Passing a function as a parameter in a MATLAB function [duplicate] - function

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Closed 10 years ago.
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Passing a function as argument to another function
Below is a simple code for the bisection method. I would like to know how to be able to pass in any function I choose as a parameter instead of hard coding functions.
% This is an implementation of the bisection method
% for a solution to f(x) = 0 over an interval [a,b] where f(a) and f(b)
% Input: endpoints (a,b),Tolerance(TOL), Max # of iterations (No).
% Output: Value p or error message.
function bjsect(a,b,TOL,No)
% Step 0
if f(a)*f(b)>0
disp('Function fails condition of f(a),f(b) w/opposite sign'\n);
return
end
% Step 1
i = 1;
FA = f(a);
% Step 2
while i <= No
% Step 3
p = a +(b - a)/2;
FP = f(p);
% Step 4
if FP == 0 || (b - a)/2 < TOL
disp(p);
return
end
% Step 5
i = i + 1;
% Step 6
if FA*FP > 0
a = p;
else
b = p;
end
% Step 7
if i > No
disp('Method failed after No iterations\n');
return
end
end
end
% Hard coded test function
function y = f(x)
y = x - 2*sin(x);
end
I know this is an important concept so any help is greatly appreciated.

The simplest method is using anonymous functions. In your example, you would define your anonymous function outside bjsect using:
MyAnonFunc = #(x) (x - 2 * sin(x));
You can now pass MyAnonFunc into bjsect as an argument. It has the object type of function handle, which can be validated using isa. Inside bjsect simply use MyAnonFunc as if it is a function, ie: MyAnonFunc(SomeInputValue).
Note, you can of course wrap any function you've written in an anonymous function, ie:
MyAnonFunc2 = #(x) (SomeOtherCustomFunction(x, OtherInputArgs));
is perfectly valid.
EDIT: Oops, just realized this is almost certainly a duplicate of another question - thanks H. Muster, I'll flag it.

Related

Matlab function in fmincon with fixed value

I have a simple model where I want to minimize the RMSE between my dependent variable y and my model values. The model is: y = alpha + beta'*x.
For minimization, I am using Matlab's fmincon function and am struggling with multiplying my parameter p(2) by x.
MWE:
% data
y = [5.072, 7.1588, 7.263, 4.255, 6.282, 6.9118, 4.044, 7.2595, 6.898, 4.8744, 6.5179, 7.3434, 5.4316, 3.38, 5.464, 5.90, 6.80, 6.193, 6.070, 5.737]
x = [18.3447, 79.86538, 85.09788, 10.5211, 44.4556, 69.567, 8.960, 86.197, 66.857, 16.875, 52.2697, 93.971, 24.35, 5.118, 25.126, 34.037, 61.4445, 42.704, 39.531, 29.988]
% initial values
p_initial = [0, 0];
% function: SEE BELOW
objective = #(p) sqrt(mean((y - y_mod(p)).^2));
% optimization
[param_opt, fval] = fmincon(objective, p_initial)
If I specify my function as follows then it works.
y_mod = #(p) p(1) + p(2).*x
However, it does not work if I use the following code. How can I multiply p(2) with x? Where x is not optimized, because the values are given.
function f = y_mod(p)
f = p(1) + p(2).*x
end
Here is the output from a script that has the function declaration:
>> modelFitExample2a
RMS Error=0.374, intercept=4.208, slope=0.0388
And here is code for the above. It has many commented lines because it includes alternate ways to fit the data: an inline declaration of y_mod(), or a multi-line declaration of y_mod(), or no y_mod() at all. This version uses the multi-line declaration of y_mod().
%modelFitExample2a.m WCR 2021-01-19
%Reply to stack exchange question on parameter fitting
clear;
global x %need this if define y_mod() separately, and in that case y_mod() must declare x global
% data
y = [5.0720, 7.1588, 7.2630, 4.2550, 6.2820, 6.9118, 4.0440, 7.2595, 6.8980, 4.8744...
6.5179, 7.3434, 5.4316, 3.3800, 5.4640, 5.9000, 6.8000, 6.1930, 6.0700, 5.7370];
x = [18.3447,79.8654,85.0979,10.5211,44.4556,69.5670, 8.9600,86.1970,66.8570,16.8750,...
52.2697,93.9710,24.3500, 5.1180,25.1260,34.0370,61.4445,42.7040,39.5310,29.9880];
% initial values
p_initial = [0, 0];
%predictive model with parameter p
%y_mod = #(p) p(1) + p(2)*x;
% objective function
%If you use y_mod(), then you must define it somewhere
objective = #(p) sqrt(mean((y - y_mod(p)).^2));
%objective = #(p) sqrt(mean((y-p(1)-p(2)*x).^2));
% optimization
options = optimset('Display','Notify');
[param_opt, fval] = fmincon(objective,p_initial,[],[],[],[],[],[],[],options);
% display results
fprintf('RMS Error=%.3f, intercept=%.3f, slope=%.4f\n',...
fval,param_opt(1),param_opt(2));
%function declaration: predictive model
%This is an alternative to the inline definition of y_mod() above.
function f = y_mod(p)
global x
f = p(1) + p(2)*x;
end
carl,
The second method, in which you declare y_mod() explicitly (at the end of your script, or in a separate file y_mod.m), does not work because y_mod() does not know what x is. Fix it by declaring x global in the main program at the top, and declare x global in y_mod().
%function declaration
function f = y_mod(p)
global x
f = p(1) + p(2)*x;
end
Of course you don't need y_mod() at all. The code also works if you use the following, and in this case, no global x is needed:
% objective function
objective = #(p) sqrt(mean((y-p(1)-p(2)*x).^2));
By the way, you don't need to multiply with .* in y_mod. You may use *, because you are multiplying a scalar by a vector.

