Matlab: Nested PDEG functions

I have originally two functions as below: The first one:

function [ X ] = faces( d,hc )
[p,e,t] = initmesh(@cardioid1,'init','off');
load('func_contents.mat');

zval_u=-hc;
zval_d=-hc-d;
t(4,:)=t(1,:);
val(:,:)=p(:,t(:,:));
valu(:,:)=val(:,:);
valu(3,:)=zval_u;
vald(:,:)=val(:,:);
vald(3,:)=zval_d;

%%%%%%%%Upper face %%%%%%%%%%%%
for i=1:size(t,2)
%  for i=1:3
X(1,i,:,:)=[valu(:,4*i-3)';valu(:,4*i-2)';valu(:,4*i-1)';valu(:,4*i)'];
end
bord1(1,:)=xt(1,:);
bord1(2,:)=yt(1,:);
end

And the second one as below:

    function [x,y,xt,yt,th] = cardioid1(bs,s) 
  %CARDIOID1 Geometry File defining the geometry of a cardioid. 
  global r0 a1;
  r0=1;
  a1=1;
  if nargin == 0  
    x = 12; % four segments in boundary
    return 
  end
  if nargin == 1
   dl = [0     pi/6    2*pi/6   3*pi/6   4*pi/6   5*pi/6    6*pi/6    7*pi/6  8*pi/6  9*pi/6      10*pi/6     11*pi/6
        pi/6   2*pi/6  3*pi/6   4*pi/6   5*pi/6   6*pi/6    7*pi/6    8*pi/6  9*pi/6  10*pi/6      11*pi/6    12*pi/6
        1      1       1          1       1       1           1           1   1       1               1       1 
        0      0       0          0       0       0           0           0   0       0               0       0];
    x = dl(:,bs);   
    return 
  end 

x = zeros(size(s)); 
y = zeros(size(s)); 
if numel(bs) == 1 % bs might need scalar expansion
  bs = bs*ones(size(s)); % expand bs
end
nth =190; % fine polygon, 100 segments per quadrant
r0=1;
th = linspace(0,2*pi,nth); % parametrization
r=r0+a1*cos(th);
xt = r.*cos(th); % Points for interpolation of arc lengths
yt = r.*sin(th)+1000;
% Compute parameters corresponding to the arc length values in s
th = pdearcl(th,[xt;yt],s,0,2*pi); % th contains the parameters
% Now compute x and y for the parameters th
r=r0+a1*cos(th);
x(:) = r.*cos(th);
y(:) = r.*sin(th)+1000;
save('func_contents.mat','-v6') 
end
Inside the "faces" function I access the second function by @cardioid1 and when cardioid1 runs I pass its parameters to "faces" by saving of the workspace and loading it inside "faces" again.

Since I want to change this format to parallel, they mix up the names, since all will save under a single name.mat in a single directory.

Now I thought to make it nested function, so that each parallel process locally and directly have access to parameters of cardioid1.

So I changed it to below code:

function [ X ] = faces2( d,hc )
cardioid1;
        function [x,y,xt,yt,th] = cardioid1(bs,s) 
                %CARDIOID1 Geometry File defining the geometry of a cardioid. 
                global r0 a1;
                a1=0.1;
                a2=0.1;
                a3=0.5;
                if nargin == 0  
                  x = 12; % four segments in boundary
                  return 
                end

                  if nargin == 1
                   dl = [0     pi/6    2*pi/6   3*pi/6   4*pi/6   5*pi/6    6*pi/6    7*pi/6  8*pi/6  9*pi/6      10*pi/6     11*pi/6
                        pi/6   2*pi/6  3*pi/6   4*pi/6   5*pi/6   6*pi/6    7*pi/6    8*pi/6  9*pi/6  10*pi/6      11*pi/6    12*pi/6
                        1      1       1          1       1       1           1           1   1       1               1       1 
                        0      0       0          0       0       0           0           0   0       0               0       0];
                    x = dl(:,bs);   
                    return 
                  end 

                  x = zeros(size(s)); 
                  y = zeros(size(s)); 
                  if numel(bs) == 1 % bs might need scalar expansion
                    bs = bs*ones(size(s)); % expand bs
                  end
                  nth =190; % fine polygon, 100 segments per quadrant
                  r0=1;
                  th = linspace(0,2*pi,nth); % parametrization
                  r=r0+a1*cos(th);
                  xt = r.*cos(th); % Points for interpolation of arc lengths
                  yt = r.*sin(th)+1000;
                  % Compute parameters corresponding to the arc length values in s
                  th = pdearcl(th,[xt;yt],s,0,2*pi); % th contains the parameters
                  % Now compute x and y for the parameters th
                  r=r0+a1*cos(th);
                  x(:) = r.*cos(th);
                  y(:) = r.*sin(th)+1000;
  %                 save('func_contents.mat','xt','yt') 
          end
  [p,e,t] = initmesh(@cardioid1,'init','off');
  pdemesh(p,e,t)
  % load('func_contents.mat');
  zval_u=-hc;
  zval_d=-hc-d;
  t(4,:)=t(1,:);
  val(:,:)=p(:,t(:,:));
  valu(:,:)=val(:,:);
  valu(3,:)=zval_u;
  vald(:,:)=val(:,:);
  vald(3,:)=zval_d;
  %%%%%%%%Upper face %%%%%%%%%%%%
  for i=1:size(t,2)
  %  for i=1:3
  X(1,i,:,:)=[valu(:,4*i-3)';valu(:,4*i-2)';valu(:,4*i-1)';valu(:,4*i)'];
  end
  bord1(1,:)=xt(1,:);
  bord1(2,:)=yt(1,:);
  end

But I get the error: Undefined function or variable 'xt'. Error in faces (line 71) bord1(1,:)=xt(1,:);

My question as well has an open thread in here

Answer 1

[Stephen23]

@Soheil Smz: what do you expect to happen? You have two possible solutions:

1. Define the variable at the start of the parent function, which can then be accessed by the nested function.
2. Use output arguments, exactly as Geoff Hayes advised you to do.

