Constrained Inversion, basics
In this example, we consider as inple constrained optimization problem an look at bot SPG and PQN algorithms
using SlimOptim, LinearAlgebra, PyPlotProblem definition
We define a standard least square problem wuth constraints on the solution
n = 512
A = randn(n, n);Setup constraints
# x has to be be bigger than 2
function proj(x)
xp = deepcopy(x)
xp[xp .< 2] .= 2
return xp
endproj (generic function with 1 method)x_true = 2 .+ randn(n)
x_true = proj(x_true);
b = A*x_true;Define in place objective and gradient functions
function f(x)
return .5*norm(A*x - b)^2
end
function g!(g, x)
g .= A'*(A*x - b)
end
function fg!(g, x)
f = .5*norm(A*x - b)^2
g .= A'*(A*x - b)
return f
endfg! (generic function with 1 method)Inversion
spgopt = spg_options(maxIter=200)
pqnopt = pqn_options(maxIter=200)SlimOptim.PQN_params(1, 1.0f-5, 1.0f-7, 200, 0.0001f0, 10, false, true, false, 1.0f-6, 1.0f-7, 10, false, 20)solspg = spg(f, g!, fg!, zeros(n), proj, spgopt);Running SPG...
Number of objective function to store: 2
Using spectral projection : true
Maximum number of iterations: 200
SPG optimality tolerance: 1.00e-05
SPG progress tolerance: 1.00e-07
Iteration FunEvals GradEvals Projections Step Length alpha Function Val Opt Cond
0 0 0 0 0.00000e+00 0.00000e+00 6.43586e+04 1.74158e+03
1 2 2 6 1.00000e+00 1.14838e-04 5.16928e+04 1.56670e+03
2 3 3 10 1.00000e+00 9.11654e-04 9.55011e+03 4.37705e+02
3 4 4 14 1.00000e+00 9.36248e-04 4.28123e+03 3.22887e+02
4 5 5 18 1.00000e+00 1.06696e-03 2.38016e+03 1.71788e+02
5 6 6 22 1.00000e+00 1.21052e-03 1.53794e+03 1.98450e+02
6 7 7 26 1.00000e+00 1.09634e-03 1.08454e+03 1.20651e+02
7 8 8 30 1.00000e+00 8.51613e-04 7.68486e+02 1.02098e+02
8 9 9 34 1.00000e+00 8.04981e-04 6.06793e+02 6.65342e+01
9 10 10 38 1.00000e+00 1.25878e-03 4.57186e+02 5.82597e+01
10 11 11 42 1.00000e+00 2.91370e-03 3.51207e+02 9.53526e+01
11 13 12 46 3.24310e-01 2.15600e-03 2.27043e+02 3.61941e+01
12 14 13 50 1.00000e+00 6.34114e-04 2.02552e+02 3.01056e+01
13 15 14 54 1.00000e+00 1.63976e-03 1.61018e+02 2.82961e+01
14 16 15 58 1.00000e+00 8.51908e-03 1.11194e+02 6.02229e+01
15 18 16 62 1.09690e-01 5.92810e-03 5.58230e+01 1.24917e+01
16 19 17 66 1.00000e+00 6.11612e-04 5.03563e+01 9.13537e+00
17 20 18 70 1.00000e+00 1.59110e-03 4.36738e+01 8.05800e+00
18 21 19 74 1.00000e+00 4.85664e-03 3.31495e+01 1.16047e+01
19 23 20 78 1.35093e-01 6.49465e-03 2.90944e+01 9.40102e+00
20 24 21 82 1.00000e+00 7.98379e-04 2.72993e+01 5.77931e+00
21 25 22 86 1.00000e+00 1.40035e-03 2.50584e+01 6.42402e+00
22 26 23 90 1.00000e+00 4.66894e-03 2.41955e+01 2.28105e+01
23 28 24 94 2.31175e-01 2.57794e-03 1.80724e+01 4.79904e+00
24 29 25 98 1.00000e+00 5.85974e-04 1.74156e+01 4.17424e+00
25 30 26 102 1.00000e+00 4.27422e-03 1.37208e+01 4.43414e+00
