CDPL::Math Namespace Reference

Contains classes and functions related to mathematics. More...

Classes
class	MatrixReference
	Lightweight matrix expression that proxies a reference to an underlying matrix container. More...
class	Vector
	Dynamically-sized dense vector with configurable underlying storage. More...
class	Matrix
	Dynamically-sized dense row-major matrix with configurable underlying storage. More...
class	RotationMatrix
	\( N \times N \) rotation matrix backed by a unit quaternion (or an axis-angle representation). More...
class	ScalingMatrix
	\( N \times N \) diagonal scaling matrix. More...
class	TranslationMatrix
	\( N \times N \) translation matrix in homogeneous coordinates. More...
class	BFGSMinimizer
	Fletcher's implementation of the BFGS method. More...
struct	CommonType
	Trait that resolves the common arithmetic type of T1 and T2 via std::common_type. More...
class	DirectAssignmentProxy
	Proxy that converts an assignment to a Math container into the corresponding direct-assignment call on the container (assign / plusAssign / minusAssign) bypassing alias detection. More...
class	Expression
	CRTP base class for all numeric expression types in the Math namespace (Barton-Nackman idiom). More...
class	VectorExpression
	CRTP base class for all vector expression types. More...
class	MatrixExpression
	CRTP base class for all matrix expression types. More...
class	QuaternionExpression
	CRTP base class for all quaternion expression types. More...
class	GridExpression
	CRTP base class for all grid expression types. More...
class	VectorContainer
	Refinement of Math::VectorExpression marking the derived type as a concrete (writable) vector container. More...
class	MatrixContainer
	Refinement of Math::MatrixExpression marking the derived type as a concrete (writable) matrix container. More...
class	QuaternionContainer
	Refinement of Math::QuaternionExpression marking the derived type as a concrete (writable) quaternion container. More...
class	GridContainer
	Refinement of Math::GridExpression marking the derived type as a concrete (writable) grid container. More...
struct	ScalarBinaryAssignmentFunctor
	Base class for binary in-place assignment functors of the form F::apply(T1, const T2&). More...
struct	ScalarAssignment
	Scalar plain-assignment functor: apply(t1, t2) performs t1 = t2. More...
struct	ScalarAdditionAssignment
	Scalar in-place addition functor: apply(t1, t2) performs t1 += t2. More...
struct	ScalarSubtractionAssignment
	Scalar in-place subtraction functor: apply(t1, t2) performs t1 -= t2. More...
struct	ScalarMultiplicationAssignment
	Scalar in-place multiplication functor: apply(t1, t2) performs t1 *= t2. More...
struct	ScalarDivisionAssignment
	Scalar in-place division functor: apply(t1, t2) performs t1 /= t2. More...
struct	ScalarUnaryFunctor
	Base class for unary scalar functors of the form F::apply(const T&) returning a T result. More...
struct	ScalarNegation
	Scalar negation functor: apply(v) returns -v. More...
struct	ScalarConjugation
	Scalar complex-conjugation functor: apply(v) returns \( \overline{v} \) (identity for real types). More...
struct	ScalarRealUnaryFunctor
	Base class for unary scalar functors that return the real part of T (Math::ScalarReal, Math::ScalarImaginary). More...
struct	ScalarReal
	Scalar real-part functor: apply(v) returns \( \mathrm{Re}(v) \) (identity for real types). More...
struct	ScalarImaginary
	Scalar imaginary-part functor: apply(v) returns \( \mathrm{Im}(v) \) (zero for real types). More...
struct	ScalarBinaryFunctor
	Base class for binary scalar functors of the form F::apply(const T1&, const T2&) returning a Math::CommonType result. More...
struct	ScalarAddition
	Scalar binary addition functor: apply(t1, t2) returns t1 + t2. More...
struct	ScalarSubtraction
	Scalar binary subtraction functor: apply(t1, t2) returns t1 - t2. More...
struct	ScalarMultiplication
	Scalar binary multiplication functor: apply(t1, t2) returns t1 * t2. More...
struct	ScalarDivision
	Scalar binary division functor: apply(t1, t2) returns t1 / t2. More...
struct	VectorScalarBinaryFunctor
	Base class for binary functors that take two vectors and return a scalar (Math::VectorInnerProduct, Math::VectorAngleCosine). More...
struct	VectorInnerProduct
	Vector inner-product functor: apply(e1, e2) returns \( \sum_i e_1(i) \cdot e_2(i) \). More...
struct	VectorAngleCosine
	Functor returning the cosine of the angle between two vectors (optionally clamped to [-1, 1]). More...
struct	VectorBooleanBinaryFunctor
	Base class for binary functors that take two vectors and return a boolean (Math::VectorEquality and similar). More...
struct	VectorEquality
	Vector equality functor: apply(e1, e2) tests element-wise equality of two vector expressions. More...
struct	Scalar3VectorBooleanTernaryFunctor
	Base class for ternary functors that take two vectors and a scalar tolerance and return a boolean (Math::VectorToleranceEquality). More...
struct	VectorToleranceEquality
	Vector tolerance-equality functor: apply(e1, e2, eps) tests element-wise equality within an absolute tolerance. More...
struct	VectorBinaryFunctor
	Base class for binary functors that take two vectors and return a vector (Math::VectorCrossProduct). More...
struct	VectorCrossProduct
	Vector cross-product functor: apply(e1, e2, i) returns the i-th component of the 3-vector cross product \( e_1 \times e_2 \). More...
struct	VectorScalarUnaryFunctor
	Base class for unary functors that take a vector and return a scalar (Math::VectorElementSum). More...
struct	VectorElementSum
	Functor returning the sum of all elements of a vector expression. More...
struct	VectorScalarRealUnaryFunctor
	Base class for unary functors that take a vector and return a real-valued scalar (Math::VectorNorm1, Math::VectorNorm2, Math::VectorNormInfinity). More...
struct	VectorNorm1
	Functor returning the L1 norm of a vector expression. More...
struct	VectorNorm2
	Functor returning the L2 (Euclidean) norm of a vector expression. More...
struct	VectorNormInfinity
	Functor returning the L∞ (maximum-magnitude) norm of a vector expression. More...
struct	VectorScalarIndexUnaryFunctor
	Base class for unary functors that take a vector and return a vector-element index (Math::VectorNormInfinityIndex). More...
struct	VectorNormInfinityIndex
	Functor returning the index of the vector element with the largest L∞ norm. More...
struct	MatrixBooleanBinaryFunctor
	Base class for binary functors that take two matrix expressions and return a bool result (Math::MatrixEquality). More...
struct	MatrixEquality
	Functor checking element-wise equality of two matrix expressions. More...
struct	Scalar3MatrixBooleanTernaryFunctor
	Base class for ternary functors that take two matrix expressions plus a tolerance scalar and return a bool result (Math::MatrixToleranceEquality). More...
struct	MatrixToleranceEquality
	Functor checking element-wise approximate equality of two matrix expressions within an absolute tolerance. More...
struct	MatrixScalarUnaryFunctor
	Base class for unary functors that take a matrix expression and return a scalar result (Math::MatrixElementSum, Math::MatrixTrace). More...
struct	MatrixElementSum
	Functor returning the sum of all elements of a matrix expression. More...
struct	MatrixTrace
	Functor returning the trace (sum of diagonal entries) of a matrix expression. More...
struct	MatrixScalarRealUnaryFunctor
	Base class for unary functors that take a matrix expression and return a real-valued scalar (Math::MatrixNorm1, Math::MatrixNormFrobenius, Math::MatrixNormInfinity). More...
struct	MatrixNorm1
	Functor returning the L1 (maximum absolute column sum) norm of a matrix expression. More...
struct	MatrixNormFrobenius
	Functor returning the Frobenius norm of a matrix expression. More...
struct	MatrixNormInfinity
	Functor returning the L∞ (maximum absolute row sum) norm of a matrix expression. More...
struct	VectorMatrixUnaryFunctor
	Base class for unary functors that produce a matrix element from a vector expression and (i, j) cell indices (Math::DiagonalMatrixFromVector, Math::CrossProductMatrixFromVector). More...
struct	DiagonalMatrixFromVector
	Functor producing the diagonal-matrix entry at (i, j) from a vector expression ( \( e(i) \) on the diagonal, 0 elsewhere). More...
struct	CrossProductMatrixFromVector
	Functor producing the cross-product (skew-symmetric) matrix entry at (i, j) for a 3-vector expression. More...
struct	MatrixVectorBinaryFunctor
	Base class for binary functors that take a matrix expression and a vector expression and return a vector-element scalar result (Math::MatrixVectorProduct, Math::VectorMatrixProduct). More...
struct	MatrixVectorProduct
	Functor returning element i of the matrix-vector product \( e_1 \cdot e_2 \). More...
struct	VectorMatrixProduct
	Functor returning element i of the vector-matrix product \( e_1 \cdot e_2 \). More...
struct	MatrixBinaryFunctor
	Base class for binary functors that take two matrix expressions and return a matrix-element scalar result (Math::MatrixProduct). More...
struct	MatrixProduct
	Functor returning entry (i, j) of the matrix product \( e_1 \cdot e_2 \). More...
struct	QuaternionBooleanBinaryFunctor
	Base class for binary functors that take two quaternion expressions and return a bool result (Math::QuaternionEquality). More...
struct	QuaternionEquality
	Functor checking component-wise equality of two quaternion expressions. More...
struct	Scalar3QuaternionBooleanTernaryFunctor
	Base class for ternary functors that take two quaternion expressions plus a tolerance scalar and return a bool result (Math::QuaternionToleranceEquality). More...
struct	QuaternionToleranceEquality
	Functor checking component-wise approximate equality of two quaternion expressions within an absolute tolerance. More...
struct	QuaternionScalarUnaryFunctor
	Base class for unary functors that take a quaternion expression and return a scalar result (Math::QuaternionElementSum). More...
struct	QuaternionElementSum
	Functor returning the sum of the four components of a quaternion expression. More...
struct	QuaternionScalarRealUnaryFunctor
	Base class for unary functors that take a quaternion expression and return a real-valued scalar (Math::QuaternionNorm, Math::QuaternionNorm2). More...
struct	QuaternionNorm
	Functor returning the (Euclidean) norm \( \|e\| \) of a quaternion expression. More...
struct	QuaternionNorm2
	Functor returning the squared norm \( \|e\|^2 \) of a quaternion expression. More...
struct	QuaternionUnaryFunctor
	Base class for per-component unary functors that take a quaternion expression and produce a quaternion result via applyC1 / applyC2 / applyC3 / applyC4 (Math::QuaternionUnreal, Math::QuaternionConjugate). More...
struct	QuaternionUnreal
	Per-component functor returning the unreal (pure-quaternion) part of a quaternion expression (zeros C1, keeps C2/C3/C4). More...
struct	QuaternionConjugate
	Per-component functor returning the quaternion conjugate (keeps C1, negates C2/C3/C4). More...
struct	Scalar1QuaternionBinaryFunctor
	Base class for per-component binary functors that take a scalar T (lhs) and a quaternion expression (Math::Scalar1QuaternionAddition, Math::Scalar1QuaternionSubtraction). More...
struct	Scalar1QuaternionAddition
	Per-component functor returning \( t + e \) (scalar t added to the real component of e). More...
struct	Scalar1QuaternionSubtraction
	Per-component functor returning \( t - e \) (scalar t with the quaternion e subtracted). More...
struct	Scalar2QuaternionBinaryFunctor
	Base class for per-component binary functors that take a quaternion expression (lhs) and a scalar T (Math::Scalar2QuaternionAddition, Math::Scalar2QuaternionSubtraction, Math::QuaternionInverse). More...
struct	Scalar2QuaternionAddition
	Per-component functor returning \( e + t \) (scalar t added to the real component of e). More...
struct	Scalar2QuaternionSubtraction
	Per-component functor returning \( e - t \) (scalar t subtracted from the real component of e). More...
struct	QuaternionInverse
	Per-component functor returning the multiplicative inverse \( \overline{e} / \|e\|^2 \) of a quaternion expression (n2 is the precomputed squared norm). More...
struct	QuaternionBinaryFunctor
	Base class for per-component binary functors that take two quaternion expressions and produce a quaternion result (Math::QuaternionProduct). More...
struct	QuaternionProduct
	Per-component functor returning the Hamilton product \( e_1 \cdot e_2 \) of two quaternion expressions. More...
struct	Scalar3QuaternionTernaryFunctor
	Base class for per-component ternary functors that take two quaternion expressions plus a scalar (Math::QuaternionDivision). More...
struct	QuaternionDivision
	Per-component functor returning the quaternion division \( e_1 \cdot e_2^{-1} \) (n2 is the precomputed squared norm of e_2). More...
struct	Scalar13QuaternionTernaryFunctor
	Base class for per-component ternary functors that take a scalar T1 (lhs), a quaternion expression, and a scalar T2 (Math::ScalarQuaternionDivision). More...
struct	ScalarQuaternionDivision
	Per-component functor returning the scalar/quaternion division \( t \cdot e^{-1} \) (n2 is the precomputed squared norm of e). More...
struct	QuaternionVectorBinaryFunctor
	Base class for binary functors that take a quaternion expression and a vector expression and return a vector-element scalar (Math::QuaternionVectorRotation). More...
struct	QuaternionVectorRotation
	Functor returning element i of the rotated 3-dimensional vector \( e_1 \cdot e_2 \cdot e_1^{-1} \) (quaternion rotation of \( e_2 \) by \( e_1 \)). More...
struct	GridBooleanBinaryFunctor
	Base class for binary functors that take two grid expressions and return a bool result (Math::GridEquality). More...
struct	GridEquality
	Functor checking cell-wise equality of two grid expressions. More...
struct	Scalar3GridBooleanTernaryFunctor
	Base class for ternary functors that take two grid expressions plus a tolerance scalar and return a bool result (Math::GridToleranceEquality). More...
struct	GridToleranceEquality
	Functor checking cell-wise approximate equality of two grid expressions within an absolute tolerance. More...
struct	GridScalarUnaryFunctor
	Base class for unary functors that take a grid expression and return a scalar result (Math::GridElementSum). More...
struct	GridElementSum
	Functor returning the sum of all cells of a grid expression. More...
class	GridReference
	Lightweight grid expression that proxies a reference to an underlying grid container. More...
class	Grid
	Dynamically-sized dense 3D grid ( \( d_1 \times d_2 \times d_3 \)) with configurable underlying storage. More...
class	ZeroGrid
	Constant grid expression whose cells are all zero. More...
class	ScalarGrid
	Constant grid expression in which every cell equals the same scalar value. More...
struct	GridTemporaryTraits< GridReference< G > >
	Math::GridTemporaryTraits specialization inheriting the temporary type of the underlying grid for a Math::GridReference view. More...
struct	GridTemporaryTraits< const GridReference< G > >
	Math::GridTemporaryTraits specialization inheriting the temporary type of the underlying grid for a const Math::GridReference view. More...
class	GridUnary
	Expression-template node applying a unary functor F element-wise to a grid expression E. More...
struct	GridUnaryTraits
	Traits selecting the expression-template node and its result type for the Math::GridUnary instantiation <E, F>. More...
class	GridBinary1
	Expression-template node combining two grid expressions E1 and E2 element-wise via the binary functor F. More...
struct	GridBinary1Traits
	Traits selecting the expression-template node and its result type for the Math::GridBinary1 instantiation Binary <E1, E2, F>. More...
class	Scalar1GridBinary
	Expression-template node combining a scalar E1 (lhs) and a grid expression E2 (rhs) element-wise via the binary functor F. More...
struct	Scalar1GridBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar1GridBinary instantiation <E1, E2, F>. More...
class	Scalar2GridBinary
	Expression-template node combining a grid expression E1 (lhs) and a scalar E2 (rhs) element-wise via the binary functor F. More...
struct	Scalar2GridBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar2GridBinary instantiation <E1, E2, F>. More...
class	KabschAlgorithm
	Implementation of the Kabsch algorithm [KABA]. More...
class	InitListMatrix
	Lightweight matrix container that wraps a nested std::initializer_list of T values. More...
class	SparseMatrix
	Sparse matrix that stores only non-default entries keyed by a packed (row, column) identifier. More...
class	BoundedVector
	Variable-size vector with a fixed upper capacity N stored in a stack-allocated array. More...
class	BoundedMatrix
	Variable-size matrix with fixed upper capacities M \( \times \) N stored in a stack-allocated array. More...
class	CMatrix
	Fixed-size dense matrix of dimensions M \( \times \) N backed by a 2D C-array (no dynamic allocation). More...
class	ZeroMatrix
	Constant matrix expression whose entries are all zero. More...
class	ScalarMatrix
	Constant matrix expression in which every entry equals the same scalar value. More...
class	IdentityMatrix
	Constant identity-matrix expression ( \( 1 \) on the diagonal, \( 0 \) elsewhere). More...
struct	VectorTemporaryTraits< MatrixReference< M > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying matrix for a Math::MatrixReference view. More...
struct	VectorTemporaryTraits< const MatrixReference< M > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying matrix for a const Math::MatrixReference view. More...
struct	MatrixTemporaryTraits< MatrixReference< M > >
	Math::MatrixTemporaryTraits specialization inheriting the temporary type of the underlying matrix for a Math::MatrixReference view. More...
struct	MatrixTemporaryTraits< const MatrixReference< M > >
	Math::MatrixTemporaryTraits specialization inheriting the temporary type of the underlying matrix for a const Math::MatrixReference view. More...
class	Range
	Half-open index range \( [start, stop) \) used for slicing vector and matrix expressions. More...
struct	Lower
	Tag selecting the lower-triangular view (entries strictly above the diagonal read as zero) for Math::TriangularAdapter. More...
struct	UnitLower
	Tag selecting the unit-lower-triangular view (zero above the diagonal, one on the diagonal) for Math::TriangularAdapter. More...
struct	Upper
	Tag selecting the upper-triangular view (entries strictly below the diagonal read as zero) for Math::TriangularAdapter. More...
struct	UnitUpper
	Tag selecting the unit-upper-triangular view (zero below the diagonal, one on the diagonal) for Math::TriangularAdapter. More...
class	TriangularAdapter
	Matrix expression that exposes only the triangular part of an underlying matrix M selected by the policy Tri (Math::Lower, Math::UnitLower, Math::Upper or Math::UnitUpper). More...
struct	VectorTemporaryTraits< TriangularAdapter< M, Tri > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a Math::TriangularAdapter view. More...
struct	VectorTemporaryTraits< const TriangularAdapter< M, Tri > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a const Math::TriangularAdapter view. More...
struct	MatrixTemporaryTraits< TriangularAdapter< M, Tri > >
	Math::MatrixTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a Math::TriangularAdapter view. More...
struct	MatrixTemporaryTraits< const TriangularAdapter< M, Tri > >
	Math::MatrixTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a const Math::TriangularAdapter view. More...
class	MatrixUnary
	Expression-template node applying a unary functor F element-wise to a matrix expression E. More...
struct	MatrixUnaryTraits
	Traits selecting the expression-template node and its result type for the Math::MatrixUnary instantiation <E, F>. More...
class	VectorMatrixUnary
	Expression-template node interpreting a vector expression E as a column matrix via the per-element functor F. More...
struct	VectorMatrixUnaryTraits
	Traits selecting the expression-template node and its result type for the Math::VectorMatrixUnary instantiation <E, F>. More...
class	MatrixBinary1
	Expression-template node combining two matrix expressions E1 and E2 element-wise via the binary functor F. More...
struct	MatrixBinary1Traits
	Traits selecting the expression-template node and its result type for the Math::MatrixBinary1 instantiation <E1, E2, F>. More...
class	MatrixBinary2
	Expression-template node combining two matrix expressions E1 and E2 via a binary functor F that is invoked with both expressions plus the (i, j) cell indices. More...
struct	MatrixBinary2Traits
	Traits selecting the expression-template node and its result type for the Math::MatrixBinary2 instantiation <E1, E2, F>. More...
class	VectorMatrixBinary
	Expression-template node interpreting a binary combination of two vector expressions as a matrix (e.g. outer product), via the per-cell functor F invoked with both expressions and the cell coordinates. More...
struct	VectorMatrixBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::VectorMatrixBinary instantiation <E1, E2, F>. More...
class	Matrix1VectorBinary
	Expression-template node interpreting a binary combination of a matrix expression E1 and a vector expression E2 as a vector (e.g. matrix-vector product), via the per-element functor F invoked with both expressions and the index. More...
struct	Matrix1VectorBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Matrix1VectorBinary instantiation <E1, E2, F>. More...
class	Matrix2VectorBinary
	Expression-template node interpreting a binary combination of a vector expression E1 and a matrix expression E2 as a vector (e.g. vector-matrix product), via the per-element functor F invoked with both expressions and the index. More...
struct	Matrix2VectorBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Matrix2VectorBinary instantiation <E1, E2, F>. More...
class	Scalar1MatrixBinary
	Expression-template node combining a scalar E1 (lhs) and a matrix expression E2 (rhs) element-wise via the binary functor F. More...
struct	Scalar1MatrixBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar1MatrixBinary instantiation <E1, E2, F>. More...
class	Scalar2MatrixBinary
	Expression-template node combining a matrix expression E1 (lhs) and a scalar E2 (rhs) element-wise via the binary functor F. More...
struct	Scalar2MatrixBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar2MatrixBinary instantiation <E1, E2, F>. More...
class	MatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
struct	VectorTemporaryTraits< MatrixTranspose< M > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a Math::MatrixTranspose view. More...
struct	VectorTemporaryTraits< const MatrixTranspose< M > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a const Math::MatrixTranspose view. More...
struct	MatrixTemporaryTraits< MatrixTranspose< M > >
	Math::MatrixTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a Math::MatrixTranspose view. More...
struct	MatrixTemporaryTraits< const MatrixTranspose< M > >
	Math::MatrixTemporaryTraits specialization inheriting the temporary type of the wrapped matrix for a const Math::MatrixTranspose view. More...
class	MatrixRow
	Vector-expression proxy that views a single row of an underlying matrix. More...
class	MatrixColumn
	Vector-expression proxy that views a single column of an underlying matrix. More...
class	MatrixRange
	Matrix-expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	MatrixSlice
	Matrix-expression proxy that views a strided rectangular slice of an underlying matrix. More...
struct	VectorTemporaryTraits< MatrixRow< M > >
	Vector-temporary trait specialization for Math::MatrixRow — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< const MatrixRow< M > >
	Vector-temporary trait specialization for const Math::MatrixRow — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< MatrixRow< M > >
	Matrix-temporary trait specialization for Math::MatrixRow — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< const MatrixRow< M > >
	Matrix-temporary trait specialization for const Math::MatrixRow — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< MatrixColumn< M > >
	Vector-temporary trait specialization for Math::MatrixColumn — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< const MatrixColumn< M > >
	Vector-temporary trait specialization for const Math::MatrixColumn — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< MatrixColumn< M > >
	Matrix-temporary trait specialization for Math::MatrixColumn — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< const MatrixColumn< M > >
	Matrix-temporary trait specialization for const Math::MatrixColumn — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< MatrixRange< M > >
	Vector-temporary trait specialization for Math::MatrixRange — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< const MatrixRange< M > >
	Vector-temporary trait specialization for const Math::MatrixRange — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< MatrixRange< M > >
	Matrix-temporary trait specialization for Math::MatrixRange — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< const MatrixRange< M > >
	Matrix-temporary trait specialization for const Math::MatrixRange — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< MatrixSlice< M > >
	Vector-temporary trait specialization for Math::MatrixSlice — inherits the temporary type from the wrapped matrix. More...
struct	VectorTemporaryTraits< const MatrixSlice< M > >
	Vector-temporary trait specialization for const Math::MatrixSlice — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< MatrixSlice< M > >
	Matrix-temporary trait specialization for Math::MatrixSlice — inherits the temporary type from the wrapped matrix. More...
struct	MatrixTemporaryTraits< const MatrixSlice< M > >
	Matrix-temporary trait specialization for const Math::MatrixSlice — inherits the temporary type from the wrapped matrix. More...
struct	MinimizerVariableArrayTraits
	Traits template that adapts arbitrary variable-array types to the linear-algebra operations required by minimizer implementations (dot, norm2, axpy, clear, assign, multiply, sub). More...
struct	MinimizerVariableArrayTraits< VectorArray< V > >
	Math::MinimizerVariableArrayTraits specialization for Math::VectorArray storage (a sequence of fixed-size vectors). More...
struct	MinimizerVariableArrayTraits< std::vector< V > >
	Math::MinimizerVariableArrayTraits specialization for std::vector storage of fixed-size vectors. More...
class	MLRModel
	Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...
class	QuaternionReference
	Lightweight quaternion expression that proxies a reference to an underlying quaternion container. More...
class	Quaternion
	General 4-component quaternion \( q = c_1 + c_2 i + c_3 j + c_4 k \). More...
class	RealQuaternion
	Pure-real quaternion \( q = c_1 + 0i + 0j + 0k \) that stores only the real component. More...
struct	QuaternionTemporaryTraits< const QuaternionReference< Q > >
	Math::QuaternionTemporaryTraits specialization inheriting the temporary type of the underlying quaternion for a const Math::QuaternionReference view. More...
struct	QuaternionTemporaryTraits< QuaternionReference< Q > >
	Math::QuaternionTemporaryTraits specialization inheriting the temporary type of the underlying quaternion for a Math::QuaternionReference view. More...
class	QuaternionVectorAdapter
	View adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	CVector
	Fixed-size vector of dimension N backed by a C-array (no dynamic allocation). More...
struct	VectorTemporaryTraits< QuaternionVectorAdapter< Q > >
	Math::VectorTemporaryTraits specialization selecting Math::CVector as the temporary type for a Math::QuaternionVectorAdapter view. More...
struct	VectorTemporaryTraits< const QuaternionVectorAdapter< Q > >
	Math::VectorTemporaryTraits specialization selecting Math::CVector as the temporary type for a const Math::QuaternionVectorAdapter view. More...
class	QuaternionUnary1
	Expression-template node applying a unary functor F that returns a quaternion result to a quaternion expression E. More...
struct	QuaternionUnary1Traits
	Traits selecting the expression-template node and its result type for the Math::QuaternionUnary1 instantiation <E, F>. More...
class	QuaternionUnary2
	Expression-template node applying a per-component functor F to a quaternion expression E, where F exposes four separate apply methods (applyC1 / applyC2 / applyC3 / applyC4) operating on the whole source expression. More...
struct	QuaternionUnary2Traits
	Traits selecting the expression-template node and its result type for the Math::QuaternionUnary2 instantiation <E, F>. More...
class	QuaternionBinary1
	Expression-template node combining two quaternion expressions E1 and E2 component-wise via the binary functor F. More...
struct	QuaternionBinary1Traits
	Traits selecting the expression-template node and its result type for the Math::QuaternionBinary1 instantiation <E1, E2, F>. More...
class	QuaternionBinary2
	Expression-template node combining two quaternion expressions E1 and E2 via the per-component functor F (which exposes four separate applyC1 / applyC2 / applyC3 / applyC4 methods operating on the whole source expressions). More...
struct	QuaternionBinary2Traits
	Traits selecting the expression-template node and its result type for the Math::QuaternionBinary2 instantiation <E1, E2, F>. More...
class	Scalar1QuaternionBinary1
	Expression-template node combining a scalar E1 (lhs) and a quaternion expression E2 (rhs) component-wise via the binary functor F. More...
struct	Scalar1QuaternionBinary1Traits
	Traits selecting the expression-template node and its result type for the Math::Scalar1QuaternionBinary1 instantiation <E1, E2, F>. More...
class	Scalar1QuaternionBinary2
	Expression-template node combining a scalar E1 (lhs) and a quaternion expression E2 (rhs) via the per-component functor F (which exposes applyC1 / applyC2 / applyC3 / applyC4 methods). More...
struct	Scalar1QuaternionBinary2Traits
	Traits selecting the expression-template node and its result type for the Math::Scalar1QuaternionBinary2 instantiation <E1, E2, F>. More...
class	Scalar2QuaternionBinary1
	Expression-template node combining a quaternion expression E1 (lhs) and a scalar E2 (rhs) component-wise via the binary functor F. More...
struct	Scalar2QuaternionBinary1Traits
	Traits selecting the expression-template node and its result type for the Math::Scalar2QuaternionBinary1 instantiation <E1, E2, F>. More...
class	Scalar2QuaternionBinary2
	Expression-template node combining a quaternion expression E1 (lhs) and a scalar E2 (rhs) via the per-component functor F (which exposes applyC1 / applyC2 / applyC3 / applyC4 methods). More...
struct	Scalar2QuaternionBinary2Traits
	Traits selecting the expression-template node and its result type for the Math::Scalar2QuaternionBinary2 instantiation <E1, E2, F>. More...
class	Scalar3QuaternionTernary
	Expression-template node combining two quaternion expressions E1 (lhs) and E2 (middle) with a scalar E3 (rhs) via the per-component ternary functor F. More...
struct	Scalar3QuaternionTernaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar3QuaternionTernary instantiation <E1, E2, E3, F>. More...
class	Scalar13QuaternionTernary
	Expression-template node combining a scalar E1 (lhs), a quaternion expression E2 (middle), and a scalar E3 (rhs) via the per-component ternary functor F. More...
struct	Scalar13QuaternionTernaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar13QuaternionTernary instantiation <E1, E2, E3, F>. More...
struct	GridCoordinatesMatrixTransformTraits
	Reusable transformation traits used by Math::RegularSpatialGrid when the coordinate transform is a 4x4 matrix. More...
struct	GridCoordinatesTransformTraits
	Primary traits template for grid-coordinate transformations of type T (left unspecialized; specialize for new transform types). More...
struct	GridCoordinatesTransformTraits< CMatrix< T, 4, 4 > >
	Math::GridCoordinatesTransformTraits specialization for the fixed-size Math::CMatrix 4x4 transformation type. More...
struct	GridCoordinatesTransformTraits< BoundedMatrix< T, 4, 4 > >
	Math::GridCoordinatesTransformTraits specialization for the bounded Math::BoundedMatrix 4x4 transformation type. More...
class	RegularSpatialGrid
	3D grid data structure combining a Math::Grid data store with a coordinate-system transformation that maps grid-cell indices to 3D world positions. More...
class	Slice
	Index slice ( \( start, stride, size \)) used for strided slicing of vector and matrix expressions. More...
class	SparseContainerElement
	Proxy that exposes a single (key, value) entry of a sparse container as a writable reference. More...
struct	TypeTraits< SparseContainerElement< C > >
	Math::TypeTraits specialization that delegates to the underlying value type of a Math::SparseContainerElement. More...
struct	ScalarAbsImpl
	Helper class template for retrieving the absolute value of scalar arithmetic types. More...
struct	ScalarAbsImpl< false >
	Specialization of Math::ScalarAbsImpl for unsigned types. More...
struct	ScalarTraits
	Common operations and type aliases for scalar arithmetic types. More...
struct	TypeTraits
	Primary traits template for scalar arithmetic value types. More...
struct	ComplexTraits
	Common operations and type aliases for complex arithmetic types. More...
struct	TypeTraits< std::complex< T > >
	Math::TypeTraits specialization for complex arithmetic value types. More...
struct	VectorTemporaryTraits
	Selects a concrete temporary vector type compatible with the vector expression V. More...
struct	MatrixTemporaryTraits
	Selects a concrete temporary matrix type compatible with the matrix expression M. More...
struct	QuaternionTemporaryTraits
	Selects a concrete temporary quaternion type compatible with the quaternion expression Q. More...
struct	GridTemporaryTraits
	Selects a concrete temporary grid type compatible with the grid expression G. More...
struct	IsScalar
	Type trait identifying T as a scalar arithmetic type (true for built-in arithmetic types). More...
struct	IsScalar< std::complex< T > >
	Math::IsScalar specialization that treats std::complex<T> as scalar when T is arithmetic. More...
class	VectorReference
	Lightweight vector expression that proxies a reference to an underlying vector container. More...
class	InitListVector
	Lightweight vector container that wraps a std::initializer_list for construction-style initialization. More...
class	SparseVector
	Sparse vector that stores only non-default entries in an associative key-to-value container. More...
class	ZeroVector
	Constant vector expression whose elements are all zero. More...
class	UnitVector
	Constant vector expression \( e_i \) that contains 1 at a single specified index and 0 elsewhere. More...
class	ScalarVector
	Constant vector expression in which every element equals the same scalar value. More...
struct	VectorTemporaryTraits< const VectorReference< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying vector for a const Math::VectorReference view. More...
struct	VectorTemporaryTraits< VectorReference< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying vector for a Math::VectorReference view. More...
class	HomogenousCoordsAdapter
	Vector expression that exposes a vector V as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	VectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
struct	QuaternionTemporaryTraits< VectorQuaternionAdapter< V > >
	Math::QuaternionTemporaryTraits specialization selecting Math::Quaternion as the temporary type for a Math::VectorQuaternionAdapter view. More...
struct	QuaternionTemporaryTraits< const VectorQuaternionAdapter< V > >
	Math::QuaternionTemporaryTraits specialization selecting Math::Quaternion as the temporary type for a const Math::VectorQuaternionAdapter view. More...
struct	VectorTemporaryTraits< HomogenousCoordsAdapter< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the wrapped vector for a Math::HomogenousCoordsAdapter view. More...
struct	VectorTemporaryTraits< const HomogenousCoordsAdapter< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the wrapped vector for a const Math::HomogenousCoordsAdapter view. More...
class	VectorArray
	Array data type for the ordered storage of vector objects. More...
class	VectorArrayAlignmentCalculator
	Convenience wrapper around Math::KabschAlgorithm that operates directly on Math::VectorArray inputs. More...
class	VectorUnary
	Expression-template node applying a unary functor F element-wise to a vector expression E. More...
struct	VectorUnaryTraits
	Traits selecting the expression-template node and its result type for the Math::VectorUnary instantiation <E, F>. More...
class	VectorBinary1
	Expression-template node combining two vector expressions E1 and E2 element-wise via the binary functor F. More...
struct	VectorBinary1Traits
	Traits selecting the expression-template node and its result type for the Math::VectorBinary1 instantiation <E1, E2, F>. More...
class	VectorBinary2
	Expression-template node combining two vector expressions E1 and E2 via a binary functor F invoked with both expressions plus the element index i. More...
struct	VectorBinary2Traits
	Traits selecting the expression-template node and its result type for the Math::VectorBinary2 instantiation <E1, E2, F>. More...
class	Scalar1VectorBinary
	Expression-template node combining a scalar E1 (lhs) and a vector expression E2 (rhs) element-wise via the binary functor F. More...
struct	Scalar1VectorBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar1VectorBinary instantiation <E1, E2, F>. More...
class	Scalar2VectorBinary
	Expression-template node combining a vector expression E1 (lhs) and a scalar E2 (rhs) element-wise via the binary functor F. More...
struct	Scalar2VectorBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::Scalar2VectorBinary instantiation <E1, E2, F>. More...
class	QuaternionVectorBinary
	Expression-template node combining a quaternion expression E1 and a vector expression E2 into a vector expression via the per-element functor F (used e.g. for quaternion-vector rotation). More...
struct	QuaternionVectorBinaryTraits
	Traits selecting the expression-template node and its result type for the Math::QuaternionVectorBinary instantiation <E1, E2, F>. More...
class	VectorElementAccessor
	Access functor used by Math::VectorIteratorTraits to read mutable vector elements via Util::IndexedElementIterator. More...
class	VectorElementAccessor< const E >
	Specialization of Math::VectorElementAccessor for const vector references (read-only iteration). More...
struct	VectorIteratorTraits
	Traits selecting the element accessor and Util::IndexedElementIterator specialization for mutable iteration over E. More...
struct	VectorIteratorTraits< const E >
	Specialization of Math::VectorIteratorTraits for read-only iteration over E. More...
class	VectorRange
	Vector-expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	VectorSlice
	Vector-expression proxy that views a strided slice of an underlying vector. More...
struct	VectorTemporaryTraits< VectorRange< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying vector for a Math::VectorRange view. More...
struct	VectorTemporaryTraits< const VectorRange< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying vector for a const Math::VectorRange view. More...
struct	VectorTemporaryTraits< VectorSlice< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying vector for a Math::VectorSlice view. More...
struct	VectorTemporaryTraits< const VectorSlice< V > >
	Math::VectorTemporaryTraits specialization inheriting the temporary type of the underlying vector for a const Math::VectorSlice view. More...

