CDPL.Math Package Reference

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

Classes
class	ConstDGridExpression
class	ConstDHomogenousCoordsAdapter
class	ConstDMatrixColumn
class	ConstDMatrixExpression
class	ConstDMatrixRange
class	ConstDMatrixRow
class	ConstDMatrixSlice
class	ConstDMatrixTranspose
class	ConstDQuaternionExpression
class	ConstDQuaternionVectorAdapter
class	ConstDVectorExpression
class	ConstDVectorQuaternionAdapter
class	ConstDVectorRange
class	ConstDVectorSlice
class	ConstFGridExpression
class	ConstFHomogenousCoordsAdapter
class	ConstFMatrixColumn
class	ConstFMatrixExpression
class	ConstFMatrixRange
class	ConstFMatrixRow
class	ConstFMatrixSlice
class	ConstFMatrixTranspose
class	ConstFQuaternionExpression
class	ConstFQuaternionVectorAdapter
class	ConstFVectorExpression
class	ConstFVectorQuaternionAdapter
class	ConstFVectorRange
class	ConstFVectorSlice
class	ConstLHomogenousCoordsAdapter
class	ConstLMatrixColumn
class	ConstLMatrixExpression
class	ConstLMatrixRange
class	ConstLMatrixRow
class	ConstLMatrixSlice
class	ConstLMatrixTranspose
class	ConstLQuaternionExpression
class	ConstLQuaternionVectorAdapter
class	ConstLVectorExpression
class	ConstLVectorQuaternionAdapter
class	ConstLVectorRange
class	ConstLVectorSlice
class	ConstLowerTriangularDMatrixAdapter
class	ConstLowerTriangularFMatrixAdapter
class	ConstLowerTriangularLMatrixAdapter
class	ConstLowerTriangularULMatrixAdapter
class	ConstULHomogenousCoordsAdapter
class	ConstULMatrixColumn
class	ConstULMatrixExpression
class	ConstULMatrixRange
class	ConstULMatrixRow
class	ConstULMatrixSlice
class	ConstULMatrixTranspose
class	ConstULQuaternionExpression
class	ConstULQuaternionVectorAdapter
class	ConstULVectorExpression
class	ConstULVectorQuaternionAdapter
class	ConstULVectorRange
class	ConstULVectorSlice
class	ConstUnitLowerTriangularDMatrixAdapter
class	ConstUnitLowerTriangularFMatrixAdapter
class	ConstUnitLowerTriangularLMatrixAdapter
class	ConstUnitLowerTriangularULMatrixAdapter
class	ConstUnitUpperTriangularDMatrixAdapter
class	ConstUnitUpperTriangularFMatrixAdapter
class	ConstUnitUpperTriangularLMatrixAdapter
class	ConstUnitUpperTriangularULMatrixAdapter
class	ConstUpperTriangularDMatrixAdapter
class	ConstUpperTriangularFMatrixAdapter
class	ConstUpperTriangularLMatrixAdapter
class	ConstUpperTriangularULMatrixAdapter
class	DGrid
	Unbounded dense grid storing floating point values of type double. More...
class	DGridExpression
class	DHomogenousCoordsAdapter
class	DIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type double. More...
class	DKabschAlgorithm
class	DMLRModel
	Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...
class	DMatrix
	Unbounded dense matrix holding floating point values of type double. More...
class	DMatrixColumn
class	DMatrixExpression
class	DMatrixRange
class	DMatrixRow
class	DMatrixSlice
class	DMatrixTranspose
class	DQuaternion
	General 4-component quaternion with component values of type double. More...
class	DQuaternionExpression
class	DQuaternionVectorAdapter
class	DRealQuaternion
	A memory-efficient pure-real quaternion with component values of type double. More...
class	DRegularSpatialGrid
	Unbounded dense regular grid storing floating point values of type double. More...
class	DRotationMatrix
class	DScalarGrid
	Immutable grid where all elements have the same value of type double. More...
class	DScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type double. More...
class	DScalarVector
	Memory-efficient immutable vector where all elements have the same value of type double. More...
class	DScalingMatrix
class	DTranslationMatrix
class	DUnitVector
	Memory-efficient immutable unit vector with element values of type double. More...
class	DVector
	Unbounded dense vector holding floating point values of type double. More...
class	DVectorBFGSMinimizer
	Fletcher's implementation of the BFGS method. More...
class	DVectorExpression
class	DVectorQuaternionAdapter
class	DVectorRange
class	DVectorSlice
class	DZeroGrid
	Immutable grid where all elements have the value zero of type double. More...
class	DZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type double. More...
class	DZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type double. More...
class	DoubleDVector2Functor
class	DoubleDVectorFunctor
class	DoubleVector2DArray2Functor
class	DoubleVector2DArrayFunctor
class	DoubleVector3DArray2Functor
class	DoubleVector3DArrayFunctor
class	FGrid
	Unbounded dense grid storing floating point values of type float. More...
class	FGridExpression
class	FHomogenousCoordsAdapter
class	FIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type float. More...
class	FKabschAlgorithm
class	FMLRModel
	Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...
class	FMatrix
	Unbounded dense matrix holding floating point values of type float. More...
class	FMatrixColumn
class	FMatrixExpression
class	FMatrixRange
class	FMatrixRow
class	FMatrixSlice
class	FMatrixTranspose
class	FQuaternion
	General 4-component quaternion with component values of type float. More...
class	FQuaternionExpression
class	FQuaternionVectorAdapter
class	FRealQuaternion
	A memory-efficient pure-real quaternion with component values of type float. More...
class	FRegularSpatialGrid
	Unbounded dense regular grid storing floating point values of type float. More...
class	FRotationMatrix
class	FScalarGrid
	Immutable grid where all elements have the same value of type float. More...
class	FScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type float. More...
class	FScalarVector
	Memory-efficient immutable vector where all elements have the same value of type float. More...
class	FScalingMatrix
class	FTranslationMatrix
class	FUnitVector
	Memory-efficient immutable unit vector with element values of type float. More...
class	FVector
	Unbounded dense vector holding floating point values of type float. More...
class	FVectorBFGSMinimizer
	Fletcher's implementation of the BFGS method. More...
class	FVectorExpression
class	FVectorQuaternionAdapter
class	FVectorRange
class	FVectorSlice
class	FZeroGrid
	Immutable grid where all elements have the value zero of type float. More...
class	FZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type float. More...
class	FZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type float. More...
class	FloatFVector2Functor
class	FloatFVectorFunctor
class	FloatVector2FArray2Functor
class	FloatVector2FArrayFunctor
class	FloatVector3FArray2Functor
class	FloatVector3FArrayFunctor
class	LHomogenousCoordsAdapter
class	LIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type long. More...
class	LMatrix
	Unbounded dense matrix holding signed integers of type long. More...
class	LMatrixColumn
class	LMatrixExpression
class	LMatrixRange
class	LMatrixRow
class	LMatrixSlice
class	LMatrixTranspose
class	LQuaternion
	General 4-component quaternion with component values of type long. More...
class	LQuaternionExpression
class	LQuaternionVectorAdapter
class	LRealQuaternion
