return the second moments for bingham test
Syntax
[chat, T, Tv, n] = c_hat(varargin)Input
| o | EBSD / orientation / @grain |
Output
| chat | 4x4 tensor |
| T | eigenvalues |
| Tv | eigenvectors |
| n | number of points |
- Functions
-
Geometry
- Overview
-
vector3d
- vector3d
- abs
- accumarray
- angle
- angle_outer
- arrow3d
- byPolar
- calcCluster
- calcDelaunay
- calcDensity
- calcQuadratureWeights
- calcVoronoi
- calcVoronoiArea
- cat
- centroid
- char
- circle
- conj
- contour
- contourf
- convhull
- cross
- cross_outer
- ctranspose
- cumsum
- det
- display
- dot
- dot_outer
- double
- dyad
- eig
- end
- eq
- exp
- export
- find
- fullDouble
- gridify
- histogram
- horzcat
- interp
- isPerp
- isempty
- isscalar
- length
- line
- lineIntersect
- load
- mapScatter
- matrix
- mean
- meshNorm
- minus
- mpower
- mrdivide
- mtimes
- nan
- nan2zero
- nanmean
- ndims
- ne
- norm
- normalize
- numel
- ones
- orth
- orthProj
- pcolor
- perp
- planeIntersect
- plot
- plot3d
- plotCustom
- plus
- polar
- polyArea
- power
- project2FundamentalRegion
- quiver
- quiver3
- rand
- rank
- rdivide
- refine
- region
- repmat
- reshape
- rotate
- rotate_outer
- round
- round2zero
- scatter
- scatter3d
- setdiff
- size
- smooth
- sparse
- subSet
- subsasgn
- subsref
- sum
- surf
- symmetrise
- text
- text3
- times
- transpose
- uminus
- unique
- vertcat
- zeros
- Miller
-
symmetry
- symmetry
- Laue
- LaueName
- WignerD
- calcAngleDistribution
- calcAxisDistribution
- check
- disjoint
- elements
- ensureCS
- eq
- factor
- fundamentalRegion
- fundamentalRegionEuler
- fundamentalSector
- isLaue
- isProper
- maxAngle
- mtimes
- multiplicityZ
- ne
- nfold
- numProper
- numSym
- plot
- properGroup
- properSubGroup
- quaternion
- rotation
- rotation_special
- union
- crystalSymmetry
- specimenSymmetry
-
crystalShape
- crystalShape
- albite
- amphibole
- analcime
- andalusite
- anorthite
- antigorite
- apatite
- aragonite
- augite
- biotite
- brucite
- calcite
- chromite
- clinochlore
- cordierite
- corundum
- diamond
- diopside
- dolomite
- enstatite
- epidote
- fluorite
- fluorite_complex
- forsterite
- garnet
- gypsum
- halite
- ice_VI
- ilmenite
- kyanite
- magnesite
- magnetite
- microcline
- monazite
- muscovite
- olivine
- orthoclase
- plagioclase
- quartz
- rutile
- spinel
- staurolite
- titanite
- topaz
- tourmaline
- zircon
- zoisite
- display
- fitArea
- innerFace
- length
- mtimes
- plot
- plotInnerDirection
- plotInnerFace
- plotSlipSystem
- plus
- repmat
- rotate
- rotate_outer
- size
- subSet
- subsref
- times
- rotation
-
orientation
- orientation
- BCV
- KLCV
- LSCV
- accumarray
- angle
- axis
- bingham_test
- byAxisAngle
- byEuler
- byMatrix
- byMiller
- byRodrigues
- calcAngleDistribution
- calcBinghamODF
- calcCluster
- calcFourierODF
- calcInvTaylor
- calcKernel
- calcKernelODF
- calcMIndex
- calcTensor
- calcVoronoi
- char
- crossCorrelation
- ctranspose
- display
- doHClustering
- dot
- dot_outer
- exp
- export_VPSC
- fibreVolume
- find
- fit
- getFundamentalRegion
- gridify
- isMisorientation
- ldivide
- load
- log
- logm
- map
- matchLattice
- mean
- mldivide
- mtimes
- multiplicity
- niceEuler
- parents
- plot
- plotIPDF