Typedefs
typedef ScalingMatrix< float >	FScalingMatrix
typedef ScalingMatrix< double >	DScalingMatrix
typedef ScalingMatrix< long >	LScalingMatrix
typedef ScalingMatrix< unsigned long >	ULScalingMatrix
typedef RotationMatrix< float >	FRotationMatrix
typedef RotationMatrix< double >	DRotationMatrix
typedef RotationMatrix< long >	LRotationMatrix
typedef RotationMatrix< unsigned long >	ULRotationMatrix
typedef TranslationMatrix< float >	FTranslationMatrix
typedef TranslationMatrix< double >	DTranslationMatrix
typedef TranslationMatrix< long >	LTranslationMatrix
typedef TranslationMatrix< unsigned long >	ULTranslationMatrix
typedef ZeroGrid< float >	FZeroGrid
	Immutable grid where all elements have the value zero of type float. More...
typedef ZeroGrid< double >	DZeroGrid
	Immutable grid where all elements have the value zero of type double. More...
typedef ScalarGrid< float >	FScalarGrid
	Immutable grid where all elements have the same value of type float. More...
typedef ScalarGrid< double >	DScalarGrid
	Immutable grid where all elements have the same value of type double. More...
typedef Grid< float >	FGrid
	Unbounded dense grid storing floating point values of type float. More...
typedef Grid< double >	DGrid
	Unbounded dense grid storing floating point values of type double. More...
typedef ZeroMatrix< float >	FZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type float. More...
typedef ZeroMatrix< double >	DZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type double. More...
typedef ZeroMatrix< long >	LZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type long. More...
typedef ZeroMatrix< unsigned long >	ULZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type unsigned long. More...
typedef ScalarMatrix< float >	FScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type float. More...
typedef ScalarMatrix< double >	DScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type double. More...
typedef ScalarMatrix< long >	LScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type long. More...
typedef ScalarMatrix< unsigned long >	ULScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type unsigned long. More...
typedef IdentityMatrix< float >	FIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type float. More...
typedef IdentityMatrix< double >	DIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type double. More...
typedef IdentityMatrix< long >	LIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type long. More...
typedef IdentityMatrix< unsigned long >	ULIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type unsigned long. More...
typedef Matrix< float >	FMatrix
	Unbounded dense matrix holding floating point values of type float.. More...
typedef Matrix< double >	DMatrix
	Unbounded dense matrix holding floating point values of type double.. More...
typedef Matrix< long >	LMatrix
	Unbounded dense matrix holding signed integers of type long. More...
typedef Matrix< unsigned long >	ULMatrix
	Unbounded dense matrix holding unsigned integers of type unsigned long. More...
typedef CMatrix< float, 2, 2 >	Matrix2F
	Bounded 2x2 matrix holding floating point values of type float. More...
typedef CMatrix< float, 3, 3 >	Matrix3F
	Bounded 3x3 matrix holding floating point values of type float. More...
typedef CMatrix< float, 4, 4 >	Matrix4F
	Bounded 4x4 matrix holding floating point values of type float. More...
typedef CMatrix< double, 2, 2 >	Matrix2D
	Bounded 2x2 matrix holding floating point values of type double. More...
typedef CMatrix< double, 3, 3 >	Matrix3D
	Bounded 3x3 matrix holding floating point values of type double. More...
typedef CMatrix< double, 4, 4 >	Matrix4D
	Bounded 4x4 matrix holding floating point values of type double. More...
typedef CMatrix< long, 2, 2 >	Matrix2L
	Bounded 2x2 matrix holding signed integers of type long. More...
typedef CMatrix< long, 3, 3 >	Matrix3L
	Bounded 3x3 matrix holding signed integers of type long. More...
typedef CMatrix< long, 4, 4 >	Matrix4L
	Bounded 4x4 matrix holding signed integers of type long. More...
typedef CMatrix< unsigned long, 2, 2 >	Matrix2UL
	Bounded 2x2 matrix holding unsigned integers of type unsigned long. More...
typedef CMatrix< unsigned long, 3, 3 >	Matrix3UL
	Bounded 3x3 matrix holding unsigned integers of type unsigned long. More...
typedef CMatrix< unsigned long, 4, 4 >	Matrix4UL
	Bounded 4x4 matrix holding unsigned integers of type unsigned long. More...
typedef SparseMatrix< float >	SparseFMatrix
	Unbounded sparse matrix holding floating point values of type float.. More...
typedef SparseMatrix< double >	SparseDMatrix
	Unbounded sparse matrix holding floating point values of type double.. More...
typedef SparseMatrix< long >	SparseLMatrix
	Unbounded sparse matrix holding signed integers of type long. More...
typedef SparseMatrix< unsigned long >	SparseULMatrix
	Unbounded sparse matrix holding unsigned integers of type unsigned long. More...
typedef Quaternion< float >	FQuaternion
	General 4-component quaternion with component values of type float. More...
typedef Quaternion< double >	DQuaternion
	General 4-component quaternion with component values of type double. More...
typedef Quaternion< long >	LQuaternion
	General 4-component quaternion with component values of type long. More...
typedef Quaternion< unsigned long >	ULQuaternion
	General 4-component quaternion with component values of type unsigned long. More...
typedef RealQuaternion< float >	FRealQuaternion
	A memory-efficient pure-real quaternion with component values of type float. More...
typedef RealQuaternion< double >	DRealQuaternion
	A memory-efficient pure-real quaternion with component values of type double. More...
typedef RealQuaternion< long >	LRealQuaternion
	A memory-efficient pure-real quaternion with component values of type long. More...
typedef RealQuaternion< unsigned long >	ULRealQuaternion
	A memory-efficient pure-real quaternion with component values of type unsigned long. More...
typedef RegularSpatialGrid< float >	FRegularSpatialGrid
	Unbounded dense regular grid storing floating point values of type float. More...
typedef RegularSpatialGrid< double >	DRegularSpatialGrid
	Unbounded dense regular grid storing floating point values of type double. More...
typedef ScalarVector< float >	FScalarVector
	Memory-efficient immutable vector where all elements have the same value of type float. More...
typedef ScalarVector< double >	DScalarVector
	Memory-efficient immutable vector where all elements have the same value of type double. More...
typedef ScalarVector< long >	LScalarVector
	Memory-efficient immutable vector where all elements have the same value of type long. More...
typedef ScalarVector< unsigned long >	ULScalarVector
	Memory-efficient immutable vector where all elements have the same value of type unsigned long. More...
typedef ZeroVector< float >	FZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type float. More...
typedef ZeroVector< double >	DZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type double. More...
typedef ZeroVector< long >	LZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type long. More...
typedef ZeroVector< unsigned long >	ULZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type unsigned long. More...
typedef UnitVector< float >	FUnitVector
	Memory-efficient immutable unit vector with element values of type float. More...
typedef UnitVector< double >	DUnitVector
	Memory-efficient immutable unit vector with element values of type double. More...
typedef UnitVector< long >	LUnitVector
	Memory-efficient immutable unit vector with element values of type long. More...
typedef UnitVector< unsigned long >	ULUnitVector
	Memory-efficient immutable unit vector with element values of type unsigned long. More...
typedef CVector< float, 2 >	Vector2F
	Bounded 2 element vector holding floating point values of type float. More...
typedef CVector< float, 3 >	Vector3F
	Bounded 3 element vector holding floating point values of type float. More...
typedef CVector< float, 4 >	Vector4F
	Bounded 4 element vector holding floating point values of type float. More...
typedef CVector< double, 2 >	Vector2D
	Bounded 2 element vector holding floating point values of type double. More...
typedef CVector< double, 3 >	Vector3D
	Bounded 3 element vector holding floating point values of type double. More...
typedef CVector< double, 4 >	Vector4D
	Bounded 4 element vector holding floating point values of type double. More...
typedef CVector< double, 7 >	Vector7D
	Bounded 7 element vector holding floating point values of type double. More...
typedef CVector< long, 2 >	Vector2L
	Bounded 2 element vector holding signed integers of type long. More...
typedef CVector< long, 3 >	Vector3L
	Bounded 3 element vector holding signed integers of type long. More...
typedef CVector< long, 4 >	Vector4L
	Bounded 4 element vector holding signed integers of type long. More...
typedef CVector< unsigned long, 2 >	Vector2UL
	Bounded 2 element vector holding unsigned integers of type unsigned long. More...
typedef CVector< unsigned long, 3 >	Vector3UL
	Bounded 3 element vector holding unsigned integers of type unsigned long. More...
typedef CVector< unsigned long, 4 >	Vector4UL
	Bounded 4 element vector holding unsigned integers of type unsigned long. More...
typedef Vector< float >	FVector
	Unbounded dense vector holding floating point values of type float. More...
typedef Vector< double >	DVector
	Unbounded dense vector holding floating point values of type double. More...
typedef Vector< long >	LVector
	Unbounded dense vector holding signed integers of type long. More...
typedef Vector< unsigned long >	ULVector
	Unbounded dense vector holding unsigned integers of type unsigned long. More...
typedef SparseVector< float >	SparseFVector
	Unbounded sparse vector holding floating point values of type float. More...
typedef SparseVector< double >	SparseDVector
	Unbounded sparse vector holding floating point values of type double. More...
typedef SparseVector< long >	SparseLVector
	Unbounded sparse vector holding signed integers of type long. More...
typedef SparseVector< unsigned long >	SparseULVector
	Unbounded sparse vector holding unsigned integers of type unsigned long. More...
typedef VectorArray< Vector2F >	Vector2FArray
	Array storing vectors of type Math::Vector2F. More...
typedef VectorArray< Vector3F >	Vector3FArray
	Array storing vectors of type Math::Vector3F. More...
typedef VectorArray< Vector2D >	Vector2DArray
	Array storing vectors of type Math::Vector2D. More...
typedef VectorArray< Vector3D >	Vector3DArray
	Array storing vectors of type Math::Vector3D. More...
typedef VectorArray< Vector2L >	Vector2LArray
	Array storing vectors of type Math::Vector2L. More...
typedef VectorArray< Vector3L >	Vector3LArray
	Array storing vectors of type Math::Vector3L. More...
typedef VectorArray< Vector2UL >	Vector2ULArray
	Array storing vectors of type Math::Vector2UL. More...
typedef VectorArray< Vector3UL >	Vector3ULArray
	Array storing vectors of type Math::Vector3UL. More...

