relax SVN archive

Speed up of the target_functions.relax_fit C module.

The variances are now precalculated in the setup() function from the errors, so that the use of the
square() function is minimised. The chi-squared equation, gradient, and Hessian functions now
accept the variance rather than standard deviation argument and hence the squaring of errors has
been removed. This avoids a lot of duplicated maths operations.

First attempt at properly implementing the target_functions.relax_fit.jacobian() function.

This is now the Jacobian of the chi-squared function. A new jacobian_matrix data structure has been
created for holding the matrix data prior to converting it into a Python list of lists. The
equation used was simply the chi-squared gradient whereby the sum over i has been dropped and the i
elements are stored in the second dimension of matrix.

Various precision fixes for different machine precision.

This is in: verify_r1rho_kjaergaard_missing_r1

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

Reverted the logic, that the chi2 Jacobian should be used.

Instead, the direct Jacobian exponential is used instead.

When fitting with the estimated errors from the Direct Jacobian, the results are MUCH better, and comparable
to 2000 Monte-Carlo simulations.

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

More locking of values.

This actually shows, that errors should be estimated from the Direct Jacobian.
Not, the chi2 Jacobian.

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

More locking off values, when trying to use different methods for estimating R2eff err values.

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

Locked values for systemtest test_estimate_r2eff_err, to estimate how the R2eff error estimation reflects on fitted parameters.

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

Added digit to print out in R2eff estimate module.

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

Modified systemtest verify_estimate_r2eff_err_compare_mc() to first use the direct function Jacobian, and then the chi2 derived Jacobian.

This shows the result better.

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

Made the user function, which estimates the R2eff errors, use the Jacobian derived from chi2 function.

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