Namespace containing all symbols from the Eigen library. More...

Classes
class	aligned_allocator
class	AlignedBox
class	AlignedVector3
	A vectorization friendly 3D vector. More...
class	AMDOrdering
class	AngleAxis
class	ArithmeticSequence
class	Array
class	ArrayBase
class	ArrayWrapper
struct	ArrayXpr
class	AutoDiffScalar
	A scalar type replacement with automatic differentiation capability. More...
class	BDCSVD
class	BiCGSTAB
class	Block
class	BlockImpl< XprType, BlockRows, BlockCols, InnerPanel, Sparse >
class	BlockSparseMatrix
	A versatile sparse matrix representation where each element is a block. More...
class	CholmodBase
class	CholmodDecomposition
class	CholmodSimplicialLDLT
class	CholmodSimplicialLLT
class	CholmodSupernodalLLT
class	COLAMDOrdering
class	ColPivHouseholderQR
class	CommaInitializer
class	CompleteOrthogonalDecomposition
class	ComplexEigenSolver
class	ComplexSchur
class	ConjugateGradient
class	CwiseBinaryOp
class	CwiseNullaryOp
class	CwiseTernaryOp
class	CwiseUnaryOp
class	CwiseUnaryView
struct	Dense
class	DenseBase
class	DenseCoeffsBase< Derived, DirectAccessors >
class	DenseCoeffsBase< Derived, DirectWriteAccessors >
class	DenseCoeffsBase< Derived, ReadOnlyAccessors >
class	DenseCoeffsBase< Derived, WriteAccessors >
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
class	DiagonalBase
class	DiagonalMatrix
class	DiagonalPreconditioner
class	DiagonalWrapper
class	DynamicSGroup
	Dynamic symmetry group. More...
class	EigenBase
class	EigenSolver
class	EulerAngles
	Represents a rotation in a 3 dimensional space as three Euler angles. More...
class	EulerSystem
	Represents a fixed Euler rotation system. More...
class	ForceAlignedAccess
class	FullPivHouseholderQR
class	FullPivLU
class	GeneralizedEigenSolver
class	GeneralizedSelfAdjointEigenSolver
class	GMRES
	A GMRES solver for sparse square problems. More...
class	HessenbergDecomposition
class	Homogeneous
class	HouseholderQR
class	HouseholderSequence
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
class	IdentityPreconditioner
class	IDRS
	The Induced Dimension Reduction method (IDR(s)) is a short-recurrences Krylov method for sparse square problems. More...
class	IDRSTABL
	The IDR(s)STAB(l) is a combination of IDR(s) and BiCGSTAB(l). It is a short-recurrences Krylov method for sparse square problems. It can outperform both IDR(s) and BiCGSTAB(l). IDR(s)STAB(l) generally closely follows the optimal GMRES convergence in terms of the number of Matrix-Vector products. However, without the increasing cost per iteration of GMRES. IDR(s)STAB(l) is suitable for both indefinite systems and systems with complex eigenvalues. More...
class	IncompleteCholesky
class	IncompleteLUT
class	IndexedView
class	InnerIterator
class	InnerStride
class	Inverse
class	IOFormat
class	IterativeSolverBase
class	IterScaling
	iterative scaling algorithm to equilibrate rows and column norms in matrices More...
class	JacobiRotation
class	JacobiSVD
class	KahanSum
	Kahan algorithm based accumulator. More...
class	KdBVH
	A simple bounding volume hierarchy based on AlignedBox. More...
class	KroneckerProduct
	Kronecker tensor product helper class for dense matrices. More...
class	KroneckerProductBase
	The base class of dense and sparse Kronecker product. More...
class	KroneckerProductSparse
	Kronecker tensor product helper class for sparse matrices. More...
class	LDLT
class	LeastSquareDiagonalPreconditioner
class	LeastSquaresConjugateGradient
class	LevenbergMarquardt
	Performs non linear optimization over a non-linear function, using a variant of the Levenberg Marquardt algorithm. More...
class	LLT
class	Map
class	Map< const Quaternion< Scalar_ >, Options_ >
class	Map< Quaternion< Scalar_ >, Options_ >
class	Map< SparseMatrixType >
class	MapBase< Derived, ReadOnlyAccessors >
class	MapBase< Derived, WriteAccessors >
class	Matrix
class	MatrixBase
class	MatrixComplexPowerReturnValue
	Proxy for the matrix power of some matrix (expression). More...
struct	MatrixExponentialReturnValue
	Proxy for the matrix exponential of some matrix (expression). More...
class	MatrixFunctionReturnValue
	Proxy for the matrix function of some matrix (expression). 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 for computing matrix powers. More...
class	MatrixPowerParenthesesReturnValue
	Proxy for the matrix power of some matrix. More...
class	MatrixPowerReturnValue
	Proxy for the matrix power of some matrix (expression). More...
class	MatrixSquareRootReturnValue
	Proxy for the matrix square root of some matrix (expression). More...
class	MatrixWrapper
struct	MatrixXpr
class	MaxSizeVector
class	MetisOrdering
class	MINRES
	A minimal residual solver for sparse symmetric problems. More...
class	NaturalOrdering
class	NestByValue
class	NNLS
	Implementation of the Non-Negative Least Squares (NNLS) algorithm. More...
class	NoAlias
class	NumericalDiff
class	NumTraits
class	OuterStride
class	ParametrizedLine
class	PardisoLDLT
class	PardisoLLT
class	PardisoLU
class	PartialPivLU
class	PartialReduxExpr
class	PastixLDLT
class	PastixLLT
class	PastixLU
class	PermutationBase
class	PermutationMatrix
struct	PermutationStorage
class	PermutationWrapper
class	PlainObjectBase
class	PolynomialSolver
	A polynomial solver. More...
class	PolynomialSolverBase
	Defined to be inherited by polynomial solvers: it provides convenient methods such as. More...
class	Product
class	Quaternion
class	QuaternionBase
