Hi Troels,
I've now implemented the exponential curve-fitting dfunc() function
for calculating the gradient. This includes:
- The Python wrapper function
specific_analyses.relax_fit.optimisation.dfunc_wrapper(),
- The target_functions/c_chi2.c function dchi2(),
- The target_functions/exponential.c functions exponential_dI0() and
exponential_dR(),
- The target_functions.relax_fit C module dfunc() Python function.
I have tested the gradient using the numerical integration in the
test_suite/shared_data/curve_fitting/numeric_gradient/integrate.py
file to determine what the chi-squared gradient should be at different
parameter combinations. And this has been converted into a few unit
tests. As this works, that means that the jacobian() function of the
C module should also be correct and bug-free, hence you should be able
to use it to obtain the covariance matrix.
This is all I will do for now. All that is left is to do for the
target_functions.relax_fit C module is simply the same thing, but for
the Hessian. Feel free to give this a go if you are interested. If I
have time in the future, I might add this too.
Regards,
Edward
On 24 August 2014 17:56, Troels E. Linnet
<NO-REPLY.INVALID-ADDRESS@xxxxxxx> wrote:
URL:
<http://gna.org/task/?7822>
Summary: Implement user function to estimate R2eff and
associated errors for exponential curve fitting.
Project: relax
Submitted by: tlinnet
Submitted on: Sun 24 Aug 2014 03:56:36 PM UTC
Should Start On: Sun 24 Aug 2014 12:00:00 AM UTC
Should be Finished on: Sun 24 Aug 2014 12:00:00 AM UTC
Category: relax's source code
Priority: 5 - Normal
Status: In Progress
Percent Complete: 0%
Assigned to: tlinnet
Open/Closed: Open
Discussion Lock: Any
Effort: 0.00
_______________________________________________________
Details:
A verification script, showed that using scipy.optimize.leastsq reaches
the
exact same parameters as minfx for exponential curve fitting.
The verification script is in:
test_suite/shared_data/curve_fitting/profiling/profiling_relax_fit.py
test_suite/shared_data/curve_fitting/profiling/verify_error.py
The profiling script shows that a 10 X increase in speed can be reached
by
removing
the linear constraints when using minfx.
The profiling also shows that scipy.optimize.leastsq is 10X as fast as
using
minfx, even without linear constraints.
scipy.optimize.leastsq is a wrapper around wrapper around MINPACK's
lmdif and
lmder algorithms.
MINPACK is a FORTRAN90 library which solves systems of nonlinear
equations, or
carries out the least squares minimization of the residual of a set of
linear
or nonlinear equations.
The verification script also shows, that a very heavy and time consuming
monte carlo simulation of 2000 steps, reaches the same errors as the
errors
reported by scipy.optimize.leastsq.
The return from scipy.optimize.leastsq, gives the estimated co-variance.
Taking the square root of the co-variance corresponds with 2X error
reported
by minfx after 2000 Monte-Carlo simulations.
This could be an extremely time saving step, when performing model
fitting in
R1rho, where the errors of the R2eff values, are estimated by Monte-Carlo
simulations.
The following setup illustrates the problem.
This was analysed on a: MacBook Pro, 13-inch, Late 2011.
With no multi-core setup.
Script running is:
test_suite/shared_data/dispersion/Kjaergaard_et_al_2013/2_pre_run_r2eff.py
This script analyses just the R2eff values for 15 residues.
It estimates the errors of R2eff based on 2000 Monte Carlo simulations.
For each residues, there is 14 exponential graphs.
The script was broken after 35 simulations.
This was measured to 20 minutes.
So 500 simulations would take about 4.8 Hours.
The R2eff values and errors can by scipy.optimize.leastsq can instead be
calculated in: 15 residues * 0.02 seconds = 0.3 seconds.
_______________________________________________________
Reply to this item at:
<http://gna.org/task/?7822>
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