An additional layer of equations to simplify the relaxation equations, gradients, and hessians.
The R1 and R2 equations are left alone, while the NOE is decomposed into the cross relaxation rate equation and the R1 equation.
The relaxation hessians
~~~~~~~~~~~~~~~~~~~~~~~
Data structure: self.data.d2ri
Dimension: 3D, (parameters, parameters, relaxation data)
Type: Numeric array, Float64
Dependencies: self.data.ri_prime, self.data.dri_prime, self.data.d2ri_prime
Required by: self.data.d2chi2
Formulae
~~~~~~~~
d2R1() d2R1'()
--------------- = ---------------
dthetaj.dthetak dthetaj.dthetak
d2R2() d2R2'()
--------------- = ---------------
dthetaj.dthetak dthetaj.dthetak
d2NOE() gH 1 / / dR1() dR1() d2R1() \
--------------- = -- . ------- . | sigma_noe() . | 2 . ------- . ------- - R1() . --------------- |
dthetaj.dthetak gN R1()**3 \ \ dthetaj dthetak dthetaj.dthetak /
/ dsigma_noe() dR1() dR1() dsigma_noe() d2sigma_noe() \ \
- R1() . | ------------ . ------- + ------- . ------------ - R1() . --------------- | |
\ dthetaj dthetak dthetaj dthetak dthetaj.dthetak / /
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