I am going to try and explain myself simply in the hopes of getting a simple answer.
Let's say I have a function 'calculate' that takes the inputs [t,k,r,x] and outputs [A,B,C,D] as follows:
function [A,B,C,D] = calculate(t,k,r,x)
Now lets say I have another function that takes these outputs as the inputs, and spits out more, different outputs, eg.
function [M,N] = again(A,B,C,D)
How do I link [M,N] to say k and t? The overall aim is to minimise both M and N by optimising k and t, and I can guess that it has something to do with nested functions and passing parameters but I'm not sure how to start, and the start is all I want. Thanks
Take a look at the Matlab optimization toolbox. It provides functions for a multitude of optimization problems. Although I believe these functions only take one function as a parameter. Therefore for your case it would probably be best, if you do it like this if you can:
Write function calculate.m with parameters (t,k,r,x) and save it.
Write function again.m with parameters(t,k,r,x) and save it.
Function again calls function calculate with parameters (t,k,r,x) and then continues to determine (M,N) from the output of calculate.
in the Matlab toolbox optimization function, e.g.: fmincon(fun,x0,A,b), you then have to use again.m as the function you want to optimize (fun).
Hope that's good enough for a start.
Related
Using deal we can write anonymous functions that have multiple output arguments, like for example
minmax = #(x)deal(min(x),max(x));
[u,v] = minmax([1,2,3,4]); % outputs u = 1, v = 4
But if you want to provide a function with its gradient to the optimization function fminunc this does not work. The function fminunc calls the input function sometimes with one and sometimes with two output arguments. (EDIT: This is not true, you just have to specify whether you actually want to use the gradient or not, using e.g. optimset('SpecifyObjectiveGradient',true). Then within one call it always asks for the same number of arguments.)
We have to provide something like
function [f,g] = myFun(x)
f = x^2; % function
g = 2*x; % gradient
which can be called with one or two output arguments.
So is there a way to do the same inline without using the function keyword?
Yes there is, it involves a technique used in this question about recursive anonymous functions. First we define a helper function
helper = #(c,n)deal(c{1:n});
which accepts a cell array c of the possible outputs as well as an integer n that says how many outputs we need. To write our actual function we just need to define the cell array and pass nargout (the number of expected output arguments) to helper:
myFun = #(x)helper({x^2,2*x,2},nargout);
This now works perfectly when calling fminunc:
x = fminunc(myFun,1);
The OP's solution is good in that it's concise and useful in many cases.
However, it has one main shortcoming, in that it's less scalable than otherwise possible. This claim is made because all functions ({x^2,2*x,2}) are evaluated, regardless of whether they're needed as outputs or not - which results in "wasted" computation time and memory consumption when less than 3 outputs are requested.
In the example of this question this is not an issue because the function and its derivatives are very easy to compute and the input x is a scalar, but under different circumstances, this can be a very real issue.
I'm providing a modified version, which although uglier, avoids the aforementioned problem and is somewhat more general:
funcs_to_apply = {#(x)x.^2, #(x)2*x, #(x)2};
unpacker = #(x)deal(x{:});
myFun = #(x)unpacker(cellfun(#(c)feval(c,x),...
funcs_to_apply(1:evalin('caller','nargout')),...
'UniformOutput',false)...
);
Notes:
The additional functions I use are cellfun, evalin and feval.
The 'UniformOutput' argument was only added so that the output of cellfun is a cell (and can be "unpacked" to a comma-separated list; we could've wrapped it in num2cell instead).
The evalin trick is required since in the myFun scope we don't know how many outputs were requested from unpacker.
While eval in its various forms (here: evalin) is usually discouraged, in this case we know exactly who the caller is and that this is a safe operation.
Suppose we have an 3-D array (tensor) and we want to apply in each slice a function, e.g., myFun = #(x)mean(x). Is there any way to do this without for loop using build-in functions (possibly withbsxfun, or arrayfun, or accumarray)?
For loop example:
inputA = rand(10,5,20);
for sl = 1:size(A,3)
inputB = myFun(inputA(:,:,sl));
end
Thank you.
EDIT:
inputB = arrayfun(#(iterSlice) myFun(inputA(:,:,iterSlice), 1:size(inputA,3))
PS: I would like to mention, that the handler function applied is more complicated in each slice, mean was an example included in the handler function.
A for loop is already the best possibility to iterate. The only way to further improve the performance is to get rid of the iteration and have a single function call of myFun which processes all data in a vectorized way. For your example function that very simple:
myFun=#(x)permute(mean(x,1),[3,2,1])
Now it accepts 3d inputs and in the rows you find the results of the previous iterative code. You have to modify your function, there is no generic wrapper on top which can do this for you.
