adding references

ENUME/projectA/indicatedMethod.asv

@@ -0,0 +1,117 @@
+function x = indicatedMethod(Matrix, Vector) % Name of the method as in the textbook
+% x stands for obtained result
+    checkIfMatrixIsSquareMatrix(Matrix);
+    [Matrix, Vector, x] = solveSystem(Matrix, Vector);
+    originalSolution = x;
+    errorBeforeResidualCorrection = norm(Matrix*x - Vector);
+    x = iterativeResidualCorrection(Matrix, x, Vector); % Improve on the solution
+    disp("errorBeforeResidualCorrection")
+    disp(errorBeforeResidualCorrection);
+    disp("errorAfterResidualCorrection")
+    disp(norm(Matrix*x - Vector));
+    disp("Solution before residual correction:")
+    disp(originalSolution);
+    disp("Solution after residual correction:")
+    disp(x);
+    disp("A\b solution:")
+    disp(Matrix\Vector);
+    disp("A\b error:")
+    disp(Matrix\Vector - );
+
+end % end function
+
+function [Matrix, Vector, x] = solveSystem(Matrix, Vector)
+    [~,Columns] = size(Matrix); % We need to know how big the matrix is in next steps
+    % notice the '~', since we assume we use square matrix, we do not need
+    % to have another variable for number of rows since it is the same as
+    % number of columns
+    [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector); 
+    % Change matrix to upper triangular matrix
+    [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector); 
+    % Get the solution
+end % end function
+
+function checkIfMatrixIsSquareMatrix(Matrix)
+    [Rows,Columns] = size(Matrix);
+    if Rows ~= Columns
+        error ('Matrix is not square matrix!');
+    end % end if
+end % end function
+
+function [Matrix, Vector] = gaussianEliminationWithPartialPivoting(Columns, Matrix, Vector)
+    for j = 1 : Columns
+            centralElement = max(Matrix(j:Columns,j)); 
+            % we stay in the same row (j) but we change columns, as in the
+            % textbook
+            [Matrix, Vector] = partialPivoting(Matrix, Vector, j, centralElement, Columns);
+            % ensures that a_kk != 0 and reduces errors
+            [Matrix, Vector] = gaussianElimination(j, Columns, Matrix, Vector);
+            % change matrix into upper triangular matrix
+    end % end for
+end % end function
+
+function [Matrix, Vector] = partialPivoting(Matrix, Vector, j, centralElement, Columns)
+    for k = j : Columns
+        partialPivotingSwapOneRow(Matrix, Vector, j, k, centralElement);
+    end % end for
+end % end function
+
+function [Matrix, Vector] = partialPivotingSwapOneRow(Matrix, Vector, j, k, centralElement)
+    if Matrix(k,j) == centralElement
+    swapRowMatrix(Matrix, j, k); % swap jth row with kth row
+    swapValueVector(Vector, j, k); % swap jth value with kth value
+    end % end if
+end % end function
+
+function Matrix = swapRowMatrix(Matrix, j, k) 
+    temp =  Matrix(j , :); % ' : ' denote "all elements in jth row"
+    Matrix(j , :) = Matrix(k, :);
+    Matrix(k, :) = temp; % temp equal to previous value of jth row
+end
+
+function Vector = swapValueVector(Vector, j, k) 
+    temp = Vector(j);
+    Vector(j) = Vector(k);
+    Vector(k) = temp;  % temp equal to previous value of k element of vector
+end % end function
+
+function [Matrix, Vector] = gaussianElimination(j, Columns, Matrix, Vector)        
+    for i = j + 1 : Columns       
+        rowMultiplier = Matrix(i,j) / Matrix(j,j);
+        [Matrix, Vector] = substractRows(Matrix, Vector, i, rowMultiplier, j, Columns);            
+    end % end for
+end % end function
+
+function [Matrix, Vector] = substractRows(Matrix, Vector, i, rowMultiplier, j, Columns)
+    Vector(i) = Vector(i) - rowMultiplier * Vector(j);
+    for curentColumn = 1 : Columns
+        Matrix(i,curentColumn) = Matrix(i,curentColumn) - rowMultiplier * Matrix(j, curentColumn);
+    end % end for
+end % end function
+
+function [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector)
+    for k = Columns : -1 : 1 
+    % Start at final column and move by -1 each iteration until we reach 1
+        equation = 0;
+        for j = k+1 : Columns
+            equation = equation + Matrix(k,j) * x(j, 1); 
+            % even though x is a vector we still need to put '1' to ensure
+            % that number of columns in the first matrix matches number of
+            % rows in second matrix
+        end % end for
+      
+        x(k, 1) = (Vector(k,1) - equation) / Matrix(k,k);
+        % even though x is a vector we still need to put '1' to ensure
+        % that we do not exceed array bounds
+    end % end for
+end % end function
+
+function x = iterativeResidualCorrection(A, x, b)
+    r = A*x - b;
+    for i = 1 : 100
+        [A, b, deltaX] = solveSystem(A, r);
+        newX = x - deltaX;
+        r = A*newX - b;
+        x = newX;
+    end 
+end % end function

