Code needs to be fixed.I am not getting any plots and despite the changes, I keep getting the same type of errors. Publish the entire edited code once ensuring the code actually runs and there are plots. Here is the code: import numpy as np

from scipy.linalg import solve, cholesky

from scipy.optimize import minimize

from skopt import gp$\_$minimize

import matplotlib.pyplot as plt

def gaussian$\_$rbf$($x$,$ x$\_$prime, beta$)$:

return np$.$exp$(-$beta $*$ np$.$linalg.norm$($x $-$ x$\_$prime$)**2)$

def construct$\_$interpolation$\_$matrix$($nodes$,$ beta$)$:

N $=$ len$($nodes$)$

K $=$ np$.$zeros$(($N$,$ N$))$

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

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

K$[$i$,$ j$]=$ gaussian$\_$rbf$($nodes$[$i$],$ nodes$[$j$],$ beta$)$

return K

def conditioning$\_$analysis$($N$,$ m$,$ beta$)$:

nodes $=$ np$.$linspace$(0,1,$ N$)$

K $=$ construct$\_$interpolation$\_$matrix$($nodes$,$ beta$)$

selected$\_$indices $=$ np$.$random.choice$($N$,$ m$,$ replace$=$False$)$

selected$\_$nodes $=$ nodes$[$selected$\_$indices$]$

condition$\_$full $=$ np$.$linalg.cond$($K$)$

condition$\_$partial $=$ np$.$linalg.cond$($K$[$selected$\_$indices$][$:$,$ selected$\_$indices$])$

return condition$\_$full, condition$\_$partial

def objective$\_$function$($x$)$:

x$\_$scalar $=$ np$.$atleast$\_1$d$($x$)[0]$

return $-$float$($x$\_$scalar$**2+$ np$.$sin$(5*$ x$\_$scalar$))$ # Ensure a scalar value is returned

def gradient$\_$hessian$($x$)$:

df$\_$dx $=2*$ x $*$ np$.$exp$(-(1-$ x$)**2)-4*$ x $*(1-$ x$)*$ np$.$exp$(-(1-$ x$)**2)$

d$2$f$\_$dx$2=-2*$ np$.$exp$(-(1-$ x$)**2)+4*$ x $*(1-$ x$)*$ np$.$exp$(-(1-$ x$)**2)-4*(1-$ x$)*$ np$.$exp$(-(1-$ x$)**2)$

return df$\_$dx$,$ d$2$f$\_$dx$2$

def optimize$\_$with$\_$newton$($initial$\_$guess, max$\_$iter$=10)$:

x$\_$opt $=$ initial$\_$guess

for $\_$ in range$($max$\_$iter$)$:

df$\_$dx$,$ d$2$f$\_$dx$2=$ gradient$\_$hessian$($x$\_$opt$)$

x$\_$opt $=$ x$\_$opt $-$ df$\_$dx $/$ d$2$f$\_$dx$2$

return x$\_$opt

def gaussian$\_$process$\_$optimization$($initial$\_$points, objective$\_$function, bounds, n$\_$iter$=10)$:

def objective$\_$function$\_$gp$($X$)$:

return $[-$float$($objective$\_$function$($x$))$ for x in X$]$ # Ensure a list of scalars is returned

result $=$ gp$\_$minimize$($objective$\_$function$\_$gp$,$ bounds, acq$\_$func$="$LCB$",$ n$\_$calls$=$n$\_$iter $+1,$ random$\_$state$=42,$ x$0=$initial$\_$points$)$

return result.x$[0]$

# Task $1$: Analyze conditioning

N $=10$

m $=5$

beta $=1\mathrm{.}0$

condition$\_$full, condition$\_$partial $=$ conditioning$\_$analysis$($N$,$ m$,$ beta$)$

print$($f$"$Conditioning for full matrix: $\{$condition$\_$full$\}")$

print$($f$"$Conditioning for partial matrix: $\{$condition$\_$partial$\}")$

# Task $2$: Optimize with Newton's method

initial$\_$guess$\_$newton $=0\mathrm{.}5$

x$\_$opt$\_$newton $=$ optimize$\_$with$\_$newton$($initial$\_$guess$\_$newton$)$

print$($f$"$Optimal solution with Newton's method: $\{$x$\_$opt$\_$newton$\}")$

# Task $3$: Gaussian process optimization

initial$\_$points$\_$gp $=[[0\mathrm{.}2],[0\mathrm{.}5],[0\mathrm{.}8]]$ # Example initial points

bounds$\_$gp $=[(0\mathrm{.}0,1\mathrm{.}0)]$

x$\_$opt$\_$gp $=$ gaussian$\_$process$\_$optimization$($initial$\_$points$\_$gp$,$ objective$\_$function, bounds$\_$gp$,$ n$\_$iter$=13)$ # Set n$\_$iter to $13$ or higher

print$($f$"$Optimal solution with Gaussian process optimization: $\{$x$\_$opt$\_$gp$\}")$

# Task $4$: Compare methods

x$\_$values $=$ np$.$linspace$(0,1,1000)$

y$\_$true $=$ objective$\_$function$($x$\_$values$)$

plt$.$plot$($x$\_$values, y$\_$true, label$=$"True Function"$)$

plt$.$scatter$($x$\_$opt$\_$newton, objective$\_$function$($x$\_$opt$\_$newton$),$ color$=$"red", label$=$"Newton's Method"$)$

plt$.$scatter$($x$\_$opt$\_$gp$,$ objective$\_$function$($x$\_$opt$\_$gp$),$ color$=$"green", label$=$"Gaussian Process"$)$

plt$.$legend$()$

plt$.$xlabel$("$x$")$

plt$.$ylabel$("$f$($x$)")$

plt$.$title$("$Comparison of Optimization Methods"$)$

plt$.$show$()$