Class dJw

Instance Methods

__init__(self)
Function for creating the model-free spectral density gradients.

calc_djw_dS2_iso_m13(self, i, frq_index)
Calculate the model 1 and 3 S2 derivative of the spectral density function for isotropic rotational diffusion.

calc_djw_dS2_iso_m24(self, i, frq_index)
Calculate the model 2 and 4 S2 derivative of the spectral density function for isotropic rotational diffusion.

calc_djw_dS2f_iso_m5(self, i, frq_index)
Calculate the model 5 S2f derivative of the spectral density function for isotropic rotational diffusion.

calc_djw_dS2s_iso_m5(self, i, frq_index)
Calculate the model 5 S2f derivative of the spectral density function for isotropic rotational diffusion.

calc_djw_dae_iso_m24(self, i, frq_index)
Calculate the model 2 and 4 te derivative of the spectral density function for isotropic rotational diffusion.

calc_djw_das_iso_m5(self, i, frq_index)
Calculate the model 5 ts derivative of the spectral density function for isotropic rotational diffusion.

dJw(self)
Function to create model-free spectral density gradients.

Method Details

dJw(self)

Function to create model-free spectral density gradients.

The spectral density gradients
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Data structure:  self.data.djw
Dimension:  3D, (number of NMR frequencies, 5 spectral density frequencies, model-free parameters)
Type:  Numeric 3D matrix, Float64
Dependencies:  None
Required by:  self.data.dri, self.data.d2ri


Formulae
~~~~~~~~

Parameter transformations
~~~~~~~~~~~~~~~~~~~~~~~~~
        ae  =  c.te

        af  =  c.tf

        as  =  c.ts


        therefore:

                          tm.ae
                te'  =  ---------
                        ae + c.tm

                          tm.af
                tf'  =  ---------
                        af + c.tm

                          tm.as
                ts'  =  ---------
                        as + c.tm


Original
~~~~~~~~

        dJ(w)     2.tm /       1                 (ae + c.tm) . ae        \ 
        -----  =  ---- | -------------  -  ----------------------------- |
         dS2       5   \ 1 + (w.tm)**2     (ae + c.tm)**2 + (w.tm.ae)**2 /


        dJ(w)     2                           (ae + c.tm)**2 - (w.tm.ae)**2
        -----  =  - . c . tm**2 . (1 - S2) . ----------------------------------
         dae      5                          ((ae + c.tm)**2 + (w.tm.ae)**2)**2


        dJ(w)
        -----  =  0
        dRex


        dJ(w)
        -----  =  0
        dcsa


        dJ(w)
        -----  =  0
         dr


Extended
~~~~~~~~

        dJ(w)     2.tm /      S2s                (af + c.tm) . af              (1 - S2s)(as + c.tm) . as   \ 
        -----  =  ---- | -------------  +  -----------------------------  +  ----------------------------- |
        dS2f       5   \ 1 + (w.tm)**2     (af + c.tm)**2 + (w.tm.af)**2     (as + c.tm)**2 + (w.tm.as)**2 /


        dJ(w)     2.S2f.tm /       1                 (as + c.tm) . as        \ 
        -----  =  -------- | -------------  +  ----------------------------- |
        dS2s         5     \ 1 + (w.tm)**2     (as + c.tm)**2 + (w.tm.as)**2 /


        dJ(w)     2                            (af + c.tm)**2 - (w.tm.af)**2
        -----  =  - . c . tm**2 . (1 - S2f) . ----------------------------------
         daf      5                           ((af + c.tm)**2 + (w.tm.af)**2)**2


        dJ(w)     2                             (as + c.tm)**2 - (w.tm.as)**2
        -----  =  - . c . tm**2 . (S2f - S2) . ----------------------------------
         das      5                            ((as + c.tm)**2 + (w.tm.as)**2)**2


        dJ(w)
        -----  =  0
        dRex


        dJ(w)
        -----  =  0
        dcsa


        dJ(w)
        -----  =  0
         dr