ffeatools.modules.FFEA_rod.anal_rod Class Reference

Public Member Functions
def	__init__ (self, rod)
def	get_deflection (self)
def	get_EI_from_deflection (self, force_applied)
def	get_persistence_length (self)
def	get_entire_rod_stretch_energy (self)
def	get_bending_response (self)
def	get_bending_response_mutual (self, rotate=False)
def	get_twist_amount (self, set_twist_amount=False)
def	get_equipartition (self)
def	get_constant_EI (self)
def	get_constant_parameter (self, constant_index)
def	get_starting_length (self)
def	get_average_quantities (self)
def	get_stretch_energy (self)
def	plot (self, force=None, temp=None)
def	persistence_segments (self)
def	do_stretch_symmetry_test (self)
def	do_bend_symmetry_test (self)
def	get_delta_r (self)
def	get_L_i (self)
def	get_absolute_length (self, starting_node, ending_node, frame, equil=False, path=True, non_path_axis=0)
def	whole_rod_avg (self, thing)
def	filter_x (self, thing, dimension)
def	apply_transformation_4x4 (self, pos_array, T)
def	align_to_equil (self)
def	thin (self, target_num_frames)
def	get_node_rmsd (self, align=False)
def	get_B_eigenvalues (self)
def	get_time_rmsd (self, is_aligned=False, max_frame_index=-1)
def	subdivide (self, iterations)
def	decimate (self, determine_simplification_func, target_length, margin=0.5)

Data Fields
	rod
	py_rod_math
	analytical_P
	analytical_deflection
	analytical_kbT
	get_p_i
	deflections
	EI_from_deflection
	p_i
	P
	equil_p_i
	stretching_energy
	bending_energy
	twist_amount
	twist_energy
	average_twist_energy
	EI
	starting_length
	stretch_energy
	delta_r_x
	delta_r_y
	delta_r_z
	delta_twist

Detailed Description

The rod analysis class. This is where the actual tests happen. It's initialised
using a rod object. It doesn't modify that object, but it does a load of
measurements on it. It also plots the results of those measurements.

Much like the rod itself, many quantities here are given as numpy arrays,
of the form [frame][element][x,y,z] or sometimes [frame][element][quantity].

For reference, the tests that it does are:
    - Equipartition of energy
    - Euler beam dynamics
    - Persistence length
    - Symmetry of energies and forces
    
The attributes are:
    rod: rod object.
    rod_math: instance of the py_rod_math object, containing rod-specific
    math functions.
    analytical_P: value of the persistence length converted analytically.
    analytical_deflection: deflection calculated analytically (for the bending
    beam test).
    analytical_kbT: analytical thermal energy, for the equipartition test
    p_i, equil_p_i - array containing values of p_i for each frame and element
    deflections: value of deflection for each frame (bending beam test)
    EI_from_deflection: value of EI calculated from euler beam theory for
    each frame.
    P: persistence length (again, given for each frame)
    bending_energy: bending energy between each adjacent pair of elements
    for each frame. Note that this is not actually calculated during the
    simulation (only the derivatives are).
    twist_amount: the value of delta_theta - equil_delta_theta in the
    twist energy formula.
    twist_energy: the value of twist energy between pairs of elements
    in the rod.
    p_i_extension: similar to the above, but this time for the quantity of
    r-r_equil for the stretching energy. There's also p_i_extension_x, y and
    z.
    average_twist_energy: twist energy averaged over the entire rod, given
    by frame.
    EI: the analytical value of EI, also known as the bending modulus B.
    starting_length: the length of the rod (along the contours) on the
    first frame.
    average_extension: the average p_i_extension for each frame. Also given
    in terms of x, y and z.
    delta_x, delta_y, delta_z, delta_twist - how much the rod has moved
    between each frame! 

Constructor & Destructor Documentation

__init__()

def ffeatools.modules.FFEA_rod.anal_rod.__init__	(		self,
			rod
	)

Initialize the rod analysis. This doens't do much, other than setting
a few internal variables and firing up an instane of py_rod_math.
Params: rod, an instance of FFEA_rod.
Returns: nothing.