	A memory-efficient pure-real quaternion with component values of type long. More...
class	LRotationMatrix
class	LScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type long. More...
class	LScalarVector
	Memory-efficient immutable vector where all elements have the same value of type long. More...
class	LScalingMatrix
class	LTranslationMatrix
class	LUnitVector
	Memory-efficient immutable unit vector with element values of type long. More...
class	LVector
	Unbounded dense vector holding signed integers of type long. More...
class	LVectorExpression
class	LVectorQuaternionAdapter
class	LVectorRange
class	LVectorSlice
class	LZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type long. More...
class	LZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type long. More...
class	Lower
	Tag selecting the lower-triangular view (entries strictly above the diagonal read as zero) for Math.TriangularAdapter. More...
class	Matrix2D
	Bounded 2x2 matrix holding floating point values of type double. More...
class	Matrix2F
	Bounded 2x2 matrix holding floating point values of type float. More...
class	Matrix2L
	Bounded 2x2 matrix holding signed integers of type long. More...
class	Matrix2UL
	Bounded 2x2 matrix holding unsigned integers of type unsigned long. More...
class	Matrix3D
	Bounded 3x3 matrix holding floating point values of type double. More...
class	Matrix3F
	Bounded 3x3 matrix holding floating point values of type float. More...
class	Matrix3L
	Bounded 3x3 matrix holding signed integers of type long. More...
class	Matrix3UL
	Bounded 3x3 matrix holding unsigned integers of type unsigned long. More...
class	Matrix4D
	Bounded 4x4 matrix holding floating point values of type double. More...
class	Matrix4F
	Bounded 4x4 matrix holding floating point values of type float. More...
class	Matrix4L
	Bounded 4x4 matrix holding signed integers of type long. More...
class	Matrix4UL
	Bounded 4x4 matrix holding unsigned integers of type unsigned long. More...
class	Range
	Half-open index range \( [start, stop) \) used for slicing vector and matrix expressions. More...
class	Slice
	Index slice ( \( start, stride, size \)) used for strided slicing of vector and matrix expressions. More...
class	SparseDMatrix
	Unbounded sparse matrix holding floating point values of type double. More...
class	SparseDVector
	Unbounded sparse vector holding floating point values of type double. More...
class	SparseFMatrix
	Unbounded sparse matrix holding floating point values of type float. More...
class	SparseFVector
	Unbounded sparse vector holding floating point values of type float. More...
class	SparseLMatrix
	Unbounded sparse matrix holding signed integers of type long. More...
class	SparseLVector
	Unbounded sparse vector holding signed integers of type long. More...
class	SparseULMatrix
	Unbounded sparse matrix holding unsigned integers of type unsigned long. More...
class	SparseULVector
	Unbounded sparse vector holding unsigned integers of type unsigned long. More...
class	ULHomogenousCoordsAdapter
class	ULIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type unsigned long. More...
class	ULMatrix
	Unbounded dense matrix holding unsigned integers of type unsigned long. More...
class	ULMatrixColumn
class	ULMatrixExpression
class	ULMatrixRange
class	ULMatrixRow
class	ULMatrixSlice
class	ULMatrixTranspose
class	ULQuaternion
	General 4-component quaternion with component values of type unsigned long. More...
class	ULQuaternionExpression
class	ULQuaternionVectorAdapter
class	ULRealQuaternion
	A memory-efficient pure-real quaternion with component values of type unsigned long. More...
class	ULRotationMatrix
class	ULScalarMatrix
	Memory-efficient immutable matrix where all elements have the same value of type unsigned long. More...
class	ULScalarVector
	Memory-efficient immutable vector where all elements have the same value of type unsigned long. More...
class	ULScalingMatrix
class	ULTranslationMatrix
class	ULUnitVector
	Memory-efficient immutable unit vector with element values of type unsigned long. More...
class	ULVector
	Unbounded dense vector holding unsigned integers of type unsigned long. More...
class	ULVectorExpression
class	ULVectorQuaternionAdapter
class	ULVectorRange
class	ULVectorSlice
class	ULZeroMatrix
	Memory-efficient immutable matrix where all elements have the value zero of type unsigned long. More...
class	ULZeroVector
	Memory-efficient immutable vector where all elements have the value zero of type unsigned long. More...
class	UnitLower
	Tag selecting the unit-lower-triangular view (zero above the diagonal, one on the diagonal) for Math.TriangularAdapter. More...
class	UnitUpper
	Tag selecting the unit-upper-triangular view (zero below the diagonal, one on the diagonal) for Math.TriangularAdapter. More...
class	Upper
	Tag selecting the upper-triangular view (entries strictly below the diagonal read as zero) for Math.TriangularAdapter. More...
class	Vector2D
	Bounded 2 element vector holding floating point values of type double. More...
class	Vector2DArray
	Array storing vectors of type Math.Vector2D. More...
class	Vector2DArrayAlignmentCalculator
class	Vector2DArrayBFGSMinimizer
class	Vector2F
	Bounded 2 element vector holding floating point values of type float. More...
class	Vector2FArray
	Array storing vectors of type Math.Vector2F. More...
class	Vector2FArrayAlignmentCalculator
class	Vector2FArrayBFGSMinimizer
class	Vector2L
	Bounded 2 element vector holding signed integers of type long. More...
class	Vector2LArray
	Array storing vectors of type Math.Vector2L. More...
class	Vector2UL
	Bounded 2 element vector holding unsigned integers of type unsigned long. More...
class	Vector2ULArray
	Array storing vectors of type Math.Vector2UL. More...
class	Vector3D
	Bounded 3 element vector holding floating point values of type double. More...
class	Vector3DArray
	Array storing vectors of type Math.Vector3D. More...
class	Vector3DArrayAlignmentCalculator
class	Vector3DArrayBFGSMinimizer
class	Vector3F
	Bounded 3 element vector holding floating point values of type float. More...
class	Vector3FArray
	Array storing vectors of type Math.Vector3F. More...
class	Vector3FArrayAlignmentCalculator
class	Vector3FArrayBFGSMinimizer
class	Vector3L
	Bounded 3 element vector holding signed integers of type long. More...
class	Vector3LArray
	Array storing vectors of type Math.Vector3L. More...
class	Vector3UL
	Bounded 3 element vector holding unsigned integers of type unsigned long. More...
class	Vector3ULArray
	Array storing vectors of type Math.Vector3UL. More...
class	Vector4D
	Bounded 4 element vector holding floating point values of type double. More...
class	Vector4F
	Bounded 4 element vector holding floating point values of type float. More...
class	Vector4L
	Bounded 4 element vector holding signed integers of type long. More...
class	Vector4UL
	Bounded 4 element vector holding unsigned integers of type unsigned long. More...
class	Vector7D
	Bounded 7 element vector holding floating point values of type double. More...

