Gaussian Elimination with Partial Pivoting, how do I swap rows

Question

Susanna Westersund 2020-10-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/626948-gaussian-elimination-with-partial-pivoting-how-do-i-swap-rows

评论： WAGDI AL-BAADANI 2021-3-26

function output= pivGauss(A)

%% Problem Setup

% Get the size of the problem (number of equations / unknowns)

i=1;

[n,~]=size(A);

% Get the coefficient matrix and the RHS vector

C=A(1:n,1:n);

rhs=(1:n,1:n+1);

%% Forward Elimination w/ Partial Piviting

% for each FE iteration:

% 1) find the rows to switch (hint: find the right commands to use from ML3 Tutorial slides)

% 2) switch the rows (hint: you can create a temp variable to hold one set of the values as an intermediate step)

% 3) perform elimination of unknown variables (reminder: use nested loops and MATLAB vector/matrix operations to replace unnecessary loops)

P=(1:n); %pivoting vector

[m,I]=max(abs(A(k:n,k))

for i=1:n-1

piv=i; %selecting the pivot

for j=(i+1):n

if abs(A(j,i))>abs(A(i,i))

U=A(i,:);

A(i,:)=A(j,:);

A(j,:)=U;

end

for j=i+1:n

x=A(j,i)/A(i,i);

for k=i+1:n+1

A(j,k)=A(j,k)-x*A(i,k);

end

fprintf('\n\nIteration #%2d:\n', i)

fprintf(' The row that is to be switched is %.4e\n', U)

fprintf(' The coefficient matrix is ', A)

fprintf(' The right-hand side vector is ', x)

end

%% Back Substitution

% Use Question 4 in C17_InClass as a reference

% This code has unnecessary loops that can be replaced by MATLAB vector/matrix operations though.

x(n)=Z(n)/U(n,n);

for i=n-1:-1:1

sum=Z(i);

for j=i+1:1:n

sum=sum-U(i,j)*x(j);

end

x(i)=sum/U(i,i);

end

%% Final Display and Output

output=[U, x]

disp(output)

end

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WAGDI AL-BAADANI 2021-3-26

function output= pivGauss(A)

↑

Error: Function definition not supported in this context. Create functions in code file.

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Answer 1

Pratyush Roy 2020-11-12

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在 MATLAB Online 中打开

Hi Susanna,

The variable 'k' seems to be not defined for the line given below:

[m,I]=max(abs(A(k:n,k))

Can you furnish some more information regarding the variable k?

Regards,

Pratyush

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Gaussian Elimination with Partial Pivoting, how do I swap rows

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