iterative scaling algorithm to equilibrate rows and column norms in matrices More...

Namespaces
	Architecture

	HybridNonLinearSolverSpace

	internal

	LevenbergMarquardtSpace

	numext

Classes
class	aligned_allocator
	STL compatible allocator to use with with 16 byte aligned types. More...

class	aligned_allocator_indirection

class	AlignedBox
	An axis aligned box. More...

class	AMDOrdering

class	AngleAxis
	Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...

class	Array
	General-purpose arrays with easy API for coefficient-wise operations. More...

class	ArrayBase
	Base class for all 1D and 2D array, and related expressions. More...

class	ArrayWrapper
	Expression of a mathematical vector or matrix as an array object. More...

struct	ArrayXpr

class	AutoDiffJacobian

class	AutoDiffScalar
	A scalar type replacement with automatic differentation capability. More...

class	AutoDiffVector

class	BiCGSTAB
	A bi conjugate gradient stabilized solver for sparse square problems. More...

class	Block
	Expression of a fixed-size or dynamic-size block. More...

class	BlockImpl

class	BlockImpl< SparseMatrix< _Scalar, _Options, _Index >, BlockRows, BlockCols, true, Sparse >

class	BlockImpl< XprType, BlockRows, BlockCols, InnerPanel, Dense >

class	BlockImpl< XprType, BlockRows, BlockCols, InnerPanel, Sparse >

class	BlockImpl< XprType, BlockRows, BlockCols, true, Sparse >

class	CholmodBase
	The base class for the direct Cholesky factorization of Cholmod. More...

class	CholmodDecomposition
	A general Cholesky factorization and solver based on Cholmod. More...

class	CholmodSimplicialLDLT
	A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod. More...

class	CholmodSimplicialLLT
	A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod. More...

class	CholmodSupernodalLLT
	A supernodal Cholesky (LLT) factorization and solver based on Cholmod. More...

class	CoeffBasedProduct

class	COLAMDOrdering

class	ColPivHouseholderQR
	Householder rank-revealing QR decomposition of a matrix with column-pivoting. More...

class	CommaInitializer
	Helper class used by the comma initializer operator. More...

class	ComplexEigenSolver
	Computes eigenvalues and eigenvectors of general complex matrices. More...

class	ComplexSchur
	Performs a complex Schur decomposition of a real or complex square matrix. More...

class	Conjugate

class	ConjugateGradient
	A conjugate gradient solver for sparse self-adjoint problems. More...

class	Cross

class	Cwise
	Pseudo expression providing additional coefficient-wise operations. More...

class	CwiseBinaryOp
	Generic expression where a coefficient-wise binary operator is applied to two expressions. More...

class	CwiseBinaryOpImpl

class	CwiseBinaryOpImpl< BinaryOp, Lhs, Rhs, Dense >

class	CwiseBinaryOpImpl< BinaryOp, Lhs, Rhs, Sparse >

class	CwiseNullaryOp
	Generic expression of a matrix where all coefficients are defined by a functor. More...

class	CwiseUnaryOp
	Generic expression where a coefficient-wise unary operator is applied to an expression. More...

class	CwiseUnaryOpImpl

class	CwiseUnaryOpImpl< UnaryOp, MatrixType, Sparse >

class	CwiseUnaryOpImpl< UnaryOp, XprType, Dense >

class	CwiseUnaryView
	Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector. More...

class	CwiseUnaryViewImpl

class	CwiseUnaryViewImpl< ViewOp, MatrixType, Dense >

class	CwiseUnaryViewImpl< ViewOp, MatrixType, Sparse >

struct	Dense

class	DenseBase
	Base class for all dense matrices, vectors, and arrays. More...

class	DenseCoeffsBase

class	DenseCoeffsBase< Derived, DirectAccessors >
	Base class providing direct read-only coefficient access to matrices and arrays. More...

class	DenseCoeffsBase< Derived, DirectWriteAccessors >
	Base class providing direct read/write coefficient access to matrices and arrays. More...

class	DenseCoeffsBase< Derived, ReadOnlyAccessors >
	Base class providing read-only coefficient access to matrices and arrays. More...

class	DenseCoeffsBase< Derived, WriteAccessors >
	Base class providing read/write coefficient access to matrices and arrays. More...

struct	DenseSparseProductReturnType

struct	DenseSparseProductReturnType< Lhs, Rhs, 1 >

class	DenseStorage

class	DenseStorage< T, 0, _Rows, _Cols, _Options >

class	DenseStorage< T, 0, _Rows, Dynamic, _Options >

class	DenseStorage< T, 0, Dynamic, _Cols, _Options >

class	DenseStorage< T, 0, Dynamic, Dynamic, _Options >

class	DenseStorage< T, Dynamic, _Rows, Dynamic, _Options >

class	DenseStorage< T, Dynamic, Dynamic, _Cols, _Options >

class	DenseStorage< T, Dynamic, Dynamic, Dynamic, _Options >

class	DenseStorage< T, Size, _Rows, Dynamic, _Options >

class	DenseStorage< T, Size, Dynamic, _Cols, _Options >

class	DenseStorage< T, Size, Dynamic, Dynamic, _Options >

class	DenseTimeSparseProduct

class	DenseTimeSparseSelfAdjointProduct

class	DGMRES
	A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse linear systems. The basis is built with modified Gram-Schmidt. At each restart, a few approximated eigenvectors corresponding to the smallest eigenvalues are used to build a preconditioner for the next cycle. This preconditioner for deflation can be combined with any other preconditioner, the IncompleteLUT for instance. The preconditioner is applied at right of the matrix and the combination is multiplicative. More...

class	Diagonal
	Expression of a diagonal/subdiagonal/superdiagonal in a matrix. More...

class	DiagonalBase

class	DiagonalMatrix
	Represents a diagonal matrix with its storage. More...

class	DiagonalPreconditioner
	A preconditioner based on the digonal entries. More...

class	DiagonalProduct

class	DiagonalWrapper
	Expression of a diagonal matrix. More...

class	DynamicSkylineMatrix

class	DynamicSparseMatrix
	A sparse matrix class designed for matrix assembly purpose. More...

struct	ei_cleantype

struct	ei_cleantype< const T & >

struct	ei_cleantype< const T * >

struct	ei_cleantype< const T >

struct	ei_cleantype< T & >

struct	ei_cleantype< T * >

struct	ei_is_same_type

struct	ei_is_same_type< T, T >

struct	ei_meta_false

struct	ei_meta_if

struct	ei_meta_if< false, Then, Else >

class	ei_meta_sqrt

class	ei_meta_sqrt< Y, InfX, SupX, true >

struct	ei_meta_true

struct	ei_quaternion_assign_impl

struct	ei_quaternion_assign_impl< Other, 3, 3 >

struct	ei_quaternion_assign_impl< Other, 4, 1 >

struct	ei_traits

struct	ei_traits< AngleAxis< _Scalar > >

struct	ei_traits< Quaternion< _Scalar > >

struct	ei_traits< Rotation2D< _Scalar > >

struct	ei_transform_product_impl

struct	ei_transform_product_impl< Other, Dim, HDim, Dim, 1 >

struct	ei_transform_product_impl< Other, Dim, HDim, Dim, Dim >

struct	ei_transform_product_impl< Other, Dim, HDim, HDim, 1 >

struct	ei_transform_product_impl< Other, Dim, HDim, HDim, HDim >

struct	ei_unconst

struct	ei_unconst< const T >

struct	ei_unconst< T const & >

struct	ei_unconst< T const * >

struct	ei_unpointer

struct	ei_unpointer< T * >

struct	ei_unpointer< T *const >

struct	ei_unref

struct	ei_unref< T & >

struct	EigenBase

class	EigenSolver
	Computes eigenvalues and eigenvectors of general matrices. More...

class	Flagged
	Expression with modified flags. More...

class	ForceAlignedAccess
	Enforce aligned packet loads and stores regardless of what is requested. More...

class	FullPivHouseholderQR
	Householder rank-revealing QR decomposition of a matrix with full pivoting. More...

class	FullPivLU
	LU decomposition of a matrix with complete pivoting, and related features. More...

struct	general_product_to_triangular_selector

struct	general_product_to_triangular_selector< MatrixType, ProductType, UpLo, false >

struct	general_product_to_triangular_selector< MatrixType, ProductType, UpLo, true >

class	GeneralizedEigenSolver
	Computes the generalized eigenvalues and eigenvectors of a pair of general matrices. More...

class	GeneralizedSelfAdjointEigenSolver
	Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem. More...

class	GeneralProduct
	Expression of the product of two general matrices or vectors. More...

class	GeneralProduct< Lhs, Rhs, GemmProduct >

class	GeneralProduct< Lhs, Rhs, GemvProduct >

class	GeneralProduct< Lhs, Rhs, InnerProduct >

class	GeneralProduct< Lhs, Rhs, OuterProduct >

struct	GenericNumTraits

class	GMRES
	A GMRES solver for sparse square problems. More...

class	HessenbergDecomposition
	Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation. More...

class	Homogeneous
	Expression of one (or a set of) homogeneous vector(s) More...

class	HouseholderQR
	Householder QR decomposition of a matrix. More...

class	HouseholderSequence
	Sequence of Householder reflections acting on subspaces with decreasing size. More...

class	HybridNonLinearSolver
	Finds a zero of a system of n nonlinear functions in n variables by a modification of the Powell hybrid method ("dogleg"). More...

class	Hyperplane
	A hyperplane. More...

class	IdentityPreconditioner
	A naive preconditioner which approximates any matrix as the identity matrix. More...

class	IncompleteCholesky
	Modified Incomplete Cholesky with dual threshold. More...

class	IncompleteLU

class	IncompleteLUT
	Incomplete LU factorization with dual-threshold strategy. More...

class	InnerStride
	Convenience specialization of Stride to specify only an inner stride See class Map for some examples. More...

class	IOFormat
	Stores a set of parameters controlling the way matrices are printed. More...

class	IterationController
	Controls the iterations of the iterative solvers. More...

class	IterativeSolverBase
	Base class for linear iterative solvers. More...

class	IterScaling

class	JacobiRotation
	Rotation given by a cosine-sine pair. More...

class	JacobiSVD
	Two-sided Jacobi SVD decomposition of a rectangular matrix. More...

class	KdBVH
	A simple bounding volume hierarchy based on AlignedBox. More...

class	KroneckerProduct
	Kronecker tensor product helper class for dense matrices. More...

class	KroneckerProductSparse
	Kronecker tensor product helper class for sparse matrices. More...

struct	LazyProductReturnType

class	LDLT
	Robust Cholesky decomposition of a matrix with pivoting. More...

class	LevenbergMarquardt
	Performs non linear optimization over a non-linear function, using a variant of the Levenberg Marquardt algorithm. More...

class	LLT
	Standard Cholesky decomposition (LL^T) of a matrix and associated features. More...

class	LU

class	Map
	A matrix or vector expression mapping an existing array of data. More...

class	Map< const Quaternion< _Scalar >, _Options >
	Quaternion expression mapping a constant memory buffer. More...

class	Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >

class	Map< Quaternion< _Scalar >, _Options >
	Expression of a quaternion from a memory buffer. More...

class	Map< Transpositions< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, PacketAccess >

class	MapBase
	Base class for Map and Block expression with direct access. More...

