mythos.observables.wlc
======================

.. py:module:: mythos.observables.wlc

.. autoapi-nested-parse::

   Utility functions for computing worm-like chain (WLC) fit.



Functions
---------

.. autoapisummary::

   mythos.observables.wlc.coth
   mythos.observables.wlc.calculate_extension
   mythos.observables.wlc.loss
   mythos.observables.wlc.fit_wlc


Module Contents
---------------

.. py:function:: coth(x: mythos.utils.types.ARR_OR_SCALAR) -> mythos.utils.types.ARR_OR_SCALAR

   Hyperbolic cotangent function.


.. py:function:: calculate_extension(force: mythos.utils.types.ARR_OR_SCALAR, l0: mythos.utils.types.ARR_OR_SCALAR, lp: mythos.utils.types.ARR_OR_SCALAR, k: mythos.utils.types.ARR_OR_SCALAR, kT: float) -> mythos.utils.types.ARR_OR_SCALAR

   Computes the extension under a specified force under the wormlike chain (WLC) model.

   Via the model of Odijk, the extension of an extensible wormlike chain (WLC) under a force
   F can be computed as

   .. math::
     x = L_0 \left (1 + \frac{F}{K} - \frac{kT}{2F} [1 + y\coth y] \right)

   where

   .. math::
     y = \left( \frac{FL_0^2}{L_p kT} \right)^{1/2}

   where `L_0` is the contour length and `L_p` is the persistence length.
   This function computes implements this model for computing the extension.

   :param force: the force applied to the duplex
   :type force: jd_types.ARR_OR_SCALAR
   :param l0: the contour length
   :type l0: jd_types.ARR_OR_SCALAR
   :param lp: the persistence length
   :type lp: jd_types.ARR_OR_SCALAR
   :param k: the extensional modulus
   :type k: jd_types.ARR_OR_SCALAR
   :param kT: the temperature
   :type kT: float

   :returns: the predicted extension
   :rtype: jd_types.ARR_OR_SCALAR


.. py:function:: loss(coeffs: jax.numpy.ndarray, extensions: jax.numpy.ndarray, forces: jax.numpy.ndarray, kT: float) -> jax.numpy.ndarray

   An objective function for the WLC model compatible with JAX solvers.

   :param coeffs: The parameters of the WLC model, ordered as [L_0, L_p, K]
   :type coeffs: jnp.ndarray
   :param extensions: The measured extensions (via simulation) to which we are fitting the model
   :type extensions: jnp.ndarray
   :param forces: The forces under which the extensions were measured
   :type forces: jnp.ndarray
   :param kT: the temperature
   :type kT: float

   :returns: the residual for each measured extension
   :rtype: jnp.ndarray


.. py:function:: fit_wlc(extensions: jax.numpy.ndarray, forces: jax.numpy.ndarray, init_guess: jax.numpy.ndarray, kT: float, *, implicit_diff: bool = True) -> jax.numpy.ndarray

   Fit the WLC model via nonlinear least squares given a set of forces and measured extensions.

   :param extensions: The measured extensions (via simulation) to which we are fitting the model
   :type extensions: jnp.ndarray
   :param forces: The forces under which the extensions were measured
   :type forces: jnp.ndarray
   :param init_guess: An initial guess for the parameters of the WLC model, ordered as [L_0, L_p, K]
   :type init_guess: jnp.ndarray
   :param kT: the temperature
   :type kT: float
   :param implicit_diff: Whether or not to use implicit differentiation for the numerical solver
   :type implicit_diff: bool

   :returns: the fit parameters of the WLC model, ordered as [L_0, L_p, K]
   :rtype: jnp.ndarray