$95.$ We construct the SPCA process using the R language. The process is repeated to observe how each element of the vector $\backslash ($ v $\backslash )$ changes with the number of iterations. Fill in the blanks, execute the process, and display the output as a graph.

$```$

# Data Generation

n $=100$; p $=5$; x $=$ np$.$randon.normal$($size$=$n$*$p$).$reshape$(-$l$,$

p$)$

lambd$\_$seq $=$ np$.$arange $(0,1$l$)/10$

# computation of u$,$v

lanbd $=[0\mathrm{.}001,0\mathrm{.}00001]$; nl $=100$

g $=$ np : zeros$(($n$,$ p$))$

for j in range $($p$)$: x$[$:$,$ j$]=$ x$[$:$,$ j$]-$ np$.$nean$($x$[$:$,$ j$])$

for j in range $($p$)$: x$[$:$,$ j$]=$ x$[$:$,$ j$]/$ np$.$sqrt$($np$.$sum$($np$.$

square$($x$[$:$,$ j$])))$

r $=[0]*$ n; v $=$ np$.$randon nornal $($size$=$p$)$

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

z $=$ np$.$dot$($x$,$ v$)$; u $=$ np$.$dot$($x$.$T$,$ z$)$

if np$.$sum$($np$.$square$($u$))>0\mathrm{.}00001$: u $=$ u $/$ np$.$sqrt$($np$.$

sum$($np$.$square$($u$)))$

for k in range $($p$)$:

nl $=$ list$($np$.$arange$($k$))$; nl $=$ list$($np$.$arange$($k$+$l$,$ p

$))$; z $=$ nl $+$ nl

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

r$[$i$]=($np$.$sum$($u $*$ x$[$i$,$:$])$

$-$ np$.$sum$($np$.$square$($u$))*$ sum$($x$[$i$,$ z$]*$

v$[$z$]))$

s $=$ np$.$sum$($np$.$dot$($x$[$:$,$ k$],$ r$))/$n

v$[$k$]=$ ## Blank$($I$)$ ##

if np$.$sum$($np$.$square$($v$))>0\mathrm{.}0000$l: v $=$ ## Blank$(2)$ ##

g$[$h$,$:$]=$ v

# Display

g$\_$nax $=$ np$.$max$($g$)$; g$\_$nin $=$ np$.$min$($g$)$

cycle $=$ plt$.$rcParams$["$axes$.$prop$\_$cycle"$].$by$\_$key$()["$color$"]$

fig $=$ plt$.$figure$($figsize$=(8,5))$

$```$