Code to run script multiple times

I have two codes, one is a big system of equations (NFRO3), and one is a script that runs fsolve(NFRO3Script). How do I write a code that runs the script multiple times while changing one number in the original code each time? (basically, one of my equations is like f(50) = x(49) - .r and I want to change that r from in .001 increments from like .7 to 1 [r = .7:.001:1]). (the equations only converge for very specific r values and i don't want to manually test them)

[per isakson]

Read fsolve, Solve system of nonlinear equations and notice especially that the first input argument of fsolve shall be a function handle or a function name. (I assume that NFRO3Script is a script (in Matlab's meaning of the word).)

[Alice Shen]

Yeah, so far how i've been solving it is like writing the script to be:

clear all

fun = @NFRO3Rec;

x0 = [(some guesses)]

x = fsolve(fun, x0);

and if i just click run script at the top of the page and it solves it for me. I don't even know if it's possible but I'd just like to write a code or something that would run this script many times for different values of a constant in the system of equations.

[per isakson]

So why did you write "fsolve(NFRO3Script)" in your question?

[Alex Mcaulley]

for loop??

Answer 1

[madhan ravi]

https://in.mathworks.com/help/matlab/math/parameterizing-functions.html - parameterize your function (by turning your script into a function file) [Make use of function! FUNCTION] and run a loop through it.

[Alice Shen]

thank you, but I'm not sure if this works on a system of equations? i have like 110 equations :(

[madhan ravi]

It should! Well upload your script file which contains your equations, let’s see what your dealing with.

[Alice Shen]

Thank you for your help! I ended up just copying per isakson's code, and it works fine! If you are interested though (and I am!!) about parameterizing my functions, I've attached my system of equations code and the script that solves it. Either way, I'm really grateful for your help too!

[madhan ravi]

See the attached file. If your using version prior to 2016b you may need to save the function separately in the name of the function (I believe you know how to do it).

[Alice Shen]

wow this is an amazing code! Thank you so much, it's very easy to understand and use :)

Answer 2

[per isakson]

Assumtions:

1. NFRO3Rec is a function that "accepts a vector x and returns a vector F"
2. r is not changed in your code

Alternate solutions:

1. see Passing Extra Parameters ( recommended)
2. make r global in NFRO3Rec and NFRO3Script (not recommended)
3. use persistent according to the outline below (not tested)
4. modify the code of NFRO3Rec.m (not recommended)
5. and others, which I cannot think of

%% NFRO3Script
fun = @NFRO3Rec;
x0 = [(some guesses)];
for  r = 0.7 : 0.001 : 1
    NFRO3Rec( [], r );
    x = fsolve( fun, x0 );
    % assign x together with r to an array
    x0 = x;
end

and

function    F = NFRO3Rec( x, varargin )
    persistent r
    if isempty( r )
        r = nan;    % anything that will produce an error
    end
    if nargin == 2
        r = varargin{1};
        F = [];
        return
    end
    % your code
    f(50) = x(49) - r; % I assume the period, ".", is a typo
    % more code
end

It's easier to test NFRO3Rec if it's in a separate file.

[madhan ravi]

Per as far as I know globals are not recommended but is persistent not recommended too? . Just curious.

[Alice Shen]

Thank you for such a thorough answer!! Sorry though, I am still kind of confused... :( My NFRO3Rec function is system of like 110 equations, so how do I make that into a vector x?

Here is an excerpt:

function f = NFRO3Rec(x)
%NF mass balances
f(1) = x(1)*x(2) + x(11)*x(12) - x(41)*x(42);
f(2) = x(1)*x(3) + x(11)*x(13) - x(41)*x(43);
f(3) = x(1)*x(4) + x(11)*x(14) - x(41)*r; %(I want to change this r value by .001 each iteration of the loop)

and then my script is like:

clear all
fun = @NFRO3Rec;
x0 = [997.9163 0.1030	0.0875]
x = fsolve(fun, x0);
x = x';

would I make it a vector like: x = [f(1), f(2), f(3)]?

[Alice Shen]

wait haha I'm dumb I just copied your code over and it works really well, thank you so much!!!

[per isakson]

@Madhan

Caveat: I answered this question to try fsolve. I'm a beginner. The recommendations are mine.

I don't want to encourage anybody to use globals. In a small script with a local function globals might not hurt, but it's better to ban them so that one doesn't makes it a habbit using them.

The construct based on persistent isn't in the documentation as far as I can see. Now I've made a simple implementation based on an example of the documentation.

