Help with implicit functions in vector form

I've been trying to plot a line, for example: 3x+y+4=0 in implicit form as follow:

w=[3 1 4];
fimplicit(@(x,y) [x y 1]*w')

The output is correct, however it takes ages to compute and this warning sign appears:

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

When I write the code this way:

w=[3 1 4];
fimplicit(@(x,y) w(1)*x+w(2)*y+w(3))

it works the same but without the warning, and with short computation time.

I have no clue why this happens since the two expressions are exactly the same.

Any help?

[Dyuman Joshi]

fimplicit is optimized for array operations. (My guess is that fimplicit evaluates the input function on a meshgrid of x and y values, for which array operations are faster and robust as well)

From the documentation - "Use element-wise operators for the best performance and to avoid a warning message." Also "Use array operators instead of matrix operators for the best performance. For example, use .* (times) instead of * (mtimes)."

The first piece of code uses matrix operation and thus you get the warning. The final expressions are same, but the method used are different.

Answer 1

[Torsten]

I have no clue why this happens since the two expressions are exactly the same.

The reason is that [x y 1]*w' cannot be evaluated for x,y being vectors, but w(1)*x+w(2)*y+w(3) can.

So you always should try to write your function such that it can evaluate for vector inputs.

If this is not possible, you may use:

fimplicit(@(X,Y)arrayfun(@(x,y)fun(x,y),X,Y))

e.g.

w=[3 1 4];
fun = @(x,y) [x y 1]*w';
fimplicit(@(X,Y)arrayfun(@(x,y)fun(x,y),X,Y))