26 32 27 106 1.48690e-01 2.15869e-02 1.24107e+01 6.42103e+00
27 34 28 110 2.52438e-01 3.01332e-03 1.12370e+01 4.52461e+00
28 35 29 114 1.00000e+00 7.01221e-04 1.07647e+01 3.46244e+00
29 36 30 118 1.00000e+00 1.52617e-03 9.99953e+00 3.70082e+00
30 37 31 122 1.00000e+00 8.97359e-03 1.06643e+01 1.73156e+01
31 39 32 126 1.46551e-01 3.94351e-03 6.28357e+00 2.43527e+00
32 40 33 130 1.00000e+00 5.65261e-04 6.03481e+00 2.32069e+00
33 41 34 134 1.00000e+00 2.11063e-03 5.49935e+00 2.35977e+00
34 42 35 138 1.00000e+00 9.18688e-03 5.45901e+00 1.00254e+01
35 44 36 142 1.45842e-01 4.66951e-03 3.79408e+00 2.51679e+00
36 45 37 146 1.00000e+00 6.46365e-04 3.50514e+00 1.94783e+00
37 46 38 150 1.00000e+00 1.07985e-03 3.33493e+00 1.70397e+00
38 47 39 154 1.00000e+00 3.56875e-03 2.94898e+00 2.06227e+00
39 49 40 158 1.07987e-01 8.99418e-03 2.81982e+00 2.15922e+00
40 50 41 162 1.00000e+00 9.34325e-04 2.71215e+00 1.75633e+00
41 51 42 166 1.00000e+00 1.22895e-03 2.59750e+00 2.03036e+00
42 52 43 170 1.00000e+00 1.91834e-03 2.50071e+00 2.73450e+00
43 53 44 174 1.00000e+00 1.44214e-03 2.53060e+00 4.55847e+00
44 54 45 178 1.00000e+00 6.87398e-04 2.24458e+00 1.69277e+00
45 55 46 182 1.00000e+00 5.95108e-04 2.18113e+00 1.39991e+00
46 56 47 186 1.00000e+00 1.26538e-03 2.08476e+00 1.28360e+00
47 57 48 190 1.00000e+00 3.12573e-02 1.13868e+00 7.48942e+00
48 60 49 194 2.78684e-02 2.64729e-02 5.88753e-01 1.18377e+00
49 61 50 198 1.00000e+00 6.31294e-04 5.31991e-01 5.48474e-01
50 62 51 202 1.00000e+00 9.64354e-04 5.07279e-01 7.24977e-01
51 63 52 206 1.00000e+00 2.79142e-03 4.65269e-01 7.72654e-01
52 65 53 210 2.00245e-01 6.64484e-03 4.49914e-01 8.13937e-01
53 66 54 214 1.00000e+00 1.20801e-03 4.36760e-01 1.01442e+00
54 67 55 218 1.00000e+00 8.86314e-04 4.20876e-01 7.06753e-01
55 68 56 222 1.00000e+00 7.79660e-04 4.09282e-01 6.23354e-01
56 69 57 226 1.00000e+00 1.14761e-03 3.96290e-01 5.73528e-01
57 70 58 230 1.00000e+00 3.77588e-03 3.75249e-01 1.39934e+00
58 72 59 234 2.00884e-01 3.26817e-03 3.49641e-01 5.27126e-01
59 73 60 238 1.00000e+00 6.33287e-04 3.42935e-01 5.19730e-01
60 74 61 242 1.00000e+00 2.85248e-03 3.16989e-01 4.58775e-01
61 76 62 246 1.55660e-01 3.80934e-02 2.89599e-01 1.46763e+00
62 78 63 250 1.10876e-01 5.78621e-03 2.64492e-01 4.46932e-01
63 79 64 254 1.00000e+00 6.20831e-04 2.59305e-01 4.56014e-01
64 80 65 258 1.00000e+00 2.94896e-03 2.39454e-01 3.74111e-01
65 82 66 262 2.20546e-01 2.62773e-02 2.19553e-01 1.19150e+00
66 84 67 266 1.30750e-01 5.53293e-03 2.02102e-01 4.27416e-01
67 85 68 270 1.00000e+00 6.80472e-04 1.96687e-01 4.40527e-01
68 86 69 274 1.00000e+00 1.53392e-03 1.88652e-01 3.32734e-01
69 87 70 278 1.00000e+00 9.35367e-03 1.77606e-01 1.79186e+00
70 89 71 282 1.02542e-01 5.96778e-03 1.44448e-01 3.28094e-01
