Namespaces | Classes | Typedefs | Enumerations | Functions | Variables
Eigen Namespace Reference

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, AffineAffine2d
 
typedef Transform< float, 2, AffineAffine2f
 
typedef Transform< double, 3, AffineAffine3d
 
typedef Transform< float, 3, AffineAffine3f
 
typedef Transform< double, 2, AffineCompactAffineCompact2d
 
typedef Transform< float, 2, AffineCompactAffineCompact2f
 
typedef Transform< double, 3, AffineCompactAffineCompact3d
 
typedef Transform< float, 3, AffineCompactAffineCompact3f
 
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, IsometryIsometry2d
 
typedef Transform< float, 2, IsometryIsometry2f
 
typedef Transform< double, 3, IsometryIsometry3d
 
typedef Transform< float, 3, IsometryIsometry3f
 
typedef Transform< double, 2, ProjectiveProjective2d
 
typedef Transform< float, 2, ProjectiveProjective2f
 
typedef Transform< double, 3, ProjectiveProjective3d
 
typedef Transform< float, 3, ProjectiveProjective3f
 
typedef Quaternion< double > Quaterniond
 
typedef Quaternion< float > Quaternionf
 
typedef Map< Quaternion< double >, AlignedQuaternionMapAlignedd
 
typedef Map< Quaternion< float >, AlignedQuaternionMapAlignedf
 
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 >
Tei_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 $p$ is the degree and $m+1$ 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, OnTheRightoperator* (const MatrixBase< Derived > &matrix, const TranspositionsBase< TranspositionsDerived > &transpositions)
 
template<typename Derived , typename TranspositionDerived >
const internal::transposition_matrix_product_retval< TranspositionDerived, Derived, OnTheLeftoperator* (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, OnTheRightoperator* (const MatrixBase< Derived > &matrix, const PermutationBase< PermutationDerived > &permutation)
 
template<typename Derived , typename PermutationDerived >
const internal::permut_matrix_product_retval< PermutationDerived, Derived, OnTheLeftoperator* (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, OnTheRightrightHouseholderSequence (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 Ty { 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);
// 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
_MatrixTypethe 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

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.

Enumerator
GetAction 
SetAction 

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

Enumerator
SkylineTimeDenseProduct 
SkylineTimeSkylineProduct 
DenseTimeSkylineProduct 

Definition at line 23 of file SkylineUtil.h.

Enumerator
CholmodAuto 
CholmodSimplicialLLt 
CholmodSupernodalLLt 
CholmodLDLt 

Definition at line 147 of file CholmodSupport.h.

Enumerator
Default 

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

Enumerator
NoChange 

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

Enumerator
Forward 
Central 

Definition at line 18 of file NumericalDiff.h.

Enumerator
Sequential 

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

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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.

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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.

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]ptsThe data points to which a spline should be fit.
[out]chord_lengthsThe 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  )
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]parametersThe input parameters. During interpolation one for each data point.
[in]degreeThe spline degree which is used during the interpolation.
[out]knotsThe 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
aDense matrix a
bDense 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
aDense/sparse matrix a
bDense/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
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
numPointsthe number of points
pointsthe array of pointers to the points on which to perform the linear regression
resultpointer 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 $n=Size$, $r_i=result[i]$, and $f=funcOfOthers$. Denote by $x_0,\ldots,x_{n-1}$ the n coordinates in the n-dimensional space. Then the resulting equation is:

\[ x_f = r_0 x_0 + \cdots + r_{f-1}x_{f-1} + r_{f+1}x_{f+1} + \cdots + r_{n-1}x_{n-1} + r_n. \]

funcOfOthersDetermines which coord to express as a function of the others. Coords are numbered starting from 0, so that a value of 0 means $x$, 1 means $y$, 2 means $z$, ...
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]otherMatrix being multiplied.
[in]hHouseholderSequence 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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.
[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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.
[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. $ 3 + x^2 $ is stored as a vector $ [ 3, 0, 1 ] $.

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:

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

Definition at line 68 of file SparseUtil.h.

const unsigned int Eigen::SelfAdjointBit = SelfAdjoint

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

const unsigned int Eigen::SkylineBit = 0x1200

Definition at line 21 of file SkylineUtil.h.

const unsigned int Eigen::UnitDiagBit = UnitDiag

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

const unsigned int Eigen::UnitLowerTriangular = UnitLower

Definition at line 23 of file Eigen2Support/TriangularSolver.h.

const unsigned int Eigen::UnitUpperTriangular = UnitUpper

Definition at line 22 of file Eigen2Support/TriangularSolver.h.

const unsigned int Eigen::UpperTriangular = Upper

Definition at line 20 of file Eigen2Support/TriangularSolver.h.

const unsigned int Eigen::UpperTriangularBit = Upper

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

const AutoDiffScalar< DerType > & Eigen::y { return (x <= y ? x : y)

Definition at line 539 of file AutoDiffScalar.h.



acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:27