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
