Inverse sign of off-diagonal Hessian elements

[Konjkov]

Formula for off-diagonal Hessian elements in /src/bin/findif/fd_geoms_freq_0.cc has inverse sing:
3-point - off-diagonal
O(1/h^2): new-way: [f(1,1)+f(-1,-1)+2f(0,0) -f(1,0) -f(-1,0) -f(0,1) -f(0,-1)]/(2h^2)
Implementation is the same.
But off-diagonal elements of the Hessian matrix (cross-derivatives) is:
[f(1,0) + f(-1,0) - f(1,1) - f(0,0)] + [f(0,1) + f(0,-1) - f(-1,-1) - f(0,0)]/(2h^2)
with a negative sign at f(0,0).
Does it mean that off-diagonal Hessian elements are calculated and stored with an opposite sign? or it is an issue?

[psi-rking]

The 3-point coded formula is correct. I confirmed it analytically and with the 5-point formula for the analytic function f(x,y) = x y^2 at point (2,3). Off-diagonal second derivative is +6.

[Konjkov]

Thanks for the exact answer. I found a mistake in my equation.