use nested functions in matlab M-file - matlab

i have question,about which i am too much interested,suppose that i have two M-file in matlab, in the first one i have described following function for calculating peaks and peaks indeces
function [peaks,peak_indices] = find_peaks(row_vector)
A = [0 row_vector 0];
j = 1;
for i=1:length(A)-2
temp=A(i:i+2);
if(max(temp)==temp(2))
peaks(j) = row_vector(i);
peak_indices(j) = i;
j = j+1;
end
end
end
and in second M-file i have code for describing sinusoidal model for given data sample
function [ x ]=generate(N,m,A3)
f1 = 100;
f2 = 200;
T = 1./f1;
t = (0:(N*T/m):(N*T))';
wn = rand(length(t),1).*2 - 1;
x = 20.*sin(2.*pi.*f1.*t) + 30.*cos(2.*pi.*f2.*t) + A3.*wn;
end
my question is how to combine it together?one solution would be just create two M-file into folder,then call function from one M-file and made operation on given vector and get result,and then call second function from another M file on given result and finally get what we want,but i would like to build it in one big M-file,in c++,in java,we can create classes,but i am not sure if we can do same in matlab too,please help me to clarify everything and use find_peaks function into generate function
UPDATED:
ok now i would like to show simple change what i have made in my code
function [ x ] = generate(N,m,A3)
f1 = 100;
f2 = 200;
T = 1./f1;
t = (0:(N*T/m):(N*T))'; %'
wn = rand(length(t),1).*2 - 1;
x = 20.*sin(2.*pi.*f1.*t) + 30.*cos(2.*pi.*f2.*t) + A3.*wn;
[pks,locs] = findpeaks(x);
end
i used findpeaks built-in function in matlab,but i am getting following error
generate(1000,50,50)
Undefined function 'generate' for input arguments of type 'double'.
also i am interested what would be effective sampling rate to avoid alliasing?

You can simply put both in one file. The file must have the same name as the first function therein, and you will not be able to access subsequently defined functions from outside that file. See the MATLAB documentation on functions http://www.mathworks.co.uk/help/matlab/ref/function.html (particularly the examples section).
Also note that MATLAB has a built-in function findpeaks().
(By the way, you're still sampling at too low a frequency and will most certainly get aliasing - see http://en.wikipedia.org/wiki/Aliasing#Sampling_sinusoidal_functions )
Edit: As you requested it, here is some more information on the sampling theorem. A good and simple introduction to these basics is http://www.dspguide.com/ch3/2.htm and for further reading you should search for the Shannon/Nyquist sampling theorem.

Try with this, within a single MATLAB script
function test()
clc, clear all, close all
x = generate(1000,50,50);
[p,i] = find_peaks(x)
end
function x = generate(N,m,A3)
f1 = 100;
f2 = 200;
T = 1./f1;
t = (0:(N*T/m):(N*T))'; %'
wn = rand(length(t),1).*2 - 1;
x = 20.*sin(2.*pi.*f1.*t) + 30.*cos(2.*pi.*f2.*t) + A3.*wn;
end
function [peaks,peak_indices] = find_peaks(row_vector)
A = [0;row_vector;0];
j = 1;
for i=1:length(A)-2
temp=A(i:i+2);
if(max(temp)==temp(2))
peaks(j) = row_vector(i);
peak_indices(j) = i;
j = j+1;
end
end
end