class	MapBase< Derived, ReadOnlyAccessors >

class	MapBase< Derived, WriteAccessors >

class	MappedSkylineMatrix

class	MappedSparseMatrix
	Sparse matrix. More...

class	Matrix
	The matrix class, also used for vectors and row-vectors. More...

class	MatrixBase
	Base class for all dense matrices, vectors, and expressions. More...

class	MatrixExponential
	Class for computing the matrix exponential. More...

struct	MatrixExponentialReturnValue
	Proxy for the matrix exponential of some matrix (expression). More...

class	MatrixFunction
	Class for computing matrix functions. More...

class	MatrixFunction< MatrixType, AtomicType, 0 >

class	MatrixFunction< MatrixType, AtomicType, 1 >

class	MatrixFunctionAtomic
	Helper class for computing matrix functions of atomic matrices. More...

class	MatrixFunctionReturnValue
	Proxy for the matrix function of some matrix (expression). More...

class	MatrixLogarithmAtomic
	Helper class for computing matrix logarithm of atomic matrices. More...

class	MatrixLogarithmReturnValue
	Proxy for the matrix logarithm of some matrix (expression). More...

class	MatrixMarketIterator
	Iterator to browse matrices from a specified folder. More...

class	MatrixPower
	Class for computing matrix powers. More...

class	MatrixPowerAtomic

class	MatrixPowerProduct

class	MatrixPowerReturnValue
	Proxy for the matrix power of some matrix (expression). More...

class	MatrixPowerRetval

class	MatrixSquareRoot
	Class for computing matrix square roots of general matrices. More...

class	MatrixSquareRoot< MatrixType, 0 >

class	MatrixSquareRoot< MatrixType, 1 >

class	MatrixSquareRootQuasiTriangular
	Class for computing matrix square roots of upper quasi-triangular matrices. More...

class	MatrixSquareRootReturnValue
	Proxy for the matrix square root of some matrix (expression). More...

class	MatrixSquareRootTriangular
	Class for computing matrix square roots of upper triangular matrices. More...

class	MatrixWrapper
	Expression of an array as a mathematical vector or matrix. More...

struct	MatrixXpr

class	MetisOrdering

class	Minor
	Expression of a minor. More...

class	MINRES
	A minimal residual solver for sparse symmetric problems. More...

class	NaturalOrdering

class	NestByValue
	Expression which must be nested by value. More...

class	NoAlias
	Pseudo expression providing an operator = assuming no aliasing. More...

class	NumericalDiff

class	NumTraits
	Holds information about the various numeric (i.e. scalar) types allowed by Eigen. More...

struct	NumTraits< Array< Scalar, Rows, Cols, Options, MaxRows, MaxCols > >

struct	NumTraits< double >

struct	NumTraits< float >

struct	NumTraits< long double >

struct	NumTraits< std::complex< _Real > >

class	OuterStride
	Convenience specialization of Stride to specify only an outer stride See class Map for some examples. More...

class	ParametrizedLine
	A parametrized line. More...

class	PardisoImpl

class	PardisoLDLT
	A sparse direct Cholesky (LDLT) factorization and solver based on the PARDISO library. More...

class	PardisoLLT
	A sparse direct Cholesky (LLT) factorization and solver based on the PARDISO library. More...

class	PardisoLU
	A sparse direct LU factorization and solver based on the PARDISO library. More...

class	PartialPivLU
	LU decomposition of a matrix with partial pivoting, and related features. More...

class	PartialReduxExpr
	Generic expression of a partially reduxed matrix. More...

class	PastixBase

class	PastixLDLT
	A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library. More...

class	PastixLLT
	A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library. More...

class	PastixLU
	Interface to the PaStix solver. More...

class	PermutationBase
	Base class for permutations. More...

class	PermutationMatrix
	Permutation matrix. More...

struct	PermutationStorage

class	PermutationWrapper
	Class to view a vector of integers as a permutation matrix. More...

class	PermutedImpl

class	PlainObjectBase
	Dense storage base class for matrices and arrays. More...

class	PolynomialSolver
	A polynomial solver. More...

class	PolynomialSolver< _Scalar, 1 >

class	PolynomialSolverBase
	Defined to be inherited by polynomial solvers: it provides convenient methods such as. More...

class	ProductBase

class	ProductReturnType
	Helper class to get the correct and optimized returned type of operator*. More...

struct	ProductReturnType< Lhs, Rhs, CoeffBasedProductMode >

struct	ProductReturnType< Lhs, Rhs, LazyCoeffBasedProductMode >

class	QR

class	Quaternion
	The quaternion class used to represent 3D orientations and rotations. More...

class	QuaternionBase
	Base class for quaternion expressions. More...

class	RandomSetter
	The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access. More...

class	RealQZ
	Performs a real QZ decomposition of a pair of square matrices. More...

class	RealSchur
	Performs a real Schur decomposition of a square matrix. More...

class	Ref
	A matrix or vector expression mapping an existing expressions. More...

class	Ref< const TPlainObjectType, Options, StrideType >

class	RefBase

class	Replicate
	Expression of the multiple replication of a matrix or vector. More...

class	ReturnByValue

class	Reverse
	Expression of the reverse of a vector or matrix. More...

class	Rotation2D
	Represents a rotation/orientation in a 2 dimensional space. More...

class	RotationBase
	Common base class for compact rotation representations. More...

class	ScaledProduct

class	Scaling
	Represents a possibly non uniform scaling transformation. More...

class	Select
	Expression of a coefficient wise version of the C++ ternary operator ?: More...

struct	selfadjoint_product_selector

struct	selfadjoint_product_selector< MatrixType, OtherType, UpLo, false >

struct	selfadjoint_product_selector< MatrixType, OtherType, UpLo, true >

struct	selfadjoint_rank1_update

struct	selfadjoint_rank1_update< Scalar, Index, ColMajor, UpLo, ConjLhs, ConjRhs >

struct	selfadjoint_rank1_update< Scalar, Index, RowMajor, UpLo, ConjLhs, ConjRhs >

class	SelfAdjointEigenSolver
	Computes eigenvalues and eigenvectors of selfadjoint matrices. More...

struct	SelfadjointProductMatrix

struct	SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >

struct	SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >

struct	SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >

class	SelfAdjointView
	Expression of a selfadjoint matrix from a triangular part of a dense matrix. More...

class	SelfCwiseBinaryOp

class	SimplicialCholesky

class	SimplicialCholeskyBase
	A direct sparse Cholesky factorizations. More...

class	SimplicialLDLT
	A direct sparse LDLT Cholesky factorizations without square root. More...

class	SimplicialLLT
	A direct sparse LLT Cholesky factorizations. More...

class	SkylineInplaceLU
	Inplace LU decomposition of a skyline matrix and associated features. More...

class	SkylineMatrix
	The main skyline matrix class. More...

class	SkylineMatrixBase
	Base class of any skyline matrices or skyline expressions. More...

class	SkylineProduct

struct	SkylineProductReturnType

class	SkylineStorage

class	SkylineVector

struct	SluMatrix

struct	SluMatrixMapHelper

struct	SluMatrixMapHelper< Matrix< Scalar, Rows, Cols, Options, MRows, MCols > >

struct	SluMatrixMapHelper< SparseMatrixBase< Derived > >

class	SparseDenseOuterProduct

struct	SparseDenseProductReturnType

struct	SparseDenseProductReturnType< Lhs, Rhs, 1 >

class	SparseDiagonalProduct

class	SparseLU
	Sparse supernodal LU factorization for general matrices. More...

struct	SparseLUMatrixLReturnType

struct	SparseLUMatrixUReturnType

class	SparseMatrix
	A versatible sparse matrix representation. More...

class	SparseMatrixBase
	Base class of any sparse matrices or sparse expressions. More...

class	SparseQR
	Sparse left-looking rank-revealing QR factorization. More...

struct	SparseQR_QProduct

struct	SparseQRMatrixQReturnType

struct	SparseQRMatrixQTransposeReturnType

class	SparseSelfAdjointTimeDenseProduct

class	SparseSelfAdjointView
	Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix. More...

class	SparseSparseProduct

struct	SparseSparseProductReturnType

class	SparseSymmetricPermutationProduct

class	SparseTimeDenseProduct

class	SparseTriangularView

class	SparseVector
	a sparse vector class More...

class	SparseView

class	Spline
	A class representing multi-dimensional spline curves. More...

struct	SplineFitting
	Spline fitting methods. More...

struct	SplineTraits

struct	SplineTraits< Spline< _Scalar, _Dim, _Degree >, _DerivativeOrder >
	Compile-time attributes of the Spline class for fixed degree. More...

struct	SplineTraits< Spline< _Scalar, _Dim, _Degree >, Dynamic >
	Compile-time attributes of the Spline class for Dynamic degree. More...

class	SPQR
	Sparse QR factorization based on SuiteSparseQR library. More...

struct	SPQR_QProduct

struct	SPQRMatrixQReturnType

struct	SPQRMatrixQTransposeReturnType

struct	StdMapTraits

class	StdStemFunctions
	Stem functions corresponding to standard mathematical functions. More...

class	Stride
	Holds strides information for Map. More...

class	SuperLU
	A sparse direct LU factorization and solver based on the SuperLU library. More...

class	SuperLUBase
	The base class for the direct and incomplete LU factorization of SuperLU. More...

class	SVD
	Standard SVD decomposition of a matrix and associated features. More...

class	SwapWrapper

class	Transform
	Represents an homogeneous transformation in a N dimensional space. More...

class	Translation
	Represents a translation transformation. More...

class	Transpose
	Expression of the transpose of a matrix. More...

class	Transpose< PermutationBase< Derived > >

class	Transpose< TranspositionsBase< TranspositionsDerived > >

class	TransposeImpl

class	TransposeImpl< MatrixType, Dense >

class	TransposeImpl< MatrixType, Sparse >

class	Transpositions
	Represents a sequence of transpositions (row/column interchange) More...

class	TranspositionsBase

class	TranspositionsWrapper

class	TriangularBase

struct	TriangularProduct

struct	TriangularProduct< Mode, false, Lhs, true, Rhs, false >

struct	TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >

struct	TriangularProduct< Mode, true, Lhs, false, Rhs, true >

class	TriangularView
	Base class for triangular part in a matrix. More...

class	Tridiagonalization
	Tridiagonal decomposition of a selfadjoint matrix. More...

class	Triplet
	A small structure to hold a non zero as a triplet (i,j,value). More...

class	UmfPackLU
	A sparse LU factorization and solver based on UmfPack. More...

class	UniformScaling

class	VectorBlock
	Expression of a fixed-size or dynamic-size sub-vector. More...

class	VectorwiseOp
	Pseudo expression providing partial reduction operations. More...

class	WithFormat
	Pseudo expression providing matrix output with given format. More...

