From 5c984d09a78d19773099bc1ca36713f3611653b2 Mon Sep 17 00:00:00 2001 From: PolishPigeon Date: Thu, 11 Nov 2021 19:19:57 +0100 Subject: [PATCH] Task 2 code --- ENUME/projectA/jacobiMethod.asv | 43 +++++++ ENUME/projectA/jacobiMethod.m | 50 ++++++++ ENUME/projectA/pdflatex36032.fls | 4 + ENUME/projectA/projectA.aux | 52 +++++---- ENUME/projectA/projectA.fdb_latexmk | 35 +++--- ENUME/projectA/projectA.fls | 7 +- ENUME/projectA/projectA.log | 70 ++++++----- ENUME/projectA/projectA.out | 43 +++---- ENUME/projectA/projectA.pdf | Bin 278345 -> 296296 bytes ENUME/projectA/projectA.synctex.gz | Bin 166811 -> 188334 bytes ENUME/projectA/projectA.tex | 162 ++++++++++++++++++++++++-- ENUME/projectA/projectA.toc | 50 ++++---- ENUME/projectA/task2Matrix.m | 2 + ENUME/projectA/task2MatrixAndVector.m | 4 + ENUME/projectA/task2Vector.m | 6 + ENUME/projectA/usefullinks.txt | 11 +- 16 files changed, 421 insertions(+), 118 deletions(-) create mode 100644 ENUME/projectA/jacobiMethod.asv create mode 100644 ENUME/projectA/jacobiMethod.m create mode 100644 ENUME/projectA/pdflatex36032.fls create mode 100644 ENUME/projectA/task2Matrix.m create mode 100644 ENUME/projectA/task2MatrixAndVector.m create mode 100644 ENUME/projectA/task2Vector.m diff --git a/ENUME/projectA/jacobiMethod.asv b/ENUME/projectA/jacobiMethod.asv new file mode 100644 index 00000000..1077178a --- /dev/null +++ b/ENUME/projectA/jacobiMethod.asv @@ -0,0 +1,43 @@ +function x = jacobiMethod(Matrix, Vector) + [Rows,~] = size(Matrix); + D = diag(diag(Matrix)); + inverseD = inv(D); + 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 + initial_x = ones(Rows, 1); + initial_x = - inverseD * ( ( L + U ) * initial_x) + inverseD * initial_x; % As per formula + % We will be using D \ initial_x and D \ () since it is faster and more + % accurate according to matlab + whichIterationAreWeOn = 0; + currentError = inf; % We set it to inf so that it the algorithm will always start + % (See condition below) + demandedTolerance = 1e-10; + while currentError >= demandedTolerance + + x = - inverseD * ( ( L + U ) * initial_x) + inverseD * initial_x; % As per formula + + currentError = norm(x - initial_x); + disp(currentError); + if currentError <= demandedTolerance + currentError = norm(Matrix*x-Vector); + disp(currentError); + if currentError <= demandedTolerance + break; + else + demandedTolerance = demandedTolerance * 2; + end + end + initial_x = x; + whichIterationAreWeOn = whichIterationAreWeOn + 1; + end + disp("Final demandedTolerance"); + disp(demandedTolerance); + disp("Final Iteration: "); + disp(whichIterationAreWeOn); + disp("A\b matlab:"); + disp(Matrix / Vector); +end \ No newline at end of file diff --git a/ENUME/projectA/jacobiMethod.m b/ENUME/projectA/jacobiMethod.m new file mode 100644 index 00000000..14f33db3 --- /dev/null +++ b/ENUME/projectA/jacobiMethod.m @@ -0,0 +1,50 @@ +function x = jacobiMethod(Matrix, Vector) + [Rows,~] = size(Matrix); + [L, D, U] = decomposeMatrix(Matrix); + initial_x = ones(Rows, 1); + whichIterationAreWeOn = 0; + currentError = inf; % We set it to inf so that the algorithm will always start + % (See condition below) + demandedTolerance = 1e-10; + while currentError >= demandedTolerance + + x = jacobiEquation(D, L, U, initial_x, Vector); + + currentError = norm(x - initial_x); + %disp(currentError); + if currentError <= demandedTolerance + currentError = norm(Matrix*x-Vector); + %disp(currentError); + if currentError <= demandedTolerance + break; + else + demandedTolerance = demandedTolerance * 2; + end + end + initial_x = x; + whichIterationAreWeOn = whichIterationAreWeOn + 1; + end + disp("Final demandedTolerance"); + disp(demandedTolerance); + disp("Final Iteration: "); + disp(whichIterationAreWeOn); + disp("A\b matlab:"); + disp(Matrix \ Vector); +end + +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 + + +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 \ No newline at end of file diff --git a/ENUME/projectA/pdflatex36032.fls b/ENUME/projectA/pdflatex36032.fls new file mode 100644 index 00000000..469be781 --- /dev/null +++ b/ENUME/projectA/pdflatex36032.fls @@ -0,0 +1,4 @@ +PWD 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