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The community-run support site for relax, a program for the study of molecular dynamics using experimental NMR data.
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These are the first and second partial derivatives of the equations of the DPL94 relaxation dispersion model.
Equation
[math]
\mathrm{R}_{1\rho}= \mathrm{R}_1\cos^2\theta + \left( \mathrm{R}_{1\rho}{´} + \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) \sin^2\theta
[/math]
Jacobian
sympy
<source lang="python">
from sympy import *
- In contrast to other Computer Algebra Systems, in SymPy you have to declare symbolic variables explicitly:
R1 = Symbol('R1')
theta = Symbol('theta')
R1rho_p = Symbol('R1rho_p')
phi_ex = Symbol('phi_ex')
kex = Symbol('kex')
we = Symbol('we')
- Define function
f = R1 * cos(theta)**2 + (R1rho_p + ( (phi_ex * kex) / (kex**2 + we**2) ) ) * sin(theta)**2
print("Now calculate the Jacobian. ..→
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