Typedefs
typedef Transform< double, 2, Affine >	Affine2d

typedef Transform< float, 2, Affine >	Affine2f

typedef Transform< double, 3, Affine >	Affine3d

typedef Transform< float, 3, Affine >	Affine3f

typedef Transform< double, 2, AffineCompact >	AffineCompact2d

typedef Transform< float, 2, AffineCompact >	AffineCompact2f

typedef Transform< double, 3, AffineCompact >	AffineCompact3d

typedef Transform< float, 3, AffineCompact >	AffineCompact3f

typedef DiagonalMatrix< double, 2 >	AlignedScaling2d

typedef DiagonalMatrix< float, 2 >	AlignedScaling2f

typedef DiagonalMatrix< double, 3 >	AlignedScaling3d

typedef DiagonalMatrix< float, 3 >	AlignedScaling3f

typedef AngleAxis< double >	AngleAxisd

typedef AngleAxis< float >	AngleAxisf

typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE	DenseIndex

typedef Transform< double, 2, Isometry >	Isometry2d

typedef Transform< float, 2, Isometry >	Isometry2f

typedef Transform< double, 3, Isometry >	Isometry3d

typedef Transform< float, 3, Isometry >	Isometry3f

typedef Transform< double, 2, Projective >	Projective2d

typedef Transform< float, 2, Projective >	Projective2f

typedef Transform< double, 3, Projective >	Projective3d

typedef Transform< float, 3, Projective >	Projective3f

typedef Quaternion< double >	Quaterniond

typedef Quaternion< float >	Quaternionf

typedef Map< Quaternion< double >, Aligned >	QuaternionMapAlignedd

typedef Map< Quaternion< float >, Aligned >	QuaternionMapAlignedf

typedef Map< Quaternion< double >, 0 >	QuaternionMapd

typedef Map< Quaternion< float >, 0 >	QuaternionMapf

typedef Rotation2D< double >	Rotation2Dd

typedef Rotation2D< float >	Rotation2Df

typedef Scaling< double, 2 >	Scaling2d

typedef Scaling< float, 2 >	Scaling2f

typedef Scaling< double, 3 >	Scaling3d

typedef Scaling< float, 3 >	Scaling3f

typedef Spline< double, 2 >	Spline2d
	2D double B-spline with dynamic degree. More...

typedef Spline< float, 2 >	Spline2f
	2D float B-spline with dynamic degree. More...

typedef Spline< double, 3 >	Spline3d
	3D double B-spline with dynamic degree. More...

typedef Spline< float, 3 >	Spline3f
	3D float B-spline with dynamic degree. More...

typedef Transform< double, 2 >	Transform2d

typedef Transform< float, 2 >	Transform2f

typedef Transform< double, 3 >	Transform3d

typedef Transform< float, 3 >	Transform3f

typedef Translation< double, 2 >	Translation2d

typedef Translation< float, 2 >	Translation2f

typedef Translation< double, 3 >	Translation3d

typedef Translation< float, 3 >	Translation3f

Enumerations
enum	{ Large = 2, Small = 3 }

enum	{ DontAlignCols = 1 }

enum	{ StreamPrecision = -1, FullPrecision = -2 }

enum	{ Lower =0x1, Upper =0x2, UnitDiag =0x4, ZeroDiag =0x8, UnitLower =UnitDiag\|Lower, UnitUpper =UnitDiag\|Upper, StrictlyLower =ZeroDiag\|Lower, StrictlyUpper =ZeroDiag\|Upper, SelfAdjoint =0x10, Symmetric =0x20 }

enum	{ Unaligned =0, Aligned =1 }

enum	{ DefaultTraversal, LinearTraversal, InnerVectorizedTraversal, LinearVectorizedTraversal, SliceVectorizedTraversal, InvalidTraversal, AllAtOnceTraversal }

enum	{ NoUnrolling, InnerUnrolling, CompleteUnrolling }

enum	{ Specialized, BuiltIn }

enum	{ ColMajor = 0, RowMajor = 0x1, AutoAlign = 0, DontAlign = 0x2 }

enum	{ OnTheLeft = 1, OnTheRight = 2 }

enum	{ IsDense = 0, IsSparse }

enum	{ CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct }

enum	{ IsSkyline = SkylineBit }

enum	{ SPD = 0x100, NonSymmetric = 0x0 }

enum	AccessorLevels { ReadOnlyAccessors, WriteAccessors, DirectAccessors, DirectWriteAccessors }

enum	Action { GetAction, SetAction }

enum	AdditionalProductEvaluationMode { SkylineTimeDenseProduct, SkylineTimeSkylineProduct, DenseTimeSkylineProduct }

enum	CholmodMode { CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt }

enum	ComputationInfo { Success = 0, NumericalIssue = 1, NoConvergence = 2, InvalidInput = 3 }

enum	CornerType { TopLeft, TopRight, BottomLeft, BottomRight }

enum	DecompositionOptions { Pivoting = 0x01, NoPivoting = 0x02, ComputeFullU = 0x04, ComputeThinU = 0x08, ComputeFullV = 0x10, ComputeThinV = 0x20, EigenvaluesOnly = 0x40, ComputeEigenvectors = 0x80, EigVecMask = EigenvaluesOnly \| ComputeEigenvectors, Ax_lBx = 0x100, ABx_lx = 0x200, BAx_lx = 0x400, GenEigMask = Ax_lBx \| ABx_lx \| BAx_lx }

enum	Default_t { Default }

enum	DirectionType { Vertical, Horizontal, BothDirections }

enum	NoChange_t { NoChange }

enum	NumericalDiffMode { Forward, Central }

enum	QRPreconditioners { NoQRPreconditioner, HouseholderQRPreconditioner, ColPivHouseholderQRPreconditioner, FullPivHouseholderQRPreconditioner }

enum	Sequential_t { Sequential }

enum	SimplicialCholeskyMode { SimplicialCholeskyLLT, SimplicialCholeskyLDLT }

enum	TransformTraits { Isometry = 0x1, Affine = 0x2, AffineCompact = 0x10 \| Affine, Projective = 0x20 }

Functions
template<typename DerTypeA , typename DerTypeB >
const AutoDiffScalar< Matrix< typename internal::traits< DerTypeA >::Scalar, Dynamic, 1 > >	atan2 (const AutoDiffScalar< DerTypeA > &a, const AutoDiffScalar< DerTypeB > &b)

template<typename DerType , typename T >
	AutoDiffScalar< DerType > (min)(const AutoDiffScalar< DerType > &x

template<typename DerType , typename T >
	AutoDiffScalar< DerType > (max)(const AutoDiffScalar< DerType > &x

template<typename SplineType , typename DerivativeType >
void	basisFunctionDerivativesImpl (const SplineType &spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType &N_)

template<typename BVH , typename Intersector >
void	BVIntersect (const BVH &tree, Intersector &intersector)

template<typename BVH1 , typename BVH2 , typename Intersector >
void	BVIntersect (const BVH1 &tree1, const BVH2 &tree2, Intersector &intersector)

template<typename BVH , typename Minimizer >
Minimizer::Scalar	BVMinimize (const BVH &tree, Minimizer &minimizer)

template<typename BVH1 , typename BVH2 , typename Minimizer >
Minimizer::Scalar	BVMinimize (const BVH1 &tree1, const BVH2 &tree2, Minimizer &minimizer)

template<typename Polynomial >
NumTraits< typename Polynomial::Scalar >::Real	cauchy_max_bound (const Polynomial &poly)

template<typename Polynomial >
NumTraits< typename Polynomial::Scalar >::Real	cauchy_min_bound (const Polynomial &poly)

template<typename Scalar >
std::complex< Scalar >	cdiv (const Scalar &xr, const Scalar &xi, const Scalar &yr, const Scalar &yi)

template<typename PointArrayType , typename KnotVectorType >
void	ChordLengths (const PointArrayType &pts, KnotVectorType &chord_lengths)
	Computes chord length parameters which are required for spline interpolation. More...

template<typename DerType >
const AutoDiffScalar< DerType > &	conj (const AutoDiffScalar< DerType > &x)

template<typename SplineType , typename DerivativeType >
void	derivativesImpl (const SplineType &spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType &der)

template<typename T >
NumTraits< T >::Real	ei_abs (const T &x)

template<typename T >
NumTraits< T >::Real	ei_abs2 (const T &x)

template<typename T >
void	ei_aligned_delete (T *ptr, size_t size)

void	ei_aligned_free (void *ptr)

void *	ei_aligned_malloc (size_t size)

template<typename T >
T *	ei_aligned_new (size_t size)

void *	ei_aligned_realloc (void *ptr, size_t new_size, size_t old_size)

template<typename T >
T	ei_atan2 (const T &x, const T &y)

template<bool Align>
void	ei_conditional_aligned_free (void *ptr)

template<bool Align>
void *	ei_conditional_aligned_malloc (size_t size)

template<bool Align>
void *	ei_conditional_aligned_realloc (void *ptr, size_t new_size, size_t old_size)

template<typename T >
T	ei_conj (const T &x)

template<typename T >
T	ei_cos (const T &x)

template<typename T >
T	ei_exp (const T &x)

void	ei_handmade_aligned_free (void *ptr)

void *	ei_handmade_aligned_malloc (size_t size)

template<typename T >
NumTraits< T >::Real	ei_imag (const T &x)

template<typename Scalar >
bool	ei_isApprox (const Scalar &x, const Scalar &y, typename NumTraits< Scalar >::Real precision=NumTraits< Scalar >::dummy_precision())

template<typename Scalar >
bool	ei_isApproxOrLessThan (const Scalar &x, const Scalar &y, typename NumTraits< Scalar >::Real precision=NumTraits< Scalar >::dummy_precision())

template<typename Scalar , typename OtherScalar >
bool	ei_isMuchSmallerThan (const Scalar &x, const OtherScalar &y, typename NumTraits< Scalar >::Real precision=NumTraits< Scalar >::dummy_precision())

template<typename T >
T	ei_log (const T &x)

template<typename T >
T	ei_pow (const T &x, const T &y)

template<typename Scalar >
Quaternion< Scalar >	ei_quaternion_product (const Quaternion< Scalar > &a, const Quaternion< Scalar > &b)

template<typename T >
T	ei_random ()

template<typename T >
T	ei_random (const T &x, const T &y)

template<typename T >
NumTraits< T >::Real	ei_real (const T &x)

template<typename T >
T	ei_sin (const T &x)

template<typename T >
T	ei_sqrt (const T &x)

template<typename Scalar , int Dim>
static Matrix< Scalar, 2, 2 >	ei_toRotationMatrix (const Scalar &s)

template<typename Scalar , int Dim, typename OtherDerived >
static Matrix< Scalar, Dim, Dim >	ei_toRotationMatrix (const RotationBase< OtherDerived, Dim > &r)

template<typename Scalar , int Dim, typename OtherDerived >
static const MatrixBase< OtherDerived > &	ei_toRotationMatrix (const MatrixBase< OtherDerived > &mat)

	EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY (abs, using std::abs;return ReturnType(abs(x.value()), x.derivatives()*(x.value()< 0?-1:1));) EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2

	EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY (sqrt, using std::sqrt;Scalar sqrtx=sqrt(x.value());return ReturnType(sqrtx, x.derivatives()*(Scalar(0.5)/sqrtx));) EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos

	EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY (sin, using std::sin;using std::cos;return ReturnType(sin(x.value()), x.derivatives()*cos(x.value()));) EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp

	EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY (log, using std::log;return ReturnType(log(x.value()), x.derivatives()*(Scalar(1)/x.value()));) template< typename DerType > inline const Eigen

	EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY (tan, using std::tan;using std::cos;return ReturnType(tan(x.value()), x.derivatives()*(Scalar(1)/numext::abs2(cos(x.value()))));) EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin

	EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY (acos, using std::sqrt;using std::acos;return ReturnType(acos(x.value()), x.derivatives()*(Scalar(-1)/sqrt(1-numext::abs2(x.value()))));) template< typename DerType > struct NumTraits< AutoDiffScalar< DerType > >

template<typename ExpressionType >
EIGEN_STRONG_INLINE const	EIGEN_CWISE_UNOP_RETURN_TYPE (internal::scalar_abs_op) Cwise< ExpressionType >

template<typename ExpressionType >
const	EIGEN_CWISE_UNOP_RETURN_TYPE (internal::scalar_sqrt_op) Cwise< ExpressionType >

template<typename VectorType , typename HyperplaneType >
void	fitHyperplane (int numPoints, VectorType *points, HyperplaneType result, typename NumTraits< typename VectorType::Scalar >::Real *soundness=0)

bool	getMarketHeader (const std::string &filename, int &sym, bool &iscomplex, bool &isvector)

template<typename VectorsType , typename CoeffsType >
HouseholderSequence< VectorsType, CoeffsType >	householderSequence (const VectorsType &v, const CoeffsType &h)
	Convenience function for constructing a Householder sequence. More...

template<typename DerType >
DerType::Scalar	imag (const AutoDiffScalar< DerType > &)

void	initParallel ()

template<typename KnotVectorType >
void	KnotAveraging (const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)
	Computes knot averages.The knots are computed as $\begin{align} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align}$ where is the degree and the number knots of the desired interpolating spline. More...

template<typename A , typename B >
KroneckerProduct< A, B >	kroneckerProduct (const MatrixBase< A > &a, const MatrixBase< B > &b)

template<typename A , typename B >
KroneckerProductSparse< A, B >	kroneckerProduct (const EigenBase< A > &a, const EigenBase< B > &b)

std::ptrdiff_t	l1CacheSize ()

std::ptrdiff_t	l2CacheSize ()

template<typename VectorType >
void	linearRegression (int numPoints, VectorType *points, VectorType result, int funcOfOthers)

template<typename SparseMatrixType >
bool	loadMarket (SparseMatrixType &mat, const std::string &filename)

template<typename VectorType >
bool	loadMarketVector (VectorType &vec, const std::string &filename)

template<typename T >
T	machine_epsilon ()

int	nbThreads ()

template<typename SparseDerived , typename PermDerived >
const internal::permut_sparsematrix_product_retval< PermutationBase< PermDerived >, SparseDerived, OnTheRight, false >	operator* (const SparseMatrixBase< SparseDerived > &matrix, const PermutationBase< PermDerived > &perm)

template<typename SparseDerived , typename PermDerived >
const internal::permut_sparsematrix_product_retval< PermutationBase< PermDerived >, SparseDerived, OnTheLeft, false >	operator* (const PermutationBase< PermDerived > &perm, const SparseMatrixBase< SparseDerived > &matrix)

template<typename SparseDerived , typename PermDerived >
const internal::permut_sparsematrix_product_retval< PermutationBase< PermDerived >, SparseDerived, OnTheRight, true >	operator* (const SparseMatrixBase< SparseDerived > &matrix, const Transpose< PermutationBase< PermDerived > > &tperm)

template<typename SparseDerived , typename PermDerived >
const internal::permut_sparsematrix_product_retval< PermutationBase< PermDerived >, SparseDerived, OnTheLeft, true >	operator* (const Transpose< PermutationBase< PermDerived > > &tperm, const SparseMatrixBase< SparseDerived > &matrix)

template<typename Derived , typename Lhs , typename Rhs >
const ScaledProduct< Derived >	operator* (const ProductBase< Derived, Lhs, Rhs > &prod, const typename Derived::Scalar &x)

template<typename Derived , typename Lhs , typename Rhs >
internal::enable_if<!internal::is_same< typename Derived::Scalar, typename Derived::RealScalar >::value, const ScaledProduct< Derived > >::type	operator* (const ProductBase< Derived, Lhs, Rhs > &prod, const typename Derived::RealScalar &x)

template<typename Derived , typename Lhs , typename Rhs >
const ScaledProduct< Derived >	operator* (const typename Derived::Scalar &x, const ProductBase< Derived, Lhs, Rhs > &prod)

template<typename Derived , typename Lhs , typename Rhs >
internal::enable_if<!internal::is_same< typename Derived::Scalar, typename Derived::RealScalar >::value, const ScaledProduct< Derived > >::type	operator* (const typename Derived::RealScalar &x, const ProductBase< Derived, Lhs, Rhs > &prod)

template<typename Derived , typename TranspositionsDerived >
const internal::transposition_matrix_product_retval< TranspositionsDerived, Derived, OnTheRight >	operator* (const MatrixBase< Derived > &matrix, const TranspositionsBase< TranspositionsDerived > &transpositions)

template<typename Derived , typename TranspositionDerived >
const internal::transposition_matrix_product_retval< TranspositionDerived, Derived, OnTheLeft >	operator* (const TranspositionsBase< TranspositionDerived > &transpositions, const MatrixBase< Derived > &matrix)

template<typename OtherDerived , typename VectorsType , typename CoeffsType , int Side>
internal::matrix_type_times_scalar_type< typename VectorsType::Scalar, OtherDerived >::Type	operator* (const MatrixBase< OtherDerived > &other, const HouseholderSequence< VectorsType, CoeffsType, Side > &h)
	Computes the product of a matrix with a Householder sequence. More...

template<typename Derived , typename PermutationDerived >
const internal::permut_matrix_product_retval< PermutationDerived, Derived, OnTheRight >	operator* (const MatrixBase< Derived > &matrix, const PermutationBase< PermutationDerived > &permutation)

template<typename Derived , typename PermutationDerived >
const internal::permut_matrix_product_retval< PermutationDerived, Derived, OnTheLeft >	operator* (const PermutationBase< PermutationDerived > &permutation, const MatrixBase< Derived > &matrix)

template<typename Derived >
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_inverse_mult_op< typename Derived::Scalar >, const Derived >	operator/ (const typename Derived::Scalar &s, const Eigen::ArrayBase< Derived > &a)
	Component-wise division of a scalar by array elements. More...

template<typename Polynomials , typename T >
T	poly_eval (const Polynomials &poly, const T &x)

template<typename Polynomials , typename T >
T	poly_eval_horner (const Polynomials &poly, const T &x)

template<typename Derived >
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_pow_op< typename Derived::Scalar >, const Derived >	pow (const Eigen::ArrayBase< Derived > &x, const typename Derived::Scalar &exponent)

template<typename Derived >
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_binary_pow_op< typename Derived::Scalar, typename Derived::Scalar >, const Derived, const Derived >	pow (const Eigen::ArrayBase< Derived > &x, const Eigen::ArrayBase< Derived > &exponents)

template<typename T >
T	precision ()

template<typename DerType >
const AutoDiffScalar< DerType > &	real (const AutoDiffScalar< DerType > &x)

return	ReturnType (abs2(x.value()), x.derivatives()(Scalar(2)x.value()))

return	ReturnType (cos(x.value()), x.derivatives()*(-sin(x.value())))

return	ReturnType (expx, x.derivatives()*expx)

return	ReturnType (asin(x.value()), x.derivatives()*(Scalar(1)/sqrt(1-numext::abs2(x.value()))))

template<typename VectorsType , typename CoeffsType >
HouseholderSequence< VectorsType, CoeffsType, OnTheRight >	rightHouseholderSequence (const VectorsType &v, const CoeffsType &h)
	Convenience function for constructing a Householder sequence. More...

template<typename RootVector , typename Polynomial >
void	roots_to_monicPolynomial (const RootVector &rv, Polynomial &poly)

template<typename SparseMatrixType >
bool	saveMarket (const SparseMatrixType &mat, const std::string &filename, int sym=0)

template<typename VectorType >
bool	saveMarketVector (const VectorType &vec, const std::string &filename)

static UniformScaling< float >	Scaling (float s)

static UniformScaling< double >	Scaling (double s)

template<typename RealScalar >
static UniformScaling< std::complex< RealScalar > >	Scaling (const std::complex< RealScalar > &s)

template<typename Scalar >
static DiagonalMatrix< Scalar, 2 >	Scaling (const Scalar &sx, const Scalar &sy)

template<typename Scalar >
static DiagonalMatrix< Scalar, 3 >	Scaling (const Scalar &sx, const Scalar &sy, const Scalar &sz)

template<typename Derived >
static const DiagonalWrapper< const Derived >	Scaling (const MatrixBase< Derived > &coeffs)

void	setCpuCacheSizes (std::ptrdiff_t l1, std::ptrdiff_t l2)

void	setNbThreads (int v)

template<typename Derived , typename OtherDerived >
internal::umeyama_transform_matrix_type< Derived, OtherDerived >::type	umeyama (const MatrixBase< Derived > &src, const MatrixBase< OtherDerived > &dst, bool with_scaling=true)
	Returns the transformation between two point sets. More...

void	umfpack_free_numeric (void **Numeric, double)

void	umfpack_free_numeric (void **Numeric, std::complex< double >)

void	umfpack_free_symbolic (void **Symbolic, double)

void	umfpack_free_symbolic (void **Symbolic, std::complex< double >)

int	umfpack_get_determinant (double Mx, double Ex, void *NumericHandle, double User_Info[UMFPACK_INFO])

int	umfpack_get_determinant (std::complex< double > Mx, double Ex, void *NumericHandle, double User_Info[UMFPACK_INFO])

int	umfpack_get_lunz (int lnz, int unz, int n_row, int n_col, int nz_udiag, void Numeric, double)

int	umfpack_get_lunz (int lnz, int unz, int n_row, int n_col, int nz_udiag, void Numeric, std::complex< double >)

int	umfpack_get_numeric (int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[], int P[], int Q[], double Dx[], int do_recip, double Rs[], void Numeric)

int	umfpack_get_numeric (int Lp[], int Lj[], std::complex< double > Lx[], int Up[], int Ui[], std::complex< double > Ux[], int P[], int Q[], std::complex< double > Dx[], int do_recip, double Rs[], void Numeric)

int	umfpack_numeric (const int Ap[], const int Ai[], const double Ax[], void Symbolic, void *Numeric, const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])

int	umfpack_numeric (const int Ap[], const int Ai[], const std::complex< double > Ax[], void Symbolic, void *Numeric, const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])

int	umfpack_solve (int sys, const int Ap[], const int Ai[], const double Ax[], double X[], const double B[], void *Numeric, const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])

int	umfpack_solve (int sys, const int Ap[], const int Ai[], const std::complex< double > Ax[], std::complex< double > X[], const std::complex< double > B[], void *Numeric, const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])

int	umfpack_symbolic (int n_row, int n_col, const int Ap[], const int Ai[], const double Ax[], void **Symbolic, const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])

int	umfpack_symbolic (int n_row, int n_col, const int Ap[], const int Ai[], const std::complex< double > Ax[], void **Symbolic, const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])

template<typename _Scalar , int _Options, typename _Index >
cholmod_sparse	viewAsCholmod (SparseMatrix< _Scalar, _Options, _Index > &mat)

template<typename _Scalar , int _Options, typename _Index >
const cholmod_sparse	viewAsCholmod (const SparseMatrix< _Scalar, _Options, _Index > &mat)

template<typename _Scalar , int _Options, typename _Index , unsigned int UpLo>
cholmod_sparse	viewAsCholmod (const SparseSelfAdjointView< SparseMatrix< _Scalar, _Options, _Index >, UpLo > &mat)

template<typename Derived >
cholmod_dense	viewAsCholmod (MatrixBase< Derived > &mat)

template<typename Scalar , int Flags, typename Index >
MappedSparseMatrix< Scalar, Flags, Index >	viewAsEigen (cholmod_sparse &cm)