Regarding your edit: arrayfun is known to be slow
I am trying to use parallel computing with GPU in Matlab, and I would like to apply a function to a large array (to avoid the use of a for loop, which is quite slow). I have read Matlab's documentation, and I can use arrayfun, but only if I want to do elementwise operations. Maybe I am confused, but I would appreciate if someone can help me to use it. As an example of what I want to do, imagine that I would like to perform the following operation,
$X_t = B Z_t + Q\varepsilon_t$
where $X_t$ is 2x1, $B$ is 2x5, and $Z_t$ is 5x1, with $Q$ 2x2. I define a function,
function X = propose(Z,B,Q)
X=Z*B+Q*rand(2,1);
end
Now, suppose that I have an array $Z_p$ which is 5x1000. To each of the 1000 columns I would like to apply the previous function, for given matrices $B$ and $Q$, to get an array $X_p$ which is 2x1000.
Given the documentation for arrayfun I can not do this,
X=arrayfun(#propose,Zp,B,Q)
So, is there any possibility to do it?
Thanks!
PS: Yes, I know that in this simple example I can just do the multiplication without a for loop, but the application I have in mind is more complicated and I cannot do it. I just put this example as an illustration.
This question may initially appear similar to this other question but my situation is a little bit different.
I have a function 'deriv' that takes a symbolic expression as its input, then takes the first derivative of that symbolic expression. That derivative is then converted into an anonymous function using matlabFunction(), and is then evaluated over an array of points. I also use the anonymous function later in some other code.
The problem I'm having is that sometimes the input symbolic expression happens to be linear, and thus the derivative is constant; therefore the anonymous function is also a constant. When I evaluate the anonymous function over the array of points, I only get one output instead of an array of outputs.
Here's some code showing what I'm doing. For the sake of simplicity here, let's assume that the symbolic input expressions will involve only one symbolic variable called q.
function[derivFun,derivVals] = deriv(input)
derivSym = diff(input,q);
derivFun = matlabFunction(derivSym,'vars',q);
evalPoints = [1;2;3;4;5]; %in my true application, a much larger array
derivVals = derivFun(evalPoints);
end
So if the input is q^2, then the output derivVals will be [2;4;6;8;10]. But if the input happens to be, say, 3*q, then derivVals will be 3 (just a single scalar). What I'd like is for derivVals to be [3;3;3;3;3].
That is, I'd like derivVals to be the same size as evalPoints even if the input function happens to be linear (or constant). And I don't know ahead of time what the input expression will be.
Can anyone give suggestions for a scheme that would do that? I understand that a constant anonymous function will just return a single constant scalar, regardless of the size of its input. What I'm hoping for is perhaps some way to recognize when the anonymous function is constant and then still cause derivVals to be the same size as evalPoints.
I know that I could use a for loop to evaluate derivFun for every row of evalPoints, but I'd like to avoid using such a loop if possible.
Thank you for your time and consideration.
I think that this is a slightly simpler solution. The issue is that you're using matlabFunction, which simplifies down the equations and doesn't allow much customization. However, you can create an anonymous function of an anonymous function. Just add the this line right after your matlabFunction line:
derivFun = #(evalPoints)derivFun(evalPoints)+zeros(size(evalPoints));
This only evaluates the original derivFun once. However, I do like you symvar solution (just remember that adding zeros is always better than multiplying ones).
Not 100% sure I got the problem correctly.
Would this solve your issue?:
if isscalar(derivVals)
derivVals = repmat(derivVals, size(evalPoints));
end
When using a multiple-output matlab function, do i need to callback all variables? or can I just take the first two variables? (if so..is it not recommended?)
lets say in function.m
[a, b, c] = function( )
in main.m
[var1, var2] = function;
When calling (almost) any function in matlab you can request fewer outputs than it specifies. So, yes the example you give should work perfectly fine.
There are some clever things you can do with this, such as using nargout within a function to see how many output arguments have been requested and only calculating the values that have been requested as an optimisation trick.
It depends on the definition of the function, and exactly which of the outputs you want to get.
Not all the function allow to do it, you can find all the options for each function in the beginning of the help documentation on the specific function.
If you want only the 2nd, or 3rd outputs, and you want also to save the computation-time of the results that does not interesting, you can use ~ option, like this (for versions 2009b and later):
[~, var1, var2]=function
Many functions allow for options to passed that change how the function behaves. I used/wrote various numerical solving functions a bit and one that nice amount of option, for instance is the LSMR function(s).
Otherwise, if you can manipulate the original either introduce an input(s) to do so before or at the end with an inline subroutine to generate the outputs you want.
Or if you can't it will return as either a cell array or a vector and you can pass an anonymous function to generate the desired outputs that way.
Really, can be done many ways. Very contextual.