They should be the same ordering as the parameter vector, as each column is a partial derivative with respect to that parameter. The rows should be the x data or the time points. Well, I hope this is correct, it's been many years since I coded the model-free Jacobian matrix. Rather than using the new C code, maybe a test data set should be calculated by hand to determine if the covariance matrix calculation, and Jacobian calculation, is correct.
Regards, Edward On 25 August 2014 17:47, Troels Emtekær Linnet <tlin...@nmr-relax.com> wrote: > Is the order of the columns in the Jacobian matrix important? > > Best > Troels > > 2014-08-25 17:42 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >> That looks correct. If you calculate: >> >> linalg.inv(dot(transpose(mat), mat)) >> >> Do you get the covariance matrix? >> >> Regards, >> >> Edward >> >> >> >> On 25 August 2014 17:35, Troels Emtekær Linnet <tlin...@nmr-relax.com> wrote: >>> Let me exemplify: >>> >>> There is 4 time points. >>> >>> df_d_i0 = - ( 2. * ( self.values - i0 / exp(r2eff * self.relax_times) >>> ) ) / ( exp(r2eff * self.relax_times) * self.errors**2) >>> df_d_r2eff = (2 * i0 * self.relax_times * (self.values - i0 / >>> exp(r2eff * self.relax_times) ) ) / ( exp(r2eff * self.relax_times) * >>> self.errors**2) >>> >>> Should the return then be: >>> >>> print df_d_i0.shape, df_d_i0 >>> (4,) [-0.004826723918314 -0.00033019968656 0.002366308749814 >>> -0.000232558176186] >>> >>> print df_d_r2eff.shape, df_d_r2eff >>> (4,) [ 0. 2.66126225080615 -47.678483702132965 >>> 9.371576058231405] >>> >>> mat = transpose(array( [df_d_i0, df_d_r2eff ]) ) >>> print mat.shape, mat >>> >>> >>> (4, 2) [[ -4.826723918313830e-03 0.000000000000000e+00] >>> [ -3.301996865596296e-04 2.661262250806150e+00] >>> [ 2.366308749814298e-03 -4.767848370213297e+01] >>> [ -2.325581761857821e-04 9.371576058231405e+00]] >>> >>> >>> Best >>> Troels >>> >>> 2014-08-25 17:27 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >>>> Hi, >>>> >>>> I may have explained this incorrectly earlier: >>>> >>>> - The vector of partial derivatives with respect to the chi-squared >>>> equation is the gradient. >>>> - The vector of partial derivatives with respect to the exponential >>>> function is the Jacobian. >>>> >>>> The equations and code for the exponential partial derivatives are the >>>> same in both. It's just that they are used differently. Does this >>>> help? >>>> >>>> Regards, >>>> >>>> Edward >>>> >>>> On 25 August 2014 17:26, Troels Emtekær Linnet <tlin...@nmr-relax.com> >>>> wrote: >>>>> Hi Edward. >>>>> >>>>> When writing the Jacobian, do you then derivative according to ( i0 * >>>>> exp( -times * r2eff) ) >>>>> or do you do the derivative according to chi2 function? >>>>> >>>>> I have a little hard time to figure out the code text. >>>>> >>>>> From minfx: >>>>> @keyword func: The function which returns the value. >>>>> @type func: func >>>>> >>>>> So, this is the chi2 function. >>>>> >>>>> @keyword dfunc: The function which returns the gradient. >>>>> @type dfunc: func >>>>> >>>>> So, this must be the derivative of the chi2 function? >>>>> >>>>> So in essence. >>>>> >>>>> Does minfx expect a "dfunc" function which calculate the: >>>>> >>>>> one gradient chi2 value, subject to the input parameters? >>>>> >>>>> Or >>>>> A jacobian matrix of the form: >>>>> m X n matrix, where m is the number of time elements and n is number >>>>> of parameters = 2. >>>>> >>>>> Best >>>>> Troels >>>>> >>>>> 2014-08-25 15:52 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >>>>>> Hi Troels, >>>>>> >>>>>> Please see below: >>>>>> >>>>>> On 25 August 2014 13:01, Troels Emtekær Linnet <tlin...@nmr-relax.com> >>>>>> wrote: >>>>>>> 2014-08-25 11:19 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >>>>>>>> Hi Troels, >>>>>>>> >>>>>>>> Unfortunately you have gone ahead an implemented a solution without >>>>>>>> first discussing or planning it. Hence the current solution has a >>>>>>>> number of issues: >>>>>>>> >>>>>>>> 1) Target function replication. The solution should have reused the >>>>>>>> C modules. The original Python code for fitting exponential curves >>>>>>>> was converted to C code for speed >>>>>>>> (http://gna.org/forum/forum.php?forum_id=1043). Note that two point >>>>>>>> exponentials that decay to zero is not the only way that data can be >>>>>>>> collected, and that is the reason for Sebastien Morin's >>>>>>>> inversion-recovery branch (which was never completed). Anyway, the >>>>>>>> code duplication is not acceptable. If the C module is extended with >>>>>>>> new features, such as having the true gradient and Hessian functions, >>>>>>>> then the Python module will then be out of sync. And vice-versa. If >>>>>>>> a bug is found in one module and fixed, it may still be present in the >>>>>>>> second. This is a very non-ideal situation for relax to be in, and is >>>>>>>> the exact reason why I did not allow the cst branch to be merged back >>>>>>>> to trunk. >>>>>>> >>>>>>> Hi Edward. >>>>>>> >>>>>>> I prefer not to make this target function dependent on C-code >>>>>>> compilation. >>>>>>> >>>>>>> Compilation of code on windows can be quite a hairy thing. >>>>>>> >>>>>>> For example see: >>>>>>> http://wiki.nmr-relax.com/Installation_windows_Python_x86-32_Visual_Studio_Express_for_Windows_Desktop#Install_Visual_Studio_Express_2012_for_Windows_Desktop >>>>>>> >>>>>>> Visua Studio Express is several hundreds of megabyte installation, for >>>>>>> just compiling an exponential curve. ? >>>>>>> This is way, way overkill for this situation. >>>>>> >>>>>> The C code compilation has been a requirement in relax since 2006. >>>>>> This was added not only for speed, but as a framework to copy for >>>>>> other analysis types in the future. Once a Python target function has >>>>>> been fully optimised, for the last speed up the code can be converted >>>>>> to C. This is the future plan for a number of the relax analyses. >>>>>> But first the Python code is used for prototyping and for finding the >>>>>> fastest implementation/algorithm. >>>>>> >>>>>> The C compilation will become an even greater requirement once I write >>>>>> C wrapper code for QUADPACK to eliminate the last dependencies on >>>>>> Scipy. And the C compilation framework allows for external C and >>>>>> FORTRAN libraries to be added to the 'extern' package in the future, >>>>>> as there are plenty of open source libraries out there with compatible >>>>>> licences which could be very useful to use within relax. >>>>>> >>>>>> >>>>>>>> 2) Scipy is now a dependency for the dispersion analysis! Why was >>>>>>>> this not discussed? Coding a function for calculating the covariance >>>>>>>> matrix is basic. Deriving and coding the real gradient function is >>>>>>>> also basic. I do not understand why Scipy is now a dependency. I >>>>>>>> have been actively trying to remove Scipy as a relax dependency and >>>>>>>> only had a single call for numeric quadratic intergration via QUADPACK >>>>>>>> wrappers left to remove for the frame order analysis. Now Scipy is >>>>>>>> back :( >>>>>>> >>>>>>> Hi Edward. >>>>>>> >>>>>>> Scipy is a dependency for trying calculation with >>>>>>> scipy.optimize.leastsq. >>>>>>> >>>>>>> How could it be anymore different? >>>>>>> >>>>>>> What you are aiming at, is to add yet another feature for estimating >>>>>>> the errors. >>>>>>> A third solution. >>>>>>> >>>>>>> What ever the third solution would come up with of dependency, would >>>>>>> depend on the method implemented. >>>>>>> One could also possible imagine to extend this procedures in R, Matlab >>>>>>> or whatever. >>>>>>> >>>>>>> Byt they would also need to meet some dependencies. >>>>>>> >>>>>>> Of course the best solution would always try to make relax most >>>>>>> independent. >>>>>>> >>>>>>> But if the desire is to try with scipy.optimize.leastsq, then you are >>>>>>> bound with this dependency. >>>>>> >>>>>> That's why I asked if only the covariance matrix is required. Then we >>>>>> can replace the use of scipy.optimize.leastsq() with a single function >>>>>> for calculating the covariance matrix. >>>>>> >>>>>> >>>>>>>> 3) If the covariance function was coded, then the specific analysis >>>>>>>> API could be extended with a new covariance method and the >>>>>>>> relax_disp.r2eff_estimate user function could have simply been called >>>>>>>> error_estimate.covariance_matrix, or something like that. Then this >>>>>>>> new error_estimate.covariance_matrix user function could replace the >>>>>>>> monte_carlo user functions for all analyses, as a rough error >>>>>>>> estimator. >>>>>>> >>>>>>> That would be the third possibility. >>>>>> >>>>>> ..., that would give the same result, save