71 90 72 286 1.00000e+00 5.91003e-04 1.40992e-01 3.53038e-01
72 91 73 290 1.00000e+00 1.92408e-03 1.33911e-01 2.56879e-01
73 92 74 294 1.00000e+00 1.04385e-02 1.16970e-01 9.48452e-01
74 94 75 298 1.15285e-01 9.14863e-03 1.00148e-01 3.88615e-01
75 95 76 302 1.00000e+00 9.66191e-04 9.58649e-02 3.34602e-01
76 96 77 306 1.00000e+00 1.15562e-03 9.29120e-02 2.81519e-01
77 97 78 310 1.00000e+00 1.66852e-03 9.00812e-02 4.96070e-01
78 98 79 314 1.00000e+00 1.51303e-03 8.96729e-02 5.30551e-01
79 99 80 318 1.00000e+00 7.83530e-04 8.42805e-02 3.94196e-01
80 100 81 322 1.00000e+00 6.23772e-04 8.21698e-02 1.99996e-01
81 101 82 326 1.00000e+00 9.43575e-04 8.01988e-02 2.40000e-01
82 102 83 330 1.00000e+00 1.61758e-02 5.71616e-02 6.44812e-01
83 105 84 334 3.16824e-02 2.59486e-02 5.09751e-02 3.45698e-01
84 106 85 338 1.00000e+00 6.08080e-04 4.93079e-02 1.69315e-01
85 107 86 342 1.00000e+00 8.57215e-04 4.81917e-02 1.87468e-01
86 108 87 346 1.00000e+00 8.60290e-03 3.92177e-02 3.30372e-01
87 110 88 350 1.00000e-01 2.79467e-02 4.56392e-02 9.18815e-01
88 111 89 354 1.00000e+00 8.23956e-04 3.78282e-02 4.78190e-01
89 112 90 358 1.00000e+00 5.56082e-04 3.46577e-02 1.57008e-01
90 113 91 362 1.00000e+00 5.77477e-04 3.41425e-02 1.44116e-01
91 114 92 366 1.00000e+00 1.28378e-02 2.45330e-02 1.51747e-01
92 116 93 370 1.00000e-01 5.46516e-02 2.62654e-02 5.08009e-01
93 118 94 374 3.24711e-01 2.03086e-03 2.15315e-02 1.53104e-01
94 119 95 378 1.00000e+00 6.56394e-04 2.07614e-02 1.00206e-01
95 120 96 382 1.00000e+00 1.30909e-03 1.99643e-02 1.19791e-01
96 121 97 386 1.00000e+00 4.42527e-03 1.83588e-02 2.39983e-01
97 123 98 390 1.04091e-01 6.89148e-03 1.75954e-02 1.32551e-01
98 124 99 394 1.00000e+00 6.99256e-04 1.72595e-02 8.89980e-02
99 125 100 398 1.00000e+00 2.12107e-03 1.64101e-02 1.24349e-01
100 127 101 402 1.91372e-01 1.60548e-02 1.57003e-02 2.29814e-01
101 129 102 406 2.38220e-01 2.94678e-03 1.49852e-02 1.26915e-01
102 130 103 410 1.00000e+00 6.63368e-04 1.47116e-02 8.40596e-02
103 131 104 414 1.00000e+00 2.02212e-03 1.40189e-02 1.08352e-01
104 133 105 418 2.13794e-01 2.18712e-02 1.31642e-02 2.50550e-01
105 135 106 422 1.41080e-01 4.51125e-03 1.23259e-02 1.05294e-01
106 136 107 426 1.00000e+00 6.20924e-04 1.21226e-02 7.96526e-02
107 137 108 430 1.00000e+00 3.26614e-03 1.12102e-02 9.28441e-02
108 139 109 434 1.17696e-01 3.80741e-02 1.05404e-02 2.31788e-01
109 141 110 438 1.51042e-01 4.38841e-03 9.92575e-03 9.72055e-02
110 142 111 442 1.00000e+00 6.41071e-04 9.74450e-03 6.98994e-02
111 143 112 446 1.00000e+00 2.39673e-03 9.20644e-03 8.28658e-02
112 145 113 450 2.22182e-01 2.20146e-02 8.63028e-03 2.11028e-01
113 147 114 454 1.39467e-01 4.68224e-03 8.08051e-03 8.93397e-02
114 148 115 458 1.00000e+00 6.34256e-04 7.93349e-03 6.36165e-02
