Need help running simple equation over vector of data?

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Michael Ziedalski 2018-2-1

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评论： Star Strider 2018-2-3

So, I am new to Matlab and would appreciate all the help I can get. Recently, I coded an anonymous function (meant to represent a bivariate normal distribution) and was able to output a vector of results if I fed the x values to it (representing both of the means and st. deviations). This was my code

mu = [1;5]
sigma = [.5,0;0,.1]
data = mvnrnd(mu,sigma,100);
data1 = data(:,1);
data2 = data(:,2);
fun =  @(x)(1/(2*pi*x(2)*x(4)*sqrt(1-.533^2)))*exp((-1/(2-2*.533^2))*((data1-x(1)).^2./(x(3)^2)+(data2-x(2)).^2./(x(4)^2)-(2*.533*(data1-x(1)).*(data2-x(2)))./(x(3)*x(4))))
fun([1,2,3,4]) %This outputs my answers.

The last line correctly gives me a 2x100 vector of results, since I gave 100 data values. But now I want to simplify this code b/c it was giving me issues elsewhere. I wanted to include data itself as a variable of sorts, and get the same answer. But only 1 answer gets outputted from the below code and that is puzzling.

fun = @(x, data)(1/(2*pi*x(2)*x(4)*sqrt(1-.533^2)))*exp((-1/(2-2*.533^2))*((data(1)-x(1)).^2./(x(3)^2)+(data(2)-x(2)).^2./(x(4)^2)-(2*.533*(data(1)-x(1)).*(data(2)-x(2)))./(x(3)*x(4))))
fun([1,2,3,4],[data]) 
ans =
      0.0233

What am I missing here? Is the function somehow summing up all the values, or just calculating the result for the first row?

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Answer 1

Star Strider 2018-2-1

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在 MATLAB Online 中打开

You are passing ‘data’ as a (100x2) matrix. You need to refer to the individual columns of ‘data’ in your function:

fun = @(x, data)(1/(2*pi*x(2)*x(4)*sqrt(1-.533^2)))*exp((-1/(2-2*.533^2))*((data(:,1)-x(1)).^2./(x(3)^2)+(data(:,2)-x(2)).^2./(x(4)^2)-(2*.533*(data(:,1)-x(1)).*(data(:,2)-x(2)))./(x(3)*x(4))));

That works correctly when I run it.

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Walter Roberson 2018-2-3

在 MATLAB Online 中打开

"Would there be any way to make this code work then without defining the anonymous function before the data?"

Yes, I can think of several ways:

assign some value to data in a containing function, and create the function handle inside a nested function, and then later either in the containing function or a different nested function, change the value of data as required. When you refer to a shared variable in an anonymous function, a reference to the shared variable is taken, so changes to the shared variable affect the anonymous function
assign some value to data (a local variable) before creating the function handle. Arrange to have the anonymous function call a function that gets the new value of data from somewhere and does an assignin('caller') to update the data variable of the anonymous function
make your data into a function instead of a variable, and have it fetch the correct values from somewhere

I do not recommend any of these. I recommend instead that you define

lh = @(x, data)sum(-log(fun(x,data)));

and then at the time you would have used lh, such as

[theta,max] = fminunc(lh,guesses,options) % ERROR here.

instead use

[theta,max] = fminunc(@(x) lh(x,data), guesses, options)

You can construct a function handle that is dependent upon a parameter data as soon as you know all of the other variables that will be used in the function handle, and then you can construct the final function handle once data is known. The kind of call I show above, where an anonymous function is constructed as an expression and passed in to a minimizer (or ode* function) is quite common and is the recommended design (except in some cases where you need to do heavy optimization.)

Michael Ziedalski 2018-2-3

Walter and Star Strider, through your answers I have figured out little, but substantial, Matlab details that have haunted me for the past couple of weeks. Especially after Strider's answer, now my code works perfectly; thank you very much, all.