%% NFRO3Script
fun = @NFRO3Rec_persistent;
x0  = [0;0];
opt = optimoptions('fsolve','Display','none');  % don't ask me why this helps
Result = struct( 'x', cell(11,1), 'r', cell(11,1) );
jj = 0;
for  r = 0.40 : 0.01 : 0.60
    NFRO3Rec_persistent( [], r );
    x = fsolve( fun, x0, opt );
    jj = jj + 1;
    Result(jj).r = r;
    Result(jj).x = x;
    x0 = x;
end
figure;
plot( [Result.r], [Result.x], 'd' );
%
function    F = NFRO3Rec_persistent( x, varargin )
    persistent r
    if isempty( r )
        r = nan;    % anything that will produce an error
    end
    if nargin == 2
        r = varargin{1};
        F = [];
        return
    end
    F = NFRO3Rec( x, r );
end

and

function    F = NFRO3Rec( x, r )
    F(1) = exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2);
    F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - r;
end

Now I've tested the approach:

1. It seems to work well.
2. It's conceptually fairly simple
3. NFRO3Rec is hardly modified and doesn't contain any strange code
4. the function handle is created outside the loop
5. problems will surely surface after some use.

I realized too late that I was reinventing the wheel and searched the documetation and added the link. The MathWorks' solution shall be recommended. Or I recommended to read the documentation.

[madhan ravi]

@Per: What’s your point? Are you saying using persistent is not a big deal? Paremeterizing the function should do the trick right?

[per isakson]

@Madhan

The problem is to paremeterize the function without changing the signature that fsolve uses. (Users shouldn't modify fsolve.)

There are three constructs on the page, "Passing Extra Parameters"

1. Anonymous Functions
2. Nested Functions
3. Global Variables

The two first "embed" the parameters values in the function handle. Thus, the function handle must be recreated in every iteration.

At the moment I think my persistent-construct is a big deal, since its relatively simple and not included in the page, "Passing Extra Parameters"

There is another page, Pass Extra Parameters in Problem-Based Approach. I don't know if it's relevant to the current problem. (There are many pages, which I've never read.)

[Stephen23]

"The two first "embedd" the parameters values in the function handle. "

Nested functions do not have to "embed" any parameters in the function handle.

Why would it be necessary that "the function handle must be recreated in every iteration" for a nested function? I use nested function often for parameterizing functions, and I have not experienced any need to "recreate" the function handle just because a variable in the parent workspace has changed. That would entirely defeat the point of nested functions!

A nested function would also be simpler than using persistent (which requires special cases added to the objective function).

[per isakson]

Yes, I was mistaken regarding nested function.

An even bigger mistake was that I answered the question without knowing that the documentation includes good solutions. I searched the documentation and added the link as an afterthought.

In this thread of comments I showed a somewhat better version of my "persistent" construct. And here is my current version (still missing error checking and documentation):

function    F = objective_function_proxy( x, varargin )
%
% Syntax    
%   x = objective_function_proxy( x )
%   x = objective_function_proxy( [], objective_function )
%   x = objective_function_proxy( [], [], p1, p2, p3, ... )

    persistent objective_function parameters 
    if isempty( objective_function )
        parameters = {nan};         % something that will produce an error
        objective_function = '';
    end
    if nargin == 2
        objective_function = varargin{1};
        F = [];
        return
    end
    if nargin >= 3
        parameters = varargin(2:end);
        F = [];
        return
    end
    F = feval( objective_function, x, parameters{:} );
end

Example of using objective_function_proxy()

%% NFRO3Script
fun = @objective_function_proxy;
x0  = [0;0];
opt = optimoptions('fsolve','Display','none');
Result = struct( 'x', cell(11,1), 'r', cell(11,1) );
jj = 0;
fun( [], 'NFRO3Rec' );              % set objective function
for  r = 0.40 : 0.01 : 0.60
    fun( [], [], r );               % set parameter value
    x = fsolve( fun, x0, opt );     % call fsolve
    jj = jj + 1;
    Result(jj).r = r;
    Result(jj).x = x;
    x0 = x;
end
figure;
plot( [Result.r], [Result.x], 'd' );

where

function    F = NFRO3Rec( x, r )
    F(1) = exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2);
    F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - r;
end

Comments:

1. objective_function_proxy() doesn't contain any case specific code, i.e. no references to NFRO3.
2. objective_function_proxy() should be possible to use in different cases without any modification.
3. NFRO3Script includes two calls of objective_function_proxy(), but no code that depends on the inner workings of objective_function_proxy().
4. The objective function, NFRO3Rec(), has no special code added.