Function Reference

Classes representing Geometry
Classes for Quantitative Texture Analysis
Auxiliary Functions Helper functions making life easier Below you can find a series of powerfull all purpose tools provided by the MTEX toolbox.

Classes representing Geometry

Specimen Directions (The Class @vector3d) This section describes the class *vector3d* and gives an overview how to deal with specimen directions in MTEX.
Crystal Directions (The Class @Miller) This section describes the class *Miller* and gives an overview how to deal with crystal directions in MTEX.
Discretisation of 1-Sphere (The Class @S1Grid) S1Grid is a class of purely internal use
Discretisation of 2 - Sphere (The Class @S2Grid) represents a grid of nodes on the sphere
Quaternions (The Class @quaternion) class representing orientations
Rotations (The Class @rotation) This section describes the class <rotation.rotation.html *rotation*> and gives an overview on how to work with rotations in MTEX.
Crystal and Specimen Symmetries (The Class @symmetry) This section describes the class *symmetry* and gives an overview how to deal with crystal symmetries in MTEX.
Crystal Orientations (The Class @orientation) This sections describes the class *orientation* and gives an overview how to work with crystal orientation in MTEX.
Discretisation of Orientation Space (The Class SO3Grid) represents a set of orientations

Specimen Directions (The Class @vector3d)

SchmidTensor computes the Schmidt tensor
TSP traveling salesman problem on the 2 dimensional unit-sphere
abs length of vector
angle angle between two vectors Input v1, v2 - @vector3d
angle_outer angle between two vectors
arrow3d plot three dimensional arrows
calcDelaunay compute the Delaynay triangulation for a spherical grid
calcQuadratureWeights compute the area of the Voronoi decomposition
calcVoronoi compute the area of the Voronoi decomposition
calcVoronoiArea compute the area of the Voronoi decomposition
cat
char convert to char
circle annotated a circle
contour spherical contour plot
contourf spherical filled contour plot
cross pointwise cross product of two vector3d
cross_outer pointwise cross product of two vector3d
ctranspose transpose vector
display standard output
dot pointwise inner product
dot_outer outer dot product
double converts vector3d to double
end overloaded end function
eq ? v1 == v2
export
find return index of all points in a epsilon neighborhood of a vector
horzcat overloads [v1,v2,v3..]
interp dirty spherical interpolation - including some smoothing
isPerp check whether v1 and v2 are orthogonal
isempty overloads isempty
kernelDensityEstimation calculates a density function out of (weighted) unit vectors
length overloads length
line
mean computes the mean vector
minus overload minus
mtimes scalar multiplication
ne ? v1 == v2
norm vector norm
normalize normalize a vector
orth an arbitrary orthogonal vector
patchPatala Syntax
pcolor spherical contour plot
perp conmpute an vector best orthogonal to a list of directions
plot plot three dimensional vector
plot3d plot spherical data
plotCustom Syntax plotcustom(v,@(x,y) drawCommand(x,y)) %
plus poitwise addition
polar cartesian to spherical coordinates Input v - @vector3d Output theta - polar angle rho - azimuthal angle r - radius
project2FundamentalRegion projects vectors to the fundamental sector of the inverse pole figure
quiver Syntax quiver(v,d)
rdivide scalar division
refine refine vectors
region
repmat overloads repmat
reshape overloads reshape
rotate rotate vector3d by quaternion
scatter Syntax scatter(v) % scatter(v,data) % scatter(v,text)
scatter3d plot spherical data
size overloads size
smooth Syntax
subSet subindex vector3d
subsasgn overloads subsasgn
subsref overloads subsref
sum sum of vectors
surf Syntax
symmetrise symmetrcially equivalent directions and its multiple
text display a text in a spherical plot
text3 plot three dimensional arrows
times .* - componenwtise multiplication
transpose transpose vector
uminus overloads unitary minus
unique disjoint list of vectors
vector3d
vertcat overloads [v1,v2,v3..]

