diff --git a/ENUME/projectA/backSubstitutionPhase.m b/ENUME/projectA/backSubstitutionPhase.m new file mode 100644 index 00000000..654e09c8 --- /dev/null +++ b/ENUME/projectA/backSubstitutionPhase.m @@ -0,0 +1,11 @@ +function [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector) + for i3 = Columns : -1 : 1 + + E = 0; + for iter = i3+1 : Columns + E = E + Matrix(i3,iter) * x(iter,1); + end % end for + + x(i3, 1) = (Vector(i3,1) - E) / Matrix(i3,i3); + end % end for +end % end function \ No newline at end of file diff --git a/ENUME/projectA/checkIfMatrixIsSquareMatrix.m b/ENUME/projectA/checkIfMatrixIsSquareMatrix.m new file mode 100644 index 00000000..66d7a6f4 --- /dev/null +++ b/ENUME/projectA/checkIfMatrixIsSquareMatrix.m @@ -0,0 +1,5 @@ +function checkIfMatrixIsSquareMatrix(Matrix) +[Rows,Columns] = size(Matrix); +if Rows ~= Columns + error ('Matrix is not square matrix!'); +end % end if \ No newline at end of file diff --git a/ENUME/projectA/debilMode b/ENUME/projectA/debilMode deleted file mode 100644 index d199cd12..00000000 --- a/ENUME/projectA/debilMode +++ /dev/null @@ -1,71 +0,0 @@ -% ------- Solving a system of n linear equations Ax = b. ------- % -% -------------------- The Indicated Method -------------------- % -function x = Indicated_Method(A, b) - -[M,N] = size(A); -if M ~= N - -error ('A is not square matrix!'); -end -for j = 1 : N - 1 -%--- Find the greatest value within column ---% - -m = max(A(j:N,j)); -%--- Find row whitin greatest value occure ---% -for k = j : N -if A(k,j) == m -%--- SwapRow in matrix A ---% - -tempRow = A(j , :); - -A(j , :) = A(k, :); - -A(k, :) = tempRow; -%--- SwapValue in vector b ---% - -tempVal = b(j); - -b(j) = b(k); - -b(k) = tempVal; -break; -end -end -for i = j + 1 : N - -l = A(i,j) / A(j,j); - -b(i,1) = b(i,1) - l * b(j, 1); -for t = 1 : N - -A(i,t) = A(i,t) - l * A(j, t); -end -end -end - -x = zeros(N,1); -% -------------------- The back-substitution phase -------------------- % -for k = N : -1 : 1 - -E = 0; -for iter = k+1 : N - - - -E = E + A(k,iter) * x(iter,1); -end - -x(k, 1) = (b(k,1) - E) / A(k,k); -end - -euclideanNormOfR = norm(r); - - r = A*x - b; - euclideanNormOfR = norm(r); - new_euclideanNormOfR = euclideanNormOfR; -while new_euclideanNormOfR <= euclideanNormOfR - euclideanNormOfR = new_euclideanNormOfR; - r = A*x - b; - x = x - r; - new_euclideanNormOfR = norm(r); -end \ No newline at end of file diff --git a/ENUME/projectA/debilMode.asv b/ENUME/projectA/debilMode.asv deleted file mode 100644 index a6ab023c..00000000 --- a/ENUME/projectA/debilMode.asv +++ /dev/null @@ -1,71 +0,0 @@ -% ------- Solving a system of n linear equations Ax = b. ------- % -% -------------------- The Indicated Method -------------------- % -function x = debilMode(A, b) - - [M,N] = size(A); - if M ~= N - error ('A is not square matrix!'); - end % end if - - for j = 1 : N - 1 - %--- Find the greatest value within column ---% - - m = max(A(j:N,j)); - %--- Find row whitin greatest value occure ---% - for k = j : N - if A(k,j) == m - %--- SwapRow in matrix A ---% - - tempRow = A(j , :); - - A(j , :) = A(k, :); - - A(k, :) = tempRow; - %--- SwapValue in vector b ---% - - tempVal = b(j); - - b(j) = b(k); - - b(k) = tempVal; - break; - end % end if - end % end for - for i = j + 1 : N - - l = A(i,j) / A(j,j); - - b(i,1) = b(i,1) - l * b(j, 1); - for t = 1 : N - - A(i,t) = A(i,t) - l * A(j, t); - end % end for - end % end for - end - - x = zeros(N,1); - % -------------------- The back-substitution phase -------------------- % - for k = N : -1 : 1 - - E = 0; - for