NEML2 2.1.0
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Classes | Functions | Variables
neml2.postprocessing.polefigure Namespace Reference

Classes

class  StereographicProjection
class  LambertProjection
class  IPFReduction

Functions

 arbitrary_hemispherical_quadrature (points, rtol=1e-5, atol=1e-8)
 symmetry_operators_as_R2 (orbifold, device=torch.device("cpu"))
 pole_figure_odf (odf, pole, projection="stereographic", crystal_symmetry="1", nradial=20, ntheta=40, nquad=50, nchunk=1000, offset_fraction=1e-2)
 pretty_plot_pole_figure_odf (odf, pole, projection="stereographic", crystal_symmetry="1", nradial=20, ntheta=40, nquad=50, nchunk=1000, limits=None, ncontour=20)
 pole_figure_points (orientations, pole, projection="stereographic", crystal_symmetry="1", sample_symmetry="1")
 cart2polar (v)
 pretty_plot_pole_figure_points (orientations, pole, projection="stereographic", crystal_symmetry="1", sample_symmetry="1", point_size=10.0)
 inverse_pole_figure_points (orientations, direction, projection="stereographic", crystal_symmetry="1", sample_symmetry="1", reduction=IPFReduction())
 pretty_plot_inverse_pole_figure (orientations, direction, projection="stereographic", crystal_symmetry="1", sample_symmetry="1", reduction=IPFReduction(), point_size=10.0, axis_labels=["100", "110", "111"], nline=100, lw=2.0)

Variables

dict available_projections

Function Documentation

◆ arbitrary_hemispherical_quadrature()

arbitrary_hemispherical_quadrature ( points,
rtol = 1e-5,
atol = 1e-8 ) 
Calculate the weights for a spherical quadrature rule on the upper hemisphere

Args:
    points (torch.tensor): tensor of shape (..., 3) of cartesian points on the upper hemisphere

Keyword Args:
    rtol (float): relative tolerance for determining if points are on the equator
    atol (float): absolute tolerance for determining if points are on the equator

Returns:
    torch.tensor: tensor of shape (...) giving the weights

◆ cart2polar()

cart2polar ( v) 
Convert cartesian 2D points to polar coordinates

Args:
    v (torch.tensor): tensor of shape (...,2)

◆ inverse_pole_figure_points()

inverse_pole_figure_points ( orientations,
direction,
projection = "stereographic",
crystal_symmetry = "1",
sample_symmetry = "1",
reduction = IPFReduction() ) 
Project points onto an inverse pole figure

Args:
    orientations (torch.tensor or neml2.tensors.Rot): tensor of orientation as *modified* Rodrigues
        parameters in the *active* convention with arbitrary batch shape
    direction (torch.tensor or neml2.tensors.Vec): pole to project, must broadcast with orientations

Keyword Args:
    projection (str): which projection to use
    crystal_symmetry (str): crystal symmetry to apply
    sample_symmetry (str): sample symmetry to appy
    reduction (IPFReduction): function to reduce the poles to a fundamental region

◆ pole_figure_odf()

pole_figure_odf ( odf,
pole,
projection = "stereographic",
crystal_symmetry = "1",
nradial = 20,
ntheta = 40,
nquad = 50,
nchunk = 1000,
offset_fraction = 1e-2 ) 
Project an ODF onto a pole figure

Args:
    odf (neml2.odf.ODF): ODF to project
    pole (torch.tensor or neml2.tensors.Vec): pole to project

Keyword Args:
    projection (str): which polar projection to use, options are "stereographic" and "lambert"
    crystal_symmetry (str): string giving the orbifold notation for the crystal symmetry to apply to the base orientations, default "1"
    nradial (int): number of radial points to use
    ntheta (int): number of angular points to use
    nquad (int): number of points to integrate the pole figure
    nchunk (int): subbatch size to use in evaluating odf
    offset_fraction (float): fraction of the radial range to offset the pole figure to avoid singularities
Returns:
    (values, mesh): tuple of the projected values and the (theta, R) mesh points used to make a contour plot

◆ pole_figure_points()

pole_figure_points ( orientations,
pole,
projection = "stereographic",
crystal_symmetry = "1",
sample_symmetry = "1" ) 
Project crystal orientations to points on a pole figure

