Computational effort of a derivation

How great is the computational effort of a derivation ?

If I calculate e.g. f(x)=N*4N*2N , than the effort would scale with N^3 -but what is the effort for df(x)/dx ?

Multiplying 3 numbers does not scale as N^3.  It scales as ln(N)^3.

I don't think there's an answer for the general case, because there are too many functions.  How are you even characterizing function growth?

Indeed you are right -each N actually stands for a sum of gauss functions from 1 to N.

...it's actually the computational cost of a SCF-cycle (quantum chemistry;) I'm interested in...or the derivation thereof to be precise.

>>1
>>3
YO DAWG I HERD YOU LIKE FUNCTIONS SO WE PUT A FUNCTION IN YO FUNCTION SO YOU CAN DERIVE WHILE YOU DERIVE

I dunno lol.

Well if f=8N^3, then f'=24N^2, so the time it takes to calculate f goes as N^3 and the time it takes to calculate f' goes as N^2, right? 

Or do you mean long it takes to actually find the derivative?  I can't believe that's related at all to how long it takes to calculate the function itself.  It would take days for a computer to calculate N^2000! but I can find the derivative in a second. (Errr... about two seconds actually, in Maple)

>>2
>>4

or maybe

>if goes as ln(N)^3 and the time it takes to calculate f' goes as ln(N)^2, right?

¯\(°_o)/¯

Well...perhaps it makes more sense to write down the actual problem:

E = sum from {%my%ny} P_{%my%ny} h_{%my%ny} + 1 over 2 sum from {%my%ny%kappa%lambda} P_{%my%ny} P_{%kappa%lambda} ( %Chi_%my %Chi_%ny "|" %Chi_%kappa %chi_lambda ) <-this step scales with N^4

...I'm looking for the computational cost of dE/dx

E = \sum_{\my \ny} P_{\my \ny} h_{\my \ny} + 0.5 \sum_{\my \ny \kappa \lambda} P_{\my \ny} P_{\kappa \lambda} (\chi_\my \chi_\ny "|" \chi_\kappa \chi_\lambda )

sigh I fail...hard. Guess I'll have to do more research myself...

liek dis?

E = \sum_{\mu \nu} P_{\mu \nu} h_{\mu \nu} + 0.5 \sum_{\mu \nu \kappa \lambda} P_{\mu \nu} P_{\kappa \lambda} (\chi_\mu \chi_\nu "|" \chi_\kappa \chi_\lambda )

There really needs to be a post preview thingee here.

Goddammit

[math]E = \sum_{\mu \nu} P_{\mu \nu} h_{\mu \nu} + 0.5 \sum_{\mu \nu \kappa \lambda} P_{\mu \nu} P_{\kappa \lambda} (\chi_\mu \chi_\nu "|" \chi_\kappa \chi_\lambda )[math]


[math]\delta[math]
\delta

>>9
O SHI-  It worked the first time, whoops.

Now if only I knew what the hell it meant.

yes -exactly like @9 (sans the "" -thx btw)...this equation describes a method to calculate the energy E of a given chemical system (e.g. DNA, water, etc.) -it scales (as mentioned) with N^4.

I'm interested how the scaling behavior changes when I form the derivation of this equation dE/dx