Is the order of the columns in the Jacobian matrix important? Best Troels
2014-08-25 17:42 GMT+02:00 Edward d'Auvergne <[email protected]>: > 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 <[email protected]> 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 <[email protected]>: >>> 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 <[email protected]> >>> 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 <[email protected]>: >>>>> Hi Troels, >>>>> >>>>> Please see below: >>>>> >>>>> On 25 August 2014 13:01, Troels Emtekær Linnet <[email protected]> >>>>> wrote: >>>>>> 2014-08-25 11:19 GMT+02:00 Edward d'Auvergne <[email protected]>: >>>>>>> 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 [email protected] 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