Functions
template<typename C >
DirectAssignmentProxy< const C >	direct (const C &lvalue)
	Convenience factory creating a Math::DirectAssignmentProxy for a const lvalue. More...
template<typename C >
DirectAssignmentProxy< C >	direct (C &lvalue)
	Convenience factory creating a Math::DirectAssignmentProxy for a mutable lvalue. More...
template<template< typename T1, typename T2 > class F, typename G , typename E >
void	gridAssignGrid (G &g, const GridExpression< E > &e)
	Applies the element-wise functor F to every (grid cell, source cell) pair, i.e. F::apply(g(i,j,k), e()(i,j,k)). More...
template<template< typename T1, typename T2 > class F, typename G , typename T >
void	gridAssignScalar (G &g, const T &t)
	Applies the element-wise functor F to every (grid cell, scalar) pair, i.e. F::apply(g(i,j,k), t). More...
template<typename G , typename E >
void	gridSwap (G &g, GridExpression< E > &e)
	Swaps the cells of two equally sized grid expressions cell by cell. More...
template<typename E >
GridUnaryTraits< E, ScalarNegation< typename E::ValueType > >::ResultType	operator- (const GridExpression< E > &e)
	Returns the element-wise negation of the grid expression e. More...
template<typename E >
const E &	operator+ (const GridExpression< E > &e)
	Returns the grid expression e unchanged (unary +). More...
template<typename E1 , typename E2 >
GridBinary1Traits< E1, E2, ScalarAddition< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator+ (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2)
	Returns the element-wise sum of the grid expressions e1 and e2. More...
template<typename E1 , typename E2 >
GridBinary1Traits< E1, E2, ScalarSubtraction< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator- (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2)
	Returns the element-wise difference of the grid expressions e1 and e2. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2GridBinaryTraits< E, T, ScalarMultiplication< typename E::ValueType, T > >::ResultType >::type	operator* (const GridExpression< E > &e, const T &t)
	Returns the element-wise product of the grid expression e and the scalar t. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar1GridBinaryTraits< T, E, ScalarMultiplication< T, typename E::ValueType > >::ResultType >::type	operator* (const T &t, const GridExpression< E > &e)
	Returns the element-wise product of the scalar t and the grid expression e. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2GridBinaryTraits< E, T, ScalarDivision< typename E::ValueType, T > >::ResultType >::type	operator/ (const GridExpression< E > &e, const T &t)
	Returns the element-wise quotient of the grid expression e by the scalar t. More...
template<typename E1 , typename E2 >
GridEquality< E1, E2 >::ResultType	operator== (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2)
	Tells whether the grid expressions e1 and e2 are element-wise equal. More...
template<typename E1 , typename E2 >
GridEquality< E1, E2 >::ResultType	operator!= (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2)
	Tells whether the grid expressions e1 and e2 differ in at least one element. More...
template<typename E1 , typename E2 , typename T >
std::enable_if< std::is_arithmetic< T >::value, typename GridToleranceEquality< E1, E2, T >::ResultType >::type	equals (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2, const T &eps)
	Tells whether the grid expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
template<typename E >
GridUnaryTraits< E, ScalarConjugation< typename E::ValueType > >::ResultType	conj (const GridExpression< E > &e)
	Returns the element-wise complex conjugate of the grid expression e (identity for real-valued grids). More...
template<typename E >
GridUnaryTraits< E, ScalarConjugation< typename E::ValueType > >::ResultType	herm (const GridExpression< E > &e)
	Returns the Hermitian conjugate of the grid expression e (alias of conj() for grids). More...
template<typename E >
GridUnaryTraits< E, ScalarReal< typename E::ValueType > >::ResultType	real (const GridExpression< E > &e)
	Returns the element-wise real part of the grid expression e. More...
template<typename E >
GridUnaryTraits< E, ScalarImaginary< typename E::ValueType > >::ResultType	imag (const GridExpression< E > &e)
	Returns the element-wise imaginary part of the grid expression e. More...
template<typename E1 , typename E2 >
GridBinary1Traits< E1, E2, ScalarDivision< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemDiv (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2)
	Returns the element-wise quotient of the grid expressions e1 and e2. More...
template<typename E1 , typename E2 >
GridBinary1Traits< E1, E2, ScalarMultiplication< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemProd (const GridExpression< E1 > &e1, const GridExpression< E2 > &e2)
	Returns the element-wise product of the grid expressions e1 and e2 (Hadamard product). More...
template<typename E >
GridElementSum< E >::ResultType	sum (const GridExpression< E > &e)
	Returns the sum of all elements of the grid expression e. More...
template<typename C , typename T , typename E >
std::basic_ostream< C, T > &	operator<< (std::basic_ostream< C, T > &os, const VectorExpression< E > &e)
	Writes a textual representation of the vector expression e to os. More...
template<typename C , typename T , typename E >
std::basic_ostream< C, T > &	operator<< (std::basic_ostream< C, T > &os, const MatrixExpression< E > &e)
	Writes a textual representation of the matrix expression e to os: More...
template<typename C , typename T , typename E >
std::basic_ostream< C, T > &	operator<< (std::basic_ostream< C, T > &os, const QuaternionExpression< E > &e)
	Writes a textual representation of the quaternion expression e to os. More...
template<typename C , typename T , typename E >
std::basic_ostream< C, T > &	operator<< (std::basic_ostream< C, T > &os, const GridExpression< E > &e)
	Writes a textual representation of the grid expression e to os. More...
template<typename M1 , typename V , typename M2 >
bool	jacobiDiagonalize (MatrixExpression< M1 > &a, VectorExpression< V > &d, MatrixExpression< M2 > &v, std::size_t max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...
template<typename E1 , typename E2 >
bool	solveLower (const MatrixExpression< E1 > &e1, VectorExpression< E2 > &e2)
	Solves \( L\,x = b \) in place by forward-substitution, where e1 is a lower-triangular matrix. More...
template<typename E1 , typename E2 >
bool	solveUnitLower (const MatrixExpression< E1 > &e1, VectorExpression< E2 > &e2)
	Solves \( L\,x = b \) in place by forward-substitution, where e1 is a unit lower-triangular matrix (1 on the diagonal). More...
template<typename E1 , typename E2 >
bool	solveLower (const MatrixExpression< E1 > &e1, MatrixExpression< E2 > &e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
template<typename E1 , typename E2 >
bool	solveUnitLower (const MatrixExpression< E1 > &e1, MatrixExpression< E2 > &e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
template<typename E1 , typename E2 >
bool	solveUpper (const MatrixExpression< E1 > &e1, VectorExpression< E2 > &e2)
	Solves \( U\,x = b \) in place by back-substitution, where e1 is an upper-triangular matrix. More...
template<typename E1 , typename E2 >
bool	solveUnitUpper (const MatrixExpression< E1 > &e1, VectorExpression< E2 > &e2)
	Solves \( U\,x = b \) in place by back-substitution, where e1 is a unit upper-triangular matrix (1 on the diagonal). More...
template<typename E1 , typename E2 >
bool	solveUpper (const MatrixExpression< E1 > &e1, MatrixExpression< E2 > &e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
template<typename E1 , typename E2 >
bool	solveUnitUpper (const MatrixExpression< E1 > &e1, MatrixExpression< E2 > &e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
template<typename E >
E::SizeType	luDecompose (MatrixExpression< E > &e)
	Computes an in-place LU decomposition of the matrix e without partial pivoting. More...
template<typename E , typename PV , typename T >
E::SizeType	luDecompose (MatrixExpression< E > &e, PV &pv, T &num_row_swaps)
	Computes an in-place LU decomposition of the matrix e with partial (row) pivoting. More...
template<typename E , typename PV >
void	swapRows (VectorExpression< E > &e, const PV &pv)
	Applies the permutation vector pv to the vector expression e by swapping element i with element pv[i]. More...
template<typename E , typename PV >
void	swapRows (MatrixExpression< E > &e, const PV &pv)
	Applies the permutation vector pv to the rows of the matrix expression e by swapping row i with row pv[i]. More...
template<typename E1 , typename E2 >
bool	luSubstitute (const MatrixExpression< E1 > &lu, VectorExpression< E2 > &b)
	Solves \( LU\,x = b \) for b in place, given the LU decomposition lu (without pivoting). More...
template<typename E1 , typename E2 , typename PV >
bool	luSubstitute (const MatrixExpression< E1 > &lu, const PV &pv, VectorExpression< E2 > &b)
	Solves \( LU\,x = b \) for b in place, given the LU decomposition lu and pivot vector pv. More...
template<typename E1 , typename E2 >
bool	luSubstitute (const MatrixExpression< E1 > &lu, MatrixExpression< E2 > &b)
	Solves \( LU\,X = B \) for the matrix b in place, given the LU decomposition lu (without pivoting). More...
template<typename E1 , typename E2 , typename PV >
bool	luSubstitute (const MatrixExpression< E1 > &lu, const PV &pv, MatrixExpression< E2 > &b)
	Solves \( LU\,X = B \) for the matrix b in place, given the LU decomposition lu and pivot vector pv. More...
template<typename E >
E::ValueType	det (const MatrixExpression< E > &e)
	Returns the determinant of the matrix expression e. More...
template<typename C >
C::ValueType	det (const MatrixContainer< C > &c)
	Returns the determinant of the matrix container c (specialization avoiding an extra temporary copy when possible). More...
template<typename E , typename C >
bool	invert (const MatrixExpression< E > &e, MatrixContainer< C > &c)
	Computes the inverse of the matrix expression e and stores it in c. More...
template<typename C >
bool	invert (MatrixContainer< C > &c)
	Computes the inverse of the matrix container c in place. More...
template<typename Tri , typename E >
TriangularAdapter< E, Tri >	triang (MatrixExpression< E > &e)
	Creates a Math::TriangularAdapter view of the matrix expression e using the triangular policy Tri. More...
template<typename Tri , typename E >
TriangularAdapter< const E, Tri >	triang (const MatrixExpression< E > &e)
	Creates a constant Math::TriangularAdapter view of the matrix expression e using the triangular policy Tri. More...
template<template< typename T1, typename T2 > class F, typename M , typename E >
void	matrixAssignMatrix (M &m, const MatrixExpression< E > &e)
	Applies the element-wise functor F to every (matrix element, source element) pair, i.e. F::apply(m(i,j), e()(i,j)). More...
template<template< typename T1, typename T2 > class F, typename M , typename T >
void	matrixAssignScalar (M &m, const T &t)
	Applies the element-wise functor F to every (matrix element, scalar) pair, i.e. F::apply(m(i,j), t). More...
template<typename M , typename E >
void	matrixSwap (M &m, MatrixExpression< E > &e)
	Swaps the elements of two equally sized matrix expressions element by element. More...
template<typename E >
MatrixUnaryTraits< E, ScalarNegation< typename E::ValueType > >::ResultType	operator- (const MatrixExpression< E > &e)
	Returns the element-wise negation of the matrix expression e. More...
template<typename E >
const E &	operator+ (const MatrixExpression< E > &e)
	Returns the matrix expression e unchanged (unary +). More...
template<typename E1 , typename E2 >
MatrixBinary1Traits< E1, E2, ScalarAddition< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator+ (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the element-wise sum of the matrix expressions e1 and e2. More...
template<typename E1 , typename E2 >
MatrixBinary1Traits< E1, E2, ScalarSubtraction< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator- (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the element-wise difference of the matrix expressions e1 and e2. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2MatrixBinaryTraits< E, T, ScalarMultiplication< typename E::ValueType, T > >::ResultType >::type	operator* (const MatrixExpression< E > &e, const T &t)
	Returns the element-wise product of the matrix expression e and the scalar t. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar1MatrixBinaryTraits< T, E, ScalarMultiplication< T, typename E::ValueType > >::ResultType >::type	operator* (const T &t, const MatrixExpression< E > &e)
	Returns the element-wise product of the scalar t and the matrix expression e. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2MatrixBinaryTraits< E, T, ScalarDivision< typename E::ValueType, T > >::ResultType >::type	operator/ (const MatrixExpression< E > &e, const T &t)
	Returns the element-wise quotient of the matrix expression e by the scalar t. More...
template<typename E1 , typename E2 >
MatrixEquality< E1, E2 >::ResultType	operator== (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Tells whether the matrix expressions e1 and e2 are element-wise equal. More...
template<typename E1 , typename E2 >
MatrixEquality< E1, E2 >::ResultType	operator!= (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Tells whether the matrix expressions e1 and e2 differ in at least one element. More...
template<typename E1 , typename E2 , typename T >
std::enable_if< std::is_arithmetic< T >::value, typename MatrixToleranceEquality< E1, E2, T >::ResultType >::type	equals (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2, const T &eps)
	Tells whether the matrix expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
template<typename E >
MatrixUnaryTraits< E, ScalarConjugation< typename E::ValueType > >::ResultType	conj (const MatrixExpression< E > &e)
	Returns the element-wise complex conjugate of the matrix expression e (identity for real-valued matrices). More...
template<typename E >
MatrixUnaryTraits< E, ScalarConjugation< typename E::ValueType > >::ResultType	herm (const MatrixExpression< E > &e)
	Returns the Hermitian conjugate (conjugate transpose) of the matrix expression e — currently aliased to conj() pending transpose support. More...
template<typename E >
MatrixUnaryTraits< E, ScalarReal< typename E::ValueType > >::ResultType	real (const MatrixExpression< E > &e)
	Returns the element-wise real part of the matrix expression e. More...
template<typename E >
MatrixUnaryTraits< E, ScalarImaginary< typename E::ValueType > >::ResultType	imag (const MatrixExpression< E > &e)
	Returns the element-wise imaginary part of the matrix expression e. More...
template<typename E1 , typename E2 >
VectorMatrixBinaryTraits< E1, E2, ScalarMultiplication< typename E1::ValueType, typename E2::ValueType > >::ResultType	outerProd (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the outer product of the vector expressions e1 and e2 as a matrix expression \( e_1 \cdot e_2^T \). More...
template<typename E1 , typename E2 >
MatrixBinary1Traits< E1, E2, ScalarDivision< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemDiv (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the element-wise quotient of the matrix expressions e1 and e2. More...
template<typename E1 , typename E2 >
MatrixBinary1Traits< E1, E2, ScalarMultiplication< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemProd (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the element-wise product (Hadamard product) of the matrix expressions e1 and e2. More...
template<typename E1 , typename E2 >
Matrix1VectorBinaryTraits< E1, E2, MatrixVectorProduct< E1, E2 > >::ResultType	operator* (const MatrixExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the matrix-vector product \( e_1 \cdot e_2 \) as a vector expression. More...
template<typename E1 , typename E2 >
Matrix1VectorBinaryTraits< E1, E2, MatrixVectorProduct< E1, E2 > >::ResultType	prod (const MatrixExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the matrix-vector product \( e_1 \cdot e_2 \) as a vector expression (named-function form of operator*). More...
template<typename C , typename E1 , typename E2 >
C &	prod (const MatrixExpression< E1 > &e1, const VectorExpression< E2 > &e2, VectorContainer< C > &c)
	Computes the matrix-vector product \( e_1 \cdot e_2 \) and stores it in c. More...
template<typename E1 , typename E2 >
Matrix2VectorBinaryTraits< E1, E2, VectorMatrixProduct< E1, E2 > >::ResultType	operator* (const VectorExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the vector-matrix product \( e_1 \cdot e_2 \) as a vector expression. More...
template<typename E1 , typename E2 >
Matrix2VectorBinaryTraits< E1, E2, VectorMatrixProduct< E1, E2 > >::ResultType	prod (const VectorExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the vector-matrix product \( e_1 \cdot e_2 \) as a vector expression (named-function form of operator*). More...
template<typename C , typename E1 , typename E2 >
C &	prod (const VectorExpression< E1 > &e1, const MatrixExpression< E2 > &e2, VectorContainer< C > &c)
	Computes the vector-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
template<typename E1 , typename E2 >
MatrixBinary2Traits< E1, E2, MatrixProduct< E1, E2 > >::ResultType	operator* (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression. More...
template<typename E1 , typename E2 >
MatrixBinary2Traits< E1, E2, MatrixProduct< E1, E2 > >::ResultType	prod (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
template<typename C , typename E1 , typename E2 >
C &	prod (const MatrixExpression< E1 > &e1, const MatrixExpression< E2 > &e2, MatrixContainer< C > &c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
template<typename E >
MatrixTrace< E >::ResultType	trace (const MatrixExpression< E > &e)
	Returns the trace (sum of diagonal elements) of the matrix expression e. More...
template<typename E >
MatrixNorm1< E >::ResultType	norm1 (const MatrixExpression< E > &e)
	Returns the L1 (maximum absolute column sum) norm of the matrix expression e. More...
template<typename E >
MatrixNormFrobenius< E >::ResultType	normFrob (const MatrixExpression< E > &e)
	Returns the Frobenius norm of the matrix expression e ( \( \sqrt{\sum_{i, j} |e(i, j)|^2} \)). More...
template<typename E >
MatrixNormInfinity< E >::ResultType	normInf (const MatrixExpression< E > &e)
	Returns the L∞ (maximum absolute row sum) norm of the matrix expression e. More...
template<typename E >
VectorMatrixUnaryTraits< E, DiagonalMatrixFromVector< E > >::ResultType	diag (const VectorExpression< E > &e)
	Returns a diagonal matrix whose diagonal entries are the components of the vector expression e. More...
template<typename E >
VectorMatrixUnaryTraits< E, CrossProductMatrixFromVector< E > >::ResultType	cross (const VectorExpression< E > &e)
	Returns the cross-product (skew-symmetric) matrix corresponding to the 3-vector expression e (such that cross(e) * v == crossProd(e, v)). More...
template<typename E >
MatrixTranspose< E >	trans (MatrixExpression< E > &e)
	Returns a mutable Math::MatrixTranspose view of the matrix expression e. More...
template<typename E >
MatrixTranspose< const E >	trans (const MatrixExpression< E > &e)
	Returns a constant Math::MatrixTranspose view of the matrix expression e. More...
template<typename E >
MatrixElementSum< E >::ResultType	sum (const MatrixExpression< E > &e)
	Returns the sum of all elements of the matrix expression e. More...
template<typename M >
MatrixRow< M >	row (MatrixExpression< M > &e, typename MatrixRow< M >::SizeType i)
	Returns a mutable row proxy for row i of the matrix expression e. More...
template<typename M >
MatrixRow< const M >	row (const MatrixExpression< M > &e, typename MatrixRow< const M >::SizeType i)
	Returns a const row proxy for row i of the matrix expression e. More...
template<typename M >
MatrixColumn< M >	column (MatrixExpression< M > &e, typename MatrixColumn< M >::SizeType j)
	Returns a mutable column proxy for column j of the matrix expression e. More...
template<typename M >
MatrixColumn< const M >	column (const MatrixExpression< M > &e, typename MatrixColumn< const M >::SizeType j)
	Returns a const column proxy for column j of the matrix expression e. More...
template<typename E >
MatrixRange< E >	range (MatrixExpression< E > &e, const typename MatrixRange< E >::RangeType &r1, const typename MatrixRange< E >::RangeType &r2)
	Returns a mutable matrix range proxy viewing rows in r1 and columns in r2 of e. More...
template<typename E >
MatrixRange< const E >	range (const MatrixExpression< E > &e, const typename MatrixRange< const E >::RangeType &r1, const typename MatrixRange< const E >::RangeType &r2)
	Returns a const matrix range proxy viewing rows in r1 and columns in r2 of e. More...
template<typename E >
MatrixRange< E >	range (MatrixExpression< E > &e, typename MatrixRange< E >::RangeType::SizeType start1, typename MatrixRange< E >::RangeType::SizeType stop1, typename MatrixRange< E >::RangeType::SizeType start2, typename MatrixRange< E >::RangeType::SizeType stop2)
	Returns a mutable matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
template<typename E >
MatrixRange< const E >	range (const MatrixExpression< E > &e, typename MatrixRange< const E >::RangeType::SizeType start1, typename MatrixRange< const E >::RangeType::SizeType stop1, typename MatrixRange< const E >::RangeType::SizeType start2, typename MatrixRange< const E >::RangeType::SizeType stop2)
	Returns a const matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
template<typename E >
MatrixSlice< E >	slice (MatrixExpression< E > &e, const typename MatrixSlice< E >::SliceType &s1, const typename MatrixSlice< E >::SliceType &s2)
	Returns a mutable matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
template<typename E >
MatrixSlice< const E >	slice (const MatrixExpression< E > &e, const typename MatrixSlice< const E >::SliceType &s1, const typename MatrixSlice< const E >::SliceType &s2)
	Returns a const matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
template<typename E >
MatrixSlice< E >	slice (MatrixExpression< E > &e, typename MatrixSlice< E >::SliceType::SizeType start1, typename MatrixSlice< E >::SliceType::DifferenceType stride1, typename MatrixSlice< E >::SliceType::SizeType size1, typename MatrixSlice< E >::SliceType::SizeType start2, typename MatrixSlice< E >::SliceType::DifferenceType stride2, typename MatrixSlice< E >::SliceType::SizeType size2)
	Returns a mutable matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
template<typename E >
MatrixSlice< const E >	slice (const MatrixExpression< E > &e, typename MatrixSlice< const E >::SliceType::SizeType start1, typename MatrixSlice< const E >::SliceType::DifferenceType stride1, typename MatrixSlice< const E >::SliceType::SizeType size1, typename MatrixSlice< const E >::SliceType::SizeType start2, typename MatrixSlice< const E >::SliceType::DifferenceType stride2, typename MatrixSlice< const E >::SliceType::SizeType size2)
	Returns a const matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
template<typename T >
std::enable_if< IsScalar< T >::value, RealQuaternion< T > >::type	quat (const T &t)
	Constructs a Math::RealQuaternion from the scalar t (its real component). More...
template<typename T1 , typename T2 >
Quaternion< typename CommonType< T1, T2 >::Type >	quat (const T1 &t1, const T2 &t2)
	Constructs a Math::Quaternion from two scalar components t1 and t2 (C1, C2) — remaining components are zero. More...
template<typename T1 , typename T2 , typename T3 >
Quaternion< typename CommonType< typename CommonType< T1, T2 >::Type, T3 >::Type >	quat (const T1 &t1, const T2 &t2, const T3 &t3)
	Constructs a Math::Quaternion from three scalar components (C1, C2, C3) — C4 is zero. More...
template<typename T1 , typename T2 , typename T3 , typename T4 >
Quaternion< typename CommonType< typename CommonType< typename CommonType< T1, T2 >::Type, T3 >::Type, T4 >::Type >	quat (const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4)
	Constructs a Math::Quaternion from four scalar components (C1, C2, C3, C4). More...
template<typename E >
QuaternionVectorAdapter< E >	vec (QuaternionExpression< E > &e)
	Creates a mutable Math::QuaternionVectorAdapter view of the quaternion expression e. More...
template<typename E >
QuaternionVectorAdapter< const E >	vec (const QuaternionExpression< E > &e)
	Creates a constant Math::QuaternionVectorAdapter view of the quaternion expression e. More...
template<template< typename T1, typename T2 > class F, typename Q , typename E >
void	quaternionAssignQuaternion (Q &q, const QuaternionExpression< E > &e)
	Applies the binary functor F componentwise between the destination quaternion q and the source quaternion expression e. More...
template<template< typename T1, typename T2 > class F, typename Q , typename T >
void	quaternionAssignScalar (Q &q, const T &t)
	Applies the element-wise functor F to every (quaternion component, scalar) pair. More...
template<typename Q , typename E >
void	quaternionSwap (Q &q, QuaternionExpression< E > &e)
	Swaps the components of two quaternion expressions component by component. More...
template<typename E >
QuaternionUnary1Traits< E, ScalarNegation< typename E::ValueType > >::ResultType	operator- (const QuaternionExpression< E > &e)
	Returns the component-wise negation of the quaternion expression e. More...
template<typename E >
const E &	operator+ (const QuaternionExpression< E > &e)
	Returns the quaternion expression e unchanged (unary +). More...
template<typename E1 , typename E2 >
QuaternionBinary1Traits< E1, E2, ScalarAddition< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator+ (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Returns the component-wise sum of the quaternion expressions e1 and e2. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2QuaternionBinary2Traits< E, T, Scalar2QuaternionAddition< E, T > >::ResultType >::type	operator+ (const QuaternionExpression< E > &e, const T &t)
	Adds the scalar t to the real component (C1) of the quaternion expression e. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar1QuaternionBinary2Traits< T, E, Scalar1QuaternionAddition< T, E > >::ResultType >::type	operator+ (const T &t, const QuaternionExpression< E > &e)
	Adds the scalar t to the real component (C1) of the quaternion expression e (commutative form). More...
template<typename E1 , typename E2 >
QuaternionBinary1Traits< E1, E2, ScalarSubtraction< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator- (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Returns the component-wise difference of the quaternion expressions e1 and e2. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2QuaternionBinary2Traits< E, T, Scalar2QuaternionSubtraction< E, T > >::ResultType >::type	operator- (const QuaternionExpression< E > &e, const T &t)
	Subtracts the scalar t from the real component (C1) of the quaternion expression e. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar1QuaternionBinary2Traits< T, E, Scalar1QuaternionSubtraction< T, E > >::ResultType >::type	operator- (const T &t, const QuaternionExpression< E > &e)
	Subtracts the quaternion expression e from the scalar t (forming \( t - e \) as a quaternion expression). More...
template<typename E1 , typename E2 >
QuaternionBinary2Traits< E1, E2, QuaternionProduct< E1, E2 > >::ResultType	operator* (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Returns the (Hamilton) product of the quaternion expressions e1 and e2. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2QuaternionBinary1Traits< E, T, ScalarMultiplication< typename E::ValueType, T > >::ResultType >::type	operator* (const QuaternionExpression< E > &e, const T &t)
	Returns the component-wise product of the quaternion expression e and the scalar t. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar1QuaternionBinary1Traits< T, E, ScalarMultiplication< T, typename E::ValueType > >::ResultType >::type	operator* (const T &t, const QuaternionExpression< E > &e)
	Returns the component-wise product of the scalar t and the quaternion expression e. More...
template<typename E1 , typename E2 >
Scalar3QuaternionTernaryTraits< E1, E2, typename QuaternionNorm2< E2 >::ResultType, QuaternionDivision< E1, E2, typename QuaternionNorm2< E2 >::ResultType > >::ResultType	operator/ (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Returns the quaternion division \( e_1 \cdot e_2^{-1} \) as an expression-template node. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2QuaternionBinary1Traits< E, T, ScalarDivision< typename E::ValueType, T > >::ResultType >::type	operator/ (const QuaternionExpression< E > &e, const T &t)
	Returns the component-wise quotient of the quaternion expression e by the scalar t. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar13QuaternionTernaryTraits< T, E, typename QuaternionNorm2< E >::ResultType, ScalarQuaternionDivision< T, E, typename QuaternionNorm2< E >::ResultType > >::ResultType >::type	operator/ (const T &t, const QuaternionExpression< E > &e)
	Returns the quaternion division of the scalar t by the quaternion expression e ( \( t \cdot e^{-1} \)). More...
template<typename E1 , typename E2 >
QuaternionEquality< E1, E2 >::ResultType	operator== (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Tells whether the quaternion expressions e1 and e2 are component-wise equal. More...
template<typename E1 , typename E2 >
QuaternionEquality< E1, E2 >::ResultType	operator!= (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Tells whether the quaternion expressions e1 and e2 differ in at least one component. More...
template<typename E1 , typename E2 , typename T >
std::enable_if< std::is_arithmetic< T >::value, typename QuaternionToleranceEquality< E1, E2, T >::ResultType >::type	equals (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2, const T &eps)
	Tells whether the quaternion expressions e1 and e2 agree component-wise within the absolute tolerance eps. More...
template<typename E1 , typename E2 >
QuaternionBinary1Traits< E1, E2, ScalarDivision< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemDiv (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Returns the component-wise quotient of the quaternion expressions e1 and e2. More...
template<typename E1 , typename E2 >
QuaternionBinary1Traits< E1, E2, ScalarMultiplication< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemProd (const QuaternionExpression< E1 > &e1, const QuaternionExpression< E2 > &e2)
	Returns the component-wise product (Hadamard product) of the quaternion expressions e1 and e2. More...
template<typename E >
E::ValueType	real (const QuaternionExpression< E > &e)
	Returns the real component (C1) of the quaternion expression e. More...
template<typename E >
QuaternionUnary2Traits< E, QuaternionUnreal< E > >::ResultType	unreal (const QuaternionExpression< E > &e)
	Returns the unreal (pure-quaternion) part of the quaternion expression e (with C1 zeroed out). More...
template<typename E >
QuaternionUnary2Traits< E, QuaternionConjugate< E > >::ResultType	conj (const QuaternionExpression< E > &e)
	Returns the quaternion conjugate of the quaternion expression e (negates C2, C3, C4). More...
template<typename E >
Scalar2QuaternionBinary2Traits< E, typename QuaternionNorm2< E >::ResultType, QuaternionInverse< E, typename QuaternionNorm2< E >::ResultType > >::ResultType	inv (const QuaternionExpression< E > &e)
	Returns the multiplicative inverse of the quaternion expression e ( \( \overline{e} / |e|^2 \)). More...
template<typename E >
QuaternionNorm< E >::ResultType	norm (const QuaternionExpression< E > &e)
	Returns the norm (Euclidean length) of the quaternion expression e. More...
template<typename E >
QuaternionNorm2< E >::ResultType	norm2 (const QuaternionExpression< E > &e)
	Returns the squared norm of the quaternion expression e. More...
template<typename E >
QuaternionElementSum< E >::ResultType	sum (const QuaternionExpression< E > &e)
	Returns the sum of the four components of the quaternion expression e. More...
Range< std::size_t >	range (std::size_t start, std::size_t stop)
	Convenience factory for Math::Range with std::size_t indices. More...
template<typename T , typename C , typename GD , typename XF , typename V >
T	interpolateTrilinear (const RegularSpatialGrid< T, C, GD, XF > &grid, const V &pos, bool local_pos)
	Returns the trilinearly-interpolated value of grid at pos. More...
Slice< std::size_t, std::ptrdiff_t >	slice (std::size_t start, std::ptrdiff_t stride, std::size_t size)
	Convenience factory for Math::Slice with std::size_t indices and std::ptrdiff_t stride. More...
template<typename T >
T	factorial (unsigned int n)
	Computes the factorial \( n! \) of the non-negative integer n. More...
template<typename T >
T	pythag (const T &a, const T &b)
	Computes \( \sqrt{a^2 + b^2} \) without destructive underflow or overflow. More...
template<typename T1 , typename T2 >
T1	sign (const T1 &a, const T2 &b)
	Returns the magnitude of parameter a times the sign of parameter b. More...
template<typename T >
T	lnGamma (const T &z)
	Computes \( \ln[\Gamma(z)] \) for \( z > 0 \). More...
template<typename T >
T	gammaQ (const T &a, const T &x)
	Computes the incomplete gamma function \( Q(a, x) = 1 - P(a, x) \) (see [NRIC] for details). More...
template<typename T >
T	generalizedBell (const T &x, const T &a, const T &b, const T &c)
	Computes the generalized bell function \( Bell(x) = \frac{1}{1 + |\frac{x-c}{a}|^{2b}} \) at x. More...
template<typename M1 , typename V1 , typename M2 , typename V2 , typename V3 >
void	svBackSubstitution (const M1 &u, const V1 &w, const M2 &v, const V2 &b, V3 &x)
	Solves \( A \cdot X = B \) for a vector \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
template<typename A , typename W , typename V >
bool	svDecompose (MatrixExpression< A > &a, VectorExpression< W > &w, MatrixExpression< V > &v, std::size_t max_iter=0)
	Computes the Singular Value Decomposition [WSVD] \( A = UWV^T \) of a \( M \times N \)-dimensional matrix a. More...
template<typename U , typename W , typename V , typename B , typename X >
void	svSubstitute (const MatrixExpression< U > &u, const VectorExpression< W > &w, const MatrixExpression< V > &v, const VectorExpression< B > &b, VectorExpression< X > &x)
	Solves \( A \cdot X = B \) for a vector \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
template<typename U , typename W , typename V , typename B , typename X >
void	svSubstitute (const MatrixExpression< U > &u, const VectorExpression< W > &w, const MatrixExpression< V > &v, const MatrixExpression< B > &b, MatrixExpression< X > &x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
template<typename T1 , typename T2 >
CVector< typename CommonType< T1, T2 >::Type, 2 >	vec (const T1 &t1, const T2 &t2)
	Constructs a Math::CVector of size 2 from the components t1 and t2. More...
template<typename T1 , typename T2 , typename T3 >
CVector< typename CommonType< typename CommonType< T1, T2 >::Type, T3 >::Type, 3 >	vec (const T1 &t1, const T2 &t2, const T3 &t3)
	Constructs a Math::CVector of size 3 from the components t1, t2 and t3. More...
template<typename T1 , typename T2 , typename T3 , typename T4 >
CVector< typename CommonType< typename CommonType< typename CommonType< T1, T2 >::Type, T3 >::Type, T4 >::Type, 4 >	vec (const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4)
	Constructs a Math::CVector of size 4 from the components t1, t2, t3 and t4. More...
template<typename E >
VectorQuaternionAdapter< E >	quat (VectorExpression< E > &e)
	Creates a mutable Math::VectorQuaternionAdapter view of the 4-element vector expression e. More...
template<typename E >
VectorQuaternionAdapter< const E >	quat (const VectorExpression< E > &e)
	Creates a constant Math::VectorQuaternionAdapter view of the 4-element vector expression e. More...
template<typename E >
HomogenousCoordsAdapter< E >	homog (VectorExpression< E > &e)
	Creates a mutable Math::HomogenousCoordsAdapter view of the vector expression e (extends e by an implicit 1). More...
template<typename E >
HomogenousCoordsAdapter< const E >	homog (const VectorExpression< E > &e)
	Creates a constant Math::HomogenousCoordsAdapter view of the vector expression e. More...
template<typename T , std::size_t Dim, typename T1 >
void	transform (VectorArray< CVector< T, Dim > > &va, const CMatrix< T1, Dim, Dim > &xform)
	Transforms each \( N \)-dimensional vector in the array with the \( N \)-dimensional square matrix xform. More...
template<typename T , std::size_t Dim, typename T1 >
void	transform (VectorArray< CVector< T, Dim > > &va, const CMatrix< T1, Dim+1, Dim+1 > &xform)
	Transforms each \( N \)-dimensional vector in the array with the \( N+1 \)-dimensional square matrix xform. More...
template<typename T , std::size_t Dim, typename T1 >
bool	calcCentroid (const VectorArray< CVector< T, Dim > > &va, CVector< T1, Dim > &ctr)
	Calculates the centroid of the array elements. More...
template<typename T , std::size_t Dim>
T	calcRMSD (const VectorArray< CVector< T, Dim > > &va1, const VectorArray< CVector< T, Dim > > &va2)
	Calculates the root-mean-square distance between the corresponding elements of va1 and va2. More...
template<typename T , std::size_t Dim, typename T1 >
T	calcRMSD (const VectorArray< CVector< T, Dim > > &va1, const VectorArray< CVector< T, Dim > > &va2, const CMatrix< T1, Dim+1, Dim+1 > &va1_xform)
	Calculates the root-mean-square distance between corresponding elements of va1 and va2 after applying the \( (N+1) \times (N+1) \) homogeneous transformation va1_xform to the elements of va1. More...
template<template< typename T1, typename T2 > class F, typename V , typename E >
void	vectorAssignVector (V &v, const VectorExpression< E > &e)
	Applies the element-wise functor F to every (vector element, source element) pair, i.e. F::apply(v(i), e()(i)). More...
template<template< typename T1, typename T2 > class F, typename V , typename T >
void	vectorAssignScalar (V &v, const T &t)
	Applies the element-wise functor F to every (vector element, scalar) pair, i.e. F::apply(v(i), t). More...
template<typename V , typename E >
void	vectorSwap (V &v, VectorExpression< E > &e)
	Swaps the elements of two equally sized vector expressions element by element. More...
template<typename E >
VectorUnaryTraits< E, ScalarNegation< typename E::ValueType > >::ResultType	operator- (const VectorExpression< E > &e)
	Returns the element-wise negation of the vector expression e. More...
template<typename E >
const E &	operator+ (const VectorExpression< E > &e)
	Returns the vector expression e unchanged (unary +). More...
template<typename E1 , typename E2 >
VectorBinary1Traits< E1, E2, ScalarAddition< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator+ (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the element-wise sum of the vector expressions e1 and e2. More...
template<typename E1 , typename E2 >
VectorBinary1Traits< E1, E2, ScalarSubtraction< typename E1::ValueType, typename E2::ValueType > >::ResultType	operator- (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the element-wise difference of the vector expressions e1 and e2. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2VectorBinaryTraits< E, T, ScalarMultiplication< typename E::ValueType, T > >::ResultType >::type	operator* (const VectorExpression< E > &e, const T &t)
	Returns the element-wise product of the vector expression e and the scalar t. More...
template<typename T , typename E >
std::enable_if< IsScalar< T >::value, typename Scalar1VectorBinaryTraits< T, E, ScalarMultiplication< T, typename E::ValueType > >::ResultType >::type	operator* (const T &t, const VectorExpression< E > &e)
	Returns the element-wise product of the scalar t and the vector expression e. More...
template<typename E , typename T >
std::enable_if< IsScalar< T >::value, typename Scalar2VectorBinaryTraits< E, T, ScalarDivision< typename E::ValueType, T > >::ResultType >::type	operator/ (const VectorExpression< E > &e, const T &t)
	Returns the element-wise quotient of the vector expression e by the scalar t. More...
template<typename E1 , typename E2 >
VectorEquality< E1, E2 >::ResultType	operator== (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Tells whether the vector expressions e1 and e2 are element-wise equal. More...
template<typename E1 , typename E2 >
VectorEquality< E1, E2 >::ResultType	operator!= (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Tells whether the vector expressions e1 and e2 differ in at least one element. More...
template<typename E1 , typename E2 , typename T >
std::enable_if< std::is_arithmetic< T >::value, typename VectorToleranceEquality< E1, E2, T >::ResultType >::type	equals (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2, const T &eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
template<typename E >
VectorUnaryTraits< E, ScalarConjugation< typename E::ValueType > >::ResultType	conj (const VectorExpression< E > &e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
template<typename E >
VectorUnaryTraits< E, ScalarConjugation< typename E::ValueType > >::ResultType	herm (const VectorExpression< E > &e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
template<typename E >
VectorUnaryTraits< E, ScalarReal< typename E::ValueType > >::ResultType	real (const VectorExpression< E > &e)
	Returns the element-wise real part of the vector expression e. More...
template<typename E >
VectorUnaryTraits< E, ScalarImaginary< typename E::ValueType > >::ResultType	imag (const VectorExpression< E > &e)
	Returns the element-wise imaginary part of the vector expression e. More...
template<typename E1 , typename E2 >
VectorBinary1Traits< E1, E2, ScalarDivision< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemDiv (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
template<typename E1 , typename E2 >
VectorBinary1Traits< E1, E2, ScalarMultiplication< typename E1::ValueType, typename E2::ValueType > >::ResultType	elemProd (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
template<typename E1 , typename E2 >
VectorBinary2Traits< E1, E2, VectorCrossProduct< E1, E2 > >::ResultType	crossProd (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node. More...
template<typename E1 , typename E2 >
VectorInnerProduct< E1, E2 >::ResultType	innerProd (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Returns the inner (dot) product of the vector expressions e1 and e2. More...
template<typename E1 , typename E2 , typename T >
VectorAngleCosine< E1, E2, T >::ResultType	angleCos (const VectorExpression< E1 > &e1, const VectorExpression< E2 > &e2, const T &sd, bool clamp=true)
	Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]). More...
template<typename E >
VectorElementSum< E >::ResultType	sum (const VectorExpression< E > &e)
	Returns the sum of all elements of the vector expression e. More...
template<typename E >
VectorNorm1< E >::ResultType	norm1 (const VectorExpression< E > &e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
template<typename E >
VectorNorm2< E >::ResultType	norm2 (const VectorExpression< E > &e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
template<typename E >
VectorNormInfinity< E >::ResultType	normInf (const VectorExpression< E > &e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
template<typename E >
VectorNormInfinityIndex< E >::ResultType	normInfIndex (const VectorExpression< E > &e)
	Returns the (first) index at which the vector expression e attains its L∞ norm. More...
template<typename E >
VectorNorm2< E >::ResultType	length (const VectorExpression< E > &e)
	Returns the length (L2 norm) of the vector expression e (alias of norm2()). More...
template<typename E >
const E &	trans (const VectorExpression< E > &e)
	Returns the transpose of the vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
template<typename E >
E &	trans (VectorExpression< E > &e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
template<typename E1 , typename E2 >
QuaternionVectorBinaryTraits< E1, E2, QuaternionVectorRotation< E1, E2 > >::ResultType	rotate (const QuaternionExpression< E1 > &e1, const VectorExpression< E2 > &e2)
	Rotates the vector expression e2 by the quaternion expression e1. More...
template<typename E >
VectorIteratorTraits< E >::IteratorType	vectorBegin (VectorExpression< E > &e)
	Returns a mutable iterator pointing to the first element of the vector expression e. More...
template<typename E >
VectorIteratorTraits< E >::IteratorType	vectorEnd (VectorExpression< E > &e)
	Returns a mutable iterator pointing one past the last element of the vector expression e. More...
template<typename E >
VectorIteratorTraits< const E >::IteratorType	vectorBegin (const VectorExpression< E > &e)
	Returns a constant iterator pointing to the first element of the vector expression e. More...
template<typename E >
VectorIteratorTraits< const E >::IteratorType	vectorEnd (const VectorExpression< E > &e)
	Returns a constant iterator pointing one past the last element of the vector expression e. More...
template<typename E >
VectorRange< E >	range (VectorExpression< E > &e, const typename VectorRange< E >::RangeType &r)
	Creates a mutable Math::VectorRange view of the subrange r of the vector expression e. More...
template<typename E >
VectorRange< const E >	range (const VectorExpression< E > &e, const typename VectorRange< const E >::RangeType &r)
	Creates a constant Math::VectorRange view of the subrange r of the vector expression e. More...
template<typename E >
VectorRange< E >	range (VectorExpression< E > &e, typename VectorRange< E >::RangeType::SizeType start, typename VectorRange< E >::RangeType::SizeType stop)
	Creates a mutable Math::VectorRange view of the subrange [start, stop) of the vector expression e. More...
template<typename E >
VectorRange< const E >	range (const VectorExpression< E > &e, typename VectorRange< const E >::RangeType::SizeType start, typename VectorRange< const E >::RangeType::SizeType stop)
	Creates a constant Math::VectorRange view of the subrange [start, stop) of the vector expression e. More...
template<typename E >
VectorSlice< E >	slice (VectorExpression< E > &e, const typename VectorSlice< E >::SliceType &s)
	Creates a mutable Math::VectorSlice view of the slice s of the vector expression e. More...
template<typename E >
VectorSlice< const E >	slice (const VectorExpression< E > &e, const typename VectorSlice< const E >::SliceType &s)
	Creates a constant Math::VectorSlice view of the slice s of the vector expression e. More...
template<typename E >
VectorSlice< E >	slice (VectorExpression< E > &e, typename VectorSlice< E >::SliceType::SizeType start, typename VectorSlice< E >::SliceType::DifferenceType stride, typename VectorSlice< E >::SliceType::SizeType size)
	Creates a mutable Math::VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
template<typename E >
VectorSlice< const E >	slice (const VectorExpression< E > &e, typename VectorSlice< const E >::SliceType::SizeType start, typename VectorSlice< const E >::SliceType::DifferenceType stride, typename VectorSlice< const E >::SliceType::SizeType size)
	Creates a constant Math::VectorSlice view of the slice (start, stride, size) of the vector expression e. More...