Variables
const unsigned int	ActualPacketAccessBit = 0x0

const unsigned int	AlignedBit = 0x80

const int	CoherentAccessPattern = 0x1

const unsigned int	DirectAccessBit = 0x40

const int	Dynamic = -1

const int	DynamicIndex = 0xffffff

const unsigned int	EvalBeforeAssigningBit = 0x4

const unsigned int	EvalBeforeNestingBit = 0x2

Scalar	expx = exp(x.value())

const unsigned int	HereditaryBits

const int	Infinity = -1

const int	InnerRandomAccessPattern = 0x2 \| CoherentAccessPattern

const unsigned int	LinearAccessBit = 0x10

const unsigned int	LowerTriangular = Lower

const unsigned int	LowerTriangularBit = Lower

const unsigned int	LvalueBit = 0x20

const unsigned int	NestByRefBit = 0x100

const int	OuterRandomAccessPattern = 0x4 \| CoherentAccessPattern

const unsigned int	PacketAccessBit = 0x8

const int	RandomAccessPattern = 0x8 \| OuterRandomAccessPattern \| InnerRandomAccessPattern

const unsigned int	RowMajorBit = 0x1

const unsigned int	SelfAdjointBit = SelfAdjoint

const unsigned int	SkylineBit = 0x1200

const unsigned int	UnitDiagBit = UnitDiag

const unsigned int	UnitLowerTriangular = UnitLower

const unsigned int	UnitUpperTriangular = UnitUpper

const unsigned int	UpperTriangular = Upper

const unsigned int	UpperTriangularBit = Upper

const T &	y { return (x <= y ? x : y)

Detailed Description

iterative scaling algorithm to equilibrate rows and column norms in matrices

This class can be used as a preprocessing tool to accelerate the convergence of iterative methods

This feature is useful to limit the pivoting amount during LU/ILU factorization The scaling strategy as presented here preserves the symmetry of the problem NOTE It is assumed that the matrix does not have empty row or column,

Example with key steps

VectorXd x(n), b(n);
SparseMatrix<double> A;
// fill A and b;
IterScaling<SparseMatrix<double> > scal; 
// Compute the left and right scaling vectors. The matrix is equilibrated at output
scal.computeRef(A); 
// Scale the right hand side
b = scal.LeftScaling().cwiseProduct(b); 
// Now, solve the equilibrated linear system with any available solver
// Scale back the computed solution
x = scal.RightScaling().cwiseProduct(x); 

Template Parameters

_MatrixType the type of the matrix. It should be a real square sparsematrix

References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552

See also: IncompleteLUT

Typedef Documentation

typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE Eigen::DenseIndex

Definition at line 27 of file XprHelper.h.

typedef Spline<double,2> Eigen::Spline2d

2D double B-spline with dynamic degree.

Definition at line 80 of file SplineFwd.h.

typedef Spline<float,2> Eigen::Spline2f

2D float B-spline with dynamic degree.

Definition at line 74 of file SplineFwd.h.

typedef Spline<double,3> Eigen::Spline3d

3D double B-spline with dynamic degree.

Definition at line 83 of file SplineFwd.h.

typedef Spline<float,3> Eigen::Spline3f

3D float B-spline with dynamic degree.

Definition at line 77 of file SplineFwd.h.

Enumeration Type Documentation

anonymous enum

Enumerator
Large
Small

Definition at line 38 of file GeneralProduct.h.

anonymous enum

Enumerator
DontAlignCols

Definition at line 16 of file IO.h.

anonymous enum

Enumerator
StreamPrecision
FullPrecision

Definition at line 17 of file IO.h.

anonymous enum

Enumerator
DefaultTraversal
LinearTraversal
InnerVectorizedTraversal
LinearVectorizedTraversal
SliceVectorizedTraversal
InvalidTraversal
AllAtOnceTraversal

Definition at line 220 of file eigen3/Eigen/src/Core/util/Constants.h.

anonymous enum

Enumerator
NoUnrolling
InnerUnrolling
CompleteUnrolling

Definition at line 242 of file eigen3/Eigen/src/Core/util/Constants.h.

anonymous enum

Enumerator
Specialized
BuiltIn

Definition at line 254 of file eigen3/Eigen/src/Core/util/Constants.h.

anonymous enum

Enumerator
IsDense
IsSparse

Definition at line 300 of file eigen3/Eigen/src/Core/util/Constants.h.

anonymous enum

Enumerator
CoeffBasedProductMode
LazyCoeffBasedProductMode
OuterProduct
InnerProduct
GemvProduct
GemmProduct

Definition at line 421 of file eigen3/Eigen/src/Core/util/Constants.h.

anonymous enum

Enumerator
IsSkyline

Definition at line 24 of file SkylineUtil.h.

anonymous enum

Enumerator
SPD
NonSymmetric

Definition at line 16 of file MatrixMarketIterator.h.

enum Eigen::Action

Enumerator
GetAction
SetAction

Definition at line 425 of file eigen3/Eigen/src/Core/util/Constants.h.

enum Eigen::AdditionalProductEvaluationMode

Enumerator
SkylineTimeDenseProduct
SkylineTimeSkylineProduct
DenseTimeSkylineProduct

Definition at line 23 of file SkylineUtil.h.

enum Eigen::CholmodMode

Enumerator
CholmodAuto
CholmodSimplicialLLt
CholmodSupernodalLLt
CholmodLDLt

Definition at line 147 of file CholmodSupport.h.

enum Eigen::Default_t

Enumerator
Default

Definition at line 296 of file eigen3/Eigen/src/Core/util/Constants.h.

enum Eigen::NoChange_t

Enumerator
NoChange

Definition at line 294 of file eigen3/Eigen/src/Core/util/Constants.h.

enum Eigen::NumericalDiffMode

Enumerator
Forward
Central

Definition at line 18 of file NumericalDiff.h.

enum Eigen::Sequential_t

Enumerator
Sequential

Definition at line 295 of file eigen3/Eigen/src/Core/util/Constants.h.

enum Eigen::SimplicialCholeskyMode

Enumerator
SimplicialCholeskyLLT
SimplicialCholeskyLDLT

Definition at line 15 of file SimplicialCholesky.h.

Function Documentation

template<typename DerTypeA , typename DerTypeB >

const AutoDiffScalar<Matrix<typename internal::traits<DerTypeA>::Scalar,Dynamic,1> > Eigen::atan2	(	const AutoDiffScalar< DerTypeA > &	a,
		const AutoDiffScalar< DerTypeB > &	b
	)

inline

Definition at line 593 of file AutoDiffScalar.h.

template<typename DerType , typename T >

Eigen::AutoDiffScalar< DerType > ( min ) const

inline

template<typename DerType , typename T >

Eigen::AutoDiffScalar< DerType > ( max ) const

inline

template<typename SplineType , typename DerivativeType >

void Eigen::basisFunctionDerivativesImpl	(	const SplineType &	spline,
		typename SplineType::Scalar	u,
		DenseIndex	order,
		DerivativeType &	N_
	)

Definition at line 350 of file Spline.h.

template<typename BVH , typename Intersector >

void Eigen::BVIntersect	(	const BVH &	tree,
		Intersector &	intersector
	)

Given a BVH, runs the query encapsulated by intersector. The Intersector type must provide the following members:

bool intersectVolume(const BVH::Volume &volume) //returns true if volume intersects the query

bool intersectObject(const BVH::Object &object) //returns true if the search should terminate immediately

Definition at line 79 of file BVAlgorithms.h.

template<typename BVH1 , typename BVH2 , typename Intersector >

void Eigen::BVIntersect	(	const BVH1 &	tree1,
		const BVH2 &	tree2,
		Intersector &	intersector
	)

Given two BVH's, runs the query on their Cartesian product encapsulated by intersector. The Intersector type must provide the following members:

bool intersectVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2) //returns true if product of volumes intersects the query
bool intersectVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2) //returns true if the volume-object product intersects the query
bool intersectObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2) //returns true if the volume-object product intersects the query
bool intersectObjectObject(const BVH1::Object &o1, const BVH2::Object &o2) //returns true if the search should terminate immediately

Definition at line 93 of file BVAlgorithms.h.

template<typename BVH , typename Minimizer >

Minimizer::Scalar Eigen::BVMinimize	(	const BVH &	tree,
		Minimizer &	minimizer
	)

Given a BVH, runs the query encapsulated by minimizer.

Returns: the minimum value. The Minimizer type must provide the following members:
typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)
Scalar minimumOnVolume(const BVH::Volume &volume)
Scalar minimumOnObject(const BVH::Object &object)

Definition at line 219 of file BVAlgorithms.h.

template<typename BVH1 , typename BVH2 , typename Minimizer >

Minimizer::Scalar Eigen::BVMinimize	(	const BVH1 &	tree1,
		const BVH2 &	tree2,
		Minimizer &	minimizer
	)

Given two BVH's, runs the query on their cartesian product encapsulated by minimizer.

Returns: the minimum value. The Minimizer type must provide the following members:
typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)
Scalar minimumOnVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2)
Scalar minimumOnVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2)
Scalar minimumOnObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2)
Scalar minimumOnObjectObject(const BVH1::Object &o1, const BVH2::Object &o2)

Definition at line 235 of file BVAlgorithms.h.

template<typename Polynomial >

NumTraits<typename Polynomial::Scalar>::Real Eigen::cauchy_max_bound ( const Polynomial & poly )

inline

Returns: a maximum bound for the absolute value of any root of the polynomial.

Parameters

[in] poly : the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .

Precondition: the leading coefficient of the input polynomial poly must be non zero

Definition at line 75 of file PolynomialUtils.h.

template<typename Polynomial >

NumTraits<typename Polynomial::Scalar>::Real Eigen::cauchy_min_bound ( const Polynomial & poly )

inline

Returns: a minimum bound for the absolute value of any non zero root of the polynomial.

Parameters

[in] poly : the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .

Definition at line 98 of file PolynomialUtils.h.

template<typename Scalar >

std::complex<Scalar> Eigen::cdiv	(	const Scalar &	xr,
		const Scalar &	xi,
		const Scalar &	yr,
		const Scalar &	yi
	)

Definition at line 413 of file EigenSolver.h.

template<typename PointArrayType , typename KnotVectorType >

void Eigen::ChordLengths	(	const PointArrayType &	pts,
		KnotVectorType &	chord_lengths
	)

Computes chord length parameters which are required for spline interpolation.

Parameters

[in]	pts	The data points to which a spline should be fit.
[out]	chord_lengths	The resulting chord lenggth vector.