Member Function Documentation

align_to_equil()

def ffeatools.modules.FFEA_rod.anal_rod.align_to_equil

(

self

)

Align the trajectory to the equilibrium configuration using the icp
(iterative closest point) library.
Params: none
Retruns: none, but updates self.rod.current_r

apply_transformation_4x4()

def ffeatools.modules.FFEA_rod.anal_rod.apply_transformation_4x4	(		self,
			pos_array,
			T
	)

Apply a 4x4 transformation matrix to our 2-D array of 3-D points. Returns
the newly translated array.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.align_to_equil(), and ffeatools.modules.FFEA_rod.anal_rod.get_node_rmsd().

decimate()

def ffeatools.modules.FFEA_rod.anal_rod.decimate	(		self,
			determine_simplification_func,
			target_length,
			margin = 0.5
	)

For a given rod or rod trajectory, reduce the number of nodes in that
trajectory, by averaging about nodes, grouped by their indices.
Params:
    determine_simplification_func: the function that reduces the number
    of nodes in an ndarray, normally ndc_extractor.determine_simplification
    target_length: the desired number of nodes. Note: the actual
    rod you get out might be a number nearby this but not exactly it,
    to try and make the step size (e.g. the number of nodes that are
    averaged together) even.
    margin: how much to adjust the target length to make the step size
    even.
Returns: noting. But updates all the self.rod arrays.

do_bend_symmetry_test()

def ffeatools.modules.FFEA_rod.anal_rod.do_bend_symmetry_test

(

self

)

For a rod created with the symmetry test function in rod_tests, this
checks that the energies and dynamics are symmetric about the central
node, for bend energy.
Params:none
returns: True if all tests pass, False otherwise, and prints some info.

do_stretch_symmetry_test()

def ffeatools.modules.FFEA_rod.anal_rod.do_stretch_symmetry_test

(

self

)

For a rod created with the symmetry test function in rod_tests, this
checks that the energies and dynamics are symmetric about the central
node, for stretch energy.
Params:none
returns: True if all tests pass, False otherwise, and prints some info.

filter_x()

def ffeatools.modules.FFEA_rod.anal_rod.filter_x	(		self,
			thing,
			dimension
	)

Given an array of form [frame][element][x,y,z], this returns an array
of the form [frame][element][thing], where thing is the quantitiy for
the dimension specified as a parameter.
Params: thing, the array to filter, and dimension, the dimension to
filter to.
Returns: the filtered array.

get_absolute_length()

def ffeatools.modules.FFEA_rod.anal_rod.get_absolute_length	(		self,
			starting_node,
			ending_node,
			frame,
			equil = False,
			path = True,
			non_path_axis = 0
	)

Get the length along the rod (the contour length) of a subset of the
rod, or the whole rod, in meters.
Params: starting noe, ending node - indices of the start and end
of the range of nodes to be measured.
Frame: index of the frame to be used.
Returns: length, a float.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

get_average_quantities()

def ffeatools.modules.FFEA_rod.anal_rod.get_average_quantities

(

self

)

Sets the average quantities as they are used in the equipartition test.
Basically identical to the equipartition test, only it also sets
self.average_extension_sq, which we need.
Params:none
Returns: none, but sets self.average_extension_sq, and also
average_extension_sq_x, average_extension_sq_y, average_extension_sq_z.

get_B_eigenvalues()

def ffeatools.modules.FFEA_rod.anal_rod.get_B_eigenvalues

(

self

)

Get the eigenvalues of the B matrix for each node.
Params: none
Returns: an array of the eigenvalues. Each B value will have two
eigenvalues, so the resulting array will be (n-2)x2, where n is the
number of nodes (-2 because the nodes at the end of the rod do not) have
bending energies associated with them!).

get_bending_response()

def ffeatools.modules.FFEA_rod.anal_rod.get_bending_response

(

self

)

Get the bending energy between adjacent rod elements for every pair of
rod elements in every frame. Mathematically, this is identical to what
goes on inside the rod simulation proper (although it happens 8x more there).
Params: none
Returns: none, but it populates self.bending_energy, an array.

get_bending_response_mutual()

def ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual	(		self,
			rotate = False
	)

Get the bending energy between adjacent rod elements for every pair of
rod elements in every frame, using the mutual parallel transport method.
Params: none
Returns: none, but it populates self.bending_energy, an array.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_equipartition().

