From fc66144833a5e94863ba814618e2f678cef1efc4 Mon Sep 17 00:00:00 2001
From: PolishPigeon <krzysztofrudnicki0@gmail.com>
Date: Fri, 12 Nov 2021 08:41:21 +0100
Subject: [PATCH] Fixing QRNoShifts

---
 ENUME/projectA/QRNoShifts.asv | 39 ++++++++++++++-------
 ENUME/projectA/QRNoShifts.m   | 64 +++++++++++++++++++++++------------
 ENUME/projectA/QRShifts.m     |  7 ++--
 3 files changed, 74 insertions(+), 36 deletions(-)

diff --git a/ENUME/projectA/QRNoShifts.asv b/ENUME/projectA/QRNoShifts.asv
index 4ee40386..ff3ed3ef 100644
--- a/ENUME/projectA/QRNoShifts.asv
+++ b/ENUME/projectA/QRNoShifts.asv
@@ -1,17 +1,8 @@
 function [eigenValues, whichIterationAreWeOn, Matrix] = QRNoShifts(Matrix)
+    startingMatrix = Matrix;
+    matlabEigen = eig(Matrix);
     [whichIterationAreWeOn, threshold] = initializeValues();
-    while threshold > 1e-6
-        [Q, R] = gramSchmidtAlgorithm(Matrix);
-        Matrix = R * Q;
-        whichIterationAreWeOn = whichIterationAreWeOn + 1;
-        
-        % iterate until all non-diagonal elements are below the threshold
-        nondiag = Matrix - diag(diag(Matrix)); % first diag converts Matrix 
-        % into vector consisting of values on the diagonal of matrix, 
-        % second diag converts this vector into matrix with zeros on
-        % everything except diagonal
-        threshold = max(abs(nondiag));
-    end
+    [Matrix, whichIterationAreWeOn, eigenValues] = QRNoShiftsLoop(threshold, Matrix, whichIterationAreWeOn);
     
     % convert eigenvalue matrix to vector
     eigenValues = diag(Matrix)';
@@ -21,6 +12,30 @@ function [eigenValues, whichIterationAreWeOn, Matrix] = QRNoShifts(Matrix)
     disp(Matrix);
 end
 
+function [Matrix, whichIterationAreWeOn, eigenValues] = QRNoShiftsLoop(threshold, Matrix, whichIterationAreWeOn)
+    while threshold > 1e-6
+        [Q, R] = gramSchmidtAlgorithm(Matrix);
+        Matrix = R * Q;
+        whichIterationAreWeOn = whichIterationAreWeOn + 1;
+        
+        % iterate until all non-diagonal elements are below the threshold
+        matrixWithoutDiagonal = Matrix - diag(diag(Matrix)); % first diag converts Matrix 
+        % into vector consisting of values on the diagonal of matrix, 
+        % second diag converts this vector into matrix with zeros on
+        % everything except diagonal
+        % If we substract it from Matrix we get original Matrix with zeros
+        % on a diagonal
+        threshold = max(abs(matrixWithoutDiagonal));
+    end
+end
+
+function displayResults(eigenValues, whichIterationsAreWeOn, Matrix, startingMatrix, matlabEigen)
+    disp("How many iterations it took:")
+    disp(whichIterationsAreWeOn);
+    disp("Starting matrix:")
+    disp(M)
+end
+
 function [whichIterationAreWeOn, threshold] = initializeValues()
     whichIterationAreWeOn = 0;
     threshold = inf;
diff --git a/ENUME/projectA/QRNoShifts.m b/ENUME/projectA/QRNoShifts.m
index 8669d237..31301c80 100644
--- a/ENUME/projectA/QRNoShifts.m
+++ b/ENUME/projectA/QRNoShifts.m
@@ -1,31 +1,51 @@
 function [eigenValues, whichIterationAreWeOn, Matrix] = QRNoShifts(Matrix)
-    [whichIterationAreWeOn, threshold] = initializeValues();
-    while threshold > 1e-6
-        [Q, R] = gramSchmidtAlgorithm(Matrix);
-        Matrix = R * Q;
-        whichIterationAreWeOn = whichIterationAreWeOn + 1;
-        
-        % iterate until all non-diagonal elements are below the threshold
-        matrixWithoutDiagonal = Matrix - diag(diag(Matrix)); % first diag converts Matrix 
-        % into vector consisting of values on the diagonal of matrix, 
-        % second diag converts this vector into matrix with zeros on
-        % everything except diagonal
-        % If we substract it from Matrix we get original Matrix with zeros
-        % on a diagonal
-        threshold = max(abs(matrixWithoutDiagonal));
-    end
-    
-    % convert eigenvalue matrix to vector
+
+    [whichIterationAreWeOn, threshold, startingMatrix, matlabEigen] = initializeValues(Matrix);
+    [Matrix, whichIterationAreWeOn] = QRNoShiftsLoop(threshold, Matrix, whichIterationAreWeOn);
     eigenValues = diag(Matrix)';
-    disp("Iterations it took: ");
-    disp(whichIterationAreWeOn);
-    disp("Final matrix: ");
-    disp(Matrix);
+    displayResults(whichIterationAreWeOn, Matrix, startingMatrix, matlabEigen);
 end
 