- plotPDF
- plotSection
- plotSectionOutOfFR
- power
- project
- project2EulerFR
- project2FundamentalRegion
- qqplot
- quiver
- quiverSection
- round2Miller
- scatter
- sphereVolume
- symmetrise
- tensor
- times
- transformReferenceFrame
- unique
- variants
- volume
- MoritoOrder
- calcParent
- calcParent2Child
- calcVariantId
- plotVariants
- orientationRegion
- sphericalRegion
- fibre
- slipSystem
- dislocationSystem
- plane3d
-
quaternion
- quaternion
- Euler
- Rodrigues
- accumarray
- angle
- angle_outer
- axis
- calcVoronoi
- calcVoronoiVolume
- cat
- char
- cross
- ctranspose
- cubochoric
- display
- dot
- dot_angle
- dot_outer
- double
- end
- eq
- export
- find
- geodesic
- homochoric
- horzcat
- inv
- isempty
- isnan
- isscalar
- itimes
- length
- log
- logm
- matrix
- mean
- mean_CS
- minus
- mldivide
- mpower
- mrdivide
- mtimes
- ndims
- ne
- norm
- normalize
- numel
- permute
- perturbe
- plot
- plus
- power
- prod
- project2EulerFR
- project2FundamentalRegion
- qmatrix
- rdivide
- real
- repmat
- reshape
- scatter
- setSubSet
- size
- std
- subSet
- subsasgn
- subsref
- sum
- symmetrise
- times
- transpose
- uminus
- unique
- vertcat
- S1Grid
- S2Grid
- S2Triangulation
- SO3Grid
- embedding
-
misc functions
- CSL
- EulerAngleConvention
- HEALPixS2Grid
- allHKL
- axis2quat
- axis2quat_outer
- cubo2homo
- doHClustering
- ensureCompatibleTangentSpaces
- equispacedS2Grid
- equispacedSO3Grid
- euler2quat
- expquat
- extractSphericalRegion
- fibre2quat
- hexNeighbors
- homo2cubo
- hr2quat
- isLaue
- isProper
- loadCIF
- loadPHL
- localOrientationGrid
- mat2quat
- plotS2Grid
- plotSO3Grid
- polySgnArea
- polySgnArea3
- reflection
- regularS2Grid
- regularSO3Grid
- squareNeighbors
- squareNeighbors2
- xvector
- yvector
- zvector
- Phase Transistion Analysis
-
EBSD Analysis
- Overview
-
EBSD
- EBSD
- KAM
- calcGROD
- calcGrains
- calcMisorientation
- calcTensor
- calcTraces
- cat
- char
- curvature
- display
- export
- export_ang
- export_crc
- export_ctf
- export_h5
- extent
- fill
- fillByGrainId
- findByLocation
- findByOrientation
- getCPRInfo
- grainMean
- gridify
- id2ind
- inpolygon
- interp
- isnan
- load
- minus
- plot
- plotUnitCells
- plus
- project2FundamentalRegion
- quiver
- reduce
- reshape
- rotate
- rotate_outer
- selectInteractive
- shift
- smooth
- spatialProfile
- subSet
- subsasgn
- subsind
- subsref
- text
- transform2PolarRefernceFrame
- updateUnitCell
- weightedBurgersVec
- simulateEBSD
- EBSDsquare
- EBSDhex
-
grain2d
- grain2d
- area
- aspectRatio
- boundarySize
- calcTraces
- caliper
- cat
- centroid
- checkInside
- convexhullProps
- diameter
- display
- eq
- equivalentPerimeter
- equivalentRadius
- findByLocation
- findByOrientation
- fitEllipse
- hasHole
- hist
- histogram
- hull
- id2ind
- inpolygon
- isBoundary
- isInclusion
- isOuterBoundary
- load
- longAxis
- merge
- minus
- ne
- neighbors
- numNeighbors
- paris
- paror
- perimeter
- plot
- plus
- principalComponents
- quiver
- reduceBoundary
- refineBoundary
- rotate
- rotate2Plane
- selectInteractive
- shapeFactor
- shortAxis
- smooth
- subBoundaryLength
- subBoundarySize
- subSet
- subsasgn
- subsref
- text
- grainBoundary
- triplePointList
