update

HW4/README.md

@@ -21,7 +21,7 @@ heading `# Homework #4` in your `README.md` file
 
     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
     theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in

lecture_11/LU_naive.m

@@ -0,0 +1,27 @@
+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

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

lecture_11/lecture_11.aux

@@ -0,0 +1,28 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\providecommand \oddpage@label [2]{}
+\@writefile{toc}{\contentsline {section}{\numberline {1}LU Decomposition}{1}{section.1}}
+\newlabel{lu-decomposition}{{1}{1}{LU Decomposition}{section.1}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.0.1}efficient storage of matrices for solutions}{1}{subsubsection.1.0.1}}
+\newlabel{efficient-storage-of-matrices-for-solutions}{{1.0.1}{1}{efficient storage of matrices for solutions}{subsubsection.1.0.1}{}}
+\@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}{}}

lecture_11/lecture_11.blg

@@ -0,0 +1,48 @@
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+(There were 3 error messages)