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High-level Reduction Operations

The following high-level reduction operations are also implemented. They can be defined in terms of the basic reduction operations above.
average:
The algebraic mean of the values

\begin{displaymath}\mathrm{average} := \mathrm{sum} / \mathrm{count} \end{displaymath}

norm1:
The $L_1$ norm, i.e., the sum of the absolute values

\begin{displaymath}\mathrm{norm1} := \mathrm{sumabs} / \mathrm{count} \end{displaymath}

norm2:
The $L_2$ norm, i.e., the Pythagorean norm

\begin{displaymath}\mathrm{norm2} := \sqrt{\mathrm{sumabs2} / \mathrm{count}} \end{displaymath}

norm_inf:
The $L_\infty$ norm

\begin{displaymath}\mathrm{norm\_inf} := \mathrm{maxabs} \end{displaymath}