mirror of
https://github.com/kuhyx/WUT_Computer_Science.git
synced 2026-07-04 14:43:08 +02:00
Combining all functions into one file
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@ -1,11 +0,0 @@
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function [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector)
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for i3 = Columns : -1 : 1
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E = 0;
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for iter = i3+1 : Columns
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E = E + Matrix(i3,iter) * x(iter,1);
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end % end for
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x(i3, 1) = (Vector(i3,1) - E) / Matrix(i3,i3);
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end % end for
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end % end function
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@ -1,5 +0,0 @@
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function checkIfMatrixIsSquareMatrix(Matrix)
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[Rows,Columns] = size(Matrix);
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if Rows ~= Columns
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error ('Matrix is not square matrix!');
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end % end if
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@ -1 +0,0 @@
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fileattrib debilMode.m
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Binary file not shown.
@ -1,61 +0,0 @@
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function x = gaussianElimination(A, b) % A - matrix, b - vector
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[~, Height] = size(A);
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% Find column with greatest value element
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for i = 1 : Height - 1
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m = max(A(i:Height, i));
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% Find row with greatest value element
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for k = i : Height
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if A(k, i) == m % If the element has the biggest value we now
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% have the value of two rows that we want to swap
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% Swap row in matrix A %
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swapRow(A, i, k);
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swapValue(b, i, k);
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break;
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end % end if
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end % end for
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% Swap value in vector B %
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end % end for
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for j = i + 1 : Height
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l = A(j, i) / A(i, i);
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b(j, 1) = b(j, 1) - l * b(i, 1);
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for t = 1 : Height
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A(j, t) = A(j, t) - l * A(i, t);
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end % end for
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end % end for
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x = zeros(Height, 1);
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for k = Height: -1:1
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E = 0;
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for iter = k + 1 : Height
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E = E + A(k, iter) * x(iter, 1);
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end
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x(k, 1) = (b(k, 1) - E) / A(k, k);
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end
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end % end function
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function swapRow(A, j, k)
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temp = A(j, :);
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A(j, :) = A(k, :);
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A(k, :) = temp;
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end % end function
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function swapValue(b, j, k)
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temp = b(j);
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b(j) = b(k);
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b(k) = temp;
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end % end function
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@ -1,8 +0,0 @@
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function [Matrix, Vector] = gaussianElimination(i1, Columns, Matrix, Vector)
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for i2 = i1 + 1 : Columns
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l = Matrix(i2,i1) / Matrix(i1,i1);
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[Matrix, Vector] = substractRows(Matrix, Vector, i2, l, i1, Columns);
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end % end for
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end % end function
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@ -1,7 +0,0 @@
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function [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector)
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for i1 = 1 : Columns - 1
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m = max(Matrix(i1:Columns,i1));
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partialPivoting(Matrix, Vector, i1, m);
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[Matrix, Vector] = gaussianElimination(i1, Columns, Matrix, Vector);
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end % end for
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end % end function
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@ -1,8 +0,0 @@
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function x = improveSolution(x, new_euclideanColumnsormOfR, euclideanColumnsormOfR, Matrix, Vector)
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while new_euclideanColumnsormOfR <= euclideanColumnsormOfR
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euclideanColumnsormOfR = new_euclideanColumnsormOfR;
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r = Matrix*x - Vector;
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x = x - r;
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new_euclideanColumnsormOfR = norm(r);
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end % end while
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end % end function
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@ -1,7 +0,0 @@
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function x = indicatedMethod(Matrix, Vector)
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[~,Columns] = size(Matrix);
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checkIfMatrixIsSquareMatrix(Matrix);
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[Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector);
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[Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector);
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x = iterativeResidualCorrection(Matrix, x, Vector);
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end % end function
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@ -4,4 +4,89 @@ function x = indicatedMethod(Matrix, Vector)
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[Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector);
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[Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector);
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x = iterativeResidualCorrection(Matrix, x, Vector);
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end % end function
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function checkIfMatrixIsSquareMatrix(Matrix)
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[Rows,Columns] = size(Matrix);
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if Rows ~= Columns
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error ('Matrix is not square matrix!');
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end % end if
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end % end function
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function [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector)
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for i1 = 1 : Columns - 1
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m = max(Matrix(i1:Columns,i1));
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partialPivoting(Matrix, Vector, i1, m);
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[Matrix, Vector] = gaussianElimination(i1, Columns, Matrix, Vector);
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end % end for
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end % end function
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function [Matrix, Vector] = partialPivoting(Matrix, Vector, i1, m)
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[~,Columns] = size(Matrix);