iter = k+1 : N - - - - E = E + A(k,iter) * x(iter,1); - end - - x(k, 1) = (b(k,1) - E) / A(k,k); - end - - r = A*x - b; - euclideanNormOfR = norm(r); - new_euclideanNormOfR = euclideanNormOfR; - while new_euclideanNormOfR <= euclideanNormOfR - euclideanNormOfR = new_euclideanNormOfR; - r = A*x - b; - x = x - r; - new_euclideanNormOfR = norm(r); - end - -end % end function \ No newline at end of file diff --git a/ENUME/projectA/debilMode.m b/ENUME/projectA/debilMode.m deleted file mode 100644 index c2d8fb86..00000000 --- a/ENUME/projectA/debilMode.m +++ /dev/null @@ -1,67 +0,0 @@ -% ------- Solving a system of n linear equations Ax = b. ------- % -% -------------------- The Indicated Method -------------------- % -function x = debilMode(A, b) - - [M,N] = size(A); - if M ~= N - error ('A is not square matrix!'); - end % end if - - for j = 1 : N - 1 - %--- Find the greatest value within column ---% - - m = max(A(j:N,j)); - %--- Find row whitin greatest value occure ---% - for k = j : N - if A(k,j) == m - %--- SwapRow in matrix A ---% - - tempRow = A(j , :); - - A(j , :) = A(k, :); - - A(k, :) = tempRow; - %--- SwapValue in vector b ---% - - tempVal = b(j); - - b(j) = b(k); - - b(k) = tempVal; - break; - end % end if - end % end for - for i = j + 1 : N - - l = A(i,j) / A(j,j); - - b(i,1) = b(i,1) - l * b(j, 1); - for t = 1 : N - A(i,t) = A(i,t) - l * A(j, t); - end % end for - end % end for - end % end for - - x = zeros(N,1); - % -------------------- The back-substitution phase -------------------- % - for k = N : -1 : 1 - - E = 0; - for iter = k+1 : N - E = E + A(k,iter) * x(iter,1); - end % end for - - x(k, 1) = (b(k,1) - E) / A(k,k); - end % end for - - r = A*x - b; - euclideanNormOfR = norm(r); - new_euclideanNormOfR = euclideanNormOfR; - while new_euclideanNormOfR <= euclideanNormOfR - euclideanNormOfR = new_euclideanNormOfR; - r = A*x - b; - x = x - r; - new_euclideanNormOfR = norm(r); - end % end while - -end % end function \ No newline at end of file diff --git a/ENUME/projectA/fileAttrib.m b/ENUME/projectA/fileAttrib.m new file mode 100644 index 00000000..ce9b8a4b --- /dev/null +++ b/ENUME/projectA/fileAttrib.m @@ -0,0 +1 @@ +fileattrib debilMode.m \ No newline at end of file diff --git a/ENUME/projectA/gaussianElimination.asv b/ENUME/projectA/gaussianElimination.asv old mode 100644 new mode 100755 diff --git a/ENUME/projectA/gaussianElimination.m b/ENUME/projectA/gaussianElimination.m old mode 100644 new mode 100755 index 435cfd01..da90cef0 --- a/ENUME/projectA/gaussianElimination.m +++ b/ENUME/projectA/gaussianElimination.m @@ -1,61 +1,8 @@ -function x = gaussianElimination(A, b) % A - matrix, b - vector - [~, Height] = size(A); - % Find column with greatest value element - for i = 1 : Height - 1 - m = max(A(i:Height, i)); - % Find row with greatest value element - for k = i : Height - if A(k, i) == m % If the element has the biggest value we now - % have the value of two rows that we want to swap - % Swap row in matrix A % - swapRow(A, i, k); - swapValue(b, i, k); - break; - end % end if - end % end for - % Swap value in vector B % - +function [Matrix, Vector] = gaussianElimination(i1, Columns, Matrix, Vector) + for i2 = i1 + 1 : Columns + + l = Matrix(i2,i1) / Matrix(i1,i1); + [Matrix, Vector] = substractRows(Matrix, Vector, i2, l, i1, Columns); + end % end for - - for j = i + 1 : Height - l = A(j, i) / A(i, i); - b(j, 1) = b(j, 1) - l * b(i, 1); - - for t = 1 : Height - A(j, t) = A(j, t) - l * A(i, t); - end % end for - end % end for - - - -x = zeros(Height, 1); - - - -for k = Height: -1:1 - E = 0; - for iter = k + 1 : Height - E = E + A(k, iter) * x(iter, 1); - end - - x(k, 1) = (b(k, 1) - E) / A(k, k); -end - - -end % end function - - - - -function swapRow(A, j, k) - temp = A(j, :); - A(j, :) = A(k, :); - A(k, :) = temp; -end % end function - -function swapValue(b, j, k) - temp = b(j); - b(j) = b(k); - b(k) = temp; -end % end function - +end % end function \ No newline at end of file diff --git a/ENUME/projectA/gaussianEliminationWithPartialPivoting.m b/ENUME/projectA/gaussianEliminationWithPartialPivoting.m new file mode 100644 index 00000000..71556374 --- /dev/null +++ b/ENUME/projectA/gaussianEliminationWithPartialPivoting.m @@ -0,0 +1,7 @@ +function [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector) + for i1 = 1 : Columns - 1 + m = max(Matrix(i1:Columns,i1)); + partialPivoting(Matrix, Vector, i1, m); + [Matrix, Vector] = gaussianElimination(i1, Columns, Matrix, Vector); + end % end for +end % end function \ No newline at end of file diff --git a/ENUME/projectA/improveSolution.m b/ENUME/projectA/improveSolution.m new file mode 100644 index 00000000..f535adfa --- /dev/null +++ b/ENUME/projectA/improveSolution.m @@ -0,0 +1,8 @@ +function x = improveSolution(x, new_euclideanColumnsormOfR, euclideanColumnsormOfR, Matrix, Vector) + while new_euclideanColumnsormOfR <= euclideanColumnsormOfR + euclideanColumnsormOfR = new_euclideanColumnsormOfR; + r = Matrix*x - Vector; + x = x - r; + new_euclideanColumnsormOfR = norm(r); + end % end while +end % end function \ No newline at end of file diff --git a/ENUME/projectA/indicatedMethod.asv b/ENUME/projectA/indicatedMethod.asv new file mode 100644 index 00000000..25552cd7 --- /dev/null +++ b/ENUME/projectA/indicatedMethod.asv @@ -0,0 +1,7 @@ +function x = indicatedMethod(Matrix, Vector) + [~,Columns] = size(Matrix); + checkIfMatrixIsSquareMatrix(Matrix); + [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector); + [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector); + x = iterativeResidualCorrection(Matrix, x, Vector); +end % end function \ No newline at end of file diff --git a/ENUME/projectA/indicatedMethod.m b/ENUME/projectA/indicatedMethod.m new file mode 100644 index 00000000..25552cd7 --- /dev/null +++ b/ENUME/projectA/indicatedMethod.m @@ -0,0 +1,7 @@ +function x = indicatedMethod(Matrix, Vector) + [~,Columns] = size(Matrix); + checkIfMatrixIsSquareMatrix(Matrix); + [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector); + [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector); + x = iterativeResidualCorrection(Matrix, x, Vector); +end % end function \ No newline at end of file diff --git a/ENUME/projectA/iterativeResidualCorrection.m b/ENUME/projectA/iterativeResidualCorrection.m new file mode 100644 index 00000000..77af1d37 --- /dev/null +++ b/ENUME/projectA/iterativeResidualCorrection.m @@ -0,0 +1,6 @@ +function x = iterativeResidualCorrection(Matrix, x, Vector) + r = Matrix*x - Vector; + euclideanColumnsormOfR = norm(r); + new_euclideanColumnsormOfR = euclideanColumnsormOfR; + x = improveSolution(x, new_euclideanColumnsormOfR, euclideanColumnsormOfR, Matrix, Vector); +end % end function \ No newline at end of file diff --git a/ENUME/projectA/matrixA.m b/ENUME/projectA/matrixA.m old mode 100644 new mode 100755 diff --git a/ENUME/projectA/matrixB.m b/ENUME/projectA/matrixB.m old mode 100644 new mode 100755 diff --git a/ENUME/projectA/partialPivoting.m b/ENUME/projectA/partialPivoting.m new file mode 100644 index 00000000..00fb8c5f --- /dev/null +++ b/ENUME/projectA/partialPivoting.m @@ -0,0 +1,6 @@ +function [Matrix, Vector] = partialPivoting(Matrix, Vector, i1, m) + [~,Columns] = size(Matrix); + for i3 = i1 : Columns + partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m); + end % end for +end % end function \ No newline at end of file diff --git a/ENUME/projectA/partialPivotingSwap.m b/ENUME/projectA/partialPivotingSwap.m new file mode 100644 index 00000000..2c6b3d83 --- /dev/null +++ b/ENUME/projectA/partialPivotingSwap.m @@ -0,0 +1,6 @@ +function [Matrix, Vector] = partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m) + if Matrix(i3,i1) == m + swapRowMatrix(Matrix, i1, i3); + swapValueVector(Vector, i1, i3); + end % end if +end % end function \ No newline at end of file diff --git a/ENUME/projectA/partialPivotingSwapOneRow.m b/ENUME/projectA/partialPivotingSwapOneRow.m new file mode 100644 index 00000000..2c6b3d83 --- /dev/null +++ b/ENUME/projectA/partialPivotingSwapOneRow.m @@ -0,0 +1,6 @@ +function [Matrix, Vector] = partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m) + if Matrix(i3,i1) == m + swapRowMatrix(Matrix, i1, i3); + swapValueVector(Vector, i1, i3); + end % end if +end % end function \ No newline at end of file diff --git a/ENUME/projectA/pro1.txt b/ENUME/projectA/pro1.txt old mode 100644 new mode 100755 diff --git a/ENUME/projectA/projectA.aux b/ENUME/projectA/projectA.aux old mode 100644 new mode 100755 diff --git a/ENUME/projectA/projectA.fdb_latexmk b/ENUME/projectA/projectA.fdb_latexmk old mode 100644 new mode 100755 index d55512ff..df7283a1 --- a/ENUME/projectA/projectA.fdb_latexmk +++ b/ENUME/projectA/projectA.fdb_latexmk @@ -1,6 +1,6 @@ # Fdb version 3 -["pdflatex"] 1635438957 "projectA.tex" "projectA.pdf" "projectA" 1635449229 - 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"projectA.aux" - "projectA.out" - "projectA.log" - "projectA.toc" "projectA.pdf" + "projectA.log" + "projectA.out" + "projectA.aux" + "projectA.toc" diff --git a/ENUME/projectA/projectA.fls b/ENUME/projectA/projectA.fls index a9811bd0..791a171d 100644 --- a/ENUME/projectA/projectA.fls +++ b/ENUME/projectA/projectA.fls @@ -1,4 +1,4 @@ -PWD /home/kuchy/Zlew/Studia/SEM_5/enume_done/matlabproject/projectA +PWD /home/kuchy/Zlew/Studia/SEM_5/enume_done/Project/matlabproject/ENUME_Project_31/projectA INPUT /etc/texmf/web2c/texmf.cnf INPUT /usr/share/texmf/web2c/texmf.cnf INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf diff --git a/ENUME/projectA/projectA.log b/ENUME/projectA/projectA.log old mode 100644 new mode 100755 index af3436e2..3c529ce5 --- a/ENUME/projectA/projectA.log +++ b/ENUME/projectA/projectA.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.6.28) 28 OCT 2021 18:35 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.10.23) 6 NOV 2021 03:10 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -541,15 +541,15 @@ Package rerunfilecheck Info: File `projectA.out' has not changed. ) Here is how much of TeX's memory you used: 12275 strings out of 479304 - 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PDF statistics: 302 PDF objects out of 1000 (max. 8388607) 269 compressed objects within 3 object streams diff --git a/ENUME/projectA/projectA.out b/ENUME/projectA/projectA.out old mode 100644 new mode 100755 diff --git a/ENUME/projectA/projectA.pdf b/ENUME/projectA/projectA.pdf old mode 100644 new mode 100755 index f466c3aa..72e20282 Binary files a/ENUME/projectA/projectA.pdf and b/ENUME/projectA/projectA.pdf differ diff --git a/ENUME/projectA/projectA.synctex.gz b/ENUME/projectA/projectA.synctex.gz index 8695ee63..a58c1a8f 100644 Binary files