# Rosenbrock banana¶

Here, we perform optimization for the Rosenbrock banana function, which does not require an AMICI model. In particular, we try several ways of specifying derivative information.

[1]:

import pypesto
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

%matplotlib inline


## Define the objective and problem¶

[2]:

# first type of objective
objective1 = pypesto.Objective(fun=sp.optimize.rosen,
hess=sp.optimize.rosen_hess)

# second type of objective
def rosen2(x):
return sp.optimize.rosen(x), sp.optimize.rosen_der(x), sp.optimize.rosen_hess(x)

dim_full = 10
lb = -2 * np.ones((dim_full, 1))
ub = 2 * np.ones((dim_full, 1))

problem1 = pypesto.Problem(objective=objective1, lb=lb, ub=ub)
problem2 = pypesto.Problem(objective=objective2, lb=lb, ub=ub)


## Illustration¶

[3]:

x = np.arange(-2, 2, 0.1)
y = np.arange(-2, 2, 0.1)
x, y = np.meshgrid(x, y)
z = np.zeros_like(x)
for j in range(0, x.shape[0]):
for k in range(0, x.shape[1]):
z[j,k] = objective1([x[j,k], y[j,k]], (0,))

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_surface(X=x, Y=y, Z=z)

[3]:

<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x121e42908>


## Run optimization¶

[4]:

optimizer = pypesto.ScipyOptimizer()
n_starts = 20

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


## Compute profiles¶

The profiling routine needs a problem, a results object and an optimizer.

Moreover it accepts an index of integer (profile_index), whether or not a profile should be computed.

Finally, an integer (result_index) can be passed, in order to specify the local optimum, from which profiling should be started.

[5]:


result1 = pypesto.parameter_profile(
problem=problem1,
result=result1,
optimizer=optimizer,
profile_index=np.array([0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]),
result_index=1)


## Visualize and analyze results¶

pypesto offers easy-to-use visualization routines:

[6]:

import pypesto.visualize

pypesto.visualize.waterfall(result1)
pypesto.visualize.parameters(result1)

# specify the parameters, for which profiles should be computed
pypesto.visualize.profiles(result1, profile_indices = [1,2,5])

[6]:

[<matplotlib.axes._subplots.AxesSubplot at 0x124363d68>,
<matplotlib.axes._subplots.AxesSubplot at 0x1245114a8>,
<matplotlib.axes._subplots.AxesSubplot at 0x1245230f0>]


If the result needs to be examined in more detail, it can easily be exported as a pandas.DataFrame:

[7]:

result1.optimize_result.as_dataframe(['fval', 'n_fval', 'n_grad', 'n_hess', 'n_res', 'n_sres', 'time'])

[7]:

fval n_fval n_grad n_hess n_res n_sres time
0 3.864669e-12 89 89 0 0 0 0.016705
1 5.391376e-12 83 83 0 0 0 0.015477
2 6.878944e-12 88 88 0 0 0 0.119707
3 7.215911e-12 91 91 0 0 0 0.037070
4 9.545020e-12 69 69 0 0 0 0.022376
5 1.244748e-11 83 83 0 0 0 0.022337
6 1.263889e-11 88 88 0 0 0 0.018748
7 1.562623e-11 86 86 0 0 0 0.022854
8 4.085166e-11 73 73 0 0 0 0.011622
9 7.246517e-11 79 79 0 0 0 0.026188
10 8.612691e-11 67 67 0 0 0 0.012368
11 1.823874e-10 76 76 0 0 0 0.013582
12 1.861598e-10 78 78 0 0 0 0.046079
13 1.922645e-10 90 90 0 0 0 0.025491
14 2.231378e-10 89 89 0 0 0 0.021747
15 2.499322e-10 73 73 0 0 0 0.042578
16 3.054340e-10 81 81 0 0 0 0.018495
17 3.370285e-10 76 76 0 0 0 0.017206
18 1.678268e-09 75 75 0 0 0 0.014224
19 3.986579e+00 71 71 0 0 0 0.043969
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