clear all; close all; $\%$ Start fresh

$\%$Organizing Inputs$\%$

f $=$ @$($x$)$ sin$(3*$pi$*$cos$(2*$pi$*$x$).*$sin$($pi$*$x$))$;

a $=-3$; b $=5$; n $=4^9$;

x$0=$ linspace$($a$,$b$,$n$)$; $\%$ Vector containing initial starting points

q $=$ zeros$($size$($x$0))$; $\%$ Preallocate a vector for storing roots.

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

tic

for i$=1$:n

q$($i$)=$ fzero$($f$,$x$0($i$))$;

end

t$1=$toc

$\%$Processing Outputs$\%$

q $=$ unique$($q$)$; $\%$ keep roots with unique values only.

showsavePlot $=$ true;

switch showsavePlot

case true

$\%$Plot the function and roots if possible

xx $=$ linspace$($a$,$b$,1001)$;

fig $=$ figure$(\text{'}$Position$\text{'},[1001001200300])$;

plot$($xx$,$f$($xx$),\text{'}-$k$\text{'},$'linewidth',$2)$;

hold on

plot$($q$,$f$($q$),\text{'}$o$\text{'},$'markerfacecolor',$\text{'}$r$\text{'})$

xlim$([$a$,$b$])$; ylim$([-1,1])$;

yticks$([-101])$

xlabel$(\text{'}$x$\text{'})$; ylabel$(\text{'}$f$($x$)\text{'})$;

pbaspect$([411])$

print$($fig$,$'MySavedPlot',$\text{'}-$dpng$\text{'})$

end

$\%$ Create a parallel pool if none exists

if isempty$($gcp$())$

parpool$()$;

end

tic

parfor i$=1$:n

q$($i$)=$ fzero$($f$,$x$0($i$))$;

end

tp$=$ toc

$\%$Processing Outputs$\%$

$\%$q $=$ unique$($q$)$; $\%$ keep roots with unique values only.

q$=$ uniquetol$($q$,1$e$-10)$;

showsavePlot $=$ true;

switch showsavePlot

case true

$\%$Plot the function and roots if possible

xx $=$ linspace$($a$,$b$,1001)$;

fig $=$ figure$(\text{'}$Position$\text{'},[1001001200300])$;

plot$($xx$,$f$($xx$),\text{'}-$k$\text{'},$'linewidth',$2)$;

hold on

plot$($q$,$f$($q$),\text{'}$o$\text{'},$'markerfacecolor',$\text{'}$r$\text{'})$

xlim$([$a$,$b$])$; ylim$([-1,1])$;

yticks$([-101])$

xlabel$(\text{'}$x$\text{'})$; ylabel$(\text{'}$f$($x$)\text{'})$;

pbaspect$([411])$

print$($fig$,$'MySavedPlot',$\text{'}-$dpng$\text{'})$

end

speedup$=$t$1/$tp

eff$=$ speedup$/$n

Convert the above code of matlab to python and R