Processing math: 100%

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
  - Miller
  - calcDensity
  - cat
  - char
  - cross
  - display
  - dot
  - dot_outer
  - dspacing
  - exp
  - gridify
  - mean
  - multiplicity
  - perp
  - project2FundamentalRegion
  - region
  - rotate
  - rotate_outer
  - round
  - scatter
  - smooth
  - surf
  - symmetrise
  - text
  - transformReferenceFrame
  - unique
- 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
  - crystalSymmetry
  - add
  - alignment
  - axesDual
  - basicHKL
  - byElements
  - char
  - dispLine
  - display
  - eq
  - load
  - plotHKL
  - plotUVW
  - transformationMatrix
- specimenSymmetry
  - specimenSymmetry
  - char
  - dispLine
- 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
  - plotInnerFace
  - plotSlipSystem
  - plus
  - repmat
  - rotate
  - rotate_outer
  - size
  - subSet
  - subsref
  - times
- rotation
  - rotation
  - byAxisAngle
  - byEuler
  - byMatrix
  - byRodrigues
  - calcDensity
  - cat
  - char
  - display
  - dot
  - dot_outer
  - double
  - fit
  - getMinAxes
  - interp
  - isImproper
  - line
  - load
  - map
  - matrix
  - mldivide
  - mtimes
  - permute
  - plotSection
  - power
  - project2FundamentalRegion
  - repmat
  - reshape
  - subSet
  - subsasgn
  - subsref
  - times
  - transpose
  - uminus
  - unique
- 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
  - fit
  - getFundamentalRegion
  - gridify
  - isMisorientation
  - ldivide
  - load
  - log
  - logm
  - map
  - matchLattice
  - mean
  - mldivide
  - mtimes
  - multiplicity
  - niceEuler
  - parents
  - plot
  - plotIPDF
  - plotPDF
  - plotSection
  - power
  - project
  - project2EulerFR
  - project2FundamentalRegion
  - qqplot
  - quiver
  - quiverSection
  - round2Miller
  - scatter
  - sphereVolume
  - symmetrise
  - tensor
  - times
  - transformReferenceFrame
  - unique
  - variants
  - volume
  - MoritoOrder
  - calcParent
  - calcParent2Child
  - calcVariantId
  - plotVariants
- orientationRegion
  - orientationRegion
  - angle
  - axisSector
  - calcAngleDistribution
  - calcAxisDistribution
  - checkInside
  - cleanUp
  - display
  - eq
  - horzcat
  - maxAngle
  - minAngle
  - ne
  - plot
  - rotate
  - volume
- sphericalRegion
  - sphericalRegion
  - boundary
  - byVertices
  - char
  - checkInside
  - cleanUp
  - display
  - eq
  - isLower
  - isUpper
  - plot
  - polarCoordinates
  - restrict2Lower
  - restrict2Upper
  - rhoRange
  - rotate
  - rotate_outer
  - triangle
  - volume
- fibre
  - fibre
  - angle
  - cat
  - display
  - end
  - eq
  - fit
  - horzcat
  - isempty
  - length
  - multiplicity
  - ne
  - orientation
  - plot
  - plotIPDF
  - plotPDF
  - rotation
  - size
  - subSet
  - subsref
  - symmetrise
  - transpose
  - vertcat
- slipSystem
  - slipSystem
  - SchmidFactor
  - SchmidTensor
  - cat
  - deformationTensor
  - end
  - eq
  - horzcat
  - isempty
  - isscalar
  - length
  - mPrime
  - mtimes
  - ne
  - residualBurgersVector
  - rotate
  - rotate_outer
  - size
  - subSet
  - subsasgn
  - subsref
  - symmetrise
  - trace
  - transpose
  - uminus
  - vertcat
- dislocationSystem
  - dislocationSystem
  - cat
  - end
  - eq
  - horzcat
  - isempty
  - length
  - ne
  - rotate
  - rotate_outer
  - size
  - subSet
  - subsasgn
  - subsref
  - symmetrise
  - tensor
  - transpose
  - uminus
  - vertcat
- 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