get_constant_EI()

def ffeatools.modules.FFEA_rod.anal_rod.get_constant_EI

(

self

)

This returns the value of EI (basically the value of the diagonal elements
of B) but only if the rod is isotropic and the value of B is constant.
Parameters: none
Returns: none, but sets self.EI, a float.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_bending_response(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual(), and ffeatools.modules.FFEA_rod.anal_rod.plot().

get_constant_parameter()

def ffeatools.modules.FFEA_rod.anal_rod.get_constant_parameter	(		self,
			constant_index
	)

Get the value of a material parameter based on the index (0 for stretch,
1 for twist). Only if that parameter is constant for the whole rod and
the whole trajectory.
Params: constant index, an int.
Returns: the value of that parameter in SI units, a float.

get_deflection()

def ffeatools.modules.FFEA_rod.anal_rod.get_deflection

(

self

)

Get the vertical deflection away from the equilibrium at the end of the rod.
Used in the euler beam test. 
Params: none.
Returns: none, but it sets self.deflections, an array.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_EI_from_deflection().

get_delta_r()

def ffeatools.modules.FFEA_rod.anal_rod.get_delta_r

(

self

)

Get the value of delta_r from the rod dynamics by subtracting the
positions of the nth nodes from the nth plus 1th nodes.
Params: none
Returns: none, but sets delta_r_x, delta_r_y, delta_r_z, delta_twist,
all arrays.

get_EI_from_deflection()

def ffeatools.modules.FFEA_rod.anal_rod.get_EI_from_deflection	(		self,
			force_applied
	)

This gets the approximate value of EI (B) for rods with isotropic
bending response. W=(PL^3)/(3EI) where W is the deflection, P is the
force applied to the end of the beam, L is the beam length.
Params: force_applied, the force applied to the end of the beam in N (a
float).
Returns: none, but sets self.EI_from_deflection, an array.

get_entire_rod_stretch_energy()

def ffeatools.modules.FFEA_rod.anal_rod.get_entire_rod_stretch_energy

(

self

)

get_equipartition()

def ffeatools.modules.FFEA_rod.anal_rod.get_equipartition

(

self

)

This gets all the quantities needed for an equipartition test, including
stretching, bending and twisting energy. Basically, run this and then
plot(temp=300) for the full equipartition experience.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_average_quantities().

get_L_i()

def ffeatools.modules.FFEA_rod.anal_rod.get_L_i

(

self

)

get_node_rmsd()

def ffeatools.modules.FFEA_rod.anal_rod.get_node_rmsd	(		self,
			align = False
	)

Get the per-node RMSD for the rod. Otherwise known as the time-averaged
RMSD for each node.
Params: align - whether the trajectory has already been aligned to the
equilibrium configuration. If not, it uses the iterative closest point
algorithm to align them. Please note: this algorithm can get confused
with very bendy rods. If you see a gigantic spike in the middle of your
RMSD, then it's confused (easier to spot in get_time_rmsd).
Returns: the rmsd, a 1d numpy array indexed by node.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_time_rmsd().

get_persistence_length()

def ffeatools.modules.FFEA_rod.anal_rod.get_persistence_length

(

self

)

Get the value of the persistence length P from the current state of the
rod.
P = -L/log(<cos \theta>) where P is the persistence length, L is the
length of the rod, and cos \theta is the cosine of the angle between
the element at the start of the rod and the element at the end.
Params: none.
Returns: none, but populates self.P, an array containing a value for
the persistence length for each frame.

get_starting_length()

def ffeatools.modules.FFEA_rod.anal_rod.get_starting_length

(

self

)

Get the end to end length of the rod on the first frae.
Params: none.
Returns: none, but sets self.starting_length, a float.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

get_stretch_energy()

def ffeatools.modules.FFEA_rod.anal_rod.get_stretch_energy

(

self

)

Computes the stretch energy for the rod using the new discretisation-
independent formula.
Params: none
Returns: none, but sets self.stretch_energy

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_equipartition().

get_time_rmsd()

def ffeatools.modules.FFEA_rod.anal_rod.get_time_rmsd	(		self,
			is_aligned = False,
			max_frame_index = -1
	)