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for i3 = i1 : Columns
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partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m);
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end % end for
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end % end function
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function [Matrix, Vector] = partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m)
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if Matrix(i3,i1) == m
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swapRowMatrix(Matrix, i1, i3);
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swapValueVector(Vector, i1, i3);
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end % end if
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end % end function
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function Matrix = swapRowMatrix(Matrix, i1, i3)
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tempRow = Matrix(i1 , :);
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Matrix(i1 , :) = Matrix(i3, :);
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Matrix(i3, :) = tempRow;
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end
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function Vector = swapValueVector(Vector, i1, i3)
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tempVal = Vector(i1);
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Vector(i1) = Vector(i3);
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Vector(i3) = tempVal;
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end % end function
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function [Matrix, Vector] = gaussianElimination(i1, Columns, Matrix, Vector)
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for i2 = i1 + 1 : Columns
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l = Matrix(i2,i1) / Matrix(i1,i1);
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[Matrix, Vector] = substractRows(Matrix, Vector, i2, l, i1, Columns);
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end % end for
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end % end function
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function [Matrix, Vector] = substractRows(Matrix, Vector, i2, l, i1, Columns)
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Vector(i2,1) = Vector(i2,1) - l * Vector(i1, 1);
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for t = 1 : Columns
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Matrix(i2,t) = Matrix(i2,t) - l * Matrix(i1, t);
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end % end for
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end % end function
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function [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector)
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for i3 = Columns : -1 : 1
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E = 0;
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for iter = i3+1 : Columns
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E = E + Matrix(i3,iter) * x(iter,1);
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end % end for
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x(i3, 1) = (Vector(i3,1) - E) / Matrix(i3,i3);
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end % end for
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end % end function
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function x = iterativeResidualCorrection(Matrix, x, Vector)
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r = Matrix*x - Vector;
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euclideanColumnsormOfR = norm(r);
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new_euclideanColumnsormOfR = euclideanColumnsormOfR;
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x = improveSolution(x, new_euclideanColumnsormOfR, euclideanColumnsormOfR, Matrix, Vector);
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end % end function
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function x = improveSolution(x, new_euclideanColumnsormOfR, euclideanColumnsormOfR, Matrix, Vector)
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while new_euclideanColumnsormOfR <= euclideanColumnsormOfR
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euclideanColumnsormOfR = new_euclideanColumnsormOfR;
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r = Matrix*x - Vector;
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x = x - r;
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new_euclideanColumnsormOfR = norm(r);
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end % end while
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end % end function
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@ -1,6 +0,0 @@
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function x = iterativeResidualCorrection(Matrix, x, Vector)
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r = Matrix*x - Vector;
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euclideanColumnsormOfR = norm(r);
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new_euclideanColumnsormOfR = euclideanColumnsormOfR;
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x = improveSolution(x, new_euclideanColumnsormOfR, euclideanColumnsormOfR, Matrix, Vector);
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end % end function
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@ -1,6 +0,0 @@
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function [Matrix, Vector] = partialPivoting(Matrix, Vector, i1, m)
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[~,Columns] = size(Matrix);
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for i3 = i1 : Columns
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partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m);
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end % end for
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end % end function
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@ -1,6 +0,0 @@
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function [Matrix, Vector] = partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m)
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if Matrix(i3,i1) == m
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swapRowMatrix(Matrix, i1, i3);
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swapValueVector(Vector, i1, i3);
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end % end if
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end % end function
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@ -1,6 +0,0 @@
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function [Matrix, Vector] = partialPivotingSwapOneRow(Matrix, Vector, i1, i3, m)
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if Matrix(i3,i1) == m
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swapRowMatrix(Matrix, i1, i3);
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swapValueVector(Vector, i1, i3);
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end % end if
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end % end function
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@ -1,58 +0,0 @@
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\relax
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\providecommand\hyper@newdestlabel[2]{}
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\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
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\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
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\global\let\oldcontentsline\contentsline
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\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
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\global\let\oldnewlabel\newlabel
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\gdef\newlabel#1#2{\newlabelxx{#1}#2}
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\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
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\AtEndDocument{\ifx\hyper@anchor\@undefined
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\let\contentsline\oldcontentsline
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\let\newlabel\oldnewlabel
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\fi}
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\fi}
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\global\let\hyper@last\relax
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\gdef\HyperFirstAtBeginDocument#1{#1}
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\providecommand\HyField@AuxAddToFields[1]{}
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\@writefile{lof}{\addvspace {10\p@ }}
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\@writefile{toc}{\contentsline {subsubsection}{Zeroing second column}{6}{section*.4}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{Zeroing next columns}{6}{section*.5}\protected@file@percent }
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\bibcite{texbook}{1}
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\gdef \@abspage@last{11}
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@ -1,149 +0,0 @@
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# Fdb version 3
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[6] [7]
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Chapter 3.
