
# List of gradients

gradient of the distance functions first argument
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% gradDistance(M,x,y,p) gradient of f(x) = 1/p d^p(x,y)for fixed y in M.


The gradient of $f(x) = \tfrac{1}{p} d^p(x,y)$ for a fixed value $y\in\M$ and $p\geq1$, with standard $p=2$.

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gradient of the second order TV mid point model
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%  gradientSecondOrderLog(M,f,alpha,beta) --- compute the gradient of


For data $x\colon\Grid\to\M$ on a $m$-dimensional grid $\Grid$ this function returns the gradient $\gradM F$ of the first and second order total variation additive mid point model.

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gradient of the TV prior
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% gradTV(M,x) compute the gradient of the manifold total variation


For data $x\colon\Grid\to\M$ on a $m$-dimensional grid $\Grid$ with $N_{\vect{k}} = \bigl\{\vect{l} : \vect{l}+\vect{e}_j,\ j\in\{1,\ldots,m\}\bigr\}\cap G$ this function comutes the gradient of the TV prior

with respect to all entries of $x$, i.e. $\gradM F\colon\Grid\to T\M$.

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gradient of the second order TV mid point model prior
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% gradTV2Midpoint(M,x) compute gradient of the second order mid point model


For data $x\colon\Grid\to\M$ on a $m$-dimensional grid $\Grid$ this function returns the gradient $\gradM F$ of the absolute second order total variation prior.

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