PMFT Module¶

The PMFT Module allows for the calculation of the Potential of Mean Force and Torque (PMFT) [Cit2] in a number of different coordinate systems.

Note

the coordinate system in which the calculation is performed is not the same as the coordinate system in which particle positions and orientations should be supplied; only certain coordinate systems are available for certain particle positions and orientations:

2D particle coordinates (position: [x, y, 0], orientation: \(\theta\)):
- X, Y
- X, Y, \(\theta_2\)
- \(r\), \(\theta_1\), \(\theta_2\)
3D particle coordinates -> X, Y, Z

Coordinate System: \(x\), \(y\), \(\theta_2\)¶

class freud.pmft.PMFTXYT(x_max, y_max, n_x, n_y, n_t)¶

Computes the PMFT [Cit2] for a given set of points.

A given set of reference points is given around which the PCF is computed and averaged in a sea of data points. Computing the PCF results in a pcf array listing the value of the PCF at each given \(x\), \(y\), \(\theta\) listed in the x, y, and t arrays.

The values of x, y, t to compute the pcf at are controlled by x_max, y_max and n_bins_x, n_bins_y, n_bins_t parameters to the constructor. x_max, y_max determine the minimum/maximum x, y values (\(\min \left( \theta \right) = 0\), (\(\max \left( \theta \right) = 2\pi\)) at which to compute the pcf and n_bins_x, n_bins_y, n_bins_t is the number of bins in x, y, t.

Note

2D: This calculation is defined for 2D systems only. However particle positions are still required to be (x, y, 0)

Module author: Eric Harper <harperic@umich.edu>

Parameters:	x_max (float) – maximum x distance at which to compute the pmft y_max (float) – maximum y distance at which to compute the pmft n_x (unsigned int) – number of bins in x n_y (unsigned int) – number of bins in y n_t (unsigned int) – number of bins in t

PCF¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

PMFT¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

T¶

Get the array of t-values for the PCF histogram

Returns:	bin centers of t-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta}\right)\), dtype= `numpy.float32`

X¶

Get the array of x-values for the PCF histogram

Returns:	bin centers of x-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{x}\right)\), dtype= `numpy.float32`

Y¶

Get the array of y-values for the PCF histogram

Returns:	bin centers of y-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

accumulate(self, box, ref_points, ref_orientations, points, orientations, nlist=None)¶

Calculates the positional correlation function and adds to the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of particles to use in calculation
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

bin_counts¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.uint32`

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)¶

Calculates the positional correlation function for the given points. Will overwrite the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of particles to use in calculation
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

getBinCounts(self)¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta}, N_{y}, N_{x}\right)\), dtype= `numpy.uint32`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box`

getJacobian(self)¶

Get the jacobian used in the pmft

Returns:	Inverse Jacobian
Return type:	float

getNBinsT(self)¶

Get the number of bins in the t-dimension of histogram

Returns:	\(N_{\theta}\)
Return type:	unsigned int

getNBinsX(self)¶

Get the number of bins in the x-dimension of histogram

Returns:	\(N_x\)
Return type:	unsigned int

getNBinsY(self)¶

Get the number of bins in the y-dimension of histogram

Returns:	\(N_y\)
Return type:	unsigned int

getPCF(self)¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta}, N_{y}, N_{x}\right)\), dtype= `numpy.float32`

getPMFT(self)¶

Get the Potential of Mean Force and Torque.

Returns:	PMFT
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta}, N_{y}, N_{x}\right)\), dtype= `numpy.float32`

getRCut(self)¶

Get the r_cut value used in the cell list

Returns:	r_cut
Return type:	float

getT(self)¶

Get the array of t-values for the PCF histogram

Returns:	bin centers of t-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta}\right)\), dtype= `numpy.float32`

getX(self)¶

Get the array of x-values for the PCF histogram

Returns:	bin centers of x-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{x}\right)\), dtype= `numpy.float32`

getY(self)¶

Get the array of y-values for the PCF histogram

Returns:	bin centers of y-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

jacobian¶

Get the jacobian used in the pmft

Returns:	Inverse Jacobian
Return type:	float

n_bins_T¶

Get the number of bins in the T-dimension of histogram

Returns:	\(N_{\theta}\)
Return type:	unsigned int

n_bins_X¶

Get the number of bins in the x-dimension of histogram

Returns:	\(N_x\)
Return type:	unsigned int

n_bins_Y¶

Get the number of bins in the y-dimension of histogram

Returns:	\(N_y\)
Return type:	unsigned int

r_cut¶

Get the r_cut value used in the cell list

Returns:	r_cut
Return type:	float

reducePCF(self)¶: Reduces the histogram in the values over N processors to a single histogram. This is called automatically by freud.pmft.PMFTXYT.getPCF().

resetPCF(self)¶: Resets the values of the pcf histograms in memory

Coordinate System: \(x\), \(y\)¶

class freud.pmft.PMFTXY2D(x_max, y_max, n_x, n_y)¶

Computes the PMFT [Cit2] for a given set of points.

