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Thomas Ressler authored and Thomas Ressler committed Feb 23, 2017
2 parents 7e6928c + 46f626e commit aa5b273
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2 changes: 1 addition & 1 deletion HW4/README.md
Expand Up @@ -21,7 +21,7 @@ heading `# Homework #4` in your `README.md` file


PE_s=1/2\*K \*(DL)^2 PE_s=1/2\*K \*(DL)^2


where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) and K=30 N/m.


b. Use the `goldmin.m` function to solve for the minimum potential energy at xc when b. Use the `goldmin.m` function to solve for the minimum potential energy at xc when
theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in
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27 changes: 27 additions & 0 deletions lecture_11/LU_naive.m
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function [L, U] = LU_naive(A)
% GaussNaive: naive Gauss elimination
% x = GaussNaive(A,b): Gauss elimination without pivoting.
% input:
% A = coefficient matrix
% y = right hand side vector
% output:
% x = solution vector
[m,n] = size(A);
if m~=n, error('Matrix A must be square'); end
nb = n;
L=diag(ones(n,1));
U=A;
% forward elimination
for k = 1:n-1
for i = k+1:n
fik = U(i,k)/U(k,k);
L(i,k)=fik;
U(i,k:nb) = U(i,k:nb)-fik*U(k,k:nb);
end
end
%% back substitution
%x = zeros(n,1);
%x(n) = Aug(n,nb)/Aug(n,n);
%for i = n-1:-1:1
% x(i) = (Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i);
%end
36 changes: 36 additions & 0 deletions lecture_11/LU_pivot.m
@@ -0,0 +1,36 @@
function [L,U,P] = LU_pivot(A)
% GaussPivot: Gauss elimination pivoting
% x = GaussPivot(A,b): Gauss elimination with pivoting.
% input:
% A = coefficient matrix
% b = right hand side vector
% output:
% x = solution vector
[m,n]=size(A);
if m~=n, error('Matrix A must be square'); end
nb = n;
L=diag(ones(n,1));
U=A;
P=diag(ones(n,1));
% forward elimination
for k = 1:n-1
% partial pivoting
[big,i]=max(abs(U(k:n,k)));
ipr=i+k-1;
if ipr~=k
P([k,ipr],:)=P([ipr,k],:); % if the max is not the current index ipr, pivot count
%L([k,ipr],:)=L([ipr,k],:);
%U([k,ipr],:)=U([ipr,k],:);
end
for i = k+1:n
fik=U(i,k)/U(k,k);
L(i,k)=fik;
U(i,k:nb)=U(i,k:nb)-fik*U(k,k:nb);
end
end
% back substitution
%x=zeros(n,1);
%x(n)=Aug(n,nb)/Aug(n,n);
%for i = n-1:-1:1
% x(i)=(Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i);
%end
28 changes: 28 additions & 0 deletions lecture_11/lecture_11.aux
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\@writefile{toc}{\contentsline {section}{\numberline {1}LU Decomposition}{1}{section.1}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Pivoting for LU factorization}{2}{subsection.1.1}}
\newlabel{pivoting-for-lu-factorization}{{1.1}{2}{Pivoting for LU factorization}{subsection.1.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Springs-masses\relax }}{5}{figure.caption.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Cholesky Factorization}{6}{subsection.1.2}}
\newlabel{cholesky-factorization}{{1.2}{6}{Cholesky Factorization}{subsection.1.2}{}}
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48 changes: 48 additions & 0 deletions lecture_11/lecture_11.blg
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This is BibTeX, Version 0.99d (TeX Live 2015/Debian)
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The top-level auxiliary file: lecture_11.aux
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