Inverse Gradient

The inverse function of gradient().

INVGRADIENT Basically the opposite of gradient(), aka Inverse Gradient.

F_bar = INVGRADIENT(dFx,dFy) reverses GRADIENT(F), where unit spacing is assumed.

F_bar = INVGRADIENT(dFx,dFy,H), where H is scalar, uses H as the spacing between points.

F_bar = INVGRADIENT(dFx,dFy,Hx,Hy) is basically the same, except that both x- and y-spacings are specified. Obviously, the DC offset of the integrated function is arbitrary. Also,

INVGRADIENT is limited to 2-dimensions at the moment, ie no 3-dimensional matrices, or vectors. If dFx and dFy aren't self-consistent then no exact solution can be integrated. In this case% the optimal solution, in the least squares sense, will be found. So if you do F_bar = INVGRADIENT(dFx,dFy), F_bar will be found such that doing [dFx_ dFy_] = GRADIENT(F_bar) will give you dFx_ and dFy_ that are as close as possible to the original dFx and dFy.

Patrick Lu
April 5, 2005
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