A given set of reference points is given around which the PCF is computed and averaged in a sea of data points. Computing the PCF results in a pcf array listing the value of the PCF at each given \(x\), \(y\) listed in the x and y arrays.

The values of x and y to compute the pcf at are controlled by x_max, y_max, n_x, and n_y parameters to the constructor. x_max and y_max determine the minimum/maximum distance at which to compute the pcf and n_x and n_y are the number of bins in x and y.

Note

2D: This calculation is defined for 2D systems only.

Module author: Eric Harper <harperic@umich.edu>

Parameters:	x_max (float) – maximum x distance at which to compute the pmft y_max (float) – maximum y distance at which to compute the pmft n_x (unsigned int) – number of bins in x n_y (unsigned int) – number of bins in y

PCF¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

PMFT¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

X¶

Get the array of x-values for the PCF histogram

Returns:	bin centers of x-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{x}\right)\), dtype= `numpy.float32`

Y¶

Get the array of y-values for the PCF histogram

Returns:	bin centers of y-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

accumulate(self, box, ref_points, ref_orientations, points, orientations, nlist=None)¶

Calculates the positional correlation function and adds to the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – orientations of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – orientations of particles to use in calculation
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

bin_counts¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.uint32`

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)¶

Calculates the positional correlation function for the given points. Will overwrite the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – orientations of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – orientations of particles to use in calculation
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

getBinCounts(self)¶

Get the raw bin counts (non-normalized).

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}, N_{x}\right)\), dtype= `numpy.uint32`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box`

getJacobian(self)¶

Get the jacobian

Returns:	jacobian
Return type:	float

getNBinsX(self)¶

Get the number of bins in the x-dimension of histogram

Returns:	\(N_x\)
Return type:	unsigned int

getNBinsY(self)¶

Get the number of bins in the y-dimension of histogram

Returns:	\(N_y\)
Return type:	unsigned int

getPCF(self)¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}, N_{y}\right)\), dtype= `numpy.float32`

getPMFT(self)¶

Get the Potential of Mean Force and Torque.

Returns:	PMFT
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}, N_{x}\right)\), dtype= `numpy.float32`

getRCut(self)¶

Get the r_cut value used in the cell list

Returns:	r_cut
Return type:	float

getX(self)¶

Get the array of x-values for the PCF histogram

Returns:	bin centers of x-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{x}\right)\), dtype= `numpy.float32`

getY(self)¶

Get the array of y-values for the PCF histogram

Returns:	bin centers of y-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

jacobian¶

Get the jacobian used in the pmft

Returns:	Inverse Jacobian
Return type:	float

n_bins_X¶

Get the number of bins in the x-dimension of histogram

Returns:	\(N_x\)
Return type:	unsigned int

n_bins_Y¶

Get the number of bins in the y-dimension of histogram

Returns:	\(N_y\)
Return type:	unsigned int

r_cut¶

Get the r_cut value used in the cell list

Returns:	r_cut
Return type:	float

reducePCF(self)¶: Reduces the histogram in the values over N processors to a single histogram. This is called automatically by freud.pmft.PMFTXY2D.getPCF().

resetPCF(self)¶: Resets the values of the pcf histograms in memory

Coordinate System: \(r\), \(\theta_1\), \(\theta_2\)¶

class freud.pmft.PMFTR12(r_max, n_r, n_t1, n_t2)¶

Computes the PMFT [Cit2] for a given set of points.

A given set of reference points is given around which the PCF is computed and averaged in a sea of data points. Computing the PCF results in a pcf array listing the value of the PCF at each given \(r\), \(\theta_1\), \(\theta_2\) listed in the r, t1, and t2 arrays.

The values of r, t1, t2 to compute the pcf at are controlled by r_max and nbins_r, nbins_t1, nbins_t2 parameters to the constructor. rmax determines the minimum/maximum r (\(\min \left( \theta_1 \right) = \min \left( \theta_2 \right) = 0\), (\(\max \left( \theta_1 \right) = \max \left( \theta_2 \right) = 2\pi\)) at which to compute the pcf and nbins_r, nbins_t1, nbins_t2 is the number of bins in r, t1, t2.