-function [whichIterationAreWeOn, threshold] = initializeValues()
+function [Matrix, whichIterationAreWeOn] = QRNoShiftsLoop(threshold, Matrix, whichIterationAreWeOn)
+    while threshold > 1e-6
+        [Matrix, whichIterationAreWeOn, threshold] = QRNoShiftsInsideLoop(Matrix, whichIterationAreWeOn);
+    end
+end
+
+function [Matrix, whichIterationAreWeOn, threshold] = QRNoShiftsInsideLoop(Matrix, whichIterationAreWeOn)
+    [Q, R] = gramSchmidtAlgorithm(Matrix);
+    Matrix = R * Q;
+    whichIterationAreWeOn = whichIterationAreWeOn + 1;
+    
+    % iterate until all non-diagonal elements are below the threshold
+    matrixWithoutDiagonal = Matrix - diag(diag(Matrix)); % first diag converts Matrix 
+    % into vector consisting of values on the diagonal of matrix, 
+    % second diag converts this vector into matrix with zeros on
+    % everything except diagonal
+    % If we substract it from Matrix we get original Matrix with zeros
+    % on a diagonal
+    threshold = max(max(abs(matrixWithoutDiagonal)));
+    % first max returns vector of elements 
+    % second max returns max element from this vector
+end
+
+function displayResults(whichIterationsAreWeOn, Matrix, startingMatrix, matlabEigen)
+    disp("How many iterations it took:")
+    disp(whichIterationsAreWeOn)
+    disp("Starting Matrix:")
+    disp(startingMatrix)
+    disp("Final Matrix:")
+    disp(Matrix)
+    disp("eig(Matrix) eigen values:")
+    disp(matlabEigen)
+    disp("Our eigen values:")
+end
+
+function [whichIterationAreWeOn, threshold, startingMatrix, matlabEigen] = initializeValues(Matrix)
     whichIterationAreWeOn = 0;
     threshold = inf;
+    startingMatrix = Matrix;
+    matlabEigen = eig(Matrix);
 end
 
 % performs QR or QRdash decomposition of a matrix
diff --git a/ENUME/projectA/QRShifts.m b/ENUME/projectA/QRShifts.m
index feec8a68..17b0dbf9 100644
--- a/ENUME/projectA/QRShifts.m
+++ b/ENUME/projectA/QRShifts.m
@@ -1,9 +1,10 @@
 % finds the eigenValues of a matrix using QR with shifts
 function [eigenValues, whatIterationAreWeOn, Matrix] = QRShifts(Matrix)
     eigenFromMatlab = eig(Matrix);
+    initialMatrix = Matrix;
     [eigenValues, whatIterationAreWeOn, matrixSize, minThreshold] = initiateValues(Matrix);
     [Matrix, whatIterationAreWeOn, eigenValues] = QRShiftLoop(matrixSize, Matrix, eigenValues, minThreshold, whatIterationAreWeOn);
-    dispResults(Matrix, whatIterationAreWeOn, eigenFromMatlab);
+    dispResults(Matrix, whatIterationAreWeOn, eigenFromMatlab, initialMatrix);
 end 
 
 function [eigenValues, whatIterationAreWeOn, matrixSize, minThreshold] = initiateValues(Matrix)
@@ -121,7 +122,9 @@ function [Q, R] = normalizeColumns(columns, Q, R)
     end
 end
 
-function dispResults(Matrix, whatIterationAreWeOn, eigenFromMatlab)
+function dispResults(Matrix, whatIterationAreWeOn, eigenFromMatlab, initialMatrix)
+    disp("Initial matrix: ");
+    disp(initialMatrix);
     disp("Final matrix: ");
     disp(Matrix);
     disp("Number of iterations: ");