Function Reference
Classes representing Geometry | |
Classes for Quantitative Texture Analysis | |
Auxiliary Functions | Helper functions making life easier Below you can find a series of powerful 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. |
specimenSymmetry | defines a specimen symmetry |
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. |
Fibres | This sections describes the class <fibre_index.html fibre> and gives an overview how to work with fibres in MTEX. |
Quaternions (The Class @quaternion) | class representing orientations |
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 |
Discretisation of Orientation Space (The Class SO3Grid) | represents a set of orientations |
fundamentalRegion | get the fundamental zone in orientation space for a symmetry |
plotAngleDistribution | plot axis distribution |
plotAxisDistribution | plot axis distribution |
strainTensor | |
stressTensor |
Specimen Directions (The Class @vector3d)
SchmidTensor | computes the Schmidt tensor |
abs | length of vector |
angle | angle between two vectors |
angle_outer | angle between two vectors Input v1, v2 - @vector3d |
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 Input v - @vector3d Output x, y, z - double |
end | overloaded end function |
eq | ? v1 == v2 |
export | export quaternions to a ascii file |
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 |
orthProj | |
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 rotation or orientation |
rotate_outer | rotate vector3d by quaternion |
scatter | Syntax scatter(v) % plot the directions v scatter(v,data) % colorize directions according to data scatter(v,'label',text) % plot text below markers scatter(v,'label',text,'textaboveMarker') % plot text above markers |
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 | define a crystal direction by Miller indice |
cat | concatenate lists of Miller indices to one list |
char | Miller indece to string |
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 |
rotate_outer | rotate crystal directions |
round | tries to round miller indizes to greatest common divisor |
scatter | plot Miller indece |
smooth | plot Miller indece |
surf | Syntax |
symmetrise | directions symmetrically equivalent to m |
text | plot Miller indece |
transformReferenceFrame | change reference frame while keeping hkl or uvw |
unique | disjoint list of Miller indices |
no title
Rotations (The Class @rotation)
cat | |
char | quaternion to char |
display | standart output |
dot | compute rot1 . rot2 |
dot_outer | dot_outer |
getMinAxes | |
isImproper | |
line | draw rotations connected by lines |
matrix | quaternion to direction cosine matrix conversion converts direction cosine matrix to quaternion |
mldivide | o \ v |
mtimes | r = a * b |
permute | overloads permute |
power | r.^n |
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* |
calcAngleDistribution | compute the angle distribution of a uniform ODF for a crystal symmetry |
calcAxisDistribution | compute the axis distribution of an uniform ODF or MDF |
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 |
factor | factorizes s1 and s2 into l, d, r such that s1 = l * d and s2 = d * r |
fundamentalRegion | fundamental region in orientation space for a (pair) of symmetries |
fundamentalRegionEuler | get the fundamental region in Euler angles |
fundamentalSector | get the fundamental sector for a symmetry in the inverse pole figure |
length | number of symmetry elements |
maxAngle | get the maximum angle of the fundamental region |
multiplicityPerpZ | maximum angle rho |
multiplicityZ | maximum angle rho |
nfold | maximal n-fold of symmetry axes |
plot | visualize symmetry elements according to international table |
properGroup | return the corresponding Laue group |
properSubGroup | 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 an misorientation or two orientations |
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 |
calcInvTaylor | Taylor factor from orientation gradient |
calcKernel | compute an optimal kernel function for ODF estimation |
calcKernelODF | calculate ODF from individuel orientations via kernel density estimation |
calcMDF | computes an MDF from individuel orientations or misorientations |
calcMIndex | TODO!!! |
calcODF | computes an ODF from individuel orientations |
calcTensor | compute the average tensor for a vector of orientations |
cluster | sort orientations into clusters |
crossCorrelation | computes the cross correlation for the kernel density estimator |
ctranspose | inverse orientation |
display | standart output |
dot | compute minimum dot(o1,o2) modulo symmetry |