Functions
float	angleCos (ConstDVectorExpression e1, ConstDVectorExpression e2, float sd, bool clamp=True)
	Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]). More...
float	angleCos (ConstFVectorExpression e1, ConstFVectorExpression e2, float sd, bool clamp=True)
	Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]). More...
int	angleCos (ConstLVectorExpression e1, ConstLVectorExpression e2, int sd, bool clamp=True)
	Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]). More...
int	angleCos (ConstULVectorExpression e1, ConstULVectorExpression e2, int sd, bool clamp=True)
	Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]). More...
bool	calcCentroid (Vector2DArray va, Vector2D ctr)
bool	calcCentroid (Vector2FArray va, Vector2F ctr)
bool	calcCentroid (Vector2LArray va, Vector2L ctr)
bool	calcCentroid (Vector2ULArray va, Vector2UL ctr)
bool	calcCentroid (Vector3DArray va, Vector3D ctr)
bool	calcCentroid (Vector3FArray va, Vector3F ctr)
bool	calcCentroid (Vector3LArray va, Vector3L ctr)
bool	calcCentroid (Vector3ULArray va, Vector3UL ctr)
float	calcRMSD (Vector2DArray va1, Vector2DArray va2)
float	calcRMSD (Vector2DArray va1, Vector2DArray va2, Matrix3D va1_xform)
float	calcRMSD (Vector2FArray va1, Vector2FArray va2)
float	calcRMSD (Vector2FArray va1, Vector2FArray va2, Matrix3F va1_xform)
int	calcRMSD (Vector2LArray va1, Vector2LArray va2)
int	calcRMSD (Vector2LArray va1, Vector2LArray va2, Matrix3L va1_xform)
int	calcRMSD (Vector2ULArray va1, Vector2ULArray va2)
int	calcRMSD (Vector2ULArray va1, Vector2ULArray va2, Matrix3UL va1_xform)
float	calcRMSD (Vector3DArray va1, Vector3DArray va2)
float	calcRMSD (Vector3DArray va1, Vector3DArray va2, Matrix4D va1_xform)
float	calcRMSD (Vector3FArray va1, Vector3FArray va2)
float	calcRMSD (Vector3FArray va1, Vector3FArray va2, Matrix4F va1_xform)
int	calcRMSD (Vector3LArray va1, Vector3LArray va2)
int	calcRMSD (Vector3LArray va1, Vector3LArray va2, Matrix4L va1_xform)
int	calcRMSD (Vector3ULArray va1, Vector3ULArray va2)
int	calcRMSD (Vector3ULArray va1, Vector3ULArray va2, Matrix4UL va1_xform)
ConstDMatrixColumn	column (ConstDMatrixExpression e, int i)
ConstFMatrixColumn	column (ConstFMatrixExpression e, int i)
ConstLMatrixColumn	column (ConstLMatrixExpression e, int i)
ConstULMatrixColumn	column (ConstULMatrixExpression e, int i)
DMatrixColumn	column (DMatrixExpression e, int i)
FMatrixColumn	column (FMatrixExpression e, int i)
LMatrixColumn	column (LMatrixExpression e, int i)
ULMatrixColumn	column (ULMatrixExpression e, int i)
ConstDGridExpression	conj (ConstDGridExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstDMatrixExpression	conj (ConstDMatrixExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstDQuaternionExpression	conj (ConstDQuaternionExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstDVectorExpression	conj (ConstDVectorExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstFGridExpression	conj (ConstFGridExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstFMatrixExpression	conj (ConstFMatrixExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstFQuaternionExpression	conj (ConstFQuaternionExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstFVectorExpression	conj (ConstFVectorExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstLMatrixExpression	conj (ConstLMatrixExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstLQuaternionExpression	conj (ConstLQuaternionExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstLVectorExpression	conj (ConstLVectorExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstULMatrixExpression	conj (ConstULMatrixExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstULQuaternionExpression	conj (ConstULQuaternionExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstULVectorExpression	conj (ConstULVectorExpression e)
	Returns the element-wise complex conjugate of the vector expression e (identity for real-valued vectors). More...
ConstDMatrixExpression	cross (ConstDVectorExpression e)
	Returns the cross-product (skew-symmetric) matrix corresponding to the 3-vector expression e (such that cross(e) * v == crossProd(e, v)). More...
ConstFMatrixExpression	cross (ConstFVectorExpression e)
	Returns the cross-product (skew-symmetric) matrix corresponding to the 3-vector expression e (such that cross(e) * v == crossProd(e, v)). More...
ConstLMatrixExpression	cross (ConstLVectorExpression e)
	Returns the cross-product (skew-symmetric) matrix corresponding to the 3-vector expression e (such that cross(e) * v == crossProd(e, v)). More...
ConstULMatrixExpression	cross (ConstULVectorExpression e)
	Returns the cross-product (skew-symmetric) matrix corresponding to the 3-vector expression e (such that cross(e) * v == crossProd(e, v)). More...
ConstDVectorExpression	crossProd (ConstDVectorExpression e1, ConstDVectorExpression e2)
	Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node. More...
ConstFVectorExpression	crossProd (ConstFVectorExpression e1, ConstFVectorExpression e2)
	Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node. More...
ConstLVectorExpression	crossProd (ConstLVectorExpression e1, ConstLVectorExpression e2)
	Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node. More...
ConstULVectorExpression	crossProd (ConstULVectorExpression e1, ConstULVectorExpression e2)
	Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node. More...
float	det (ConstDMatrixExpression e)
	Returns the determinant of the matrix expression e. More...
float	det (ConstFMatrixExpression e)
	Returns the determinant of the matrix expression e. More...
int	det (ConstLMatrixExpression e)
	Returns the determinant of the matrix expression e. More...
int	det (ConstULMatrixExpression e)
	Returns the determinant of the matrix expression e. More...
ConstDMatrixExpression	diag (ConstDVectorExpression e)
	Returns a diagonal matrix whose diagonal entries are the components of the vector expression e. More...
ConstFMatrixExpression	diag (ConstFVectorExpression e)
	Returns a diagonal matrix whose diagonal entries are the components of the vector expression e. More...
ConstLMatrixExpression	diag (ConstLVectorExpression e)
	Returns a diagonal matrix whose diagonal entries are the components of the vector expression e. More...
ConstULMatrixExpression	diag (ConstULVectorExpression e)
	Returns a diagonal matrix whose diagonal entries are the components of the vector expression e. More...
ConstDGridExpression	elemDiv (ConstDGridExpression e1, ConstDGridExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstDMatrixExpression	elemDiv (ConstDMatrixExpression e1, ConstDMatrixExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstDQuaternionExpression	elemDiv (ConstDQuaternionExpression e1, ConstDQuaternionExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstDVectorExpression	elemDiv (ConstDVectorExpression e1, ConstDVectorExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstFGridExpression	elemDiv (ConstFGridExpression e1, ConstFGridExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstFMatrixExpression	elemDiv (ConstFMatrixExpression e1, ConstFMatrixExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstFQuaternionExpression	elemDiv (ConstFQuaternionExpression e1, ConstFQuaternionExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstFVectorExpression	elemDiv (ConstFVectorExpression e1, ConstFVectorExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstLMatrixExpression	elemDiv (ConstLMatrixExpression e1, ConstLMatrixExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstLQuaternionExpression	elemDiv (ConstLQuaternionExpression e1, ConstLQuaternionExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstLVectorExpression	elemDiv (ConstLVectorExpression e1, ConstLVectorExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstULMatrixExpression	elemDiv (ConstULMatrixExpression e1, ConstULMatrixExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstULQuaternionExpression	elemDiv (ConstULQuaternionExpression e1, ConstULQuaternionExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstULVectorExpression	elemDiv (ConstULVectorExpression e1, ConstULVectorExpression e2)
	Returns the element-wise quotient of the vector expressions e1 and e2. More...
ConstDGridExpression	elemProd (ConstDGridExpression e1, ConstDGridExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstDMatrixExpression	elemProd (ConstDMatrixExpression e1, ConstDMatrixExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstDQuaternionExpression	elemProd (ConstDQuaternionExpression e1, ConstDQuaternionExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstDVectorExpression	elemProd (ConstDVectorExpression e1, ConstDVectorExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstFGridExpression	elemProd (ConstFGridExpression e1, ConstFGridExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstFMatrixExpression	elemProd (ConstFMatrixExpression e1, ConstFMatrixExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstFQuaternionExpression	elemProd (ConstFQuaternionExpression e1, ConstFQuaternionExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstFVectorExpression	elemProd (ConstFVectorExpression e1, ConstFVectorExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstLMatrixExpression	elemProd (ConstLMatrixExpression e1, ConstLMatrixExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstLQuaternionExpression	elemProd (ConstLQuaternionExpression e1, ConstLQuaternionExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstLVectorExpression	elemProd (ConstLVectorExpression e1, ConstLVectorExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstULMatrixExpression	elemProd (ConstULMatrixExpression e1, ConstULMatrixExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstULQuaternionExpression	elemProd (ConstULQuaternionExpression e1, ConstULQuaternionExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
ConstULVectorExpression	elemProd (ConstULVectorExpression e1, ConstULVectorExpression e2)
	Returns the element-wise product (Hadamard product) of the vector expressions e1 and e2. More...