Detailed Description

Contains classes and functions related to mathematics.

Typedef Documentation

FScalingMatrix

typedef ScalingMatrix<float> CDPL::Math::FScalingMatrix

DScalingMatrix

typedef ScalingMatrix<double> CDPL::Math::DScalingMatrix

LScalingMatrix

typedef ScalingMatrix<long> CDPL::Math::LScalingMatrix

ULScalingMatrix

typedef ScalingMatrix<unsigned long> CDPL::Math::ULScalingMatrix

FRotationMatrix

typedef RotationMatrix<float> CDPL::Math::FRotationMatrix

DRotationMatrix

typedef RotationMatrix<double> CDPL::Math::DRotationMatrix

LRotationMatrix

typedef RotationMatrix<long> CDPL::Math::LRotationMatrix

ULRotationMatrix

typedef RotationMatrix<unsigned long> CDPL::Math::ULRotationMatrix

FTranslationMatrix

typedef TranslationMatrix<float> CDPL::Math::FTranslationMatrix

DTranslationMatrix

typedef TranslationMatrix<double> CDPL::Math::DTranslationMatrix

LTranslationMatrix

typedef TranslationMatrix<long> CDPL::Math::LTranslationMatrix

ULTranslationMatrix

typedef TranslationMatrix<unsigned long> CDPL::Math::ULTranslationMatrix

FZeroGrid

typedef ZeroGrid<float> CDPL::Math::FZeroGrid

Immutable grid where all elements have the value zero of type float.

DZeroGrid

typedef ZeroGrid<double> CDPL::Math::DZeroGrid

Immutable grid where all elements have the value zero of type double.

FScalarGrid

typedef ScalarGrid<float> CDPL::Math::FScalarGrid

Immutable grid where all elements have the same value of type float.

DScalarGrid

typedef ScalarGrid<double> CDPL::Math::DScalarGrid

Immutable grid where all elements have the same value of type double.

FGrid

typedef Grid<float> CDPL::Math::FGrid

Unbounded dense grid storing floating point values of type float.

DGrid

typedef Grid<double> CDPL::Math::DGrid

Unbounded dense grid storing floating point values of type double.

FZeroMatrix

typedef ZeroMatrix<float> CDPL::Math::FZeroMatrix

Memory-efficient immutable matrix where all elements have the value zero of type float.

DZeroMatrix

typedef ZeroMatrix<double> CDPL::Math::DZeroMatrix

Memory-efficient immutable matrix where all elements have the value zero of type double.

LZeroMatrix

typedef ZeroMatrix<long> CDPL::Math::LZeroMatrix

Memory-efficient immutable matrix where all elements have the value zero of type long.

ULZeroMatrix

typedef ZeroMatrix<unsigned long> CDPL::Math::ULZeroMatrix

Memory-efficient immutable matrix where all elements have the value zero of type unsigned long.

FScalarMatrix

typedef ScalarMatrix<float> CDPL::Math::FScalarMatrix

Memory-efficient immutable matrix where all elements have the same value of type float.

DScalarMatrix

typedef ScalarMatrix<double> CDPL::Math::DScalarMatrix

Memory-efficient immutable matrix where all elements have the same value of type double.

LScalarMatrix

typedef ScalarMatrix<long> CDPL::Math::LScalarMatrix

Memory-efficient immutable matrix where all elements have the same value of type long.

ULScalarMatrix

typedef ScalarMatrix<unsigned long> CDPL::Math::ULScalarMatrix

Memory-efficient immutable matrix where all elements have the same value of type unsigned long.

FIdentityMatrix

typedef IdentityMatrix<float> CDPL::Math::FIdentityMatrix

Memory-efficient immutable identity matrix with element values of type float.

DIdentityMatrix

typedef IdentityMatrix<double> CDPL::Math::DIdentityMatrix

Memory-efficient immutable identity matrix with element values of type double.

