relax SVN archive

Fixes for the relax_disp.r2eff_estimate user function documentation.

This is to allow the relax manual to compile again as the original documentation was causing LaTeX
failures.

Tried to implement a safety test for linearly-dependent columns in the co-variance matrix.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.

Implemented the Jacobian of exponential function in Python Code.

This now also gets the same error as leastsq and C code.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.

Fixed naming of functions, to better represent what they do in module of estimating R2eff.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.

By using minfx, and the reported Jacobian, it is now possible to get the exact same error estimation as scipy.optimize.leastsq.

The fatal error was to set the weighting matrix with diagonal elements as the error.
There weights are 1/errors**2.

There is though some un-answered questions left.

The Jacobian used, is the direct derivative of the function.

It is not the chi2 derivative Jacobian.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.

Changed the optimisation description in the relaxation curve-fitting chapter of the manual.

The script example has been converted to match the sample script, replacing the Nelder-Mead simplex
algorithm with Newton optimisation, and removing the argument turning diagonal scaling off. All the
text about only the simplex algorithm being supported due to the missing gradients and Hessians in
the C module have been deleted. The text that linear constraints are not supported has also been
removed - but this was fixed when the logarithmic barrier constraint algorithm was added to minfx.

Changed the relax_fit.py sample script to use Newton rather than Simplex optimisation.

This can lead to significantly faster optimisation times, as shown in the commit message
http://article.gmane.org/gmane.science.nmr.relax.scm/23081.

Implemented the use of "Newton" as minimisation algorithm for R2eff curve fitting instead of simplex.

Running the test script:
test_suite/shared_data/dispersion/Kjaergaard_et_al_2013/2_pre_run_r2eff.py

For 50 Monte-Carlo simulations, the time drop from:
3 minutes and 13 s, to 1 min an 5 seconds.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.

Set the constraints=False, when doing Monte-Carlo simulations for R2eff.

This is to speed-up the Monte-Carlo simulations by a factor X10, when estimating the error for R2eff.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.

Tried to verify solution to profiling script.

task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.