Args:
    orientations (torch.tensor or neml2.tensors.Rot): tensor of orientations as *modified* Rodrigues
        parameters in the *active* convention with arbitrary batch shape.
    pole (torch.tensor or neml2.tensors.Vec): pole to project, must broadcast with orientations

Keyword Args:
    projection (str): which polar projection to use, options are "stereographic" and "lambert"
    crystal_symmetry (str): string giving the orbifold notation for the crystal symmetry to apply to the base orientations, default "1"
    sample_symmetry (str): string giving the orbifold notation for the sample symmetry to apply to the projected points, default "1"

Returns:
    torch.tensor: tensor with same batch shape as orientations but with end dimension (2,) giving each point

◆ pretty_plot_inverse_pole_figure()

pretty_plot_inverse_pole_figure ( orientations,
direction,
projection = "stereographic",
crystal_symmetry = "1",
sample_symmetry = "1",
reduction = IPFReduction(),
point_size = 10.0,
axis_labels = ["100", "110", "111"],
nline = 100,
lw = 2.0 ) 
Project and then make a pretty plot for an inverse pole figure

Args:
    orientations (torch.tensor or neml2.tensors.Rot): tensor of orientation as *modified* Rodrigues
        parameters in the *active* convention with arbitrary batch shape
    direction (torch.tensor or neml2.tensors.Vec): pole to project, must broadcast with orientations

Keyword Args:
    projection (str): which projection to use
    crystal_symmetry (str): crystal symmetry to apply
    sample_symmetry (str): sample symmetry to appy
    reduction (IPFReduction): function to reduce the poles to a fundamental region
    point_size (float): size of points
    axis_labels (list of str): labels for the three corners
    nline (int): resolution for drawing lines
    lw (float): line width for lines

◆ pretty_plot_pole_figure_odf()

pretty_plot_pole_figure_odf ( odf,
pole,
projection = "stereographic",
crystal_symmetry = "1",
nradial = 20,
ntheta = 40,
nquad = 50,
nchunk = 1000,
limits = None,
ncontour = 20 ) 
Project an ODF onto a pole figure

Args:
    odf (neml2.odf.ODF): ODF to project
    pole (torch.tensor or neml2.tensors.Vec): pole to project

Keyword Args:
    projection (str): which polar projection to use, options are "stereographic" and "lambert"
    crystal_symmetry (str): string giving the orbifold notation for the crystal symmetry to apply to the base orientations, default "1"
    nradial (int): number of radial points to use
    ntheta (int): number of angular points to use
    nquad (int): number of points to integrate the pole figure
    nchunk (int): subbatch size to use in evaluating odf
    limits ((float,float)): (vmin, vmax) to pass to contourf
    ncontour (int): number of contours to use, only used if limits is provided

◆ pretty_plot_pole_figure_points()

pretty_plot_pole_figure_points ( orientations,
pole,
projection = "stereographic",
crystal_symmetry = "1",
sample_symmetry = "1",
point_size = 10.0 ) 
Project and then make a pretty plot for a pole figure given points as input

Args:
    orientations (torch.tensor or neml2.tensors.Rot): tensor of orientations as *modified* Rodrigues
        parameters in the *active* convention with arbitrary batch shape.
    pole (torch.tensor or neml2.tensors.Vec): pole to project, must broadcast with orientations

Keyword Args:
    projection (str): which polar projection to use, options are "stereographic" and "lambert"
    crystal_symmetry (str): string giving the orbifold notation for the crystal symmetry to apply to the base orientations, default "1"
    sample_symmetry (str): string giving the orbifold notation for the sample symmetry to apply to the projected points, default "1"
    point_size (float): size of matplotlib points to plot

◆ symmetry_operators_as_R2()

symmetry_operators_as_R2 ( orbifold,
device = torch.device("cpu") ) 
Return the symmetry operators for a given symmetry group as a batch of rank two tensors

Args:
    orbifold (str): symmetry group in orbifold notation

Keyword Args:
    device (torch.device): which device to place the tensors

Variable Documentation

◆ available_projections

dict available_projections
Initial value:
1= {
2 "stereographic": StereographicProjection(),
3 "lambert": LambertProjection(),
4}