LIdentityMatrix

typedef IdentityMatrix<long> CDPL::Math::LIdentityMatrix

Memory-efficient immutable identity matrix with element values of type long.

ULIdentityMatrix

typedef IdentityMatrix<unsigned long> CDPL::Math::ULIdentityMatrix

Memory-efficient immutable identity matrix with element values of type unsigned long.

FMatrix

typedef Matrix<float> CDPL::Math::FMatrix

Unbounded dense matrix holding floating point values of type float..

DMatrix

typedef Matrix<double> CDPL::Math::DMatrix

Unbounded dense matrix holding floating point values of type double..

LMatrix

typedef Matrix<long> CDPL::Math::LMatrix

Unbounded dense matrix holding signed integers of type long.

ULMatrix

typedef Matrix<unsigned long> CDPL::Math::ULMatrix

Unbounded dense matrix holding unsigned integers of type unsigned long.

Matrix2F

typedef CMatrix<float, 2, 2> CDPL::Math::Matrix2F

Bounded 2x2 matrix holding floating point values of type float.

Matrix3F

typedef CMatrix<float, 3, 3> CDPL::Math::Matrix3F

Bounded 3x3 matrix holding floating point values of type float.

Matrix4F

typedef CMatrix<float, 4, 4> CDPL::Math::Matrix4F

Bounded 4x4 matrix holding floating point values of type float.

Matrix2D

typedef CMatrix<double, 2, 2> CDPL::Math::Matrix2D

Bounded 2x2 matrix holding floating point values of type double.

Matrix3D

typedef CMatrix<double, 3, 3> CDPL::Math::Matrix3D

Bounded 3x3 matrix holding floating point values of type double.

Matrix4D

typedef CMatrix<double, 4, 4> CDPL::Math::Matrix4D

Bounded 4x4 matrix holding floating point values of type double.

Matrix2L

typedef CMatrix<long, 2, 2> CDPL::Math::Matrix2L

Bounded 2x2 matrix holding signed integers of type long.

Matrix3L

typedef CMatrix<long, 3, 3> CDPL::Math::Matrix3L

Bounded 3x3 matrix holding signed integers of type long.

Matrix4L

typedef CMatrix<long, 4, 4> CDPL::Math::Matrix4L

Bounded 4x4 matrix holding signed integers of type long.

Matrix2UL

typedef CMatrix<unsigned long, 2, 2> CDPL::Math::Matrix2UL

Bounded 2x2 matrix holding unsigned integers of type unsigned long.

Matrix3UL

typedef CMatrix<unsigned long, 3, 3> CDPL::Math::Matrix3UL

Bounded 3x3 matrix holding unsigned integers of type unsigned long.

Matrix4UL

typedef CMatrix<unsigned long, 4, 4> CDPL::Math::Matrix4UL

Bounded 4x4 matrix holding unsigned integers of type unsigned long.

SparseFMatrix

typedef SparseMatrix<float> CDPL::Math::SparseFMatrix

Unbounded sparse matrix holding floating point values of type float..

SparseDMatrix

typedef SparseMatrix<double> CDPL::Math::SparseDMatrix

Unbounded sparse matrix holding floating point values of type double..

SparseLMatrix

typedef SparseMatrix<long> CDPL::Math::SparseLMatrix

Unbounded sparse matrix holding signed integers of type long.

SparseULMatrix

typedef SparseMatrix<unsigned long> CDPL::Math::SparseULMatrix

Unbounded sparse matrix holding unsigned integers of type unsigned long.

FQuaternion

typedef Quaternion<float> CDPL::Math::FQuaternion

General 4-component quaternion with component values of type float.

DQuaternion

typedef Quaternion<double> CDPL::Math::DQuaternion

General 4-component quaternion with component values of type double.

LQuaternion

typedef Quaternion<long> CDPL::Math::LQuaternion

General 4-component quaternion with component values of type long.

ULQuaternion

typedef Quaternion<unsigned long> CDPL::Math::ULQuaternion

General 4-component quaternion with component values of type unsigned long.

FRealQuaternion

typedef RealQuaternion<float> CDPL::Math::FRealQuaternion

A memory-efficient pure-real quaternion with component values of type float.

DRealQuaternion

typedef RealQuaternion<double> CDPL::Math::DRealQuaternion

A memory-efficient pure-real quaternion with component values of type double.

LRealQuaternion

typedef RealQuaternion<long> CDPL::Math::LRealQuaternion

A memory-efficient pure-real quaternion with component values of type long.

ULRealQuaternion

typedef RealQuaternion<unsigned long> CDPL::Math::ULRealQuaternion

A memory-efficient pure-real quaternion with component values of type unsigned long.

FRegularSpatialGrid

typedef RegularSpatialGrid<float> CDPL::Math::FRegularSpatialGrid

Unbounded dense regular grid storing floating point values of type float.

DRegularSpatialGrid

typedef RegularSpatialGrid<double> CDPL::Math::DRegularSpatialGrid

Unbounded dense regular grid storing floating point values of type double.

FScalarVector

typedef ScalarVector<float> CDPL::Math::FScalarVector

Memory-efficient immutable vector where all elements have the same value of type float.

DScalarVector

typedef ScalarVector<double> CDPL::Math::DScalarVector

Memory-efficient immutable vector where all elements have the same value of type double.

LScalarVector

typedef ScalarVector<long> CDPL::Math::LScalarVector

Memory-efficient immutable vector where all elements have the same value of type long.

ULScalarVector

typedef ScalarVector<unsigned long> CDPL::Math::ULScalarVector

Memory-efficient immutable vector where all elements have the same value of type unsigned long.

FZeroVector

typedef ZeroVector<float> CDPL::Math::FZeroVector

Memory-efficient immutable vector where all elements have the value zero of type float.

DZeroVector

typedef ZeroVector<double> CDPL::Math::DZeroVector

Memory-efficient immutable vector where all elements have the value zero of type double.

LZeroVector

typedef ZeroVector<long> CDPL::Math::LZeroVector

Memory-efficient immutable vector where all elements have the value zero of type long.

ULZeroVector

typedef ZeroVector<unsigned long> CDPL::Math::ULZeroVector

Memory-efficient immutable vector where all elements have the value zero of type unsigned long.

FUnitVector

typedef UnitVector<float> CDPL::Math::FUnitVector

Memory-efficient immutable unit vector with element values of type float.

DUnitVector

typedef UnitVector<double> CDPL::Math::DUnitVector

Memory-efficient immutable unit vector with element values of type double.

LUnitVector

typedef UnitVector<long> CDPL::Math::LUnitVector

Memory-efficient immutable unit vector with element values of type long.

ULUnitVector

typedef UnitVector<unsigned long> CDPL::Math::ULUnitVector

Memory-efficient immutable unit vector with element values of type unsigned long.

Vector2F

typedef CVector<float, 2> CDPL::Math::Vector2F

Bounded 2 element vector holding floating point values of type float.

Vector3F

typedef CVector<float, 3> CDPL::Math::Vector3F

Bounded 3 element vector holding floating point values of type float.

Vector4F

typedef CVector<float, 4> CDPL::Math::Vector4F

Bounded 4 element vector holding floating point values of type float.

Vector2D

typedef CVector<double, 2> CDPL::Math::Vector2D

Bounded 2 element vector holding floating point values of type double.

Vector3D

typedef CVector<double, 3> CDPL::Math::Vector3D

Bounded 3 element vector holding floating point values of type double.

Vector4D

typedef CVector<double, 4> CDPL::Math::Vector4D

Bounded 4 element vector holding floating point values of type double.

Vector7D

typedef CVector<double, 7> CDPL::Math::Vector7D

Bounded 7 element vector holding floating point values of type double.

Vector2L

typedef CVector<long, 2> CDPL::Math::Vector2L

Bounded 2 element vector holding signed integers of type long.

Vector3L

typedef CVector<long, 3> CDPL::Math::Vector3L

Bounded 3 element vector holding signed integers of type long.

Vector4L

typedef CVector<long, 4> CDPL::Math::Vector4L

Bounded 4 element vector holding signed integers of type long.

Vector2UL

typedef CVector<unsigned long, 2> CDPL::Math::Vector2UL

Bounded 2 element vector holding unsigned integers of type unsigned long.

Vector3UL

typedef CVector<unsigned long, 3> CDPL::Math::Vector3UL

Bounded 3 element vector holding unsigned integers of type unsigned long.

Vector4UL

typedef CVector<unsigned long, 4> CDPL::Math::Vector4UL

Bounded 4 element vector holding unsigned integers of type unsigned long.

FVector

typedef Vector<float> CDPL::Math::FVector

Unbounded dense vector holding floating point values of type float.

DVector

typedef Vector<double> CDPL::Math::DVector

Unbounded dense vector holding floating point values of type double.

LVector

typedef Vector<long> CDPL::Math::LVector

Unbounded dense vector holding signed integers of type long.

ULVector

typedef Vector<unsigned long> CDPL::Math::ULVector

Unbounded dense vector holding unsigned integers of type unsigned long.

SparseFVector

typedef SparseVector<float> CDPL::Math::SparseFVector

Unbounded sparse vector holding floating point values of type float.

SparseDVector

typedef SparseVector<double> CDPL::Math::SparseDVector

Unbounded sparse vector holding floating point values of type double.

SparseLVector

typedef SparseVector<long> CDPL::Math::SparseLVector

Unbounded sparse vector holding signed integers of type long.

SparseULVector

typedef SparseVector<unsigned long> CDPL::Math::SparseULVector

Unbounded sparse vector holding unsigned integers of type unsigned long.

Vector2FArray

typedef VectorArray<Vector2F> CDPL::Math::Vector2FArray

Array storing vectors of type Math::Vector2F.

Vector3FArray

typedef VectorArray<Vector3F> CDPL::Math::Vector3FArray

Array storing vectors of type Math::Vector3F.

Vector2DArray

typedef VectorArray<Vector2D> CDPL::Math::Vector2DArray

Array storing vectors of type Math::Vector2D.

Vector3DArray

typedef VectorArray<Vector3D> CDPL::Math::Vector3DArray

Array storing vectors of type Math::Vector3D.

Vector2LArray

typedef VectorArray<Vector2L> CDPL::Math::Vector2LArray

Array storing vectors of type Math::Vector2L.

Vector3LArray

typedef VectorArray<Vector3L> CDPL::Math::Vector3LArray

Array storing vectors of type Math::Vector3L.

Vector2ULArray

typedef VectorArray<Vector2UL> CDPL::Math::Vector2ULArray

Array storing vectors of type Math::Vector2UL.

Vector3ULArray

typedef VectorArray<Vector3UL> CDPL::Math::Vector3ULArray

Array storing vectors of type Math::Vector3UL.

Function Documentation

direct() [1/2]

template<typename C >

DirectAssignmentProxy<const C> CDPL::Math::direct

(

const C &

lvalue

)

Convenience factory creating a Math::DirectAssignmentProxy for a const lvalue.

Template Parameters

C	The container type.

Parameters

lvalue

The lvalue to wrap.

Returns

A Math::DirectAssignmentProxy bound to lvalue.

direct() [2/2]

template<typename C >

DirectAssignmentProxy<C> CDPL::Math::direct

(

C &

lvalue

)

Convenience factory creating a Math::DirectAssignmentProxy for a mutable lvalue.

Template Parameters

C	The container type.

Parameters

lvalue

The lvalue to wrap.

Returns

A Math::DirectAssignmentProxy bound to lvalue.

gridAssignGrid()

template<template< typename T1, typename T2 > class F, typename G , typename E >

void CDPL::Math::gridAssignGrid	(	G &	g,
		const GridExpression< E > &	e
	)

Applies the element-wise functor F to every (grid cell, source cell) pair, i.e. F::apply(g(i,j,k), e()(i,j,k)).

Template Parameters

F	The element-wise binary functor template.
G	The destination grid container type.
E	The source grid expression type.

Parameters

g	The destination grid.
e	The source grid expression.

Exceptions

Base::SizeError

if the dimensions of g and e differ.

gridAssignScalar()

template<template< typename T1, typename T2 > class F, typename G , typename T >

void CDPL::Math::gridAssignScalar	(	G &	g,
		const T &	t
	)

Applies the element-wise functor F to every (grid cell, scalar) pair, i.e. F::apply(g(i,j,k), t).

Template Parameters

F	The element-wise binary functor template.
G	The destination grid container type.
T	The scalar type.

Parameters

g	The destination grid.
t	The scalar value applied to every cell.

gridSwap()

template<typename G , typename E >

void CDPL::Math::gridSwap	(	G &	g,
		GridExpression< E > &	e
	)

Swaps the cells of two equally sized grid expressions cell by cell.

Template Parameters

G	The first grid container type.
E	The second grid expression type.

Parameters

g	The first grid.
e	The second grid expression.

Exceptions

Base::SizeError

if the dimensions of g and e differ.

operator-() [1/10]

template<typename E >

GridUnaryTraits<E, ScalarNegation<typename E::ValueType> >::ResultType CDPL::Math::operator-

(

const GridExpression< E > &

e

)

Returns the element-wise negation of the grid expression e.

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

An expression-template node representing \( -e \).

operator+() [1/10]

template<typename E >

const E& CDPL::Math::operator+

(

const GridExpression< E > &

e

)

Returns the grid expression e unchanged (unary +).

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

A const reference to e.

operator+() [2/10]

template<typename E1 , typename E2 >

GridBinary1Traits<E1, E2, ScalarAddition<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator+	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2
	)

Returns the element-wise sum of the grid expressions e1 and e2.

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.

Parameters

e1	The first grid expression.
e2	The second grid expression.

Returns

An expression-template node representing \( e_1 + e_2 \).

operator-() [2/10]

template<typename E1 , typename E2 >

GridBinary1Traits<E1, E2, ScalarSubtraction<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator-	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2
	)

Returns the element-wise difference of the grid expressions e1 and e2.

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.

Parameters

e1	The first grid expression.
e2	The second grid expression.

Returns

An expression-template node representing \( e_1 - e_2 \).

operator*() [1/12]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2GridBinaryTraits<E, T, ScalarMultiplication<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator*	(	const GridExpression< E > &	e,
		const T &	t
	)

Returns the element-wise product of the grid expression e and the scalar t.

Template Parameters

E	The grid expression type.
T	The scalar type.

Parameters

e	The grid expression.
t	The scalar multiplier.

Returns

An expression-template node representing \( e \cdot t \).

operator*() [2/12]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar1GridBinaryTraits<T, E, ScalarMultiplication<T, typename E::ValueType> >::ResultType>::type CDPL::Math::operator*	(	const T &	t,
		const GridExpression< E > &	e
	)

Returns the element-wise product of the scalar t and the grid expression e.

Template Parameters

T	The scalar type.
E	The grid expression type.

Parameters

t	The scalar multiplier.
e	The grid expression.

Returns

An expression-template node representing \( t \cdot e \).

operator/() [1/6]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2GridBinaryTraits<E, T, ScalarDivision<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator/	(	const GridExpression< E > &	e,
		const T &	t
	)

Returns the element-wise quotient of the grid expression e by the scalar t.

Template Parameters

E	The grid expression type.
T	The scalar type.

Parameters

e	The grid expression.
t	The scalar divisor.

Returns

An expression-template node representing \( e / t \).

operator==() [1/4]

template<typename E1 , typename E2 >

GridEquality<E1, E2>::ResultType CDPL::Math::operator==	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2
	)

Tells whether the grid expressions e1 and e2 are element-wise equal.

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.

Parameters

e1	The first grid expression.
e2	The second grid expression.

Returns

true if both grids have equal sizes and equal elements, and false otherwise.

operator!=() [1/4]

template<typename E1 , typename E2 >

GridEquality<E1, E2>::ResultType CDPL::Math::operator!=	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2
	)

Tells whether the grid expressions e1 and e2 differ in at least one element.

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.

Parameters

e1	The first grid expression.
e2	The second grid expression.

Returns

true if the grids differ in size or in any element, and false otherwise.

equals() [1/4]

template<typename E1 , typename E2 , typename T >

std::enable_if<std::is_arithmetic<T>::value, typename GridToleranceEquality<E1, E2, T>::ResultType>::type CDPL::Math::equals	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2,
		const T &	eps
	)

Tells whether the grid expressions e1 and e2 agree element-wise within the absolute tolerance eps.

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.
T	The numeric tolerance type.

Parameters

e1	The first grid expression.
e2	The second grid expression.
eps	The non-negative absolute tolerance.

Returns

true if all elements agree within eps, and false otherwise.

conj() [1/4]

template<typename E >

GridUnaryTraits<E, ScalarConjugation<typename E::ValueType> >::ResultType CDPL::Math::conj

(

const GridExpression< E > &

e

)

Returns the element-wise complex conjugate of the grid expression e (identity for real-valued grids).

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

An expression-template node representing \( \overline{e} \).

herm() [1/3]

template<typename E >

GridUnaryTraits<E, ScalarConjugation<typename E::ValueType> >::ResultType CDPL::Math::herm

(

const GridExpression< E > &

e

)

Returns the Hermitian conjugate of the grid expression e (alias of conj() for grids).

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

An expression-template node representing \( \overline{e} \).

real() [1/4]

template<typename E >

GridUnaryTraits<E, ScalarReal<typename E::ValueType> >::ResultType CDPL::Math::real

(

const GridExpression< E > &

e

)

Returns the element-wise real part of the grid expression e.

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

An expression-template node representing the real part of e.

imag() [1/3]

template<typename E >

GridUnaryTraits<E, ScalarImaginary<typename E::ValueType> >::ResultType CDPL::Math::imag

(

const GridExpression< E > &

e

)

Returns the element-wise imaginary part of the grid expression e.

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

An expression-template node representing the imaginary part of e.

elemDiv() [1/4]

template<typename E1 , typename E2 >

GridBinary1Traits<E1, E2, ScalarDivision<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemDiv	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2
	)

Returns the element-wise quotient of the grid expressions e1 and e2.

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.

Parameters

e1	The numerator grid expression.
e2	The denominator grid expression.

Returns

An expression-template node representing the element-wise quotient \( e_1 / e_2 \).

elemProd() [1/4]

template<typename E1 , typename E2 >

GridBinary1Traits<E1, E2, ScalarMultiplication<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemProd	(	const GridExpression< E1 > &	e1,
		const GridExpression< E2 > &	e2
	)

Returns the element-wise product of the grid expressions e1 and e2 (Hadamard product).

Template Parameters

E1	The first grid expression type.
E2	The second grid expression type.

Parameters

e1	The first grid expression.
e2	The second grid expression.

Returns

An expression-template node representing the element-wise product \( e_1 \odot e_2 \).

sum() [1/4]

template<typename E >

GridElementSum<E>::ResultType CDPL::Math::sum

(

const GridExpression< E > &

e

)

Returns the sum of all elements of the grid expression e.

Template Parameters

E	The grid expression type.

Parameters

e	The grid expression.

Returns

\( \sum_{i, j, k} e(i, j, k) \).

operator<<() [1/4]

template<typename C , typename T , typename E >

std::basic_ostream<C, T>& CDPL::Math::operator<<	(	std::basic_ostream< C, T > &	os,
		const VectorExpression< E > &	e
	)

Writes a textual representation of the vector expression e to os.

Output format: size

Template Parameters

C	The stream character type.
T	The stream character traits.
E	The vector expression type.

Parameters

os	The output stream.
e	The vector expression to write.

Returns

A reference to os.

operator<<() [2/4]

template<typename C , typename T , typename E >

std::basic_ostream<C, T>& CDPL::Math::operator<<	(	std::basic_ostream< C, T > &	os,
		const MatrixExpression< E > &	e
	)

Writes a textual representation of the matrix expression e to os:

Output format: rows,cols

where M = rows - 1 and N = cols - 1.

Empty matrices are written as [rows,cols]().

Template Parameters

C	The stream character type.
T	The stream character traits.
E	The matrix expression type.

Parameters

os	The output stream.
e	The matrix expression to write.

Returns

A reference to os.

operator<<() [3/4]

template<typename C , typename T , typename E >

std::basic_ostream<C, T>& CDPL::Math::operator<<	(	std::basic_ostream< C, T > &	os,
		const QuaternionExpression< E > &	e
	)

Writes a textual representation of the quaternion expression e to os.

Output format: (c1,c2,c3,c4)

Template Parameters

C	The stream character type.
T	The stream character traits.
E	The quaternion expression type.

Parameters

os	The output stream.
e	The quaternion expression to write.

Returns

A reference to os.

operator<<() [4/4]

template<typename C , typename T , typename E >

std::basic_ostream<C, T>& CDPL::Math::operator<<	(	std::basic_ostream< C, T > &	os,
		const GridExpression< E > &	e
	)

Writes a textual representation of the grid expression e to os.

Output format: d1,d2,d3

where each planeI is itself formatted as (row0,row1,...,rowD2) and each row as (e0,e1,...,eD3). Comma-separators are used at every level.

Empty grids are written as [d1,d2,d3]().

Template Parameters

C	The stream character type.
T	The stream character traits.
E	The grid expression type.

Parameters

os	The output stream.
e	The grid expression to write.

Returns

A reference to os.

jacobiDiagonalize()

template<typename M1 , typename V , typename M2 >

bool CDPL::Math::jacobiDiagonalize	(	MatrixExpression< M1 > &	a,
		VectorExpression< V > &	d,
		MatrixExpression< M2 > &	v,
		std::size_t	max_iter = 50
	)

Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ].

On output, elements of a above the diagonal are destroyed. The vector d returns the eigenvalues of a. The columns of matrix v contain, on output, the normalized eigenvectors of a. For implementation details see [NRIC].

Parameters

a	The real symmetric matrix for which to compute eigenvalues and eigenvectors.
d	The output vector which will contain the eigenvalues of a.
v	The matrix whose columns will contain the normalized eigenvectors of a.
max_iter	The maximum number of iterations to perform.

Returns

true if a is a non-empty symmetric matrix and convergence has been reached in max_iter iterations, and false otherwise.

Precondition

a is symmetric and non-empty, i.e. a().getSize1() == a().getSize2() && a().getSize1() != 0, and furthermore d().getSize() >= a().getSize1().

Exceptions

Base::SizeError

if preconditions are violated.

solveLower() [1/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveLower	(	const MatrixExpression< E1 > &	e1,
		VectorExpression< E2 > &	e2
	)

Solves \( L\,x = b \) in place by forward-substitution, where e1 is a lower-triangular matrix.

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The vector expression type of the right-hand side.

Parameters

e1	The lower-triangular coefficient matrix.
e2	The right-hand side vector, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square, dimensions do not match, or a zero diagonal pivot is encountered.

solveUnitLower() [1/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveUnitLower	(	const MatrixExpression< E1 > &	e1,
		VectorExpression< E2 > &	e2
	)

Solves \( L\,x = b \) in place by forward-substitution, where e1 is a unit lower-triangular matrix (1 on the diagonal).

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The vector expression type of the right-hand side.

Parameters

e1	The unit lower-triangular coefficient matrix (diagonal entries are taken as 1).
e2	The right-hand side vector, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square or dimensions do not match.

solveLower() [2/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveLower	(	const MatrixExpression< E1 > &	e1,
		MatrixExpression< E2 > &	e2
	)

Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix.

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The matrix expression type of the right-hand side.

Parameters

e1	The lower-triangular coefficient matrix.
e2	The right-hand side matrix, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square, dimensions do not match, or a zero diagonal pivot is encountered.

solveUnitLower() [2/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveUnitLower	(	const MatrixExpression< E1 > &	e1,
		MatrixExpression< E2 > &	e2
	)

Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix.

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The matrix expression type of the right-hand side.

