Force zeros to be be symbolic

In the following code,

syms x y
f{1,1} = @(x,y) x+y
bad = 1;
if bad
    f{1,2} = @(x,y) 0
else
    f{1,2}=@(x,y) sym(0)
end
fMat = cellfun(@(z) feval(z,x,y),f)

the last line will throw an error.

The reason is that the first element of f is symbolic, but second is numeric, and cellfun doesn't like that.

A workaround is to change 0 to sym(0) as the example illustrates, when you set bad to 0.

Matlab's recommended solution is to add '

un',0 

to the cellfun command. This works for this toy example, but in my complex application, 'un',0 creates all sorts of other problems.

My current code computes the matlab derivatives, and then, if they are zero, converts the 0's to sym(0) using strrep. This is incredibly awful and is likely to cause all sorts of problems in other settings.

The ideal solution for me would be to have the matlab symbolic diff command return everything as symbolic, including integers. Is there a way to impose that? Thanks for any suggestions.

Answer 1

[Walter Roberson]

"The reason I'm having problems is that I'm converting the output from diff to a character string and then writing it to a file. when I run the file"

Do not write it out plain. Write it out with a str2sym() wrapper. You need that anyhow in order to get constants back in with full accuracy.

You have another challenge as well: when you emit @(x,y)0 then you cannot integral() the handle. integral() requires that the output be the same size as the input but @(x,y)0 is scalar 0. To work with a constant C you need @(x,y)C*ones(size(x)) which is not something that matlabFunction() will emit automatically.

[Leo Simon]

@Walter Roberson, Thanks. I tried playing around with sym2str, using fprintf to write to a file that I could then load, but I couldn't get anything to work, would you mind providing an example? In case anybody is reading this, I found another, trivial solution which worked well for me: I created a symbolic variable ZERO, and changed all my 0's to ZERO using strrep.

[Paul]

I can't speak for @Walter Roberson, but it may be helpful to show what what you're actually doing, i.e., what is being written to the file and what you intend to do with the file after it's written.

[Walter Roberson]

filename = fullfile(tempdir, 'test_str2sym.m');

syms x y
z = x + y

z = 

dz = diff(z,x)

dz = 

1

d2z = diff(dz,x)

d2z = 

0

names_to_write = {'z', 'dz', 'd2z'};
vars_to_write = {z, dz, d2z};

fid = fopen(filename, 'w');
for K = 1 : length(names_to_write)
  fprintf(fid, "%s = str2sym('%s');\n", names_to_write{K}, char(vars_to_write{K}));
end
fclose(fid)

ans = 0

type(filename)

z = str2sym('x + y');
dz = str2sym('1');
d2z = str2sym('0');

clearvars x y z dz d2z
addpath(fileparts(filename));
test_str2sym();

whos

  Name                Size            Bytes  Class     Attributes

  K                   1x1                 8  double              
  ans                 1x1                 8  double              
  d2z                 1x1                 8  sym                 
  dz                  1x1                 8  sym                 
  fid                 1x1                 8  double              
  filename            1x19               38  char                
  names_to_write      1x3               324  cell                
  vars_to_write       1x3               336  cell                
  z                   1x1                 8  sym                 

z

z = 

dz

dz = 

1

d2z

d2z = 

0

Answer 2

[Paul]

I'm not familiar with this?

un',0

Can you show that in a cellfun command?

In any case, diff() always returns a symbolic expression, doesn't it? (though the doc page does even have an Output section that says so explicitly).

syms x
d1 = diff(3*x)

d1 = 

3

d2 = diff(0*x)

d2 = 

0

whos

  Name      Size            Bytes  Class    Attributes

  d1        1x1                 8  sym                
  d2        1x1                 8  sym                
  x         1x1                 8  sym                

[Leo Simon]

@Paul 'un',0 means Uniform output false, and you can create a cell array with some elements symbolic and others numeric. You're right about diff! I didn't realize that. The reason I'm having problems is that I'm converting the output from diff to a character string and then writing it to a file. when I run the file and an element of f encounters a symbolic variable, all is well, but if it encounters a 0, it treats it as numeric.

This makes my problem much harder to fix, it seems, I'm afraid.