Get the time RMSD for the rod. That is, get the average RMSD of all the
nodes for each frame in the trajectory.
Params:
    is_aligned: whether the equilibrium and current structures are
    aligned or not. If they aren't aligned, they need to be, or you
    won't get best-fit RMSD, which is really the only useful RMSD.
    max_frame_index: find the rmsd for all frames up to this one.
Returns:
    the time rmsd, a 1d numpy array.

get_twist_amount()

def ffeatools.modules.FFEA_rod.anal_rod.get_twist_amount	(		self,
			set_twist_amount = False
	)

Get the twist energy between adjacent rod elements for every pair of
rod elements in every frame. Mathematically, this is identical to what
goes on inside the rod simulation proper (although it happens 8x more there).
Params: none
Returns: none, but it populates self.twist_energy, an array.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_equipartition().

persistence_segments()

def ffeatools.modules.FFEA_rod.anal_rod.persistence_segments

(

self

)

Todo: this is an alternative version of the persistence length calulation
that omits some of the worm-like chain assumptions.

plot()

def ffeatools.modules.FFEA_rod.anal_rod.plot	(		self,
			force = None,
			temp = None
	)

For any tests you've done, this will plot the results.
If you've run self.get_average_quantities(), it will plot the
equipartition results. If you've run get_persistence_length, it plots
those results, if you've run get_deflection, it plots that.
The plots are saved as PDFs whose names are based on the filename of
the loaded rod.
Params:
    force, the force applied to the end node in the bending beam test
    (a float)
    temp, the temperature of the rod in kelvin (needed for the equipartition
    and persistence length tests.

subdivide()

def ffeatools.modules.FFEA_rod.anal_rod.subdivide	(		self,
			iterations
	)

For a given rod (but not a trajectory!) create new nodes which are
linearly interpolated to be between the positions of the existing nodes.
Params: iterations - number of iterations to run. Each iteration
doubles the number of nodes in the rod.
Returns: nothing, but updates all the self.rod ndarrays.

thin()

def ffeatools.modules.FFEA_rod.anal_rod.thin	(		self,
			target_num_frames
	)

Remove frames from the trajectory.
Params: target_num_frames - the number of frames you desire.
Returns: nothing, but it changes all the self.rod arrays.
Also, like decimate, it might not give you exactly the number
of frames you asked for, because it goes for an even interval
instead.

whole_rod_avg()

def ffeatools.modules.FFEA_rod.anal_rod.whole_rod_avg	(		self,
			thing
	)

Given an array of form [frame][element][thing], this function returns
the average [thing] over every element for each frame.
Params: thing, an array.
Returns: the average over the whole rod, also an array.

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

Field Documentation

analytical_deflection

ffeatools.modules.FFEA_rod.anal_rod.analytical_deflection

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

analytical_kbT

ffeatools.modules.FFEA_rod.anal_rod.analytical_kbT

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

analytical_P

ffeatools.modules.FFEA_rod.anal_rod.analytical_P

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

average_twist_energy

ffeatools.modules.FFEA_rod.anal_rod.average_twist_energy

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

bending_energy

ffeatools.modules.FFEA_rod.anal_rod.bending_energy

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual(), and ffeatools.modules.FFEA_rod.anal_rod.plot().

deflections

ffeatools.modules.FFEA_rod.anal_rod.deflections

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_EI_from_deflection(), and ffeatools.modules.FFEA_rod.anal_rod.plot().

delta_r_x

ffeatools.modules.FFEA_rod.anal_rod.delta_r_x

delta_r_y

ffeatools.modules.FFEA_rod.anal_rod.delta_r_y

delta_r_z

ffeatools.modules.FFEA_rod.anal_rod.delta_r_z

delta_twist

ffeatools.modules.FFEA_rod.anal_rod.delta_twist

EI

ffeatools.modules.FFEA_rod.anal_rod.EI

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

EI_from_deflection

ffeatools.modules.FFEA_rod.anal_rod.EI_from_deflection

equil_p_i

ffeatools.modules.FFEA_rod.anal_rod.equil_p_i

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_absolute_length(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual(), ffeatools.modules.FFEA_rod.anal_rod.get_equipartition(), ffeatools.modules.FFEA_rod.anal_rod.get_L_i(), ffeatools.modules.FFEA_rod.anal_rod.get_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_twist_amount(), ffeatools.modules.FFEA_rod.anal_rod.persistence_segments(), and ffeatools.modules.FFEA_rod.anal_rod.thin().

