__init__(self,
init_params=None,
param_set=None,
diff_type=None,
diff_params=None,
scaling_matrix=None,
num_res=None,
equations=None,
param_types=None,
param_values=None,
relax_data=None,
errors=None,
bond_length=None,
csa=None,
num_frq=0,
frq=None,
num_ri=None,
remap_table=None,
noe_r1_table=None,
ri_labels=None,
gx=0,
gh=0,
g_ratio=0,
h_bar=0,
mu0=0,
num_params=None,
vectors=None)
(Constructor)
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The model-free minimisation class.
This class should be initialised before every calculation.
Arguments
~~~~~~~~~
equation: The model-free equation string which should be either 'mf_orig' or 'mf_ext'.
param_types: An array of the parameter types used in minimisation.
relax_data: An array containing the experimental relaxation values.
errors: An array containing the experimental errors.
bond_length: The fixed bond length in meters.
csa: The fixed CSA value.
diff_type: The diffusion tensor string which should be either 'sphere', 'spheroid', or
'ellipsoid'.
diff_params: An array with the diffusion parameters.
scaling_matrix: A diagonal matrix of scaling factors.
Additional layer of equations to simplify the relaxation equations, gradients, and Hessians.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The R1 and R2 equations are left alone, while the NOE is calculated from the R1 and
sigma_noe values.
The relaxation equations
~~~~~~~~~~~~~~~~~~~~~~~~
Data structure: data.ri
Dimension: 1D, (relaxation data)
Type: Numeric array, Float64
Dependencies: data.ri_prime
Required by: data.chi2, data.dchi2, data.d2chi2
R1() = R1'()
R2() = R2'()
gH sigma_noe()
NOE() = 1 + -- . -----------
gN R1()
The relaxation gradients
~~~~~~~~~~~~~~~~~~~~~~~~
Data structure: data.dri
Dimension: 2D, (parameters, relaxation data)
Type: Numeric array, Float64
Dependencies: data.ri_prime, data.dri_prime
Required by: data.dchi2, data.d2chi2
dR1() dR1'()
------- = -------
dthetaj dthetaj
dR2() dR2'()
------- = -------
dthetaj dthetaj
dNOE() gH 1 / dsigma_noe() dR1() \
------- = -- . ------- . | R1() . ------------ - sigma_noe() . ------- |
dthetaj gN R1()**2 \ dthetaj dthetaj /
The relaxation Hessians
~~~~~~~~~~~~~~~~~~~~~~~
Data structure: data.d2ri
Dimension: 3D, (parameters, parameters, relaxation data)
Type: Numeric array, Float64
Dependencies: data.ri_prime, data.dri_prime, data.d2ri_prime
Required by: data.d2chi2
d2R1() d2R1'()
--------------- = ---------------
dthetai.dthetaj dthetai.dthetaj
d2R2() d2R2'()
--------------- = ---------------
dthetai.dthetaj dthetai.dthetaj
d2NOE() gH 1 / / dR1() dR1() d2R1() \
--------------- = -- . ------- . | sigma_noe() . | 2 . ------- . ------- - R1() . --------------- |
dthetai.dthetaj gN R1()**3 \ \ dthetai dthetaj dthetai.dthetaj /
/ dsigma_noe() dR1() dR1() dsigma_noe() d2sigma_noe() \ \
- R1() . | ------------ . ------- + ------- . ------------ - R1() . --------------- | |
\ dthetai dthetaj dthetai dthetaj dthetai.dthetaj / /
The chi-sqared equation
~~~~~~~~~~~~~~~~~~~~~~~
_n_
\ (Ri - Ri()) ** 2
Chi2 = > ----------------
/__ sigma_i ** 2
i=1
where:
Ri are the values of the measured relaxation data set.
Ri() are the values of the back calculated relaxation data set.
sigma_i are the values of the error set.
The chi-sqared gradient
~~~~~~~~~~~~~~~~~~~~~~~
_n_
dChi2 \ / Ri - Ri() dRi() \
------- = -2 > | ---------- . ------- |
dthetaj /__ \ sigma_i**2 dthetaj /
i=1
where:
Ri are the values of the measured relaxation data set.
Ri() are the values of the back calculated relaxation data set.
sigma_i are the values of the error set.
The chi-sqared Hessian
~~~~~~~~~~~~~~~~~~~~~~
_n_
d2chi2 \ 1 / dRi() dRi() d2Ri() \
--------------- = 2 > ---------- | ------- . ------- - (Ri - Ri()) . --------------- |
dthetaj.dthetak /__ sigma_i**2 \ dthetaj dthetak dthetaj.dthetak /
i=1
where:
Ri are the values of the measured relaxation data set.
Ri() are the values of the back calculated relaxation data set.
sigma_i are the values of the error set.
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