Need help solving function thanks def minGolden$($func$,$ xl$,$ xu$,$ tol $=1$e$-4,$ maxit $=50,*$args$)$: #minGolden function

$"""$Finds the minimum of a function using golden section search method

minGolden$($func$,$ xl$,$ xu$,$ tol $=1$e$-4,$ maxit $=50,*$args$)$

Finds the minimum of a one$-$dimensional function within an interval

using golden section search method

Input:

$-$ func: an anonymous function for f$($x$)$

$-$ xl$,$ xu: lower and upper limits of the interval

$-$ tol : error tolerance $(\%)($default $=0\mathrm{.}0001\%)$

$-$ maxit: maximum number of iterations $($default $=50)$

$-*$args: any extra arguments to func $($optional$)$

Output:

$-$ xmin: the location of the minimum

$-$ fx: the minimum value of function

$-$ err: relative approximate error $(\%)$

$-$ iter: number of iterations

$"""$

small $=1$e$-20$ # a small number

phi $=(1+5**0\mathrm{.}5)/2$; #golden ratio

iter $=0$ # initial value of iteration count

err $=1000$ # initial value of relative approximate error $(\%)$

d $=($phi $-1)*($xu $-$ xl$)$

x$1=$ xl $+$ d

x$2=$ xu $-$ d

f$1=$ func$($x$1,*$args$)$ #func value at x$1$

f$2=$ func$($x$2,*$args$)$ #func value at x$2$

# d $----->|$

# arrangement of points: xl $.....$ x$2.....$ x$1.....$ xu

# d $------>|$

while err $>$ tol and iter $$ maxit: # while err is greater than the tolerance $($tol$)$

# and iter $$ maxit continue the loop

iter $=$ iter $+1$ # increment iter

dx $=$ xu $-$ xl

if f$1$ f$2$: # x$1$ is the new estimate of min $->$ xmin$=$x$1,$ discard $[$xl$,$x$2]$

xmin $=$ x$1$

xl $=$ x$2$

x$2=$ x$1$

f$2=$ f$1$

d $=($phi $-1)*($xu $-$ xl$)$

x$1=$ xl $+$ d

f$1=$ func$($x$1,*$args$)$

else: # f$2>=$ f$1$: x$2$ is the new estimate of min $->$ xmin$=$x$2,$ discard $[$x$2,$xu$]$

xmin $=$ x$2$

xu $=$ x$1$

x$1=$ x$2$

f$1=$ f$2$

d $=($phi $-1)*($xu $-$ xl$)$

x$2=$ xu $-$ d

f$2=$ func$($x$2,*$args$)$

err $=(2-$ phi$)*$ abs$($dx $/($xmin $+$ small$))*100$ # relative approximate error $(\%)$

# $($a small number is added to the

# denominator to avoid $/0$ in case xm$=0)$

fmin $=$ func$($xmin$,*$args$)$

if iter $==$ maxit: # show a warning if the function is terminated due to iter$=$maxit

print$(\text{'}$Warning: minGolden function is terminated because iter$=$maxit;$\text{'})$

print$(\text{'}$ error $$ tolerance stopping criterion may not be satisfied'$)$

return xmin, fmin, err, iter #returns xmin, fmin, err, iter