Hi, Just a hint, the answer should look a lot like the chi-squared gradient (http://www.nmr-relax.com/manual/chi_squared_gradient.html), but probably without the sum and a few other differences.
Regards, Edward On 28 August 2014 15:41, Edward d'Auvergne <[email protected]> wrote: > Hi, > > No, that's not correct. Try performing the maths yourself and try to > derive the chi-squared partial derivative. You will see that it's a > little different. > > Regards, > > Edward > > > > On 28 August 2014 15:38, Troels Emtekær Linnet <[email protected]> wrote: >> Hi Edward. >> >> I is just target_functions/c_chi2.c where you dont sum the elements, but >> return as array. >> >> Best >> Troels >> >> 2014-08-28 15:30 GMT+02:00 Edward d'Auvergne <[email protected]>: >>> Hi Troels, >>> >>> Could you derive the chi-squared Jacobian? Maybe the Jacobian I have >>> been using is not correct - this is the one required for the >>> Levenberg-Marquardt optimisation algorithm. Because the chi-squared >>> is squared, its derivative will have a factor of 2 out the front, just >>> like the gradient: >>> >>> http://www.nmr-relax.com/manual/chi_squared_gradient.html >>> >>> It might be useful to add a Jacobian section to this part of the >>> manual with the equations. >>> >>> Cheers, >>> >>> Edward >>> >>> >>> >>> On 28 August 2014 15:14, <[email protected]> wrote: >>>> Author: tlinnet >>>> Date: Thu Aug 28 15:14:16 2014 >>>> New Revision: 25379 >>>> >>>> URL: http://svn.gna.org/viewcvs/relax?rev=25379&view=rev >>>> Log: >>>> Modified systemtest test Relax_disp.test_estimate_r2eff_err_methods() to >>>> show the difference between using the direct function Jacobian, or the >>>> chi2 function Jacobian. >>>> >>>> Added also the functionality to the estimate R2eff module, to switch >>>> between using the different Jacobians. >>>> >>>> The results show, that R2eff can be estimated better. >>>> >>>> ---------------------- >>>> The results are: >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 431.0. >>>> r2eff=8.646/8.646 r2eff_err=0.0348/0.0692 i0=202664.191/202664.191 >>>> i0_err=699.6443/712.4201 >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 651.2. >>>> r2eff=10.377/10.377 r2eff_err=0.0403/0.0810 i0=206049.558/206049.558 >>>> i0_err=776.4215/782.1833 >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 800.5. >>>> r2eff=10.506/10.506 r2eff_err=0.0440/0.0853 i0=202586.332/202586.332 >>>> i0_err=763.9678/758.7052 >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 984.0. >>>> r2eff=10.903/10.903 r2eff_err=0.0476/0.0922 i0=203455.021/203455.021 >>>> i0_err=837.8779/828.7280 >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 1341.1. >>>> r2eff=10.684/10.684 r2eff_err=0.0446/0.0853 i0=218670.412/218670.412 >>>> i0_err=850.0210/830.9558 >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 1648.5. >>>> r2eff=10.501/10.501 r2eff_err=0.0371/0.0742 i0=206502.512/206502.512 >>>> i0_err=794.0523/772.9843 >>>> >>>> R1rho at 799.8 MHz, for offset=124.247 ppm and dispersion point 1341.1. >>>> r2eff=11.118/11.118 r2eff_err=0.0413/0.0827 i0=216447.241/216447.241 >>>> i0_err=784.6562/788.0384 >>>> >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 800.5. >>>> r2eff=7.866/7.866 r2eff_err=0.0347/0.0695 i0=211869.715/211869.715 >>>> i0_err=749.2776/763.6930 >>>> >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 1341.1. >>>> r2eff=9.259/9.259 r2eff_err=0.0331/0.0661 i0=217703.151/217703.151 >>>> i0_err=682.2137/685.5838 >>>> >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 1648.5. >>>> r2eff=9.565/9.565 r2eff_err=0.0373/0.0745 i0=211988.939/211988.939 >>>> i0_err=839.0313/827.0373 >>>> >>>> R1rho at 799.8 MHz, for offset=142.754 ppm and dispersion point 800.5. >>>> r2eff=3.240/3.240 r2eff_err=0.0127/0.0253 i0=214417.382/214417.382 >>>> i0_err=595.8865/613.4378 >>>> >>>> R1rho at 799.8 MHz, for offset=142.754 ppm and dispersion point 