class	RandomSetter
	The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access. More...
class	RealQZ
class	RealSchur
class	Ref
class	Ref< SparseMatrixType, Options >
class	Ref< SparseVectorType >
class	Replicate
class	Reshaped
class	Reverse
class	Rotation2D
class	RotationBase
class	ScalarBinaryOpTraits
class	SelfAdjointEigenSolver
class	SelfAdjointView
class	Serializer
class	SGroup
	Symmetry group, initialized from template arguments. More...
class	SimplicialCholesky
class	SimplicialCholeskyBase
class	SimplicialLDLT
class	SimplicialLLT
class	SimplicialNonHermitianLDLT
class	SimplicialNonHermitianLLT
class	SkewSymmetricBase
class	SkewSymmetricMatrix3
class	SkewSymmetricWrapper
class	Solve
class	SolverBase
struct	SolverStorage
class	SolveWithGuess
struct	Sparse
class	SparseCompressedBase
class	SparseInverse
	calculate sparse subset of inverse of sparse matrix More...
class	SparseLU
class	SparseMapBase< Derived, ReadOnlyAccessors >
class	SparseMapBase< Derived, WriteAccessors >
class	SparseMatrix
class	SparseMatrixBase
class	SparseQR
class	SparseSelfAdjointView
class	SparseSolverBase
class	SparseVector
class	SparseView
class	Spline
	A class representing multi-dimensional spline curves. More...
struct	SplineFitting
	Spline fitting methods. More...
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
class	StaticSGroup
	Static symmetry group. More...
struct	StdMapTraits
struct	StdUnorderedMapTraits
class	Stride
class	SuperILU
class	SuperLU
class	SuperLUBase
class	SVDBase
class	Tensor
	The tensor class. More...
class	TensorAssignOp
class	TensorAsyncDevice
	Pseudo expression providing an operator = that will evaluate its argument asynchronously on the specified device. Currently only ThreadPoolDevice implements proper asynchronous execution, while the default and GPU devices just run the expression synchronously and call m_done() on completion.. More...
class	TensorBase
	The tensor base class. More...
class	TensorBroadcastingOp
class	TensorChippingOp
class	TensorConcatenationOp
	Tensor concatenation class. More...
class	TensorContractionOp
class	TensorConversionOp
	Tensor conversion class. This class makes it possible to vectorize type casting operations when the number of scalars per packet in the source and the destination type differ. More...
class	TensorConvolutionOp
class	TensorCostModel
	A cost model used to limit the number of threads used for evaluating tensor expression. More...
class	TensorCustomBinaryOp
	Tensor custom class. More...
class	TensorCustomUnaryOp
	Tensor custom class. More...
class	TensorCwiseBinaryOp
	Tensor binary expression. More...
class	TensorCwiseNullaryOp
	Tensor nullary expression. More...
class	TensorCwiseUnaryOp
	Tensor unary expression. More...
class	TensorDevice
	Pseudo expression providing an operator = that will evaluate its argument on the specified computing 'device' (GPU, thread pool, ...). More...
struct	TensorEvaluator
	The tensor evaluator class. More...
class	TensorFFTOp
	Tensor FFT class. More...
class	TensorFixedSize
	The fixed sized version of the tensor class. More...
class	TensorForcedEvalOp
	Tensor reshaping class. More...
class	TensorGeneratorOp
	Tensor generator class. More...
class	TensorImagePatchOp
	Patch extraction specialized for image processing. This assumes that the input has a least 3 dimensions ordered as follow: 1st dimension: channels (of size d) 2nd dimension: rows (of size r) 3rd dimension: columns (of size c) There can be additional dimensions such as time (for video) or batch (for bulk processing after the first 3. Calling the image patch code with patch_rows and patch_cols is equivalent to calling the regular patch extraction code with parameters d, patch_rows, patch_cols, and 1 for all the additional dimensions. More...
class	TensorIndexPairOp
	Tensor + Index Pair class. More...
class	TensorInflationOp
	Tensor inflation class. More...
class	TensorMap
	A tensor expression mapping an existing array of data. More...
class	TensorPaddingOp
	Tensor padding class. At the moment only padding with a constant value is supported. More...
class	TensorPatchOp
	Tensor patch class. More...
class	TensorReductionOp
	Tensor reduction class. More...
class	TensorRef
	A reference to a tensor expression The expression will be evaluated lazily (as much as possible). More...
class	TensorRef< const PlainObjectType >
	A reference to a constant tensor expression The expression will be evaluated lazily (as much as possible). More...
class	TensorReshapingOp
	Tensor reshaping class. More...
class	TensorReverseOp
	Tensor reverse elements class. More...
class	TensorRollOp
	Tensor roll (circular shift) elements class. More...
class	TensorScanOp
	Tensor scan class. More...
class	TensorShufflingOp
	Tensor shuffling class. More...
class	TensorStridingOp
	Tensor striding class. More...
class	TensorTraceOp
	Tensor Trace class. More...
class	TensorVolumePatchOp
	Patch extraction specialized for processing of volumetric data. This assumes that the input has a least 4 dimensions ordered as follows: More...
class	Transform
class	Translation
class	Transpose
class	Transpositions
struct	TranspositionsStorage
class	TriangularBase
class	TriangularView
class	TriangularViewImpl< MatrixType, Mode, Sparse >
class	TriangularViewImpl< MatrixType_, Mode_, Dense >
class	Tridiagonalization
class	Triplet
class	UmfPackLU
class	UniformScaling
class	VectorBlock
class	VectorwiseOp
class	WithFormat

