Package functions :: Module d2jw_mf_trans :: Class d2Jw
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Class d2Jw

source code


Instance Methods [hide private]
 
__init__(self)
Function for creating the model-free spectral density hessians.
source code
 
calc_d2jw_dS2dae_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.
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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.
source code
 
calc_d2jw_dS2fdas_iso_m5(self, i, frq_index)
Calculate the model 5 S2f/ts partial derivative of the spectral density function for isotropic rotational diffusion.
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calc_d2jw_dS2sdas_iso_m5(self, i, frq_index)
Calculate the model 5 S2s/ts partial derivative of the spectral density function for isotropic rotational diffusion.
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calc_d2jw_dae2_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.
source code
 
calc_d2jw_das2_iso_m5(self, i, frq_index)
Calculate the model 5 ts/ts partial derivative of the spectral density function for isotropic rotational diffusion.
source code
 
d2Jw(self)
Function to create model-free spectral density hessians.
source code
Method Details [hide private]

d2Jw(self)

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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
~~~~~~~~

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

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


         d2J(w)       2                (ae + c.tm)**2 - (w.tm.ae)**2
        -------  =  - - . c . tm**2 . ----------------------------------
        dS2.dae       5               ((ae + c.tm)**2 + (w.tm.ae)**2)**2


        d2J(w)       4                          (ae + c.tm)**3 + 3.c.tm**3.ae.w**2.(ae + c.tm) - (1/ae).(w.tm.ae)**4
        ------  =  - - . c . tm**2 . (1 - S2) . --------------------------------------------------------------------
        dae**2       5                                          ((ae + c.tm)**2 + (w.tm.ae)**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
        dae.dRex            dae.dcsa              dae.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 /       1                 (as + c.tm) . as        \ 
        ---------  =  ---- | -------------  -  ----------------------------- |
        dS2f.dS2s      5   \ 1 + (w.tm)**2     (as + c.tm)**2 + (w.tm.as)**2 /


         d2J(w)        2                (af + c.tm)**2 - (w.tm.af)**2    
        --------  =  - - . c . tm**2 . ----------------------------------
        dS2f.daf       5               ((af + c.tm)**2 + (w.tm.af)**2)**2


         d2J(w)      2                            (as + c.tm)**2 - (w.tm.as)**2
        --------  =  - . c . tm**2 . (1 - S2s) . ----------------------------------
        dS2f.das     5                           ((as + c.tm)**2 + (w.tm.as)**2)**2


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


         d2J(w)        2                      (as + c.tm)**2 - (w.tm.as)**2
        --------  =  - - . c . tm**2 . S2f . ----------------------------------
        dS2s.das       5                     ((as + c.tm)**2 + (w.tm.as)**2)**2


        d2J(w)       4                           (af + c.tm)**3 + 3.c.tm**3.af.w**2.(af + c.tm) - (1/af).(w.tm.af)**4
        ------  =  - - . c . tm**2 . (1 - S2f) . --------------------------------------------------------------------
        daf**2       5                                          ((af + c.tm)**2 + (w.tm.af)**2)**3


         d2J(w)
        -------  =  0
        daf.das


        d2J(w)       4                                 (as + c.tm)**3 + 3.c.tm**3.as.w**2.(as + c.tm) - (1/as).(w.tm.as)**4
        ------  =  - - . c . tm**2 . S2f . (1 - S2s) . --------------------------------------------------------------------
        das**2       5                                                ((as + c.tm)**2 + (w.tm.as)**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
        daf.dRex             daf.dcsa             daf.dr


         d2J(w)               d2J(w)              d2J(w)
        --------  =  0   ,   --------  =  0   ,   ------  =  0
        das.dRex             das.dcsa             das.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