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Task 2 Add comments and code task3
This commit is contained in:
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@ -9,7 +9,7 @@ function [L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, flag] =
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[L, D, U] = decomposeMatrix(Matrix);
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[L, D, U] = decomposeMatrix(Matrix);
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initial_x = ones(Rows, 1);
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initial_x = ones(Rows, 1);
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whichIterationAreWeOn = 0;
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whichIterationAreWeOn = 0;
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demandedTolerance = 1e-10;
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demandedTolerance = 1e-10; % as per task description
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flag = 0;
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flag = 0;
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end
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end
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@ -24,7 +24,7 @@ function [L, D, U] = decomposeMatrix(Matrix)
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end
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end
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function [x, whichIterationAreWeOn, demandedTolerance] = jacobiLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector, flag)
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function [x, whichIterationAreWeOn, demandedTolerance] = jacobiLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector, flag)
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while flag ~= 1
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while flag ~= 1 % flag denotes whether norm(Matrix*x-Vector) <= demandedTolerance
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[x, whichIterationAreWeOn, demandedTolerance, flag, initial_x] = jacobiInsideLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector);
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[x, whichIterationAreWeOn, demandedTolerance, flag, initial_x] = jacobiInsideLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector);
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end
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end
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end
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end
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@ -42,16 +42,16 @@ function x = jacobiEquation(D, L, U, initial_x, Vector)
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end
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end
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function [flag, demandedTolerance] = checkError(x, initial_x, demandedTolerance, Matrix, Vector)
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function [flag, demandedTolerance] = checkError(x, initial_x, demandedTolerance, Matrix, Vector)
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flag = 0;
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flag = 0;
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currentError = norm(x - initial_x);
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currentError = norm(x - initial_x);
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if currentError <= demandedTolerance
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if currentError <= demandedTolerance
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currentError = norm(Matrix*x-Vector);
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currentError = norm(Matrix*x-Vector);
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if currentError <= demandedTolerance
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if currentError <= demandedTolerance % if sequence as per textbook
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flag = 1;
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flag = 1;
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else
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else
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demandedTolerance = demandedTolerance * 2;
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demandedTolerance = demandedTolerance * 2; % arbitrary value
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end
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end
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end
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end
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end
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end
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function [initial_x, whichIterationAreWeOn, flag] = endOfLoop(x, whichIterationAreWeOn)
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function [initial_x, whichIterationAreWeOn, flag] = endOfLoop(x, whichIterationAreWeOn)
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@ -60,8 +60,6 @@ function [initial_x, whichIterationAreWeOn, flag] = endOfLoop(x, whichIterationA
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flag = 0;
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flag = 0;
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end
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end
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function dispFinalResults(demandedTolerance, whichIterationAreWeOn, Matrix, Vector)
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function dispFinalResults(demandedTolerance, whichIterationAreWeOn, Matrix, Vector)
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disp("Final demandedTolerance");
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disp("Final demandedTolerance");
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disp(demandedTolerance);
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disp(demandedTolerance);
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@ -79,5 +79,15 @@
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\bibcite{texbook}{1}
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@ -1,5 +1,5 @@
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@ -1,4 +1,4 @@
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@ -39,3 +39,13 @@
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\BOOKMARK [2][-]{subsection.5.1.10}{backSubstitutionPhase}{section.5.1}% 39
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\BOOKMARK [1][-]{section.5.2}{Task 3e code}{chapter.5}% 42
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\BOOKMARK [2][-]{subsection.5.2.1}{jacobiMethod}{section.5.2}% 43
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\BOOKMARK [2][-]{subsection.5.2.2}{initializeValues}{section.5.2}% 44
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\BOOKMARK [2][-]{subsection.5.2.3}{decomposeMatrix}{section.5.2}% 45
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\BOOKMARK [2][-]{subsection.5.2.4}{jacobiLoop}{section.5.2}% 46
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@ -748,6 +748,124 @@ end % end function
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\end{lstlisting}
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\end{lstlisting}
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\end{simplechar}
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\end{simplechar}
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\section{Task 3e code}
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\subsection{jacobiMethod}
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\begin{simplechar}
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\begin{lstlisting}
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function x = jacobiMethod(Matrix, Vector)
