Gaussian Elimination Example (with partial pivoting): GEE, it's simple!: gee_its_short (A, b) - File Exchange

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Highlights from
Gaussian Elimination Example (with partial pivoting): GEE, it's simple!

gee_its_short (A, b) GEE_ITS_SHORT x=A\b, few comments, no error checking (just for line count)
gee_its_simple (A, b) GEE_ITS_SIMPLE solves A*x=b using a Gaussian Elimination Example (it's simple!)
gee_its_simple_backsolve (U, ... GEE_ITS_SIMPLE_BACKSOLVE x=U\b where U is upper triangular
gee_its_simple_factorize (A) GEE_ITS_SIMPLE_FACTORIZE Gaussian Elimination Example, with partial pivoting
gee_its_simple_forwardsolve (... GEE_ITS_SIMPLE_FORWARDSOLVE computes x=L\b where L is unit lower triangular
gee_its_simple_resid (A, x, b) GEE_ITS_SIMPLE_RESID compute the relative residual for x=A\b
gee_its_simple_test GEE_ITS_SIMPLE_TEST tests the "Gee! It's Simple!" package
gee_its_sweet (A, b) GEE_ITS_SWEET solves Ax=b with just x=A\b; it doesn't get sweeter than this
gee_its_too_short (A, b) GEE_ITS_TOO_SHORT x=A\b, no pivoting (thus unstable!), just bare bones
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from Gaussian Elimination Example (with partial pivoting): GEE, it's simple! by Tim Davis
A set of simple functions that illustrate Gaussian Elimination with partial pivoting

gee_its_short (A, b)

function b = gee_its_short (A, b)
%GEE_ITS_SHORT x=A\b, few comments, no error checking (just for line count)
% Example:
%   x = gee_its_short (A,b) ;       % same as x=A\b for square A
% See also: mldivide, gee_its_simple

% Copyright 2006-2007, Timothy A. Davis.
% http://www.cise.ufl.edu/research/sparse

n = size (A,1) ;
for k = 1:n
    [x i] = max (abs (A (k:n,k))) ;
    i = i+k-1 ;
    A ([k i],:) = A ([i k],:) ;
    b ([k i],:) = b ([i k],:) ;
    A (k+1:n,k) = A (k+1:n,k) / A (k,k) ;
    A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - A (k+1:n,k) * A (k,k+1:n) ;
    b (k+1:n,:) = b (k+1:n,:) - A (k+1:n,k) * b (k,:) ;
end
for k = n:-1:1
    b (k,:) = b (k,:) / A (k,k) ;
    b (1:k-1,:) = b (1:k-1,:) - A (1:k-1,k) * b (k,:) ;
end

Highlights from Gaussian Elimination Example (with partial pivoting): GEE, it's simple!

Highlights from
Gaussian Elimination Example (with partial pivoting): GEE, it's simple!