Crystal Directions (The Class @Miller)

Miller (InferiorClasses = {?vector3d,?S2Grid})
cat concatenate lists of Miller indices to one list
char Miller indece to string
checkFundamentalRegion checks Miller indice to be within the fundamental region
display standard output
dot inner product between two Miller indece
dot_outer inner product between two Miller indece
dspacing space between crystal planes
project2FundamentalRegion projects vectors to the fundamental sector of the inverse pole figure
region return spherical region associated to a set of crystal directions
rotate rotate crystal directions
round tries to round miller indizes to greatest common divisor
scatter plot Miller indece
smooth plot Miller indece
symmetrise directions symmetrically equivalent to m
text plot Miller indece
transformReferenceFrame change reference frame
unique disjoint list of Miller indices

Discretisation of 1-Sphere (The Class @S1Grid)

GridLength return number of points
S1Grid
coarser makes S1Grid more coarse
delete delte points from S1Grid
display standart output
dist distance to all points of S1Grid
dist_outer distance to all points of S1Grid
double convert to double
eq implements G1 == G2
find find close points
max return maximum value
min return maximum value
minus
plot plot grid
plus
refine refine S1Grid
shift shifts S1Grid by delta
subGrid epsilon - neighborhood of a point in the grid

Discretisation of 2 - Sphere (The Class @S2Grid)

S2Grid Syntax S2Grid(theta,rho) % fills a Sphere with N--nodes regularS2Grid(...) % construct regular polar and azimuthal spacing equispacedS2Grid(...) % construct equispaced nodes
cat
copy copy certain condition from grid
delete elilinates points from grid
display standard output
find return index of all points in a epsilon neighborhood of a vector
getdata return index of all points in a epsilon neighborhood of a vector
polar polar coordinates of S2Grid
refine refine S2Grid
subGrid subgrid
subsasgn overloads subsasgn
subsref overloads subsref

Quaternions (The Class @quaternion)

Euler quaternion to euler angle
Rodrigues quaternion to rodrigues representation
angle calcualtes the rotational angle between rotations q1 and q2
angle_outer calcualtes the rotational angle between all rotations q1 and q2
axis rotational axis of the quaternion
calcVoronoi compute the the Voronoi decomposition for unit quaternions
cat
char quaternion to char
cross pointwise cross product of three quaternions
ctranspose transpose quaternion
display standart output
dot inner product of quaternions g1 and g2
dot_angle compute minimum q1 . q2 modulo rotation about zaxis and angle omega
dot_outer outer inner product between two quaternions
double quaternion to double
end overloads end function
eq ? q1 == q2
export export quaternions to a ascii file
find return indece and distance of all nodes within a eps neighborhood
horzcat implements [q1,q2,q3..]
inv quaternion of the inverse roation
isempty overloads isempty
length overloads length
matrix quaternion to direction cosine matrix conversion converts direction cosine matrix to quaternion
mean mean of a list of quaternions, principle axes and moments of inertia
mean_CS fast mean of
minus overloads minus
mldivide
mpower q^n
mrdivide scalar division
mtimes quaternionen multiplication q1 * q2
ndims overloads ndims
ne q1 ~= q2 ?
norm quaternion norm sqrt(a^2+b^2+c^2+c^2)
normalize normalize quaternion
permute overloads permute
pertube pertube data randomly by epsilon
perturbe pertube data randomly by epsilon
plot
plus pointwise addition
power q.^n
prod overloads q1 * q2 * q3
project2EulerFR projects quaternions to a fundamental region
project2FundamentalRegion projects quaternions to a fundamental region
qmatrix returns the quaternion multiplication matrix
qq returns w * q' * q
quaternion
rdivide scalar division
real real-part of of quaternion
repmat overloads repmat
reshape overloads reshape
scatter plot function
setSubSet indexing of quaternions
size overloads size
subSet indexing of quaternions
subsasgn overloads subsasgn
subsref overloads subsref
sum overloads sum
symmetrise symmetrcially equivalent orientations
times implements quaternion .* quaternion and quaternion .* vector3d
transpose transpose array of quaternions
uminus overload unitary minus
unique disjoint list of quaternions
vertcat implements [q1;q2;q3..]

Rotations (The Class @rotation)

cat
char quaternion to char
display standart output
dot compute rot1 . rot2
dot_outer dot_outer
getMinAxes
isImproper
matrix quaternion to direction cosine matrix conversion converts direction cosine matrix to quaternion
mldivide o \ v
mtimes r = a * b
permute overloads permute
project2FundamentalRegion projects rotation to a fundamental region
repmat overloads repmat
reshape overloads reshape
rotation defines an rotation
subSet indexing of rotation
subsasgn overloads subsasgn
subsref overloads subsref
times r = a .* b
transpose transpose array of rotations
uminus implements -rotation
unique disjoint list of rotations

Crystal and Specimen Symmetries (The Class @symmetry)

