Octave“FUN必须是字符串或内联函数”

Question

Question

What is the meaning of "FUN must be a string or inline function" message in Octave?

In Octave 4.2.0 (Windows) I am trying to run Gradients, Gradient Plots and Tangent Planes which is originally implemented in MATLAB 7.8, and got the error as below.

Kindly suggest this is due to Octave being incompatible with MATLAB or due to other causes. If there is a workaround, kindly suggest.

>> syms x y z
>> f=((x^2-1)+(y^2-4)+(x^2-1)*(y^2-4))/(x^2+y^2+1)^2
f = (sym)

   2    2   / 2    \ / 2    \
  x  + y  + \x  - 1/*\y  - 4/ - 5
  -------------------------------
                        2
           / 2    2    \
           \x  + y  + 1/

>> gradf=jacobian(f,[x,y])
gradf = (sym 1x2 matrix)

  [      / 2    2   / 2    \ / 2    \    \       / 2    \              / 2    2
  [  4*x*\x  + y  + \x  - 1/*\y  - 4/ - 5/   2*x*\y  - 4/ + 2*x    4*y*\x  + y
  [- ------------------------------------- + ------------------  - -------------
  [                           3                             2
  [              / 2    2    \                 / 2    2    \                   /
  [              \x  + y  + 1/                 \x  + y  + 1/                   \

    / 2    \ / 2    \    \       / 2    \      ]
  + \x  - 1/*\y  - 4/ - 5/   2*y*\x  - 1/ + 2*y]
  ------------------------ + ------------------]
              3                             2  ]
   2    2    \                 / 2    2    \   ]
  x  + y  + 1/                 \x  + y  + 1/   ]

>> [xx, yy] = meshgrid(-3:.1:3,-3:.1:3);
>> ffun = @(x,y) eval(vectorize(f));
>> fxfun = @(x,y) eval(vectorize(gradf(1)));
>> fyfun = @(x,y) eval(vectorize(gradf(2)));
>> contour(xx, yy, ffun(xx,yy), 30)
error: vectorize: FUN must be a string or inline function
error: called from
    @<anonymous> at line 1 column 15

Answer 1

It seems that vectorize expects a string literal, and fails to obtain the function handle from a symbolic expression, but you can use function_handle instead:

ffun = function_handle(f)

which results in the following vector-friendly function:

ffun =
@(x, y) (x .^ 2 + y .^ 2 + (x .^ 2 - 1) .* (y .^ 2 - 4) - 5) ./ (x .^ 2 + y .^ 2 + 1) .^ 2

that can be used onwards, for example with your contour call:

contour(xx, yy, ffun(xx,yy), 30)