Package maths_fns :: Module ri_comps

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Module ri_comps

source code

Functions

[hide private]

ri_comps(data, params)
Calculate the ri function components.

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ri_comps_rex(data, params)
Calculate the ri function components.

source code

ri_comps_r(data, params)
Calculate the ri function components.

source code

ri_comps_csa(data, params)
Calculate the ri function components.

source code

ri_comps_r_csa(data, params)
Calculate the ri function components.

source code

ri_comps_r_rex(data, params)
Calculate the ri function components.

source code

ri_comps_csa_rex(data, params)
Calculate the ri function components.

source code

ri_comps_r_csa_rex(data, params)
Calculate the ri function components.

source code

r1_comps(data, i, params)
Calculate the r1 function components.

source code

dri_comps(data, params)
Calculate the dri gradient components.

source code

dri_comps_rex(data, params)
Calculate the dri gradient components.

source code

dri_comps_r(data, params)
Calculate the dri gradient components.

source code

dri_comps_csa(data, params)
Calculate the dri gradient components.

source code

dri_comps_r_csa(data, params)
Calculate the dri gradient components.

source code

dri_comps_r_rex(data, params)
Calculate the dri gradient components.

source code

dri_comps_csa_rex(data, params)
Calculate the dri gradient components.

source code

dri_comps_r_csa_rex(data, params)
Calculate the dri gradient components.

source code

dr1_comps(data, i, params)
Calculate the dr1 gradient components.

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d2ri_comps(data, params)
Calculate the d2ri Hessian components.

source code

d2ri_comps_r(data, params)
Calculate the d2ri Hessian components.

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d2ri_comps_csa(data, params)
Calculate the d2ri Hessian components.

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d2ri_comps_r_csa(data, params)
Calculate the d2ri Hessian components.

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d2r1_comps(data, i, params)
Calculate the d2ri Hessian components.

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calc_fixed_dip(data)
Calculate the fixed component of the dipolar constant.

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calc_fixed_csa(data)
Calculate the fixed component of the CSA constants.

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comp_dip_const_func(data, bond_length)
Calculate the dipolar constant.

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comp_dip_const_grad(data, bond_length)
Calculate the derivative of the dipolar constant.

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comp_dip_const_hess(data, bond_length)
Calculate the second derivative of the dipolar constant.

source code

comp_csa_const_func(data, csa)
Calculate the CSA constant.

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comp_csa_const_grad(data, csa)
Calculate the derivative of the CSA constant.

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comp_csa_const_hess(data, params)
Calculate the second derivative of the CSA constant.

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comp_rex_const_func(rhoex, frq)
Calculate the Rex value.

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comp_rex_const_grad(frq)
Calculate the Rex gradient.

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comp_r2_dip_const(dip_const_data)
Calculate the R1 dipolar constant components.

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comp_r1_csa_const(csa_const_data)
Calculate the R1 CSA constant components.

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comp_r2_csa_const(csa_const_data)
Calculate the R2 CSA constant.

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comp_r1_dip_jw(jw_data, frq_num)
Calculate the R1 dipolar J(w) components.

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comp_r2_dip_jw(jw_data, frq_num)
Calculate the R2 dipolar J(w) components.

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comp_sigma_noe_dip_jw(jw_data, frq_num)
Calculate the sigma_noe dipolar J(w) components.

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comp_r1_csa_jw(jw_data, frq_num)
Calculate the R1 CSA J(w) components.

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comp_r2_csa_jw(jw_data, frq_num)
Calculate the R1 CSA J(w) components.

source code

Imports: pi, Float64, zeros

Function Details

[hide private]

ri_comps(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar J(w) components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    Dipolar constant components.
    CSA constant components.

ri_comps_rex(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar J(w) components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    Dipolar constant components.
    CSA constant components.

ri_comps_r(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    CSA constant components.

ri_comps_csa(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    Dipolar constant components.

ri_comps_r_csa(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.

ri_comps_r_rex(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    CSA constant components.

ri_comps_csa_rex(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    Dipolar constant components.

ri_comps_r_csa_rex(data, params)

source code

Calculate the ri function components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    None.

dri_comps(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar J(w) components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    Dipolar constant components.
    CSA constant components.

dri_comps_rex(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar J(w) components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    Dipolar constant components.
    CSA constant components.

dri_comps_r(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    CSA constant components.

dri_comps_csa(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    Dipolar constant components.

dri_comps_r_csa(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.

dri_comps_r_rex(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    CSA constant components.

dri_comps_csa_rex(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    Dipolar constant components.

dri_comps_r_csa_rex(data, params)

source code

Calculate the dri gradient components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
    Rex constant components.
Pre-calculated:
    None.

d2ri_comps(data, params)

source code

Calculate the d2ri Hessian components.

Calculated:
    Dipolar J(w) components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    Dipolar constant components.
    CSA constant components.

d2ri_comps_r(data, params)

source code

Calculate the d2ri Hessian components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    CSA constant components.

d2ri_comps_csa(data, params)

source code

Calculate the d2ri Hessian components.

Calculated:
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.
    Dipolar constant components.

d2ri_comps_r_csa(data, params)

source code

Calculate the d2ri Hessian components.

Calculated:
    Dipolar constant components.
    Dipolar J(w) components.
    CSA constant components.
    CSA J(w) components.
Pre-calculated:
    Rex constant components.

calc_fixed_dip(data)

source code

Calculate the fixed component of the dipolar constant.

                    / mu0  \ 2
dip_const_fixed  =  | ---- |  . (gH.gN.h_bar)**2
                    \ 4.pi /

calc_fixed_csa(data)

source code

Calculate the fixed component of the CSA constants.

                    wN**2
csa_const_fixed  =  -----
                      3

comp_dip_const_func(data, bond_length)

source code

Calculate the dipolar constant.