Parameters

e1	The unit lower-triangular coefficient matrix (diagonal entries are taken as 1).
e2	The right-hand side matrix, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square or dimensions do not match.

solveUpper() [1/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveUpper	(	const MatrixExpression< E1 > &	e1,
		VectorExpression< E2 > &	e2
	)

Solves \( U\,x = b \) in place by back-substitution, where e1 is an upper-triangular matrix.

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The vector expression type of the right-hand side.

Parameters

e1	The upper-triangular coefficient matrix.
e2	The right-hand side vector, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square, dimensions do not match, or a zero diagonal pivot is encountered.

solveUnitUpper() [1/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveUnitUpper	(	const MatrixExpression< E1 > &	e1,
		VectorExpression< E2 > &	e2
	)

Solves \( U\,x = b \) in place by back-substitution, where e1 is a unit upper-triangular matrix (1 on the diagonal).

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The vector expression type of the right-hand side.

Parameters

e1	The unit upper-triangular coefficient matrix (diagonal entries are taken as 1).
e2	The right-hand side vector, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square or dimensions do not match.

solveUpper() [2/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveUpper	(	const MatrixExpression< E1 > &	e1,
		MatrixExpression< E2 > &	e2
	)

Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix.

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The matrix expression type of the right-hand side.

Parameters

e1	The upper-triangular coefficient matrix.
e2	The right-hand side matrix, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square, dimensions do not match, or a zero diagonal pivot is encountered.

solveUnitUpper() [2/2]

template<typename E1 , typename E2 >

bool CDPL::Math::solveUnitUpper	(	const MatrixExpression< E1 > &	e1,
		MatrixExpression< E2 > &	e2
	)

Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix.

Template Parameters

E1	The matrix expression type of the coefficient matrix.
E2	The matrix expression type of the right-hand side.

Parameters

e1	The unit upper-triangular coefficient matrix (diagonal entries are taken as 1).
e2	The right-hand side matrix, overwritten with the solution.

Returns

true if the substitution succeeded, and false if the system is not square or dimensions do not match.

luDecompose() [1/2]

template<typename E >

E::SizeType CDPL::Math::luDecompose

(

MatrixExpression< E > &

e

)

Computes an in-place LU decomposition of the matrix e without partial pivoting.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix to decompose (modified in place).

Returns

The 1-based row index of the first singular pivot, or 0 if the matrix is non-singular.

luDecompose() [2/2]

template<typename E , typename PV , typename T >

E::SizeType CDPL::Math::luDecompose	(	MatrixExpression< E > &	e,
		PV &	pv,
		T &	num_row_swaps
	)

Computes an in-place LU decomposition of the matrix e with partial (row) pivoting.

Template Parameters

E	The matrix expression type.
PV	The permutation-vector type (must support indexed write access).
T	An arithmetic counter type.

Parameters

e	The matrix to decompose (modified in place).
pv	The output permutation vector recording the row pivots (pv[i] = pivot row index for step i).
num_row_swaps	The output count of executed row swaps.

Returns

The 1-based row index of the first singular pivot, or 0 if the matrix is non-singular.

swapRows() [1/2]

template<typename E , typename PV >

void CDPL::Math::swapRows	(	VectorExpression< E > &	e,
		const PV &	pv
	)

Applies the permutation vector pv to the vector expression e by swapping element i with element pv[i].

Template Parameters

E	The vector expression type.
PV	The permutation-vector type.

Parameters

e	The vector to permute in place.
pv	The permutation vector.

swapRows() [2/2]

template<typename E , typename PV >

void CDPL::Math::swapRows	(	MatrixExpression< E > &	e,
		const PV &	pv
	)

Applies the permutation vector pv to the rows of the matrix expression e by swapping row i with row pv[i].

Template Parameters

E	The matrix expression type.
PV	The permutation-vector type.

Parameters

e	The matrix to permute in place.
pv	The permutation vector.

luSubstitute() [1/4]

template<typename E1 , typename E2 >

bool CDPL::Math::luSubstitute	(	const MatrixExpression< E1 > &	lu,
		VectorExpression< E2 > &	b
	)

Solves \( LU\,x = b \) for b in place, given the LU decomposition lu (without pivoting).

Template Parameters

E1	The matrix expression type of lu.
E2	The vector expression type of b.

Parameters

lu	The LU decomposition.
b	The right-hand side vector, overwritten with the solution.

Returns

true if the back-substitution succeeded, and false if a zero pivot was encountered.

luSubstitute() [2/4]

template<typename E1 , typename E2 , typename PV >

bool CDPL::Math::luSubstitute	(	const MatrixExpression< E1 > &	lu,
		const PV &	pv,
		VectorExpression< E2 > &	b
	)

Solves \( LU\,x = b \) for b in place, given the LU decomposition lu and pivot vector pv.

Template Parameters

E1	The matrix expression type of lu.
E2	The vector expression type of b.
PV	The permutation-vector type.

Parameters

lu	The LU decomposition (with pivoting).
pv	The permutation vector recorded during the LU decomposition.
b	The right-hand side vector, overwritten with the solution.

Returns

true if the back-substitution succeeded, and false if a zero pivot was encountered.

luSubstitute() [3/4]

template<typename E1 , typename E2 >

bool CDPL::Math::luSubstitute	(	const MatrixExpression< E1 > &	lu,
		MatrixExpression< E2 > &	b
	)

Solves \( LU\,X = B \) for the matrix b in place, given the LU decomposition lu (without pivoting).

Template Parameters

E1	The matrix expression type of lu.
E2	The matrix expression type of b.

Parameters

lu	The LU decomposition.
b	The right-hand side matrix, overwritten with the solution.

Returns

true if the back-substitution succeeded, and false if a zero pivot was encountered.

luSubstitute() [4/4]

template<typename E1 , typename E2 , typename PV >

bool CDPL::Math::luSubstitute	(	const MatrixExpression< E1 > &	lu,
		const PV &	pv,
		MatrixExpression< E2 > &	b
	)

Solves \( LU\,X = B \) for the matrix b in place, given the LU decomposition lu and pivot vector pv.

Template Parameters

E1	The matrix expression type of lu.
E2	The matrix expression type of b.
PV	The permutation-vector type.

Parameters

lu	The LU decomposition (with pivoting).
pv	The permutation vector recorded during the LU decomposition.
b	The right-hand side matrix, overwritten with the solution.

Returns

true if the back-substitution succeeded, and false if a zero pivot was encountered.

det() [1/2]

template<typename E >

E::ValueType CDPL::Math::det

(

const MatrixExpression< E > &

e

)

Returns the determinant of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

The determinant of e.

det() [2/2]

template<typename C >

C::ValueType CDPL::Math::det

(

const MatrixContainer< C > &

c

)

Returns the determinant of the matrix container c (specialization avoiding an extra temporary copy when possible).

Template Parameters

C	The matrix container type.

Parameters

c	The matrix container.

Returns

The determinant of c.

invert() [1/2]

template<typename E , typename C >

bool CDPL::Math::invert	(	const MatrixExpression< E > &	e,
		MatrixContainer< C > &	c
	)

Computes the inverse of the matrix expression e and stores it in c.

Template Parameters

E	The source matrix expression type.
C	The output matrix container type.

Parameters

e	The matrix expression to invert.
c	The output container receiving the inverse of e.

Returns

true if e is invertible and the inverse was computed, and false if e is singular.

invert() [2/2]

template<typename C >

bool CDPL::Math::invert

(

MatrixContainer< C > &

c

)

Computes the inverse of the matrix container c in place.

Template Parameters

C	The matrix container type.

Parameters

c	The matrix container to invert in place.

Returns

true if c is invertible and the inverse was computed, and false if c is singular.

triang() [1/2]

template<typename Tri , typename E >

TriangularAdapter<E, Tri> CDPL::Math::triang

(

MatrixExpression< E > &

e

)

Creates a Math::TriangularAdapter view of the matrix expression e using the triangular policy Tri.

Template Parameters

Tri	The triangular-view selection policy (Math::Lower, Math::UnitLower, Math::Upper or Math::UnitUpper).
E	The matrix expression type.

Parameters

e	The matrix expression to wrap.

Returns

A mutable triangular view of e.

triang() [2/2]

template<typename Tri , typename E >

TriangularAdapter<const E, Tri> CDPL::Math::triang

(

const MatrixExpression< E > &

e

)

Creates a constant Math::TriangularAdapter view of the matrix expression e using the triangular policy Tri.

Template Parameters

Tri	The triangular-view selection policy (Math::Lower, Math::UnitLower, Math::Upper or Math::UnitUpper).
E	The matrix expression type.

Parameters

e	The matrix expression to wrap.

Returns

A constant triangular view of e.

matrixAssignMatrix()

template<template< typename T1, typename T2 > class F, typename M , typename E >

void CDPL::Math::matrixAssignMatrix	(	M &	m,
		const MatrixExpression< E > &	e
	)

Applies the element-wise functor F to every (matrix element, source element) pair, i.e. F::apply(m(i,j), e()(i,j)).

Template Parameters

F	The element-wise binary functor template.
M	The destination matrix container type.
E	The source matrix expression type.

Parameters

m	The destination matrix.
e	The source matrix expression.

Exceptions

Base::SizeError

if the dimensions of m and e differ.

matrixAssignScalar()

template<template< typename T1, typename T2 > class F, typename M , typename T >

void CDPL::Math::matrixAssignScalar	(	M &	m,
		const T &	t
	)

Applies the element-wise functor F to every (matrix element, scalar) pair, i.e. F::apply(m(i,j), t).

Template Parameters

F	The element-wise binary functor template.
M	The destination matrix container type.
T	The scalar type.

Parameters

m	The destination matrix.
t	The scalar value applied to every element.

matrixSwap()

template<typename M , typename E >

void CDPL::Math::matrixSwap	(	M &	m,
		MatrixExpression< E > &	e
	)

Swaps the elements of two equally sized matrix expressions element by element.

Template Parameters

M	The first matrix container type.
E	The second matrix expression type.

Parameters

m	The first matrix.
e	The second matrix expression.

Exceptions

Base::SizeError

if the dimensions of m and e differ.

operator-() [3/10]

template<typename E >

MatrixUnaryTraits<E, ScalarNegation<typename E::ValueType> >::ResultType CDPL::Math::operator-

(

const MatrixExpression< E > &

e

)

Returns the element-wise negation of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

An expression-template node representing \( -e \).

operator+() [3/10]

template<typename E >

const E& CDPL::Math::operator+

(

const MatrixExpression< E > &

e

)

Returns the matrix expression e unchanged (unary +).

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

A const reference to e.

operator+() [4/10]

template<typename E1 , typename E2 >

MatrixBinary1Traits<E1, E2, ScalarAddition<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator+	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the element-wise sum of the matrix expressions e1 and e2.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

An expression-template node representing \( e_1 + e_2 \).

operator-() [4/10]

template<typename E1 , typename E2 >

MatrixBinary1Traits<E1, E2, ScalarSubtraction<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator-	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the element-wise difference of the matrix expressions e1 and e2.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

An expression-template node representing \( e_1 - e_2 \).

operator*() [3/12]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2MatrixBinaryTraits<E, T, ScalarMultiplication<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator*	(	const MatrixExpression< E > &	e,
		const T &	t
	)

Returns the element-wise product of the matrix expression e and the scalar t.

Template Parameters

E	The matrix expression type.
T	The scalar type.

Parameters

e	The matrix expression.
t	The scalar multiplier.

Returns

An expression-template node representing \( e \cdot t \).

operator*() [4/12]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar1MatrixBinaryTraits<T, E, ScalarMultiplication<T, typename E::ValueType> >::ResultType>::type CDPL::Math::operator*	(	const T &	t,
		const MatrixExpression< E > &	e
	)

Returns the element-wise product of the scalar t and the matrix expression e.

Template Parameters

T	The scalar type.
E	The matrix expression type.

Parameters

t	The scalar multiplier.
e	The matrix expression.

Returns

An expression-template node representing \( t \cdot e \).

operator/() [2/6]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2MatrixBinaryTraits<E, T, ScalarDivision<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator/	(	const MatrixExpression< E > &	e,
		const T &	t
	)

Returns the element-wise quotient of the matrix expression e by the scalar t.

Template Parameters

E	The matrix expression type.
T	The scalar type.

Parameters

e	The matrix expression.
t	The scalar divisor.

Returns

An expression-template node representing \( e / t \).

operator==() [2/4]

template<typename E1 , typename E2 >

MatrixEquality<E1, E2>::ResultType CDPL::Math::operator==	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Tells whether the matrix expressions e1 and e2 are element-wise equal.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

true if both matrices have equal dimensions and equal elements, and false otherwise.

operator!=() [2/4]

template<typename E1 , typename E2 >

MatrixEquality<E1, E2>::ResultType CDPL::Math::operator!=	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Tells whether the matrix expressions e1 and e2 differ in at least one element.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

true if the matrices differ in dimension or in any element, and false otherwise.

equals() [2/4]

template<typename E1 , typename E2 , typename T >

std::enable_if<std::is_arithmetic<T>::value, typename MatrixToleranceEquality<E1, E2, T>::ResultType>::type CDPL::Math::equals	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2,
		const T &	eps
	)

Tells whether the matrix expressions e1 and e2 agree element-wise within the absolute tolerance eps.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.
T	The numeric tolerance type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.
eps	The non-negative absolute tolerance.

Returns

true if all elements agree within eps, and false otherwise.

conj() [2/4]

template<typename E >

MatrixUnaryTraits<E, ScalarConjugation<typename E::ValueType> >::ResultType CDPL::Math::conj

(

const MatrixExpression< E > &

e

)

Returns the element-wise complex conjugate of the matrix expression e (identity for real-valued matrices).

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

An expression-template node representing \( \overline{e} \).

herm() [2/3]

template<typename E >

MatrixUnaryTraits<E, ScalarConjugation<typename E::ValueType> >::ResultType CDPL::Math::herm

(

const MatrixExpression< E > &

e

)

Returns the Hermitian conjugate (conjugate transpose) of the matrix expression e — currently aliased to conj() pending transpose support.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

An expression-template node representing \( \overline{e} \).

real() [2/4]

template<typename E >

MatrixUnaryTraits<E, ScalarReal<typename E::ValueType> >::ResultType CDPL::Math::real

(

const MatrixExpression< E > &

e

)

Returns the element-wise real part of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

An expression-template node representing the real part of e.

imag() [2/3]

template<typename E >

MatrixUnaryTraits<E, ScalarImaginary<typename E::ValueType> >::ResultType CDPL::Math::imag

(

const MatrixExpression< E > &

e

)

Returns the element-wise imaginary part of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

An expression-template node representing the imaginary part of e.

outerProd()

template<typename E1 , typename E2 >

VectorMatrixBinaryTraits<E1, E2, ScalarMultiplication<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::outerProd	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the outer product of the vector expressions e1 and e2 as a matrix expression \( e_1 \cdot e_2^T \).

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

An expression-template node representing the outer product.

elemDiv() [2/4]

template<typename E1 , typename E2 >

MatrixBinary1Traits<E1, E2, ScalarDivision<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemDiv	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the element-wise quotient of the matrix expressions e1 and e2.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The numerator matrix expression.
e2	The denominator matrix expression.

Returns

An expression-template node representing the element-wise quotient \( e_1 / e_2 \).

elemProd() [2/4]

template<typename E1 , typename E2 >

MatrixBinary1Traits<E1, E2, ScalarMultiplication<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemProd	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the element-wise product (Hadamard product) of the matrix expressions e1 and e2.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

An expression-template node representing the element-wise product \( e_1 \odot e_2 \).

operator*() [5/12]

template<typename E1 , typename E2 >

Matrix1VectorBinaryTraits<E1, E2, MatrixVectorProduct<E1, E2> >::ResultType CDPL::Math::operator*	(	const MatrixExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the matrix-vector product \( e_1 \cdot e_2 \) as a vector expression.

Template Parameters

E1	The matrix expression type.
E2	The vector expression type.

Parameters

e1	The matrix expression.
e2	The vector expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

prod() [1/6]

template<typename E1 , typename E2 >

Matrix1VectorBinaryTraits<E1, E2, MatrixVectorProduct<E1, E2> >::ResultType CDPL::Math::prod	(	const MatrixExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the matrix-vector product \( e_1 \cdot e_2 \) as a vector expression (named-function form of operator*).

Template Parameters

E1	The matrix expression type.
E2	The vector expression type.

Parameters

e1	The matrix expression.
e2	The vector expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

prod() [2/6]

template<typename C , typename E1 , typename E2 >

C& CDPL::Math::prod	(	const MatrixExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2,
		VectorContainer< C > &	c
	)

Computes the matrix-vector product \( e_1 \cdot e_2 \) and stores it in c.

Template Parameters

C	The output vector container type.
E1	The matrix expression type.
E2	The input vector expression type.

Parameters

e1	The matrix expression.
e2	The input vector expression.
c	The output vector container receiving the result.

Returns

A reference to c.

operator*() [6/12]

template<typename E1 , typename E2 >

Matrix2VectorBinaryTraits<E1, E2, VectorMatrixProduct<E1, E2> >::ResultType CDPL::Math::operator*	(	const VectorExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the vector-matrix product \( e_1 \cdot e_2 \) as a vector expression.

Template Parameters

E1	The vector expression type.
E2	The matrix expression type.

Parameters

e1	The vector expression.
e2	The matrix expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

prod() [3/6]

template<typename E1 , typename E2 >

Matrix2VectorBinaryTraits<E1, E2, VectorMatrixProduct<E1, E2> >::ResultType CDPL::Math::prod	(	const VectorExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the vector-matrix product \( e_1 \cdot e_2 \) as a vector expression (named-function form of operator*).

Template Parameters

E1	The vector expression type.
E2	The matrix expression type.

Parameters

e1	The vector expression.
e2	The matrix expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

prod() [4/6]

template<typename C , typename E1 , typename E2 >

C& CDPL::Math::prod	(	const VectorExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2,
		VectorContainer< C > &	c
	)

Computes the vector-matrix product \( e_1 \cdot e_2 \) and stores it in c.

Template Parameters

C	The output vector container type.
E1	The input vector expression type.
E2	The matrix expression type.

Parameters

e1	The input vector expression.
e2	The matrix expression.
c	The output vector container receiving the result.

Returns

A reference to c.

operator*() [7/12]

template<typename E1 , typename E2 >

MatrixBinary2Traits<E1, E2, MatrixProduct<E1, E2> >::ResultType CDPL::Math::operator*	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression.

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

prod() [5/6]

template<typename E1 , typename E2 >

MatrixBinary2Traits<E1, E2, MatrixProduct<E1, E2> >::ResultType CDPL::Math::prod	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2
	)

Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*).

Template Parameters

E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

prod() [6/6]

template<typename C , typename E1 , typename E2 >

C& CDPL::Math::prod	(	const MatrixExpression< E1 > &	e1,
		const MatrixExpression< E2 > &	e2,
		MatrixContainer< C > &	c
	)

Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c.

Template Parameters

C	The output matrix container type.
E1	The first matrix expression type.
E2	The second matrix expression type.

Parameters

e1	The first matrix expression.
e2	The second matrix expression.
c	The output matrix container receiving the result.

Returns

A reference to c.

trace()

template<typename E >

MatrixTrace<E>::ResultType CDPL::Math::trace

(

const MatrixExpression< E > &

e

)

Returns the trace (sum of diagonal elements) of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

\( \sum_i e(i, i) \).

norm1() [1/2]

template<typename E >

MatrixNorm1<E>::ResultType CDPL::Math::norm1

(

const MatrixExpression< E > &

e

)

Returns the L1 (maximum absolute column sum) norm of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

The L1 norm of e.

normFrob()

template<typename E >

MatrixNormFrobenius<E>::ResultType CDPL::Math::normFrob

(

const MatrixExpression< E > &

e

)

Returns the Frobenius norm of the matrix expression e ( \( \sqrt{\sum_{i, j} |e(i, j)|^2} \)).

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

The Frobenius norm of e.

normInf() [1/2]

template<typename E >

MatrixNormInfinity<E>::ResultType CDPL::Math::normInf

(

const MatrixExpression< E > &

e

)

Returns the L∞ (maximum absolute row sum) norm of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

The L∞ norm of e.

diag()

template<typename E >

VectorMatrixUnaryTraits<E, DiagonalMatrixFromVector<E> >::ResultType CDPL::Math::diag

(

const VectorExpression< E > &

e

)

Returns a diagonal matrix whose diagonal entries are the components of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

An expression-template node representing the diagonal matrix.

cross()

template<typename E >

VectorMatrixUnaryTraits<E, CrossProductMatrixFromVector<E> >::ResultType CDPL::Math::cross

(

const VectorExpression< E > &

e

)

Returns the cross-product (skew-symmetric) matrix corresponding to the 3-vector expression e (such that cross(e) * v == crossProd(e, v)).

Template Parameters

E	The vector expression type.

Parameters

e	The 3-vector expression.

Returns

An expression-template node representing the skew-symmetric matrix.

trans() [1/4]

template<typename E >

MatrixTranspose<E> CDPL::Math::trans

(

MatrixExpression< E > &

e

)

Returns a mutable Math::MatrixTranspose view of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression to transpose.

Returns

A mutable transpose view of e.

trans() [2/4]

template<typename E >

MatrixTranspose<const E> CDPL::Math::trans

(

const MatrixExpression< E > &

e

)

Returns a constant Math::MatrixTranspose view of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression to transpose.

Returns

A constant transpose view of e.

sum() [2/4]

template<typename E >

MatrixElementSum<E>::ResultType CDPL::Math::sum

(

const MatrixExpression< E > &

e

)

Returns the sum of all elements of the matrix expression e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.

Returns

\( \sum_{i, j} e(i, j) \).

row() [1/2]

template<typename M >

MatrixRow<M> CDPL::Math::row	(	MatrixExpression< M > &	e,
		typename MatrixRow< M >::SizeType	i
	)

Returns a mutable row proxy for row i of the matrix expression e.

Template Parameters

M	The matrix expression type.

Parameters

e	The matrix expression.
i	The zero-based row index.

Returns

A Math::MatrixRow proxy referring to row i of e.

row() [2/2]

template<typename M >

MatrixRow<const M> CDPL::Math::row	(	const MatrixExpression< M > &	e,
		typename MatrixRow< const M >::SizeType	i
	)

Returns a const row proxy for row i of the matrix expression e.

Template Parameters

M	The matrix expression type.

Parameters

e	The matrix expression.
i	The zero-based row index.

Returns

A Math::MatrixRow proxy referring to row i of e.

column() [1/2]

template<typename M >

MatrixColumn<M> CDPL::Math::column	(	MatrixExpression< M > &	e,
		typename MatrixColumn< M >::SizeType	j
	)

Returns a mutable column proxy for column j of the matrix expression e.

Template Parameters

M	The matrix expression type.

Parameters

e	The matrix expression.
j	The zero-based column index.

Returns

A Math::MatrixColumn proxy referring to column j of e.

column() [2/2]

template<typename M >

MatrixColumn<const M> CDPL::Math::column	(	const MatrixExpression< M > &	e,
		typename MatrixColumn< const M >::SizeType	j
	)

Returns a const column proxy for column j of the matrix expression e.

Template Parameters

M	The matrix expression type.

Parameters

e	The matrix expression.
j	The zero-based column index.

Returns

A Math::MatrixColumn proxy referring to column j of e.

range() [1/9]

template<typename E >

MatrixRange<E> CDPL::Math::range	(	MatrixExpression< E > &	e,
		const typename MatrixRange< E >::RangeType &	r1,
		const typename MatrixRange< E >::RangeType &	r2
	)

Returns a mutable matrix range proxy viewing rows in r1 and columns in r2 of e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
r1	The row index range.
r2	The column index range.

