for and while loop

Hi

I am looking to run a while loop that solves a rootfinding problem for two initail values, stored in a matrix as described below. It should store the two solved coordiantes in xysolve.

The while loop works fine when running with ii = 1 or ii = 2 (indexing the two initial values) independtly.

However it does not work within the for loop, that I want to use to run the rootfinding for both initail values, one after the other.

Not sure what is the problem here.

Many thanks in advance for any help.

T

%% Solving
% Initial estimates are 2 2x1 vectors: [-10; 10] and [10;-10]
% These are stored together in 2x2 matrix xy

xy = [-10 10 ; 10 10]; 
iter = 0; imax=100; tol=0.001; err=tol;

xysolve = zeros(2,2)

for ii = 1:2
while iter <= imax && err >= tol 
iter = iter + 1;
xy_new = xy(:,ii) - Jacob(xy(:,ii))\f(xy(:,ii));

err = norm(f(xy(:,ii)));
xy = [0 0 ; 0 0]
xy(:,ii) = xy(:,ii) + xy_new
xysolve = xy 
end
end

[Bob Thompson]

'However it does not work within the for loop'

What does this mean? What exactly isn't working? Are you getting an error, or what about your results is telling you that it isn't working?

[T]

no error. it evaluates xy_solve as [ 0 Nan; 0 Nan]

[T]

xy = [-10 10 ; 10 10]; 
% iter = 0; imax=100; tol=0.001; err=tol;

xysolve = zeros(2,2)
for ii = 1:2
iter = 0; imax=100; tol=0.001; err=tol;
while iter <= imax && err >= tol 
iter = iter + 1;
xy_new = xy(:,ii) - Jacob(xy(:,ii))\f(xy(:,ii));

err = norm(f(xy(:,ii)));
xy = [0 0 ; 0 0]
xy(:,ii) = xy(:,ii) + xy_new
xysolve = xy 
end
xysolve %LINE
end

so if I make a break at the indicate LINE, xysolve shows that it has solved the root finding for the first coordinates.

so something is not working in repeating the whole loop now with ii = 2.

Thanks

Answer 1

[Rik]

You need to reset the error term and iteration count at the start of the for loop. Otherwise it will keep the previous values and immediately exit the while loop.

[T]

for ii = 1:2
iter = 0; imax=100; tol=0.001; err=tol;
while iter <= imax && err >= tol 
iter = iter + 1;
xy_new = xy(:,ii) - Jacob(xy(:,ii))\f(xy(:,ii));

err = norm(f(xy(:,ii)));
xy = [0 0 ; 0 0]
xy(:,ii) = xy(:,ii) + xy_new
xysolve = xy 
end
end 

Thank you for your reply. Is this what you are suggesting rik?

it doesnt work: it gives [ 0 nan; 0 nan]

[Rik]

You are wiping your initial value array as well by setting xy=zeros(2);. But otherwise, yes, this is what I meant.

As a further note: I would strongly suggest using the automatic indentation for readability. I would also suggest adding comments about what the code is doing.

[T]

Thanks for your help Rik and the suggestions.

I have worked out how to do it. Ill include it below for any future people with a similar question.

% Initial estimates are 2 2x1 vectors: [-10; 10] and [10;-10]
% These are stored together in 2x2 matrix xy

xysolve = zeros(2,2) % Blank matrix for root cooridantes.

for ii = 1:2 % Indexing to locate the two initial estiamtes in xy.
xy = [-10 10 ; 10 10]; % Initial estimates
iter = 0; imax=100; tol=0.01; err=tol; 

while iter <= imax && err >= tol 
    
    % Root finding method for a system of linear equations (using functions)
    iter = iter + 1;
    xy_new = xy(:,ii) - Jacob(xy(:,ii))\f(xy(:,ii));

    % Error for stopping criteria
    err = norm(f(xy(:,ii)));
   
    % New matrix to position evaluated coordinates back in 2x2 matrix so loop can continue.
    XY = zeros(2)
    XY(:,ii) = XY(:,ii) + xy_new
    xy = XY
end
    % xysolve matrix populated with coordiantes when stopping criteria ends while loop.
    xysolve = xysolve + xy
    
end