115 149 116 462 1.00000e+00 2.44349e-03 7.49015e-03 7.06335e-02
116 151 117 466 2.54950e-01 2.08040e-02 6.99355e-03 1.96979e-01
117 153 118 470 1.30965e-01 5.02595e-03 6.52330e-03 8.12207e-02
118 154 119 474 1.00000e+00 6.39562e-04 6.39699e-03 5.68647e-02
119 155 120 478 1.00000e+00 2.15018e-03 6.08218e-03 6.18824e-02
120 157 121 482 3.81302e-01 1.64075e-02 5.63677e-03 1.86951e-01
121 159 122 486 1.12405e-01 5.72180e-03 5.18889e-03 7.25360e-02
122 160 123 490 1.00000e+00 6.28822e-04 5.08574e-03 5.10345e-02
123 161 124 494 1.00000e+00 2.09091e-03 4.84328e-03 5.10654e-02
124 162 125 498 1.00000e+00 1.49127e-02 4.95518e-03 3.19092e-01
125 164 126 502 1.00000e-01 7.02326e-03 3.48282e-03 9.38520e-02
126 165 127 506 1.00000e+00 6.11246e-04 3.28122e-03 4.20319e-02
127 166 128 510 1.00000e+00 9.00684e-04 3.18446e-03 4.07260e-02
128 167 129 514 1.00000e+00 2.99236e-03 2.97272e-03 4.04108e-02
129 169 130 518 1.99761e-01 1.51574e-02 2.85064e-03 9.12819e-02
130 171 131 522 2.61380e-01 2.84341e-03 2.73003e-03 4.74350e-02
131 172 132 526 1.00000e+00 6.96021e-04 2.67897e-03 3.95732e-02
132 173 133 530 1.00000e+00 1.68761e-03 2.57989e-03 3.69408e-02
133 175 134 534 3.37065e-01 1.43071e-02 2.43289e-03 1.10250e-01
134 177 135 538 1.41059e-01 4.50086e-03 2.27779e-03 3.60251e-02
135 178 136 542 1.00000e+00 6.19790e-04 2.24287e-03 3.39566e-02
136 179 137 546 1.00000e+00 3.44626e-03 2.07536e-03 3.16146e-02
137 181 138 550 1.01888e-01 4.49385e-02 1.95620e-03 9.37649e-02
138 183 139 554 1.46707e-01 4.50337e-03 1.84551e-03 3.48796e-02
139 184 140 558 1.00000e+00 6.38116e-04 1.81479e-03 3.13642e-02
140 185 141 562 1.00000e+00 2.56214e-03 1.71406e-03 2.84151e-02
141 187 142 566 1.80796e-01 2.59253e-02 1.61527e-03 8.90130e-02
142 189 143 570 1.46007e-01 4.53963e-03 1.52159e-03 3.21633e-02
143 190 144 574 1.00000e+00 6.38811e-04 1.49573e-03 2.85293e-02
144 191 145 578 1.00000e+00 2.42806e-03 1.41727e-03 2.53309e-02
145 193 146 582 2.17186e-01 2.26229e-02 1.33315e-03 8.37420e-02
146 195 147 586 1.40569e-01 4.71374e-03 1.25282e-03 2.93042e-02
147 196 148 590 1.00000e+00 6.38375e-04 1.23112e-03 2.56410e-02
148 197 149 594 1.00000e+00 2.34300e-03 1.16895e-03 2.27124e-02
149 199 150 598 2.54560e-01 1.99862e-02 1.09831e-03 7.67894e-02
150 201 151 602 1.37898e-01 4.82629e-03 1.03025e-03 2.67566e-02
151 202 152 606 1.00000e+00 6.40271e-04 1.01187e-03 2.31600e-02
152 203 153 610 1.00000e+00 2.20297e-03 9.63819e-04 2.02366e-02
153 205 154 614 3.11264e-01 1.74953e-02 9.03234e-04 7.13382e-02
154 207 155 618 1.30045e-01 5.08196e-03 8.43516e-04 2.40218e-02
155 208 156 622 1.00000e+00 6.36926e-04 8.28144e-04 2.08700e-02
156 209 157 626 1.00000e+00 2.14805e-03 7.89800e-04 1.76924e-02
157 211 158 630 3.70495e-01 1.59062e-02 7.37685e-04 6.60600e-02
158 213 159 634 1.22799e-01 5.39672e-03 6.85385e-04 2.23752e-02