Laue return the corresponding Laue group
LaueName get Laue name
alignment return alignment of the reference frame as string, e.g. x||a, y||b*
angleDistribution compute the angle distribution of a uniform ODF for a crystal symmetry
calcQuat calculate quaternions for Laue groups
check check symmetry
disjoint returns the disjoint of two symmetry groups
ensureCS ensures that an obj has the right crystal symmetry
eq check S1 == S2
fundamentalSector get the fundamental sector for a symmetry in the inverse pole figure
getFundamentalRegion get the fundamental region in Euler angles
getFundamentalRegionRodrigues get the fundamental region for a crystal and specimen symmetry
getFundamentalRegionRodriguez get the fundamental region for a crystal and specimen symmetry
getMaxAngle get the maximum angle of a fundamental region without interplay
getMaxAngleDir get the fundamental region for a crystal and specimen symmetry
getMaxAngleFundamentalRegion get the maximum angle of a fundamental region
length number of symmetry elements
maxAngle get the maximum angle of a fundamental region without interplay
multiplicityPerpZ maximum angle rho
multiplicityZ maximum angle rho
nfold maximal n-fold of symmetry axes
plot plot symmetry
plotAngleDistribution plot axis distribution
properGroup return the corresponding Laue group
rotation_special returns symmetry elements different from rotation about c-axis
subsref overloads subsref
symmetry Supported Symmetries
union returns the union of two symmetry groups

Crystal Orientations (The Class @orientation)

BCV biased cross validation
KLCV Kullback Leibler cross validation for optimal kernel estimation
LSCV least squares cross valiadation
angle calculates rotational angle between orientations
axis rotational axis of the orientation or misorientation
bingham_test bingham test for spherical/prolat/oblat case
calcAngleDistribution calculate angle distribution
calcBinghamODF calculate ODF from individuel orientations via kernel density estimation
calcFourierODF calculate ODF from individuel orientations via kernel density estimation
calcKernel compute an optimal kernel function for ODF estimation
calcKernelODF calculate ODF from individuel orientations via kernel density estimation
calcODF computes an ODF from individuel orientations
calcTensor compute the average tensor for a vector of orientations
checkFundamentalRegion checks whether a orientation sits within the fundamental region
crossCorrelation computes the cross correlation for the kernel density estimator
display standart output
dot compute minimum dot(o1,o2) modulo symmetry
dot_outer dot_outer
fibreVolume ratio of orientations close to a certain fibre
getFundamentalRegion projects orientations to a fundamental region
inv inverse of an orientation
isMisorientation check whether o is a misorientation
ldivide o .\ v
mean mean of a list of orientations, principle axes and moments of inertia
mldivide o \ v
mtimes orientation times Miller and orientation times orientation
niceEuler orientation to euler angle
orientation orientation - class representing orientations
plot annotate a orientation to an existing plot
plotAngleDistribution plot the angle distribution
plotAxisDistribution plot uncorrelated axis distribution
plotIPDF plot orientations into inverse pole figures
plotODF Plot EBSD data at ODF sections
plotPDF plot orientations into pole figures
project2EulerFR projects orientation to a fundamental region
project2FundamentalRegion projects orientation to a fundamental region
project2ODFsection project orientation to ODF sections used by plotODF
qqplot quantile-quantile of misorientation angle against random angular misorientation
scatter plots ebsd data as scatter plot
sphereVolume ratio of orientations with a certain orientation
symmetrise all crystallographically equivalent orientations
times vec = ori .* Miller
transformReferenceFrame only applicable for crystal symmetry
unique disjoint list of quaternions
volume ratio of orientations with a certain orientation

Discretisation of Orientation Space (The Class SO3Grid)

SO3Grid Syntax S3G = SO3Grid(nodes,CS,SS) S3G = SO3Grid(points,CS,SS) S3G = SO3Grid(resolution,CS,SS)
char convert to char
copy copy nodes by indece
delete clear nodes by indece Input SOG - @SO3Grid indece - int32
display standard output
dot_outer return outer inner product of all nodes within a eps neighborhood
find return indece and distance of all nodes within a eps neighborhood
mtimes outer quaternion multiplication
spy spy distance matrix
subGrid sub-SO3Grid as epsilon neigborhood of a node
subsasgn overloads subsasgn
subsref overloads subsref

Classes for Quantitative Texture Analysis

Orientation Density Functions (The Class @ODF) This sections describes the class *ODF* and gives an overview how to work with orientation density functions in MTEX.
Standard ODFs predefined ODFs
ODF Shapes (The class @kernel) standard distributions on SO(3)
Pole Figure Data (The Class @PoleFigure) This section describes the class *PoleFigure* and gives an overview over the functionality MTEX offers to analyze pole figure data.
Electron Backscatter Diffraction Data (The Class @EBSD) This section describes the class *EBSD* and gives an overview over the functionality that MTEX offers to analyze EBSD data.
Material Tensors (The Class @tensor)

