loiseaujc

# --> Import standard Python libraries.
import numpy as np

# --> Import sklearn utility functions to create derived-class objects.
from sklearn.base import BaseEstimator, ClassifierMixin

# --> Redefine the Heavisde function.
H = lambda x: np.heaviside(x, 1).astype(np.int)

class Rosenblatt(BaseEstimator, ClassifierMixin):

loiseaujc

"""
Spectral Proper Orthogonal Decomposition
-----------------------------------------

This module implements the Spectral Proper Orthogonal Decomposition class. The
present implementation corresponds to the batch algorithm originally proposed
in [1]. Note that a streaming algorithm has also been proposed in [2].

References
----------

loiseaujc

# --> Import standard Python libraries.
import numpy as np

# --> Import sklearn utility functions to create derived-class objects.
from sklearn.base import BaseEstimator, ClassifierMixin

# --> Redefine the Heaviside function.
def H(x): return np.heaviside(x-0.5, 1).astype(np.int)

loiseaujc

# --> Import standard Python libraries.
import numpy as np
from scipy.special import expit
from scipy.linalg import norm

# --> Import sklearn utility functions.
from sklearn.base import BaseEstimator, ClassifierMixin


class LogisticRegression_GD(BaseEstimator, ClassifierMixin):

loiseaujc

# --> Import standard Python libraries.
import numpy as np
from scipy.special import expit
from scipy.linalg import norm

# --> Import sklearn utility functions.
from sklearn.base import BaseEstimator, ClassifierMixin


class LogisticRegression_Newton(BaseEstimator, ClassifierMixin):

loiseaujc

# Author : Jean-Christophe Loiseau <[email protected]>
# Date : July 2020

# --> Standard python libraries.
import numpy as np
from scipy.linalg import pinv, eigh, eig

def dmd_analysis(x, y=None, rank=2):
  
  # --> Partition data matrix into X and Y.

loiseaujc

# --> Import standard Python libraries.
import numpy as np
from scipy.special import softmax
from scipy.linalg import norm
from scipy.optimize import line_search, minimize_scalar

# --> Import sklearn utility functions.
from sklearn.base import BaseEstimator, ClassifierMixin

def SoftMax(x):

loiseaujc

using LinearAlgebra

function sensor_placement(Ψ)
	# --> Compute the QR w/ column pivoting decomposition of Ψ.
	_, _, p = qr(transpose(Ψ), Val(true))
	return p[1:size(Ψ, 2)]
end

loiseaujc

from scipy.linalg import qr

def sensor_placement(Psi):
  # --> Perform QR w/ column pivoting.
  _, _, p = qr(Psi.T, pivoting=True, mode="economic")
  return p[:Psi.shape[1]]

loiseaujc

using LinearAlgebra
using Convex, SCS

# --> Direct resolution of the measurement equation.
lstsq(Θ, y) = Θ \ y

# --> Constrained least-squares formulation.
function cstrnd_lstsq(Θ, y, Σ)
        # --> Optimization variable.
        a = Convex.Variable(length(Σ))