See also: Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data

Definition at line 62 of file SplineFitting.h.

template<typename DerType >

const AutoDiffScalar<DerType>& Eigen::conj ( const AutoDiffScalar< DerType > & x )

inline

Definition at line 533 of file AutoDiffScalar.h.

template<typename SplineType , typename DerivativeType >

void Eigen::derivativesImpl	(	const SplineType &	spline,
		typename SplineType::Scalar	u,
		DenseIndex	order,
		DerivativeType &	der
	)

Definition at line 292 of file Spline.h.

template<typename T >

NumTraits<T>::Real Eigen::ei_abs ( const T & x )

inline

Definition at line 18 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

NumTraits<T>::Real Eigen::ei_abs2 ( const T & x )

inline

Definition at line 19 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

void Eigen::ei_aligned_delete	(	T *	ptr,
		size_t	size
	)

inline

Definition at line 38 of file Eigen2Support/Memory.h.

void Eigen::ei_aligned_free ( void * ptr )

inline

Definition at line 16 of file Eigen2Support/Memory.h.

void* Eigen::ei_aligned_malloc ( size_t size )

inline

Definition at line 15 of file Eigen2Support/Memory.h.

template<typename T >

T* Eigen::ei_aligned_new ( size_t size )

inline

Definition at line 34 of file Eigen2Support/Memory.h.

void* Eigen::ei_aligned_realloc	(	void *	ptr,
		size_t	new_size,
		size_t	old_size
	)

inline

Definition at line 17 of file Eigen2Support/Memory.h.

template<typename T >

T Eigen::ei_atan2	(	const T &	x,
		const T &	y
	)

inline

Definition at line 25 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<bool Align>

void Eigen::ei_conditional_aligned_free ( void * ptr )

inline

Definition at line 25 of file Eigen2Support/Memory.h.

template<bool Align>

void* Eigen::ei_conditional_aligned_malloc ( size_t size )

inline

Definition at line 21 of file Eigen2Support/Memory.h.

template<bool Align>

void* Eigen::ei_conditional_aligned_realloc	(	void *	ptr,
		size_t	new_size,
		size_t	old_size
	)

inline

Definition at line 29 of file Eigen2Support/Memory.h.

template<typename T >

T Eigen::ei_conj ( const T & x )

inline

Definition at line 17 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_cos ( const T & x )

inline

Definition at line 24 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_exp ( const T & x )

inline

Definition at line 21 of file Eigen/src/Eigen2Support/MathFunctions.h.

void Eigen::ei_handmade_aligned_free ( void * ptr )

inline

Definition at line 19 of file Eigen2Support/Memory.h.

void* Eigen::ei_handmade_aligned_malloc ( size_t size )

inline

Definition at line 18 of file Eigen2Support/Memory.h.

template<typename T >

NumTraits<T>::Real Eigen::ei_imag ( const T & x )

inline

Definition at line 16 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename Scalar >

bool Eigen::ei_isApprox	(	const Scalar &	x,
		const Scalar &	y,
		typename NumTraits< Scalar >::Real	precision = `NumTraits<Scalar>::dummy_precision()`
	)

inline

Definition at line 42 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename Scalar >

bool Eigen::ei_isApproxOrLessThan	(	const Scalar &	x,
		const Scalar &	y,
		typename NumTraits< Scalar >::Real	precision = `NumTraits<Scalar>::dummy_precision()`
	)

inline

Definition at line 49 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename Scalar , typename OtherScalar >

bool Eigen::ei_isMuchSmallerThan	(	const Scalar &	x,
		const OtherScalar &	y,
		typename NumTraits< Scalar >::Real	precision = `NumTraits<Scalar>::dummy_precision()`
	)

inline

Definition at line 35 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_log ( const T & x )

inline

Definition at line 22 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_pow	(	const T &	x,
		const T &	y
	)

inline

Definition at line 26 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename Scalar >

Quaternion<Scalar> Eigen::ei_quaternion_product	(	const Quaternion< Scalar > &	a,
		const Quaternion< Scalar > &	b
	)

inline

Definition at line 215 of file Eigen2Support/Geometry/Quaternion.h.

template<typename T >

T Eigen::ei_random ( )

inline

Definition at line 27 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_random	(	const T &	x,
		const T &	y
	)

inline

Definition at line 28 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

NumTraits<T>::Real Eigen::ei_real ( const T & x )

inline

Definition at line 15 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_sin ( const T & x )

inline

Definition at line 23 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename T >

T Eigen::ei_sqrt ( const T & x )

inline

Definition at line 20 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename Scalar , int Dim>

static Matrix<Scalar,2,2> Eigen::ei_toRotationMatrix ( const Scalar & s )

inlinestatic

Definition at line 103 of file Eigen2Support/Geometry/RotationBase.h.

template<typename Scalar , int Dim, typename OtherDerived >

static Matrix<Scalar,Dim,Dim> Eigen::ei_toRotationMatrix ( const RotationBase< OtherDerived, Dim > & r )

inlinestatic

Definition at line 110 of file Eigen2Support/Geometry/RotationBase.h.

template<typename Scalar , int Dim, typename OtherDerived >

static const MatrixBase<OtherDerived>& Eigen::ei_toRotationMatrix ( const MatrixBase< OtherDerived > & mat )

inlinestatic

Definition at line 116 of file Eigen2Support/Geometry/RotationBase.h.

Eigen::EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY	(	abs	,
		using std::abs;return ReturnType(abs(x.value()), x.derivatives()*(x.value()< 0?-1:1));
	)

Eigen::EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY	(	sqrt	,
		using std::sqrt;Scalar	sqrtx = `sqrt(x.value()); return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));`
	)

Eigen::EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY	(	sin	,
		using std::sin;using std::cos;return ReturnType(sin(x.value()), x.derivatives()*cos(x.value()));
	)

Eigen::EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY	(	log	,
		using std::log;return ReturnType(log(x.value()), x.derivatives()*(Scalar(1)/x.value()));
	)		const

Definition at line 575 of file AutoDiffScalar.h.

Eigen::EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY	(	tan	,
		using std::tan;using std::cos;return ReturnType(tan(x.value()), x.derivatives()*(Scalar(1)/numext::abs2(cos(x.value()))));
	)

Eigen::EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY	(	acos	,
		using std::sqrt;using std::acos;return ReturnType(acos(x.value()), x.derivatives()*(Scalar(-1)/sqrt(1-numext::abs2(x.value()))));
	)

Definition at line 622 of file AutoDiffScalar.h.

template<typename ExpressionType >

EIGEN_STRONG_INLINE const Eigen::EIGEN_CWISE_UNOP_RETURN_TYPE ( internal::scalar_abs_op )

Deprecated:: ArrayBase::abs()

Deprecated:: ArrayBase::abs2()

Deprecated:: ArrayBase::exp()

Deprecated:: ArrayBase::log()

Deprecated:: ArrayBase::operator*()

Deprecated:: ArrayBase::operator/()

Deprecated:: ArrayBase::operator*=()

Definition at line 22 of file CwiseOperators.h.

template<typename ExpressionType >

const Eigen::EIGEN_CWISE_UNOP_RETURN_TYPE ( internal::scalar_sqrt_op )

inline

Deprecated:: ArrayBase::sqrt()

Deprecated:: ArrayBase::cos()

Deprecated:: ArrayBase::sin()

Deprecated:: ArrayBase::log()

Deprecated:: ArrayBase::inverse()

Deprecated:: ArrayBase::square()

Deprecated:: ArrayBase::cube()

Deprecated:: ArrayBase::operator<()

Deprecated:: ArrayBase::<=()

Deprecated:: ArrayBase::operator>()

Deprecated:: ArrayBase::operator>=()

Deprecated:: ArrayBase::operator==()

Deprecated:: ArrayBase::operator!=()

Deprecated:: ArrayBase::operator<(Scalar)

Deprecated:: ArrayBase::operator<=(Scalar)

Deprecated:: ArrayBase::operator>(Scalar)

Deprecated:: ArrayBase::operator>=(Scalar)

Deprecated:: ArrayBase::operator==(Scalar)

Deprecated:: ArrayBase::operator!=(Scalar)

Deprecated:: ArrayBase::operator+(Scalar)

Deprecated:: ArrayBase::operator+=(Scalar)

Definition at line 94 of file CwiseOperators.h.

template<typename VectorType , typename HyperplaneType >

void Eigen::fitHyperplane	(	int	numPoints,
		VectorType **	points,
		HyperplaneType *	result,
		typename NumTraits< typename VectorType::Scalar >::Real *	soundness = `0`
	)

This function is quite similar to linearRegression(), so we refer to the documentation of this function and only list here the differences.

The main difference from linearRegression() is that this function doesn't take a funcOfOthers argument. Instead, it finds a general equation of the form

$r_0 x_0 + \cdots + r_{n-1}x_{n-1} + r_n = 0,$

where $n=Size$ , $r_i=retCoefficients[i]$ , and we denote by $x_0,\ldots,x_{n-1}$ the n coordinates in the n-dimensional space.

Thus, the vector retCoefficients has size $n+1$ , which is another difference from linearRegression().

In practice, this function performs an hyper-plane fit in a total least square sense via the following steps: 1 - center the data to the mean 2 - compute the covariance matrix 3 - pick the eigenvector corresponding to the smallest eigenvalue of the covariance matrix The ratio of the smallest eigenvalue and the second one gives us a hint about the relevance of the solution. This value is optionally returned in soundness.

See also: linearRegression()

Definition at line 130 of file LeastSquares.h.

bool Eigen::getMarketHeader	(	const std::string &	filename,
		int &	sym,
		bool &	iscomplex,
		bool &	isvector
	)

inline

Definition at line 109 of file MarketIO.h.

template<typename VectorsType , typename CoeffsType >

HouseholderSequence<VectorsType,CoeffsType> Eigen::householderSequence	(	const VectorsType &	v,
		const CoeffsType &	h
	)

Convenience function for constructing a Householder sequence.

\

Returns: A HouseholderSequence constructed from the specified arguments.

Definition at line 422 of file HouseholderSequence.h.

template<typename DerType >

DerType::Scalar Eigen::imag ( const AutoDiffScalar< DerType > & )

inline

Definition at line 537 of file AutoDiffScalar.h.

void Eigen::initParallel ( )

inline

Must be call first when calling Eigen from multiple threads

Definition at line 48 of file Parallelizer.h.

template<typename KnotVectorType >

void Eigen::KnotAveraging	(	const KnotVectorType &	parameters,
		DenseIndex	degree,
		KnotVectorType &	knots
	)

Computes knot averages.The knots are computed as

$\begin{align*} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align*}$

where $p$ is the degree and $m+1$ the number knots of the desired interpolating spline.

Parameters

[in]	parameters	The input parameters. During interpolation one for each data point.
[in]	degree	The spline degree which is used during the interpolation.
[out]	knots	The output knot vector.

See also: Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data

Definition at line 41 of file SplineFitting.h.

template<typename A , typename B >

KroneckerProduct<A,B> Eigen::kroneckerProduct	(	const MatrixBase< A > &	a,
		const MatrixBase< B > &	b
	)

Computes Kronecker tensor product of two dense matrices

Warning: If you want to replace a matrix by its Kronecker product with some matrix, do NOT do this:
A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
instead, use eval() to work around this:
A = kroneckerProduct(A,B).eval();

Parameters

a	Dense matrix a
b	Dense matrix b

Returns: Kronecker tensor product of a and b

Definition at line 220 of file KroneckerTensorProduct.h.

template<typename A , typename B >

KroneckerProductSparse<A,B> Eigen::kroneckerProduct	(	const EigenBase< A > &	a,
		const EigenBase< B > &	b
	)

Computes Kronecker tensor product of two matrices, at least one of which is sparse

Parameters

a	Dense/sparse matrix a
b	Dense/sparse matrix b

Returns: Kronecker tensor product of a and b, stored in a sparse matrix

Definition at line 237 of file KroneckerTensorProduct.h.

std::ptrdiff_t Eigen::l1CacheSize ( )

inline

Returns: the currently set level 1 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.