159 214 160 638 1.00000e+00 6.39120e-04 6.72098e-04 1.88245e-02
160 215 161 642 1.00000e+00 1.94951e-03 6.43679e-04 1.52568e-02
161 216 162 646 1.00000e+00 1.34593e-02 6.60728e-04 1.19667e-01
162 218 163 650 1.00000e-01 6.22211e-03 4.83046e-04 2.58516e-02
163 219 164 654 1.00000e+00 5.89579e-04 4.61773e-04 1.79245e-02
164 220 165 658 1.00000e+00 1.24674e-03 4.45398e-04 1.21365e-02
165 221 166 662 1.00000e+00 3.02114e-03 4.18316e-04 1.82795e-02
166 223 167 666 1.56689e-01 1.09027e-02 4.06209e-04 2.48219e-02
167 224 168 670 1.00000e+00 1.60717e-03 4.03637e-04 3.77136e-02
168 225 169 674 1.00000e+00 8.55705e-04 3.84736e-04 2.46285e-02
169 226 170 678 1.00000e+00 6.39361e-04 3.74966e-04 1.48661e-02
170 227 171 682 1.00000e+00 8.24889e-04 3.68213e-04 1.15919e-02
171 228 172 686 1.00000e+00 1.02920e-02 2.99248e-04 2.85499e-02
172 231 173 690 3.98923e-02 3.06388e-02 2.91577e-04 2.66898e-02
173 232 174 694 1.00000e+00 7.19203e-04 2.80528e-04 1.43093e-02
174 233 175 698 1.00000e+00 6.98499e-04 2.75673e-04 1.03118e-02
175 234 176 702 1.00000e+00 2.02359e-03 2.64012e-04 1.37560e-02
176 236 177 706 2.19335e-01 1.64022e-02 2.52442e-04 2.84481e-02
177 238 178 710 1.95547e-01 3.43519e-03 2.40661e-04 1.36585e-02
178 239 179 714 1.00000e+00 6.47704e-04 2.36916e-04 9.50043e-03
179 240 180 718 1.00000e+00 2.48786e-03 2.24573e-04 1.18934e-02
180 242 181 722 1.52068e-01 3.45029e-02 2.10746e-04 3.12955e-02
181 244 182 726 1.21951e-01 5.13687e-03 1.97529e-04 1.16588e-02
182 245 183 730 1.00000e+00 6.16235e-04 1.94671e-04 8.85038e-03
183 246 184 734 1.00000e+00 3.66105e-03 1.79817e-04 1.01547e-02
184 248 185 738 1.12626e-01 4.98514e-02 1.67959e-04 2.99766e-02
185 250 186 742 1.14981e-01 5.51092e-03 1.57084e-04 1.07548e-02
186 251 187 746 1.00000e+00 6.22669e-04 1.54643e-04 7.88595e-03
187 252 188 750 1.00000e+00 2.90795e-03 1.45251e-04 8.88077e-03
188 254 189 754 2.06668e-01 2.98051e-02 1.34978e-04 2.63712e-02
189 256 190 758 1.09154e-01 5.93661e-03 1.25592e-04 1.02315e-02
190 257 191 762 1.00000e+00 6.35426e-04 1.23350e-04 7.10132e-03
191 258 192 766 1.00000e+00 2.10923e-03 1.17856e-04 7.87428e-03
192 259 193 770 1.00000e+00 1.54463e-02 1.22851e-04 4.91207e-02
193 261 194 774 1.00000e-01 6.91379e-03 8.57157e-05 1.24458e-02
194 262 195 778 1.00000e+00 5.97581e-04 8.10100e-05 6.08195e-03
195 263 196 782 1.00000e+00 8.82323e-04 7.87873e-05 6.21306e-03
196 264 197 786 1.00000e+00 2.81259e-03 7.41525e-05 5.85756e-03
197 266 198 790 2.80248e-01 1.62852e-02 7.02357e-05 1.53048e-02
198 268 199 794 1.64326e-01 4.20594e-03 6.62986e-05 6.09616e-03
199 269 200 798 1.00000e+00 6.68458e-04 6.51450e-05 5.77133e-03
200 270 201 802 1.00000e+00 2.02537e-03 6.23930e-05 5.16853e-03solpqn = pqn(f, g!, fg!, zeros(n), proj, pqnopt);Running PQN...