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[L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, flag] = initializeValues(Matrix);
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[x, whichIterationAreWeOn, demandedTolerance] = jacobiLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector, flag);
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dispFinalResults(demandedTolerance, whichIterationAreWeOn, Matrix, Vector);
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end
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\end{lstlisting}
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\end{simplechar}
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\subsection{initializeValues}
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\begin{simplechar}
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\begin{lstlisting}
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function [L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, flag] = initializeValues(Matrix)
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[Rows, ~] = size(Matrix);
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[L, D, U] = decomposeMatrix(Matrix);
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initial_x = ones(Rows, 1);
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whichIterationAreWeOn = 0;
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demandedTolerance = 1e-10; % as per task description
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flag = 0;
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end
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\end{lstlisting}
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\end{simplechar}
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||||||
|
\subsection{decomposeMatrix}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function [L, D, U] = decomposeMatrix(Matrix)
|
||||||
|
D = diag(diag(Matrix));
|
||||||
|
U = triu(Matrix, 1); % Generates upper triangular part of matrix
|
||||||
|
% where the second variable denotes on which diagonal of matrix should we
|
||||||
|
% start
|
||||||
|
L = tril(Matrix, -1); % Generates lower triangular part of matrix
|
||||||
|
% where the second variable denotes on which diagonal of matrix should we
|
||||||
|
% start
|
||||||
|
end
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
|
\subsection{jacobiLoop}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function [x, whichIterationAreWeOn, demandedTolerance] = jacobiLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector, flag)
|
||||||
|
while flag ~= 1 % flag denotes whether norm(Matrix*x-Vector) <= demandedTolerance
|
||||||
|
[x, whichIterationAreWeOn, demandedTolerance, flag, initial_x] = jacobiInsideLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
|
\subsection{jacobiInsideLoop}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function [x, whichIterationAreWeOn, demandedTolerance, flag, initial_x] = jacobiInsideLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector)
|
||||||
|
x = jacobiEquation(D, L, U, initial_x, Vector);
|
||||||
|
[flag, demandedTolerance] = checkError(x, initial_x, demandedTolerance, Matrix, Vector);
|
||||||
|
[initial_x, whichIterationAreWeOn] = endOfLoop(x, whichIterationAreWeOn);
|
||||||
|
end
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
|
\subsection{jacobiEquation}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function x = jacobiEquation(D, L, U, initial_x, Vector)
|
||||||
|
x = - D \ ( L + U ) * initial_x + D \ Vector; % As per formula
|
||||||
|
% We will be using D \ Vector and D \ ( ) instead of inverseD since
|
||||||
|
% this is faster according to matlab
|
||||||
|
end
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
|
\subsection{checkError}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function [flag, demandedTolerance] = checkError(x, initial_x, demandedTolerance, Matrix, Vector)
|
||||||
|
flag = 0;
|
||||||
|
currentError = norm(x - initial_x);
|
||||||
|
if currentError <= demandedTolerance
|
||||||
|
currentError = norm(Matrix*x-Vector);
|
||||||
|
if currentError <= demandedTolerance % if sequence as per textbook
|
||||||
|
flag = 1;
|
||||||
|
else
|
||||||
|
demandedTolerance = demandedTolerance * 2; % arbitrary value
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
|
\subsection{endOfLoop}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function [initial_x, whichIterationAreWeOn, flag] = endOfLoop(x, whichIterationAreWeOn)
|
||||||
|
initial_x = x;
|
||||||
|
whichIterationAreWeOn = whichIterationAreWeOn + 1;
|
||||||
|
flag = 0;
|
||||||
|
end
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
|
\subsection{dispFinalResults}
|
||||||
|
\begin{simplechar}
|
||||||
|
\begin{lstlisting}
|
||||||
|
function dispFinalResults(demandedTolerance, whichIterationAreWeOn, Matrix, Vector)
|
||||||
|
disp("Final demandedTolerance");
|
||||||
|
disp(demandedTolerance);
|
||||||
|
disp("Final Iteration: ");
|
||||||
|
disp(whichIterationAreWeOn);
|
||||||
|
disp("A\b matlab:");
|
||||||
|
disp(Matrix \ Vector);
|
||||||
|
end
|
||||||
|
\end{lstlisting}
|
||||||
|
\end{simplechar}
|
||||||
|
|
||||||
\begin{thebibliography}{9}
|
\begin{thebibliography}{9}
|
||||||
\bibitem{texbook}
|
\bibitem{texbook}
|
||||||
Piotr Tatjewski (2014) \emph{Numerical Methods}, Oficyna Wydawnicza Politechniki Warszawskiej
|
Piotr Tatjewski (2014) \emph{Numerical Methods}, Oficyna Wydawnicza Politechniki Warszawskiej
|
||||||
|
|||||||
@ -51,3 +51,13 @@
|
|||||||
\contentsline {subsection}{\numberline {5.1.10}backSubstitutionPhase}{22}{subsection.5.1.10}%
|
\contentsline {subsection}{\numberline {5.1.10}backSubstitutionPhase}{22}{subsection.5.1.10}%
|
||||||
\contentsline {subsection}{\numberline {5.1.11}iterativeResidualCorrection}{22}{subsection.5.1.11}%
|
\contentsline {subsection}{\numberline {5.1.11}iterativeResidualCorrection}{22}{subsection.5.1.11}%
|
||||||
\contentsline {subsection}{\numberline {5.1.12}improveSolution}{22}{subsection.5.1.12}%
|
\contentsline {subsection}{\numberline {5.1.12}improveSolution}{22}{subsection.5.1.12}%
|
||||||
|
\contentsline {section}{\numberline {5.2}Task 3e code}{23}{section.5.2}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.1}jacobiMethod}{23}{subsection.5.2.1}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.2}initializeValues}{23}{subsection.5.2.2}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.3}decomposeMatrix}{23}{subsection.5.2.3}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.4}jacobiLoop}{24}{subsection.5.2.4}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.5}jacobiInsideLoop}{24}{subsection.5.2.5}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.6}jacobiEquation}{24}{subsection.5.2.6}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.7}checkError}{24}{subsection.5.2.7}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.8}endOfLoop}{25}{subsection.5.2.8}%
|
||||||
|
\contentsline {subsection}{\numberline {5.2.9}dispFinalResults}{25}{subsection.5.2.9}%
|
||||||
|
|||||||
@ -0,0 +1,37 @@
|
|||||||
|
\relax
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {0}Abstract}{1}{}\protected@file@percent }
|
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|
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\newlabel{eq:1}{{3.1}{7}}
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|
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\gdef \@abspage@last{13}
|
||||||
@ -0,0 +1,67 @@
|
|||||||
|
# Fdb version 3
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||||||
|
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[8] [9] [10] [11] [12] [13] (./projAreport.aux) )
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ENUME/references/szopinski-enume/projA/report/projAreport.pdf
Normal file
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