八度-圆函数的渐变无法正确绘制

Question

Question

Trying to follow Gradients, Gradient Plots and Tangent Planes .

The gradient vectors of (X^2 + Y^2) do not show up correctly in Octave 4.2.0 on Windows. With the code, expected the gradients of a circle diverge from center outwards. However the actual is diagonal.

Please assist to understand what is wrong.

syms x y
f1 = x^2 + y^2; 
gradf1 = jacobian(f1,[x,y]);

f1fun  = function_handle(f1);
f1xfun = function_handle(gradf1(1));
f1yfun = function_handle(gradf1(2));

[xx, yy] = meshgrid(-1:.1:1,-1:.1:1);

hold on

contour(xx, yy, f1fun(xx, yy), 10)
quiver(xx, yy, f1xfun(xx, yy), f1yfun(xx, yy), 0.5)
axis equal tight

hold off

Expected

Actual

Answer 1

I think you have a bug in your code and the call to quiver should be

quiver(xx, yy, f1xfun(xx), f1yfun(yy), 0.5)

which then gives (with colormap("jet") )

Answer 2

When you perform:

f1xfun = function_handle(gradf1(1));
f1yfun = function_handle(gradf1(2));

The output is:

f1xfun = 
  @(x) 2 * x        % note: single-argument function
f1yfun =
  @(y) 2 * y        % note: single-argument function

that is AS OPPOSED TO

f1xfun = 
  @(x,y) 2 * x      % two-argument function
f1yfun = 
  @(x,y) 2 * y      % two-argument function

which is what you seem to think was happening. (ie the resulting functions actually only take a single input, not both x and y ).

Therefore later on when you call f1yfun with two inputs, the second input (ie y ) is simply silently discarded , and you are essentially calculating 2*x in both axes, hence the diagonal arrows.

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tl;dr Your call to quiver should be:

 quiver(xx, yy, f1xfun(xx), f1yfun(yy), 0.5);