the same amount of time, >>>>>> but would avoid the new Scipy dependency and be compatible with all >>>>>> analysis types ;) >>>>>> >>>>>> >>>>>>>> 4) For the speed of optimisation part of the new >>>>>>>> relax_disp.r2eff_estimate user function, this is not because scipy is >>>>>>>> faster than minfx!!! It is the choice of algorithms, the numerical >>>>>>>> gradient estimate, etc. >>>>>>>> (http://thread.gmane.org/gmane.science.nmr.relax.scm/22979/focus=6812). >>>>>>> >>>>>>> This sound good. >>>>>>> >>>>>>> But I can only say, that as I user I meet a "big wall of time >>>>>>> consumption", for the error >>>>>>> estimation of R2eff via Monte-Carlo. >>>>>>> >>>>>>> As a user, I needed more options to try out. >>>>>> >>>>>> The idea of adding the covariance matrix error estimate to relax is a >>>>>> great idea. Despite its lower quality, it is hugely faster than Monte >>>>>> Carlo simulations. It has been considered it before, see >>>>>> http://thread.gmane.org/gmane.science.nmr.relax.user/602/focus=629 and >>>>>> the discussions in that thread. But the time required for Monte Carlo >>>>>> simulations was never an issue so the higher quality estimate remained >>>>>> the only implementation. >>>>>> >>>>>> What I'm trying to do, is to direct your solution to be general and >>>>>> reusable. I'm also thinking of other techniques at the same time, >>>>>> Jackknife simulations for example, which could be added in the future >>>>>> by developers with completely different interests. >>>>>> >>>>>> >>>>>>>> 5) Back to Scipy. Scipy optimisation is buggy full stop. The >>>>>>>> developers ignored my feedback back in 2003. I assumed that the >>>>>>>> original developers had just permanently disappeared, and they really >>>>>>>> never came back. The Scipy optimisation code did not change for many, >>>>>>>> many years. While it looks like optimisation works, in some cases it >>>>>>>> does fails hard, stopping in a position in the space where there is no >>>>>>>> minimum! I added the dx.map user function to relax to understand >>>>>>>> these Scipy rubbish results. And I created minfx to work around these >>>>>>>> nasty hidden failures. I guess such failures are due to them not >>>>>>>> testing the functions as part of a test suite. Maybe they have fixed >>>>>>>> the bugs now, but I really can no longer trust Scipy optimisation. >>>>>>>> >>>>>>> >>>>>>> I am sorry to hear about this. >>>>>>> >>>>>>> And I am totally convinced that minfx is better for minimising the >>>>>>> dispersion models. >>>>>>> You have proven that quite well in your papers. >>>>>>> >>>>>>> I do though have a hard time believing that minimisation of an >>>>>>> exponential function should be >>>>>>> subject to erroneous results. >>>>>>> >>>>>>> Anyway, this is still left to "freedom of choice" for the user. >>>>>> >>>>>> The error in the original Scipy optimisation code was causing quite >>>>>> different results. The 3 algorithms, now that I look back at my >>>>>> emails from 2003, are: >>>>>> >>>>>> - Nelder-Mead simplex, >>>>>> - Levenberg-Marquardt, >>>>>> - NCG. >>>>>> >>>>>> These are still all present in Scipy, though I don't know if the code >>>>>> is different from back in 2003. The error in the Levenberg-Marquardt >>>>>> algorithm was similar to the Modelfree4 problem, in that a lamba >>>>>> matrix updating condition was incorrectly checked for. When the >>>>>> gradient was positive, i.e. up hill, the matrix should update and the >>>>>> algorithm continue to try to find a downhill step. If the conditions >>>>>> are not correctly checked for, the algorithm thinks that the up hill >>>>>> step means that it is at the minimum. But this is not the case, it is >>>>>> just pointing in the wrong direction. I don't remember what the NCG >>>>>> bug was, but that one was much more severe and the results were >>>>>> strange. >>>>>> >>>>>> Failures of optimisation algorithms due to bugs can be quite random. >>>>>> And you often don't see them, as you don't know what the true result >>>>>> really is. But such bugs will affect exponential functions, despite >>>>>> their simplicity. >>>>>> >>>>>> Regards, >>>>>> >>>>>> Edward _______________________________________________ relax (http://www.nmr-relax.com) This is the relax-devel mailing list relax-devel@gna.org To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-devel