How to pass variadic arguments in Octave

I would like to implement a function duration = timer(n, f, arguments_of_f) that would measure how much time does a method f with arguments arguments_of_f need to run n times. My attempt was the following:
function duration = timer(n, f, arguments_of_f)
duration = 0;
for i=1:n
t0 = cputime;
f(arguments_of_f);
t1 = cputime;
duration += t1 - t0;
end
In another file, I have
function y = f(x)
y = x + 1;
end
The call d1 = timer(100, #f, 3); works as expected.
In another file, I have
function y = g(x1, x2)
y = x1 + x2;
end
but the call d2 = timer(100, #g, 1, 2); gives an error about undefined
argument x2, which is, when I look back, somehow expected, since I pass only
1 to g and 2 is never used.
So, how to implement the function timer in Octave, so that the call like
timer(4, #g, x1, ... , xK) would work? How can one pack the xs together?
So, I am looking for the analogue of Pythons *args trick:
def use_f(f, *args):
f(*args)
works if we define def f(x, y): return x + y and call use_f(f, 3, 4).
You don't need to pack all the arguments together, you just need to tell Octave that there is more than one argument coming and that they are all necessary. This is very easy to do using variadic arguments.
Your original implementation is nearly spot on: the necessary change is minimal. You need to change the variable arguments_to_f to the special name varargin, which is a magical cell array containing all your arbitrary undeclared arguments, and pass it with expansion instead of directly:
function duration = timer(n, f, varargin)
duration = 0;
for i=1:n
t0 = cputime;
f(varargin{:});
t1 = cputime;
duration += t1 - t0;
end
That's it. None of the other functions need to change.

GNUPLOT : Plotting a user defined equations which operates indifferent intervals

Hi there I need some help!
I am new to Gnuplot and have difficulties with the scripts.
Actually my equation is a lot more complicated. It is a parametric equation consisting of 7 parts each defined into a specific interval, with a bunch of parameters.
I just need a lead. So let me simplify the problem.
Suppose I have a function defined as follows f(x)= a*x+cos(x) : for 0 <= x <= 3;
and f(x)= b*1/cos(x) : for 3 < x <=10
my question is how do I instruct GNUPLOT:
1-) to consider "a" and "b" as parameters
2-) to plot "my user-defined" equation into the intervals of definition of f(x)
So far I have used the "set parametric" command but the problem is always at the end at the "PLOT f(x)" command for which I really don't know how to deal with the intervals.
I am using Windows 7 with the latest gnuplot.
Please help
You can define your f(x) as a (conditional) piece-wise function:
f(x) = 0 <= x && x <= 3 ? a*x+cos(x) : 3 < x && x <= 10 ? b/cos(x) : 1/0
The 1/0 above makes sure the function is not defined outside of the given intervals. The parameters a and b are already implicitly treated as parameters by gnuplot. When you change their values, f(x) is updated automatically. Example:
set xrange [-2:12]
a = 1.; b = 1.
plot f(x)
If you want more flexibility, you can take a and b as variables and do the following:
f(x,a,b) = 0 <= x && x <= 3 ? a*x+cos(x) : 3 < x && x <= 10 ? b/cos(x) : 1/0
set xrange [-2:12]
plot f(x,1,1), f(x,2,3)

