
-0.0479
0.0320
-0.0534
-0.0065
0.0190
-0.0751
-0.0358
0.0088
-0.1475
0.0515
0.1325
0.0298
-0.0652
-0.0131
-0.1252
0.0757
0.0041
-0.0127
-0.1301
-0.0467
-0.1099
-0.0928
-0.1112
-0.1451
-0.1397
-0.0957
-0.2175
[sol ,fval] = solve(lsqprob,x0)
Solving problem using lsqnonlin.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
sol = struct with fields:
A: 2.0035
a: [2×1 double]
fval = 0.9375
Alan Weiss
MATLAB mathematical toolbox documentation