Typedefs
typedef EulerAngles< double, EulerSystemXYZ >	EulerAnglesXYZd
typedef EulerAngles< float, EulerSystemZYZ >	EulerAnglesZYZf
typedef EulerSystem< EULER_X, EULER_Y, EULER_Z >	EulerSystemXYZ
typedef Spline< double, 2 >	Spline2d
	2D double B-spline with dynamic degree.
typedef Spline< float, 2 >	Spline2f
	2D float B-spline with dynamic degree.
typedef Spline< double, 3 >	Spline3d
	3D double B-spline with dynamic degree.
typedef Spline< float, 3 >	Spline3f
	3D float B-spline with dynamic degree.

Enumerations
enum	EulerAxis { EULER_X , EULER_Y , EULER_Z }
	Representation of a fixed signed rotation axis for EulerSystem. More...

Functions
template<typename Derived, typename OtherDerived>
Derived::Scalar	accurateDot (const SparseMatrixBase< Derived > &A, const SparseMatrixBase< OtherDerived > &other)
	computes an accurate dot product on two sparse vectors
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i0_op< typename Derived::Scalar >, const Derived >	bessel_i0 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i0e_op< typename Derived::Scalar >, const Derived >	bessel_i0e (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1_op< typename Derived::Scalar >, const Derived >	bessel_i1 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1e_op< typename Derived::Scalar >, const Derived >	bessel_i1e (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_j0_op< typename Derived::Scalar >, const Derived >	bessel_j0 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_j1_op< typename Derived::Scalar >, const Derived >	bessel_j1 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k0_op< typename Derived::Scalar >, const Derived >	bessel_k0 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k0e_op< typename Derived::Scalar >, const Derived >	bessel_k0e (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1_op< typename Derived::Scalar >, const Derived >	bessel_k1 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1e_op< typename Derived::Scalar >, const Derived >	bessel_k1e (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_y0_op< typename Derived::Scalar >, const Derived >	bessel_y0 (const Eigen::ArrayBase< Derived > &x)
template<typename Derived>
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_y1_op< typename Derived::Scalar >, const Derived >	bessel_y1 (const Eigen::ArrayBase< Derived > &x)
template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>
const Eigen::CwiseTernaryOp< Eigen::internal::scalar_betainc_op< typename ArgXDerived::Scalar >, const ArgADerived, const ArgBDerived, const ArgXDerived >	betainc (const Eigen::ArrayBase< ArgADerived > &a, const Eigen::ArrayBase< ArgBDerived > &b, const Eigen::ArrayBase< ArgXDerived > &x)
template<typename ADerived, typename BDerived, typename XDerived>
const TensorCwiseTernaryOp< internal::scalar_betainc_op< typename XDerived::Scalar >, const ADerived, const BDerived, const XDerived >	betainc (const Eigen::TensorBase< ADerived, ReadOnlyAccessors > &a, const Eigen::TensorBase< BDerived, ReadOnlyAccessors > &b, const Eigen::TensorBase< XDerived, ReadOnlyAccessors > &x)
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< typenamePolynomial::Scalar >::Real	cauchy_max_bound (const Polynomial &poly)
template<typename Polynomial>
NumTraits< typenamePolynomial::Scalar >::Real	cauchy_min_bound (const Polynomial &poly)
template<typename PointArrayType, typename KnotVectorType>
void	ChordLengths (const PointArrayType &pts, KnotVectorType &chord_lengths)
	Computes chord length parameters which are required for spline interpolation.
template<typename AlphaDerived, typename SampleDerived>
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_gamma_sample_der_alpha_op< typename AlphaDerived::Scalar >, const AlphaDerived, const SampleDerived >	gamma_sample_der_alpha (const Eigen::ArrayBase< AlphaDerived > &alpha, const Eigen::ArrayBase< SampleDerived > &sample)
