Where's the bug in the following codes?

Question

Shawn Miller 2015-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/247592-where-s-the-bug-in-the-following-codes

评论： Stephen23 2015-10-10

fun=@(x,y)100*(y-x^2)^2+(1-x)^2;
x=-10:1:10;
y=-10:1:10;
[z,val]=fminsearch(fun,3,3);

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Answer 1

Star Strider 2015-10-9

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You have to give fminsearch a function of one parameter vector. I created two versions of your ‘fun’ function, one to use as an argument to fminsearch and one for the plot, vectorising both functions so they will work:

% MAPPING:  b(1) = x,   b(2) = y
fun=@(b)100*(b(2)-b(1).^2).^2+(1-b(1)).^2;      % Argument To ‘fminsearch’
[z,val]=fminsearch(fun,[3,3])
x=-10:1:10;
y=-10:1:10;
[X,Y] = meshgrid(x,y);                          % Create Matrix Arguments
funplot=@(x,y)100*(y-x^2)^2+(1-x)^2;            % Plotting Version 
figure(1)
surfc(X, Y, funplot(X,Y))
grid on

I could have used the same function for both, but this is more straightforward.

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Star Strider 2015-10-10

编辑：Star Strider 2015-10-10

在 MATLAB Online 中打开

@Shawn — Yes it should. I miscopied it somehow. (The code worked and produced the correct plot with the correct element-wise function operators.) It should look like ‘fun’:

funplot=@(x,y)100*(y-x.^2).^2+(1-x).^2; % Plotting Version

EDIT — To plot the minimum as well as the function, the code becomes:

fun=@(b)100*(b(2)-b(1).^2).^2+(1-b(1)).^2;      % Argument To ‘fminsearch’
[z,val]=fminsearch(fun,[3,3])
x=-10:1:10;
y=-10:1:10;
[X,Y] = meshgrid(x,y);                          % Create Matrix Arguments
funplot=@(x,y)100*(y-x.^2).^2+(1-x).^2;         % Plotting Version
figure(1)
surfc(X, Y, funplot(X,Y))
hold on
plot3(z(1), z(2), funplot(z(1),z(2)), 'mp', 'MarkerSize',15, 'MarkerFaceColor','c')
hold off
grid on
view(-15, 30)

It plots the minimum with a slightly buried magenta pentagram with a red outline.

Stephen23 2015-10-10

@Shawn Miller: one can vectorize funplot, and this can be called (and plotted) with vector/matrix inputs. funfmin stays the same.

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Answer 2

Stalin Samuel 2015-10-9

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yrfun = @(x)100*(x(2)-x(1)^2)^2+(1-x(1))^2;
[z,val]=fminsearch(yrfun,[-10 10]);

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Shawn Miller 2015-10-9

编辑：Shawn Miller 2015-10-9

Thanks Stalin, I actually know that using a vector x in the anonymous function works, however, the problem appeared when I tried to plot the fun, and it makes it difficult to plot using vector x I suspect. This is why I turn to use x and y as independent variables. Do you know if fminsearch supports function defined in my way/if you don't think so, how do you plot the function using vector x as input?

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