dot_outer | dot_outer |
export_VPSC | export individual orientations to the VPSC format |
fibreVolume | ratio of orientations close to a certain fibre |
getFundamentalRegion | projects orientations to a fundamental region |
isMisorientation | check whether o is a misorientation |
ldivide | o .\ v |
log | the inverse of the exponential map |
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 |
plotIPDF | plot orientations into inverse pole figures |
plotPDF | plot orientations into pole figures |
plotSection | plot orientations to ODF sections |
power | ori.^n |
project2EulerFR | projects orientation to a fundamental region |
project2FundamentalRegion | projects orientation to a fundamental region |
qqplot | quantile-quantile of misorientation angle against random angular misorientation |
rVariant | calculates rotational angle between orientations |
round2Miller | find h1,h2,d1,d2 such that ori * h1 = h2 and ori*d1=d2 |
scatter | plots orientations in 3d |
sphereVolume | ratio of orientations with a certain orientation |
symmetrise | all crystallographically equivalent orientations |
times | vec = ori .* Miller |
transformReferenceFrame | change reference frame of an orientation |
unique | disjoint list of quaternions |
volume | ratio of orientations with a certain orientation |
Fibres
angle | angle fibre to orientation or fibre to fibre |
cat | |
display | standard output |
end | overloaded end function |
eq | ? sS1 == sS2 |
fibre | fibre is a class representing a fibre in orientation space. Examples are alpha, beta or gamma fibres. In general a fibre is defined by a crystal direction h of type <Miller_index.html Miller> and a specimen direction of type <vector3d_index.html vector3d>. |
horzcat | overloads [v1,v2,v3..] |
isempty | overloads isempty |
length | overloads length |
ne | ? sS1 ~= sS2 |
orientation | generate a list of orientation out of a fibre |
plot | |
plotIPDF | plot orientations into inverse pole figures |
plotPDF | plot a fibre into pole figures |
size | overloads size |
subSet | subindex vector3d |
subsref | overloads subsref |
symmetrise | all crystallographically equivalent fibres |
transpose | transpose list of slipSystem |
vertcat | overloads [v1,v2,v3..] |
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 |
isnan | check for nan values |
length | overloads length |
log | project a quaternion into the tangential space |
logm | the dislocation tensor for a rotation |
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 |
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 | quaternion .* quaternion and quaternion .* vector3d |
transpose | transpose array of quaternions |
uminus | overload unitary minus |
unique | disjoint list of quaternions |
vertcat | implements [q1;q2;q3..] |
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 |
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 of 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)
FourierODF | compute FourierODF from another ODF |
ODF | |
bandwidth | bandwidth of the ODF |
calcAngleDistribution | compute the angle distribution of an ODF or an MDF |
calcAxisDistribution | compute the axis distribution of an ODF or MDF |
calcAxisVolume | amount of orientations with a specific misorientation axis |
calcError | calculate approximation error between two ODFs |
calcFourier | compute Fourier coefficients of odf |
calcMDF | calculate the uncorrelated misorientation distribution function (MDF) from one or two ODF |
calcMIndex | M-index of Skemer et al.(2005) based on the difference between uncorrelated and uniform misorientation angle distributions |
calcModes | heuristic to find modal orientations |
calcOrientations | draw random orientations from ODF |
calcPDF | calculate pdf |
calcPoleFigure | simulate pole figures from an ODF |
calcTensor | compute the average tensor for an ODF |
calcpdf_special3 | compute the pdf for h = (theta,rhoh), r = (theta,rhor) |
centerSpecimen | rotatates an odf with specimen symmetry into its symmetry axes |
concentration | not yet implemeted |
conv | convolute ODF with kernel psi |
discreteSample | draw a random sample |
display | standard output |
entropy | caclulate entropy of ODF |
eval | evaluate an odf at orientation g |
export | export an ODF to an ASCII file |
export_VPSC | export an ODF to the VPSC format |
export_generic | export an ODF to an ASCII file |
export_mtex | export an ODF into the MTEX format |
fibreVolume | ratio of orientations with a certain orientation |
hist | calcualtes a histogram of ODF |
isFourier | check whether odf is given by Fourier coefficients |
max | heuristic to find local modal orientations |
