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Splitting task 2 matlab function into smaller functions

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root 2021-11-06 04:01:04 +01:00
parent 159ae4e1e9
commit adf1f954e3
38 changed files with 129 additions and 293 deletions
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11
ENUME/projectA/backSubstitutionPhase.m Normal file
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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

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ENUME/projectA/checkIfMatrixIsSquareMatrix.m Normal file
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function checkIfMatrixIsSquareMatrix(Matrix)
[Rows,Columns] = size(Matrix);
if Rows ~= Columns
error ('Matrix is not square matrix!');
end % end if

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ENUME/projectA/debilMode
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% ------- 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

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ENUME/projectA/debilMode.asv
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% ------- 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

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ENUME/projectA/debilMode.m
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% ------- 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

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fileattrib debilMode.m

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ENUME/projectA/gaussianElimination.asv Normal file → Executable file
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ENUME/projectA/gaussianElimination.m Normal file → Executable file
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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

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ENUME/projectA/gaussianEliminationWithPartialPivoting.m Normal file
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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

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ENUME/projectA/improveSolution.m Normal file
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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

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ENUME/projectA/indicatedMethod.asv Normal file
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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

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ENUME/projectA/indicatedMethod.m Normal file
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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

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ENUME/projectA/iterativeResidualCorrection.m Normal file
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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

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ENUME/projectA/partialPivoting.m Normal file
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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

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ENUME/projectA/partialPivotingSwap.m Normal file
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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

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ENUME/projectA/partialPivotingSwapOneRow.m Normal file
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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

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@ -216,7 +216,7 @@ And so on, for $x_k$:
Gaussian elimination method has one flaw, where it can come into halt if:
\[ a_{kk}^{(k)} = 0 \]
To avoid it we use method of pivoting, in our case we will use partial pivoting method.
Before each Gaussian elimination step, we do it before each Gaussian elimination step since this will lead to smaller error.
We do it before each Gaussian elimination step since this will lead to smaller error.
\\We first find a row $i$ such that:
\[ |{a_{ik}^{k}}| = \underset{j}{max} \{ |{a_{kk}^{k}}|, |{a_{k+1, k}^{k}}|, \cdots, |{a_{nk}^{k}}|\} \]

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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

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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

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function Matrix = swapRowMatrix(Matrix, i1, i3)
tempRow = Matrix(i1 , :);
Matrix(i1 , :) = Matrix(i3, :);
Matrix(i3, :) = tempRow;
end

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function Vector = swapValueVector(Vector, i1, i3)
tempVal = Vector(i1);
Vector(i1) = Vector(i3);
Vector(i3) = tempVal;
end % end function

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function Vector = swapValueVector(Vector, i1, i3)
tempVal = Vector(i1);
Vector(i1) = Vector(i3);
Vector(i3) = tempVal;
end % end function

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jebaćdsia

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ENUME/projectA/vectorA.m Normal file → Executable file
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ENUME/projectA/vectorB.m Normal file → Executable file
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