a/ENUME/projectA/projectA.synctex.gz and b/ENUME/projectA/projectA.synctex.gz differ diff --git a/ENUME/projectA/projectA.tex b/ENUME/projectA/projectA.tex index 31b61078..91b20756 100755 --- a/ENUME/projectA/projectA.tex +++ b/ENUME/projectA/projectA.tex @@ -216,7 +216,7 @@ And so on, for $x_k$: Gaussian elimination method has one flaw, where it can come into halt if: \[ a_{kk}^{(k)} = 0 \] To avoid it we use method of pivoting, in our case we will use partial pivoting method. -Before each Gaussian elimination step, we do it before each Gaussian elimination step since this will lead to smaller error. +We do it before each Gaussian elimination step since this will lead to smaller error. \\We first find a row $i$ such that: \[ |{a_{ik}^{k}}| = \underset{j}{max} \{ |{a_{kk}^{k}}|, |{a_{k+1, k}^{k}}|, \cdots, |{a_{nk}^{k}}|\} \] diff --git a/ENUME/projectA/projectA.toc b/ENUME/projectA/projectA.toc old mode 100644 new mode 100755 diff --git a/ENUME/projectA/substractRows b/ENUME/projectA/substractRows new file mode 100644 index 00000000..1c4c4ed9 --- /dev/null +++ b/ENUME/projectA/substractRows @@ -0,0 +1,6 @@ +function [Matrix, Vector] substractRows(Vector, i2, l, i1, t, Columns) + Vector(i2,1) = Vector(i2,1) - l * Vector(i1, 1); + for t = 1 : Columns + Matrix(i2,t) = Matrix(i2,t) - l * Matrix(i1, t); + end % end for +end % end function \ No newline at end of file diff --git a/ENUME/projectA/substractRows.m b/ENUME/projectA/substractRows.m new file mode 100644 index 00000000..cf3e92cc --- /dev/null +++ b/ENUME/projectA/substractRows.m @@ -0,0 +1,6 @@ +function [Matrix, Vector] = substractRows(Matrix, Vector, i2, l, i1, Columns) + Vector(i2,1) = Vector(i2,1) - l * Vector(i1, 1); + for t = 1 : Columns + Matrix(i2,t) = Matrix(i2,t) - l * Matrix(i1, t); + end % end for +end % end function \ No newline at end of file diff --git a/ENUME/projectA/swapRowMatrix.m b/ENUME/projectA/swapRowMatrix.m new file mode 100644 index 00000000..916a57a3 --- /dev/null +++ b/ENUME/projectA/swapRowMatrix.m @@ -0,0 +1,5 @@ +function Matrix = swapRowMatrix(Matrix, i1, i3) + tempRow = Matrix(i1 , :); + Matrix(i1 , :) = Matrix(i3, :); + Matrix(i3, :) = tempRow; +end \ No newline at end of file diff --git a/ENUME/projectA/swapValueVector b/ENUME/projectA/swapValueVector new file mode 100644 index 00000000..2a91a010 --- /dev/null +++ b/ENUME/projectA/swapValueVector @@ -0,0 +1,5 @@ +function Vector = swapValueVector(Vector, i1, i3) + tempVal = Vector(i1); + Vector(i1) = Vector(i3); + Vector(i3) = tempVal; +end % end function \ No newline at end of file diff --git a/ENUME/projectA/swapValueVector.m b/ENUME/projectA/swapValueVector.m new file mode 100644 index 00000000..2a91a010 --- /dev/null +++ b/ENUME/projectA/swapValueVector.m @@ -0,0 +1,5 @@ +function Vector = swapValueVector(Vector, i1, i3) + tempVal = Vector(i1); + Vector(i1) = Vector(i3); + Vector(i3) = tempVal; +end % end function \ No newline at end of file diff --git a/ENUME/projectA/task-USOS_1153296.pdf b/ENUME/projectA/task-USOS_1153296.pdf old mode 100644 new mode 100755 diff --git a/ENUME/projectA/untitled.m b/ENUME/projectA/untitled.m new file mode 100755 index 00000000..6d2fff4a --- /dev/null +++ b/ENUME/projectA/untitled.m @@ -0,0 +1 @@ +jebaćdsia \ No newline at end of file diff --git a/ENUME/projectA/usefullinks.txt b/ENUME/projectA/usefullinks.txt old mode 100644 new mode 100755 diff --git a/ENUME/projectA/vectorA.m b/ENUME/projectA/vectorA.m old mode 100644 new mode 100755 diff --git a/ENUME/projectA/vectorB.m b/ENUME/projectA/vectorB.m old mode 100644 new mode 100755