Calculate the numerical hessian

Hello!

I have the following function with the two variables alha and beta:

    function MSE=mseFunction(alpha,beta,Donnee_6_jours)

    moyenneMobile=zeros(240,1);
    %Calcul de la moyenne mobile
    for i=1:240
        moyenneMobile(i)=1/48.*((Donnee_6_jours(i)/2)+sum(Donnee_6_jours(i+1:i+47))+(Donnee_6_jours(i+48)/2));
    end
    moyenneMobileCentree = padarray(moyenneMobile,24,'both');
    composanteSaisonniaire=Donnee_6_jours(25:264)./moyenneMobileCentree(25:264);
    composanteSaisonniaireV2 = padarray(composanteSaisonniaire,24,'both');
    MatriceComposanteSaisonniaire = reshape(composanteSaisonniaireV2,[48,6]);
    MatriceComposanteSaisonniaire(1:24,1)=NaN;
    MatriceComposanteSaisonniaire(25:48,6)=NaN;
    MedianneComposantsSaisonniers = nanmedian(MatriceComposanteSaisonniaire,2);
    LES=zeros(288,1);
    LES(25)=moyenneMobileCentree(25);
    for i=26:264;
        LES(i)=alpha.*moyenneMobileCentree(i)+(1-alpha).*LES(i-1);
    end
    S=zeros(264,1);
    S(1:48,:)=MedianneComposantsSaisonniers;
    for j=49:264;
        S(j)=beta.*(Donnee_6_jours(j)./LES(j))+(1-beta).*S(j-48); 
    end
    PREV=zeros(264,1);
    PREV(26:264)=S(26:264).*LES(25:263);
    PREV2=padarray(PREV(:),24,'post');
    MSE = mean((Donnee_6_jours(26:264)-PREV2(26:264)).^2);

is there a way to calculate the numerical hessian.

Thanks!

Answer 1

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/67893-how-do-i-calculate-hessian-matrix-for-an-image

[amine&&]

Hello Roberson, in the link you gave me this is calculated Hessian of an image, my goal is to get the Hessian of a function.

Thanks!

[Walter Roberson]

It does not make sense to calculate the numeric Hessian of a function: it only makes sense to calculate the symbolic Hessian, or to calculate the numeric Hessian of a function that has been calculated at particular locations.

For example,

alpha_vals = linspace(.2, .87, 13);
beta_vals = logspace(-3, 2, 19);
[ALPHA, BETA] = ndgrid(alpha_vals, beta_vals);

mse = arrayfun(@alpha,beta) mseFunction(alpha, beta, Donnee_6_jours), ALPHA, BETA);

[gx, gy] = gradient(mse, alpha_vals, beta_vals);
[gxx, gxy] = gradient(gx, alpha_vals, beta_vals);
[gyx, gyy] = gradient(gy, alpha_vals, beta_vals);

subplot(1,5,1)
pcolor(ALPHA, BETA, mse);
title('MSE')

subplot(1,5,2)
pcolor(ALPHA, BETA, gxx)
title('D alpha alpha');

subplot(1,5,3)
pcolor(ALPHA, BETA, gxy)
title('D alpha beta')

and so on.

[amine&&]

Hello Roberson,

the fourth line generates an error

   mse = arrayfun(@alpha,beta) mseFunction(alpha, beta, Donnee_6_jours), ALPHA, BETA);
                               |
  Error: Unexpected MATLAB expression.

what you think of the following function use to compute the gradient :

function grad_x=gradIent(x1,x2,Donnee_6_jours)

      x=zeros(2,1);
      x(1)=x1;
      x(2)=x2;
      h=1*10^-2;
      v=eye(2,2);
      grad_x=zeros(2,1);
      for i=1:2
          T1=x+h.*v(:,i);
          T2=x-h.*v(:,i);
          grad_x(i)=(mseFunction(T1(1),T1(2),Donnee_6_jours)-mseFunction(T2(1),T2(2),Donnee_6_jours))/(2*h);
      end

Thanks Roberson.

[Walter Roberson]

mse = arrayfun(@(alpha,beta) mseFunction(alpha, beta, Donnee_6_jours), ALPHA, BETA);

Answer 2

[Matt J]

Have a look at this FEX submission, in particular at hessian(fun,x0).