running product

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running product $$\prod +$% WIDTH=60 HEIGHT=33$

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

Computes the running product 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 ``runningProduct'' 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 product of this tensor, along the horizontal dimension, is:

$\begin{displaymath} \left(\begin{array}{cccc} 1 & 2 & 6 & 24\\ 5 & 20 & 60 & 120\\ 8 & 56 & 336 & 1680 \end{array}\right) \end{displaymath}% WIDTH=339 HEIGHT=121$

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