Thank you for this useful suggestion Robert, I tried it out, unfortunately
a problem with Gnuplot now pops up:
This is my input:
m:matrix([100,16000],[200,8000],[500,3636],[1000,1818],[2000,870],[5000,323],[10000,160],[20000,83],[50000,33],[100000,20]);
lsquares_estimates (m, [x, y], y = sqrt(a^2 + (10e7/(2*%pi*x*b))^2),[a, b], initial=[10, 10]);
/* => [[a = 19.2898942613692, b = 9.89381119455951]]*/
/* b = 10 is the exact value for b.*/
/* I'll construct the mean square error as a function of a alone*/
/* and then plot it. */
mse : lsquares_mse (m, [x, y], y = sqrt(a^2 + (10e7/(2*%pi*x*b))^2));
mse1 (a) := ''(subst (b=10, mse));
plot2d (mse1, [a, 0, 100]);
This is the error message:
gnuplot> plot [0.:100.]'/home/coolens/maxout.gnuplot_pipes' index 0
notitle with lines 3
^
line 0: warning: Skipping data file with no valid points
gnuplot> plot [0.:100.]'/home/coolens/maxout.gnuplot_pipes' index 0
notitle with lines 3
^
line 0: all points y value undefined!
I'm using using Gnuplot 4.5 patchlevel 0 and Maxima 5.13.0 on a Debian Lenny system
Any idea how to modify the input-file to make Gnuplot do what it should do?
hugo
On Mon, 14 Jun 2010, Robert Dodier wrote:
> On 6/13/10, Hugo Coolens <coolens at kahosl.be> wrote:
>
>> m:matrix([100,16000],[200,8000],[500,3636],[1000,1818],[2000,870],[5000,323],[10000,160],[20000,83],[50000,33],[100000,20]);
>
> With these data (the last one has been corrected, right?)
> and the original model I get the following.
>
> lsquares_estimates (m, [x, y], y = sqrt(a^2 + (10e7/(2*%pi*x*b))^2),
> [a, b], initial=[10, 10]);
> => [[a = 19.2898942613692, b = 9.89381119455951]]
>
> I gather that b = 10 is the exact value for b. (If that's not so,
> just substitute the correct value in the following.)
> I'll construct the mean square error as a function of a alone
> and then plot it.
>
> mse : lsquares_mse (m, [x, y], y = sqrt(a^2 + (10e7/(2*%pi*x*b))^2));
> mse1 (a) := ''(subst (b=10, mse));
> plot2d (mse1, [a, 0, 100]);
>
> In the plot there is a very shallow minimum around a = 20.
> So at this point I have two observations; one is that a is not very
> strongly determined by the available data (since the MSE is almost
> the same for a wide range of a values), and anyway the lsquares
> estimates can't be too far off the mark (in the neighborhood of a = 20).
>
> You might try to make a contour plot of MSE as a function
> of both a and b.
>
> Hope this helps in some way.
>
> Robert Dodier
>