$3$ Consider the following set of nonuniform nodal points $\{hat(x{)}_i{\}}_i=0^{p+1}$ on the interval

$(-1,1)$ :

hat$(x{)}_i=cos(\frac{2i+1}{2(p+1)}),i=0,$dots,$p$

In polynomial$\_$interpolation. py you will find a function with definition

def nonuniform$\_$poly$\_$interpolation$($a$,$b$,$p$,$n$,$x$,$f$,$produce$\_$fig$)$

The function should return as output:

interpolant $-$ a numpy $.$ndarray of shape $,).$

fig $-$ a matplotlib.figure.Figure when the Boolean input produce$\_$fig

is True and None if produce$\_$fig is False.

Complete the function to evaluate the $p$ th$-$order polynomial interpolant $p_p(x)$ of

a function $f$ at a set of points $\{x_j{\}}_j=0^{n-1}.$ The nodal interpolation points should be

nonuniformly spaced over the interval $a,b$ and be a linearly scaled and shifted

version of those shown in $(2),$ using a mapping $M$:$[-1,1][a,b]$ such that

$M(-1)=$a and $M(1)=b.$

The function must call lagrange$\_$poly from Q$1$ and use tol $=1\mathrm{.}0e-10.$

If produce$\_$fig is true then the function should also plot $($on the same set

of axes$)$ the function $f$ evaluated at the points $\{x_j{\}}_j=0^{n-1}$ and the interpolant $p_p(x)$

evaluated at the same points.

give the code for non$\_$polynomial interpretation