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[8
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Chapter 4.
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[9
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@ -1,26 +0,0 @@
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\BOOKMARK [0][-]{chapter.1}{Problem 1 - Finding machine epsilion}{}% 1
|
||||
\BOOKMARK [1][-]{section.1.1}{Problem}{chapter.1}% 2
|
||||
\BOOKMARK [1][-]{section.1.2}{Theoretical Introduction}{chapter.1}% 3
|
||||
\BOOKMARK [2][-]{subsection.1.2.1}{Definition of machine epsilion}{section.1.2}% 4
|
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\BOOKMARK [2][-]{subsection.1.2.2}{Practical applications of machine epsilion}{section.1.2}% 5
|
||||
\BOOKMARK [1][-]{section.1.3}{Solution}{chapter.1}% 6
|
||||
\BOOKMARK [2][-]{subsection.1.3.1}{Matlab code}{section.1.3}% 7
|
||||
\BOOKMARK [1][-]{section.1.4}{Discussion of the result}{chapter.1}% 8
|
||||
\BOOKMARK [0][-]{chapter.2}{Problem 2 - Solving a system of n linear equations - indicated method}{}% 9
|
||||
\BOOKMARK [1][-]{section.2.1}{Problem}{chapter.2}% 10
|
||||
\BOOKMARK [1][-]{section.2.2}{Theoretical Introduction}{chapter.2}% 11
|
||||
\BOOKMARK [2][-]{subsection.2.2.1}{Transform system of equation into an upper-triangular matrix}{section.2.2}% 12
|
||||
\BOOKMARK [2][-]{subsection.2.2.2}{Backward substitution}{section.2.2}% 13
|
||||
\BOOKMARK [2][-]{subsection.2.2.3}{Partial Pivoting}{section.2.2}% 14
|
||||
\BOOKMARK [1][-]{section.2.3}{Solution}{chapter.2}% 15
|
||||
\BOOKMARK [1][-]{section.2.4}{Discussion of the result}{chapter.2}% 16
|
||||
\BOOKMARK [0][-]{chapter.3}{Problem 3 - Solving a system of n linear equations - iterative algorithm}{}% 17
|
||||
\BOOKMARK [1][-]{section.3.1}{Problem}{chapter.3}% 18
|
||||
\BOOKMARK [1][-]{section.3.2}{Theoretical introduction}{chapter.3}% 19
|
||||
\BOOKMARK [1][-]{section.3.3}{Solution}{chapter.3}% 20
|
||||
\BOOKMARK [1][-]{section.3.4}{Discussion of the result}{chapter.3}% 21
|
||||
\BOOKMARK [0][-]{chapter.4}{Problem 4 - QR method of finding eigenvalues}{}% 22
|
||||
\BOOKMARK [1][-]{section.4.1}{Problem}{chapter.4}% 23
|
||||
\BOOKMARK [1][-]{section.4.2}{Theoretical introduction}{chapter.4}% 24
|
||||
\BOOKMARK [1][-]{section.4.3}{Solution}{chapter.4}% 25
|
||||
\BOOKMARK [1][-]{section.4.4}{Discussion of the result}{chapter.4}% 26
|
||||
Binary file not shown.
