Error: "Difference order N must be a positive integer scalar" when called symbolic gradient function

 In my program, I first use command jacobian generate a symbolic gradient of my objective function.Then I call the function(gradient.m) and feed it with numeric value. But Matlab warned me like

Warning: Function "diff" is not verified to be a valid MATLAB
  function. 
  Warning: Function "diff" is not verified to be a valid
  MATLAB function. 
  Warning: Function "diff" is not verified to be a valid
  MATLAB function. 
  Error using diff
  Difference order N must be a positive integer scalar.

    Error in gradient (line 10)
    t4 = diff(t2,B1);

    Error in mini_dist_noheter (line 60)
    dfb = gradient(b(1),b(2),b(3));

The gradient function file, main file and data see the attachment.

[Torsten]

The error message seems quite clear.

In your command

t4 = diff(t2,B1)

B1 is not a positive integer.

Best wishes

Torsten.

[Lu zhang]

But B is a symbolic expression, not a real number. I also upload the generated gradient function this time.

Answer 1

[Walter Roberson]

You appear to have a problem with your MATLAB path. I suggest using

resetdefaultpath

and seeing if that helps.

[Lu zhang]

Thank you for your reply,Walter. However, after I resotredefaultpath (the suggested resetfaultpath seems not work in my 2012a version Matlab) but the same error continues.It's a little bit strange that the code runs well before some small adjustments, mainly due to how I extract the lower triangle part of a matrix and stack it as a vector. But I serious doubt it's the source of this problem.

The generated gradient of a older version of code, which is without any diff function

function dfb = gradient(B1,B2,B3)
%GRADIENT
%    DFB = GRADIENT(B1,B2,B3)

%    This function was generated by the Symbolic Math Toolbox version 5.8.
%    06-Dec-2016 01:03:01

t2 = B1-1.0;
t3 = B1.*2.0;
t4 = t3-2.0;
t5 = B3.*t4;
t6 = t2.^2;
t7 = B1.*B3.*2.0;
t8 = t5+t7;
t9 = B1.^2;
t10 = t6+t9+1.0;
t13 = B3.*t2;
t14 = B1.*B3;
t11 = B3-t13-t14;
t15 = B1.*t2;
t12 = B1-t15-1.0;
dfb = reshape([t8,-t5,-B3,0.0,0.0,0.0,0.0,0.0,t8,t11,-B3,0.0,0.0,0.0,0.0,t8,t11,-B3,0.0,0.0,0.0,t8,t11,-B3,0.0,0.0,t8,t11,-B3,0.0,t8,t11,-B3,t8,0.0,t8,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0,0.0,1.0,t10,-t6,-B1,0.0,0.0,0.0,0.0,0.0,t10,t12,-B1,0.0,0.0,0.0,0.0,t10,t12,-B1,0.0,0.0,0.0,t10,t12,-B1,0.0,0.0,t10,t12,-B1,0.0,t10,t12,-B1,t10,0.0,t10],[36, 3]);

[Walter Roberson]

Ah yes, I keep thinking restoredefaultpath is named resetdefaultpath.

What shows up for

which -all diff

[Lu zhang]

built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\diff)
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@uint8\diff)    % uint8 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@uint16\diff)   % uint16 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@uint32\diff)   % uint32 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@uint64\diff)   % uint64 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@int8\diff)     % int8 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@int16\diff)    % int16 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@int32\diff)    % int32 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@int64\diff)    % int64 method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@single\diff)   % single method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@double\diff)   % double method
built-in (C:\Program Files\MATLAB\R2012a\toolbox\matlab\datafun\@logical\diff)  % logical method
C:\Program Files\MATLAB\R2012a\toolbox\symbolic\symbolic\@char\diff.m           % char method
C:\Program Files\MATLAB\R2012a\toolbox\symbolic\symbolic\@sym\diff.m            % sym method
C:\Program Files\MATLAB\R2012a\toolbox\finance\ftseries\@fints\diff.m           % fints method
C:\Program Files\MATLAB\R2012a\toolbox\ident\ident\@iddata\diff.m               % iddata method
C:\Program Files\MATLAB\R2012a\toolbox\mbc\mbcmodels\@localtruncps\diff.m       % localtruncps method
C:\Program Files\MATLAB\R2012a\toolbox\mbc\mbcmodels\@localpspline\diff.m       % localpspline method
C:\Program Files\MATLAB\R2012a\toolbox\mbc\mbcmodels\@localpoly\diff.m          % localpoly method
C:\Program Files\MATLAB\R2012a\toolbox\robust\robust\@umat\diff.m               % umat method

[Walter Roberson]

I did not realize you were using such an old version.

The messages about diff not being verified to be a MATLAB function are coming from your matlabFunction() call applied to the result of jacobian(temp,v) . The jacobian that is generated has a bunch of diff() calls in it, and matlabFunction is warning that converting them into numeric calls might fail. Which indeed happens.

The diff() calls that are being left in are of the form

   diff(conj(VARIABLE), VARIABLE)

because it that MATLAB version, the symbolic engine does not know how to take that derivative.

My research suggests that if the variable is permitted to be complex valued then that derivative does not exist; see https://www.quora.com/What-is-the-differentiation-dz%CC%85-dz-of-a-complex-conjugate-by-the-complex-variable-If-it-is-zero-how-does-it-become-so for two proofs.

Why does the jacobian have a bunch of diff(conj(VARIABLE),VARIABLE) calls in it? It is because your variable temp has a bunch of conj(VARIABLE) in it.

Why does your variable temp have a bunch of conj(VARIABLE) in it? It is because in fcn_noheter near the end you have

trans = dif';

and ' is the complex conjugate transpose operation.

You need to ask yourself whether you instead wanted just

trans = dif .';

for the regular transpose. If you do not want just regular transpose, then when you create B1, B2, B3 you need to also

assume(B, 'real')

[Lu zhang]

Thank you so much, @Roberson, it works.