bool	equals (ConstDGridExpression e1, ConstDGridExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstDMatrixExpression e1, ConstDMatrixExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstDQuaternionExpression e1, ConstDQuaternionExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstDVectorExpression e1, ConstDVectorExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFGridExpression e1, ConstFGridExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFMatrixExpression e1, ConstFMatrixExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFQuaternionExpression e1, ConstFQuaternionExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFVectorExpression e1, ConstFVectorExpression e2, float eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstLMatrixExpression e1, ConstLMatrixExpression e2, int eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstLQuaternionExpression e1, ConstLQuaternionExpression e2, int eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstLVectorExpression e1, ConstLVectorExpression e2, int eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstULMatrixExpression e1, ConstULMatrixExpression e2, int eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstULQuaternionExpression e1, ConstULQuaternionExpression e2, int eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstULVectorExpression e1, ConstULVectorExpression e2, int eps)
	Tells whether the vector expressions e1 and e2 agree element-wise within the absolute tolerance eps. More...
int	factorial (int n)
	Computes the factorial \( n! \) of the non-negative integer n. More...
float	gammaQ (float a, float x)
	Computes the incomplete gamma function \( Q(a, x) = 1 - P(a, x) \) (see [NRIC] for details). More...
float	generalizedBell (float x, float a, float b, float c)
	Computes the generalized bell function \( Bell(x) = \frac{1}{1 + |\frac{x-c}{a}|^{2b}} \) at x. More...
ConstDGridExpression	herm (ConstDGridExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstDMatrixExpression	herm (ConstDMatrixExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstDVectorExpression	herm (ConstDVectorExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstFGridExpression	herm (ConstFGridExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstFMatrixExpression	herm (ConstFMatrixExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstFVectorExpression	herm (ConstFVectorExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstLMatrixExpression	herm (ConstLMatrixExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstLVectorExpression	herm (ConstLVectorExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstULMatrixExpression	herm (ConstULMatrixExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstULVectorExpression	herm (ConstULVectorExpression e)
	Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors). More...
ConstDHomogenousCoordsAdapter	homog (ConstDVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
ConstFHomogenousCoordsAdapter	homog (ConstFVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
ConstLHomogenousCoordsAdapter	homog (ConstLVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
ConstULHomogenousCoordsAdapter	homog (ConstULVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
DHomogenousCoordsAdapter	homog (DVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
FHomogenousCoordsAdapter	homog (FVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
LHomogenousCoordsAdapter	homog (LVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
ULHomogenousCoordsAdapter	homog (ULVectorExpression e)
	Creates a constant Math.HomogenousCoordsAdapter view of the vector expression e. More...
ConstDGridExpression	imag (ConstDGridExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstDMatrixExpression	imag (ConstDMatrixExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstDVectorExpression	imag (ConstDVectorExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstFGridExpression	imag (ConstFGridExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstFMatrixExpression	imag (ConstFMatrixExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstFVectorExpression	imag (ConstFVectorExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstLMatrixExpression	imag (ConstLMatrixExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstLVectorExpression	imag (ConstLVectorExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstULMatrixExpression	imag (ConstULMatrixExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
ConstULVectorExpression	imag (ConstULVectorExpression e)
	Returns the element-wise imaginary part of the vector expression e. More...
float	innerProd (ConstDVectorExpression e1, ConstDVectorExpression e2)
	Returns the inner (dot) product of the vector expressions e1 and e2. More...
float	innerProd (ConstFVectorExpression e1, ConstFVectorExpression e2)
	Returns the inner (dot) product of the vector expressions e1 and e2. More...
int	innerProd (ConstLVectorExpression e1, ConstLVectorExpression e2)
	Returns the inner (dot) product of the vector expressions e1 and e2. More...
int	innerProd (ConstULVectorExpression e1, ConstULVectorExpression e2)
	Returns the inner (dot) product of the vector expressions e1 and e2. More...
float	interpolateTrilinear (DRegularSpatialGrid grid, Vector3D pos, bool local_pos)
	Returns the trilinearly-interpolated value of grid at pos. More...
float	interpolateTrilinear (FRegularSpatialGrid grid, Vector3F pos, bool local_pos)
	Returns the trilinearly-interpolated value of grid at pos. More...
ConstDQuaternionExpression	inv (ConstDQuaternionExpression e)
	Returns the multiplicative inverse of the quaternion expression e ( \( \overline{e} / |e|^2 \)). More...
ConstFQuaternionExpression	inv (ConstFQuaternionExpression e)
	Returns the multiplicative inverse of the quaternion expression e ( \( \overline{e} / |e|^2 \)). More...
ConstLQuaternionExpression	inv (ConstLQuaternionExpression e)
	Returns the multiplicative inverse of the quaternion expression e ( \( \overline{e} / |e|^2 \)). More...
ConstULQuaternionExpression	inv (ConstULQuaternionExpression e)
	Returns the multiplicative inverse of the quaternion expression e ( \( \overline{e} / |e|^2 \)). More...
bool	invert (ConstDMatrixExpression e, DMatrixExpression c)
	Computes the inverse of the matrix expression e and stores it in c. More...
bool	invert (ConstFMatrixExpression e, FMatrixExpression c)
	Computes the inverse of the matrix expression e and stores it in c. More...
bool	invert (ConstLMatrixExpression e, LMatrixExpression c)
	Computes the inverse of the matrix expression e and stores it in c. More...
bool	invert (ConstULMatrixExpression e, ULMatrixExpression c)
	Computes the inverse of the matrix expression e and stores it in c. More...
bool	invert (DMatrixExpression c)
	Computes the inverse of the matrix container c in place. More...
bool	invert (FMatrixExpression c)
	Computes the inverse of the matrix container c in place. More...
bool	invert (LMatrixExpression c)
	Computes the inverse of the matrix container c in place. More...
bool	invert (ULMatrixExpression c)
	Computes the inverse of the matrix container c in place. More...
bool	jacobiDiagonalize (DMatrixExpression a, DVectorExpression d, DMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...
bool	jacobiDiagonalize (FMatrixExpression a, FVectorExpression d, FMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...
bool	jacobiDiagonalize (LMatrixExpression a, LVectorExpression d, LMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...
bool	jacobiDiagonalize (ULMatrixExpression a, ULVectorExpression d, ULMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...
float	length (ConstDVectorExpression e)
	Returns the length (L2 norm) of the vector expression e (alias of norm2()). More...
float	length (ConstFVectorExpression e)
	Returns the length (L2 norm) of the vector expression e (alias of norm2()). More...
int	length (ConstLVectorExpression e)
	Returns the length (L2 norm) of the vector expression e (alias of norm2()). More...
int	length (ConstULVectorExpression e)
	Returns the length (L2 norm) of the vector expression e (alias of norm2()). More...
float	lnGamma (float z)
	Computes \( \ln[\Gamma(z)] \) for \( z > 0 \). More...
int	luDecompose (DMatrixExpression e)
	Computes an in-place LU decomposition of the matrix e without partial pivoting. More...
int	luDecompose (DMatrixExpression e, ULVectorExpression pv)
int	luDecompose (FMatrixExpression e)
	Computes an in-place LU decomposition of the matrix e without partial pivoting. More...
int	luDecompose (FMatrixExpression e, ULVectorExpression pv)
int	luDecompose (LMatrixExpression e)
	Computes an in-place LU decomposition of the matrix e without partial pivoting. More...
int	luDecompose (LMatrixExpression e, ULVectorExpression pv)
int	luDecompose (ULMatrixExpression e)
	Computes an in-place LU decomposition of the matrix e without partial pivoting. More...
int	luDecompose (ULMatrixExpression e, ULVectorExpression pv)
bool	luSubstitute (ConstDMatrixExpression e, DVectorExpression b)
bool	luSubstitute (ConstDMatrixExpression e, ConstULVectorExpression pv, DVectorExpression b)
bool	luSubstitute (ConstDMatrixExpression e, DMatrixExpression b)
bool	luSubstitute (ConstDMatrixExpression e, ConstULVectorExpression pv, DMatrixExpression b)
bool	luSubstitute (ConstFMatrixExpression e, FVectorExpression b)
bool	luSubstitute (ConstFMatrixExpression e, ConstULVectorExpression pv, FVectorExpression b)
bool	luSubstitute (ConstFMatrixExpression e, FMatrixExpression b)
bool	luSubstitute (ConstFMatrixExpression e, ConstULVectorExpression pv, FMatrixExpression b)
bool	luSubstitute (ConstLMatrixExpression e, LVectorExpression b)
bool	luSubstitute (ConstLMatrixExpression e, ConstULVectorExpression pv, LVectorExpression b)
bool	luSubstitute (ConstLMatrixExpression e, LMatrixExpression b)
bool	luSubstitute (ConstLMatrixExpression e, ConstULVectorExpression pv, LMatrixExpression b)
bool	luSubstitute (ConstULMatrixExpression e, ULVectorExpression b)
bool	luSubstitute (ConstULMatrixExpression e, ConstULVectorExpression pv, ULVectorExpression b)
