Error Message: expression or statement is incorrect

I'm trying to create a code for least squares curve fitting, but when I make the function handle to be evaluated in the command window, I keep getting this error message saying that the the expression is incorrect. Below is the code I've made along with the inputs in the command window:

command window:

Running Least Squares Method...
  
X-Values:  [0 10 20 30 40 50 60 70 80 90 100 110]
Y-Values:  [3589 4132 6307 7814 11842 18072 27542 33141 44337 55002 65660 76201]
Function:    (@K, r, timedat) ((popdat(1) * K ) / (popdat(1) + (K - popdat(1)*exp(-r * timedat))))
Error using LeastSqMethod (line 13)
Error: Expression or statement is incorrect--possibly unbalanced (,
{, or [.

Code:

clear
clc
%% Step 1 - Inputting Data
disp('Running Least Squares Method...');
disp('  ');

timedat = input('X-Values:  ');  % Array of X Values (Time)
popdat = input('Y-Values:  ');  % Array of F(x) Values (Population)
func = input('Function:    ');  % Function to be evaluated
x0 = input('Initial Guess:  ');

%% Step 2 - Least Squares Fit Determination

fit = lsqcurvefit(func, x0, timedat, popdat)


%% Step 3 - Plotting Results

xrange = input('Enter X-Value Range:   ');
plot(timedat,popdat,'ko',xrange,func(fit,xrange),'b-')
legend('Given Data', 'Model Fit')
xlabel('Time (Years)')
ylabel('Population')
title('Population Growth in Bryan, TX')
grid on

[Walter Roberson]

the @ has to go before the (

@(K,r,timeout) .....

Answer 1

[Guillaume]

We're missing the most important part of your code, the function func that you pass to lsqcurvefit. Thankfully, it's in the error message.

The error is correct, the expression of func is incorrect. In particular, the opening bracket in the definition of the inputs should be after the @, not before, so:

func = @(K, r, timedat) ((popdat(1) * K ) / (popdat(1) + (K - popdat(1)*exp(-r * timedat))))

[Christopher]

Thank you very much! I fixed that error and the code continued, however I'm now having an issue with the initial value x0. It says I don't have enough input arguments, however, I've been putting in three (One for K, one for r, and one for timedat). I'm still very new to this so chances are I'm making an obvious mistake, but I just can't see it. I'll post the new outputs below:

command window:

Running Least Squares Method...
  
X-Values:  [0 10 20 30 40 50 60 70 80 90 100 110]
Y-Values:  [3589 4132 6307 7814 11842 18072 27542 33141 44337 55002 65660 76201]
Function:    @(K,r,timedat) ((popdat(1) * K) / (popdat(1) + (K - popdat(1))*exp(-r*timedat)))
Initial Guess:  [3600,0.05,1,1]
Not enough input arguments.

Error in LeastSqMethod>@(K,r,timedat)((popdat(1)*K)/(popdat(1)+(K-popdat(1))*exp(-r*timedat)))

Error in lsqcurvefit (line 202)
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Error in LeastSqMethod (line 18)
fit = lsqcurvefit(func, x0, timedat, popdat)

Caused by:
    Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.
   
    

Code:

    % Problem 1 - Least Squares Curve Fitting

clear
clc
%% Step 1 - Inputting Data
disp('Running Least Squares Method...');
disp('  ');

timedat = input('X-Values:  ');  % Array of X Values (Time)
popdat = input('Y-Values:  ');  % Array of F(x) Values (Population)
func = input('Function:    ');  % Function to be evaluated
x0 = input('Initial Guess:  ');

%% Step 2 - Least Squares Fit Determination

fit = lsqcurvefit(func, x0, timedat, popdat)


%% Step 3 - Plotting Results

xrange = input('Enter X-Value Range:   ');
plot(timedat,popdat,'ko',xrange,func(fit,xrange),'b-')
legend('Given Data', 'Model Fit')
xlabel('Time (Years)')
ylabel('Population')
title('Population Growth in Bryan, TX')
grid on

[Guillaume]

Oh, yes i only looked at the syntax of your function, not its actual content, but I see now that it is not a function that you can pass to lsqcurvefit. The objective function must be a function with two inputs, not three.

If both K and r are unknown, then the function should be:

fun = @(coeffs, timedat) ((popdat(1) * coeffs(1)) / (popdat(1) + (coeffs(1) - popdat(1)*exp(-coeffs(2) * timedat))))

and your x0 should be a vector of 2 elements. When the fitting is complete, fit(0) will be the value of K and fit(1), the value of r.

[Christopher]

Thank you very much for the input. My program was able to get to the plot, though it keeps running into this message: I

nitial point is a local minimum.

Optimization completed because the size of the gradient at the initial point

is less than the default value of the optimality tolerance.

<stopping criteria details>

and when it plots I just get a straight line instead of a fit. The logistic model I need to find K and r for is:

I can't get it to show well in Latex but that last term is e raised to the -rt.

[Star Strider]