bool	getMarketHeader (const std::string &filename, int &sym, bool &iscomplex, bool &isdense)
	Reads the header of a matrixmarket file and determines the properties of a matrix.
template<typename Derived, typename ExponentDerived>
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_igamma_op< typename Derived::Scalar >, const Derived, const ExponentDerived >	igamma (const Eigen::ArrayBase< Derived > &a, const Eigen::ArrayBase< ExponentDerived > &x)
template<typename Derived, typename ExponentDerived>
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_igamma_der_a_op< typename Derived::Scalar >, const Derived, const ExponentDerived >	igamma_der_a (const Eigen::ArrayBase< Derived > &a, const Eigen::ArrayBase< ExponentDerived > &x)
template<typename Derived, typename ExponentDerived>
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_igammac_op< typename Derived::Scalar >, const Derived, const ExponentDerived >	igammac (const Eigen::ArrayBase< Derived > &a, const Eigen::ArrayBase< ExponentDerived > &x)
template<typename KnotVectorType>
void	KnotAveraging (const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)
	Computes knot averages.
template<typename KnotVectorType, typename ParameterVectorType, typename IndexArray>
void	KnotAveragingWithDerivatives (const ParameterVectorType &parameters, const unsigned int degree, const IndexArray &derivativeIndices, KnotVectorType &knots)
	Computes knot averages when derivative constraints are present. Note that this is a technical interpretation of the referenced article since the algorithm contained therein is incorrect as written.
template<typename A, typename B>
KroneckerProductSparse< A, B >	kroneckerProduct (const EigenBase< A > &a, const EigenBase< B > &b)
template<typename A, typename B>
KroneckerProduct< A, B >	kroneckerProduct (const MatrixBase< A > &a, const MatrixBase< B > &b)
template<typename SparseMatrixType>
bool	loadMarket (SparseMatrixType &mat, const std::string &filename)
	Loads a sparse matrix from a matrixmarket format file.
template<typename DenseType>
bool	loadMarketDense (DenseType &mat, const std::string &filename)
	Loads a dense Matrix or Vector from a matrixmarket file. If a statically sized matrix has to be parsed and the file contains the wrong dimensions it is undefined behaviour.
template<typename VectorType>
bool	loadMarketVector (VectorType &vec, const std::string &filename)
	Same functionality as loadMarketDense, deprecated.
template<typename MatrixType, typename ResultType>
void	matrix_sqrt_quasi_triangular (const MatrixType &arg, ResultType &result)
	Compute matrix square root of quasi-triangular matrix.
template<typename MatrixType, typename ResultType>
void	matrix_sqrt_triangular (const MatrixType &arg, ResultType &result)
	Compute matrix square root of triangular matrix.
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 DerivedN, typename DerivedX>
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_polygamma_op< typename DerivedX::Scalar >, const DerivedN, const DerivedX >	polygamma (const Eigen::ArrayBase< DerivedN > &n, const Eigen::ArrayBase< DerivedX > &x)
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)
	writes a sparse Matrix to a marketmarket format file
template<typename DenseType>
bool	saveMarketDense (const DenseType &mat, const std::string &filename)
	writes a dense Matrix or vector to a marketmarket format file
template<typename VectorType>
bool	saveMarketVector (const VectorType &vec, const std::string &filename)
	Same functionality as saveMarketDense, deprecated.
template<typename DerivedX, typename DerivedQ>
const Eigen::CwiseBinaryOp< Eigen::internal::scalar_zeta_op< typename DerivedX::Scalar >, const DerivedX, const DerivedQ >	zeta (const Eigen::ArrayBase< DerivedX > &x, const Eigen::ArrayBase< DerivedQ > &q)