Note

2D: This calculation is defined for 2D systems only. However particle positions are still required to be (x, y, 0)

Module author: Eric Harper <harperic@umich.edu>

Parameters:	r_max (float) – maximum distance at which to compute the pmft n_r (unsigned int) – number of bins in r n_t1 (unsigned int) – number of bins in t1 n_t2 (unsigned int) – number of bins in t2

PCF¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

PMFT¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

R¶

Get the array of r-values for the PCF histogram

Returns:	bin centers of r-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}\right)\), dtype= `numpy.float32`

T1¶

Get the array of T1-values for the PCF histogram

Returns:	bin centers of T1-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta1}\right)\), dtype= `numpy.float32`

T2¶

Get the array of T2-values for the PCF histogram

Returns:	bin centers of T2-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta1}\right)\), dtype= `numpy.float32`

accumulate(self, box, ref_points, ref_orientations, points, orientations, nlist=None)¶

Calculates the positional correlation function and adds to the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of particles to use in calculation
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

bin_counts¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.uint32`

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)¶

Calculates the positional correlation function for the given points. Will overwrite the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}\right)\), dtype= numpy.float32) – angles of particles to use in calculation
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

getBinCounts(self)¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.uint32`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

getInverseJacobian(self)¶

Get the inverse jacobian used in the pmft

Returns:	Inverse Jacobian
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

getNBinsR(self)¶

Get the number of bins in the r-dimension of histogram

Returns:	\(N_r\)
Return type:	unsigned int

getNBinsT1(self)¶

Get the number of bins in the T1-dimension of histogram

Returns:	\(N_{\theta_1}\)
Return type:	unsigned int

getNBinsT2(self)¶

Get the number of bins in the T2-dimension of histogram

Returns:	\(N_{\theta_2}\)
Return type:	unsigned int

getPCF(self)¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

getPMFT(self)¶

Get the Potential of Mean Force and Torque.

Returns:	PMFT
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

getR(self)¶

Get the array of r-values for the PCF histogram

Returns:	bin centers of r-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}\right)\), dtype= `numpy.float32`

getRCut(self)¶

Get the r_cut value used in the cell list

Returns:	r_cut
Return type:	float

getT1(self)¶

Get the array of T1-values for the PCF histogram

Returns:	bin centers of T1-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta1}\right)\), dtype= `numpy.float32`

getT2(self)¶

Get the array of T2-values for the PCF histogram

Returns:	bin centers of T2-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta2}\right)\), dtype= `numpy.float32`

inverse_jacobian¶

Get the array of T2-values for the PCF histogram

Returns:	bin centers of T2-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{\theta1}\right)\), dtype= `numpy.float32`

n_bins_T1¶

Get the number of bins in the T1-dimension of histogram

Returns:	\(N_{\theta_1}\)
Return type:	unsigned int

n_bins_T2¶

Get the number of bins in the T2-dimension of histogram

Returns:	\(N_{\theta_2}\)
Return type:	unsigned int

n_bins_r¶

Get the number of bins in the r-dimension of histogram

Returns:	\(N_r\)
Return type:	unsigned int

r_cut¶

Get the r_cut value used in the cell list

Returns:	r_cut
Return type:	float

reducePCF(self)¶: Reduces the histogram in the values over N processors to a single histogram. This is called automatically by freud.pmft.PMFTR12.getPCF().

resetPCF(self)¶: Resets the values of the pcf histograms in memory

Coordinate System: \(x\), \(y\), \(z\)¶

class freud.pmft.PMFTXYZ(x_max, y_max, z_max, n_x, n_y, n_z)¶

Computes the PMFT [Cit2] for a given set of points.

A given set of reference points is given around which the PCF is computed and averaged in a sea of data points. Computing the PCF results in a pcf array listing the value of the PCF at each given \(x\), \(y\), \(z\), listed in the x, y, and z arrays.

The values of x, y, z to compute the pcf at are controlled by x_max, y_max, z_max, n_x, n_y, and n_z parameters to the constructor. x_max, y_max, and z_max determine the minimum/maximum distance at which to compute the pcf and n_x, n_y, n_z is the number of bins in x, y, z.

Note

3D: This calculation is defined for 3D systems only.