Number of L-BFGS Corrections to store: 10
Spectral initialization of SPG: 1
Maximum number of SPG iterations: 10
SPG optimality tolerance: 1.00e-06
SPG progress tolerance: 1.00e-07
PQN optimality tolerance: 1.00e-05
PQN progress tolerance: 1.00e-07
Quadratic initialization of line search: 0
Maximum number of iterations: 200
Iteration FunEvals GradEvals Projections Step Length Function Val Opt Cond
0 0 0 0 0.00000e+00 6.43586e+04 1.74158e+03
1 5 2 6 1.00000e-03 1.12088e+04 5.00193e+02
2 6 3 37 1.00000e+00 4.54231e+03 2.98662e+02
3 7 4 70 1.00000e+00 2.06001e+03 1.57737e+02
4 8 5 103 1.00000e+00 9.82998e+02 1.00808e+02
5 9 6 136 1.00000e+00 4.56067e+02 8.50505e+01
6 10 7 169 1.00000e+00 2.67616e+02 4.15506e+01
7 11 8 202 1.00000e+00 1.92744e+02 2.88074e+01
8 12 9 235 1.00000e+00 1.16305e+02 2.57625e+01
9 13 10 268 1.00000e+00 7.96665e+01 2.83135e+01
10 14 11 301 1.00000e+00 5.14106e+01 1.72586e+01
11 15 12 334 1.00000e+00 3.73887e+01 8.92290e+00
12 16 13 367 1.00000e+00 2.69002e+01 8.94057e+00
13 17 14 400 1.00000e+00 1.92797e+01 7.48904e+00
14 18 15 433 1.00000e+00 1.43536e+01 8.37061e+00
15 19 16 466 1.00000e+00 1.11029e+01 5.80731e+00
16 20 17 499 1.00000e+00 7.85271e+00 4.72716e+00
17 21 18 532 1.00000e+00 5.82694e+00 6.00975e+00
18 22 19 565 1.00000e+00 4.39628e+00 2.82803e+00
19 23 20 598 1.00000e+00 3.56750e+00 2.83429e+00
20 24 21 631 1.00000e+00 2.82282e+00 2.23547e+00
21 25 22 664 1.00000e+00 2.25303e+00 3.10365e+00
22 26 23 697 1.00000e+00 1.87255e+00 1.85390e+00
23 27 24 730 1.00000e+00 1.46381e+00 1.92033e+00
24 28 25 763 1.00000e+00 1.01555e+00 1.69584e+00
25 29 26 796 1.00000e+00 7.65100e-01 3.03526e+00
26 30 27 829 1.00000e+00 6.06219e-01 1.17198e+00
27 31 28 862 1.00000e+00 5.16868e-01 8.92980e-01
28 32 29 895 1.00000e+00 3.72158e-01 8.62956e-01
29 33 30 928 1.00000e+00 2.64318e-01 1.26354e+00
30 34 31 961 1.00000e+00 1.94658e-01 9.38447e-01
31 35 32 994 1.00000e+00 1.60645e-01 6.20065e-01
32 36 33 1027 1.00000e+00 1.24285e-01 6.56607e-01
33 37 34 1060 1.00000e+00 9.68606e-02 6.86179e-01
34 38 35 1093 1.00000e+00 7.48079e-02 4.35798e-01
35 39 36 1126 1.00000e+00 5.81404e-02 4.22953e-01
36 40 37 1159 1.00000e+00 4.51947e-02 6.83740e-01
37 41 38 1192 1.00000e+00 3.48079e-02 3.15936e-01
38 42 39 1225 1.00000e+00 2.82198e-02 2.54875e-01
39 43 40 1258 1.00000e+00 2.21134e-02 2.37847e-01
40 44 41 1291 1.00000e+00 1.61920e-02 2.48766e-01