Detailed Description

Namespace containing all symbols from the Eigen library.

Function Documentation

◆ accurateDot()

template<typename Derived, typename OtherDerived>

Derived::Scalar Eigen::accurateDot	(	const SparseMatrixBase< Derived > &	A,
		const SparseMatrixBase< OtherDerived > &	other )

computes an accurate dot product on two sparse vectors

Uses an accurate summation algorithm for the accumulator in order to compute an accurate dot product for two sparse vectors.

◆ bessel_i0()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i0_op< typename Derived::Scalar >, const Derived > Eigen::bessel_i0 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise i0(x) to the given arrays.

It returns the modified Bessel function of the first kind of order zero.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of i0(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_i0()

◆ bessel_i0e()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i0e_op< typename Derived::Scalar >, const Derived > Eigen::bessel_i0e ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise i0e(x) to the given arrays.

It returns the exponentially scaled modified Bessel function of the first kind of order zero.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of i0e(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_i0e()

◆ bessel_i1()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1_op< typename Derived::Scalar >, const Derived > Eigen::bessel_i1 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise i1(x) to the given arrays.

It returns the modified Bessel function of the first kind of order one.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of i1(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_i1()

◆ bessel_i1e()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1e_op< typename Derived::Scalar >, const Derived > Eigen::bessel_i1e ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise i1e(x) to the given arrays.

It returns the exponentially scaled modified Bessel function of the first kind of order one.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of i1e(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_i1e()

◆ bessel_j0()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_j0_op< typename Derived::Scalar >, const Derived > Eigen::bessel_j0 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise j0(x) to the given arrays.

It returns the Bessel function of the first kind of order zero.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of j0(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_j0()

◆ bessel_j1()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_j1_op< typename Derived::Scalar >, const Derived > Eigen::bessel_j1 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise j1(x) to the given arrays.

It returns the modified Bessel function of the first kind of order one.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of j1(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_j1()

◆ bessel_k0()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k0_op< typename Derived::Scalar >, const Derived > Eigen::bessel_k0 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise k0(x) to the given arrays.

It returns the modified Bessel function of the second kind of order zero.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of k0(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_k0()

◆ bessel_k0e()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k0e_op< typename Derived::Scalar >, const Derived > Eigen::bessel_k0e ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise k0e(x) to the given arrays.