See also: setCpuCacheSize

Definition at line 1307 of file GeneralBlockPanelKernel.h.

std::ptrdiff_t Eigen::l2CacheSize ( )

inline

Returns: the currently set level 2 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.

See also: setCpuCacheSize

Definition at line 1316 of file GeneralBlockPanelKernel.h.

template<typename VectorType >

void Eigen::linearRegression	(	int	numPoints,
		VectorType **	points,
		VectorType *	result,
		int	funcOfOthers
	)

For a set of points, this function tries to express one of the coords as a linear (affine) function of the other coords.

This is best explained by an example. This function works in full generality, for points in a space of arbitrary dimension, and also over the complex numbers, but for this example we will work in dimension 3 over the real numbers (doubles).

So let us work with the following set of 5 points given by their $(x,y,z)$ coordinates:

Vector3d points[5];
points[0] = Vector3d( 3.02, 6.89, -4.32 );
points[1] = Vector3d( 2.01, 5.39, -3.79 );
points[2] = Vector3d( 2.41, 6.01, -4.01 );
points[3] = Vector3d( 2.09, 5.55, -3.86 );
points[4] = Vector3d( 2.58, 6.32, -4.10 );

Suppose that we want to express the second coordinate ( $y$ ) as a linear expression in $x$ and $z$ , that is,

$y=ax+bz+c$

for some constants $a,b,c$ . Thus, we want to find the best possible constants $a,b,c$ so that the plane of equation $y=ax+bz+c$ fits best the five above points. To do that, call this function as follows:

Vector3d coeffs; // will store the coefficients a, b, c
linearRegression(
  5,
  &points,
  &coeffs,
  1 // the coord to express as a function of
    // the other ones. 0 means x, 1 means y, 2 means z.
);

Now the vector coeffs is approximately $( 0.495 , -1.927 , -2.906 )$ . Thus, we get $a=0.495, b = -1.927, c = -2.906$ . Let us check for instance how near points[0] is from the plane of equation $y=ax+bz+c$ . Looking at the coords of points[0], we see that:

$ax+bz+c = 0.495 * 3.02 + (-1.927) * (-4.32) + (-2.906) = 6.91.$

On the other hand, we have $y=6.89$ . We see that the values $6.91$ and $6.89$ are near, so points[0] is very near the plane of equation $y=ax+bz+c$ .

Let's now describe precisely the parameters:

Parameters

numPoints	the number of points
points	the array of pointers to the points on which to perform the linear regression
result	pointer to the vector in which to store the result. This vector must be of the same type and size as the data points. The meaning of its coords is as follows. For brevity, let , , and . Denote by $x_0,\ldots,x_{n-1}$ the n coordinates in the n-dimensional space. Then the resulting equation is: $x_f = r_0 x_0 + \cdots + r_{f-1}x_{f-1} + r_{f+1}x_{f+1} + \cdots + r_{n-1}x_{n-1} + r_n.$
funcOfOthers	Determines which coord to express as a function of the others. Coords are numbered starting from 0, so that a value of 0 means , 1 means , 2 means , ...

See also: fitHyperplane()

Definition at line 85 of file LeastSquares.h.

template<typename SparseMatrixType >

bool Eigen::loadMarket	(	SparseMatrixType &	mat,
		const std::string &	filename
	)

Definition at line 133 of file MarketIO.h.

template<typename VectorType >

bool Eigen::loadMarketVector	(	VectorType &	vec,
		const std::string &	filename
	)

Definition at line 192 of file MarketIO.h.

template<typename T >

T Eigen::machine_epsilon ( )

inline

Definition at line 31 of file Eigen/src/Eigen2Support/MathFunctions.h.

int Eigen::nbThreads ( )

inline

Returns: the max number of threads reserved for Eigen

See also: setNbThreads

Definition at line 58 of file Parallelizer.h.

template<typename SparseDerived , typename PermDerived >

const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheRight, false> Eigen::operator*	(	const SparseMatrixBase< SparseDerived > &	matrix,
		const PermutationBase< PermDerived > &	perm
	)

inline

Returns: the matrix with the permutation applied to the columns

Definition at line 112 of file SparsePermutation.h.

template<typename SparseDerived , typename PermDerived >

const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheLeft, false> Eigen::operator*	(	const PermutationBase< PermDerived > &	perm,
		const SparseMatrixBase< SparseDerived > &	matrix
	)

inline

Returns: the matrix with the permutation applied to the rows

Definition at line 121 of file SparsePermutation.h.

template<typename SparseDerived , typename PermDerived >

const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheRight, true> Eigen::operator*	(	const SparseMatrixBase< SparseDerived > &	matrix,
		const Transpose< PermutationBase< PermDerived > > &	tperm
	)

inline

Returns: the matrix with the inverse permutation applied to the columns.

Definition at line 132 of file SparsePermutation.h.

template<typename SparseDerived , typename PermDerived >

const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheLeft, true> Eigen::operator*	(	const Transpose< PermutationBase< PermDerived > > &	tperm,
		const SparseMatrixBase< SparseDerived > &	matrix
	)

inline

Returns: the matrix with the inverse permutation applied to the rows.

Definition at line 141 of file SparsePermutation.h.

template<typename Derived , typename Lhs , typename Rhs >

const ScaledProduct<Derived> Eigen::operator*	(	const ProductBase< Derived, Lhs, Rhs > &	prod,
		const typename Derived::Scalar &	x
	)

Definition at line 198 of file ProductBase.h.

template<typename Derived , typename Lhs , typename Rhs >

internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value, const ScaledProduct<Derived> >::type Eigen::operator*	(	const ProductBase< Derived, Lhs, Rhs > &	prod,
		const typename Derived::RealScalar &	x
	)

Definition at line 204 of file ProductBase.h.

template<typename Derived , typename Lhs , typename Rhs >

const ScaledProduct<Derived> Eigen::operator*	(	const typename Derived::Scalar &	x,
		const ProductBase< Derived, Lhs, Rhs > &	prod
	)

Definition at line 210 of file ProductBase.h.

template<typename Derived , typename Lhs , typename Rhs >

internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value, const ScaledProduct<Derived> >::type Eigen::operator*	(	const typename Derived::RealScalar &	x,
		const ProductBase< Derived, Lhs, Rhs > &	prod
	)

Definition at line 216 of file ProductBase.h.

template<typename Derived , typename TranspositionsDerived >

const internal::transposition_matrix_product_retval<TranspositionsDerived, Derived, OnTheRight> Eigen::operator*	(	const MatrixBase< Derived > &	matrix,
		const TranspositionsBase< TranspositionsDerived > &	transpositions
	)

inline

Returns: the matrix with the transpositions applied to the columns.

Definition at line 331 of file Transpositions.h.

template<typename Derived , typename TranspositionDerived >

const internal::transposition_matrix_product_retval<TranspositionDerived, Derived, OnTheLeft> Eigen::operator*	(	const TranspositionsBase< TranspositionDerived > &	transpositions,
		const MatrixBase< Derived > &	matrix
	)

inline

Returns: the matrix with the transpositions applied to the rows.

Definition at line 344 of file Transpositions.h.

template<typename OtherDerived , typename VectorsType , typename CoeffsType , int Side>

internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type Eigen::operator*	(	const MatrixBase< OtherDerived > &	other,
		const HouseholderSequence< VectorsType, CoeffsType, Side > &	h
	)

Computes the product of a matrix with a Householder sequence.

Parameters

[in]	other	Matrix being multiplied.
[in]	h	HouseholderSequence being multiplied.

Returns: Expression object representing the product.

This function computes $ MH $ where $ M $ is the matrix other and $ H $ is the Householder sequence represented by h.

Definition at line 409 of file HouseholderSequence.h.

template<typename Derived , typename PermutationDerived >

const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheRight> Eigen::operator*	(	const MatrixBase< Derived > &	matrix,
		const PermutationBase< PermutationDerived > &	permutation
	)

inline

Returns: the matrix with the permutation applied to the columns.

Definition at line 510 of file PermutationMatrix.h.

template<typename Derived , typename PermutationDerived >

const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheLeft> Eigen::operator*	(	const PermutationBase< PermutationDerived > &	permutation,
		const MatrixBase< Derived > &	matrix
	)

inline

Returns: the matrix with the permutation applied to the rows.

Definition at line 523 of file PermutationMatrix.h.

template<typename Derived >

const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived> Eigen::operator/	(	const typename Derived::Scalar &	s,
		const Eigen::ArrayBase< Derived > &	a
	)

inline

Component-wise division of a scalar by array elements.

Definition at line 74 of file GlobalFunctions.h.

template<typename Polynomials , typename T >

T Eigen::poly_eval	(	const Polynomials &	poly,
		const T &	x
	)

inline

Returns: the evaluation of the polynomial at x using stabilized Horner algorithm.

Parameters

[in]	poly	: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .
[in]	x	: the value to evaluate the polynomial at.

Definition at line 46 of file PolynomialUtils.h.

template<typename Polynomials , typename T >

T Eigen::poly_eval_horner	(	const Polynomials &	poly,
		const T &	x
	)

inline

Returns: the evaluation of the polynomial at x using Horner algorithm.

Parameters

[in]	poly	: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .
[in]	x	: the value to evaluate the polynomial at.

Note for stability: $|x| \le 1$

Definition at line 28 of file PolynomialUtils.h.

template<typename Derived >

const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived> Eigen::pow	(	const Eigen::ArrayBase< Derived > &	x,
		const typename Derived::Scalar &	exponent
	)

inline

Definition at line 55 of file GlobalFunctions.h.

template<typename Derived >

const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const Derived, const Derived> Eigen::pow	(	const Eigen::ArrayBase< Derived > &	x,
		const Eigen::ArrayBase< Derived > &	exponents
	)

inline

Definition at line 61 of file GlobalFunctions.h.

template<typename T >

T Eigen::precision ( )

inline

Definition at line 30 of file Eigen/src/Eigen2Support/MathFunctions.h.

template<typename DerType >

const AutoDiffScalar<DerType>& Eigen::real ( const AutoDiffScalar< DerType > & x )

inline

Definition at line 535 of file AutoDiffScalar.h.

return Eigen::ReturnType	(	abs2(x.value())	,
		x.	derivatives)(Scalar(2)x.value()
	)

return Eigen::ReturnType	(	cos(x.value())	,
		x.	derivatives)*(-sin(x.value())
	)

return Eigen::ReturnType	(	expx	,
		x.derivatives()*	expx
	)

return Eigen::ReturnType	(	asin(x.value())	,
		x.	derivatives)*(Scalar(1)/sqrt(1-numext::abs2(x.value()))
	)

template<typename VectorsType , typename CoeffsType >

HouseholderSequence<VectorsType,CoeffsType,OnTheRight> Eigen::rightHouseholderSequence	(	const VectorsType &	v,
		const CoeffsType &	h
	)

Convenience function for constructing a Householder sequence.

\

Returns: A HouseholderSequence constructed from the specified arguments.

