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I evaluated a function over a grid of points in three-dimensions. I would like to know what the standard notation is to define my grid of points?

In matlab notation the grid is defined by:

[x,y,z] = ndgrid(logspace(-8,8,31),logspace(-8,12,41),linspace(0,pi/4,25));

That is, x is spaced logarithmically (base 10) from $10^{-8}$ to $10^{8}$ using 31 points, y is spaced logarithmically from $10^{-8}$ to $10^{12}$ using 41 points, and z is spaced linearlly between $0$ and $\displaystyle \frac{\pi}{4}$ using 25 points.

What is the standard notation to define this grid of points?

Essentially, I'm trying to finish this sentence: "...we evaluated Eq. \ref{blah} over a grid of points in the parameter space defined by:..."

Any help would be greatly appreciated.

okj
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1 Answers1

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The output of ndgrid corresponds, mathematically, to a Cartesian product of its input vectors. So your sentence could be something like

"We evaluated Eq. ?? over a grid of points in the parameter space $[-8,8] \times [-8,12] \times [0,\pi/4]$."

If you need to indicate the resolution of the grid, you can use a Cartesian product of discrete sets (instead of intervals). For example:

"We evaluated Eq. ?? over a grid of points in the parameter space $S \times T \times U$, where $S = \{-8,-7.5,-7, ..., ,8\}$, $T = \{-8, -7, -6, ..., 12\}$ and $U = \{0,\pi/40, 2\pi/40,... \pi/4\}$."

Luis Mendo
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  • Thanks, that notation is pretty clean. However, it doesn't indicate the resolution of the grid. How would I enrich that notation to include the resolution? – okj Feb 03 '14 at 14:15
  • @okj In that case you would need the Cartesian product of discrete sets, not of intervals. Pleas see updated answer – Luis Mendo Feb 03 '14 at 14:41