Orientation Density Functions (The Class @ODF)

MDFAnalysis Misorientation Distribution Function Explains how to compute and analyze misorientation distribution functions.
ModelODFs Model ODFs Describes how to define model ODFs in MTEX, i.e., uniform ODFs, unimodal ODFs, fibre ODFs, Bingham ODFs and ODFs defined by its Fourier coefficients.
ODFAnalysis ODF Analysis Explains how to import and export ODFs, how to define model ODFs and how to analyze ODFs, e.g., with respect to modalorientations, textureindex, volumeportions. Pole figure simulation and single orientation simulation is explained as well.
ODFCalculations First Steps Indroduction to analysis of ODFs
ODFCharacteristics Characterizing ODFs Explains how to analyze ODFs, i.e. how to compute modal orientations, texture index, volume portions, Fourier coefficients and pole figures.
ODFImportExport Importing and Exporting ODF Data Explains how to read and write ODFs to a data file
ODFPlot Visualizing ODFs Explains all possibilities to visualize ODfs, i.e. pole figure plots, inverse pole figure plots, ODF sections, fibre sections.

Standard ODFs

ODF Shapes (The class @kernel)

K_symmetrised evaluate kernel modulo symmetries
RK_symmetrised sum Radon trasformed kernel
kernel
plot plot the kernel function
plotFourier plot the Chybeyshev coefficients of the kernel function
plotPDF plot Radon transformed kernel
volume

Pole Figure Data (The Class @PoleFigure)

ImportPoleFigureData Importing Pole Figure Data How to import Pole Figure Data
ModifyPoleFigureData Modify Pole Figure Data Explains how to manipulate pole figure data in MTEX.
PlotPoleFigures Plotting of Pole Figures Described various possibilities to visualize pole figure data.
PoleFigure2odf ODF Estimation from Pole Figure Data This page describes how to use MTEX to estimate an ODF from pole figure data.
PoleFigureAnalysis Pole Figure Analysis Explains how to import pole figure data, how to correct them, and how to recover an ODF.
PoleFigureAnalysisIntro First Steps Get in touch with PoleFigure Data in MTEX.
PoleFigureSimulation_demo Simulating Pole Figure data Simulate arbitary pole figure data
ghost_demo Ghost Effect Analysis Explains the ghost effect to ODF reconstruction and the MTEX option ghostcorrection.

Electron Backscatter Diffraction Data (The Class @EBSD)

AliginingEBSDData Aligning EBSD data to a reference frame How to align EBSD correctly to certain reference frames
AnalyzeEBSDData Analyze EBSD Data
EBSD2odf ODF Estimation from EBSD data How to estimate an ODF from single orientation measurements.
EBSDAnalysis EBSD Data Analysis Data Import of Electron Backscatter Diffraction Data, Correct Data, Estimate Orientation Density Functions out of EBSD Data, Model Grains and Misorientation Density Functions
EBSDAnalysisIntro First Steps Get in touch with EBSD Data in MTEX
EBSDBingham Bingham distribution and EBSD data testing rotational symmetry of individual orientations
EBSDModifyData Modify EBSD Data How to correct EBSD data for measurement errors.
EBSDOrientationPlots Plotting Individual Orientations Basics to the plot types for individual orientations data
EBSDSharpPlot Visualizing EBSD data with sharp textures Using spezialized orientation mappings is particularly usefull when visualizing sharp data. Let us consider the following data set which restrict to the calcite phase
EBSDSimulation_demo Simulating EBSD data How to simulate an arbitrary number of individual orientations data from any ODF.
EBSDSpatialPlots Plotting spatially indexed EBSD data How to visualize EBSD data
ImportEBSDData Importing EBSD Data How to import EBSD Data

Material Tensors (The Class @tensor)

