I have very limited knowledge on Matlab and I'm trying to make a general Newton Raphson function but every time it comes up with an error saying there are not enough input arguments. My code needs three inputs, f (the function), c0 (the initial guess) and n (the number of steps). This is my code so far:
function [c] = Q3(f,c0,n)
for i=1:n
c(0)=c0;
f=f(x);
fp=diff(f,x);
c(i)=c(i-1)-subs(f,x,c(i-1))/subs(fp,c(i-1));
end
disp(c)
I have this function written in a script file
g=#(x)(sin((pi.*x)/2)+(1/x)-(10.*x));
I then put this into the command window [c]=Q3(g(x),1,n) hoping it would work but obviously my code needs work.
Thanks
This should do the trick, the function g is defined as you stated:
g=#(x)(sin((pi.*x)/2)+(1/x)-(10.*x));
but also you should define n and c0, for example:
clearvars
g=#(x)(sin((pi.*x)/2)+(1/x)-(10.*x));
n=10
c0=1
c=Q3(g,c0,n)
And in another file you write the function for NR:
function [c] = Q3(f,c0,n)
h=1e-4;
c(1)=c0;
for i=1:n
g=f(c(i));
gp=(f(c(i)+h)-f(c(i)-h))/(2*h)
c(i+1)=c(i)-g/gp
end
disp(c)
In this case I choose h=1e-4 for the numerical derivative approximation, but you can change it. I suggest h<1e-2.
Related
I'm newbie to Matlab
I have an assignment :
Legendre polynomial Pn(x), n=0,1,2,. . . The recursive formula of is
Write recursive sub-functions and non-recursive sub-functions separately to find the value of the Legendre polynomial function
This is my code :
function P =Legendre(n,x)
syms x;
n = input('n=');
if n==0
P=1;
elseif n==1
P=x;
elseif n>=2
P=((2*n-1)/n)*x*Legendre(n-1)-((n-1)/n)*Legendre(n-2);
end
end
But I get an error message:
Unrecognized function or variable 'Legendre'.
Error in ti4 (line 9)
P=((2*n-1)/n)*x*Legendre(n-1)-((n-1)/n)*Legendre(n-2);
Sorry for the stupid question. Can anyone help me? Thank u so much
A few things are probably going on here.
File name needs to match function name (for the primary function)
In your case, the filename needs to be Legendre.m.
Symbolic toolbox OR do you want an answer
for most uses of this function, I would leave two full inputs, just as you have them. Bur I would remove the first two lines completely.
As it is, the first two lines will break your inputs. The value for n is reset by the input function. I'm actually not sure what happens when you declare an existing variable x, to a sym.
Input consistency
You are setting up a function with two inputs, named n and x. But when you maek your recursive calls you only pass in one variable. The easiest thing to do here is simply keep passing n in as the first input.
(Right now, you are trying to pass in x in the recursive calls, but it will be interpreted as n.)
I am trying to create a plot in MATLAB by iterating over values of a constant (A) with respect to a system of equations. My code is pasted below:
function F=Func1(X, A)
%X(1) is c
%X(2) is h
%X(3) is lambda
%A is technology (some constant)
%a is alpha
a=1;
F(1)=1/X(1)-X(3)
F(2)=X(3)*(X(1)-A*X(2)^a)
F(3)=-1/(24-X(2))-X(3)*A*a*X(2)^(a-1)
clear, clc
init_guess=[0,0,0]
for countA=1:0.01:10
result(countA,:)=[countA,fsolve(#Func1, init_guess)]
end
display('The Loop Has Ended')
display(result)
%plot(result(:,1),result(:,2))
The first set of code, I am defining the set of equations I am attempting to solve. In the second set of lines, I am trying to write a loop which iterates through the values of A that I want, [1,10] with an increment of 0.01. Right now, I am just trying to get my loop code to work, but I keep on getting this error:
"Failure in initial objective function evaluation. FSOLVE cannot continue."
