Class d2Jw

Instance Methods

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

calc_d2jw_dS2dte_iso_m24(self, i, frq_index)
Calculate the model 2 and 4 S2/te partial derivative of the spectral density function for isotropic rotational diffusion.

calc_d2jw_dS2fdS2s_iso_m5(self, i, frq_index)
Calculate the model 5 S2f/S2s partial derivative of the spectral density function for isotropic rotational diffusion.

calc_d2jw_dS2fdts_iso_m5(self, i, frq_index)
Calculate the model 5 S2f/ts partial derivative of the spectral density function for isotropic rotational diffusion.

calc_d2jw_dS2sdts_iso_m5(self, i, frq_index)
Calculate the model 5 S2s/ts partial derivative of the spectral density function for isotropic rotational diffusion.

calc_d2jw_dte2_iso_m24(self, i, frq_index)
Calculate the model 2 and 4 te/te partial derivative of the spectral density function for isotropic rotational diffusion.

calc_d2jw_dts2_iso_m5(self, i, frq_index)
Calculate the model 5 ts/ts partial derivative of the spectral density function for isotropic rotational diffusion.

d2Jw(self)
Function to create model-free spectral density hessians.

Method Details

d2Jw(self)

Function to create model-free spectral density hessians.

The spectral density hessians
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Data structure:  self.data.d2jw
Dimension:  4D, (number of NMR frequencies, 5 spectral density frequencies, model-free parameters, model-free parameters)
Type:  Numeric 4D matrix, Float64
Dependencies:  None
Required by:  self.data.d2ri


Formulae
~~~~~~~~

Original:  Model-free parameter - Model-free parameter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        d2J(w)
        ------  =  0
        dS2**2


         d2J(w)       2     1 - (w.te')**2      /   tm    \ 2
        -------  =  - - . ------------------- . | ------- |
        dS2.dte       5   (1 + (w.te')**2)**2   \ te + tm /


        d2J(w)       4              /   tm    \ 4           1            
        ------  =  - - . (1 - S2) . | ------- |  . ------------------- . [w**2.te'(3 - (w.te')**2) + (1 - (w.te')**4)(te + tm).tm**-2]
        dte**2       5              \ te + tm /    (1 + (w.te')**2)**3   


Original:  Other parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~

         d2J(w)               d2J(w)              d2J(w)
        --------  =  0   ,   --------  =  0   ,   ------  =  0
        dS2.dRex             dS2.dcsa             dS2.dr


         d2J(w)              d2J(w)               d2J(w)
        --------  =  0   ,  --------  =  0   ,    ------  =  0
        dte.dRex            dte.dcsa              dte.dr


         d2J(w)              d2J(w)                d2J(w)
        -------  =  0   ,  ---------  =  0   ,    -------  =  0
        dRex**2            dRex.dcsa              dRex.dr


         d2J(w)             d2J(w)
        -------  =  0   ,  -------  =  0
        dcsa**2            dcsa.dr


        d2J(w)
        ------  =  0
        dr**2


Extended:  Model-free parameter - Model-free parameter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

         d2J(w)
        -------  =  0
        dS2f**2


          d2J(w)      2 /      tm                 ts'      \ 
        ---------  =  - | -------------  -  -------------- |
        dS2f.dS2s     5 \ 1 + (w.tm)**2     1 + (w.ts')**2 /


         d2J(w)        2     1 - (w.tf')**2      /   tm    \ 2
        --------  =  - - . ------------------- . | ------- |
        dS2f.dtf       5   (1 + (w.tf')**2)**2   \ tf + tm /


         d2J(w)      2                 1 - (w.ts')**2      /   tm    \ 2
        --------  =  - . (1 - S2s) . ------------------- . | ------- |
        dS2f.dts     5               (1 + (w.ts')**2)**2   \ ts + tm /


         d2J(w)              d2J(w)
        -------  =  0   ,   --------  =  0
        dS2s**2             dS2s.dtf


         d2J(w)        2.S2f     1 - (w.ts')**2      /   tm    \ 2
        --------  =  - ----- . ------------------- . | ------- |
        dS2s.dts         5     (1 + (w.ts')**2)**2   \ ts + tm /


         d2J(w)
        -------  =  0
        dtf.dts


        d2J(w)       4               /   tm    \ 4           1            
        ------  =  - - . (1 - S2f) . | ------- |  . ------------------- . [w**2.tf'(3 - (w.tf')**2) + (1 - (w.tf')**4)(tf + tm).tm**-2]
        dtf**2       5               \ tf + tm /    (1 + (w.tf')**2)**3   


        d2J(w)       4                /   tm    \ 4           1            
        ------  =  - - . (S2f - S2) . | ------- |  . ------------------- . [w**2.ts'(3 - (w.ts')**2) + (1 - (w.ts')**4)(ts + tm).tm**-2]
        dts**2       5                \ ts + tm /    (1 + (w.ts')**2)**3   


Extended:  Other parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~

          d2J(w)                d2J(w)               d2J(w)
        ---------  =  0   ,   ---------  =  0   ,   -------  =  0
        dS2f.dRex             dS2f.dcsa             dS2f.dr


          d2J(w)                d2J(w)               d2J(w)
        ---------  =  0   ,   ---------  =  0   ,   -------  =  0
        dS2s.dRex             dS2s.dcsa             dS2s.dr


         d2J(w)               d2J(w)              d2J(w)
        --------  =  0   ,   --------  =  0   ,   ------  =  0
        dtf.dRex             dtf.dcsa             dtf.dr


         d2J(w)               d2J(w)              d2J(w)
        --------  =  0   ,   --------  =  0   ,   ------  =  0
        dts.dRex             dts.dcsa             dts.dr


         d2J(w)               d2J(w)               d2J(w)
        -------  =  0   ,   ---------  =  0   ,   -------  =  0
        dRex**2             dRex.dcsa             dRex.dr


         d2J(w)              d2J(w)
        -------  =  0   ,   -------  =  0
        dcsa**2             dcsa.dr


        d2J(w)
        ------  =  0
        dr**2