Returns

A Math::MatrixRange proxy referring to the specified rectangular subrange of e.

range() [2/9]

template<typename E >

MatrixRange<const E> CDPL::Math::range	(	const MatrixExpression< E > &	e,
		const typename MatrixRange< const E >::RangeType &	r1,
		const typename MatrixRange< const E >::RangeType &	r2
	)

Returns a const matrix range proxy viewing rows in r1 and columns in r2 of e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
r1	The row index range.
r2	The column index range.

Returns

A Math::MatrixRange proxy referring to the specified rectangular subrange of e.

range() [3/9]

template<typename E >

MatrixRange<E> CDPL::Math::range	(	MatrixExpression< E > &	e,
		typename MatrixRange< E >::RangeType::SizeType	start1,
		typename MatrixRange< E >::RangeType::SizeType	stop1,
		typename MatrixRange< E >::RangeType::SizeType	start2,
		typename MatrixRange< E >::RangeType::SizeType	stop2
	)

Returns a mutable matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
start1	The first row index (inclusive).
stop1	The last row index (exclusive).
start2	The first column index (inclusive).
stop2	The last column index (exclusive).

Returns

A Math::MatrixRange proxy referring to the specified rectangular subrange of e.

range() [4/9]

template<typename E >

MatrixRange<const E> CDPL::Math::range	(	const MatrixExpression< E > &	e,
		typename MatrixRange< const E >::RangeType::SizeType	start1,
		typename MatrixRange< const E >::RangeType::SizeType	stop1,
		typename MatrixRange< const E >::RangeType::SizeType	start2,
		typename MatrixRange< const E >::RangeType::SizeType	stop2
	)

Returns a const matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
start1	The first row index (inclusive).
stop1	The last row index (exclusive).
start2	The first column index (inclusive).
stop2	The last column index (exclusive).

Returns

A Math::MatrixRange proxy referring to the specified rectangular subrange of e.

slice() [1/9]

template<typename E >

MatrixSlice<E> CDPL::Math::slice	(	MatrixExpression< E > &	e,
		const typename MatrixSlice< E >::SliceType &	s1,
		const typename MatrixSlice< E >::SliceType &	s2
	)

Returns a mutable matrix slice proxy viewing the strided rectangular slice (s1, s2) of e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
s1	The row slice (start, stride, size).
s2	The column slice (start, stride, size).

Returns

A Math::MatrixSlice proxy referring to the specified strided rectangular slice of e.

slice() [2/9]

template<typename E >

MatrixSlice<const E> CDPL::Math::slice	(	const MatrixExpression< E > &	e,
		const typename MatrixSlice< const E >::SliceType &	s1,
		const typename MatrixSlice< const E >::SliceType &	s2
	)

Returns a const matrix slice proxy viewing the strided rectangular slice (s1, s2) of e.

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
s1	The row slice (start, stride, size).
s2	The column slice (start, stride, size).

Returns

A Math::MatrixSlice proxy referring to the specified strided rectangular slice of e.

slice() [3/9]

template<typename E >

MatrixSlice<E> CDPL::Math::slice	(	MatrixExpression< E > &	e,
		typename MatrixSlice< E >::SliceType::SizeType	start1,
		typename MatrixSlice< E >::SliceType::DifferenceType	stride1,
		typename MatrixSlice< E >::SliceType::SizeType	size1,
		typename MatrixSlice< E >::SliceType::SizeType	start2,
		typename MatrixSlice< E >::SliceType::DifferenceType	stride2,
		typename MatrixSlice< E >::SliceType::SizeType	size2
	)

Returns a mutable matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2).

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
start1	The start row index.
stride1	The row stride.
size1	The number of rows.
start2	The start column index.
stride2	The column stride.
size2	The number of columns.

Returns

A Math::MatrixSlice proxy referring to the specified strided rectangular slice of e.

slice() [4/9]

template<typename E >

MatrixSlice<const E> CDPL::Math::slice	(	const MatrixExpression< E > &	e,
		typename MatrixSlice< const E >::SliceType::SizeType	start1,
		typename MatrixSlice< const E >::SliceType::DifferenceType	stride1,
		typename MatrixSlice< const E >::SliceType::SizeType	size1,
		typename MatrixSlice< const E >::SliceType::SizeType	start2,
		typename MatrixSlice< const E >::SliceType::DifferenceType	stride2,
		typename MatrixSlice< const E >::SliceType::SizeType	size2
	)

Returns a const matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2).

Template Parameters

E	The matrix expression type.

Parameters

e	The matrix expression.
start1	The start row index.
stride1	The row stride.
size1	The number of rows.
start2	The start column index.
stride2	The column stride.
size2	The number of columns.

Returns

A Math::MatrixSlice proxy referring to the specified strided rectangular slice of e.

quat() [1/6]

template<typename T >

std::enable_if<IsScalar<T>::value, RealQuaternion<T> >::type CDPL::Math::quat

(

const T &

t

)

Constructs a Math::RealQuaternion from the scalar t (its real component).

Template Parameters

T	The scalar value type.

Parameters

t	The real component.

Returns

A real quaternion with C1 = t and zero imaginary components.

quat() [2/6]

template<typename T1 , typename T2 >

Quaternion<typename CommonType<T1, T2>::Type> CDPL::Math::quat	(	const T1 &	t1,
		const T2 &	t2
	)

Constructs a Math::Quaternion from two scalar components t1 and t2 (C1, C2) — remaining components are zero.

Template Parameters

T1	The type of the first component.
T2	The type of the second component.

Parameters

t1	The C1 component.
t2	The C2 component.

Returns

A quaternion (t1, t2, 0, 0).

quat() [3/6]

template<typename T1 , typename T2 , typename T3 >

Quaternion<typename CommonType<typename CommonType<T1, T2>::Type, T3>::Type> CDPL::Math::quat	(	const T1 &	t1,
		const T2 &	t2,
		const T3 &	t3
	)

Constructs a Math::Quaternion from three scalar components (C1, C2, C3) — C4 is zero.

Template Parameters

T1	The type of the C1 component.
T2	The type of the C2 component.
T3	The type of the C3 component.

Parameters

t1	The C1 component.
t2	The C2 component.
t3	The C3 component.

Returns

A quaternion (t1, t2, t3, 0).

quat() [4/6]

template<typename T1 , typename T2 , typename T3 , typename T4 >

Quaternion<typename CommonType<typename CommonType<typename CommonType<T1, T2>::Type, T3>::Type, T4>::Type> CDPL::Math::quat	(	const T1 &	t1,
		const T2 &	t2,
		const T3 &	t3,
		const T4 &	t4
	)

Constructs a Math::Quaternion from four scalar components (C1, C2, C3, C4).

Template Parameters

T1	The type of the C1 component.
T2	The type of the C2 component.
T3	The type of the C3 component.
T4	The type of the C4 component.

Parameters

t1	The C1 component.
t2	The C2 component.
t3	The C3 component.
t4	The C4 component.

Returns

A quaternion (t1, t2, t3, t4).

vec() [1/5]

template<typename E >

QuaternionVectorAdapter<E> CDPL::Math::vec

(

QuaternionExpression< E > &

e

)

Creates a mutable Math::QuaternionVectorAdapter view of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression to wrap.

Returns

A mutable 4-element vector view of e.

vec() [2/5]

template<typename E >

QuaternionVectorAdapter<const E> CDPL::Math::vec

(

const QuaternionExpression< E > &

e

)

Creates a constant Math::QuaternionVectorAdapter view of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression to wrap.

Returns

A constant 4-element vector view of e.

quaternionAssignQuaternion()

template<template< typename T1, typename T2 > class F, typename Q , typename E >

void CDPL::Math::quaternionAssignQuaternion	(	Q &	q,
		const QuaternionExpression< E > &	e
	)

Applies the binary functor F componentwise between the destination quaternion q and the source quaternion expression e.

For each of the four quaternion components i in {C1, C2, C3, C4}, the call F::apply(q.getCi(), e().getCi()) is performed.

Template Parameters

F	The element-wise binary functor template (instantiated as F<Q::Reference, E::ValueType>).
Q	The destination quaternion container type.
E	The source quaternion expression type.

Parameters

q	The destination quaternion.
e	The source quaternion expression.

quaternionAssignScalar()

template<template< typename T1, typename T2 > class F, typename Q , typename T >

void CDPL::Math::quaternionAssignScalar	(	Q &	q,
		const T &	t
	)

Applies the element-wise functor F to every (quaternion component, scalar) pair.

Template Parameters

F	The element-wise binary functor template.
Q	The destination quaternion container type.
T	The scalar type.

Parameters

q	The destination quaternion.
t	The scalar value applied to every component.

quaternionSwap()

template<typename Q , typename E >

void CDPL::Math::quaternionSwap	(	Q &	q,
		QuaternionExpression< E > &	e
	)

Swaps the components of two quaternion expressions component by component.

Template Parameters

Q	The first quaternion container type.
E	The second quaternion expression type.

Parameters

q	The first quaternion.
e	The second quaternion expression.

operator-() [5/10]

template<typename E >

QuaternionUnary1Traits<E, ScalarNegation<typename E::ValueType> >::ResultType CDPL::Math::operator-

(

const QuaternionExpression< E > &

e

)

Returns the component-wise negation of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

An expression-template node representing \( -e \).

operator+() [5/10]

template<typename E >

const E& CDPL::Math::operator+

(

const QuaternionExpression< E > &

e

)

Returns the quaternion expression e unchanged (unary +).

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

A const reference to e.

operator+() [6/10]

template<typename E1 , typename E2 >

QuaternionBinary1Traits<E1, E2, ScalarAddition<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator+	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Returns the component-wise sum of the quaternion expressions e1 and e2.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.

Returns

An expression-template node representing \( e_1 + e_2 \).

operator+() [7/10]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2QuaternionBinary2Traits<E, T, Scalar2QuaternionAddition<E, T> >::ResultType>::type CDPL::Math::operator+	(	const QuaternionExpression< E > &	e,
		const T &	t
	)

Adds the scalar t to the real component (C1) of the quaternion expression e.

Template Parameters

E	The quaternion expression type.
T	The scalar type.

Parameters

e	The quaternion expression.
t	The scalar summand.

Returns

An expression-template node representing \( e + t \).

operator+() [8/10]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar1QuaternionBinary2Traits<T, E, Scalar1QuaternionAddition<T, E> >::ResultType>::type CDPL::Math::operator+	(	const T &	t,
		const QuaternionExpression< E > &	e
	)

Adds the scalar t to the real component (C1) of the quaternion expression e (commutative form).

Template Parameters

T	The scalar type.
E	The quaternion expression type.

Parameters

t	The scalar summand.
e	The quaternion expression.

Returns

An expression-template node representing \( t + e \).

operator-() [6/10]

template<typename E1 , typename E2 >

QuaternionBinary1Traits<E1, E2, ScalarSubtraction<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator-	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Returns the component-wise difference of the quaternion expressions e1 and e2.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.

Returns

An expression-template node representing \( e_1 - e_2 \).

operator-() [7/10]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2QuaternionBinary2Traits<E, T, Scalar2QuaternionSubtraction<E, T> >::ResultType>::type CDPL::Math::operator-	(	const QuaternionExpression< E > &	e,
		const T &	t
	)

Subtracts the scalar t from the real component (C1) of the quaternion expression e.

Template Parameters

E	The quaternion expression type.
T	The scalar type.

Parameters

e	The quaternion expression.
t	The scalar subtrahend.

Returns

An expression-template node representing \( e - t \).

operator-() [8/10]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar1QuaternionBinary2Traits<T, E, Scalar1QuaternionSubtraction<T, E> >::ResultType>::type CDPL::Math::operator-	(	const T &	t,
		const QuaternionExpression< E > &	e
	)

Subtracts the quaternion expression e from the scalar t (forming \( t - e \) as a quaternion expression).

Template Parameters

T	The scalar type.
E	The quaternion expression type.

Parameters

t	The scalar minuend.
e	The quaternion expression to subtract.

Returns

An expression-template node representing \( t - e \).

operator*() [8/12]

template<typename E1 , typename E2 >

QuaternionBinary2Traits<E1, E2, QuaternionProduct<E1, E2> >::ResultType CDPL::Math::operator*	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Returns the (Hamilton) product of the quaternion expressions e1 and e2.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.

Returns

An expression-template node representing \( e_1 \cdot e_2 \).

operator*() [9/12]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2QuaternionBinary1Traits<E, T, ScalarMultiplication<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator*	(	const QuaternionExpression< E > &	e,
		const T &	t
	)

Returns the component-wise product of the quaternion expression e and the scalar t.

Template Parameters

E	The quaternion expression type.
T	The scalar type.

Parameters

e	The quaternion expression.
t	The scalar multiplier.

Returns

An expression-template node representing \( e \cdot t \).

operator*() [10/12]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar1QuaternionBinary1Traits<T, E, ScalarMultiplication<T, typename E::ValueType> >::ResultType>::type CDPL::Math::operator*	(	const T &	t,
		const QuaternionExpression< E > &	e
	)

Returns the component-wise product of the scalar t and the quaternion expression e.

Template Parameters

T	The scalar type.
E	The quaternion expression type.

Parameters

t	The scalar multiplier.
e	The quaternion expression.

Returns

An expression-template node representing \( t \cdot e \).

operator/() [3/6]

template<typename E1 , typename E2 >

Scalar3QuaternionTernaryTraits<E1, E2, typename QuaternionNorm2<E2>::ResultType, QuaternionDivision<E1, E2, typename QuaternionNorm2<E2>::ResultType> >::ResultType CDPL::Math::operator/	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Returns the quaternion division \( e_1 \cdot e_2^{-1} \) as an expression-template node.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The dividend quaternion expression.
e2	The divisor quaternion expression.

Returns

An expression-template node representing \( e_1 / e_2 \).

operator/() [4/6]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2QuaternionBinary1Traits<E, T, ScalarDivision<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator/	(	const QuaternionExpression< E > &	e,
		const T &	t
	)

Returns the component-wise quotient of the quaternion expression e by the scalar t.

Template Parameters

E	The quaternion expression type.
T	The scalar type.

Parameters

e	The quaternion expression.
t	The scalar divisor.

Returns

An expression-template node representing \( e / t \).

operator/() [5/6]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar13QuaternionTernaryTraits<T, E, typename QuaternionNorm2<E>::ResultType, ScalarQuaternionDivision<T, E, typename QuaternionNorm2<E>::ResultType> >::ResultType>::type CDPL::Math::operator/	(	const T &	t,
		const QuaternionExpression< E > &	e
	)

Returns the quaternion division of the scalar t by the quaternion expression e ( \( t \cdot e^{-1} \)).

Template Parameters

T	The scalar type.
E	The quaternion expression type.

Parameters

t	The scalar dividend.
e	The quaternion expression divisor.

Returns

An expression-template node representing \( t / e \).

operator==() [3/4]

template<typename E1 , typename E2 >

QuaternionEquality<E1, E2>::ResultType CDPL::Math::operator==	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Tells whether the quaternion expressions e1 and e2 are component-wise equal.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.

Returns

true if all four components agree, and false otherwise.

operator!=() [3/4]

template<typename E1 , typename E2 >

QuaternionEquality<E1, E2>::ResultType CDPL::Math::operator!=	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Tells whether the quaternion expressions e1 and e2 differ in at least one component.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.

Returns

true if at least one of the four components differs, and false otherwise.

equals() [3/4]

template<typename E1 , typename E2 , typename T >

std::enable_if<std::is_arithmetic<T>::value, typename QuaternionToleranceEquality<E1, E2, T>::ResultType>::type CDPL::Math::equals	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2,
		const T &	eps
	)

Tells whether the quaternion expressions e1 and e2 agree component-wise within the absolute tolerance eps.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.
T	The numeric tolerance type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.
eps	The non-negative absolute tolerance.

Returns

true if all four components agree within eps, and false otherwise.

elemDiv() [3/4]

template<typename E1 , typename E2 >

QuaternionBinary1Traits<E1, E2, ScalarDivision<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemDiv	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Returns the component-wise quotient of the quaternion expressions e1 and e2.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The numerator quaternion expression.
e2	The denominator quaternion expression.

Returns

An expression-template node representing the component-wise quotient.

elemProd() [3/4]

template<typename E1 , typename E2 >

QuaternionBinary1Traits<E1, E2, ScalarMultiplication<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemProd	(	const QuaternionExpression< E1 > &	e1,
		const QuaternionExpression< E2 > &	e2
	)

Returns the component-wise product (Hadamard product) of the quaternion expressions e1 and e2.

Template Parameters

E1	The first quaternion expression type.
E2	The second quaternion expression type.

Parameters

e1	The first quaternion expression.
e2	The second quaternion expression.

Returns

An expression-template node representing the component-wise product.

real() [3/4]

template<typename E >

E::ValueType CDPL::Math::real

(

const QuaternionExpression< E > &

e

)

Returns the real component (C1) of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

The real component \( \mathrm{Re}(e) \) as a scalar.

unreal()

template<typename E >

QuaternionUnary2Traits<E, QuaternionUnreal<E> >::ResultType CDPL::Math::unreal

(

const QuaternionExpression< E > &

e

)

Returns the unreal (pure-quaternion) part of the quaternion expression e (with C1 zeroed out).

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

An expression-template node representing the unreal part of e.

conj() [3/4]

template<typename E >

QuaternionUnary2Traits<E, QuaternionConjugate<E> >::ResultType CDPL::Math::conj

(

const QuaternionExpression< E > &

e

)

Returns the quaternion conjugate of the quaternion expression e (negates C2, C3, C4).

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

An expression-template node representing \( \overline{e} \).

inv()

template<typename E >

Scalar2QuaternionBinary2Traits<E, typename QuaternionNorm2<E>::ResultType, QuaternionInverse<E, typename QuaternionNorm2<E>::ResultType> >::ResultType CDPL::Math::inv

(

const QuaternionExpression< E > &

e

)

Returns the multiplicative inverse of the quaternion expression e ( \( \overline{e} / |e|^2 \)).

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

An expression-template node representing \( e^{-1} \).

norm()

template<typename E >

QuaternionNorm<E>::ResultType CDPL::Math::norm

(

const QuaternionExpression< E > &

e

)

Returns the norm (Euclidean length) of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

\( \|e\| = \sqrt{e \cdot \overline{e}} \).

norm2() [1/2]

template<typename E >

QuaternionNorm2<E>::ResultType CDPL::Math::norm2

(

const QuaternionExpression< E > &

e

)

Returns the squared norm of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

\( \|e\|^2 = e \cdot \overline{e} \).

sum() [3/4]

template<typename E >

QuaternionElementSum<E>::ResultType CDPL::Math::sum

(

const QuaternionExpression< E > &

e

)

Returns the sum of the four components of the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression.

Returns

\( \sum_{i} C_i(e) \).

range() [5/9]

Range<std::size_t> CDPL::Math::range ( std::size_t  start, std::size_t  stop  )

inline

Convenience factory for Math::Range with std::size_t indices.

Parameters

start	The lower (inclusive) bound.
stop	The upper (exclusive) bound.

Returns

The constructed Math::Range instance.

interpolateTrilinear()

template<typename T , typename C , typename GD , typename XF , typename V >

T CDPL::Math::interpolateTrilinear	(	const RegularSpatialGrid< T, C, GD, XF > &	grid,
		const V &	pos,
		bool	local_pos
	)

Returns the trilinearly-interpolated value of grid at pos.

Template Parameters

T	The grid cell value type.
C	The coordinate value type.
GD	The underlying grid data container type.
XF	The coordinate transformation type.
V	The position vector type (indexable via operator[] for 3 components).

Parameters

grid	The regular spatial grid.
pos	The query position.
local_pos	If true, pos is interpreted as local (cell-index space) coordinates; if false, pos is interpreted as world coordinates and converted via the inverse transform.

Returns

The trilinearly-interpolated cell value at pos (zero if grid is empty).

slice() [5/9]

Slice<std::size_t, std::ptrdiff_t> CDPL::Math::slice ( std::size_t  start, std::ptrdiff_t  stride, std::size_t  size  )

inline

Convenience factory for Math::Slice with std::size_t indices and std::ptrdiff_t stride.

Parameters

start	The starting global index.
stride	The signed step size between consecutive entries.
size	The number of entries.

Returns

The constructed Math::Slice instance.

factorial()

template<typename T >

T CDPL::Math::factorial

(

unsigned int

n

)

Computes the factorial \( n! \) of the non-negative integer n.

Parameters

n	The non-negative integer for which to compute the factorial.

Returns

The computed factorial of n.

pythag()

template<typename T >

T CDPL::Math::pythag	(	const T &	a,
		const T &	b
	)

Computes \( \sqrt{a^2 + b^2} \) without destructive underflow or overflow.

Parameters

a	The variable a.
b	The variable b.

Returns

The result of computing \( \sqrt{a^2 + b^2} \).

sign()

template<typename T1 , typename T2 >

T1 CDPL::Math::sign	(	const T1 &	a,
		const T2 &	b
	)

Returns the magnitude of parameter a times the sign of parameter b.

Parameters

a	The parameter a.
b	The parameter b.

Returns

a times the sign of parameter b.

lnGamma()

template<typename T >

T CDPL::Math::lnGamma

(

const T &

z

)

Computes \( \ln[\Gamma(z)] \) for \( z > 0 \).

Parameters

z	The argument to the gamma function.

Returns

The computed logarithm of the gamma function value for z.

gammaQ()

template<typename T >

T CDPL::Math::gammaQ	(	const T &	a,
		const T &	x
	)

Computes the incomplete gamma function \( Q(a, x) = 1 - P(a, x) \) (see [NRIC] for details).

Parameters

a	The function argument a.
x	The function argument x.

Returns

The computed value of the incomplete gamma function.

generalizedBell()

template<typename T >

T CDPL::Math::generalizedBell	(	const T &	x,
		const T &	a,
		const T &	b,
		const T &	c
	)

Computes the generalized bell function \( Bell(x) = \frac{1}{1 + |\frac{x-c}{a}|^{2b}} \) at x.

Parameters

x	The generalized bell function argument
a	Controls the width of the curve at \(f(x) = 0.5 \).
b	Controls the slope of the curve at \( x = c - a \) and \( x = c + a \).
c	Locates the center of the curve.

Returns

The generalized bell function value at x.

svBackSubstitution()

template<typename M1 , typename V1 , typename M2 , typename V2 , typename V3 >

void CDPL::Math::svBackSubstitution	(	const M1 &	u,
		const V1 &	w,
		const M2 &	v,
		const V2 &	b,
		V3 &	x
	)

Solves \( A \cdot X = B \) for a vector \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD].

The \( M \times N \)-dimensional matrix \( A \) is specified by its singular value decomposition \( A = UWV^T \), where \( U \) is given by the \( M \times N \)-dimensional matrix u, \( W \) by the \( N \)-dimensional vector w, and \( V \) is given by the \( N \times N \)-dimensional matrix v. The right-hand side vector \( B \) is given by the \( M \)-dimensional vector b, and x is the \( N \)-dimensional output solution vector \( X \). No input quantities are destroyed, so the routine may be called sequentially with different arguments b. For implementation details see [NRIC].

Parameters

u	The \( M \times N \)-dimensional matrix \( U \).
w	The \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
v	The \( N \times N \)-dimensional matrix \( V \).
b	The \( M \)-dimensional right-hand side vector \( B \).
x	The \( N \)-dimensional output solution vector \( X \).

Precondition

w.size() == u.size2(), v.size1() == u.size2() && v.size2() == c.size2(), and b.size() == u.size1().