I am not sure why this is the case. From what I understand, this is the result of my initial guess matrix not being the right size, but I believe it should be of size 3, as I am solving for three variables. Additionally, I'm fairly confident there's nothing wrong with how I'm referencing my Func1 code in my Loop code.
Any advice you all could provide would be sincerely appreciated. I've only been working on MATLAB for a few days, so if this is a rather trivial fix, pardon my ignorance. Thanks.
Couple of issues with your code:
1/X(1) in function Func1 is prone to the division by zero miscalculations. I would change it to 1/(X(1)+eps).
If countA is incrementing by 0.01, it cannot be used as an index for result. Perhaps introduce an index ind to increment.
I have included your constant A within the function to clarify what optimization variables are.
Here is the updated code. I don't know if the results are reasonable or not:
init_guess=[0,0,0];
ind = 1;
for countA=1:0.01:10
result(ind,:)=[countA, fsolve(#(X) Func1(X,countA), init_guess)];
ind = ind+1;
end
display('The Loop Has Ended')
display(result)
%plot(result(:,1),result(:,2))
function F=Func1(X,A)
%X(1) is c
%X(2) is h
%X(3) is lambda
%A is technology (some constant)
%a is alpha
a=1;
F(1)=1/(X(1)+eps)-X(3);
F(2)=X(3)*(X(1)-A*X(2)^a);
F(3)=-1/(24-X(2))-X(3)*A*a*X(2)^(a-1);
end
How do call a script to a function and vica versa in Matlab/Octave?
function mean_DNA_Microarray = Calc_mean_DNA_Microarray(M)
M = DNA_Microarray
mean_DNA_Microarray = M - ones(5,25)*mean(M(:,25))
end
The response is
error: invalid call to script
C:\Users\Nacho\Documents\Matlab\DNA_Microarray.m error: called from:
error: C:\Users\Nacho\Documents\Matlab\Calc_mean_DNA_Microarray.m at
line 3, column 3
Now this will work if I call DNA_Microarray a function, but the problem requires that it remain as a script.
First of all, you are not defining your function correctly, as the function does not know what M is (unless it is a global vairable, but I doubt so).
In ANY programming language, you need to tell a function which variables it is going to work with. This is not Matlab specific. In Matlab you will do it so:
function mean_DNA_Microarray = Calc_mean_DNA_Microarray(M) % Look! we are telling him what M is!
mean_DNA_Microarray = M - ones(5,25)*mean(M(:,25))
end
Then you want to all the function from somewhere else you would need to just type its name and pass in the arguments, in this case what inside the function is going to be called M
clear;
clc;
% Test code
Mnameoutofthefunction=rand(100,100);
DNAmean = DNA_Microarray(Mnameoutofthefunction); % here we are calling it!
Remember to save the function as functionname.m , in your case DNA_Microarray.m , else Matlab wont know which one it is.
But I HIGHLY recommend you to read a book about Matlab or just about programming in general, as it seems like you could benefit from some basic introduction.
Following #am304 suggestion, here you can find nice tutorials:
http://www.mathworks.co.uk/academia/student_center/tutorials/
EDIT What you want to do is create a function as follows:
function mean_DNA_Microarray = Calc_mean_DNA_Microarray(M) % Look! we are telling him what M is!
mean_DNA_Microarray = M - ones(5,25)*mean(M(:,25))
end
And then, inside your function DNA_Microarray call Calc_mean_DNA_Microarray with the input M
The functions w_d(Y,T) and q(tg,tm) are being used in a function called by the ODE solver described below:
function dPdh=gasstep1(~,P)
global rho_solid W_B S e height_dryer c_a c_b tm_o
dPdh=zeros(size(P));
Y=P(1);tg=P(2);
% Mass Balance
dPdh(1)=rho_solid*(1-e)*S*height_dryer/W_B*w_d(Y,tg);
% Enthalpy balance
dPdh(2)=-rho_solid*(1-e)*S*height_dryer/W_B*(1/(c_b+c_a*Y))...