Dipolar constant
~~~~~~~~~~~~~~~~

                       1   / mu0  \ 2  (gH.gN.h_bar)**2
    dip_const_func  =  - . | ---- |  . ----------------
                       4   \ 4.pi /         <r**6>

comp_dip_const_grad(data, bond_length)

source code

Calculate the derivative of the dipolar constant.

Dipolar constant gradient
~~~~~~~~~~~~~~~~~~~~~~~~~

                         3   / mu0  \ 2  (gH.gN.h_bar)**2
    dip_const_grad  =  - - . | ---- |  . ----------------
                         2   \ 4.pi /         <r**7>

comp_dip_const_hess(data, bond_length)

source code

Calculate the second derivative of the dipolar constant.

Dipolar constant Hessian
~~~~~~~~~~~~~~~~~~~~~~~~

                       21   / mu0  \ 2  (gH.gN.h_bar)**2
    dip_const_hess  =  -- . | ---- |  . ----------------
                       2    \ 4.pi /         <r**8>

comp_csa_const_func(data, csa)

source code

Calculate the CSA constant.

CSA constant
~~~~~~~~~~~~

                       (wN.csa)**2
    csa_const_func  =  -----------
                            3

comp_csa_const_grad(data, csa)

source code

Calculate the derivative of the CSA constant.

CSA constant gradient
~~~~~~~~~~~~~~~~~~~~~

                       2.wN**2.csa
    csa_const_grad  =  -----------
                            3

comp_csa_const_hess(data, params)

source code

Calculate the second derivative of the CSA constant.

CSA constant Hessian
~~~~~~~~~~~~~~~~~~~~

                       2.wN**2
    csa_const_hess  =  -------
                          3

comp_rex_const_func(rhoex, frq)

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Calculate the Rex value.

Rex constant
~~~~~~~~~~~~

    rex_const_func  =  rhoex * wH**2

comp_rex_const_grad(frq)

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Calculate the Rex gradient.

Rex gradient
~~~~~~~~~~~~

    rex_const_grad  =  wH**2

comp_r2_dip_const(dip_const_data)

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Calculate the R1 dipolar constant components.

dip_const_func / 2

dip_const_grad / 2

dip_const_hess / 2

comp_r1_csa_const(csa_const_data)

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Calculate the R1 CSA constant components.

csa_const_func

csa_const_grad

csa_const_hess

comp_r2_csa_const(csa_const_data)

source code

Calculate the R2 CSA constant. components

csa_const_func / 6

csa_const_grad / 6

csa_const_hess / 6

comp_r1_dip_jw(jw_data, frq_num)

source code

Calculate the R1 dipolar J(w) components.

dip_Jw_R1_func  =  J(wH-wN) + 3J(wN) + 6J(wH+wN)

                   dJ(wH-wN)         dJ(wN)         dJ(wH+wN)
dip_Jw_R1_grad  =  ---------  +  3 . ------  +  6 . ---------
                      dJw             dJw              dJw

                   d2J(wH-wN)          d2J(wN)          d2J(wH+wN)
dip_Jw_R1_hess  =  ----------  +  3 . ---------  +  6 . ----------
                   dJwi.dJwj          dJwi.dJwj         dJwi.dJwj

comp_r2_dip_jw(jw_data, frq_num)

source code

Calculate the R2 dipolar J(w) components.

dip_Jw_R2_func  =  4J(0) + J(wH-wN) + 3J(wN) + 6J(wH) + 6J(wH+wN)

                       dJ(0)     dJ(wH-wN)         dJ(wN)         dJ(wH)         dJ(wH+wN)
dip_Jw_R2_grad  =  4 . -----  +  ---------  +  3 . ------  +  6 . ------  +  6 . ---------
                        dJw         dJw             dJw            dJw              dJw

                         d2J(0)      d2J(wH-wN)          d2J(wN)           d2J(wH)          d2J(wH+wN)
dip_Jw_R2_hess  =  4 . ---------  +  ----------  +  3 . ---------  +  6 . ---------  +  6 . ----------
                       dJwi.dJwj     dJwi.dJwj          dJwi.dJwj         dJwi.dJwj         dJwi.dJwj

comp_sigma_noe_dip_jw(jw_data, frq_num)

source code

Calculate the sigma_noe dipolar J(w) components.

dip_Jw_sigma_noe_func  =  6J(wH+wN) - J(wH-wN)

                              dJ(wH+wN)     dJ(wH-wN)
dip_Jw_sigma_noe_grad  =  6 . ---------  -  ---------
                                 dJw           dJw

                              d2J(wH+wN)     d2J(wH-wN)
dip_Jw_sigma_noe_hess  =  6 . ----------  -  ----------
                              dJwi.dJwj      dJwi.dJwj

comp_r1_csa_jw(jw_data, frq_num)

source code

Calculate the R1 CSA J(w) components.

csa_Jw_R1_func  =  J(wN)

                   dJ(wN)
csa_Jw_R1_grad  =  ------
                    dJw

                    d2J(wN)
csa_Jw_R1_hess  =  ---------
                   dJwi.dJwj

comp_r2_csa_jw(jw_data, frq_num)

source code

Calculate the R1 CSA J(w) components.

csa_Jw_R2_func  =  4J(0) + 3J(wN)

                       dJ(0)         dJ(wN)
csa_Jw_R2_grad  =  4 . -----  +  3 . ------
                        dJw           dJw

                         d2J(0)           d2J(wN)
csa_Jw_R2_hess  =  4 . ---------  +  3 . ---------
                       dJwi.dJwj         dJwi.dJwj