ENUME/projectA/indicatedMethod.m

@@ -2,9 +2,15 @@ function x = indicatedMethod(Matrix, Vector) % Name of the method as in the text
 % x stands for obtained result
     checkIfMatrixIsSquareMatrix(Matrix);
     [Matrix, Vector, x] = solveSystem(Matrix, Vector);
-    norm(x)
+    errorBeforeResidualCorrection = norm(Matrix*x - Vector);
     x = iterativeResidualCorrection(Matrix, x, Vector); % Improve on the solution
-    norm(x)
+    disp("errorBeforeResidualCorrection")
+    disp(errorBeforeResidualCorrection);
+    disp("errorAfterResidualCorrection")
+    disp(norm(Matrix*x - Vector));
+    disp("A\b error:")
+    disp(norm(Matrix *  (Matrix \ Vector)  - Vector));
+
 end % end function
 
 function [Matrix, Vector, x] = solveSystem(Matrix, Vector)
@@ -93,14 +99,13 @@ function [Matrix, Vector, x] = backSubstitutionPhase(Columns, Matrix, Vector)
     end % end for
 end % end function
 
+
 function x = iterativeResidualCorrection(A, x, b)
     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
+    for i = 1 : 10
+        deltaX = solveSystem(A, r);
+        newX = x - deltaX;
+        r = A*newX - b;
+        x = newX;
+    end 
 end % end function

ENUME/projectReferences/ENUME_Project1

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+Subproject commit 035594f28c9fc9c1fcf81a162cb79e6ac9544f56

ENUME/projectReferences/MNUM

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+Subproject commit 50b41b737ffa54606808b956e3fee9d3f1c0d3e5

ENUME/projectReferences/MNUM_Project_1

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+Subproject commit 6fa9a4f7737db7a5949c945059d215d7a46fa0be

ENUME/projectReferences/MatLabMNUM

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+Subproject commit e60c7bbbd49870f0ba297ef29717d0b935643037

ENUME/projectReferences/Metody-Numeryczne-Matlab1

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+Subproject commit c1ea8c47414b4552af22f9eafa5a40c2f03a0607

ENUME/projectReferences/Metody-numeryczne

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+Subproject commit bcfdd828024973cc31d21c8fed20f61a56160ab5

ENUME/projectReferences/Numerical-Methods-metody-numeryczne

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+Subproject commit 5e872beb1e00cedcfc73c2712314386155d61310

ENUME/projectReferences/NumericalMethods

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+Subproject commit 3a727d1411019a175ee619a0b3e08c4be2cc646e

ENUME/projectReferences/Semester-5-ENUME

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+Subproject commit d4889712132ca46ad21d1cfc5593db9fd492b0e5

ENUME/projectReferences/metody-numeryczne-3

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+Subproject commit 83c97447715198af5fe2f8478d65341f0adba46a

ENUME/projectReferences/metody_numeryczne

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+Subproject commit 6398ae4e5f5c7c9bd94d75180a4eae0a93306727

ENUME/projectReferences/numerical-methods

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+Subproject commit 7b85cc9941433b3b1148bb6e6b1b7d117f7a72a4

ENUME/projectReferences/szopinski-enume

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+Subproject commit 3a7369980bccf1e7afcb323fd5f7077dfeb89b1a