Hi,
I would first be sure to check if any of the optimization/minimization routines in IDL might be sufficient for your search space…
http://www.harrisgeospatial.com/docs/mathematics_funt_list.h tml ("Optimization")
https://www.physics.wisc.edu/~craigm/idl/fitting.html ("TNMIN" is dependable for many applications)
http://www.ncnr.nist.gov/staff/dimeo/idl_programs.html (a couple of "global optimization" approaches I have not tried)
But if you really have to search the entire space, I think I've found 38% in time savings…
nata had some good tips, and I think there are some tweaks you can make to the function(s) being called in the inner loop (each called 196,830,000,000 times for your whole project, if I understand correctly) that will make some difference. (question: is there really a "fun_bod" as well as the "fun_ant"?):
Original:
function fun_ant,time,to,Q,deltat,C_ant,dtprime,tao_ant
tprime=findgen(100)*dtprime
one= exp((-(time-tprime-to)^2)/(2*(deltat)^2))*exp(-(tprime)/tao_ ant)
constant=(-Q/(C_ant*(sqrt(2*!pi)*(deltat))))
equation=constant*Total(one)*dtprime
return, equation
end
function fun_ant2,time,to,Q,deltat,C_ant,dtprime,tao_ant
tprime=findgen(100)*dtprime
; Recording test run time for several tests
; (note: time testing is not an exact science, and your mileage may vary)
; Original:
; one= exp((-(time-tprime-to)^2)/(2*(deltat)^2))*exp(-(tprime)/tao_ ant);0.124
; Algebra helps: exp(x)*exp(y) = exp(x+y)
; one= exp( (-(time-tprime-to)^2)/(2*(deltat)^2) - (tprime)/tao_ant) ;0.092
; Factoring and reordering to put scalar operations first:
; one= exp( -0.5D / deltat^2 * (time-tprime-to)^2 - (tprime)/tao_ant) ;0.079
; Sometimes using x*x instead of x^2 helps. This didn't give a big improvement,
; but it didn't hurt
ttt = time-tprime-to
one= exp( ((-0.5D / (deltat*deltat)) * (ttt*ttt)) - (tprime/tao_ant));0.077
; Constant is Sqrt(2*!DPi)
constant=(-Q/(C_ant*(2.5066282746310002D * deltat)))
equation=constant*Total(one)*dtprime
return, equation
end
pro test_fun_ant
newtime = 0.0001D
to = 0.0001D
dtprime = 0.0000001D
C_ant = 0.01D
tao_ant = 0.0001D
tao_bod = 0.0001D
deltat = 0.00001D
q_ant = 0.000000000001D
q_bod = 0.000000000001D
nRuns = 20L
nCalls = 10000L
best_fun_ant = 1D9
FOR j=1, nRuns DO BEGIN
TIC
FOR i=1,nCalls DO x1=fun_ant(newtime,to,q_ant,deltat,C_ant,dtprime,tao_ant)
t = TOC()
IF t LT best_fun_ant THEN best_fun_ant = t
ENDFOR ; j over nRuns
best_fun_ant2 = 1D9
FOR j=1, nRuns DO BEGIN
TIC
FOR i=1,nCalls DO x2=fun_ant2(newtime,to,q_ant,deltat,C_ant,dtprime,tao_ant)
t = TOC()
IF t LT best_fun_ant2 THEN best_fun_ant2 = t
ENDFOR ; j over nRuns
Help, best_fun_ant, best_fun_ant2, x1, x2, x2-x1
END
I hope this helps… and of course, while the exhaustive search is running, you can experiment with the optimizers! :-)
Cheers,
-Dick
Dick Jackson Software Consulting Inc.
Victoria, BC, Canada --- http://www.d-jackson.com
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