bool	luSubstitute (ConstULMatrixExpression e, ULMatrixExpression b)
bool	luSubstitute (ConstULMatrixExpression e, ConstULVectorExpression pv, ULMatrixExpression b)
float	norm1 (ConstDMatrixExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
float	norm1 (ConstDVectorExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
float	norm1 (ConstFMatrixExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
float	norm1 (ConstFVectorExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
int	norm1 (ConstLMatrixExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
int	norm1 (ConstLVectorExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
int	norm1 (ConstULMatrixExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
int	norm1 (ConstULVectorExpression e)
	Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)). More...
float	norm2 (ConstDQuaternionExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
float	norm2 (ConstDVectorExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
float	norm2 (ConstFQuaternionExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
float	norm2 (ConstFVectorExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
int	norm2 (ConstLQuaternionExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
int	norm2 (ConstLVectorExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
int	norm2 (ConstULQuaternionExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
int	norm2 (ConstULVectorExpression e)
	Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)). More...
float	norm (ConstDQuaternionExpression e)
	Returns the norm (Euclidean length) of the quaternion expression e. More...
float	norm (ConstFQuaternionExpression e)
	Returns the norm (Euclidean length) of the quaternion expression e. More...
int	norm (ConstLQuaternionExpression e)
	Returns the norm (Euclidean length) of the quaternion expression e. More...
int	norm (ConstULQuaternionExpression e)
	Returns the norm (Euclidean length) of the quaternion expression e. More...
float	normFrob (ConstDMatrixExpression e)
	Returns the Frobenius norm of the matrix expression e ( \( \sqrt{\sum_{i, j} |e(i, j)|^2} \)). More...
float	normFrob (ConstFMatrixExpression e)
	Returns the Frobenius norm of the matrix expression e ( \( \sqrt{\sum_{i, j} |e(i, j)|^2} \)). More...
int	normFrob (ConstLMatrixExpression e)
	Returns the Frobenius norm of the matrix expression e ( \( \sqrt{\sum_{i, j} |e(i, j)|^2} \)). More...
int	normFrob (ConstULMatrixExpression e)
	Returns the Frobenius norm of the matrix expression e ( \( \sqrt{\sum_{i, j} |e(i, j)|^2} \)). More...
float	normInf (ConstDMatrixExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
float	normInf (ConstDVectorExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
float	normInf (ConstFMatrixExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
float	normInf (ConstFVectorExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
int	normInf (ConstLMatrixExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
int	normInf (ConstLVectorExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
int	normInf (ConstULMatrixExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
int	normInf (ConstULVectorExpression e)
	Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)). More...
int	normInfIndex (ConstDVectorExpression e)
	Returns the (first) index at which the vector expression e attains its L∞ norm. More...
int	normInfIndex (ConstFVectorExpression e)
	Returns the (first) index at which the vector expression e attains its L∞ norm. More...
int	normInfIndex (ConstLVectorExpression e)
	Returns the (first) index at which the vector expression e attains its L∞ norm. More...
int	normInfIndex (ConstULVectorExpression e)
	Returns the (first) index at which the vector expression e attains its L∞ norm. More...
ConstDMatrixExpression	outerProd (ConstDVectorExpression e1, ConstDVectorExpression e2)
	Returns the outer product of the vector expressions e1 and e2 as a matrix expression \( e_1 \cdot e_2^T \). More...
ConstFMatrixExpression	outerProd (ConstFVectorExpression e1, ConstFVectorExpression e2)
	Returns the outer product of the vector expressions e1 and e2 as a matrix expression \( e_1 \cdot e_2^T \). More...
ConstLMatrixExpression	outerProd (ConstLVectorExpression e1, ConstLVectorExpression e2)
	Returns the outer product of the vector expressions e1 and e2 as a matrix expression \( e_1 \cdot e_2^T \). More...
ConstULMatrixExpression	outerProd (ConstULVectorExpression e1, ConstULVectorExpression e2)
	Returns the outer product of the vector expressions e1 and e2 as a matrix expression \( e_1 \cdot e_2^T \). More...
int	prime (int i)
ConstDVectorExpression	prod (ConstDMatrixExpression e1, ConstDVectorExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
DVectorExpression	prod (ConstDMatrixExpression e1, ConstDVectorExpression e2, DVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstDMatrixExpression	prod (ConstDMatrixExpression e1, ConstDMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
DMatrixExpression	prod (ConstDMatrixExpression e1, ConstDMatrixExpression e2, DMatrixExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstDVectorExpression	prod (ConstDVectorExpression e1, ConstDMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
DVectorExpression	prod (ConstDVectorExpression e1, ConstDMatrixExpression e2, DVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstFVectorExpression	prod (ConstFMatrixExpression e1, ConstFVectorExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
FVectorExpression	prod (ConstFMatrixExpression e1, ConstFVectorExpression e2, FVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstFMatrixExpression	prod (ConstFMatrixExpression e1, ConstFMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
FMatrixExpression	prod (ConstFMatrixExpression e1, ConstFMatrixExpression e2, FMatrixExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstFVectorExpression	prod (ConstFVectorExpression e1, ConstFMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
FVectorExpression	prod (ConstFVectorExpression e1, ConstFMatrixExpression e2, FVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstLVectorExpression	prod (ConstLMatrixExpression e1, ConstLVectorExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
LVectorExpression	prod (ConstLMatrixExpression e1, ConstLVectorExpression e2, LVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstLMatrixExpression	prod (ConstLMatrixExpression e1, ConstLMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
LMatrixExpression	prod (ConstLMatrixExpression e1, ConstLMatrixExpression e2, LMatrixExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstLVectorExpression	prod (ConstLVectorExpression e1, ConstLMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
LVectorExpression	prod (ConstLVectorExpression e1, ConstLMatrixExpression e2, LVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstULVectorExpression	prod (ConstULMatrixExpression e1, ConstULVectorExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
ULVectorExpression	prod (ConstULMatrixExpression e1, ConstULVectorExpression e2, ULVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstULMatrixExpression	prod (ConstULMatrixExpression e1, ConstULMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
ULMatrixExpression	prod (ConstULMatrixExpression e1, ConstULMatrixExpression e2, ULMatrixExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
ConstULVectorExpression	prod (ConstULVectorExpression e1, ConstULMatrixExpression e2)
	Returns the matrix-matrix product \( e_1 \cdot e_2 \) as a matrix expression (named-function form of operator*). More...
ULVectorExpression	prod (ConstULVectorExpression e1, ConstULMatrixExpression e2, ULVectorExpression c)
	Computes the matrix-matrix product \( e_1 \cdot e_2 \) and stores it in c. More...
float	pythag (float a, float b)
	Computes \( \sqrt{a^2 + b^2} \) without destructive underflow or overflow. More...
ConstDVectorQuaternionAdapter	quat (ConstDVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
ConstFVectorQuaternionAdapter	quat (ConstFVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
ConstLVectorQuaternionAdapter	quat (ConstLVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
ConstULVectorQuaternionAdapter	quat (ConstULVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
DVectorQuaternionAdapter	quat (DVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
FVectorQuaternionAdapter	quat (FVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
LVectorQuaternionAdapter	quat (LVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
ULVectorQuaternionAdapter	quat (ULVectorExpression e)
	Creates a constant Math.VectorQuaternionAdapter view of the 4-element vector expression e. More...
FRealQuaternion	quat (float t)
	Constructs a Math.RealQuaternion from the scalar t (its real component). More...
FQuaternion	quat (float t1, float t2)
	Constructs a Math.Quaternion from two scalar components t1 and t2 (C1, C2) — remaining components are zero. More...
FQuaternion	quat (float t1, float t2, float t3)
	Constructs a Math.Quaternion from three scalar components (C1, C2, C3) — C4 is zero. More...
FQuaternion	quat (float t1, float t2, float t3, float t4)
	Constructs a Math.Quaternion from four scalar components (C1, C2, C3, C4). More...
LRealQuaternion	quat (int t)
	Constructs a Math.RealQuaternion from the scalar t (its real component). More...
LQuaternion	quat (int t1, int t2)
	Constructs a Math.Quaternion from two scalar components t1 and t2 (C1, C2) — remaining components are zero. More...
LQuaternion	quat (int t1, int t2, int t3)
	Constructs a Math.Quaternion from three scalar components (C1, C2, C3) — C4 is zero. More...
LQuaternion	quat (int t1, int t2, int t3, int t4)
	Constructs a Math.Quaternion from four scalar components (C1, C2, C3, C4). More...
ConstDMatrixRange	range (ConstDMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
ConstDMatrixRange	range (ConstDMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
ConstDVectorRange	range (ConstDVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