41 45 42 1324 1.00000e+00 1.22617e-02 1.87633e-01
42 46 43 1357 1.00000e+00 9.77544e-03 1.44600e-01
43 47 44 1390 1.00000e+00 6.78058e-03 1.25214e-01
44 48 45 1423 1.00000e+00 5.08399e-03 1.49467e-01
45 49 46 1456 1.00000e+00 3.96789e-03 1.03778e-01
46 50 47 1489 1.00000e+00 2.80505e-03 8.96870e-02
47 51 48 1522 1.00000e+00 1.98806e-03 1.16806e-01
48 52 49 1555 1.00000e+00 1.33502e-03 7.85245e-02
49 53 50 1588 1.00000e+00 9.52237e-04 5.22027e-02
50 54 51 1621 1.00000e+00 7.38365e-04 3.78488e-02
51 55 52 1654 1.00000e+00 5.64995e-04 6.53816e-02
52 56 53 1687 1.00000e+00 4.73456e-04 3.35096e-02
53 57 54 1720 1.00000e+00 3.84913e-04 2.58599e-02
54 58 55 1753 1.00000e+00 2.79461e-04 2.18399e-02
55 59 56 1786 1.00000e+00 1.68513e-04 2.76946e-02
56 60 57 1819 1.00000e+00 1.28404e-04 4.22637e-02
57 61 58 1852 1.00000e+00 9.60111e-05 2.10306e-02
58 62 59 1879 1.00000e+00 7.80537e-05 1.26640e-02
59 63 60 1900 1.00000e+00 6.08178e-05 1.03112e-02
60 64 61 1933 1.00000e+00 4.02213e-05 1.23837e-02
61 65 62 1966 1.00000e+00 2.85879e-05 1.35953e-02
62 66 63 1999 1.00000e+00 2.13626e-05 7.39491e-03
63 67 64 2027 1.00000e+00 1.56684e-05 6.16891e-03
64 68 65 2060 1.00000e+00 9.99324e-06 7.54116e-03
65 69 66 2093 1.00000e+00 6.96419e-06 8.23401e-03
66 70 67 2111 1.00000e+00 5.60443e-06 3.71143e-03
67 71 68 2124 1.00000e+00 4.71354e-06 3.86080e-03
68 72 69 2137 1.00000e+00 3.90985e-06 3.13338e-03
69 73 70 2158 1.00000e+00 2.85638e-06 4.16902e-03
70 74 71 2173 1.00000e+00 2.28482e-06 2.81712e-03
71 75 72 2186 1.00000e+00 1.84743e-06 1.91517e-03
72 76 73 2205 1.00000e+00 1.26905e-06 2.37160e-03
73 77 74 2223 1.00000e+00 9.38620e-07 3.14916e-03
74 78 75 2241 1.00000e+00 7.30946e-07 9.59953e-04
75 79 76 2251 1.00000e+00 6.29565e-07 8.13586e-04
76 80 77 2263 1.00000e+00 4.40387e-07 1.09972e-03
Function value changing by less than progTolPlot solutions
figure(figsize=(12, 4))
subplot(131)
plot(x_true, label="true", "ro", markersize=5)
plot(solspg.x, label="spg", "g*", markersize=2)
legend()
subplot(132)
plot(x_true, label="true", "ro", markersize=5)
plot(solpqn.x, label="pqn", "g^", markersize=1)
legend()
subplot(133)
plot(x_true - solspg.x, label="spg error", "r", markersize=5)
plot(x_true - solpqn.x, label="pqn error", "g", markersize=1)
legend()
tight_layout()
loglog(solspg.ϕ_trace, label="spg")
loglog(solpqn.ϕ_trace, label="pqn")
legend()
PyObject <matplotlib.legend.Legend object at 0x14372af40>