improve this following code with my suggestions.  The following code script is written in Python and uses the Ceemdan algorithm and Hilbert weighted frequency for stock predictions. now improvwmit aanc give it extrApowers to predict
#Import necessary libraries
import numpy as np
import pandas as pd
from scipy.signal import hilbert, ceemdan
#Load data
data = pd.read_csv(‘stocks.csv’)
#Compute Hilbert-weighted frequency
hilb_freq = hilbert(data, axis=0)
#Compute Ceemdan algorithm
ceem = ceemdan(hilb_freq, axis=0)
#Compute functional connectivity density (FCD)
fcd = np.zeros(data.shape[0])
for i in range(data.shape[0]):
for j in range(data.shape[1]):
fcd[i] += ceem[i, j]
#Generate a mapping of FCD values
fcd_map = pd.DataFrame(fcd)
#Display the mapping
print(fcd_map)





import numpy as np
from scipy.signal import hilbert

def hilbert_transform(imf):
“”“Compute the Hilbert transform for a given IMF.”“”
analytic_signal = hilbert(imf)
return analytic_signal


def calculate_analytical_signal(imf):
“”“Calculate the corresponding analytical signal for a given IMF.”“”
analytic_signal = hilbert_transform(imf)
amplitude_envelope = np.abs(analytic_signal)
instantaneous_phase = np.unwrap(np.angle(analytic_signal))
return amplitude_envelope, instantaneous_phase




def calculate_analytical_signal(imf):
“”“Calculate the corresponding analytical signal for a given IMF.”“”
analytic_signal = hilbert_transform(imf)
amplitude_envelope = np.abs(analytic_signal)
instantaneous_phase = np.unwrap(np.angle(analytic_signal))
return amplitude_envelope, instantaneous_phase





def calculate_hwf(amplitude_envelope, instantaneous_phase):
“”“Calculate the HWF of a given IMF.”“”
dt = 1 # Assuming a constant time interval
instantaneous_frequency = np.diff(instantaneous_phase) / (2.0 * np.pi * dt)
weighted_frequency = np.sum(amplitude_envelope * instantaneous_frequency) / np.sum(amplitude_envelope)
return weighted_frequency








for imf in imfs:
amplitude_envelope, instantaneous_phase = calculate_analytical_signal(imf)
hwf = calculate_hwf(amplitude_envelope, instantaneous_phase)
hwfs.append(hwf)
import numpy as np
import pandas as pd
from scipy.signal import hilbert, ceemdan

# Load data
data = pd.read_csv(‘stocks.csv’)

# Function to compute Hilbert Transform
def hilbert_transform(imf):
“”“Compute the Hilbert transform for a given IMF.”“”
analytic_signal = hilbert(imf)
return analytic_signal

# Function to calculate the analytical signal of IMF
def calculate_analytical_signal(imf):
“”“Calculate the corresponding analytical signal for a given IMF.”“”
analytic_signal = hilbert_transform(imf)
amplitude_envelope = np.abs(analytic_signal)
instantaneous_phase = np.unwrap(np.angle(analytic_signal))
return amplitude_envelope, instantaneous_phase

# Function to calculate HWF
def calculate_hwf(amplitude_envelope, instantaneous_phase):
“”“Calculate the HWF of a given IMF.”“”
dt = 1 # Assuming a constant time interval
instantaneous_frequency = np.diff(instantaneous_phase) / (2.0 * np.pi * dt)
weighted_frequency = np.sum(amplitude_envelope * instantaneous_frequency) / np.sum(amplitude_envelope)
return weighted_frequency

# Compute Ceemdan algorithm
imfs = ceemdan(data.values, axis=0)

# Compute Hilbert-Weighted Frequencies (HWFs) for each IMF
hwfs = []
for imf in imfs:
amplitude_envelope, instantaneous_phase = calculate_analytical_signal(imf)
hwf = calculate_hwf(amplitude_envelope, instantaneous_phase)
hwfs.append(hwf)

# Compute functional connectivity density (FCD)
fcd = np.zeros(data.shape[0])
for i in range(data.shape[0]):
for j in range(data.shape[1]):
fcd[i] += imfs[i, j]

# Generate a mapping of FCD values
fcd_map = pd.DataFrame(fcd)

# Display the mapping
print(fcd_map)
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Modularize the code: Break the code into smaller functions that can be reused and make the code more readable.

Expand the functionality: Integrate additional features and techniques from the provided research articles, such as using Deep Learning (LSTM) and other hybrid models for improved predictions.

for example commence the improvement like this  updated version of the script with improvements, and continue it:


import numpy as np import pandas as pd from scipy.signal import hilbert, ceemdan # Load data data = pd.read_csv('stocks.csv') def hilbert_transform(imf): """Compute the Hilbert transform for a given IMF.""" analytic_signal = hilbert(imf) return analytic_signal def calculate_analytical_signal(imf): """Calculate the corresponding analytical signal for a given IMF.""" analytic_signal = hilbert_transform(imf) amplitude_envelope = np.abs(analytic_signal) instantaneous_phase = np.unwrap(np.angle(analytic_signal)) return amplitude_envelope, instantaneous_phase def calculate_hwf(amplitude_envelope, instantaneous_phase): """Calculate the HWF of a given IMF.""" dt = 1 # Assuming a constant time interval instantaneous_frequency = np.diff(instantaneous_phase) / (2

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