  - qq
  - rdivide
  - real
  - repmat
  - reshape
  - scatter
  - setSubSet
  - size
  - std
  - subSet
  - subsasgn
  - subsref
  - sum
  - symmetrise
  - times
  - transpose
  - uminus
  - unique
  - vertcat
- S1Grid
  - S1Grid
  - GridLength
  - coarser
  - delete
  - display
  - dist
  - dist_outer
  - double
  - eq
  - find
  - max
  - min
  - minus
  - plot
  - plus
  - refine
  - shift
  - subGrid
- S2Grid
  - S2Grid
  - cat
  - copy
  - cross
  - delete
  - display
  - find
  - getdata
  - plus
  - polar
  - refine
  - rotate
  - rotate_outer
  - subGrid
  - subsasgn
  - subsref
  - times
  - fibonacciS2Grid
  - char
  - display
  - quadratureS2Grid
  - rotate_outer
  - subsasgn
  - subsref
- S2Triangulation
  - S2Triangulation
  - calcBario
  - checkInside
  - eq
  - plot
  - rotate
- SO3Grid
  - SO3Grid
  - char
  - copy
  - delete
  - display
  - dot_outer
  - find
  - mtimes
  - spy
  - subGrid
  - subSet
  - subsasgn
  - subsref
  - find
  - homochoricSO3Grid
  - char
  - display
  - quadratureSO3Grid
  - subsasgn
  - subsref
  - uniqueQuadratureSO3Grid
- embedding
  - embedding
  - cat
  - dot
  - double
  - horzcat
  - mean
  - minus
  - mtimes
  - norm
  - normalize
  - orientation
  - plot
  - plus
  - project
  - rdivide
  - rotate
  - rotate_outer
  - setDouble
  - sum
  - sym
  - symmetrise
  - times
  - vertcat
- 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
  - MoritoOrder
  - calcParent
  - calcParent2Child
  - calcVariantId
  - plotVariants
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
  - EBSDsquare
  - KAM
  - calcGND
  - interp
  - plotUnitCells
  - pos2ind
  - spatialProfile
  - subGrid
  - subsind
- EBSDhex
  - EBSDhex
  - KAM
  - interp
  - plotUnitCells
  - reduce
  - subsind
- 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
  - 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
  - grainBoundary
  - angle
  - calcGBND
  - calcGBND2
  - calcGBPD
  - calcMeanDirection
  - calcTriplePoints
  - characteristicShape
  - curvature
  - display
  - flip
  - inpolygon
  - intersect
  - isTwinning
  - load
  - minus
  - perimeter
  - plot
  - plus
  - quiver
  - reduce
  - reorder
  - rotate
  - segLength
  - selectByGrainId
  - subSet
  - subsasgn
  - subsref
  - surfor
- triplePointList
  - triplePointList
  - display
  - minus
  - plot
  - plus
  - rotate
  - subSet
  - subsasgn
  - subsref
- parentGrainReconstructor
ODF Analysis
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
  - strainRateTensor
- complianceTensor
- stiffnessTensor
- refractiveIndexTensor
- curvatureTensor
- spinTensor
  - spinTensor
- ChristoffelTensor
  - ChristoffelTensor
- velocityGradientTensor
- deformationGradientTensor
- dislocationDensityTensor
  - dislocationDensityTensor
  - curvature
Spherical Functions
- Overview
- S2Fun
  - S2Fun
  - abs
  - contour
  - contourf
  - conv
  - discreteSample
  - display
  - grad
  - log
  - log2
  - max
  - mean
  - min
  - minus
  - mrdivide
  - mtimes
  - norm
  - pcolor
  - plot
  - plot3d
  - plotSection
  - plus
  - quiver3
  - quiverSection
  - rdivide
  - rotate
  - rotate_outer
  - smiley
  - sum
  - surf
  - times
  - uminus
  - unimodal
  - volume
- S2FunHandle
  - S2FunHandle
  - rotate_outer
- S2FunTri
  - S2FunTri
  - abs
  - display
  - eval
  - grad
  - le
  - mean
  - min
  - plot
  - plus
  - power
  - rdivide
  - rotate
  - times
