Debug this code and ensure that the error indicated below is obtained$/$solved$.$

import numpy as np

def construct$\_$A$($n$)$:

A $=$ np$.$zeros$(($n$,$ n$))$

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

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

if i $<$ j:

A$[$i$,$ j$]=$ max$(0,$ n$/10+2*($i $-$ j$))$

else:

A$[$i$,$ j$]=$ max$(0,$ n$/10-2*($i $-$ j$))$

return A

def construct$\_$B$($n$)$:

return np$.$array$([(-1)**$i for i in range$($n$)])$

def forward$\_$substitution$($L$,$ b$)$:

n $=$ L$.$shape$[0]$

y $=$ np$.$zeros$\_$like$($b$)$

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

y$[$i$]=($b$[$i$]-$ np$.$dot$($L$[$i$,$ :i$],$ y$[$:i$]))/$ L$[$i$,$ i$]$

return y

def DOS$($A$,$ B$,$ x$0,$ w$1,$ w$2,$ tol$=1$e$-6)$:

# Handle scalar x$0$ input

if np$.$isscalar$($x$0)$:

x$0=$ np$.$full$($B$.$shape, x$0)$

D $=$ np$.$diag$($np$.$diag$($A$))$

L $=$ np$.$tril$($A$,-1)$

U $=$ np$.$triu$($A$,1)$

x $=$ x$0$

iteration$\_$count $=0$

error $=$ np$.$inf

while error $>$ tol:

# Step $1$: Solve D$*$x$($k$+1/2)=$ w$1*$D $+($w$1-1)*($L$+$U$)*$ x$($k$)+(1-$w$1)*$B

x$\_$half $=($np$.$linalg.solve$($D$,$ w$1*$ B $+(1-$ w$1)*($np$.$dot$($L $+$ U$,$ x$))))$

# Step $2$: Solve $($D$+$w$2*$L$)*$ x$($k$+1)=[(1-$w$2)*$D $-$ w$2*$U$]*$x$($k$+1/2)+$ w$2*$B

x$\_$new $=$ forward$\_$substitution$($D $+$ w$2*$ L$,(1-$ w$2)*$ np$.$dot$($D$,$ x$\_$half$)-$ w$2*$ np$.$dot$($U$,$ x$\_$half$)+$ w$2*$ B$)$

error $=$ np$.$linalg.norm$($x$\_$new $-$ x$)$

x $=$ x$\_$new

iteration$\_$count $+=1$

return x$,$ error, iteration$\_$count

# Parameters for the DOS function

n $=200$

w$1=0\mathrm{.}3$

w$2=0\mathrm{.}6$

tol $=0\mathrm{.}02$

x$0=0$ # Initial guess for the solution

A $=$ construct$\_$A$($n$)$

B $=$ construct$\_$B$($n$)$

# Execute the DOS function

solution, err, iterations $=$ DOS$($A$,$ B$,$ x$0,$ w$1,$ w$2,$ tol$)$

print$("$Solution:$",$ solution$)$

print$("$Error:$",$ err$)$

print$("$Iterations:$",$ iterations$)$

##This is the encountered error RuntimeWarning: invalid value encountered in scalar subtract y$[$i$]=($b$[$i$]-$ np$.$dot$($L$[$i$,$ :i$],$ y$[$:i$]))/$ L$[$i$,$ i$]$