ChristoffelTensor Christoffel tensor of an elasticity tensor for a given direction
EinsteinSum tensor multiplication according to Einstein summation
Fourier compute the Fourier coefficients of the tensor
PoissonRatio computes the Poisson ratio of an elasticity tensor
Voigt
YoungsModulus Young's modulus for an elasticity tensor
calcShearStress shear stress
char
checkSymmetry
conj conjugate of a tensor
ctranspose conjugate of a tensor
directionalMagnitude magnitude of a tensor in direction v
display standard output
double
eig compute the eigenvalues and eigenvectors of a tensor
eq checks whether two tensors are equal
expm matrix exponential of a tensor
horzcat overloads [T1,T2,T3..]
inv inverse of a tensor
length returns the number of tensors
linearCompressibility computes the linear compressibility of an elasticity tensor
logm matrix logarithm of a tensor
matrix return tensor as a matrix
max
min
minus add two tensors
mrdivide implements T / S
mtimes implements T1 * T2
ne checks whether two tensors are not equal
numel returns the number of tensors
plot plot a tensor T
plotS2Grid define a plotting grid suitable for tensor plots
plus add two tensors
quadric quadric
quiverGrid
rdivide
real
rotate rotate a tensor by a list of rotations
shearModulus shear modulus for an elasticity tensor
size overloads size
subsasgn overloads subsasgn
subsref overloads subsref
sum sum over all tensors allong dimension 1
symmetrise symmetrise a tensor according to its crystal symmetry
tensor
tensorSize overloads size
times multiply a tensor by a scalar
transform transform a tensor to a given crystal frame
transformReferenceFrame set properties of a tensor variable
transpose conjugate of a tensor
velocity computes the elastic wave velocity(km/s) from the elastic stiffness Cijkl tensor and density (g/cm3)
vertcat overloads [T1,T2,T3..]
volumeCompressibility computes the volume compressibility of an elasticity tensor

Auxiliary Functions

Plotting Tools Below you find a list of tools to work with data given in the Dubna format
Geometry Tools This section of geometry tools especialy contains methods to convert directions and rotations from one paramterization into another. Additionlly some basic geometrical objects are predefined.
Statistics Below you find a list of statistical tools included in the MTEX toolbox.
Plotting Below you find a list of plotting tools inlcuded in the MTEX toolbox. Of special importance is the command [[savefigure.html,savefigure]] which allows to save plots in any kinds of image files.
docopt DOCOPT Web browser for UNIX platforms. DOCOPT is an M-file that you or your system manager can edit to specify the Web browser to use with MATLAB. It is used for the WEB function with the -BROWSER option. It is also used for links to external Web sites from the the Help browser and from Web menu items. DOCOPT applies only to non-Macintosh UNIX platforms.
dynOption class to add dynamic options to a static class Detailed explanation goes here
dynProp class to add dynamic properties to a static class Detailed explanation goes here
mtexdata load of data provided with mtex and often used in documentation
mtexdegchar returns the degree character
zip_mtex zip mtex for publishing (on website)

Plotting Tools

Geometry Tools

CSL coincidence site lattice misorientations for cubic symmetry
EulerAngleConvention
Miller2quat calculate quaternion from Miller indece
axis2quat rotational axis, roational angle to Quaternion
axis2quat_outer rotational axis, roational angle to Quaternion
brassOrientation returns the cube orientation
checkEulerAngleConvention
cubeOrientation returns the cube orientation
equispacedS2Grid defines an equispaced spherical grid
equispacedSO3Grid defines a equispaced grid in the orientation space
euler2quat converts euler angle to quaternion
fibre2quat arbitrary quaternion q with q * h = r
gossOrientation returns the cube orientation
guessfibre try to find the fibre of to given rotations by finding the eigenvector of g_1*h = g_2*h -> (g_2^-1)*g_1* h = h -> R*h = (lambda)*h
hr2quat arbitrary quaternion q with q * h = r
idRotation the identical rotation
idquaternion the identical rotation - quaternion(1,0,0,0)
inversion the inversion - reflection at the origin
loadCIF import crystal symmetry from cif file
loadPHL
localOrientationGrid define a equispaced grid localized to a center orientation
mat2quat converts direction cosine matrix to quaternion
plotS2Grid create a regular S2Grid for plotting
plotSO3Grid give a regular grid in orientation space
randq returns random quaternions
randv
reflection defines a reflection at plane with normal n
regularS2Grid Syntax regularS2Grid('points',[72 19]) regularS2Grid('resolution',[5*degree 2.5*degree]) regularS2Grid('theta',theta,'rho',rho)
regularSO3Grid give a regular grid in orientation space
rodrigues2quat
vec42quat returns a quaternion q with q u_1 = v1 and q u2 = v2
xvector vector (1,0,0)
yvector vector (0,1,0)
zvector vector (0,0,1)

Statistics

c_hat return the second moments for bingham test
discretesample Samples from a discrete distribution
quantile n percent quantile of x
randp randp(lambda) returns Poisson distributed Vector with mean lambda
range RANGE Sample range. Y = RANGE(X) returns the range of the values in X. For a vector input, Y is the difference between the maximum and minimum values. For a matrix input, Y is a vector containing the range for each column. For N-D arrays, RANGE operates along the first non-singleton dimension.

Plotting