1341.1. >>>> r2eff=5.084/5.084 r2eff_err=0.0177/0.0352 i0=226358.691/226358.691 >>>> i0_err=660.5314/655.7670 >>>> >>>> R1rho at 799.8 MHz, for offset=179.768 ppm and dispersion point 1341.1. >>>> r2eff=2.208/2.208 r2eff_err=0.0091/0.0178 i0=228620.553/228620.553 >>>> i0_err=564.8353/560.0873 >>>> >>>> R1rho at 799.8 MHz, for offset=241.459 ppm and dispersion point 1341.1. >>>> r2eff=1.711/1.711 r2eff_err=0.0077/0.0155 i0=224087.486/224087.486 >>>> i0_err=539.4300/546.4217 >>>> >>>> Fitting with minfx to: 52V @N >>>> ----------------------------- >>>> >>>> min_algor='Newton', c_code=True, constraints=False, chi2_jacobian?=False >>>> ------------------------------------------------------------------------ >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 431.0, >>>> with 4 time points. r2eff=8.646 r2eff_err=0.0692, i0=202664.2, >>>> i0_err=712.4201, chi2=3.758. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 651.2, >>>> with 5 time points. r2eff=10.377 r2eff_err=0.0810, i0=206049.6, >>>> i0_err=782.1833, chi2=27.291. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 800.5, >>>> with 5 time points. r2eff=10.506 r2eff_err=0.0853, i0=202586.3, >>>> i0_err=758.7052, chi2=13.357. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 984.0, >>>> with 5 time points. r2eff=10.903 r2eff_err=0.0922, i0=203455.0, >>>> i0_err=828.7280, chi2=33.632. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=10.684 r2eff_err=0.0853, i0=218670.4, >>>> i0_err=830.9558, chi2=35.818. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 1648.5, >>>> with 5 time points. r2eff=10.501 r2eff_err=0.0742, i0=206502.5, >>>> i0_err=772.9843, chi2=7.356. >>>> R1rho at 799.8 MHz, for offset=124.247 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=11.118 r2eff_err=0.0827, i0=216447.2, >>>> i0_err=788.0384, chi2=15.587. >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 800.5, >>>> with 5 time points. r2eff=7.866 r2eff_err=0.0695, i0=211869.7, >>>> i0_err=763.6930, chi2=14.585. >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=9.259 r2eff_err=0.0661, i0=217703.2, >>>> i0_err=685.5838, chi2=79.498. >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 1648.5, >>>> with 5 time points. r2eff=9.565 r2eff_err=0.0745, i0=211988.9, >>>> i0_err=827.0373, chi2=0.447. >>>> R1rho at 799.8 MHz, for offset=142.754 ppm and dispersion point 800.5, >>>> with 5 time points. r2eff=3.240 r2eff_err=0.0253, i0=214417.4, >>>> i0_err=613.4378, chi2=1.681. >>>> R1rho at 799.8 MHz, for offset=142.754 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=5.084 r2eff_err=0.0352, i0=226358.7, >>>> i0_err=655.7670, chi2=23.170. >>>> R1rho at 799.8 MHz, for offset=179.768 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=2.208 r2eff_err=0.0178, i0=228620.6, >>>> i0_err=560.0873, chi2=7.794. >>>> R1rho at 799.8 MHz, for offset=241.459 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=1.711 r2eff_err=0.0155, i0=224087.5, >>>> i0_err=546.4217, chi2=21.230. >>>> >>>> Fitting with minfx to: 52V @N >>>> ----------------------------- >>>> >>>> min_algor='BFGS', c_code=False, constraints=False, chi2_jacobian?=True >>>> ---------------------------------------------------------------------- >>>> >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 431.0, >>>> with 4 time points. r2eff=8.646 r2eff_err=0.0524, i0=202664.2, >>>> i0_err=1239.0827, chi2=3.758. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 651.2, >>>> with 5 time points. r2eff=10.377 r2eff_err=0.0228, i0=206049.6, >>>> i0_err=178.1907, chi2=27.291. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 800.5, >>>> with 5 time points. r2eff=10.506 r2eff_err=0.0345, i0=202586.3, >>>> i0_err=705.7630, chi2=13.357. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 984.0, >>>> with 5 time points. r2eff=10.903 r2eff_err=0.0206, i0=203455.0, >>>> i0_err=186.0857, chi2=33.632. