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.
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Hello,
I want to visualize a cost function of a localization problem. However if i use fimplicit3 the following warning 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" and the plot is empty. Here is my code:
syms x y z
Jd=(-(((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2)/343 - ((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2)/343 + 166153461756515/288230376151711744)*((1227133513142857*((y - 3)^2 + (z - 1)^2 + x^2)^(1/2))/841813590016 + (8589934592000001*((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2))/5892695130112 + (500000*((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2))/343 - (1500000*((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2))/343 + 47361719490181303919776257030055/4951760157141521099596496896) - (((y - 3)^2 + (z - 1)^2 + x^2)^(1/2)/343 - ((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2)/343 + 3755404798969945/288230376151711744)*((500000*((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2))/343 - (1500000*((y - 3)^2 + (z - 1)^2 + x^2)^(1/2))/343 + (8589934592000001*((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2))/5892695130112 + (1227133513142857*((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2))/841813590016 - 75964017393466287210169242730447/4951760157141521099596496896) - (((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2)/343 - ((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2)/343 + 564171350756517/72057594037927936)*((8589934592000001*((y - 3)^2 + (z - 1)^2 + x^2)^(1/2))/5892695130112 + (1227133513142857*((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2))/841813590016 - (1500000*((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2))/343 + (500000*((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2))/343 - 4.9414e+03));
fs=@(x,y,z)double(Jd);
fimplicit3(fs,[-30 30 -30 30 -30 30]);
Due to the fact that the cost function is calculated out of a localization problem it's so huge.
采纳的回答
Walter Roberson
2020-7-13
syms x y z
Jd = (-(((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2)/343 - ((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2)/343 + 166153461756515/288230376151711744)*((1227133513142857*((y - 3)^2 + (z - 1)^2 + x^2)^(1/2))/841813590016 + (8589934592000001*((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2))/5892695130112 + (500000*((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2))/343 - (1500000*((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2))/343 + 47361719490181303919776257030055/4951760157141521099596496896) - (((y - 3)^2 + (z - 1)^2 + x^2)^(1/2)/343 - ((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2)/343 + 3755404798969945/288230376151711744)*((500000*((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2))/343 - (1500000*((y - 3)^2 + (z - 1)^2 + x^2)^(1/2))/343 + (8589934592000001*((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2))/5892695130112 + (1227133513142857*((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2))/841813590016 - 75964017393466287210169242730447/4951760157141521099596496896) - (((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2)/343 - ((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2)/343 + 564171350756517/72057594037927936)*((8589934592000001*((y - 3)^2 + (z - 1)^2 + x^2)^(1/2))/5892695130112 + (1227133513142857*((x - 9)^2 + (z - 1/10)^2 + y^2)^(1/2))/841813590016 - (1500000*((x - 5)^2 + (y - 10)^2 + (z - 3/2)^2)^(1/2))/343 + (500000*((x - 10)^2 + (y - 8)^2 + (z - 1/10)^2)^(1/2))/343 - 4.9414e+03));
N = 20;
[X, Y, Z] = ndgrid(linspace(-30, 30, N));
result = double(subs(Jd, {x, y, z}, {X, Y, Z}));
isosurface(X, Y, Z, result, 0)
xlabel('x'); ylabel('y'); zlabel('z');
Unfortunately at the moment, my system is busy so I cannot tell how well the graphic worked. I suspect you will need to increase N to get better resolution.
5 个评论
Max Lacher
2020-7-13
Walter Roberson
2020-7-13
The above did not work (empty plot), so I investigated further.
The minimum value of Jd is approximately -4E-10, over a relatively small region.
It appears to me that the implicit surface is an ellipsoid, that fits approximately in the box
x = 2.89203876360063195 to 2.89204737484551222
y = 5.02378524365726964 to 5.02379993198380337
z = 1.857973242462718 to 1.85810414034411076]
isosurface would generally be able to plot that, but your grid would have to be very fine indeed to have caught this.
And unfortunately, vpasolve(Jd) will not find solutions unless you start very close to that range -- on the order of +/- 1/1000
Fortunately, if you take
fminsearch( matlabFunction(Jd.^2,'vars',{[x,y,z]}), rand(1,3) )
then you get into the right area quickly.
Max Lacher
2020-7-13
Walter Roberson
2020-7-13
When you apply fminsearch to the square of the cost function, then provided the cost function values cannot be imaginary, what you are searching for is zeros of the cost function. This fminsearch is relatively fast, and gives you a point on (near) the surface.
A big problem with the fimplicit3 and the ndgrid approaches is that they depend upon finding very close starting points, since the formula is too complex for areas outside to be of much use in finding the surface.
Once you know a point on (near) the surface, and knowing that you are dealing with an ellipsoid, you should be able to probe around to find the extent of the ellispsoid, such as
temp = 10.^(-10:0);
delta = [-fliplr(temp), 0, temp];
now use delta as offsets to each coordinate in turn, and look for positive (outside), negative(inside), positive (outside) pattern in each dimension. Then pick a grid from that, ndgrid, evaluate, isosurface on value 0
Max Lacher
2020-7-14
更多回答（1 个）
madhan ravi
2020-7-13
fs = matlabFunction(Jd)
4 个评论
Max Lacher
2020-7-13
Max Lacher
2020-7-13
Walter Roberson
2020-7-13
fimplicit3 takes a long time to compute the faces
Max Lacher
2020-7-13
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