Fixed parameters¶

In this notebook we will show how to use fixed parameters. Therefore, we employ our Rosenbrock example. We define two problems, where for the first problem all parameters are optimized, and for the second we fix some of them to specified values.

Define problem¶

[1]:

import pypesto
import pypesto.visualize
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt

%matplotlib inline

[2]:

objective = pypesto.Objective(fun=sp.optimize.rosen,
                              grad=sp.optimize.rosen_der,
                              hess=sp.optimize.rosen_hess)

dim_full = 5
lb = -2 * np.ones((dim_full,1))
ub = 2 * np.ones((dim_full,1))

problem1 = pypesto.Problem(objective=objective, lb=lb, ub=ub)

x_fixed_indices = [1, 3]
x_fixed_vals = [1, 1]
problem2 = pypesto.Problem(objective=objective, lb=lb, ub=ub,
                           x_fixed_indices=x_fixed_indices,
                           x_fixed_vals=x_fixed_vals)

Optimize¶

[3]:

optimizer = pypesto.ScipyOptimizer()
n_starts = 10

result1 = pypesto.minimize(problem=problem1, optimizer=optimizer,
                           n_starts=n_starts)
result2 = pypesto.minimize(problem=problem2, optimizer=optimizer,
                           n_starts=n_starts)

Visualize¶

[4]:

fig, ax = plt.subplots()
pypesto.visualize.waterfall(result1, ax)
pypesto.visualize.waterfall(result2, ax)
pypesto.visualize.parameters(result1)
pypesto.visualize.parameters(result2)
pypesto.visualize.parameters(result2, free_indices_only=False)

[4]:

<matplotlib.axes._subplots.AxesSubplot at 0x7fe98fe12650>

../_images/example_fixed_parameters_8_1.png

../_images/example_fixed_parameters_8_2.png

../_images/example_fixed_parameters_8_3.png

../_images/example_fixed_parameters_8_4.png

[5]:

result1.optimize_result.as_dataframe(['fval', 'x', 'grad'])

[5]:

	fval	x	grad
0	4.689854e-14	[0.9999999815635604, 0.9999999601303594, 0.999...	[1.1618317897690609e-06, 1.2817350405303142e-0...
1	5.590260e-14	[0.9999999788673749, 0.9999999710531022, 0.999...	[-5.3696059283362676e-06, -3.17862832097996e-0...
2	3.799999e-13	[0.9999999894531796, 0.9999999867856568, 1.000...	[-3.1728126266944613e-06, -1.6951548081005115e...
3	4.110300e-13	[1.0000000452200102, 1.0000000894442573, 1.000...	[4.887460487692825e-07, 3.7999227735179252e-06...
4	6.110801e-13	[0.9999999640563018, 0.9999999933489752, 0.999...	[-2.6166434580847274e-05, 8.102944813282283e-0...
5	1.231774e-12	[1.0000000581023145, 1.000000113974549, 1.0000...	[1.0082380613547457e-06, 1.8071346123806702e-0...
6	6.918491e-12	[1.0000000005661727, 1.0000001076896814, 1.000...	[-4.262180210516511e-05, 7.700439519900304e-05...
7	2.552430e-11	[0.9999999192005172, 1.0000000369812814, 1.000...	[-7.959368869249685e-05, -8.749066771695052e-0...
8	2.855055e-11	[0.9999995268339968, 0.9999992696810054, 0.999...	[-8.735140622961871e-05, 4.373181014008344e-05...
9	3.930839e+00	[-0.9620508371994185, 0.9357391790840979, 0.88...	[5.2019939965397555e-05, 2.44790688288532e-05,...

[6]:

result2.optimize_result.as_dataframe(['fval', 'x', 'grad'])

[6]:

	fval	x	grad
0	3.757636e-21	[0.9999999999987625, 1.0, 1.0000000000008613, ...	[-9.92438575763029e-10, nan, 8.630336445497983...
1	3.403187e-16	[1.000000000296693, 1.0, 0.9999999993226122, 1...	[2.3794769983646036e-07, nan, -6.7874258776674...
2	1.078998e-15	[0.9999999994275696, 1.0, 0.9999999986532816, ...	[-4.5908920971880386e-07, nan, -1.349411838817...
3	1.986582e-15	[0.9999999981059375, 1.0, 0.9999999990468542, ...	[-1.5190380919959983e-06, nan, -9.550520753635...
4	1.777511e-14	[1.0000000013724608, 1.0, 0.9999999967022452, ...	[1.100713572463121e-06, nan, -3.30435034796972...
5	2.344376e-14	[0.9999999959141576, 1.0, 0.9999999996553852, ...	[-3.2768456252559055e-06, nan, -3.453040106231...
6	2.096868e-13	[0.9999999984695723, 1.0, 1.0000000066163943, ...	[-1.2274029922568326e-06, nan, 6.6296271449766...
7	3.989975e+00	[-0.9949747468749881, 1.0, 0.9999999997811084,...	[-3.507845658390352e-08, nan, -2.1932935463983...
8	3.989975e+00	[-0.9949747444243423, 1.0, 1.000000008470282, ...	[1.900857428349667e-06, nan, 8.487222652784575...
9	3.989975e+00	[-0.9949747299382655, 1.0, 1.0000000336260297,...	[1.334441878420023e-05, nan, 3.369328314657676...