This function differs from householderSequence() in that the template argument OnTheSide of the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft.

Definition at line 434 of file HouseholderSequence.h.

template<typename RootVector , typename Polynomial >

void Eigen::roots_to_monicPolynomial	(	const RootVector &	rv,
		Polynomial &	poly
	)

Given the roots of a polynomial compute the coefficients in the monomial basis of the monic polynomial with same roots and minimal degree. If RootVector is a vector of complexes, Polynomial should also be a vector of complexes.

Parameters

[in]	rv	: a vector containing the roots of a polynomial.
[out]	poly	: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .

Definition at line 127 of file PolynomialUtils.h.

template<typename SparseMatrixType >

bool Eigen::saveMarket	(	const SparseMatrixType &	mat,
		const std::string &	filename,
		int	sym = `0`
	)

Definition at line 224 of file MarketIO.h.

template<typename VectorType >

bool Eigen::saveMarketVector	(	const VectorType &	vec,
		const std::string &	filename
	)

Definition at line 250 of file MarketIO.h.

static UniformScaling<float> Eigen::Scaling ( float s )

inlinestatic

Constructs a uniform scaling from scale factor s

Definition at line 115 of file Eigen/src/Geometry/Scaling.h.

static UniformScaling<double> Eigen::Scaling ( double s )

inlinestatic

Constructs a uniform scaling from scale factor s

Definition at line 117 of file Eigen/src/Geometry/Scaling.h.

template<typename RealScalar >

static UniformScaling<std::complex<RealScalar> > Eigen::Scaling ( const std::complex< RealScalar > & s )

inlinestatic

Constructs a uniform scaling from scale factor s

Definition at line 120 of file Eigen/src/Geometry/Scaling.h.

template<typename Scalar >

static DiagonalMatrix<Scalar,2> Eigen::Scaling	(	const Scalar &	sx,
		const Scalar &	sy
	)

inlinestatic

Constructs a 2D axis aligned scaling

Definition at line 125 of file Eigen/src/Geometry/Scaling.h.

template<typename Scalar >

static DiagonalMatrix<Scalar,3> Eigen::Scaling	(	const Scalar &	sx,
		const Scalar &	sy,
		const Scalar &	sz
	)

inlinestatic

Constructs a 3D axis aligned scaling

Definition at line 129 of file Eigen/src/Geometry/Scaling.h.

template<typename Derived >

static const DiagonalWrapper<const Derived> Eigen::Scaling ( const MatrixBase< Derived > & coeffs )

inlinestatic

Constructs an axis aligned scaling expression from vector expression coeffs This is an alias for coeffs.asDiagonal()

Definition at line 136 of file Eigen/src/Geometry/Scaling.h.

void Eigen::setCpuCacheSizes	(	std::ptrdiff_t	l1,
		std::ptrdiff_t	l2
	)

inline

Set the cpu L1 and L2 cache sizes (in bytes). These values are use to adjust the size of the blocks for the algorithms working per blocks.

See also: computeProductBlockingSizes

Definition at line 1328 of file GeneralBlockPanelKernel.h.

void Eigen::setNbThreads ( int v )

inline

Sets the max number of threads reserved for Eigen

See also: nbThreads

Definition at line 67 of file Parallelizer.h.

void Eigen::umfpack_free_numeric	(	void **	Numeric,
		double
	)

inline

Definition at line 19 of file UmfPackSupport.h.

void Eigen::umfpack_free_numeric	(	void **	Numeric,
		std::complex< double >
	)

inline

Definition at line 22 of file UmfPackSupport.h.

void Eigen::umfpack_free_symbolic	(	void **	Symbolic,
		double
	)

inline

Definition at line 25 of file UmfPackSupport.h.

void Eigen::umfpack_free_symbolic	(	void **	Symbolic,
		std::complex< double >
	)

inline

Definition at line 28 of file UmfPackSupport.h.

int Eigen::umfpack_get_determinant	(	double *	Mx,
		double *	Ex,
		void *	NumericHandle,
		double	User_Info[UMFPACK_INFO]
	)

inline

Definition at line 99 of file UmfPackSupport.h.

int Eigen::umfpack_get_determinant	(	std::complex< double > *	Mx,
		double *	Ex,
		void *	NumericHandle,
		double	User_Info[UMFPACK_INFO]
	)

inline

Definition at line 104 of file UmfPackSupport.h.

int Eigen::umfpack_get_lunz	(	int *	lnz,
		int *	unz,
		int *	n_row,
		int *	n_col,
		int *	nz_udiag,
		void *	Numeric,
		double
	)

inline

Definition at line 73 of file UmfPackSupport.h.

int Eigen::umfpack_get_lunz	(	int *	lnz,
		int *	unz,
		int *	n_row,
		int *	n_col,
		int *	nz_udiag,
		void *	Numeric,
		std::complex< double >
	)

inline

Definition at line 78 of file UmfPackSupport.h.

int Eigen::umfpack_get_numeric	(	int	Lp[],
		int	Lj[],
		double	Lx[],
		int	Up[],
		int	Ui[],
		double	Ux[],
		int	P[],
		int	Q[],
		double	Dx[],
		int *	do_recip,
		double	Rs[],
		void *	Numeric
	)

inline

Definition at line 83 of file UmfPackSupport.h.

int Eigen::umfpack_get_numeric	(	int	Lp[],
		int	Lj[],
		std::complex< double >	Lx[],
		int	Up[],
		int	Ui[],
		std::complex< double >	Ux[],
		int	P[],
		int	Q[],
		std::complex< double >	Dx[],
		int *	do_recip,
		double	Rs[],
		void *	Numeric
	)

inline

Definition at line 89 of file UmfPackSupport.h.

int Eigen::umfpack_numeric	(	const int	Ap[],
		const int	Ai[],
		const double	Ax[],
		void *	Symbolic,
		void **	Numeric,
		const double	Control[UMFPACK_CONTROL],
		double	Info[UMFPACK_INFO]
	)

inline

Definition at line 45 of file UmfPackSupport.h.

int Eigen::umfpack_numeric	(	const int	Ap[],
		const int	Ai[],
		const std::complex< double >	Ax[],
		void *	Symbolic,
		void **	Numeric,
		const double	Control[UMFPACK_CONTROL],
		double	Info[UMFPACK_INFO]
	)

inline

Definition at line 52 of file UmfPackSupport.h.

int Eigen::umfpack_solve	(	int	sys,
		const int	Ap[],
		const int	Ai[],
		const double	Ax[],
		double	X[],
		const double	B[],
		void *	Numeric,
		const double	Control[UMFPACK_CONTROL],
		double	Info[UMFPACK_INFO]
	)

inline

Definition at line 59 of file UmfPackSupport.h.

int Eigen::umfpack_solve	(	int	sys,
		const int	Ap[],
		const int	Ai[],
		const std::complex< double >	Ax[],
		std::complex< double >	X[],
		const std::complex< double >	B[],
		void *	Numeric,
		const double	Control[UMFPACK_CONTROL],
		double	Info[UMFPACK_INFO]
	)

inline

Definition at line 66 of file UmfPackSupport.h.

int Eigen::umfpack_symbolic	(	int	n_row,
		int	n_col,
		const int	Ap[],
		const int	Ai[],
		const double	Ax[],
		void **	Symbolic,
		const double	Control[UMFPACK_CONTROL],
		double	Info[UMFPACK_INFO]
	)

inline

Definition at line 31 of file UmfPackSupport.h.

int Eigen::umfpack_symbolic	(	int	n_row,
		int	n_col,
		const int	Ap[],
		const int	Ai[],
		const std::complex< double >	Ax[],
		void **	Symbolic,
		const double	Control[UMFPACK_CONTROL],
		double	Info[UMFPACK_INFO]
	)

inline

Definition at line 38 of file UmfPackSupport.h.

template<typename _Scalar , int _Options, typename _Index >

cholmod_sparse Eigen::viewAsCholmod ( SparseMatrix< _Scalar, _Options, _Index > & mat )

Wraps the Eigen sparse matrix mat into a Cholmod sparse matrix object. Note that the data are shared.

Definition at line 52 of file CholmodSupport.h.

template<typename _Scalar , int _Options, typename _Index >

const cholmod_sparse Eigen::viewAsCholmod ( const SparseMatrix< _Scalar, _Options, _Index > & mat )

Definition at line 97 of file CholmodSupport.h.

template<typename _Scalar , int _Options, typename _Index , unsigned int UpLo>

cholmod_sparse Eigen::viewAsCholmod ( const SparseSelfAdjointView< SparseMatrix< _Scalar, _Options, _Index >, UpLo > & mat )

Returns a view of the Eigen sparse matrix mat as Cholmod sparse matrix. The data are not copied but shared.

Definition at line 106 of file CholmodSupport.h.

template<typename Derived >

cholmod_dense Eigen::viewAsCholmod ( MatrixBase< Derived > & mat )

Returns a view of the Eigen dense matrix mat as Cholmod dense matrix. The data are not copied but shared.

Definition at line 119 of file CholmodSupport.h.

template<typename Scalar , int Flags, typename Index >

MappedSparseMatrix<Scalar,Flags,Index> Eigen::viewAsEigen ( cholmod_sparse & cm )

Returns a view of the Cholmod sparse matrix cm as an Eigen sparse matrix. The data are not copied but shared.

Definition at line 140 of file CholmodSupport.h.

Variable Documentation

const unsigned int Eigen::ActualPacketAccessBit = 0x0

Definition at line 94 of file eigen3/Eigen/src/Core/util/Constants.h.

const int Eigen::CoherentAccessPattern = 0x1

Definition at line 65 of file SparseUtil.h.

const int Eigen::Dynamic = -1

This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is stored in some runtime variable.

Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.

Definition at line 21 of file eigen3/Eigen/src/Core/util/Constants.h.

const int Eigen::DynamicIndex = 0xffffff

This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its value has to be specified at runtime.

Definition at line 26 of file eigen3/Eigen/src/Core/util/Constants.h.

Scalar Eigen::expx = exp(x.value())

Definition at line 572 of file AutoDiffScalar.h.

const unsigned int Eigen::HereditaryBits

Initial value:

= RowMajorBit
                                  | EvalBeforeNestingBit
                                  | EvalBeforeAssigningBit

Definition at line 152 of file eigen3/Eigen/src/Core/util/Constants.h.

const int Eigen::Infinity = -1

This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>(). The value Infinity there means the L-infinity norm.

Definition at line 31 of file eigen3/Eigen/src/Core/util/Constants.h.

const int Eigen::InnerRandomAccessPattern = 0x2 | CoherentAccessPattern

Definition at line 66 of file SparseUtil.h.

const unsigned int Eigen::LowerTriangular = Lower

Definition at line 21 of file Eigen2Support/TriangularSolver.h.

const unsigned int Eigen::LowerTriangularBit = Lower

Definition at line 18 of file Eigen2Support/TriangularSolver.h.

const unsigned int Eigen::NestByRefBit = 0x100

Definition at line 149 of file eigen3/Eigen/src/Core/util/Constants.h.

const int Eigen::OuterRandomAccessPattern = 0x4 | CoherentAccessPattern

Definition at line 67 of file SparseUtil.h.

const int Eigen::RandomAccessPattern = 0x8 | OuterRandomAccessPattern | InnerRandomAccessPattern