See also

svDecomposition()

svDecompose()

template<typename A , typename W , typename V >

bool CDPL::Math::svDecompose	(	MatrixExpression< A > &	a,
		VectorExpression< W > &	w,
		MatrixExpression< V > &	v,
		std::size_t	max_iter = 0
	)

Computes the Singular Value Decomposition [WSVD] \( A = UWV^T \) of a \( M \times N \)-dimensional matrix a.

The matrix \( U \) replaces a on output. The diagonal matrix of singular values \( W \) is output as the \( N \)-dimensional vector w. The matrix \( V \) (not the transpose \( V^T \)) is output as the \( N \times N \)-dimensional matrix v. For implementation details see [NRIC].

Parameters

a	The decomposed \( M \times N \)-matrix \( A \) which will be replaced by \( U \) on output.
w	The \( N \)-dimensional output vector \( W \) holding the singular values.
v	The \( N \times N \)-dimensional output matrix \( V \).
max_iter	The maximum number of iterations to perform, or 0 if no limit.

Returns

true if convergence has been reached in max_iter iterations, and false otherwise.

Precondition

w().getSize() >= a().getSize2(), v().getSize1() >= a().getSize2() and v().getSize2() >= a().getSize2().

Exceptions

Base::SizeError

if preconditions are violated.

svSubstitute() [1/2]

template<typename U , typename W , typename V , typename B , typename X >

void CDPL::Math::svSubstitute	(	const MatrixExpression< U > &	u,
		const VectorExpression< W > &	w,
		const MatrixExpression< V > &	v,
		const VectorExpression< B > &	b,
		VectorExpression< X > &	x
	)

Solves \( A \cdot X = B \) for a vector \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD].

The \( M \times N \)-dimensional matrix \( A \) is specified by its singular value decomposition \( A = UWV^T \), where \( U \) is given by the \( M \times N \)-dimensional matrix u, \( W \) by the \( N \)-dimensional vector w, and \( V \) is provided by the \( N \times N \)-dimensional matrix v. The right-hand side vector \( B \) is given by the \( M \)-dimensional vector b, and x is the \( N \)-dimensional output solution vector \( X \). No input quantities are destroyed, so the routine may be called sequentially with different arguments b. For implementation details see [NRIC].

Parameters

u	The \( M \times N \)-dimensional matrix \( U \).
w	The \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
v	The \( N \times N \)-dimensional matrix \( V \).
b	The \( M \)-dimensional right-hand side vector \( B \).
x	The \( N \)-dimensional output solution vector \( X \).

Precondition

w.getSize() == u.getSize2(), v.getSize1() == u.getSize2() && v.getSize2() == u.getSize2(), x.getSize() == u.getSize2()) and b.getSize() == u.getSize1().

See also

svDecomposition()

svSubstitute() [2/2]

template<typename U , typename W , typename V , typename B , typename X >

void CDPL::Math::svSubstitute	(	const MatrixExpression< U > &	u,
		const VectorExpression< W > &	w,
		const MatrixExpression< V > &	v,
		const MatrixExpression< B > &	b,
		MatrixExpression< X > &	x
	)

Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD].

The \( M \times N \)-dimensional matrix \( A \) is specified by its singular value decomposition \( A = UWV^T \), where \( U \) is given by the \( M \times N \)-dimensional matrix u, \( W \) by the \( N \)-dimensional vector w, and \( V \) is provided by the \( N \times N \)-dimensional matrix v. The \( M \times P \)-dimensional right-hand side matrix \( B \) is given by b, and x is the \( N \times P \)-dimensional output solution matrix \( X \). No input quantities are destroyed, so the routine may be called sequentially with different arguments b. For implementation details see [NRIC].

Parameters

u	The \( M \times N \)-dimensional matrix \( U \).
w	The \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
v	The \( N \times N \)-dimensional matrix \( V \).
b	The \( M \times P \)-dimensional right-hand side matrix \( B \).
x	The \( N \times P \)-dimensional output solution matrix \( X \).

Precondition

w().getSize() == u().getSize2(), v().getSize1() == u().getSize2() && v().getSize2() == u().getSize2(), x().getSize1() == u().getSize2() and b().getSize1() == u().getSize1() && b().getSize2() == x().getSize2().

Exceptions

Base::SizeError

if preconditions are violated.

See also

svDecomposition()

vec() [3/5]

template<typename T1 , typename T2 >

CVector<typename CommonType<T1, T2>::Type, 2> CDPL::Math::vec	(	const T1 &	t1,
		const T2 &	t2
	)

Constructs a Math::CVector of size 2 from the components t1 and t2.

Template Parameters

T1	The type of the first component.
T2	The type of the second component.

Parameters

t1	The first component.
t2	The second component.

Returns

A 2-element vector with components (t1, t2).

vec() [4/5]

template<typename T1 , typename T2 , typename T3 >

CVector<typename CommonType<typename CommonType<T1, T2>::Type, T3>::Type, 3> CDPL::Math::vec	(	const T1 &	t1,
		const T2 &	t2,
		const T3 &	t3
	)

Constructs a Math::CVector of size 3 from the components t1, t2 and t3.

Template Parameters

T1	The type of the first component.
T2	The type of the second component.
T3	The type of the third component.

Parameters

t1	The first component.
t2	The second component.
t3	The third component.

Returns

A 3-element vector with components (t1, t2, t3).

vec() [5/5]

template<typename T1 , typename T2 , typename T3 , typename T4 >

CVector<typename CommonType<typename CommonType<typename CommonType<T1, T2>::Type, T3>::Type, T4>::Type, 4> CDPL::Math::vec	(	const T1 &	t1,
		const T2 &	t2,
		const T3 &	t3,
		const T4 &	t4
	)

Constructs a Math::CVector of size 4 from the components t1, t2, t3 and t4.

Template Parameters

T1	The type of the first component.
T2	The type of the second component.
T3	The type of the third component.
T4	The type of the fourth component.

Parameters

t1	The first component.
t2	The second component.
t3	The third component.
t4	The fourth component.

Returns

A 4-element vector with components (t1, t2, t3, t4).

quat() [5/6]

template<typename E >

VectorQuaternionAdapter<E> CDPL::Math::quat

(

VectorExpression< E > &

e

)

Creates a mutable Math::VectorQuaternionAdapter view of the 4-element vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression to wrap.

Returns

A mutable quaternion view of e.

quat() [6/6]

template<typename E >

VectorQuaternionAdapter<const E> CDPL::Math::quat

(

const VectorExpression< E > &

e

)

Creates a constant Math::VectorQuaternionAdapter view of the 4-element vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

homog() [1/2]

template<typename E >

HomogenousCoordsAdapter<E> CDPL::Math::homog

(

VectorExpression< E > &

e

)

Creates a mutable Math::HomogenousCoordsAdapter view of the vector expression e (extends e by an implicit 1).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression to wrap.

Returns

A mutable homogeneous-coordinates view of e.

homog() [2/2]

template<typename E >

HomogenousCoordsAdapter<const E> CDPL::Math::homog

(

const VectorExpression< E > &

e

)

Creates a constant Math::HomogenousCoordsAdapter view of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

transform() [1/2]

template<typename T , std::size_t Dim, typename T1 >

void CDPL::Math::transform	(	VectorArray< CVector< T, Dim > > &	va,
		const CMatrix< T1, Dim, Dim > &	xform
	)

Transforms each \( N \)-dimensional vector in the array with the \( N \)-dimensional square matrix xform.

Template Parameters

T	The vector value type.
Dim	The vector dimension.
T1	The matrix value type.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [2/2]

template<typename T , std::size_t Dim, typename T1 >

void CDPL::Math::transform	(	VectorArray< CVector< T, Dim > > &	va,
		const CMatrix< T1, Dim+1, Dim+1 > &	xform
	)

Transforms each \( N \)-dimensional vector in the array with the \( N+1 \)-dimensional square matrix xform.

Template Parameters

T	The vector value type.
Dim	The vector dimension.
T1	The matrix value type.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

Note

The missing vector element is taken to be 1.0.

calcCentroid()

template<typename T , std::size_t Dim, typename T1 >

bool CDPL::Math::calcCentroid	(	const VectorArray< CVector< T, Dim > > &	va,
		CVector< T1, Dim > &	ctr
	)

Calculates the centroid of the array elements.

Template Parameters

T	The vector value type.
Dim	The vector dimension.
T1	The centroid value type.

Parameters

va	The vectors for which to calculate the centroid.
ctr	Stores the calculated centroid.

Returns

true if the array is not empty, and false otherwise.

calcRMSD() [1/2]

template<typename T , std::size_t Dim>

T CDPL::Math::calcRMSD	(	const VectorArray< CVector< T, Dim > > &	va1,
		const VectorArray< CVector< T, Dim > > &	va2
	)

Calculates the root-mean-square distance between the corresponding elements of va1 and va2.

If the two arrays have different sizes, only the first min(va1.size, va2.size) elements are considered.

Template Parameters

T	The vector value type.
Dim	The vector dimension.

Parameters

va1	The first vector array.
va2	The second vector array.

Returns

The RMSD value, or 0 if either array is empty.

calcRMSD() [2/2]

template<typename T , std::size_t Dim, typename T1 >

T CDPL::Math::calcRMSD	(	const VectorArray< CVector< T, Dim > > &	va1,
		const VectorArray< CVector< T, Dim > > &	va2,
		const CMatrix< T1, Dim+1, Dim+1 > &	va1_xform
	)

Calculates the root-mean-square distance between corresponding elements of va1 and va2 after applying the \( (N+1) \times (N+1) \) homogeneous transformation va1_xform to the elements of va1.

If the two arrays have different sizes, only the first min(va1.size, va2.size) elements are considered.

Template Parameters

T	The vector value type.
Dim	The vector dimension.
T1	The transformation matrix value type.

Parameters

va1	The first vector array (transformed via va1_xform on the fly).
va2	The second vector array.
va1_xform	The transformation matrix applied to va1 (with implicit homogeneous coordinate 1).

Returns

The RMSD value, or 0 if either array is empty.

vectorAssignVector()

template<template< typename T1, typename T2 > class F, typename V , typename E >

void CDPL::Math::vectorAssignVector	(	V &	v,
		const VectorExpression< E > &	e
	)

Applies the element-wise functor F to every (vector element, source element) pair, i.e. F::apply(v(i), e()(i)).

Template Parameters

F	The element-wise binary functor template (e.g. assignment, plus-assign).
V	The destination vector container type.
E	The source vector expression type.

Parameters

v	The destination vector.
e	The source vector expression.

Exceptions

Base::SizeError

if the sizes of v and e differ.

vectorAssignScalar()

template<template< typename T1, typename T2 > class F, typename V , typename T >

void CDPL::Math::vectorAssignScalar	(	V &	v,
		const T &	t
	)

Applies the element-wise functor F to every (vector element, scalar) pair, i.e. F::apply(v(i), t).

Template Parameters

F	The element-wise binary functor template (e.g. assignment, multiply-assign).
V	The destination vector container type.
T	The scalar type.

Parameters

v	The destination vector.
t	The scalar value applied to every element.

vectorSwap()

template<typename V , typename E >

void CDPL::Math::vectorSwap	(	V &	v,
		VectorExpression< E > &	e
	)

Swaps the elements of two equally sized vector expressions element by element.

Template Parameters

V	The first vector container type.
E	The second vector expression type.

Parameters

v	The first vector.
e	The second vector expression.

Exceptions

Base::SizeError

if the sizes of v and e differ.

operator-() [9/10]

template<typename E >

VectorUnaryTraits<E, ScalarNegation<typename E::ValueType> >::ResultType CDPL::Math::operator-

(

const VectorExpression< E > &

e

)

Returns the element-wise negation of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

An expression-template node representing \( -e \).

operator+() [9/10]

template<typename E >

const E& CDPL::Math::operator+

(

const VectorExpression< E > &

e

)

Returns the vector expression e unchanged (unary +).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A const reference to e.

operator+() [10/10]

template<typename E1 , typename E2 >

VectorBinary1Traits<E1, E2, ScalarAddition<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator+	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the element-wise sum of the vector expressions e1 and e2.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

An expression-template node representing \( e_1 + e_2 \).

operator-() [10/10]

template<typename E1 , typename E2 >

VectorBinary1Traits<E1, E2, ScalarSubtraction<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::operator-	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the element-wise difference of the vector expressions e1 and e2.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

An expression-template node representing \( e_1 - e_2 \).

operator*() [11/12]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2VectorBinaryTraits<E, T, ScalarMultiplication<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator*	(	const VectorExpression< E > &	e,
		const T &	t
	)

Returns the element-wise product of the vector expression e and the scalar t.

Template Parameters

E	The vector expression type.
T	The scalar type.

Parameters

e	The vector expression.
t	The scalar multiplier.

Returns

An expression-template node representing \( e \cdot t \).

operator*() [12/12]

template<typename T , typename E >

std::enable_if<IsScalar<T>::value, typename Scalar1VectorBinaryTraits<T, E, ScalarMultiplication<T, typename E::ValueType> >::ResultType>::type CDPL::Math::operator*	(	const T &	t,
		const VectorExpression< E > &	e
	)

Returns the element-wise product of the scalar t and the vector expression e.

Template Parameters

T	The scalar type.
E	The vector expression type.

Parameters

t	The scalar multiplier.
e	The vector expression.

Returns

An expression-template node representing \( t \cdot e \).

operator/() [6/6]

template<typename E , typename T >

std::enable_if<IsScalar<T>::value, typename Scalar2VectorBinaryTraits<E, T, ScalarDivision<typename E::ValueType, T> >::ResultType>::type CDPL::Math::operator/	(	const VectorExpression< E > &	e,
		const T &	t
	)

Returns the element-wise quotient of the vector expression e by the scalar t.

Template Parameters

E	The vector expression type.
T	The scalar type.

Parameters

e	The vector expression.
t	The scalar divisor.

Returns

An expression-template node representing \( e / t \).

operator==() [4/4]

template<typename E1 , typename E2 >

VectorEquality<E1, E2>::ResultType CDPL::Math::operator==	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Tells whether the vector expressions e1 and e2 are element-wise equal.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

true if both vectors have equal sizes and equal elements, and false otherwise.

operator!=() [4/4]

template<typename E1 , typename E2 >

VectorEquality<E1, E2>::ResultType CDPL::Math::operator!=	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Tells whether the vector expressions e1 and e2 differ in at least one element.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

true if the vectors differ in size or in any element, and false otherwise.

equals() [4/4]

template<typename E1 , typename E2 , typename T >

std::enable_if<std::is_arithmetic<T>::value, typename VectorToleranceEquality<E1, E2, T>::ResultType>::type CDPL::Math::equals	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2,
		const T &	eps
	)

Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.
T	The numeric tolerance type.

Parameters

e1	The first vector expression.
e2	The second vector expression.
eps	The non-negative absolute tolerance.

Returns

true if all elements agree within eps, and false otherwise.

conj() [4/4]

template<typename E >

VectorUnaryTraits<E, ScalarConjugation<typename E::ValueType> >::ResultType CDPL::Math::conj

(

const VectorExpression< E > &

e

)

Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

An expression-template node representing \( \overline{e} \).

herm() [3/3]

template<typename E >

VectorUnaryTraits<E, ScalarConjugation<typename E::ValueType> >::ResultType CDPL::Math::herm

(

const VectorExpression< E > &

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

An expression-template node representing \( \overline{e} \).

real() [4/4]

template<typename E >

VectorUnaryTraits<E, ScalarReal<typename E::ValueType> >::ResultType CDPL::Math::real

(

const VectorExpression< E > &

e

)

Returns the element-wise real part of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

An expression-template node representing the real part of e.

imag() [3/3]

template<typename E >

VectorUnaryTraits<E, ScalarImaginary<typename E::ValueType> >::ResultType CDPL::Math::imag

(

const VectorExpression< E > &

e

)

Returns the element-wise imaginary part of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

An expression-template node representing the imaginary part of e.

elemDiv() [4/4]

template<typename E1 , typename E2 >

VectorBinary1Traits<E1, E2, ScalarDivision<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemDiv	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the element-wise quotient of the vector expressions e1 and e2.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

An expression-template node representing the element-wise quotient \( e_1 / e_2 \).

elemProd() [4/4]

template<typename E1 , typename E2 >

VectorBinary1Traits<E1, E2, ScalarMultiplication<typename E1::ValueType, typename E2::ValueType> >::ResultType CDPL::Math::elemProd	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

An expression-template node representing the element-wise product \( e_1 \odot e_2 \).

crossProd()

template<typename E1 , typename E2 >

VectorBinary2Traits<E1, E2, VectorCrossProduct<E1, E2> >::ResultType CDPL::Math::crossProd	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first 3-vector expression.
e2	The second 3-vector expression.

Returns

An expression-template node representing the cross product.

innerProd()

template<typename E1 , typename E2 >

VectorInnerProduct<E1, E2>::ResultType CDPL::Math::innerProd	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Returns the inner (dot) product of the vector expressions e1 and e2.

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.

Parameters

e1	The first vector expression.
e2	The second vector expression.

Returns

\( \sum_i e_1(i) \cdot e_2(i) \).

angleCos()

template<typename E1 , typename E2 , typename T >

VectorAngleCosine<E1, E2, T>::ResultType CDPL::Math::angleCos	(	const VectorExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2,
		const T &	sd,
		bool	clamp = true
	)

Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]).

Template Parameters

E1	The first vector expression type.
E2	The second vector expression type.
T	The norm-product scalar type.

Parameters

e1	The first vector expression.
e2	The second vector expression.
sd	The precomputed product \( \|e_1\| \cdot \|e_2\| \) of the two vector magnitudes.
clamp	If true (default), the result is clamped to the range [-1, 1].

Returns

The (optionally clamped) cosine of the angle.

sum() [4/4]

template<typename E >

VectorElementSum<E>::ResultType CDPL::Math::sum

(

const VectorExpression< E > &

e

)

Returns the sum of all elements of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

norm1() [2/2]

template<typename E >

VectorNorm1<E>::ResultType CDPL::Math::norm1

(

const VectorExpression< E > &

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

The L1 norm.

norm2() [2/2]

template<typename E >

VectorNorm2<E>::ResultType CDPL::Math::norm2

(

const VectorExpression< E > &

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

The L2 norm.

normInf() [2/2]

template<typename E >

VectorNormInfinity<E>::ResultType CDPL::Math::normInf

(

const VectorExpression< E > &

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInfIndex()

template<typename E >

VectorNormInfinityIndex<E>::ResultType CDPL::Math::normInfIndex

(

const VectorExpression< E > &

e

)

Returns the (first) index at which the vector expression e attains its L∞ norm.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

The zero-based index of the element with the maximum absolute value.

length()

template<typename E >

VectorNorm2<E>::ResultType CDPL::Math::length

(

const VectorExpression< E > &

e

)

Returns the length (L2 norm) of the vector expression e (alias of norm2()).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

The vector length.

trans() [3/4]

template<typename E >

const E& CDPL::Math::trans

(

const VectorExpression< E > &

e

)

Returns the transpose of the vector expression e (the identity for vectors — provided for matrix-API symmetry).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A const reference to e.

trans() [4/4]

template<typename E >

E& CDPL::Math::trans

(

VectorExpression< E > &

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A reference to e.

rotate()

template<typename E1 , typename E2 >

QuaternionVectorBinaryTraits<E1, E2, QuaternionVectorRotation<E1, E2> >::ResultType CDPL::Math::rotate	(	const QuaternionExpression< E1 > &	e1,
		const VectorExpression< E2 > &	e2
	)

Rotates the vector expression e2 by the quaternion expression e1.

Template Parameters

E1	The quaternion expression type.
E2	The vector expression type.

Parameters

e1	The unit quaternion expression encoding the rotation.
e2	The vector expression to rotate.

Returns

An expression-template node representing the rotated 3-vector \( e_1 \cdot e_2 \cdot e_1^{-1} \).

vectorBegin() [1/2]

template<typename E >

VectorIteratorTraits<E>::IteratorType CDPL::Math::vectorBegin

(

VectorExpression< E > &

e

)

Returns a mutable iterator pointing to the first element of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A mutable iterator pointing to the first element.

vectorEnd() [1/2]

template<typename E >

VectorIteratorTraits<E>::IteratorType CDPL::Math::vectorEnd

(

VectorExpression< E > &

e

)

Returns a mutable iterator pointing one past the last element of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A mutable iterator pointing one past the last element.

vectorBegin() [2/2]

template<typename E >

VectorIteratorTraits<const E>::IteratorType CDPL::Math::vectorBegin

(

const VectorExpression< E > &

e

)

Returns a constant iterator pointing to the first element of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A constant iterator pointing to the first element.

vectorEnd() [2/2]

template<typename E >

VectorIteratorTraits<const E>::IteratorType CDPL::Math::vectorEnd

(

const VectorExpression< E > &

e

)

Returns a constant iterator pointing one past the last element of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.

Returns

A constant iterator pointing one past the last element.

range() [6/9]

template<typename E >

VectorRange<E> CDPL::Math::range	(	VectorExpression< E > &	e,
		const typename VectorRange< E >::RangeType &	r
	)

Creates a mutable Math::VectorRange view of the subrange r of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A mutable range view of e.

range() [7/9]

template<typename E >

VectorRange<const E> CDPL::Math::range	(	const VectorExpression< E > &	e,
		const typename VectorRange< const E >::RangeType &	r
	)

Creates a constant Math::VectorRange view of the subrange r of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [8/9]

template<typename E >

VectorRange<E> CDPL::Math::range	(	VectorExpression< E > &	e,
		typename VectorRange< E >::RangeType::SizeType	start,
		typename VectorRange< E >::RangeType::SizeType	stop
	)

Creates a mutable Math::VectorRange view of the subrange [start, stop) of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A mutable range view of e.

range() [9/9]

template<typename E >

VectorRange<const E> CDPL::Math::range	(	const VectorExpression< E > &	e,
		typename VectorRange< const E >::RangeType::SizeType	start,
		typename VectorRange< const E >::RangeType::SizeType	stop
	)

Creates a constant Math::VectorRange view of the subrange [start, stop) of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A constant range view of e.

slice() [6/9]

template<typename E >

VectorSlice<E> CDPL::Math::slice	(	VectorExpression< E > &	e,
		const typename VectorSlice< E >::SliceType &	s
	)

Creates a mutable Math::VectorSlice view of the slice s of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A mutable slice view of e.

slice() [7/9]

template<typename E >

VectorSlice<const E> CDPL::Math::slice	(	const VectorExpression< E > &	e,
		const typename VectorSlice< const E >::SliceType &	s
	)

Creates a constant Math::VectorSlice view of the slice s of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [8/9]

template<typename E >

VectorSlice<E> CDPL::Math::slice	(	VectorExpression< E > &	e,
		typename VectorSlice< E >::SliceType::SizeType	start,
		typename VectorSlice< E >::SliceType::DifferenceType	stride,
		typename VectorSlice< E >::SliceType::SizeType	size
	)

Creates a mutable Math::VectorSlice view of the slice (start, stride, size) of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
start	The (inclusive) start index of the slice.
stride	The stride between successive slice elements.
size	The number of elements of the slice.

Returns

A mutable slice view of e.

slice() [9/9]

template<typename E >

VectorSlice<const E> CDPL::Math::slice	(	const VectorExpression< E > &	e,
		typename VectorSlice< const E >::SliceType::SizeType	start,
		typename VectorSlice< const E >::SliceType::DifferenceType	stride,
		typename VectorSlice< const E >::SliceType::SizeType	size
	)

Creates a constant Math::VectorSlice view of the slice (start, stride, size) of the vector expression e.

Template Parameters

E	The vector expression type.

Parameters

e	The vector expression.
start	The (inclusive) start index of the slice.
stride	The stride between successive slice elements.
size	The number of elements of the slice.

Returns

A constant slice view of e.