pkienzle
commented
5 years ago Trac update at 2018/07/05 16:57:16:
- pkienzle changed _comment0 from:
sasmodels/explore/beta/sasfit_compare.py in the beta_approx branch contains code for computing
<F^2^> P S I=PS S_eff and I_beta = PS_eff in a way that is compatible with sasview 4.2, Yun's matlab code and sasfit. As of this writing, the following alogithm is used, as cribbed from the ellipsoid_pe function: {{{
integrate over polydispersity in shape
F1 = F2 = 0 F_norm = 0 for wk, pk in distribution:
integrate over angles with u = cos(theta) substitution and z = 2*u - 1
# so that we have the equivalent of sum(F(t)*sin(t) dt) from 0 to pi/2 when # using gauss-legendre integration values and weights from -1 to 1. F1k = F2k = 0 for w,z in gaussian_weights: form = contrast*volume*F(q, pk, cos_theta = (z+1)/2) F1k += w * form / 2 F2k += w * form*form / 2 # accumulate 1D patterns over polydispersity if sasfit: F1 += wk * F1k F2 += wk * F2k F_norm += wk elif sasview or yun: F1 += wk * volume * F1k/volume F2 += wk * volume * F2k/volume F_norm += wk * volumeF1 = F1/F_norm F2 = F2/F_norm Sq = S(q) beta = F1**2/F2
if sasfit: Sq_eff = 1 + beta (Sq - 1) Pq = F2 elif sasview: Sq_eff = undefined Pq = F21e-4volfraction elif yun: Sq_eff = 1 + F_normbeta * (Sq - 1) Pq = F2/volume
Iq = PqSq Iq_beta = PqSq_eff }}}
The match to sasfit is not very good (in the order of 1% relative error), but probably good enough that we know what calculation is being performed even though we are using different numeric procedures to perform it.
Still haven't seen Yun's results for gaussian dispersion of radii; may need to adapt the algorithm a bit once these are available.
to:
1530833592125933
- pkienzle changed _comment1 from:
sasmodels/explore/beta/sasfit_compare.py in the beta_approx branch contains code for computing
<F^2^> P S I=PS S_eff and I_beta = PS_eff in a way that is compatible with sasview 4.2, Yun's matlab code and sasfit. As of this writing, the following alogithm is used, as cribbed from the ellipsoid_pe function: {{{
integrate over polydispersity in shape
F1 = F2 = 0 total_weight = total_volume = 0 for wk, pk in distribution:
integrate over angles with u = cos(theta) substitution and z = 2*u - 1
# so that we have the equivalent of sum(F(t)*sin(t) dt) from 0 to pi/2 when # using gauss-legendre integration values and weights from -1 to 1. F1k = F2k = 0 for w,z in gaussian_weights: form = contrast*volume*F(q, pk, cos_theta = (z+1)/2) F1k += w * form / 2 F2k += w * form*form / 2 # accumulate 1D patterns over polydispersity F1 += wk * F1k F2 += wk * F2k total_weight += wk total_volume += wk * volumeF1 = F1/total_weight F2 = F2/total_weight Sq = S(q) beta = F1*2/F2 Sq_eff = 1 + beta (Sq - 1) average_volume = total_volume/total_weight
if sasfit: Pq = F2 elif sasview: Pq = F2/average_volume1e-4volfraction elif yun: Pq = F2/average_volume1e8volfraction # slds not scaled by 1e-6
Iq = PqSq Iq_beta = PqSq_eff }}}
The match to sasfit is not very good (in the order of 1% relative error), but probably good enough that we know what calculation is being performed even though we are using different numeric procedures to perform it.
to:
1530834753223138
- pkienzle commented:
sasmodels/explore/beta/sasfit_compare.py in the beta_approx branch contains code for computing
As of this writing, the following alogithm is used, as cribbed from the ellipsoid_pe function:
# integrate over polydispersity in shape
F1 = F2 = 0
total_weight = total_volume = 0
for wk, pk in distribution:
# integrate over angles with u = cos(theta) substitution and z = 2*u - 1
# so that we have the equivalent of sum(F(t)*sin(t) dt) from 0 to pi/2 when
# using gauss-legendre integration values and weights from -1 to 1.
F1k = F2k = 0
for w,z in gaussian_weights:
form = contrast*volume*F(q, pk, cos_theta = (z+1)/2)
F1k += w * form / 2
F2k += w * form*form / 2
# accumulate 1D patterns over polydispersity
F1 += wk * F1k
F2 += wk * F2k
total_weight += wk
total_volume += wk * volume
F1 = F1/total_weight
F2 = F2/total_weight
average_volume = total_volume/total_weight
if sasfit:
Pq = F2
elif sasview:
Pq = F2/average_volume*1e-4*volfraction
elif yun:
Pq = F2/average_volume*1e8*volfraction # slds not scaled by 1e-6
Sq = S(q)
beta = F1**2/F2
Sq_eff = 1 + beta * (Sq - 1)
Iq = Pq*Sq
Iq_beta = Pq*Sq_effThe match to sasfit is not very good (in the order of 1% relative error), but probably good enough that we know what calculation is being performed even though we are using different numeric procedures to perform it.
RichardHeenan
Please document here detail results of testing against sasfit, Fish, own matlab codes etc, especially noting where issue were found and how these were resolved.
This will provide background information for sasview & sasmodels documentation.
Migrated from http://trac.sasview.org/ticket/1121