How do i substitute data from a list to a summation

Hello I want to substitute multiple data from an excel worksheet(Vi,Xi) to this equation:

E := sum((V[i]-xi[i]*((1+b)/(b*xi[i]^4+1))^((1+b)/(4*b)))^2, i = 1 .. 106);

Do i need to create a loop (i=i+1)or can be done by using a simple function?

Answer 1

[Star Strider]

It can be done essentially as you wrote it, without a loop, using element-wise operations:

V = randi(20,10,1);     % Create Data
xi = randi(20,10,1);    % Create Data
b = 5;                  % Create Data

E = sum(V - xi.*((1+b)./(b.*xi.^4+1)).^((1+b)./(4*b))).^2;

[Georgios Panagiotou]

If I am not wrong V = randi(20,10,1); and xi = randi(20,10,1);is to create random data.i want to import the data for Vi,xi, from an excel worksheet

[Star Strider]

I was creating data assuming you had already imported your data. You did not attach your Excel worksheet, so I cannot post the exact code I would use to read it and then process the data.

See the documentation for xlsread for details on how to read your .xls file into your MATLAB workspace.

I always use the [num,txt,raw] = xlsread(_) syntax but there are several options.

[Georgios Panagiotou]

First of all i want to thank you for the response Here i attach the data.I want to substitute those data to derivative of E to find the b

E := sum((V[i]-xi[i]*((1+b)/(b*xi[i]^4+1))^((1+b)/(4*b)))^2, i = 1 .. 185);

diff(E,b);

num=xlsread(blade);

[Georgios Panagiotou]

data

[Star Strider]

I don’t understand what you’re doing. How do you define the derivative?

‘E’ looks like an expression for a least-squares cost function. Is it?

[Georgios Panagiotou]

Yes I am trying to do a least-squares nonlinear fit for the parameter b.

diff(E,b)=0 I want to find the parameter b and afterwards I wil substitute it to E to find the E

[Star Strider]

I thought so after thinking about it later, but I wanted to be certain.

The easiest way to estimate ‘b’ is to use the fminsearch function:

fidi = fopen('BLADE.txt');
D = textscan(fidi, '%f %f', 'HeaderLines',1);
xi = D{1};
V  = D{2};

Vest = @(b,xi) xi.*((1+b)./(b.*xi.^4+1)).^((1+b)./(4*b));           % Model
E = @(b) sum(V - xi.*((1+b)./(b.*xi.^4+1)).^((1+b)./(4*b))).^2;     % Cost Function

[b,Eval] = fminsearch(E, 1);                                        % Estimate ‘b’

figure(1)
plot(xi, V, '+b')
grid
hold on
plot(xi, Vest(b,xi), '-r', 'LineWidth',1)
hold off
xlabel('Xi')
ylabel('V')

The code first imports your data, and assigns variables. I created the objective function ‘Vest’ from ‘E’, then created ‘E’ as an ‘anonymous function’ that I could use with fminsearch to estimate ‘b’ and also determine the value of ‘E’ at the minimum, since you want that. I then plotted ‘Vest’ with your data in the figure. It appears to be a good fit. The estimated value for ‘b’ here is 1.4772.

Does this do what you want?