Array dimensions not agreeing

I'm trying to calculate the magnetic field of a stack of magnet rings given the dimensions of the magnets. However, when I try to calculate the field for each of the parameters for the ring dimensions, the array dimensions of the magnetic field do not agree, giving the error "Array dimensions must match for binary array op.".

I think there is an issue with the way I am combining the arrays in the equation for Bz (see below).

%Range of axial field and step size for functions
zmin=-1;
zmax=1;
dz=0.01; % step size for the plots
nz=round((zmax-zmin)/dz)+1; %number of z steps in the limit
iz=1:nz; %index for each z step
z(iz)=linspace(zmin,zmax,nz); %values of z
 
%Structure for a magnet, defining the length of a magnet, the
%length of the stack and the position of each magnet (everthing to
%calculate the B field)
B0=1.4; % saturation of permanent magnetic material
nmag=10; % number of rings
imag=1:nmag; %ring index
zlength=(zmax-zmin)/nmag; %length of ring
zstart(imag)=zmin:zlength:(zmax-zlength); %position of ring edge with lower z value
zend(imag)=zstart+zlength; % set up a vector with the ends of each ring section
zmag(imag)=-0.9:0.2:0.9;
 
%five optimisation parameters
ia=1:5;
a(ia)=linspace(-0.2,0,ia(end));
ib=1:5;
b(ib)=linspace(-0.1,0.1,ib(end));
ic=1:5;
c(ic)=linspace(-0.1,0.1,ic(end));
id=1:5;
d(id)=linspace(-0.1,0.1,id(end));
ie=1:5;
e(ie)=linspace(-0.1,0.1,ie(end));
 
%magnet radii
or=zeros(imag(end),ia(end),ib(end));
for ib = 1:ib(end)
    or(:,:,ib) = 1 + zmag'.^2*a + b(ib)*zmag'.^4;
end
 
ir=zeros(imag(end),ic(end),id(end),ie(end));
for id = 1:id(end)
    for ie = 1:ie(end)
        ir(:,:,id,ie) = c + d(id)*zmag'.^2 + e(ie)*zmag'.^4; 
    end
end
 
Bz=zeros(nz,nmag,ia(end),ib(end),ic(end),id(end),ie(end)); % store the B field for each ring separately in Bz
 
for imag=1:imag(end)
    
    Bz=Bz+(B0*0.5*( (zend(imag)-z')./sqrt((zend(imag)-z').^2+ir(imag,:,:,:).^2/4) ...
           -(zstart(imag)-z')./sqrt((zstart(imag)-z').^2+ir(imag,:,:,:).^2/4) ...
           -(zend(imag)-z')./sqrt((zend(imag)-z').^2+or(imag,:,:).^2/4)  ...
           +(zstart(imag)-z')./sqrt((zstart(imag)-z').^2+or(imag,:,:).^2/4)   ));
end

Answer 1

[Matt J]

I think there is an issue with the way I am combining the arrays in the equation for Bz (see below).

I don't see why you would think that unless you are seeing a different error message than the one I am seeing, which occurs far earlier in line 35:

Error in test (line 35)
    or(:,:,ib) = 1 + zmag'.^2*a + b(ib)*zmag'.^4;

The output of whos() reveals the problems straight away,

K>> whos or zmag ib a
  Name       Size             Bytes  Class     Attributes

  a          5x1                 40  double              
  ib         1x1                  8  double              
  or        10x5x5             2000  double              
  zmag       1x10                80  double              

Clearly, zmag'.^2 would be a 10x1 matrix, but you are multiplying it with a matrix a that is 5x1. Because the calculation needs to end up giving a 10x5 matrix to agree with the size of or(:,:,ib), I can only guess that you meant to have zmag'.^2 * a.' ?

[JC]

Thanks for replying!

When I output whos(), a is a 1x5 matrix so I'm not getting an error for that line

  Name       Size             Bytes  Class     Attributes

  a          1x5                 40  double              
  b          1x5                 40  double              
  or        10x5x5             2000  double              
  zmag       1x10                80  double      

I'm still just getting an error in the calculation of Bz...

[Matt J]

Since you accepted my answer, I assume you figured it out?

[JC]

Sorry I thought it had worked but I'm having the same problem

[JC]

It works if ia, ib, ic, id and ie range from 1 to 10 but not for any other end value

[Matt J]

It would be both more efficient and easier to debug if you would assign some of the intermediate quantities to temporary variables, especially those that will be re-used:

for imag=1:imag(end)
    
    tmp_zend=(zend(imag)-z');
    tmp_zstart=(zstart(imag)-z');
    tmp_ir=ir(imag,:,:,:).^2/4;
    tmp_or=or(imag,:,:).^2/4;
    
    
    Bz=Bz+(B0*0.5*( tmp_zend./sqrt(tmp_zend.^2+tmp_ir) ...
           -tmp_zstart./sqrt(tmp_zstart.^2+tmp_ir) ...
           -tmp_zend./sqrt(tmp_zend.^2+tmp_or)  ...
           +tmp_zstart./sqrt(tmp_zstart.^2+tmp_ir)  ));
end

Now, we can see that the sizes of the different temporary variables do not match as needed:

K>> whos tmp*
  Name              Size               Bytes  Class     Attributes

  tmp_ir            1x5x5x5             1000  double              
  tmp_or            1x5x5                200  double              
  tmp_zend        201x1                 1608  double              
  tmp_zstart      201x1                 1608  double      

[JC]

Thank you, that's helpful!

I'm still not sure how to combine the differently sized matrices so that Bz is a 7-D array with iz, imag, ia, ib, ic, id and ie as the indices.

[Matt J]

Only you can answer that. No one in your audience can know what the intended calculation is.

[JC]

Ok I'll try to work it out. Thank you anyway!