ConstDVectorRange	range (ConstDVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
ConstFMatrixRange	range (ConstFMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
ConstFMatrixRange	range (ConstFMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
ConstFVectorRange	range (ConstFVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
ConstFVectorRange	range (ConstFVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
ConstLMatrixRange	range (ConstLMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
ConstLMatrixRange	range (ConstLMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
ConstLVectorRange	range (ConstLVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
ConstLVectorRange	range (ConstLVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
ConstULMatrixRange	range (ConstULMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
ConstULMatrixRange	range (ConstULMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
ConstULVectorRange	range (ConstULVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
ConstULVectorRange	range (ConstULVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
DMatrixRange	range (DMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
DMatrixRange	range (DMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
DVectorRange	range (DVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
DVectorRange	range (DVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
FMatrixRange	range (FMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
FMatrixRange	range (FMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
FVectorRange	range (FVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
FVectorRange	range (FVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
LMatrixRange	range (LMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
LMatrixRange	range (LMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
LVectorRange	range (LVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
LVectorRange	range (LVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
ULMatrixRange	range (ULMatrixExpression e, Range r1, Range r2)
	Returns a matrix range proxy viewing rows in r1 and columns in r2 of e. More...
ULMatrixRange	range (ULMatrixExpression e, int start1, int stop1, int start2, int stop2)
	Returns a matrix range proxy viewing rows [start1, stop1) and columns [start2, stop2) of e. More...
ULVectorRange	range (ULVectorExpression e, Range r)
	Creates a constant Math.VectorRange view of the subrange r of the vector expression e. More...
ULVectorRange	range (ULVectorExpression e, int start, int stop)
	Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e. More...
Range	range (int start, int stop)
	Convenience factory for Math.Range with std::size_t indices. More...
ConstDGridExpression	real (ConstDGridExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstDMatrixExpression	real (ConstDMatrixExpression e)
	Returns the element-wise real part of the vector expression e. More...
float	real (ConstDQuaternionExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstDVectorExpression	real (ConstDVectorExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstFGridExpression	real (ConstFGridExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstFMatrixExpression	real (ConstFMatrixExpression e)
	Returns the element-wise real part of the vector expression e. More...
float	real (ConstFQuaternionExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstFVectorExpression	real (ConstFVectorExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstLMatrixExpression	real (ConstLMatrixExpression e)
	Returns the element-wise real part of the vector expression e. More...
int	real (ConstLQuaternionExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstLVectorExpression	real (ConstLVectorExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstULMatrixExpression	real (ConstULMatrixExpression e)
	Returns the element-wise real part of the vector expression e. More...
int	real (ConstULQuaternionExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstULVectorExpression	real (ConstULVectorExpression e)
	Returns the element-wise real part of the vector expression e. More...
ConstDVectorExpression	rotate (ConstDQuaternionExpression e1, ConstDVectorExpression e2)
	Rotates the vector expression e2 by the quaternion expression e1. More...
ConstFVectorExpression	rotate (ConstFQuaternionExpression e1, ConstFVectorExpression e2)
	Rotates the vector expression e2 by the quaternion expression e1. More...
ConstLVectorExpression	rotate (ConstLQuaternionExpression e1, ConstLVectorExpression e2)
	Rotates the vector expression e2 by the quaternion expression e1. More...
ConstULVectorExpression	rotate (ConstULQuaternionExpression e1, ConstULVectorExpression e2)
	Rotates the vector expression e2 by the quaternion expression e1. More...
ConstDMatrixRow	row (ConstDMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
ConstFMatrixRow	row (ConstFMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
ConstLMatrixRow	row (ConstLMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
ConstULMatrixRow	row (ConstULMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
DMatrixRow	row (DMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
FMatrixRow	row (FMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
LMatrixRow	row (LMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
ULMatrixRow	row (ULMatrixExpression e, int i)
	Returns a row proxy for row i of the matrix expression e. More...
float	sign (float a, float b)
	Returns the magnitude of parameter a times the sign of parameter b. More...
ConstDMatrixSlice	slice (ConstDMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
ConstDMatrixSlice	slice (ConstDMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
ConstDVectorSlice	slice (ConstDVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
ConstDVectorSlice	slice (ConstDVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
ConstFMatrixSlice	slice (ConstFMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
ConstFMatrixSlice	slice (ConstFMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
ConstFVectorSlice	slice (ConstFVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
ConstFVectorSlice	slice (ConstFVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
ConstLMatrixSlice	slice (ConstLMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
ConstLMatrixSlice	slice (ConstLMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
ConstLVectorSlice	slice (ConstLVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
ConstLVectorSlice	slice (ConstLVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
ConstULMatrixSlice	slice (ConstULMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
ConstULMatrixSlice	slice (ConstULMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
ConstULVectorSlice	slice (ConstULVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
ConstULVectorSlice	slice (ConstULVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
DMatrixSlice	slice (DMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
DMatrixSlice	slice (DMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
DVectorSlice	slice (DVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
DVectorSlice	slice (DVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
FMatrixSlice	slice (FMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
FMatrixSlice	slice (FMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
FVectorSlice	slice (FVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
FVectorSlice	slice (FVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
LMatrixSlice	slice (LMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
LMatrixSlice	slice (LMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
LVectorSlice	slice (LVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
LVectorSlice	slice (LVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
ULMatrixSlice	slice (ULMatrixExpression e, Slice s1, Slice s2)
	Returns a matrix slice proxy viewing the strided rectangular slice (s1, s2) of e. More...
ULMatrixSlice	slice (ULMatrixExpression e, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a matrix slice proxy specified by row (start1, stride1, size1) and column (start2, stride2, size2). More...
ULVectorSlice	slice (ULVectorExpression e, Slice s)
	Creates a constant Math.VectorSlice view of the slice s of the vector expression e. More...
ULVectorSlice	slice (ULVectorExpression e, int start, int stride, int size)
	Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e. More...
Slice	slice (int start, int stride, int size)
	Convenience factory for Math.Slice with std::size_t indices and std::ptrdiff_t stride. More...
bool	solveLower (ConstDMatrixExpression e1, DVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstDMatrixExpression e1, DMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstFMatrixExpression e1, FVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstFMatrixExpression e1, FMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstLMatrixExpression e1, LVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstLMatrixExpression e1, LMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstULMatrixExpression e1, ULVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveLower (ConstULMatrixExpression e1, ULMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a lower-triangular matrix. More...
bool	solveUnitLower (ConstDMatrixExpression e1, DVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstDMatrixExpression e1, DMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstFMatrixExpression e1, FVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstFMatrixExpression e1, FMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstLMatrixExpression e1, LVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstLMatrixExpression e1, LMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstULMatrixExpression e1, ULVectorExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstULMatrixExpression e1, ULMatrixExpression e2)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where e1 is a unit lower-triangular matrix. More...
