loiseaujc

import numpy as np
import matplotlib.pyplot as plt
from scipy.linalg import solve_continuous_lyapunov as clyap
from scipy.linalg import svd

# --> Utility function.
vec2array = lambda x, ny, nz : x.reshape(ny, nz)
array2vec = lambda x : x.flatten()

# --> Differential operators.

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loiseaujc

using StructuredOptimization

"""
Simple implementation of basis pursuit denoising using StructuredOptimization.jl
INPUT
-----
C : The measurement matrix.
Ψ : Basis in which x is assumed to be sparse.
y : Pixel measurements.
λ : (Optional) Sparsity knob.

loiseaujc

using StructuredOptimization

"""
Simple implementation of basis pursuit denoising using StructuredOptimization.jl

INPUT
-----
m, n : Size of the image in both direction.
idx : Linear indices of the measured pixels.
y : Pixel measurements.

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))

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

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

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# --> 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

# 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.