-
parentGrainReconstructor
- parentGrainReconstructor
- calcGBFit
- calcGBVotes
- calcGrainVotes
- calcGraph
- calcParent2Child
- calcParentEBSD
- calcParentFromGraph
- calcParentFromVote
- calcTPVotes
- calcVariantGraph
- calcVariants
- clusterGraph
- clusterVariantGraph
- display
- mergeByGraph
- mergeInclusions
- mergeSimilar
- parent2ChildInfo
- plotGraph
- plotVariantPF
- revert
- selectInteractive
-
Pole Figures
- Overview
-
poleFigure
- PoleFigure
- calcError
- calcErrorPF
- calcFEMODF
- calcNormalization
- calcODF
- calcPoleFigure
- cat
- char
- correct
- display
- export
- findOutlier
- isOutlier
- isempty
- load
- max
- mean
- min
- minus
- mrdivide
- mtimes
- noisepf
- normalize
- plot
- plotDiff
- plus
- rdivide
- rotate
- rotate_outer
- scale
- select
- subsasgn
- subsref
- times
- uminus
- union
- unique
- MLSSolver
- zeroRangeMethod
- Dubna Tools
-
Tensors
- Overview
-
tensor
- tensor
- EinsteinSum
- Fourier
- Voigt
- antiSym
- cat
- char
- checkSymmetry
- colon
- conj
- ctranspose
- det
- diag
- directionalMagnitude
- display
- double
- eig
- end
- eq
- expm
- export
- horzcat
- inv
- isscalar
- length
- leviCivita
- load
- logm
- matrix
- mean
- minus
- mpower
- mrdivide
- mtimes
- ndims
- ne
- norm
- normalize
- numel
- plot
- plus
- polar
- quadric
- rdivide
- real
- reshape
- rotate
- rotate_outer
- rotation
- size
- sqrtm
- subSet
- subsasgn
- subsref
- sum
- svd
- sym
- symmetricDecomposition
- symmetrise
- tensorSize
- times
- trace
- transformReferenceFrame
- transpose
- uminus
- vector3d
- vertcat
- stressTensor
- strainTensor
- strainRateTensor
- complianceTensor
- stiffnessTensor
- refractiveIndexTensor
- curvatureTensor
- spinTensor
- ChristoffelTensor
- velocityGradientTensor
- deformationGradientTensor
- dislocationDensityTensor
-
Spherical Functions
- Overview
- S2Fun
- S2FunHandle
- S2FunTri
- BinghamS2
-
S2FunHarmonic
- S2FunHarmonic
- abs
- acos
- adjoint
- adjointNFSFT
- approximate
- calcSymAxis
- cat
- conj
- conv
- cos
- ctranspose
- display
- dot
- eig
- end
- entropy
- eval
- evalEquispacedFFT
- evalNFSFT
- even
- grad
- horzcat
- interpolate
- invRadon
- isempty
- le
- length
- log
- mean
- mtimes
- norm
- plotSpektra
- plus
- power
- quadrature
- radon
- rdivide
- regularize
- reshape
- rotate
- rotate_outer
- simultaniousCG
- sphericalHarmonicTrafo
- sqrt
- steepestDescent
- subsasgn
- subsref
- sum
- symmetrise
- times
- transpose
- truncate
- uminus
- vertcat
- volume
- S2FunHarmonicSym
- S2AxisField
- S2AxisFieldTri
- S2AxisFieldHarmonic
- S2VectorField
- S2VectorFieldHarmonic
- S2VectorFieldTri
- S2Kernel
-
Orientation Functions
- Overview
-
SO3Fun
- SO3Fun
- abs
- calcAngleDistribution
- calcAxisDistribution
- calcAxisVolume
- calcComponents
- calcError
- calcFourier
- calcMDF
- calcMIndex
- calcPDF
- calcPoleFigure
- calcTensor
- centerSpecimen
- conj
- conv
- cor
- crossCor
- discreteSample
- display
- dot
- dubna
- ensureCompatibleSymmetries
- entropy
- exp
- export
- export_VPSC
- export_generic
- export_mtex
- fibreVolume
- grad
- hist
- inv
- load
- log
- max
- mean
- min
- minus
- mrdivide
- mtimes
- norm
- plot
- plot3d
- plotDiff
- plotFibre
- plotIPDF
- plotPDF
