The profiling shows that scipy.optimize.leastsq is 10X as fast as using minfx (with no 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.
This could be an extremely time saving step, when performing model fitting in R1rho, where
the errors of the R2eff values, are estimited by Monte-Carlo simulations.
The following setup illustrates the problem.
This was analysed on a: MacBook Pro, 13-inch, Late 2011.
Witn 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.