It returns the exponentially scaled modified Bessel function of the second kind of order zero.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of k0e(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_k0e()

◆ bessel_k1()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1_op< typename Derived::Scalar >, const Derived > Eigen::bessel_k1 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise k1(x) to the given arrays.

It returns the modified Bessel function of the second kind of order one.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of k1(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_k1()

◆ bessel_k1e()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1e_op< typename Derived::Scalar >, const Derived > Eigen::bessel_k1e ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise k1e(x) to the given arrays.

It returns the exponentially scaled modified Bessel function of the second kind of order one.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of k1e(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_k1e()

◆ bessel_y0()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_y0_op< typename Derived::Scalar >, const Derived > Eigen::bessel_y0 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise y0(x) to the given arrays.

It returns the Bessel function of the second kind of order zero.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of y0(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_y0()

◆ bessel_y1()

template<typename Derived>

const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_y1_op< typename Derived::Scalar >, const Derived > Eigen::bessel_y1 ( const Eigen::ArrayBase< Derived > & x )

inline

Returns: an expression of the coefficient-wise y1(x) to the given arrays.

It returns the Bessel function of the second kind of order one.

Parameters

x	is the argument

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of y1(T) for any scalar type T to be supported.

See also: ArrayBase::bessel_y1()

◆ betainc() [1/2]

template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>

const Eigen::CwiseTernaryOp< Eigen::internal::scalar_betainc_op< typename ArgXDerived::Scalar >, const ArgADerived, const ArgBDerived, const ArgXDerived > Eigen::betainc	(	const Eigen::ArrayBase< ArgADerived > &	a,
		const Eigen::ArrayBase< ArgBDerived > &	b,
		const Eigen::ArrayBase< ArgXDerived > &	x )

inline

[c++11]

Returns: an expression of the coefficient-wise betainc(x, a, b) to the given arrays.

This function computes the regularized incomplete beta function (integral).

Note: This function supports only float and double scalar types in c++11 mode. To support other scalar types, or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar type T to be supported.

See also: Eigen::betainc(), Eigen::lgamma()

◆ betainc() [2/2]

template<typename ADerived, typename BDerived, typename XDerived>

const TensorCwiseTernaryOp< internal::scalar_betainc_op< typename XDerived::Scalar >, const ADerived, const BDerived, const XDerived > Eigen::betainc	(	const Eigen::TensorBase< ADerived, ReadOnlyAccessors > &	a,
		const Eigen::TensorBase< BDerived, ReadOnlyAccessors > &	b,
		const Eigen::TensorBase< XDerived, ReadOnlyAccessors > &	x )

inline

[c++11]

Returns: an expression of the coefficient-wise betainc(x, a, b) to the given tensors.

This function computes the regularized incomplete beta function (integral).

◆ BVIntersect() [1/2]

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

◆ BVIntersect() [2/2]

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 

◆ BVMinimize() [1/2]

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)

Eigen::Scalar

◆ BVMinimize() [2/2]

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)

◆ gamma_sample_der_alpha()

template<typename AlphaDerived, typename SampleDerived>

const Eigen::CwiseBinaryOp< Eigen::internal::scalar_gamma_sample_der_alpha_op< typename AlphaDerived::Scalar >, const AlphaDerived, const SampleDerived > Eigen::gamma_sample_der_alpha	(	const Eigen::ArrayBase< AlphaDerived > &	alpha,
		const Eigen::ArrayBase< SampleDerived > &	sample )

inline

[c++11]

Returns: an expression of the coefficient-wise gamma_sample_der_alpha(alpha, sample) to the given arrays.

This function computes the coefficient-wise derivative of the sample of a Gamma(alpha, 1) random variable with respect to the parameter alpha.

Note: This function supports only float and double scalar types in c++11 mode. To support other scalar types, or float/double in non c++11 mode, the user has to provide implementations of gamma_sample_der_alpha(T,T) for any scalar type T to be supported.

See also: Eigen::igamma(), Eigen::lgamma()

◆ igamma()

template<typename Derived, typename ExponentDerived>

const Eigen::CwiseBinaryOp< Eigen::internal::scalar_igamma_op< typename Derived::Scalar >, const Derived, const ExponentDerived > Eigen::igamma	(	const Eigen::ArrayBase< Derived > &	a,
		const Eigen::ArrayBase< ExponentDerived > &	x )

inline

[c++11]

Returns: an expression of the coefficient-wise igamma(a, x) to the given arrays.