PASSING PARAMETERS TO FUNCTION OF FUNCTION IN A SYSTEM OF ODES IN MATLAB

Please the following is my question.
I have two functions to be solved using Runge Kutta (Not ODE solver)
dy/dt=y*t/SUM
dz/dt=k*t^2/CP
My problem is I need to calculate CP and SUM by passing m1,N,N2,TP,W from a caller function (Caller function later used to call RK4 function outputs).
This was my solution
function f =fun1(t,Pdiff,m1,N,N2,TP,W)
x=m1/N % one of the calculations steps to obtain SUM
[K]= KIND(Pdiff(2),TP,N); %one of the calls made to calculate SUM
SUM=x/K;
dy/dt=y*t/SUM;
f=y*t/SUM;
The second function f=fun2(t,Pdiff,m1,N,N2,TP,W)
r=m1*N % one of the calculations steps to obtain CP
[K2]= KIND1(Pdiff(2),TP,N,W) %one of the calls made to calculate SUM
CP=K2/r;
dz/dt=k*t^2/CP % k is a constant
f=k*t^2/CP;
% note that Pdiff=[y z] and t is the independent variable
%These are then substituted into RK4 coefficients and solved with RK4 function:
function [t, Pdiff]=RK(t,Pdiff,m1,N,N2,TP,W);
k1 = h*fun1(t(I),Pdiff(I,:));
k2 = h*fun1(t(I)+0.5*h,Pdiff(I,:)+0.5*k1);
k3 = h*fun1(t(I)+0.5*h,Pdiff(I,:)+(0.5*(-1+sqrt(2)*k1))+(1-0.5*sqrt(2)*k2));
k4 = h*fun1(t(I)+h,Pdiff(I,:)-(0.5*(sqrt(2))*k2)+(1+0.5*sqrt(2))*k3);
k1 = h*fun1(t(I),Pdiff(I,:));
k2 = h*fun1(t(I)+0.5*h,Pdiff(I,:)+0.5*k1);
k3 = h*fun1(t(I)+0.5*h,Pdiff(I,:)+(0.5*(-1+sqrt(2)*k1))+(1-0.5*sqrt(2)*k2));
k4 = h*fun1(t(I)+h,Pdiff(I,:)-(0.5*(sqrt(2))*k2)+(1+0.5*sqrt(2))*k3);
Pdiff(I+1,kj) = Pdiff(I,1) + (k1 + (2-sqrt(2))*k2 + (2+sqrt(2))*k3 +k4)/6;
Pdiff(I+1,kj) = Pdiff(I,1) + (k1 + (2-sqrt(2))*k2 + (2+sqrt(2))*k3 +k4)/6;
My question is: Is it proper to pass parameters m1, N, N2, TP and W along with t,Pdiff in fun1 and fun2? Because I get error message
Not enough inputs in one of the calls.
Thank you.

How to use Newton-Raphson method in matlab to find an equation root?

I am a new user of MATLAB. I want to find the value that makes f(x) = 0, using the Newton-Raphson method. I have tried to write a code, but it seems that it's difficult to implement Newton-Raphson method. This is what I have so far:
function x = newton(x0, tolerance)
tolerance = 1.e-10;
format short e;
Params = load('saved_data.mat');
theta = pi/2;
zeta = cos(theta);
I = eye(Params.n,Params.n);
Q = zeta*I-Params.p*Params.p';
% T is a matrix(5,5)
Mroot = Params.M.^(1/2); %optimization
T = Mroot*Q*Mroot;
% Find the eigenvalues
E = real(eig(T));
% Find the negative eigenvalues
% Find the smallest negative eigenvalue
gamma = min(E);
% Now solve for lambda
M_inv = inv(Params.M); %optimization
zm = Params.zm;
x = x0;
err = (x - xPrev)/x;
while abs(err) > tolerance
xPrev = x;
x = xPrev - f(xPrev)./dfdx(xPrev);
% stop criterion: (f(x) - 0) < tolerance
err = f(x);
end
% stop criterion: change of x < tolerance % err = x - xPrev;
end
The above function is used like so:
% Calculate the functions
Winv = inv(M_inv+x.*Q);
f = #(x)( zm'*M_inv*Winv*M_inv*zm);
dfdx = #(x)(-zm'*M_inv*Winv*Q*M_inv*zm);
x0 = (-1/gamma)/2;
xRoot = newton(x0,1e-10);
The question isn't particularly clear. However, do you need to implement the root finding yourself? If not then just use Matlab's built in function fzero (not based on Newton-Raphson).
If you do need your own implementation of the Newton-Raphson method then I suggest using one of the answers to Newton Raphsons method in Matlab? as your starting point.
Edit: The following isn't answering your question, but is just a note on coding style.
It is useful to split your program up into reusable chunks. In this case your root finding should be separated from your function construction. I recommend writing your Newton-Raphson method in a separate file and call this from the script where you define your function and its derivative. Your source would then look some thing like:
% Define the function (and its derivative) to perform root finding on:
Params = load('saved_data.mat');
theta = pi/2;
zeta = cos(theta);
I = eye(Params.n,Params.n);
Q = zeta*I-Params.p*Params.p';
Mroot = Params.M.^(1/2);
T = Mroot*Q*Mroot; %T is a matrix(5,5)
E = real(eig(T)); % Find the eigen-values
gamma = min(E); % Find the smallest negative eigen value
% Now solve for lambda (what is lambda?)
M_inv = inv(Params.M);
zm = Params.zm;
Winv = inv(M_inv+x.*Q);
f = #(x)( zm'*M_inv*Winv*M_inv*zm);
dfdx = #(x)(-zm'*M_inv*Winv*Q*M_inv*zm);
x0 = (-1./gamma)/2.;
xRoot = newton(f, dfdx, x0, 1e-10);
In newton.m you would have your implementation of the Newton-Raphson method, which takes as arguments the function handles you define (f and dfdx). Using your code given in the question, this would look something like
function root = newton(f, df, x0, tol)
root = x0; % Initial guess for the root
MAXIT = 20; % Maximum number of iterations
for j = 1:MAXIT;
dx = f(root) / df(root);
root = root - dx
% Stop criterion:
if abs(dx) < tolerance
return
end
end
% Raise error if maximum number of iterations reached.
error('newton: maximum number of allowed iterations exceeded.')
end
Notice that I avoided using an infinite loop.