| Ilya Zakharevich on Sat, 1 Sep 2001 09:55:56 -0400 |
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| Re: plotminmax written/query for Jacobian functions |
On Fri, Aug 31, 2001 at 10:12:40PM +0300, Juhana Sadeharju wrote:
> plot() function:
>
> 10.900334 |''''''''''''''''''"''''''''''''''''''''''''"''''''''''''''''''|
> | : : |
> | : : |
> | " : : " |
> | : : : : |
> | : : : : |
> | : : __ : : |
> | :: :: :: :: :: |
> | :: : : :: : : :: |
> | :: : : :: : : :: |
> | : x : : :: : : x : |
> | : : : : :: : : : : |
> | : : : : : : : : : : |
> | : : " : : : : " : : |
> | : : : : : : : : : : |
> | : : : " : : " : : : |
> | x : : : : : : : : x |
> | : : : : x x : : : : |
> | : " _ : : _ " : |
> | x " _ _ " x |
> | _x "_ _" x_ __ __ _x "_ _" x_ |
> 0 "",,,,,,,,,"""",,,,,,,,,""",,,,,,,,,,""",,,,,,,,,"""",,,,,,,,,""
> 0 3.141593
>
>
> plotminmax() function:
>
> 11.111111 |'''''*''''''''''''*'''''''''''**'''''''''''*''''''''''''*'''''|
> | * ** ** ** * |
> | * ** ** ** * |
> | * ** ** ** * |
> | * ** ** ** * |
> | ** ** ** ** ** |
> | ** ** ** ** ** |
> | ** ** ** ** ** |
> | *** ** ** ** *** |
> | * * ** ** ** * * |
> | * * ** ** ** * * |
> | * * *** ** *** * * |
> | * * * * ** * * * * |
> | * * * * ** * * * * |
> | * * * * **** * * * * |
> | * * ** * * * * ** * * |
> | ** * * * * * * * * ** |
> | * ** * * * * * * ** * |
> | * * * ** ** ** ** * * * |
> | ** ** ** ** * * ** ** ** ** |
> **** ******** ******** ******** ******** ****
> 0 |..............................................................|
> 0 3.141593
>
>
> The plotminmax() shows both where the peaks are located and what are
> their peak values, but plot() shows only the locations.
... but shows them better. In the spring I had an idea on how to
increase the horizontal resolution twice (by better placements of ':'
above), as in
x x
: :
: :
: :
: vs :
x x
(on the left is the current algorithm, on the right is the algorithm
which takes into account the value at the intermediate point - the
function is concave up).
The same algorithm could be used to improve the display near "sharp"
extrema.
:
x x
: ::
: ::
:: : :
:: : :
: x vs : x
: :
: :
x x
The fact that the intermediate values are above values at the lattice
points ('x's) is shown by ':' above the value. (Similar to the
current display with ':' of the intermediate values *between* the
values at lattice points.)
Ilya
P.S. BTW, if all one wants is more points, just use 'dumb' terminal with
gnuplot output of ploth().