FGP_TV gradient

[gfardell]

The gradient and adjoint implemented don't seem to have consistent boundary conditions and I think that makes the function non-linear

Direct

if (i == dimX-1) val1 = 0.0f; else val1 = D[index] - D[j*dimX + (i+1)];
if (j == dimY-1) val2 = 0.0f; else val2 = D[index] - D[(j+1)*dimX + i];

Adjoint

if (i == 0) {val1 = 0.0f;} else {val1 = R1[j*dimX + (i-1)];}
if (j == 0) {val2 = 0.0f;} else {val2 = R2[(j-1)*dimX + i];}
D[index] = A[index] - lambda*(R1[index] + R2[index] - val1 - val2);

I think for neumann adjoint I expected a additional boundary conditions.

In 1D this will be:

for i  ==dimX -1:
    D[i] = A[i] - lambda*(-R1[i-1])

This is based on a talking to Vaggelis
finite_differences_details.pdf

I was in the process of looking at TGP_TV so I'll incorporate the additional boundary condition if you agree @dkazanc?

[dkazanc]

thanks @gfardell. Fair enough, please incorporate. I guess once fixed for FGP_TV we can make it consistent for other modules.