C$++$ Code

Diagonal dominance:$$

$$i : aii $>$

$$

j$=$i

$|$aij$|$

$$ Solve the linear system by both methods above. How accurate

is the solution?

$$ Experimment with different matrix sizes and amounts of

#include

using std::cout,std::cin;

#include

#include

using std::string;

#include

using std::ranges::views::iota,

std::ranges::views::filter,

std::ranges::views::transform;

#include

using std::accumulate;

#include

using namespace Eigen;

$//$ ::Matrix, Eigen::Vector;

$/*$

$*$ Jacobi Iterative method with seq

$*/$

template$<$ typename MatrixType,typename VectorType $>$

void JacobiSolve$1($ MatrixType A$,$VectorType sol,VectorType rhs $)\{$

auto tmp$\{$sol$\}$;

$//$ set initial guess to identically one

int siz $=$ A$.$rows$()$;

for $($ auto& v : sol $)$

v $=1.$;

$//$ for a number of iteration

for $($ auto it : iota$(0,10))\{$

$//$ one step of Jacobi

cout $<<"$it: $"<<$ it $<<\text{'}$

$\text{'}<<$ sol $<<\text{'}$

$\text{'}$;

$\}$

$\}$

$/*$

$*$ Jacobi Iterative method with ranges

$*/$

template$<$ typename MatrixType,typename VectorType $>$

void JacobiSolve$2($ MatrixType A$,$VectorType sol,VectorType rhs $)\{$

auto tmp$\{$sol$\}$;

$//$ set initial guess to identically one

int siz $=$ A$.$rows$()$;

for $($ auto& v : sol $)$

v $=1.$;

$//$ for a number of iteration

for $($ auto it : iota$(0,10))\{$

$//$ one step of Jacobi

cout $<<"$it: $"<<$ it $<<\text{'}$

$\text{'}<<$ sol $<<\text{'}$

$\text{'}$;

$\}$

$\}$

int main$()$

$\{$

const int siz$=5$;

Matrix A;

Vector sol,rhs$,$tmp;

cout $<<$ "Matrix size: $"<<$ A$.$rows$()<<","<<$ A$.$cols$()<<"("<<$ A$.$size$()<<")$

$"$;

for $($ auto& v : rhs $)$

v $=1.$;

cout $<<$ rhs $<<\text{'}$

$\text{'}$;

for $($ auto row : iota$(0,$siz$))\{$

sol$($row$)=$ static$\_$cast$($ row $)$;

A$($row$,$row$)=$ siz;

for $($ auto col : iota$(0,$siz$))\{$

if $($row$==$col$)$ continue;

A$($row$,$col$)=-1$;

$\}$

$\}$

cout $<<$ "sol:

$"<<$ sol $<<\text{'}$

$\text{'}$;

rhs $=$ A$*$sol;

cout $<<"$rhs:

$"<<$ rhs $<<\text{'}$

$\text{'}$;

cout $<<"================$ Solve $1$

$"$;

JacobiSolve$1($ A$,$sol,rhs $)$;

cout $<<"================$ Solve $2$

$"$;

JacobiSolve$2($ A$,$sol,rhs $)$;

Matrix Af$(20,20)$;

$//$ or: MatrixXf Af$(20,20)$;

return $0$;

$\}$