- plotSection
- plotSpektra
- plus
- power
- quantile
- radon
- rdivide
- rotate
- rotate_outer
- smooth
- sqrt
- steepestDescent
- sum
- times
- transformReferenceFrame
- uminus
- volume
- SO3TangentSpace
- doEulerStep
- symmetrise
- SO3FunHandle
- SO3FunBingham
- SO3FunCBF
- SO3FunComposition
- SO3FunRBF
-
SO3FunHarmonic
- SO3FunHarmonic
- L2normalizeFourierCoefficients
- WignerDmap
- adjoint
- adjointNFSOFT
- approximate
- calcFourier
- cat
- conj
- conv
- cor
- ctranspose
- display
- end
- eval
- evalEquispacedFFT
- evalNFSOFT
- evalODFSections
- example
- grad
- horzcat
- interpolate
- inv
- laplace
- length
- max
- mean
- norm
- permute
- plot
- plot3d
- plotFibre
- plotIPDF
- plotPDF
- plotSection
- plus
- quadrature
- radon
- rdivide
- regularize
- reshape
- rotate_outer
- squeeze
- subSet
- subsasgn
- subsref
- sum
- symmetrise
- times
- transpose
- uminus
- vertcat
- volume
- wignerTrafo
- SO3FunHomochoric
- SO3VectorField
- SO3VectorFieldHarmonic
- SO3VectorFieldHandle
- SO3Kernel
-
Plotting
- Overview
- mapPlot
- scaleBar
- sphericalPlot
- mtexFigure
- spherical Projections
- orientation plots
- Euler space sections
- colormaps
- directional color keys
- orientation color keys
-
tools
- annotate
- ar2rgb
- contour3s
- convertFigureRGB2ind
- ellipse
- gcm
- getCamera
- getColormaps
- getHoldState
- getPixelPos
- getUnitScale
- hsl2hsv
- ind2color
- isRGB
- mtexColorMap
- mtexColorbar
- newMapPlot
- newMtexFigure
- newODFSectionPlot
- newSphericalPlot
- nextAxis
- nextstyle
- num2rgb
- optiondraw
- optionplot
- pix2data
- plotEllipse
- plotEllipsoid
- plotEmptySphere
- plotx2east
- plotx2north
- plotx2south
- plotx2west
- plotzIntoPlane
- plotzOutOfPlane
- rgb2str
- saveFigure
- sectionLabels
- selectPolygon
- setCamera
- setColorRange
- simulateClick
- str2rgb
- switchUnit
-
Tools
- Overview
- options
-
math
- ClebschGordan
- ClebschGordanTensor
- ClenshawL
- Wigner3j
- Wigner3jPrecomputed
- Wigner3j_new
- WignerD
- Wigner_d_recursion
- allPairs
- allTriple
- bresenham
- chi2inv
- deg2dim
- det3
- dim2deg
- discreteSample
- eig2
- eig3
- ellip2ke
- ensureNonNeg
- evalkappa
- fclencurt
- findJumps
- legendre0
- legendreNodesWeights
- mhyper
- nadjacent
- nanmean
- nanmeanWeights
- nanmedian
- nanplus
- rhoInside
- smoothn
- sphericalClebschGordan
- sphericalY
- times_outer
- statistics
- graphs
-
kernel functions
- files
- pathes
- dubna xrd
-
misc
- MTEXmenu
- binsearch
- bucketSearch
- calcTDF
- characteristicShape
- choose
- circdensity
- circdiff
- closeAllButCurrentFiles
- cprintf
- cunion
- cut2unitI
- degree
- dispStruct
- displayClass
- doclink
- docmethods
- ensurecell
- equal
- erode
- fillStr
- getmem
- ind2char
- isLocalMinD
- isOctave
- isalmostreal
- isappr
- isempty_cell
- iseven
- isnull
- ispos
- logAxis
- makeDisjoint
- mtexError
- mtex_assert
- n2str
- newer_version
- out2
- pauseline
- plotTDF
- progress
- pullTemp
- pushTemp
- qwarning
- repcell
- rmallappdata
- selectMaxbyColumn
- selectMaxbyRow
- selectMinbyColumn
- selectMinbyRow
- setFont
- setNull
- size2str
- sparseConcat
- splitdata
- stripStar
- stripws
- strong
- submatrix
- trimMat
- varlink
- vdisp
- vec2cell
- wraptext
- wraptext2
- xnum2str