get_p_i

ffeatools.modules.FFEA_rod.anal_rod.get_p_i

Referenced by ffeatools.modules.FFEA_rod.anal_rod.do_stretch_symmetry_test(), ffeatools.modules.FFEA_rod.anal_rod.get_absolute_length(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual(), ffeatools.modules.FFEA_rod.anal_rod.get_entire_rod_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_equipartition(), ffeatools.modules.FFEA_rod.anal_rod.get_L_i(), ffeatools.modules.FFEA_rod.anal_rod.get_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_twist_amount(), and ffeatools.modules.FFEA_rod.anal_rod.persistence_segments().

P

ffeatools.modules.FFEA_rod.anal_rod.P

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

p_i

ffeatools.modules.FFEA_rod.anal_rod.p_i

Referenced by ffeatools.modules.FFEA_rod.anal_rod.do_stretch_symmetry_test(), ffeatools.modules.FFEA_rod.anal_rod.get_absolute_length(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual(), ffeatools.modules.FFEA_rod.anal_rod.get_entire_rod_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_equipartition(), ffeatools.modules.FFEA_rod.anal_rod.get_persistence_length(), ffeatools.modules.FFEA_rod.anal_rod.get_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_twist_amount(), ffeatools.modules.FFEA_rod.anal_rod.persistence_segments(), and ffeatools.modules.FFEA_rod.anal_rod.thin().

py_rod_math

ffeatools.modules.FFEA_rod.anal_rod.py_rod_math

Referenced by ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual().

rod

ffeatools.modules.FFEA_rod.anal_rod.rod

Referenced by ffeatools.modules.FFEA_rod.anal_rod.align_to_equil(), ffeatools.modules.FFEA_rod.anal_rod.decimate(), ffeatools.modules.FFEA_rod.anal_rod.do_bend_symmetry_test(), ffeatools.modules.FFEA_rod.anal_rod.do_stretch_symmetry_test(), ffeatools.modules.FFEA_rod.anal_rod.get_absolute_length(), ffeatools.modules.FFEA_rod.anal_rod.get_B_eigenvalues(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response(), ffeatools.modules.FFEA_rod.anal_rod.get_bending_response_mutual(), ffeatools.modules.FFEA_rod.anal_rod.get_constant_EI(), ffeatools.modules.FFEA_rod.anal_rod.get_constant_parameter(), ffeatools.modules.FFEA_rod.anal_rod.get_deflection(), ffeatools.modules.FFEA_rod.anal_rod.get_EI_from_deflection(), ffeatools.modules.FFEA_rod.anal_rod.get_entire_rod_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_equipartition(), ffeatools.modules.FFEA_rod.anal_rod.get_L_i(), ffeatools.modules.FFEA_rod.anal_rod.get_node_rmsd(), ffeatools.modules.FFEA_rod.anal_rod.get_starting_length(), ffeatools.modules.FFEA_rod.anal_rod.get_stretch_energy(), ffeatools.modules.FFEA_rod.anal_rod.get_time_rmsd(), ffeatools.modules.FFEA_rod.anal_rod.get_twist_amount(), ffeatools.modules.FFEA_rod.anal_rod.persistence_segments(), ffeatools.modules.FFEA_rod.anal_rod.plot(), ffeatools.modules.FFEA_rod.anal_rod.subdivide(), and ffeatools.modules.FFEA_rod.anal_rod.thin().

starting_length

ffeatools.modules.FFEA_rod.anal_rod.starting_length

stretch_energy

ffeatools.modules.FFEA_rod.anal_rod.stretch_energy

Referenced by ffeatools.modules.FFEA_rod.anal_rod.plot().

stretching_energy

ffeatools.modules.FFEA_rod.anal_rod.stretching_energy

twist_amount

ffeatools.modules.FFEA_rod.anal_rod.twist_amount

twist_energy

ffeatools.modules.FFEA_rod.anal_rod.twist_energy

---

The documentation for this class was generated from the following file:

• FFEA_rod.py