[cctbxbb] Structure factor calculation weirdness

Fri Dec 7 11:06:54 PST 2012

I meant to include in the previous email that I add the following lines to
the loop over dmin in Graeme's script:

    gridding = structure.crystal_symmetry().gridding(d_min=dmin)
    print "gridding: ", gridding.n_real()

giving the output:

d_min: 5.0
gridding:  (3, 3, 3)
d_min: 2.5
gridding:  (8, 8, 8)
d_min: 1.7
gridding:  (9, 9, 9)

With so few grid points it is entirely unsurprising that the FFT is such a
poor approximation of the direct summation in this case!

Cheers,

Richard

On 7 December 2012 10:49, Richard Gildea <rgildea at gmail.com> wrote:

> Hi Graeme,
>
> When you pass algorithm=None to xray.structure.structure_factors() it is
> supposed determine dynamically whether direct summation or FFT is best
> suited. However in this case (I guess because of the tiny unit cell?), the
> algorithm for choosing which method clearly fails as in this case direct
> summation would undoubtedly be better than FFT:
>
> (from cctbx_project/cctbx/xray/structure_factors/from_scatterers.py)
>
>         # rough estimate
>         if (  4*n_scatterers*self.space_group().order_p()*n_miller_indices
>             < self.crystal_gridding().n_grid_points()):
>           algorithm = "direct"
>
> Maybe there should be some special handling for small unit cells here? I
> don't know if there is a reason why you would ever want to calculate
> structure factors via FFT for unit cells this tiny?
>
> Cheers,
>
> Richard
>
>
> On 7 December 2012 09:21, Nicholas Sauter <nksauter at lbl.gov> wrote:
>
>> Graeme,
>>
>> Just as a general ballpark figure, for protein work the difference
>> between approximate FFT structure factors and the exact direct sum
>> figures is on the order of 1%.
>>
>> Nick
>>
>> On Fri, Dec 7, 2012 at 8:29 AM,  <Graeme.Winter at diamond.ac.uk> wrote:
>> > Bing! Bet Nat's hit this in one.
>> >
>> > There may be a resolution dependence for 'F' but F001 (say) should not
>> change, and should not go from 0 to non-0 no matter what. Direct summation
>> much better here...
>> >
>> > Presumably for a protein structure the effects of gridding will also be
>> much less significant.
>> >
>> > Thanks,
>> >
>> > Graeme
>> > ________________________________________
>> > From: cctbxbb-bounces at phenix-online.org [
>> cctbxbb-bounces at phenix-online.org] on behalf of Nathaniel Echols [
>> nechols at lbl.gov]
>> > Sent: 07 December 2012 15:46
>> > To: cctbx mailing list
>> > Subject: Re: [cctbxbb] Structure factor calculation weirdness
>> >
>> > On Fri, Dec 7, 2012 at 7:36 AM,  <Graeme.Winter at diamond.ac.uk> wrote:
>> >> Some confusion here at diamond – it seems that the amplitude of F(hkl)
>> >> depends on dmin
>> >
>> > Yes, because it's using the FFT method, which means it first does map
>> > sampling on a grid whose dimensions will partly depend on the
>> > resolution.  I'm not sure if there is resolution dependence for the
>> > scattering factors (I thought so, but I don't really know details),
>> > but I tried using direct summation and the resolution effect
>> > disappears.
>> >
>> >   f_calc = structure.structure_factors(
>> >     algorithm="direct",
>> >     d_min = dmin).f_calc()
>> >
>> > For your toy example the speed difference isn't noticeable - for a
>> > protein structure it will be considerable.
>> >
>> > -Nat
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>> Nicholas K. Sauter, Ph. D.
>> Computer Staff Scientist, Physical Biosciences Division
>> Lawrence Berkeley National Laboratory
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