From adf1f954e33e50e2d0379ed00679accc1f8e0050 Mon Sep 17 00:00:00 2001 From: root Date: Sat, 6 Nov 2021 04:01:04 +0100 Subject: [PATCH] Splitting task 2 matlab function into smaller functions --- ENUME/projectA/backSubstitutionPhase.m | 11 +++ ENUME/projectA/checkIfMatrixIsSquareMatrix.m | 5 ++ ENUME/projectA/debilMode | 71 ------------------ ENUME/projectA/debilMode.asv | 71 ------------------ ENUME/projectA/debilMode.m | 67 ----------------- ENUME/projectA/fileAttrib.m | 1 + ENUME/projectA/gaussianElimination.asv | 0 ENUME/projectA/gaussianElimination.m | 67 ++--------------- .../gaussianEliminationWithPartialPivoting.m | 7 ++ ENUME/projectA/improveSolution.m | 8 ++ ENUME/projectA/indicatedMethod.asv | 7 ++ ENUME/projectA/indicatedMethod.m | 7 ++ ENUME/projectA/iterativeResidualCorrection.m | 6 ++ ENUME/projectA/matrixA.m | 0 ENUME/projectA/matrixB.m | 0 ENUME/projectA/partialPivoting.m | 6 ++ ENUME/projectA/partialPivotingSwap.m | 6 ++ ENUME/projectA/partialPivotingSwapOneRow.m | 6 ++ ENUME/projectA/pro1.txt | 0 ENUME/projectA/projectA.aux | 0 ENUME/projectA/projectA.fdb_latexmk | 36 ++++----- ENUME/projectA/projectA.fls | 2 +- ENUME/projectA/projectA.log | 8 +- ENUME/projectA/projectA.out | 0 ENUME/projectA/projectA.pdf | Bin 229855 -> 229976 bytes ENUME/projectA/projectA.synctex.gz | Bin 48307 -> 48299 bytes ENUME/projectA/projectA.tex | 2 +- ENUME/projectA/projectA.toc | 0 ENUME/projectA/substractRows | 6 ++ ENUME/projectA/substractRows.m | 6 ++ ENUME/projectA/swapRowMatrix.m | 5 ++ ENUME/projectA/swapValueVector | 5 ++ ENUME/projectA/swapValueVector.m | 5 ++ ENUME/projectA/task-USOS_1153296.pdf | Bin ENUME/projectA/untitled.m | 1 + ENUME/projectA/usefullinks.txt | 0 ENUME/projectA/vectorA.m | 0 ENUME/projectA/vectorB.m | 0 38 files changed, 129 insertions(+), 293 deletions(-) create mode 100644 ENUME/projectA/backSubstitutionPhase.m create mode 100644 ENUME/projectA/checkIfMatrixIsSquareMatrix.m delete mode 100644 ENUME/projectA/debilMode delete mode 100644 ENUME/projectA/debilMode.asv delete mode 100644 ENUME/projectA/debilMode.m create mode 100644 ENUME/projectA/fileAttrib.m mode change 100644 => 100755 ENUME/projectA/gaussianElimination.asv mode change 100644 => 100755 ENUME/projectA/gaussianElimination.m create mode 100644 ENUME/projectA/gaussianEliminationWithPartialPivoting.m create mode 100644 ENUME/projectA/improveSolution.m create mode 100644 ENUME/projectA/indicatedMethod.asv create mode 100644 ENUME/projectA/indicatedMethod.m create mode 100644 ENUME/projectA/iterativeResidualCorrection.m mode change 100644 => 100755 ENUME/projectA/matrixA.m mode change 100644 => 100755 ENUME/projectA/matrixB.m create mode 100644 ENUME/projectA/partialPivoting.m create mode 100644 ENUME/projectA/partialPivotingSwap.m create mode 100644 ENUME/projectA/partialPivotingSwapOneRow.m mode change 100644 => 100755 ENUME/projectA/pro1.txt mode change 100644 => 100755 ENUME/projectA/projectA.aux mode change 100644 => 100755 ENUME/projectA/projectA.fdb_latexmk mode change 100644 => 100755 ENUME/projectA/projectA.log mode change 100644 => 100755 ENUME/projectA/projectA.out mode change 100644 => 100755 ENUME/projectA/projectA.pdf mode change 100644 => 100755 ENUME/projectA/projectA.toc create mode 100644 ENUME/projectA/substractRows create mode 100644 ENUME/projectA/substractRows.m create mode 100644 ENUME/projectA/swapRowMatrix.m create mode 100644 ENUME/projectA/swapValueVector create mode 100644 ENUME/projectA/swapValueVector.m mode change 100644 => 100755 ENUME/projectA/task-USOS_1153296.pdf create mode 100755 ENUME/projectA/untitled.m mode change 100644 => 100755 ENUME/projectA/usefullinks.txt mode change 100644 => 100755 ENUME/projectA/vectorA.m mode change 100644 => 100755 ENUME/projectA/vectorB.m 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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