I need help with the following code, specifically at Step $6($repeating the above with no noise$).$I cannot get the amplitude time series to plot all $9$ graphs exactly the same; the y axis values value between all of the EOFs. They should be exactly the same if it is only based on the signal.

import numpy as np

import matplotlib.pyplot as plt

# Step $1$: Define Parameters

T $=24$ # hours

N $=9$ # locations

Dt $=1$ # hour

omega $=2*$ np$.$pi $/$ T

#Step $6$: Repeat with no noise

# Function to generate data

def u$($x$,$ y$,$ t$,$ a$,$ b$,$ c$,$ alpha$)$:

return $($a $+$ b $*$ x $+$ c$)*$ np$.$cos$($alpha $*$ t$)*$ np$.$cos$(2*$ omega $*$ t$)$

# Generate data samples

np$.$random.seed$(42)$ # Set a consistent random seed

x$\_$values$\_$NN $=$ y$\_$values$\_$NN $=$ np$.$random.rand$($N$)$

t$\_$values$\_$NN $=$ np$.$arange$(0,$ T$,$ Dt$)$

data$\_$NN $=$ np$.$zeros$(($N$,$ N$,$ len$($t$\_$values$\_$NN$)))$

for i in range$($N$)$:

for j in range$($N$)$:

for k in range$($len$($t$\_$values$\_$NN$))$:

data$\_$NN$[$i$,$ j$,$ k$]=$ u$($x$\_$values$\_$NN$[$i$],$ y$\_$values$\_$NN$[$j$],$ t$\_$values$\_$NN$[$k$],1,2,3,0\mathrm{.}1)$

# Step $3$: Perform EOF analysis

correlation$\_$matrix$\_$NN $=$ np$.$corrcoef$($data$\_$NN$.$reshape$(($N $*$ N$,$ len$($t$\_$values$\_$NN$))))$

eigenvalues$\_$NN$,$ eigenvectors$\_$NN $=$ np$.$linalg.eig$($correlation$\_$matrix$\_$NN$)$

sorted$\_$indices$\_$NN $=$ np$.$argsort$($eigenvalues$\_$NN$)[$::$-1]$

eigenvalues$\_$NN $=$ eigenvalues$\_$NN$[$sorted$\_$indices$\_$NN$]$

eigenvectors$\_$NN $=$ eigenvectors$\_$NN$[$:$,$ sorted$\_$indices$\_$NN$]$

# Ensure eigenvectors are real

eigenvectors$\_$NN $=$ np$.$real$($eigenvectors$\_$NN$)$

# Plot the eigenvectors

for i in range$($N$)$:

plt$.$subplot$(3,3,$ i $+1)$

plt$.$imshow$($np$.$real$($eigenvectors$\_$NN$[$:$,$ i$]).$reshape$(($N$,$ N$)),$ cmap$=$'viridis'$)$

plt$.$title$($f$\text{'}$EOF Mode $\{$i $+1\}\text{'})$

# Map the eigenvectors

for i in range$($N$)$:

plt$.$subplot$(3,3,$ i $+1)$

# Reshape the eigenvector to the spatial grid

eigenvector$\_$map$\_$NN $=$ np$.$real$($eigenvectors$\_$NN$[$:$,$ i$]).$reshape$(($N$,$ N$))$

# Create a contour plot

plt$.$contourf$($eigenvector$\_$map$\_$NN$,$ cmap$=$'viridis'$)$

plt$.$title$($f$\text{'}$EOF Mode $\{$i $+1\}\text{'})$

plt$.$savefig$($f$\text{'}$EOF$\_$Mode$\_\{$i $+1\}.$png$\text{'},$ dpi$=600)$

# Calculate amplitude of time series

amplitude$\_$NN $=$ np$.$abs$($np$.$dot$($eigenvectors$\_$NN$.$T$,$ data$\_$NN$.$reshape$(($N $*$ N$,$ len$($t$\_$values$\_$NN$)))))$

# Plot the amplitude time series for each mode

amplitude$\_$NN $=$ np$.$abs$($np$.$dot$($eigenvectors$\_$NN$.$T$,$ data$\_$NN$.$reshape$(($N $*$ N$,$ len$($t$\_$values$\_$NN$)))))$

for i in range$($N$)$:

plt$.$figure$()$

plt$.$plot$($t$\_$values$\_$NN$,$ amplitude$\_$NN$[$i$,$ :$])$

plt$.$title$($f$\text{'}$Amplitude Time Series $($No Noise$)$ for Mode $\{$i $+1\}\text{'})$

plt$.$xlabel$(\text{'}$Time $($Hours$)\text{'})$

plt$.$ylabel$(\text{'}$Amplitude$\text{'})$

# Save the amplitude plot with the mode number in the filename

plt$.$savefig$($f$\text{'}$Amplitude$\_$NoNoise$\_$Mode$\{$i $+1\}.$png$\text{'},$ dpi$=600)$

# Show the correlation between A$1($t$)$ and A$2($t$)$

corr$\_12\_$NN $=$ np$.$corrcoef$($amplitude$\_$NN$[0,$ :$],$ amplitude$\_$NN$[1,$ :$])[0,1]$

plt$.$figure$()$

plt$.$plot$($np$.$arange$($len$($t$\_$values$\_$NN$)),[$corr$\_12\_$NN$]*$ len$($t$\_$values$\_$NN$))$

plt$.$title$(\text{'}$Correlation between A$1($t$)$ and A$2($t$)$ with No Noise'$)$

plt$.$xlabel$(\text{'}$Time $($Hours$)\text{'})$

plt$.$ylabel$(\text{'}$Amplitude$\text{'})$

# Save the correlation plot

plt$.$savefig$(\text{'}$Correlation$\_$NoNoise.png$\text{'},$ dpi$=600)$

# Show or save the plots as needed

plt$.$show$()$