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=10.684 r2eff_err=0.0198, i0=218670.4, >>>> i0_err=165.0420, chi2=35.818. >>>> R1rho at 799.8 MHz, for offset=118.078 ppm and dispersion point 1648.5, >>>> with 5 time points. r2eff=10.501 r2eff_err=0.0407, i0=206502.5, >>>> i0_err=321.3685, chi2=7.356. >>>> R1rho at 799.8 MHz, for offset=124.247 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=11.118 r2eff_err=0.0301, i0=216447.2, >>>> i0_err=248.9394, chi2=15.587. >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 800.5, >>>> with 5 time points. r2eff=7.866 r2eff_err=0.0280, i0=211869.7, >>>> i0_err=259.8845, chi2=14.585. >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=9.259 r2eff_err=0.0108, i0=217703.2, >>>> i0_err=88.1514, chi2=79.498. >>>> R1rho at 799.8 MHz, for offset=130.416 ppm and dispersion point 1648.5, >>>> with 5 time points. r2eff=9.565 r2eff_err=0.1630, i0=211988.9, >>>> i0_err=2054.6615, chi2=0.447. >>>> R1rho at 799.8 MHz, for offset=142.754 ppm and dispersion point 800.5, >>>> with 5 time points. r2eff=3.240 r2eff_err=0.0485, i0=214417.4, >>>> i0_err=611.7573, chi2=1.681. >>>> R1rho at 799.8 MHz, for offset=142.754 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=5.084 r2eff_err=0.0124, i0=226358.7, >>>> i0_err=122.7341, chi2=23.170. >>>> R1rho at 799.8 MHz, for offset=179.768 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=2.208 r2eff_err=0.0086, i0=228620.6, >>>> i0_err=219.4208, chi2=7.794. >>>> R1rho at 799.8 MHz, for offset=241.459 ppm and dispersion point 1341.1, >>>> with 5 time points. r2eff=1.711 r2eff_err=0.0101, i0=224087.5, >>>> i0_err=166.9081, chi2=21.230. >>>> >>>> task #7822(https://gna.org/task/index.php?7822): Implement user function >>>> to estimate R2eff and associated errors for exponential curve fitting. >>>> >>>> Modified: >>>> trunk/specific_analyses/relax_disp/estimate_r2eff.py >>>> trunk/test_suite/system_tests/relax_disp.py >>>> >>>> Modified: trunk/specific_analyses/relax_disp/estimate_r2eff.py >>>> URL: >>>> http://svn.gna.org/viewcvs/relax/trunk/specific_analyses/relax_disp/estimate_r2eff.py?rev=25379&r1=25378&r2=25379&view=diff >>>> ============================================================================== >>>> --- trunk/specific_analyses/relax_disp/estimate_r2eff.py (original) >>>> +++ trunk/specific_analyses/relax_disp/estimate_r2eff.py Thu Aug 28 >>>> 15:14:16 2014 >>>> @@ -175,7 +175,7 @@ >>>> print(print_string), >>>> >>>> >>>> -def multifit_covar(J=None, epsrel=0.0, errors=None): >>>> +def multifit_covar(J=None, epsrel=0.0, errors=None, use_weights=True): >>>> """This is the implementation of the multifit covariance. >>>> >>>> This is inspired from GNU Scientific Library (GSL). >>>> @@ -184,9 +184,15 @@ >>>> >>>> The parameter 'epsrel' is used to remove linear-dependent columns >>>> when J is rank deficient. >>>> >>>> + The weighting matrix 'W', is a square symmetric matrix. For >>>> independent measurements, this is a diagonal matrix. Larger values >>>> indicate greater significance. It is formed by multiplying the supplied >>>> errors as 1./errors^2 with an Identity matrix:: >>>> + >>>> + W = I.(1/errors^2) >>>> + >>>> + If 'use_weights' is set to 'False', the errors are set to 1.0. >>>> + >>>> The covariance matrix is given by:: >>>> >>>> - covar = (J^T J)^{-1} , >>>> + covar = (J^T.W.J)^{-1} , >>>> >>>> and is computed by QR decomposition of J with column-pivoting. Any >>>> columns of R which satisfy:: >>>> >>>> @@ -224,6 +230,8 @@ >>>> @type epsrel: float >>>> @keyword errors: The standard deviation of the measured >>>> intensity values per time point. >>>> @type errors: numpy array >>>> + @keyword use_weights: If the supplied weights should be used. >>>> + @type use_weights: bool >>>> @return: The co-variance matrix >>>> @rtype: square numpy array >>>> """ >>>> @@ -237,6 +245,10 @@ >>>> # Now form the error matrix, with errors down the diagonal. >>>> weights = 1. / errors**2 >>>> >>>> + if use_weights == False: >>>> + weights[:] = 1.0 >>>> + >>>> + # Form weight matrix. >>>> W = multiply(weights, eye_mat) >>>> >>>> # The covariance matrix (sometimes referred to as the >>>> variance-covariance matrix), Qxx, is defined as: >>>> @@ -344,7 +356,7 @@ >>>> self.factor = factor >>>> >>>> >>>> - def set_settings_minfx(self, scaling_matrix=None, >>>> min_algor='simplex', c_code=True, constraints=False, func_tol=1e-25, >>>> grad_tol=None, max_iterations=10000000): >>>> + def set_settings_minfx(self, scaling_matrix=None, >>>> min_algor='simplex', c_code=True, constraints=False, chi2_jacobian=False, >>>> func_tol=1e-25, grad_tol=None, max_iterations=10000000): >>>> """Setup options to minfx. >>>> >>>> @keyword scaling_matrix: The square and diagonal scaling >>>> matrix. >>>> @@ -355,6 +367,8 @@ >>>> @type c_code: bool >>>> @keyword constraints: If constraints should be used. >>>> @type constraints: bool >>>> + @keyword chi2_jacobian: If the chi2 Jacobian should be used. >>>> + @type chi2_jacobian: bool >>>> @keyword func_tol: The function tolerance which, when >>>> reached, terminates optimisation. Setting this to None turns of the check. >>>> @type func_tol: None or float >>>> @keyword grad_tol: The gradient tolerance which, when >>>> reached, terminates optimisation. Setting this to None turns of the check. >>>> @@ -366,6 +380,7 @@ >>>> # Store variables. >>>> self.scaling_matrix = scaling_matrix >>>> self.c_code = c_code >>>> + self.chi2_jacobian = chi2_jacobian >>>> >>>> # Scaling initialisation. >>>> self.scaling_flag = False >>>> @@ -561,7 +576,7 @@ >>>> return 1. / self.errors * (self.func_exp(self.times, *params) - >>>> self.values) >>>> >>>> >>>> -def estimate_r2eff(method='minfx', min_algor='simplex', c_code=True, >>>> constraints=False, spin_id=None, ftol=1e-15, xtol=1e-15, maxfev=10000000, >>>> factor=100.0, verbosity=1): >>>> +def estimate_r2eff(method='minfx', min_algor='simplex', c_code=True, >>>> constraints=False, chi2_jacobian=False, spin_id=None, ftol=1e-15, >>>> xtol=1e-15, maxfev=10000000, factor=100.0, verbosity=1): >>>> """Estimate r2eff and errors by exponential curve fitting with >>>> scipy.optimize.leastsq or minfx. >>>> >>>> THIS IS ONLY FOR TESTING. >>>> @@ -583,10 +598,12 @@ >>>> @type method: string >>>> @keyword min_algor: The minimisation algorithm >>>> @type min_algor: string >>>> + @keyword c_code: If optimise with C code. >>>> + @type c_code: bool >>>> @keyword constraints: If constraints should be used. >>>> @type constraints: bool >>>> - @keyword c_code: If optimise with C code. >>>> - @type c_code: bool >>>> + @keyword chi2_jacobian: If the chi2 Jacobian should be used. >>>> + @type chi2_jacobian: bool >>>> @keyword spin_id: The spin identification string. >>>> @type spin_id: str >>>> @keyword ftol: The function tolerance for the relative >>>> error desired in the sum of squares, parsed to leastsq. >>>> @@ -661,7 +678,7 @@ >>>> top += 2 >>>> subsection(file=sys.stdout, text="Fitting with %s to: >>>> %s"%(method, spin_string), prespace=top) >>>> if method == 'minfx': >>>> - subsection(file=sys.stdout, text="min_algor='%s', >>>> c_code=%s, constraints=%s"%(min_algor, c_code, constraints), prespace=0) >>>> + subsection(file=sys.stdout, text="min_algor='%s', >>>> c_code=%s, constraints=%s, chi2_jacobian?=%s"%(min_algor, c_code, >>>> constraints, chi2_jacobian), prespace=0) >>>> >>>> # Loop over each spectrometer frequency and dispersion point. >>>> for exp_type, frq, offset, point, ei, mi, oi, di in >>>> loop_exp_frq_offset_point(return_indices=True): >>>> @@ -692,7 +709,7 @@ >>>> >>>> elif method == 'minfx': >>>> # Set settings. >>>> - E.set_settings_minfx(min_algor=min_algor, c_code=c_code, >>>> constraints=constraints) >>>> + E.set_settings_minfx(min_algor=min_algor, c_code=c_code, >>>> chi2_jacobian=chi2_jacobian, constraints=constraints) >>>> >>>> # Acquire results. >>>> results = minimise_minfx(E=E) >>>> @@ -737,7 +754,7 @@ >>>> point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and >>>> dispersion point %-5.1f, with %i time points." % (exp_type, frq/1E6, >>>> offset, point, len(times)) >>>> print_strings.append(point_info) >>>> >>>> - par_info = "r2eff=%3.3f r2eff_err=%3.3f, i0=%6.1f, >>>> i0_err=%3.3f, chi2=%3.3f.