*(q(tg,tm_o)+(c_a*(tg-tm_o)*w_d(Y,tg)));
dPdh=[dPdh(1)
dPdh(2)];
end
The ODE solver is called in the following manner:
tspan=linspace(0,height_dryer,100);
format long
[h,P]=ode45(#(h,P)gasstep1(h,P),tspan,[Y_o tg_o]);
The values from the generated arrays and P are used in a for loop to compute variables:
X1=zeros(1,Nh);Tm=zeros(1,Nh);
X1(1,1)=X_o;Tm(1,1)=tm_o;
for i=1:Nh-1
% Mass balance
X1(1,i+1)=X1(1,i)-dt*((P(i+1,1)-P(i,1))/(h(i+1)-h(i)))*(W_B/S)*(1/(rho_solid*(1-e)));
% Enthalpy balance
Tm(1,i+1)=Tm(1,i)+dt*(1/(c_s+c_al*X1(1,i)))*(q(((P(i+1,2)+P(i,2))/2),Tm(1,i))-...
((c_a-c_al)*(Tm(1,i))+hv(Tm(1,i)))*w_d((P(i+1,1)-P(i,1)), ((P(i+1,2)+P(i,2))/2)));
end
The doubt I have is whether the variables in the function w_d and q also change when I call the ODE solver in a loop. I found a method to implement the ODE solver in a loop on the mathworks website (link). I have found help provided when ODE parameters need to be changed (link).
I think my final code should look something like:
for j=2:Nt
for i=1:Nh-1
% compute X1 & Tm
end
% change variables in function w_d and q
% [call the ODE]
end
Could anyone please give me an idea on how to start the loop which would help me to complete the code.
The links you pointed to should answer your question: you could make w_d and q parameters of the gasstep function, and use the function parameterization as in the second link you posted.
From the code you posteed, I understand that you want w_d and q to be dependent on X1 and Tm, right? I'm going to assume that's the case. If they depend on other parameters, just use those instead of X1 and Tm in my explanation:
make gasstep1 dependent on X1 and Tm and pass them along to w_d and q: your gasstep1 function now has 4 arguments: gasstep1(h, P, X1, Tm), and w_d and q also (w_d(Y, tg, X1, Tm) for instance). Then you only need to create gasstep2 as such:
gasstep2 = #(h,P) gasstep1(h,P,X1,Tm)
and you can call ode45 on gasstep2!
Be careful that in your final code, if you write it like you presented above, X1 and Tm are going to depend on P, which needs to be initialized!
I need to solve a system of differential equations in a selected time span, but the equations depend on some variables that change with time. I'm trying to write the function 'odefun' to use in ode45, and when I run the code with the time span and initial conditions it seems to work, but I'm not sure if the code is actually doing what I want.
function [dX]=gauss(t,X)
mu_S=1.327*10^11; T=0.06; %constants
a=X(1); e=X(2);
n=sqrt(mu_S/a^3); M=n*t; %need to change with every iteration
[E] = KeplerPicard(M,e,0.5*10^-4);
dX(1)=2/n*sqrt((1+e*cos(E))/(1-e*cos(E)))*T; %da/dt
dX(2)=2*(1-e^2)*cos(E)/(a*n*sqrt(1-e^2*(cos(E))^2))*T; %de/dt
dX=dX(:);
end
dX(1) is the derivative of a, which is my X(1), and dX(2) is the derivative of e, X(2).
The function Kepler Picard is defined as follows:
function [E] = KeplerPicard(M,e,eps)
E=M;
err=1;
while err>eps
En=e*sin(E)+M;
err=abs(En-E);
E=En;
end
I want the variable 'n' to change during time and use the new value 'a+da' (or alternatively 'X(1)+dX(1)'), but I don't know if the code is doing this. It should be noted that this way the code runs without errors, but I don't know if the results are right (if the code sees 'n' as a constant, they're definitely wrong).
Is there something I need to change? Thanks!