Oh, the text 2^(-3/2) is the most compact for the documentation, and
it separates it from the 1/nu_cpmg part.  So I'd prefer to present it
that way for compactness and cleanliness.  That can also allow us to
pre-calculate it when the target function is initialised and and send
the value of 0.35355339059327373 into the function instead.  That
would remove one exponential operation, again squeezing out a little
speed.  As nu_CPMG is fixed, even faster would be to pre-calculate an
array of 2**(-3/2) / nu_CPMG and sent that in instead.  That would
really be the maximal optimisation for this part!

Cheers,

Edward

On 3 May 2014 13:45, Edward d'Auvergne <[email protected]> wrote:
> Hi,
>
> The origin of this was exactly what Andy Baldwin said at
> http://thread.gmane.org/gmane.science.nmr.relax.devel/5410/focus=5448
> - that there are many different tau_CPMG definitions and there is an
> error in one of the equations in the original paper.  The code in
> relax is however correct.  The eta_scale value should be
> 0.35355339059327373.  Feel free to fix the equations in the
> documentation of the wiki, manual and lib.dispersion.cr72 docstring.
> I wrote these before the code was fully tested and hence there is now
> a mismatch.  As for using 2.0**(-3.0/2.0) in the code, this is for the
> fastest operation, avoiding the square root.  But now that I look at
> it, one mathematical operation can be dropped for speed and the factor
> changed to 2.0**(-1.5).
>
> Cheers,
>
> Edward
>
>
> On 3 May 2014 12:28, Troels Emtekær Linnet <[email protected]> wrote:
>> Dear Edward.
>>
>> I was inspecting the code of model CR72.
>>
>> http://svn.gna.org/viewcvs/*checkout*/relax/trunk/lib/dispersion/cr72.py?revision=HEAD
>>
>> This is calculated as:
>>
>> eta_scale = 2.0**(-3.0/2.0) = 0.35
>> which is: 1 / sqrt(2**3).
>>
>> This differs from the definition in:
>> http://wiki.nmr-relax.com/CR72_full#Equation
>> http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_model.html
>> http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html
>>
>> where:
>> eta_scale = 2.0**(2/3) = 1.58
>> which is {3}sqrt(2**2).
>>
>> If I compare to:
>> http://wiki.nmr-relax.com/B14#Equation_compared_to_Carver_Richards_72
>> (DOI: 10.1016/j.jmr.2014.02.023 , eq 70,)
>>
>> And to, (DOI: 10.1016/S0076-6879(01)39315-1 , eq 25, with the twist
>> that "tcp_Pa is the delay between 180 pulses in the CPMG pulse train",
>>  "delay/180/delay/delay/180/delay " so that tcp_Pa = 2xdelay
>>
>> Then really the manual should use:
>> eta_scale = 2.0**(-3/2)
>> or
>> 1 / 2 sqrt(2)
>>
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