maxpdf | returns the maximum orientation in a polefigure |
mean | expected value of an ODF |
minus | superposeing two ODFs |
mrdivide | scaling of the ODF |
mtimes | scaling of the ODF |
neuralgas | attempt to distribute measure-sites equally according to invers polefigure density (experimental) |
norm | caclulate texture index of ODF |
plot | plots odf |
plot3d | plots odf |
plotDiff | difference plot between two odfs or an odf and a pole figure |
plotFibre | plot odf along a fibre |
plotFourier | plots Fourier coefficients of the odf |
plotIPDF | plot inverse pole figures |
plotPDF | plot pole figures |
plotSection | plot ODF sections |
plus | superposeing two ODFs |
quantile | quantile orientations of an ODF |
rdivide | scaling of the ODF |
rotate | rotate ODF |
slope | | grad(r) | |
smooth | smooth ODF |
textureindex | caclulate texture index of ODF |
times | scaling of the ODF |
uminus | superposeing two ODFs |
volume | ratio of orientations with a certain orientation |
Standard ODFs
BinghamODF | defines a Bingham distributed ODF |
FourierODF | defines an ODF by its Fourier coefficients |
SantaFe | the SantaFe-sample ODF |
femODF | defines an ODF by finite elements |
fibreODF | defines an fibre symmetric ODF |
mix2 | mix2 sample ODF |
uniformODF | get crystal and specimen symmetry |
unimodalODF | define a unimodal ODF |
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)
PoleFigure | |
calcError | RP and mean square error |
calcErrorPF | error polefigure between meassured and recalculated pole figures |
calcFEMODF | PDF to ODF inversion |
calcNormalization | normalization of a meassured pole figure with respect to a second pole figure |
calcODF | PDF to ODF inversion |
calcPoleFigure | simulate pole figure |
cat | |
char | standard output |
correct | corrects polfigures for background and defocussing |
display | standard output |
export | export pole figure in an ASCII file |
findOutlier | find outliers in pole figures |
isOutlier | find outliers in pole figures |
isempty | overloads length |
max | maximum of two pole figures or the maximum of a single polefigure |
mean | mean of pole figure intensities |
min | minimum of two pole figures or the minimum of a single polefigure |
minus | implements pf1 - pf2 |
mrdivide | implements pf1 ./ b and a ./ pf2 |
mtimes | scaling of PoleFigures, implements pf1 * b and a * pf2 |
noisepf | simulate diffraction counts |
normalize | normalization of a meassured pole figure with respect to an ODF |
plot | plot pole figure |
plotDiff | difference plot between two pole figures or an odf and a pole figure |
plot_zero_range | implements the zero range method |
plus | implements pf1 + pf2 |
rdivide | implements pf1 ./ b and a ./ pf2 |
rotate | rotates pole figures by a certain rotation |
scale | scale polefigure by a factor |
select | select PoleFigures |
subsasgn | overloads subsasgn |
subsref | overide polefigure() and polefigure{} |
times | implements pf1 .* b and a .* pf2 |
uminus | implements -pf |
union | crytsallographic direction to one |
unique | remove dublicated points in a polefigure |
zeroRange | implements the zero range method |
Electron Backscatter Diffraction Data (The Class @EBSD)
EBSD | constructor |
KAM | intragranular average misorientation angle per orientation |
affinetrans | perform an affine transformation on spatial ebsd data |
calcGrains | 2d and 3d construction of GrainSets from spatially indexed EBSD data |
calcMisorientation | calculate uncorrelated misorientations between two ebsd phases |
calcTensor | compute the average tensor for an EBSD data set |
cat | overloads [ebsd1,ebsd2,ebsd3..] |
char | ebsd -> char |
display | standard output |
export | export EBSD data to a ascii file |
export_h5 | export EBSD data to a ascii file |
extend | returns the boundings of spatial EBSD data |
fill | extrapolate spatial EBSD data by nearest neighbour for tetragonal lattice |
fillByGrainId | extrapolate spatial EBSD data by nearest neighbour for tetragonal lattice |
findByLocation | select EBSD data by spatial coordinates |
findByOrientation | select grains by orientation |
fliplr | flip spatial ebsd-data from left to right |
flipud | flip spatial ebsd-data from upside down |
gridify | extend EBSD data to an grid |
id2ind | find ind such that ebsd.id(ind) == id |
inpolygon | checks which ebsd data are within given polygon |
mtimes | rotating the ebsd data by a certain rotation |
plot | spatial EBSD plot |
quiver | plot directions at ebsd centers |
reduce | reduce ebsd data by a factor |
rotate | rotate EBSD orientations or spatial data around point of origin |
shift | shift spatial ebsd-data about (x,y) |