Module author: Eric Harper <harperic@umich.edu>

Parameters:

x_max (float) – maximum x distance at which to compute the pmft
y_max (float) – maximum y distance at which to compute the pmft
z_max (float) – maximum z distance at which to compute the pmft
n_x (unsigned int) – number of bins in x
n_y (unsigned int) – number of bins in y
n_z (unsigned int) – number of bins in z
shiftvec (list) – vector pointing from [0,0,0] to the center of the pmft

PCF¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

PMFT¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.float32`

X¶

Get the array of x-values for the PCF histogram

Returns:	bin centers of x-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{x}\right)\), dtype= `numpy.float32`

Y¶

Get the array of y-values for the PCF histogram

Returns:	bin centers of y-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

Z¶

Get the array of z-values for the PCF histogram

Returns:	bin centers of z-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

accumulate(self, box, ref_points, ref_orientations, points, orientations, face_orientations=None, nlist=None)¶

Calculates the positional correlation function and adds to the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}, 4\right)\), dtype= numpy.float32) – orientations of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}, 4\right)\), dtype= numpy.float32) – orientations of particles to use in calculation
face_orientations (numpy.ndarray, shape= \(\left( \left(N_{particles}, \right), N_{faces}, 4\right)\), dtype= numpy.float32) – Optional - orientations of particle faces to account for particle symmetry. * If not supplied by user, unit quaternions will be supplied. * If a 2D array of shape (\(N_f\), \(4\)) or a 3D array of shape (1, \(N_f\), \(4\)) is supplied, the supplied quaternions will be broadcast for all particles

bin_counts¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{r}, N_{\theta1}, N_{\theta2}\right)\), dtype= `numpy.uint32`

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

compute(self, box, ref_points, ref_orientations, points, orientations, face_orientations, nlist=None)¶

Calculates the positional correlation function for the given points. Will overwrite the current histogram.

Parameters:

box (freud.box.Box) – simulation box
ref_points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – reference points to calculate the local density
ref_orientations (numpy.ndarray, shape= \(\left(N_{particles}, 4\right)\), dtype= numpy.float32) – orientations of reference points to use in calculation
points (numpy.ndarray, shape= \(\left(N_{particles}, 3\right)\), dtype= numpy.float32) – points to calculate the local density
orientations (numpy.ndarray, shape= \(\left(N_{particles}, 4\right)\), dtype= numpy.float32) – orientations of particles to use in calculation
face_orientations (numpy.ndarray, shape= \(\left( \left(N_{particles}, \right), N_{faces}, 4\right)\), dtype= numpy.float32) – orientations of particle faces to account for particle symmetry
nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds

getBinCounts(self)¶

Get the raw bin counts.

Returns:	Bin Counts
Return type:	`numpy.ndarray`, shape= \(\left(N_{z}, N_{y}, N_{x}\right)\), dtype= `numpy.uint32`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box`

getJacobian(self)¶

Get the jacobian

Returns:	jacobian
Return type:	float

getNBinsX(self)¶

Get the number of bins in the x-dimension of histogram

Returns:	\(N_x\)
Return type:	unsigned int

getNBinsY(self)¶

Get the number of bins in the y-dimension of histogram

Returns:	\(N_y\)
Return type:	unsigned int

getNBinsZ(self)¶

Get the number of bins in the z-dimension of histogram

Returns:	\(N_z\)
Return type:	unsigned int

getPCF(self)¶

Get the positional correlation function.

Returns:	PCF
Return type:	`numpy.ndarray`, shape= \(\left(N_{z}, N_{y}, N_{x}\right)\), dtype= `numpy.float32`

getPMFT(self)¶

Get the Potential of Mean Force and Torque.

Returns:	PMFT
Return type:	`numpy.ndarray`, shape= \(\left(N_{z}, N_{y}, N_{x}\right)\), dtype= `numpy.float32`

getX(self)¶

Get the array of x-values for the PCF histogram

Returns:	bin centers of x-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{x}\right)\), dtype= `numpy.float32`

getY(self)¶

Get the array of y-values for the PCF histogram

Returns:	bin centers of y-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{y}\right)\), dtype= `numpy.float32`

getZ(self)¶

Get the array of z-values for the PCF histogram

Returns:	bin centers of z-dimension of histogram
Return type:	`numpy.ndarray`, shape= \(\left(N_{z}\right)\), dtype= `numpy.float32`

jacobian¶

Get the jacobian used in the pmft

Returns:	Inverse Jacobian
Return type:	float

n_bins_X¶

Get the number of bins in the x-dimension of histogram

Returns:	\(N_x\)
Return type:	unsigned int

n_bins_Y¶

Get the number of bins in the y-dimension of histogram

Returns:	\(N_y\)
Return type:	unsigned int

n_bins_Z¶

Get the number of bins in the z-dimension of histogram

Returns:	\(N_z\)
Return type:	unsigned int

reducePCF(self)¶: Reduces the histogram in the values over N processors to a single histogram. This is called automatically by freud.pmft.PMFTXYZ.getPCF().

resetPCF(self)¶: Resets the values of the pcf histograms in memory