Class dJw

Instance Methods

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

dJw(self)
Function to create 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_dte_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_dts_iso_m5(self, i, frq_index)
Calculate the model 5 ts derivative of the spectral density function for isotropic rotational diffusion.

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
~~~~~~~~

Original
~~~~~~~~

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


        dJ(w)     2                1 - (w.te')**2      /   tm    \ 2
        -----  =  - . (1 - S2) . ------------------- . | ------- |
         dte      5              (1 + (w.te')**2)**2   \ te + tm /


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


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


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


Extended
~~~~~~~~

        dJ(w)     2 /    S2s.tm               tf'          (1 - S2s).ts' \ 
        -----  =  - | -------------  -  -------------- +  -------------- |
        dS2f      5 \ 1 + (w.tm)**2     1 + (w.tf')**2    1 + (w.ts')**2 /


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


        dJ(w)     2                 1 - (w.tf')**2      /   tm    \ 2
        -----  =  - . (1 - S2f) . ------------------- . | ------- |
         dtf      5               (1 + (w.tf')**2)**2   \ tf + tm /


        dJ(w)     2.S2f                 1 - (w.ts')**2      /   tm    \ 2
        -----  =  ----- . (1 - S2s) . ------------------- . | ------- |
         dts        5                 (1 + (w.ts')**2)**2   \ ts + tm /


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


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


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