\n" % ( r2eff, r2eff_err, i0, i0_err, chi2) >>>> + par_info = "r2eff=%3.3f r2eff_err=%3.4f, i0=%6.1f, >>>> i0_err=%3.4f, chi2=%3.3f.\n" % ( r2eff, r2eff_err, i0, i0_err, chi2) >>>> print_strings.append(par_info) >>>> >>>> if E.verbosity >= 2: >>>> @@ -912,14 +929,24 @@ >>>> #jacobian_matrix_exp2 = E.jacobian_matrix_exp >>>> #print jacobian_matrix_exp - jacobian_matrix_exp2 >>>> else: >>>> - # Call class, to store value. >>>> - E.func_exp_grad(param_vector) >>>> - jacobian_matrix_exp = E.jacobian_matrix_exp >>>> - #E.func_exp_chi2_grad(param_vector) >>>> - #jacobian_matrix_exp = E.jacobian_matrix_exp_chi2 >>>> + if E.chi2_jacobian: >>>> + # Call class, to store value. >>>> + E.func_exp_chi2_grad(param_vector) >>>> + jacobian_matrix_exp = E.jacobian_matrix_exp_chi2 >>>> + else: >>>> + # Call class, to store value. >>>> + E.func_exp_grad(param_vector) >>>> + jacobian_matrix_exp = E.jacobian_matrix_exp >>>> + #E.func_exp_chi2_grad(param_vector) >>>> + #jacobian_matrix_exp = E.jacobian_matrix_exp_chi2 >>>> >>>> # Get the co-variance >>>> - pcov = multifit_covar(J=jacobian_matrix_exp, errors=E.errors) >>>> + if E.chi2_jacobian: >>>> + use_weights = False >>>> + else: >>>> + use_weights = True >>>> + >>>> + pcov = multifit_covar(J=jacobian_matrix_exp, errors=E.errors, >>>> use_weights=use_weights) >>>> >>>> # To compute one standard deviation errors on the parameters, take >>>> the square root of the diagonal covariance. >>>> param_vector_error = sqrt(diag(pcov)) >>>> >>>> Modified: trunk/test_suite/system_tests/relax_disp.py >>>> URL: >>>> http://svn.gna.org/viewcvs/relax/trunk/test_suite/system_tests/relax_disp.py?rev=25379&r1=25378&r2=25379&view=diff >>>> ============================================================================== >>>> --- trunk/test_suite/system_tests/relax_disp.py (original) >>>> +++ trunk/test_suite/system_tests/relax_disp.py Thu Aug 28 15:14:16 2014 >>>> @@ -2946,12 +2946,13 @@ >>>> >>>> >>>> # Now do it manually. >>>> - estimate_r2eff(method='scipy.optimize.leastsq') >>>> - estimate_r2eff(method='minfx', min_algor='simplex', c_code=True, >>>> constraints=False) >>>> - estimate_r2eff(method='minfx', min_algor='simplex', c_code=False, >>>> constraints=False) >>>> - estimate_r2eff(method='minfx', min_algor='BFGS', c_code=True, >>>> constraints=False) >>>> - estimate_r2eff(method='minfx', min_algor='BFGS', c_code=False, >>>> constraints=False) >>>> + #estimate_r2eff(method='scipy.optimize.leastsq') >>>> + #estimate_r2eff(method='minfx', min_algor='simplex', c_code=True, >>>> constraints=False) >>>> + #estimate_r2eff(method='minfx', min_algor='simplex', >>>> c_code=False, constraints=False) >>>> + #estimate_r2eff(method='minfx', min_algor='BFGS', c_code=True, >>>> constraints=False) >>>> + #estimate_r2eff(method='minfx', min_algor='BFGS', c_code=False, >>>> constraints=False) >>>> estimate_r2eff(method='minfx', min_algor='Newton', c_code=True, >>>> constraints=False) >>>> + estimate_r2eff(method='minfx', min_algor='BFGS', c_code=False, >>>> constraints=False, chi2_jacobian=True) >>>> >>>> >>>> def test_exp_fit(self): >>>> >>>> >>>> _______________________________________________ >>>> relax (http://www.nmr-relax.com) >>>> >>>> This is the relax-commits 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-commits >>> >>> _______________________________________________ >>> 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 _______________________________________________ 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
