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Fixing QRNoShifts

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PolishPigeon 2021-11-12 08:41:21 +01:00
parent 903d1529bb
commit fc66144833
3 changed files with 74 additions and 36 deletions
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39
ENUME/projectA/QRNoShifts.asv
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@ -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;

64
ENUME/projectA/QRNoShifts.m
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@ -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

7
ENUME/projectA/QRShifts.m
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@ -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: ");