Compute sensitivity coefficient from numerical gradient

Hello everybody. I have to rewrite a very basic R script in matlab. The script performs calculation of the sensitivity coefficients, i.e., the partial derivatives, for an example of law of propagation of uncertainty.

Here the R code:

# measurement function
mass2.x <- function(x) {
m.std = x[1]; dm.d = x[2];
diff = x[3]; dm.c = x[4]; dm.B = x[5]
m.std + dm.d + diff + dm.c + dm.B
}

require(numDeriv)
m.std = 10000.005; dm.d = 0.0; diff = mean(c(0.01,0.03,0.02))
dm.c = 0.0; dm.B = 0.0;
sens = grad(func=mass2.x,x=c(m.std,dm.d,diff,dm.c,dm.B))
m.std.u = 0.0225
dm.d.u = 0.015/sqrt(3); dm.c.u = 0.010/sqrt(3)
diff.u = 0.025/sqrt(3); dm.B.u = 0.010/sqrt(3)
m.x = mass2.x(c(m.std,dm.d,diff,dm.c,dm.B))
m.x.unc = sqrt(sum(sens^2*c(m.std.u,dm.d.u,diff.u,dm.c.u,dm.B.u)^2))

basically the measurement model is like

and from the example if I were to calculate the sensitivity coefficient I need to obtain

>> sens = [1 1 1 1 1]

since the model is linear in all the parameters.

Now I tried this approach but I'm not obtaining the same results for sens:

m_std = 10000.005;
dm_d = 0.0;
diff = mean([0.01,0.03,0.02]);
dm_c = 0.0;
dm_B = 0.0;

F = [m_std, dm_d, diff, dm_c, dm_B]

sens = gradient(F)

m_std_u = 0.0225;
dm_d_u = 0.015/sqrt(3);
dm_c_u = 0.010/sqrt(3);
diff_u = 0.025/sqrt(3);
dm_B_u = 0.010/sqrt(3);
m_x = sum(F)
m_x_unc = sqrt(sum(sens.^2 .* [m_std_u,dm_d_u,diff_u,dm_c_u,dm_B_u].^2))

Surely I'm missing something and I do not know if I'm using the function correctly.

Thank you for your help.

Answer 1

[Matt J]

I have no background in R. However, if you are trying to take the numerical gradient of a function, there is no native Matlab function that will do that. However this FEX download will,

https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation

func=@(x) sum(x);

sens = gradest(func,[0,0,0,0,0])

sens = 1×5

1 1 1 1 1