running sum

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running sum $$\sum +$% WIDTH=63 HEIGHT=33$

$\includegraphics[height=10mm]{images/runningSum}% WIDTH=48 HEIGHT=45$

Computes the running sum of the input tensor along a given axis.

The optional numerical argument (in the ``edit'' dialog) can be used to specify a window over which the running sum is performed. If negative, the window is over the entire dimension.

The operator can be placed on the canvas in two ways:

From the Scan Operations (``scan'') toolbar $\resizebox{!}{2ex}{\includegraphics{images/runningSum}}% WIDTH=15 HEIGHT=14$ ; or
By typing the letters ``runningSum'' on the canvas and then pressing the Enter key.

For example, take this rank 2 tensor:

$\begin{displaymath} \left(\begin{array}{cccc} 1 & 2 & 3 & 4\\ 5 & 4 & 3 & 2\\ 8 & 7 & 6 & 5 \end{array}\right) \end{displaymath}% WIDTH=239 HEIGHT=121$

The running sum of this tensor, along the horizontal dimension, is:

$\begin{displaymath} \left(\begin{array}{cccc} 1 & 3 & 6 & 10\\ 5 & 9 & 12 & 14\\ 8 & 15 & 21 & 26 \end{array}\right) \end{displaymath}% WIDTH=289 HEIGHT=121$

Running sum will normally be applied to a Ravel or a variable defined via a Ravel.