Can not use gamma function in an external function

Dear,

I am trying to generate some random numbers with a specific distribution, but to calculate the parameters of this distribution I have to use the gamma function.

It works well when I use it in the same file, for example in live script, but from an external function does not work (see error below).

clear
mu = 0.15;
sigma = 0.03;
N = 1e3;

x0 = [2.001,1.0e3];
fun = @(x) sqrt(gamma(1-2/x)-(gamma(1-1/x)).^2)./gamma(1-1/x)-sigma/mu;
par2 = fzero(fun,x0);
par1 = mu/gamma(1-1/par2);
randomNumbers = gevrnd(1/par2,par1/par2,par1,N,1);

% checking
histogram(randomNumbers)

mu = mean(randomNumbers)

mu = 0.1482

sigma = std(randomNumbers)

sigma = 0.0275

Now trying to use it in an external function, I got the error 'Unrecognized function or variable 'gamma'.

Can someone explain why this happens?

[Dyuman Joshi]

"Now trying to use it in an external function, I got the error 'Unrecognized function or variable 'gamma'."

What is the external function? How are you calling it?

[Geovane Gomes]

This one:

obj.means = 0.15;
obj.standardDeviations = 0.03;
obj.distributions = "Frechet";
obj.nSimulations = 2e4;

randomNumbers = generaterandomnumbers(obj);

Error using fzero>localFirstFcnEvalError
FZERO cannot continue because user-supplied function_handle ==> @(x)sqrt(gamma(1-2/x)-(gamma(1-1/x)).^2)./gamma(1-1/x)-sigma/mu failed with the error below.

Unrecognized function or variable 'gamma'.

Error in fzero (line 231)
localFirstFcnEvalError(FunFcn,FunFcnIn,ME);

Error in solution>generaterandomnumbers (line 46)
par2 = fzero(fun,x0);

function randomNumbers = generaterandomnumbers(obj)

nVariables = length(obj.means);

% Pre-allocate memory for the random numbers
randomNumbers = zeros(obj.nSimulations, nVariables);

for i = 1:nVariables
    switch lower(obj.distributions{i})
        case 'normal'
            randomNumbers(:,i) = normrnd(obj.means(i), ...
                obj.standardDeviations(i), obj.nSimulations, 1);
        case 'binomial'
            randomNumbers(:,i) = binornd(obj.means(i), ...
                obj.standardDeviations(i), obj.nSimulations, 1);
        case 'lognormal'
            mu = log((obj.means(i) ^ 2) / ...
                sqrt(obj.standardDeviations(i) ^ 2 + obj.means(i) ^ 2));
            sigma = sqrt(log(obj.standardDeviations(i) ^ 2 / ...
                (obj.means(i) ^ 2) + 1));
            randomNumbers(:,i) = lognrnd(mu, sigma, obj.nSimulations, 1);
        case  {'gumbel', 'extreme type 1'}
            gamma = 0.577216;
            sigmaHat = sqrt(6) * obj.standardDeviations(i) / pi;
            muHat = obj.means(i) - gamma * sigmaHat;
            pd = makedist('GeneralizedExtremeValue', 'k', 0, ...
                'sigma', sigmaHat, 'mu', muHat);
            randomNumbers(:,i) = random(pd, obj.nSimulations, 1);
        case  {'gumbel min', 'extreme type 1 min'}
            gamma = 0.577216;
            sigmaHat = sqrt(6) * obj.standardDeviations(i) / pi;
            muHat = obj.means(i) + gamma / sigmaHat;
            randomNumbers(:,i) = evrnd(muHat, sigmaHat, ...
                obj.nSimulations, 1);
        case 'frechet'
            x0 = [2.001,1.0e3];
            mu = obj.means(i);
            sigma = obj.standardDeviations(i);
            fun = @(x) sqrt(gamma(1-2/x)-(gamma(1-1/x)).^2)./gamma(1-1/x)-sigma/mu;
            par2 = fzero(fun,x0);
            par1 = mu/gamma(1-1/par2);
            randomNumbers = gevrnd(1/par2,par1/par2,par1,N,1);
        otherwise
            error('Invalid distribution: %s', obj.distributions{i});
    end
end
end

Answer 1

[Dyuman Joshi]

Using function names as variable names is not a good idea - in your case gamma.

I have changed the names to gamma0 and added a random value for N in the frechet case (as it was not defined), and the code runs without an errror.

obj.means = 0.15;
obj.standardDeviations = 0.03;
obj.distributions = "Frechet";
obj.nSimulations = 2e4;

randomNumbers = generaterandomnumbers(obj)

randomNumbers = 5×1

0.1178 0.1207 0.1649 0.1623 0.1244

function randomNumbers = generaterandomnumbers(obj)

nVariables = length(obj.means);

% Pre-allocate memory for the random numbers
randomNumbers = zeros(obj.nSimulations, nVariables);

for i = 1:nVariables
    switch lower(obj.distributions{i})
        case 'normal'
            randomNumbers(:,i) = normrnd(obj.means(i), ...
                obj.standardDeviations(i), obj.nSimulations, 1);
        case 'binomial'
            randomNumbers(:,i) = binornd(obj.means(i), ...
                obj.standardDeviations(i), obj.nSimulations, 1);
        case 'lognormal'
            mu = log((obj.means(i) ^ 2) / ...
                sqrt(obj.standardDeviations(i) ^ 2 + obj.means(i) ^ 2));
            sigma = sqrt(log(obj.standardDeviations(i) ^ 2 / ...
                (obj.means(i) ^ 2) + 1));
            randomNumbers(:,i) = lognrnd(mu, sigma, obj.nSimulations, 1);
        case  {'gumbel', 'extreme type 1'}
            %% Name changed
            gamma0 = 0.577216;
            sigmaHat = sqrt(6) * obj.standardDeviations(i) / pi;
            muHat = obj.means(i) - gamma0 * sigmaHat;
            pd = makedist('GeneralizedExtremeValue', 'k', 0, ...
                'sigma', sigmaHat, 'mu', muHat);
            randomNumbers(:,i) = random(pd, obj.nSimulations, 1);
        case  {'gumbel min', 'extreme type 1 min'}
            %% Name changed
            gamma0 = 0.577216;
            sigmaHat = sqrt(6) * obj.standardDeviations(i) / pi;
            muHat = obj.means(i) + gamma0 / sigmaHat;
            randomNumbers(:,i) = evrnd(muHat, sigmaHat, ...
                obj.nSimulations, 1);
        case 'frechet'
            x0 = [2.001,1.0e3];
            mu = obj.means(i);
            sigma = obj.standardDeviations(i);
            fun = @(x) sqrt(gamma(1-2/x)-(gamma(1-1/x)).^2)./gamma(1-1/x)-sigma/mu;
            par2 = fzero(fun,x0);
            par1 = mu/gamma(1-1/par2);
            %% Value added
            N=5;
            randomNumbers = gevrnd(1/par2,par1/par2,par1,N,1);
        otherwise
            error('Invalid distribution: %s', obj.distributions{i});
    end
end
end

[Dyuman Joshi]

Though, variables defined within a case are not accessible to another case and MATLAB executes only one case of any switch statement.

So for the input you have provided, only the 2nd last case is executed and gamma is not over-writed. But the error still occurs. Hmmm.

[Geovane Gomes]

Thank you very much for your help. It works.

"N" is actually "obj.nSimulations". It was wrong. Thanks again.