Sunday, November 4, 2012

Mathematica Plot: Using Table to See Numerical Values

Plot with Table to See Numerical Values

We saw how to use Table to generate sample points for a ListPlot, and how to compare your own sample to Plot showing its mesh points. Here is the converse usage, using Plot to graph a function and then Table to see it numerically. We'll start with a simple sine curve.

To see numerical values, I click Control+L to regenerate the input, replace "Plot" with "Table", and specify a third argument for the iterator to give the sampling frequency. The Postfix function N tells Mathematica to give us decimal output instead of its default, exact fractional values.

In[314]:= Table[{x, Sin@x // N}, {x, 0, 2 Pi, Pi/4}] // TableForm

Let's look at a more complicated example with two decay curves that are identical except for their asymptotes, which are 0 for decay1 and 0.7 for decay 2 (shown in the Plot).

In[347]:= Clear@decay1; decay1@d_ := (q/d) + 0.7; q = .2;

In[348]:= Clear@decay2; decay2@d_ := (q/d); q = .2;

In[363]:= Plot[{decay1@d, decay2@d}, {d, .1, 4}, PlotRange -> {Automatic, {0, 3}}]

When you need to keep track of three or more columns, TableHeadings can be helpful. Here we say no row headings, but three column headings.

Table[{d, decay1@d, decay2@d}, {d, .1, 1.2, .1}] // 
 TableForm[#, TableHeadings -> {None, {"d", "decay1@d", "decay2@d"}}] &

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