I need to plot the following functions but I receive this error "Invalid indexing or function definition. When defining a function ensure that the arguments are symbolic variables ...."

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mohsen
mohsen 2016-3-8
评论： Walter Roberson 2016-3-8
x = 2:30;
y = 40:60;
u = @(x,y) 10*sin(200*x)+0.1*cos(10*y)+(100*x)./y;
v = @(x,y) 10*cos(200*x)+0.1*sin(10*y)-100*(x./y);
syms x y
ex = diff(u,x);
ey = diff(v,y);
Gxy = diff(v,x)+diff(u,y);
[X,Y] = meshgrid(x,y);
Z = ex(X,Y);
figure(1)
mesh(X, Y, Z)
[X,Y] = meshgrid(x,y);
Z = ey(X,Y);
figure(2)
mesh(X, Y, Z)
[X,Y] = meshgrid(x,y);
Z = Gxy(X,Y);
figure(3)
mesh(X, Y, Z)

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Walter Roberson
Walter Roberson 2016-3-8
You have defined
x = 2:30;
y = 40:60;
but then you have
syms x y
That is equivalent to
x = sym('x');
y = sym('y');
which is to say that it overwrites x and y, and afterwards they are no longer numeric. But afterwards you sometimes treat them as symbols and sometimes treat them as numeric. In particular,
[X,Y] = meshgrid(x,y);
attempts to treat them as numeric.
You also have
u = @(x,y) 10*sin(200*x)+0.1*cos(10*y)+(100*x)./y;
v = @(x,y) 10*cos(200*x)+0.1*sin(10*y)-100*(x./y);
ex = diff(u,x);
ey = diff(v,y);
The two diff() lines attempt to take the symbolic differentiation of a MATLAB function handle. You probably cannot do that. You can differentiate a symbolic expression, and you might be able to differentiate a symbolic function, but probably not a function handle.
ex = diff(u(x,y), x);
ey = diff(v(x,y), y)
would invoke the function handles on the symbolic parameters x and y, giving a symbolic expression as a result, and that symbolic expression can be differentiated.
  2 个评论
mohsen
mohsen 2016-3-8
I removed the syms x y
and replaced the diff with
ex = diff(u(x,y), x);
ey = diff(v(x,y), y);
but I still get an error what else I should change?
Walter Roberson
Walter Roberson 2016-3-8
With x and y numeric and u a function handle, u(x,y) would be numeric, so diff(u(x,y),x) would be a numeric difference rather than a symbolic difference. When you request a numeric difference, the second parameter must be the number of times the difference is to be taken, not a variable indicating a direction. That is not going to be what you want. You need to be using symbolic expressions and to have x and y being symbolic. What you should be doing is renaming your numeric uses of x and y.
Note: you do not need to define x or y before defining a function handle that uses those names as parameters in @(x,y) . Your first need for your numeric x and y is in your meshgrid(). You also do not need to recalculate the meshgrid() since you are not changing X or Y or the numeric x or y between your meshgrid() calls. So you could just eliminate your use of x and y as numeric and directly call
[X, Y] = meshgrid(2:30, 40:60);

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