Does 'plot' evaluate the function at random points?

[v_...@ukr.net]

Hello!
I have noticed a strange unpredictable behaviour of the "plot"
function today.

Here is the situation:
I have a data set in the following form:
[[2006, 289.575000000000],
[2007, 289.547000000000],
[2008, 289.479000000000],
[2009, 289.586000000000],
[2010, 289.620000000000]]

and a function to work with these data:

def dGT(t):
number = int(round(t))-temperature[0][0]
return round(temperature[number+1][1]- \
temperature[number][1],3)

Then I want to plot this function in some range. It turns out that the
result is more or less unpredictable. I simply do the following to test:

########## Plotting ##########
total_plot = plot(dGT, marker=".", xmin=2000, xmax=2010, color='blue',
plot_points=2010-2000+1, adaptive_recursion=0) total_plot += plot(dGT,
marker=".",xmin=2000, xmax=2010, color='red', plot_points=2010-2000+1,
adaptive_recursion=0) total_plot += plot(dGT, marker=".",xmin=2000,
xmax=2010, color='green', plot_points=2010-2000+1,
adaptive_recursion=0) total_plot += plot(dGT, marker=".",xmin=2000,
xmax=2010, color='cyan', plot_points=2010-2000+1, adaptive_recursion=0)
total_plot += plot(dGT, marker=".",xmin=2000, xmax=2010,
color='magenta', plot_points=2010-2000+1, adaptive_recursion=0)
total_plot += plot(dGT, marker=".",xmin=2000, xmax=2010,
color='yellow', plot_points=2010-2000+1, adaptive_recursion=0)
total_plot += plot(dGT, marker=".",xmin=2000, xmax=2010, color='black',
plot_points=2010-2000+1, adaptive_recursion=0)

total_plot.show(figsize=[10,4], gridlines='minor')
########## End Plotting ##########

The result looks very strange to me:
http://wombat.org.ua/plot-random-points.png

So my question is:
1. How does the "plot" function choose the exact points to use between
the starting and the ending points?
2. Is there a way to make it evaluate the function being plotted with a
certain step?

Thank you.
Vladimir

-----
<v_...@ukr.net>

[kcrisman]

> Then I want to plot this function in some range. It turns out that the
> result is more or less unpredictable. I simply do the following to test:
>
> ########## Plotting ##########
> total_plot = plot(dGT, marker=".", xmin=2000, xmax=2010, color='blue',
> plot_points=2010-2000+1, adaptive_recursion=0)

Well, here you go. You did only 11 plot points and no "adaptive
recursion". As you can see at
http://sagemath.org/doc/reference/sage/plot/plot.html#sage.plot.plot.generate_plot_points,
if you do "randomize=False" you will get what you want.

> So my question is:
> 1. How does the "plot" function choose the exact points to use between
> the starting and the ending points?

You should be able to read the code in
sage.plot.plot.generate_plot_points?? and follow it for the precise
details; the adaptive process is pretty well documented at
http://sagemath.org/doc/reference/sage/plot/plot.html#sage.plot.plot.plot
- search for "the algorithm used to insert extra points is actually
pretty simple".

> 2. Is there a way to make it evaluate the function being plotted with a
> certain step?

I think this should work. Or you could use a list comprehension and
plot the points.

sage: f(x) = sin(x)
sage: L = [(i,f(i)) for i in srange(0,3,.5)]
sage: line(L)

- kcrisman

[v_...@ukr.net]

Hello!

On Wed, 14 Dec 2011 08:20:02 -0800 (PST)
kcrisman <kcri...@gmail.com> wrote:

>... As you can see at

> http://sagemath.org/doc/reference/sage/plot/plot.html#sage.plot.plot.generate_plot_points,
> if you do "randomize=False" you will get what you want.
>

Thanks a lot! It did exactly what I wanted to get!
Still, this solution is not obvious enough, because to benefit from
it, one must know that there is such function in the 'plot' module.
I must note that there are many similar recipes to make this or that
by doing
from something.something.something import something
and get the functions you want, but how can one get the information
that there IS such a function in this particular module?

[Jason Grout]

In this case, reading the documentation for plot would have pointed you
in the right direction. You could do this by just typing "plot?" in
Sage, or I usually search using google: sage docs plot

I get this page: http://www.sagemath.org/doc/reference/sage/plot/plot.html

Then I click on the plot() command, and it talks about the adaptive
algorithm, and one of the first examples talks about the randomize
keyword. As for finding the exact function that generates the random
points, I would look at the source code for plot and trace the execution
of the function from there. You can see the source code for plot by
doing plot?? in Sage.

That said, we're always looking for ways to improve the documentation
and the discoverability of things. Patches are always welcome!

Thanks,

Jason

[Dan Drake]

Perhaps you want list_plot, since you are plotting discrete points?

Dan

--
--- Dan Drake
----- http://mathsci.kaist.ac.kr/~drake
-------