smooth | smooth spatial EBSD |
spatialProfile | select EBSD data along line segments |
subSet | indexing of EBSD data |
subsasgn | overloads subsasgn |
subsind | subindexing of EBSD data |
subsref | indexing of EBSD data |
updateUnitCell | this function should be called after the spatial coordinates of an EBSD data set have been modified |
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 |
antiSym | the antisymmetric part A = 0.5(T - T.') of a tensor |
calcShearStress | shear stress |
calcTaylor | compute Taylor factor and strain dependent orientation gradient |
char | tensor to char |
checkSymmetry | |
conj | conjugate of a tensor |
ctranspose | conjugate of a tensor |
diag | convert rank 1 or rank 0 tensor into diagonal rank 2 tensor |
directionalMagnitude | magnitude of a tensor in direction v |
display | standard output |
double | convert tensor values to matrix |
eig | compute the eigenvalues and eigenvectors of a tensor |
end | overloaded end function |
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 |
rotate_outer | 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 |
sym | the symmetric part S = 0.5(T + T.') of a tensor |
symmetrise | symmetrise a tensor according to its crystal symmetry |
tensor | |
tensorSize | overloads size |
times | multiply a tensor by a scalar |
trace | compute the trace of a rank 2 tensor |
transform | transform a tensor to a given crystal frame |
transformReferenceFrame | set properties of a tensor variable |
transpose | transpose a list of a tensors |
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 especially contains methods to convert directions and rotations from one parametrization into another. Additionally, 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 included in the MTEX toolbox. Of special importance is the command [[savefigure.html,savefigure]] which allows saving plots in any kinds of image files. |
fft_rho | project rho to interval [-1,1) |
fft_theta | project theta to interval [0,0.5] |
annotate | annotate to a existing figure |
ar2rgb | compute rgb values from angle and radius |
contour3s | contour-slices |
convertFigureRGB2ind | default resolution |
gcm | |
getCamera | get xAxis and zAxis position from axis |
getHoldState | |
hsl2hsv | |
isRGB | |
mtexColorMap | define an MTEX colormap |
mtexColorbar | overide buildin Matlab colorbar function |
newMapPlot | |
newMtexFigure | |
newODFSectionPlot | generate a new ODF section plot |
newSphericalPlot | split plot in upper and lower hemisphere |
nextstyle | NEXTSTYLE Get next plot linespec [L,C,M] = NEXTSTYLE(AX) gets the next line style, color and marker for plotting from the ColorOrder and LineStyleOrder of axes AX. |
optiondraw | apply options to handle |
optionplot | plot y against x using the options in varargin |
plota2east | set the default plot direction of the x-axis |
plota2north | set the default plot direction of the x-axis |
plota2south | set the default plot direction of the x-axis |
plota2west | set the default plot direction of the x-axis |
plotb2east | set the default plot direction of the x-axis |
plotb2north | set the default plot direction of the x-axis |
plotb2south | set the default plot direction of the x-axis |
plotb2west | set the default plot direction of the x-axis |
plotx2east | set the default plot direction of the x-axis |
plotx2north | set the default plot direction of the x-axis |
plotx2south | set the default plot direction of the x-axis |
plotx2west | set the default plot direction of the x-axis |
plotzIntoPlane | set the default plot direction of the z-axis |
plotzOutOfPlane | set the default plot direction of the z-axis |
saveFigure | save figure as graphics file |
sectionLabels | |
selectPolygon | select a polygon by mouse |
setCamera | set Camera according to xAxis and zAxis position |
setColorRange | set color range for figures |
switchUnit | returns the closest length to a known unit. For example, 10e3m will give 10km. |
xticklabel_rotate | Rotate XTickLabel |
assert_grid | check for valid grid parameters |
calcUnitCell | compute the unit cell for an EBSD data set |
check_interfaces | determine interface from file |
loadHelper | helps to load data-matrix with ColumnNames restricts also data according to conventions (e.g. >4pi) |
string2Miller | converts string to Miller indece |
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 |
expquat | matrix exponential to convert skew symmetric matrices into quaternions |
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 |
nanquaternion | the identical rotation - quaternion(1,0,0,0) |
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
MTEX 4.5.0 |