bool	solveUnitUpper (ConstDMatrixExpression e1, DVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstDMatrixExpression e1, DMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstFMatrixExpression e1, FVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstFMatrixExpression e1, FMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstLMatrixExpression e1, LVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstLMatrixExpression e1, LMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstULMatrixExpression e1, ULVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstULMatrixExpression e1, ULMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is a unit upper-triangular matrix. More...
bool	solveUpper (ConstDMatrixExpression e1, DVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstDMatrixExpression e1, DMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstFMatrixExpression e1, FVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstFMatrixExpression e1, FMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstLMatrixExpression e1, LVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstLMatrixExpression e1, LMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstULMatrixExpression e1, ULVectorExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
bool	solveUpper (ConstULMatrixExpression e1, ULMatrixExpression e2)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where e1 is an upper-triangular matrix. More...
float	sum (ConstDGridExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstDMatrixExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstDQuaternionExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstDVectorExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstFGridExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstFMatrixExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstFQuaternionExpression e)
	Returns the sum of all elements of the vector expression e. More...
float	sum (ConstFVectorExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (ConstLMatrixExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (ConstLQuaternionExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (ConstLVectorExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (ConstULMatrixExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (ConstULQuaternionExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (ConstULVectorExpression e)
	Returns the sum of all elements of the vector expression e. More...
int	sum (object e)
	Returns the sum of all elements of the vector expression e. More...
bool	svDecompose (DMatrixExpression a, DVectorExpression w, DMatrixExpression v, int max_iter=0)
	Computes the Singular Value Decomposition [WSVD] \( A = UWV^T \) of a \( M \times N \)-dimensional matrix a. More...
bool	svDecompose (FMatrixExpression a, FVectorExpression w, FMatrixExpression v, int max_iter=0)
	Computes the Singular Value Decomposition [WSVD] \( A = UWV^T \) of a \( M \times N \)-dimensional matrix a. More...
bool	svDecompose (LMatrixExpression a, LVectorExpression w, LMatrixExpression v, int max_iter=0)
	Computes the Singular Value Decomposition [WSVD] \( A = UWV^T \) of a \( M \times N \)-dimensional matrix a. More...
bool	svDecompose (ULMatrixExpression a, ULVectorExpression w, ULMatrixExpression v, int max_iter=0)
	Computes the Singular Value Decomposition [WSVD] \( A = UWV^T \) of a \( M \times N \)-dimensional matrix a. More...
None	svSubstitute (ConstDMatrixExpression u, ConstDVectorExpression w, ConstDMatrixExpression v, ConstDVectorExpression b, DVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstDMatrixExpression u, ConstDVectorExpression w, ConstDMatrixExpression v, ConstDMatrixExpression b, DMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstFMatrixExpression u, ConstFVectorExpression w, ConstFMatrixExpression v, ConstFVectorExpression b, FVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstFMatrixExpression u, ConstFVectorExpression w, ConstFMatrixExpression v, ConstFMatrixExpression b, FMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstLMatrixExpression u, ConstLVectorExpression w, ConstLMatrixExpression v, ConstLVectorExpression b, LVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstLMatrixExpression u, ConstLVectorExpression w, ConstLMatrixExpression v, ConstLMatrixExpression b, LMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstULMatrixExpression u, ConstULVectorExpression w, ConstULMatrixExpression v, ConstULVectorExpression b, ULVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
None	svSubstitute (ConstULMatrixExpression u, ConstULVectorExpression w, ConstULMatrixExpression v, ConstULMatrixExpression b, ULMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...
float	trace (ConstDMatrixExpression e)
	Returns the trace (sum of diagonal elements) of the matrix expression e. More...
float	trace (ConstFMatrixExpression e)
	Returns the trace (sum of diagonal elements) of the matrix expression e. More...
int	trace (ConstLMatrixExpression e)
	Returns the trace (sum of diagonal elements) of the matrix expression e. More...
int	trace (ConstULMatrixExpression e)
	Returns the trace (sum of diagonal elements) of the matrix expression e. More...
ConstDMatrixTranspose	trans (ConstDMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
ConstFMatrixTranspose	trans (ConstFMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
ConstLMatrixTranspose	trans (ConstLMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
ConstULMatrixTranspose	trans (ConstULMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
DMatrixTranspose	trans (DMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
FMatrixTranspose	trans (FMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
LMatrixTranspose	trans (LMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
ULMatrixTranspose	trans (ULMatrixExpression e)
	Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry). More...
None	transform (Vector2DArray va, Matrix2D xform)
None	transform (Vector2DArray va, Matrix3D xform)
None	transform (Vector2FArray va, Matrix2F xform)
None	transform (Vector2FArray va, Matrix3F xform)
None	transform (Vector2LArray va, Matrix2L xform)
None	transform (Vector2LArray va, Matrix3L xform)
None	transform (Vector2ULArray va, Matrix2UL xform)
None	transform (Vector2ULArray va, Matrix3UL xform)
None	transform (Vector3DArray va, Matrix3D xform)
None	transform (Vector3DArray va, Matrix4D xform)
None	transform (Vector3FArray va, Matrix3F xform)
None	transform (Vector3FArray va, Matrix4F xform)
None	transform (Vector3LArray va, Matrix3L xform)
None	transform (Vector3LArray va, Matrix4L xform)
None	transform (Vector3ULArray va, Matrix3UL xform)
None	transform (Vector3ULArray va, Matrix4UL xform)
ConstUpperTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, Upper type)
ConstUnitUpperTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, UnitUpper type)
ConstLowerTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, Lower type)
ConstUnitLowerTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, UnitLower type)
ConstUpperTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, Upper type)
ConstUnitUpperTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, UnitUpper type)
ConstLowerTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, Lower type)
ConstUnitLowerTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, UnitLower type)
ConstUpperTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, Upper type)
ConstUnitUpperTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, UnitUpper type)
ConstLowerTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, Lower type)
ConstUnitLowerTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, UnitLower type)
ConstUpperTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, Upper type)
ConstUnitUpperTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, UnitUpper type)
ConstLowerTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, Lower type)
ConstUnitLowerTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, UnitLower type)
ConstDQuaternionExpression	unreal (ConstDQuaternionExpression e)
	Returns the unreal (pure-quaternion) part of the quaternion expression e (with C1 zeroed out). More...
ConstFQuaternionExpression	unreal (ConstFQuaternionExpression e)
	Returns the unreal (pure-quaternion) part of the quaternion expression e (with C1 zeroed out). More...
ConstLQuaternionExpression	unreal (ConstLQuaternionExpression e)
	Returns the unreal (pure-quaternion) part of the quaternion expression e (with C1 zeroed out). More...
ConstULQuaternionExpression	unreal (ConstULQuaternionExpression e)
	Returns the unreal (pure-quaternion) part of the quaternion expression e (with C1 zeroed out). More...
ConstDQuaternionVectorAdapter	vec (ConstDQuaternionExpression e)
	Creates a constant Math.QuaternionVectorAdapter view of the quaternion expression e. More...
ConstFQuaternionVectorAdapter	vec (ConstFQuaternionExpression e)
	Creates a constant Math.QuaternionVectorAdapter view of the quaternion expression e. More...
ConstLQuaternionVectorAdapter	vec (ConstLQuaternionExpression e)
	Creates a constant Math.QuaternionVectorAdapter view of the quaternion expression e. More...
ConstULQuaternionVectorAdapter	vec (ConstULQuaternionExpression e)
	Creates a constant Math.QuaternionVectorAdapter view of the quaternion expression e. More...
Vector2F	vec (float t1, float t2)
	Constructs a Math.CVector of size 2 from the components t1 and t2. More...
Vector3F	vec (float t1, float t2, float t3)
	Constructs a Math.CVector of size 3 from the components t1, t2 and t3. More...
Vector4F	vec (float t1, float t2, float t3, float t4)
	Constructs a Math.CVector of size 4 from the components t1, t2, t3 and t4. More...
Vector2L	vec (int t1, int t2)
	Constructs a Math.CVector of size 2 from the components t1 and t2. More...
Vector3L	vec (int t1, int t2, int t3)
	Constructs a Math.CVector of size 3 from the components t1, t2 and t3. More...
Vector4L	vec (int t1, int t2, int t3, int t4)
	Constructs a Math.CVector of size 4 from the components t1, t2, t3 and t4. More...

