Running a summation for a loop for different values of N.

Hello,

I have written a function that basically uses a for loop to solve a summation from 1 to N values. I am trying to run this function for different values of N and plot the results on the same plot to compare convergence. So I would like to run the function for N=5, N=20, and N=100 and plot. What is the best way to run this function to solve for each of the different values of N and store them, so they can be plotted together? I was thinking something like:

a=1:N
b=2
c=4

for N=5
e=func(a,b,c,N)
end

for N=20
f=func(a,b,c,N)
end

for N=100
g=func(a,b,c,N)
end
plot(a,e,a,f,a,g)

Where a is length N and will be the x-axis of the plot. Is there a more efficient or better way to do this?

Answer 1

[Jan]

N = [5, 20, 100];
result = zeros(1, length(N));  % Or what ever matchs your output
for iN = 1:length(N)
   result(iN) = func(a, b, c, N(iN))
end
plot(a, result(1), a, result(2), a, result(3));

Perhaps you want something like:

     result(iN, :) = func(a, b, c, N(iN))
     % or
     result(:, iN) = func(a, b, c, N(iN))
with a corresponding pre-allocation and modifications in the PLOT line.

[Christopher]

Jan,

When I input this it solves for the first value of N (5), but then when it tries to solve for the 2nd value of N (20) I get this error:

??? In an assignment A(I) = B, the number of elements in B and I must be the same.

Any ideas on what is causing this? The code is listed below:

function [LLT_solver] = LLT_run

global b N c a alpha alphaoL e AR
type=2                   % read the input file using read_inp1.m

if type == 2
 read_inp_type2;

 N = [5, 20, 100];
result = zeros(1, length(N));  % Or what ever matchs your output
for iN = 1:length(N)
   result(iN) = LLT_type2(b,N(iN),c,a,alpha,alphaoL,e,AR)
%  LLT_type2(b,N,c,a,alpha,alphaoL,e,AR);
end
end

The function LLT_Type2 is:

function[An,CL,delta,CDi,Gamma,Cl]=LLT_type2(b,N,c,a,alpha,alphaoL,e,AR)

b;
N;
c=(c*ones(1,N))';
a=(a*ones(1,N))';
alpha=(alpha*ones(1,N))';
alphaoL=(alphaoL*ones(1,N))';
e=(e*ones(1,N))';

n=1:N;                    % n rows
theta=(n.*pi/(N+1))';     % theta values
y0=-b/2*cos(theta);       % y values for each theta

RHS=(alpha+e-alphaoL)/180*pi;  % Solving RHS

% Finding IC matrix to solve for An's
 IC = zeros(N);
 for l = 1:N;
   for m = 1:N;
     IC(l,m) = (4*b/a(l)/c(l)+m/sin(theta(l)))*sin(m*theta(l));
   end
 end
 format long
 An=IC\RHS
 CL=An(1)*pi*AR

   x=((n.*((An'./An(1))).^2));
   delta=x(2:N);
   format short
   delta=sum(delta)

   CDi=(CL^2/(pi*AR))*(1+delta)

   % calculation of the vorticity Gamma on the wing
  for i=1:N,
    Gamma(i)=2*b*sum(An(:).*sin((1:N)*theta(i))');
  end;
  Gamma

Cl=(2*Gamma)./c' 
plot(y0,Cl); ylabel('Cl / Vinf');

Thank you for your help. It's greatly appreciated.

Answer 2

[Andrei Bobrov]

N = [5 20 100]
b = 2;
c = 4;

f = arrayfun(@(x)[(1:x)',reshape(func((1:x)',b,c,x),[],1)],N,'un',0);
plot(f{:});

[Andrei Bobrov]

EDIT

[Christopher]

Andrei, how would I do this say if b was a scalar, but c was a column vector?