IPython notebooks with demo code intended as a companion to the book "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by J. Nathan Kutz and Steven L. Brunton
Home Page: http://www.databookuw.com/
In the notebook here
https://github.com/dylewsky/Data_Driven_Science_Python_Demos/blob/master/CH09/CH09_SEC03_ERA_OKID.ipynb
OKID errors if the system is not square, i.e., if q != p
The error happens in the indexing here
for i in range(LL):
Ybar1[:,:,i] = Ybar[:,QQ+(QQ+PP)*i : QQ+(QQ+PP)*i+QQ]
Ybar2[:,:,i] = Ybar[:,QQ+(QQ+PP)*i+QQ : QQ+(QQ+PP)*(i+1)]
in Chapter 1, PCA ipynb, some lines contain syntax errors:
ax2.plot(<plotting things here>,'-', Color="b", LineWidth=5)
this raises an AttributeError and can be easily fixed by:
ax2.plot(<plotting things here>,'-', c="b", lw=5) or
ax2.plot(<plotting things here>,'-', color="b", linewidth=5)
:)
As an example, the following code, from CH01_SEC04_1_Linear.ipynb,
plt.plot(a, x*a, Color='k', LineWidth=2, label='True line') # True relationship
plt.plot(a, b, 'x', Color='r', MarkerSize = 10, label='Noisy data') # Noisy measurements
should now be:
plt.plot(a, x*a, Color='k', linewidth=2, label='True line') # True relationship
plt.plot(a, b, 'x', Color='r', markersize = 10, label='Noisy data') # Noisy measurements
The scipy.optimize.minimize method tends to be really slow for solving the basis pursuit problem (ex. in the compressed sensing context) especially when we are dealing with less sparse vectors. A much faster alternative could be used by modelling the problem as a linear programming problem and using scipy.optimize.linprog instead
def basis_pursuit_v2(A, y):
"""Objective : minimize( norm(x, 1) )
Subject to: A * x == y
"""
numCols = A.shape[1]
vF = np.ones((2 * numCols, 1))
mAeq = np.hstack([A, -A])
vBeq = y
vUV = linprog(vF, None, None, mAeq, vBeq, bounds=(0, np.inf))
return vUV.x[:numCols] - vUV.x[numCols:]This answer explains the LP modelling
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