Related

How to avoid tf() command using State-space models in Matlab

I'm trying to avoid the function tf() from Matlab since it requires specific toolboxes to run.
The transfer function that I'm using is quite simple. Is the model for a heatsink temperature.
H(s) = (Rth/Tau)/(s + 1/Tau)
In order to avoid the tf() function, I've tried to substitute the transfer function with a state space model coded in Matlab.
I've used the function ss() to get te values of A,B,C and D. And I've tried to compare the results from tf() and my function.
Here's the code that I've used:
Rth = 8.3220e-04; % ºC/W
Tau = 0.0025; % s
P = rand(1,10)*1000; % Losses = input
t = 0:1:length(P)-1; % Time array
%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Transfer function %%%
%%%%%%%%%%%%%%%%%%%%%%%%%
H = tf([0 Rth/Tau],[1 1/Tau]);
Transfer_func = lsim(H,P,t);
figure, plot(Transfer_func),grid on,grid minor, title('Transfer func')
%%%%%%%%%%%%%%%%%%%%%%%%%
%%% My función ss %%%
%%%%%%%%%%%%%%%%%%%%%%%%%
% Preallocate for speed
x(1:length(P)) = 0;
y(1:length(P)) = 0;
u = P;
sys = ss(H);
A = sys.A;
B = sys.B;
C = sys.C;
D = sys.D;
for k = 1:length(u)
x(k+1) = A*x(k) + B*u(k);
y(k) = C*x(k) + D*u(k);
end
figure, plot(y), grid on,grid minor, title('With my función')
I know that the values from A,B,C and D are ok, since I've checked them using
H = tf([0 Rth/Tau],[1 1/Tau]);
sys = ss(H);
state_space_sys = ss(sys.A,sys.B,sys.C,sys.D);
state_space = lsim(state_space_sys,P,t);
figure, plot(state_space),grid on,grid minor, title('State space')
As you can see, the results obtained from my funtion and the function tf() are very different.
Is there any mistakes on the approach?
If it's not possible to avoid the tf() function in this way, is there any other way?
At the end, I found another solution. I'm posting this here, so if someone has the same problem, can use this approach.
If you take the transfer function, and develop it, we reach to the following expresion
H(s) = deltaT(s)/P(s) = (Rth/Tau)/(s + 1/Tau)
deltaT(s) * (s + 1/Tau) = (Rth/Tau) * P(s)
deltaT(s) * s = (Rth/Tau) * P(s) - deltaT(s)/Tau
Now, we know that 1/s is equal to integrate. So in the end, we have to integrate the right side of the equation. The code would be like this.
Cth = Tau/Rth;
deltaT = zeros(size(P));
for i = 2:length(P)
deltaT(i) = (1/Cth * (P(i)-deltaT(i-1)/Rth))*(time(i)-time(i-1)) + deltaT(i-1);
end
This integral has the same output as the function tf().

I want to feed in a function handle into a matlab function I made

I am trying to feed a function handle into the function I created below. I'm not exactly sure how to do this.
For example, how do I get:
conjugate_gradient(#(y) ABC(y), column_vector, initial_guess)
to not error?
If I use matlab's pcg function in the same way it will work:
pcg(#(y) ABC(y),b,tol).
I tried reading the pcg function, and they do take about this in the function description, however I'm still super inexperienced with MATLAB and had shall we say some difficulty understanding what they did.Thank You!
function [x] = conjugate_gradient(matrix, column_vector, initial_guess)
y = [];
col_size = length(column_vector);
temp = size(matrix);
mat_row_len = temp(2);
% algorithm:
r_cur = column_vector - matrix * initial_guess;
p = r_cur;
k = 0;
x_approx = initial_guess;
for i=1:mat_row_len
alpha = ( r_cur.' * r_cur ) / (p.' *(matrix* p));
x_approx = x_approx + alpha * p;
r_next = r_cur - alpha*(matrix * p);
fprintf(num2str(r_next'*r_next), num2str(i))
y = [y; i, r_next'*r_next];
%exit condition
if sqrt(r_next'*r_next) < 1e-2
y
break;
end
beta = (r_next.'* r_next )/(r_cur.' * (r_cur) );
p = r_next + beta * p;
k = k+1;
r_cur = r_next;
end
y
[x] = x_approx;
end
When you do
f = #(y) ABC(y)
You create a function handle. (Note that in this case it's the same as f=#ABC). This handle is a variable, and this can be passed to a function, but is otherwise the same as the function. Thus:
f(1)
is the same as calling
ABC(1)
You pass this handle to a function as the first argument, which you have called matrix. This seems misleading, as the variable matrix will now be a function handle, not a matrix. Inside your function you can do matrix(y) and evaluate the function for y.
However, reading your function, it seems that you treat the matrix input as an actual matrix. This is why you get errors. You cannot multiply it by a vector and expect a result!

Trying to minimise a function wrt 2 variables for robust portfolio optimisation. How to do this with fmincon?

