The code I was provided seems to have a problem.

The value of f$(0\mathrm{.}95)$ is incorrect. And the output of the code of the solution provided is different from the output obtained by running c$++.$

I want to be provided with the correct code.

Code I was provided :

$-----------------------------------$

#include

#include

#include

#include

#include

#include

$//$ Function to perform linear regression using the least$-$squares method

void linearRegression$($const std::vector& x$,$ const std::vector& y$,$ double& alpha, double& beta$)\{$

int n $=$ x$.$size$()$;

double sumX $=0,$ sumY $=0,$ sumXY $=0,$ sumXX $=0$;

for$($int i $=0$; i $$ n; i$++)\{$

sumX $+=$ x$[$i$]$;

sumY $+=$ y$[$i$]$;

sumXY $+=$ x$[$i$]*$ y$[$i$]$;

sumXX $+=$ x$[$i$]*$ x$[$i$]$;

$\}$

beta $=($n $*$ sumXY $-$ sumX $*$ sumY$)/($n $*$ sumXX $-$ sumX $*$ sumX$)$;

alpha $=($sumY $-$ beta $*$ sumX$)/$ n;

$\}$

$//$ Function to calculate R$^2($coefficient of determination$)$

double calculateRSquared$($const std::vector& y$,$ const std::vector& y$\_$fit$)\{$

double meanY $=$ std::accumulate$($y$.$begin$(),$ y$.$end$(),0\mathrm{.}0)/$ y$.$size$()$;

double ssTot $=0,$ ssRes $=0$;

for$($size$\_$t i $=0$; i $$ y$.$size$()$; i$++)\{$

ssTot $+=($y$[$i$]-$ meanY$)*($y$[$i$]-$ meanY$)$;

ssRes $+=($y$[$i$]-$ y$\_$fit$[$i$])*($y$[$i$]-$ y$\_$fit$[$i$])$;

$\}$

return $1-($ssRes $/$ ssTot$)$;

$\}$

$//$ Function to evaluate the spline at a given point x

double evaluateSpline$($const std::vector& x$,$ const std::vector& y$,$ double x$\_$eval$)\{$

int n $=$ x$.$size$()$;

std::vector h$($n $-1),$ alpha$($n $-1),$ l$($n$),$ mu$($n$),$ z$($n$),$ c$($n$),$ b$($n $-1),$ d$($n $-1)$;

$//$ Calculate h and alpha

for$($int i $=1$; i $$ n $-1$; i$++)\{$

h$[$i$]=$ x$[$i $+1]-$ x$[$i$]$;

alpha$[$i$]=(3/$ h$[$i$])*($y$[$i $+1]-$ y$[$i$])-(3/$ h$[$i $-1])*($y$[$i$]-$ y$[$i $-1])$;

$\}$

$//$ Set boundary conditions

l$[0]=1$;

mu$[0]=0$;

z$[0]=0$;

$//$ Solve the tridiagonal system

for$($int i $=1$; i $$ n $-1$; i$++)\{$

l$[$i$]=2*($x$[$i $+1]-$ x$[$i $-1])-$ h$[$i $-1]*$ mu$[$i $-1]$;

mu$[$i$]=$ h$[$i$]/$ l$[$i$]$;

z$[$i$]=($alpha$[$i$]-$ h$[$i $-1]*$ z$[$i $-1])/$ l$[$i$]$;

$\}$

$//$ Set boundary conditions

l$[$n $-1]=1$;

z$[$n $-1]=0$;

c$[$n $-1]=0$;

$//$ Calculate the coefficients

for$($int j $=$ n $-2$; j $>=0$; j$--)\{$

c$[$j$]=$ z$[$j$]-$ mu$[$j$]*$ c$[$j $+1]$;

b$[$j$]=($y$[$j $+1]-$ y$[$j$])/$ h$[$j$]-$ h$[$j$]*($c$[$j $+1]+2*$ c$[$j$])/3$;

d$[$j$]=($c$[$j $+1]-$ c$[$j$])/(3*$ h$[$j$])$;

$\}$

$//$ Evaluate the spline at x$\_$eval

int i $=$ std::lower$\_$bound$($x$.$begin$(),$ x$.$end$(),$ x$\_$eval$)-$ x$.$begin$()-1$;

double dx $=$ x$\_$eval $-$ x$[$i$]$;

double result $=$ y$[$i$]+$ b$[$i$]*$ dx $+$ c$[$i$]*$ dx $*$ dx $+$ d$[$i$]*$ dx $*$ dx $*$ dx;

return result;

$\}$

int main$()\{$

$//$ Given data points

std::vector x $=\{0\mathrm{.}0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9,1\mathrm{.}0\}$;

std::vector f $=\{0\mathrm{.}2977,0\mathrm{.}2738,0\mathrm{.}3060,0\mathrm{.}3342,0\mathrm{.}3577,0\mathrm{.}4479,0\mathrm{.}4921,0\mathrm{.}5917,0\mathrm{.}6840,0\mathrm{.}7547,0\mathrm{.}8802\}$;

$//$ Part $1$: Least$-$squares method for exponential fitting

std::vector y;

for$($double val : f$)\{$

y$.$push$\_$back$($log$($val$))$; $//$ linearize

$\}$

double alpha, beta;

linearRegression$($x$,$ y$,$ alpha, beta$)$;

double a $=$ exp$($alpha$)$;

std::vector f$\_$fit;

for$($double val : x$)\{$

f$\_$fit.push$\_$back$($a $*$ exp$($beta $*$ val$))$;

$\}$

double rSquared $=$ calculateRSquared$($f$,$ f$\_$fit$)$;

std::cout $$ "Least$-$squares method results:" $$ std::endl;

std::cout a $="$ a $$ std::endl;

std::cout $$ "beta $="$ beta $$ std::endl;

std::cout $$ "Coefficient of determination $($R$^2)="$ rSquared $$ std::endl;

$//$ Part $2$: Third$-$order spline interpolation

double x$\_$eval $=0\mathrm{.}95$;

double f$\_$eval $=$ evaluateSpline$($x$,$ f$,$ x$\_$eval$)$;

std::cout

Spline interpolation result:" $$ std::endl;

std::cout f$("$ x$\_$eval f$\_$eval $$ std::endl;

return $0$;

$\}$

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