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@ -224,6 +224,21 @@ Then we swap this row with k-th row. Since the matrix we use is assumed to be no
|
||||
|
||||
\section{Solution}
|
||||
|
||||
\subsection{Main function}
|
||||
\begin{simplechar}
|
||||
\begin{lstlisting}
|
||||
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
|
||||
\end{lstlisting}
|
||||
\end{simplechar}
|
||||
|
||||
|
||||
|
||||
\section{Discussion of the result}
|
||||
|
||||
\chapter{Problem 3 - Solving a system of n linear equations - iterative algorithm}
|
||||
|
||||
@ -1,30 +0,0 @@
|
||||
\contentsline {chapter}{\numberline {1}Problem 1 - Finding machine epsilion}{2}{chapter.1}%
|
||||
\contentsline {section}{\numberline {1.1}Problem}{2}{section.1.1}%
|
||||
\contentsline {section}{\numberline {1.2}Theoretical Introduction}{2}{section.1.2}%
|
||||
\contentsline {subsection}{\numberline {1.2.1}Definition of machine epsilion}{2}{subsection.1.2.1}%
|
||||
\contentsline {subsection}{\numberline {1.2.2}Practical applications of machine epsilion}{2}{subsection.1.2.2}%
|
||||
\contentsline {section}{\numberline {1.3}Solution}{3}{section.1.3}%
|
||||
\contentsline {subsection}{\numberline {1.3.1}Matlab code}{3}{subsection.1.3.1}%
|
||||
\contentsline {section}{\numberline {1.4}Discussion of the result}{3}{section.1.4}%
|
||||
\contentsline {chapter}{\numberline {2}Problem 2 - Solving a system of n linear equations - indicated method}{5}{chapter.2}%
|
||||
\contentsline {section}{\numberline {2.1}Problem}{5}{section.2.1}%
|
||||
\contentsline {section}{\numberline {2.2}Theoretical Introduction}{5}{section.2.2}%
|
||||
\contentsline {subsection}{\numberline {2.2.1}Transform system of equation into an upper-triangular matrix}{5}{subsection.2.2.1}%
|
||||
\contentsline {subsubsection}{Starting conditions}{5}{section*.2}%
|
||||
\contentsline {subsubsection}{Zeroing first column}{6}{section*.3}%
|
||||
\contentsline {subsubsection}{Zeroing second column}{6}{section*.4}%
|
||||
\contentsline {subsubsection}{Zeroing next columns}{6}{section*.5}%
|
||||
\contentsline {subsection}{\numberline {2.2.2}Backward substitution}{7}{subsection.2.2.2}%
|
||||
\contentsline {subsection}{\numberline {2.2.3}Partial Pivoting}{7}{subsection.2.2.3}%
|
||||
\contentsline {section}{\numberline {2.3}Solution}{7}{section.2.3}%
|
||||
\contentsline {section}{\numberline {2.4}Discussion of the result}{7}{section.2.4}%
|
||||
\contentsline {chapter}{\numberline {3}Problem 3 - Solving a system of n linear equations - iterative algorithm}{8}{chapter.3}%
|
||||
\contentsline {section}{\numberline {3.1}Problem}{8}{section.3.1}%
|
||||
\contentsline {section}{\numberline {3.2}Theoretical introduction}{8}{section.3.2}%
|
||||
\contentsline {section}{\numberline {3.3}Solution}{8}{section.3.3}%
|
||||
\contentsline {section}{\numberline {3.4}Discussion of the result}{8}{section.3.4}%
|
||||
\contentsline {chapter}{\numberline {4}Problem 4 - QR method of finding eigenvalues}{9}{chapter.4}%
|
||||
\contentsline {section}{\numberline {4.1}Problem}{9}{section.4.1}%
|
||||
\contentsline {section}{\numberline {4.2}Theoretical introduction}{9}{section.4.2}%
|
||||
\contentsline {section}{\numberline {4.3}Solution}{9}{section.4.3}%
|
||||
\contentsline {section}{\numberline {4.4}Discussion of the result}{9}{section.4.4}%
|
||||
@ -1,6 +0,0 @@
|
||||
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
|
||||
@ -1,6 +0,0 @@
|
||||
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
|
||||
@ -1,5 +0,0 @@
|
||||
function Matrix = swapRowMatrix(Matrix, i1, i3)
|
||||
tempRow = Matrix(i1 , :);
|
||||
Matrix(i1 , :) = Matrix(i3, :);
|
||||
Matrix(i3, :) = tempRow;
|
||||
end
|
||||
@ -1,5 +0,0 @@
|
||||
function Vector = swapValueVector(Vector, i1, i3)
|
||||
tempVal = Vector(i1);
|
||||
Vector(i1) = Vector(i3);
|
||||
Vector(i3) = tempVal;
|
||||
end % end function
|
||||
@ -1,5 +0,0 @@
|
||||
function Vector = swapValueVector(Vector, i1, i3)
|
||||
tempVal = Vector(i1);
|
||||
Vector(i1) = Vector(i3);
|
||||
Vector(i3) = tempVal;
|
||||
end % end function
|
||||
@ -1 +0,0 @@
|
||||
jebaćdsia
|
||||
Loading…
Reference in New Issue
Block a user