Use a separate Matlab script to perform the following:

Load the datasets, and plot them in separate figures using Matlab$$s scatter plotting function.

Which basis function is appropriate? $($trig or poly$)$

Should you use approximation or interpolation? J

Use your func$\_$fit function to perform both approximation and interpolation on the given datasets

Plot the approximator and interpolant with different colors on top of the scatter plot of each dataset.

data:$($in test.txt$)$

X$1=[1\mathrm{.}1,2\mathrm{.}2,3\mathrm{.}3,4\mathrm{.}4,0\mathrm{.}5]$

Y$1=[0\mathrm{.}1,1\mathrm{.}2,2\mathrm{.}3,3\mathrm{.}4,4\mathrm{.}5]$

X$2=[0\mathrm{.}5,1\mathrm{.}5,2\mathrm{.}5,3\mathrm{.}5,4\mathrm{.}5]$

Y$2=[4\mathrm{.}5,3\mathrm{.}5,2\mathrm{.}5,1\mathrm{.}5,0\mathrm{.}5]$

funfit:

function $[$coefficient$\_$vector$]=$ func$\_$fit$($X$,$Y$,$type,basis,parameters$)$

if contains$($type$,$ 'approximate'$)$

if contains$($basis$,$ 'poly'$)$

m $=$ parameters;

X$\_$design $=$ ones$($length$($X$),$ m$+1)$;

for i $=1$:m

X$\_$design$($:$,$ i$+1)=$ X$.^$i;

end

results $=$ X$\_$design' $*$ X$\_$design;

results $=$ results $\backslash ($X$\_$design' $*$ Y$)$;

coefficient$\_$vector $=$ results;

return

elseif contains$($basis$,$ 'trig'$)$

X$\_$trig $=[$sin$($X$),$ cos$($X$)]$;

result$2=$ X$\_$trig' $*$ X$\_$trig;

result$2$s $=$ result$2\backslash ($X$\_$trig' $*$ Y$)$;

coefficient$\_$vector $=$ result$2$s;

return

end

elseif contains$($type$,$ 'interpolate'$)$

if contains$($basis$,$'poly'$)$

x$\_$transpose $=$ X$\text{'}$;

result $=$ x$\_$transpose $*$ X;

results $=$ result $\backslash$ x$\_$transpose $*$ Y;

coefficient$\_$vector $=$ results;

return

elseif contains$($basis$,$ 'trig'$)$

X$\_$trig $=[$sin$($X$),$ cos$($X$)]$;

result$1=$ X$\_$trig' $*$ X$\_$trig;

result$1$s $=$ result$1\backslash ($X$\_$trig' $*$ Y$)$;

coefficient$\_$vector $=$ result$1$s;

return;

end

end

end