Function to create the model-free spectral density values using parameter transformations."
The spectral density equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Data structure: self.data.jw
Dimension: 2D, (number of NMR frequencies, 5 spectral density frequencies)
Type: Numeric matrix, Float64
Dependencies: None
Required by: self.data.ri, 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
~~~~~~~~
2.tm / S2 (1 - S2)(ae + c.tm) . ae \
J(w) = ---- | ------------- + ----------------------------- |
5 \ 1 + (w.tm)**2 (ae + c.tm)**2 + (w.tm.ae)**2 /
Extended
~~~~~~~~
2.tm / S2 (1 - S2f)(af + c.tm) . af (S2f - S2)(as + c.tm) . as \
J(w) = ---- | ------------- + ----------------------------- + ----------------------------- |
5 \ 1 + (w.tm)**2 (af + c.tm)**2 + (w.tm.af)**2 (as + c.tm)**2 + (w.tm.as)**2 /
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