Using Python, develop a line search algorithm $($i$.$e$.$ Algorithm $4\mathrm{.}3$ and $4\mathrm{.}4)$ that given a direction p$,$ your algorithm returns the optimal point along that line $($i$.$e$.$ the optimal step length along p$).$ Please use a bi$-$section method for the interpolation function.

Example of inputs and objective function:

p $=[1,1]$T

x$0=[2,6]$T

Slanted Quadratic Function $[$f$($x$1,$x$2)=$ x$1^2+$ x$2^2-$ B$*$x$1*$x$2]$ with B $=1\mathrm{.}5$

Outputs:

Optimal step length and point found ALONG p $($i$.$e$.$ report both $\backslash$alpha

$$ and x$($k$=1)=$ x$($k$=0)+\backslash$alpha $$p$)$ and the number of function calls required to obtain x$($k$=1).$