Geoff Hayes told you to use output augments, but I can't see any in your code:

function main2
nestfun2
     function nestfun2
        x = 5;
     end
x = x + 1
end

When I fix your code following Geoff Hayes' advice exactly, it works perfectly:

function y = main2
y = nestfun2;
  function x = nestfun2
  x = 5;
  end
y = y + 1
end

And tested:

>> main2
ans =  6

Or alternatively without output argument, but defining the variables at the start of the parent function:

function y = main3
y = 0;
nestfun2
  function nestfun2
  y = 5;
  end
y = y + 1;
end

And tested:

 >> main3
 ans =  6

Both of these are explained very well in the documentation, here is the salient info "All of the variables in nested functions or the functions that contain them must be explicitly defined. That is, you cannot call a function or script that assigns values to variables unless those variables already exist in the function workspace."

There is more to read and learn:

http://www.mathworks.com/help/matlab/matlab_prog/variables-in-nested-and-anonymous-functions.html

http://www.mathworks.com/help/matlab/matlab_prog/nested-functions.html

Answer 2

[Geoff Hayes]

Soheil - you have posted more code than you should have to your question. As such, that is likely to discourage people from attempting to answer it. I think even those on StackOverflow (given the link above) have indicated the same. In the future, post only relevant code and only enough that is necessary to reproduce the problem.

That being said, look at how you call cardiod1 from your main function:

 function [ X ] = faces( d,hc )
     cardioid1;
     function [x,y,xt,yt,th] = cardioid1(bs,s) 
         % cardioid1 body
     end

     % other stuff
 end

You are calling cardiod1 but not saving/storing any of the output parameters, one of which is your xt. So when the code in the other stuff section tries to access xt you get the expected error of undefined function or variable 'xt'. Since you are trying to make use of this output parameter, then you should change the above to

 function [ X ] = faces( d,hc )
     [x,y,xt,yt,th] = cardioid1;
     function [x,y,xt,yt,th] = cardioid1(bs,s) 
        % body of caridioid1
     end
     % other stuff
 end

so that you can get to all output parameters of the function.

I think that you have misunderstood the idea of nested functions. If function B is nested within function A, then B has access to the local variables of A. This doesn't work in the other direction which is what you are attempting (to have the local variables of the nested cardioid1 function be accessible to the "parent" faces function).

[Soheil Esmaeilzadeh]

Thank you so much for your reply and for your kind note. I summarized the code here and on stackoverflow now.

I tried your note

function [ X ] = faces( d,hc )
     [x,y,xt,yt,th] = cardioid1;
     function [x,y,xt,yt,th] = cardioid1(bs,s) 
        % body of caridioid1
     end
     % other stuff
 end

But it does not work and gives the error

"Output argument "y" (and maybe others) not assigned during call to "cardioid1""

P.S. Actually I initially when had separate functions, saved .mat file in 2nd func and loaded it on the 1st one and had access to that. But since now I want to run my whole code parallel each parallel process will do the same and they will mess up, since all will save and load with the same name. So I thought of combining the two functions. And this is where nested functions came to my mind.

I appreciate it if you could give me a hint on how to solve my current issue explained above.

some people suggested of predefining x,y,xt,yt, but that even did not work since the result of xt, yt does not come out equal to the case when you run the functions separately. and link them through a .mat file

[Soheil Esmaeilzadeh]

Even it did not work by defining global variables inside the function as below:

function [ X ] = faces2( d,hc )
cardioid1;
global xt yt;
xt=0;
yt=0;
        function [x,y,xt,yt,th] = cardioid1(bs,s) 
                %CARDIOID1 Geometry File defining the geometry of a cardioid. 
                global r0 a1 xt yt;
                a1=0.1;
                if nargin == 0
......
...
......

[Soheil Esmaeilzadeh]

And also if you have a look at here you will see function below:

function main2
nestfun2

     function nestfun2
        x = 5;
     end
x = x + 1
end

But for me does not work as well!!!

[Geoff Hayes]

For your last comment, you need to clarify what you mean by but for me does not work as well. What is happening? What are you expecting to happen?

As for the error message that indicates

 "Output argument "y" (and maybe others) not assigned during call to "cardioid1""

look at your function signature

 function [x,y,xt,yt,th] = cardioid1(bs,s)

If you exit this function before the x, y, xt, yt, and th have been defined, then you will observe this error message. (This may be due to the return that you have.) What you can do is just assign each a default value - whether this is zero or an empty matrix is entirely up to you. For example,

 function [x,y,xt,yt,th] = cardioid1(bs,s) 
 x = [];
 y = [];
 xt = [];
 yt = [];
 theta = [];

 % now follow with your code for this function