I am currently involved in a group project where we have to conduct portfolio selection and optimisation. The paper being referenced is given here: (specifically page 5 and 6, equations 7-10)
http://faculty.london.edu/avmiguel/DeMiguel-Nogales-OR.pdf
We are having trouble creating the optimisation problem using M-Portfolios, given below
min (wrt w,m) (1/T) * sum_(rho)*(w'*r_t - m) (Sorry I couldn't get the formatting to work)
s.t. w'e = 1 (just a condition saying that all weights add to 1)
So far, this is what we have attempted:
function optPortfolio = portfoliofminconM(returns,theta)
% Compute the inputs of the mean-variance model
mu = mean(returns)';
sigma = cov(returns);
% Inputs for the fmincon function
T = 120;
n = length(mu);
w = theta(1:n);
m = theta((n+1):(2*n));
c = 0.01*ones(1,n);
Aeq = ones(1,(2*n));
beq = 1;
lb = zeros(2,n);
ub = ones(2,n);
x0 = ones(n,2) / n; % Start with the equally-weighted portfolio
options = optimset('Algorithm', 'interior-point', ...
'MaxIter', 1E10, 'MaxFunEvals', 1E10);
% Nested function which is used as the objective function
function objValue = objfunction(w,m)
cRp = (w'*(returns - (ones(T,1)*m'))';
objValue = 0;
for i = 1:T
if abs(cRp(i)) <= c;
objValue = objValue + (((cRp(i))^2)/2);
else
objValue = objValue + (c*(abs(cRp(i))-(c/2)));
end
end
The problem starts at our definitions for theta being used as a vector of w and m. We don't know how to use fmincon with 2 variables in the objective function properly. In addition, the value of the objective function is conditional on another value (as shown in the paper) and this needs to be done over a rolling time window of 120 months for a total period of 264 months.(hence the for-loop and if-else)
If any more information is required, I will gladly provide it!
If you can additionally provide an example that deals with a similar problem, can you please link us to it.
Thank you in advance.
The way you minimize a function of two scalars with fmincon is to write your objective function as a function of a single, two-dimensional vector. For example, you would write f(x,y) = x.^2 + 2*x*y + y.^2 as f(x) = x(1)^2 + 2*x(1)*x(2) + x(2)^2.
More generally, you would write a function of two vectors as a function of a single, large vector. In your case, you could rewrite your objfunction or do a quick hack like:
objfunction_for_fmincon = #(x) objfunction(x(1:n), x(n+1:2*n));

Trapezoidal Numerical Integration in MATLAB without using a FOR loop?

I'm following a Numerical Methods course and I made a small MATLAB script to compute integrals using the trapezoidal method. However my script uses a FOR loop and my friend told me I'm doing something wrong if I use a FOR loop in Matlab. Is there a way to convert this script to a Matlab-friendly one?
%Number of points to use
N = 4;
%Integration interval
a = 0;
b = 0.5;
%Width of the integration segments
h = (b-a) / N;
F = exp(a);
for i = 1:N-1
F = F + 2*exp(a+i*h);
end
F = F + exp(b);
F = h/2*F
Vectorization is important speed and clarity, but so is using built-in functions whenever possible. Matlab has a built in function for trapezoidal numerical integration called trapz. Here is an example.
x = 0:.125:.5
y = exp(x)
F = trapz(x,y)
It is recommended to vectorize your code.
%Number of points to use
N = 4;
%Integration interval
a = 0;
b = 0.5;
%Width of the integration segments
h = (b-a) / N;
x = 1:1:N-1;
F = h/2*(exp(a) + sum(2*exp(a+x*h)) + exp(b));
However, I've read that Matlab is no longer slow at for loops.

MATLAB - how to count the number of function calls

Currently I'm doing a code on the Secant Method, and so far the code runs ok.
However, I still have to update my "count.funcCount" by counting the number of function calls that I used in the "secant" function. How should I modify my code ?
This is what I have so far for the code:
function [ root, fcneval, count ] = secant(f, x0, x1, my_options)
my_options = optimset('MaxIter', 50, 'TolFun', 1.0e-5);
count = struct('iterations',0,'funcCount',0,'message',{'empty'});
xp = x0; %# Initialize xp and xc to match with
xc = x1; %# x0 and x1, respectively
MaxIter = 100;
TolFun = 1.0e-5;
%# Secant Method Loop
for i = 2:MaxIter
fd = f(xc) - f(xp); %# Together, the ratio of d and fd yields
d = xc - xp; %# the slope of the secant line going through xc and xp
xn = ((xc * fd) - (f(xc) * d)) / fd; %# Secant Method step
if (abs(xc - xn) < TolFun) && (abs(f(xn)) < TolFun) %# Stopping condition
break;
elseif i > MaxIter %# If still can't find a root after maximum
%# 100 iterations, consider not converge
count.message = sprintf('Do not converge');
end
xp = xc; % Update variables xc and xp
xc = xn;
end
%# Get outputs:
root = xn;
fcneval = f(root);
count.iterations = i;
end %# end function
---------------------------------------
function [f] = fun(x)
f = cos(x) + x;
end
Please help me, thank you in advance
Although I did not understand your question but still I think you can use a counter. Initialize it with zero and increment it every time your function is called. You are using an inbuilt function, just make necessary changes in its source code( FYI :you can do this in matlab) then save it with a new name and then use it in your main code.
You could create a nested function which have access to the variables of its parent function (including the function f and the counter count.funcCount). This function would call the actual method which does the computation, and then increment the counter.
Here is a rather silly example to illustrate the concept:
function [output,count] = myAlgorithm(f, x0)
count = 0;
output = x0;
while rand()<0.99 %# simulate a long loop
output = output + fcn(x0);
end
%# nested function with closure
function y = fcn(x)
%# access `f` and `count` inside the parent function
y = f(x); %# call the function
count = count + 1; %# increment counter
end
end
Now you call it as:
[output,count] = myAlgorithm(#(x)cos(x)+x, 1)