  - uminus
  - volume
- BinghamS2
  - BinghamS2
  - fit
  - rotate
- S2FunHarmonic
  - S2FunHarmonic
  - abs
  - acos
  - adjoint
  - approximate
  - calcSymAxis
  - cat
  - conj
  - conv
  - cos
  - ctranspose
  - display
  - dot
  - eig
  - end
  - entropy
  - eval
  - even
  - grad
  - horzcat
  - interpolate
  - isempty
  - le
  - length
  - log
  - mean
  - mtimes
  - norm
  - plotSpektra
  - plus
  - power
  - quadrature
  - radon
  - rdivide
  - regularize
  - reshape
  - rotate
  - rotate_outer
  - simultaniousCG
  - sqrt
  - steepestDescent
  - subsasgn
  - subsref
  - sum
  - symmetrise
  - times
  - transpose
  - truncate
  - uminus
  - vertcat
  - volume
- S2FunHarmonicSym
  - S2FunHarmonicSym
  - display
  - plot
  - plus
  - power
  - quadrature
  - rdivide
  - times
- S2AxisField
  - S2AxisField
  - angle
  - plot
  - quiver
  - quiver3
- S2AxisFieldTri
  - S2AxisFieldTri
  - angle
  - cross
  - dot
  - eval
- S2AxisFieldHarmonic
  - S2AxisFieldHarmonic
  - approximate
  - cross
  - display
  - dot
  - eval
  - interpolate
  - quadrature
- S2VectorField
  - S2VectorField
  - angle
  - display
  - dot
  - n
  - norm
  - normal
  - normalize
  - plot
  - plotSection
  - polar
  - quiver
  - quiver3
  - quiverSection
  - rho
  - sigma
  - tangential
  - theta
- S2VectorFieldHarmonic
  - S2VectorFieldHarmonic
  - approximate
  - cross
  - display
  - dot
  - eval
  - interpolate
  - mean
  - minus
  - mtimes
  - norm
  - plus
  - quadrature
  - rdivide
  - rotate
  - times
  - uminus
- S2VectorFieldTri
  - S2VectorFieldTri
  - angle
  - cross
  - display
  - dot
  - eval
  - minus
  - norm
  - plus
  - rdivide
  - times
  - uminus
- S2Kernel
  - S2Kernel
  - conv
  - grad
  - plotSpektra
  - radon
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
  - SO3FunHandle
  - display
  - eval
  - example
  - length
  - numel
  - rotate_outer
  - size
- SO3FunBingham
  - SO3FunBingham
  - approximate
  - display
  - eval
  - example
  - interpolate
  - mean
  - radon
  - rotate
  - times
  - uminus
- SO3FunCBF
  - SO3FunCBF
  - calcFourier
  - conv
  - discreteSample
  - display
  - eval
  - example
  - grad
  - mean
  - radon
  - rotate
  - times
  - uminus
- SO3FunComposition
  - SO3FunComposition
  - calcFourier
  - char
  - discreteSample
  - display
  - eval
  - example
  - grad
  - mean
  - radon
  - rotate
  - rotate_outer
  - smooth
  - times
  - uminus
  - volume
- SO3FunRBF
  - SO3FunRBF
  - approximate
  - calcFourier
  - cat
  - conv
  - discreteSample
  - display
  - eval
  - example
  - grad
  - horzcat
  - interpolate
  - inv
  - mean
  - plus
  - radon
  - rotate
  - sum
  - times
  - uminus
  - vertcat
  - volume
- 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
  - plot
  - plot3d
  - plotFibre
  - plotIPDF
  - plotPDF
  - plotSection
  - plus
  - quadrature
  - radon
  - rdivide
  - regularize
  - reshape
  - rotate_outer
  - subsasgn
  - subsref
  - sum
  - symmetrise
  - times
  - transpose
  - uminus
  - vertcat
  - volume
  - wignerTrafo
- SO3FunHomochoric
  - SO3FunHomochoric
  - eval
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volumeCompressibility

volumeCompressibility edit page

computes the volume compressibility of an elasticity tensor

Description

$\beta(x) = S_{iikk}$

Syntax

beta = volumeCompressibility(S)

Input

`C`	`elastic stiffness tensor`

Output

beta volume compressibility