On 12/6/08, David Joyner <[EMAIL PROTECTED]> wrote:
> (1) Sage calls Maxima and asks it to do lots of definite integrals
> (about 30 in this case, each involving a sine or cosine) - these are the
> Fourier coefficients,
> (2) Sage multiplies each of these coefficients by a sine or cosine function
> and adds them up - call this finite sum f(x),
> (3) Sage calls Maxima to evaluate f(x) at lots of points to plot the graph
> (maybe 100 point-wise evaluations of f(x)),
> (4) calls matplotlib to create the plot of f.
OK, I hope the following script (see PS) follows these steps.
> This was repeated (for timing purposes) 10 times. In an example involving
> about 30 terms, the first took about 10-11 seconds, and repeated
> evaluations took longer and longer, with the 10th taking about 30-35 seconds.
With the script as shown in the PS, I don't see an increase of
run time over 100 iterations. It takes about 16 seconds (varies
between 15.something to 17.something) with Maxima 5.17.0 + Clisp 2.46
on CentOS Linux, 3.4 GHz Intel x86.
Incidentally some integrals cause messages to be printed;
these originate in the Taylor series code, which is called from
integration.
Hope I've understood the question & haven't messed up something.
Robert Dodier
PS.
$ maxima --batch sage_fourier_helper.mac 1> 1.out 2> 2.out
$ tail 1.out
$ cat sage_fourier.mac
fc_all(n):=fc_ab(-1,n,-%pi,(-%pi)/2)+fc_ab(2,n,-%pi/2,0)
+fc_ab(-1,n,0,%pi/2)+fc_ab(2,n,%pi/2,%pi)$
fc_ab(e,n,a,b):=if n = 0 then [integrate(e,x,a,b)/(2*%pi),0]
else fc1_ab(e,n,a,b)$
fc1_ab(e,n,a,b):=[integrate(e*cos(n*x),x,a,b)/%pi,
integrate(e*sin(n*x),x,a,b)/%pi]$
coefs : map (fc_all, makelist (i, i, 0, 15));
fsum : sum (coefs[1 + n][1] * cos (n*x) + coefs[1 + n][2] * sin (n*x), n, 0, 15)
;
xx : makelist ((i - 1) * 2 * %pi / 100 - %pi, i, 1, 101), numer;
fsum_xx : makelist (''fsum, x, xx), numer;
$ cat sage_fourier_helper.mac
load ("./sage_fourier.mac");
load ("./sage_fourier.mac");
... (lots more to make 100 in all) ...
load ("./sage_fourier.mac");
load ("./sage_fourier.mac");
map (time, labels (%o));
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