This function computes the coefficient-wise incomplete gamma function.

Note: This function supports only float and double scalar types in c++11 mode. To support other scalar types, or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar type T to be supported.

See also: Eigen::igammac(), Eigen::lgamma()

◆ igamma_der_a()

template<typename Derived, typename ExponentDerived>

const Eigen::CwiseBinaryOp< Eigen::internal::scalar_igamma_der_a_op< typename Derived::Scalar >, const Derived, const ExponentDerived > Eigen::igamma_der_a	(	const Eigen::ArrayBase< Derived > &	a,
		const Eigen::ArrayBase< ExponentDerived > &	x )

inline

[c++11]

Returns: an expression of the coefficient-wise igamma_der_a(a, x) to the given arrays.

This function computes the coefficient-wise derivative of the incomplete gamma function with respect to the parameter a.

Note: This function supports only float and double scalar types in c++11 mode. To support other scalar types, or float/double in non c++11 mode, the user has to provide implementations of igamma_der_a(T,T) for any scalar type T to be supported.

See also: Eigen::igamma(), Eigen::lgamma()

◆ igammac()

template<typename Derived, typename ExponentDerived>

const Eigen::CwiseBinaryOp< Eigen::internal::scalar_igammac_op< typename Derived::Scalar >, const Derived, const ExponentDerived > Eigen::igammac	(	const Eigen::ArrayBase< Derived > &	a,
		const Eigen::ArrayBase< ExponentDerived > &	x )

inline

[c++11]

Returns: an expression of the coefficient-wise igammac(a, x) to the given arrays.

This function computes the coefficient-wise complementary incomplete gamma function.

Note: This function supports only float and double scalar types in c++11 mode. To support other scalar types, or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar type T to be supported.

See also: Eigen::igamma(), Eigen::lgamma()

◆ polygamma()

template<typename DerivedN, typename DerivedX>

const Eigen::CwiseBinaryOp< Eigen::internal::scalar_polygamma_op< typename DerivedX::Scalar >, const DerivedN, const DerivedX > Eigen::polygamma	(	const Eigen::ArrayBase< DerivedN > &	n,
		const Eigen::ArrayBase< DerivedX > &	x )

inline

[c++11]

Returns: an expression of the coefficient-wise polygamma(n, x) to the given arrays.

It returns the n -th derivative of the digamma(psi) evaluated at x.

Note: This function supports only float and double scalar types in c++11 mode. To support other scalar types, or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar type T to be supported.

See also: Eigen::digamma()

◆ zeta()

template<typename DerivedX, typename DerivedQ>

const Eigen::CwiseBinaryOp< Eigen::internal::scalar_zeta_op< typename DerivedX::Scalar >, const DerivedX, const DerivedQ > Eigen::zeta	(	const Eigen::ArrayBase< DerivedX > &	x,
		const Eigen::ArrayBase< DerivedQ > &	q )

inline

Returns: an expression of the coefficient-wise zeta(x, q) to the given arrays.

It returns the Riemann zeta function of two arguments x and q:

Parameters

x	is the exponent, it must be > 1
q	is the shift, it must be > 0

Note: This function supports only float and double scalar types. To support other scalar types, the user has to provide implementations of zeta(T,T) for any scalar type T to be supported.

See also: ArrayBase::zeta()

Classes

Typedefs

Enumerations

Functions

Detailed Description

Function Documentation

◆ accurateDot()

◆ bessel_i0()

◆ bessel_i0e()

◆ bessel_i1()

◆ bessel_i1e()

◆ bessel_j0()

◆ bessel_j1()

◆ bessel_k0()

◆ bessel_k0e()

◆ bessel_k1()

◆ bessel_k1e()

◆ bessel_y0()

◆ bessel_y1()

◆ betainc() [1/2]

◆ betainc() [2/2]

◆ BVIntersect() [1/2]

◆ BVIntersect() [2/2]

◆ BVMinimize() [1/2]

◆ BVMinimize() [2/2]

◆ gamma_sample_der_alpha()

◆ igamma()

◆ igamma_der_a()

◆ igammac()

◆ polygamma()

◆ zeta()