Detailed Description

Contains classes and functions related to mathematics.

Function Documentation

angleCos() [1/4]

float CDPL.Math.angleCos	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2,
		float	sd,
		bool	clamp = True
	)

Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]).

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.

angleCos() [2/4]

float CDPL.Math.angleCos	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2,
		float	sd,
		bool	clamp = True
	)

Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]).

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.

angleCos() [3/4]

int CDPL.Math.angleCos	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2,
		int	sd,
		bool	clamp = True
	)

Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]).

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.

angleCos() [4/4]

int CDPL.Math.angleCos	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2,
		int	sd,
		bool	clamp = True
	)

Returns the cosine of the angle between the vector expressions e1 and e2 (optionally clamped to [-1, 1]).

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.

calcCentroid() [1/8]

bool CDPL.Math.calcCentroid	(	Vector2DArray	va,
		Vector2D	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [2/8]

bool CDPL.Math.calcCentroid	(	Vector2FArray	va,
		Vector2F	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [3/8]

bool CDPL.Math.calcCentroid	(	Vector2LArray	va,
		Vector2L	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [4/8]

bool CDPL.Math.calcCentroid	(	Vector2ULArray	va,
		Vector2UL	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [5/8]

bool CDPL.Math.calcCentroid	(	Vector3DArray	va,
		Vector3D	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [6/8]

bool CDPL.Math.calcCentroid	(	Vector3FArray	va,
		Vector3F	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [7/8]

bool CDPL.Math.calcCentroid	(	Vector3LArray	va,
		Vector3L	ctr
	)

Parameters

va
ctr

Returns

calcCentroid() [8/8]

bool CDPL.Math.calcCentroid	(	Vector3ULArray	va,
		Vector3UL	ctr
	)

Parameters

va
ctr

Returns

calcRMSD() [1/16]

float CDPL.Math.calcRMSD	(	Vector2DArray	va1,
		Vector2DArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [2/16]

float CDPL.Math.calcRMSD	(	Vector2DArray	va1,
		Vector2DArray	va2,
		Matrix3D	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [3/16]

float CDPL.Math.calcRMSD	(	Vector2FArray	va1,
		Vector2FArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [4/16]

float CDPL.Math.calcRMSD	(	Vector2FArray	va1,
		Vector2FArray	va2,
		Matrix3F	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [5/16]

int CDPL.Math.calcRMSD	(	Vector2LArray	va1,
		Vector2LArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [6/16]

int CDPL.Math.calcRMSD	(	Vector2LArray	va1,
		Vector2LArray	va2,
		Matrix3L	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [7/16]

int CDPL.Math.calcRMSD	(	Vector2ULArray	va1,
		Vector2ULArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [8/16]

int CDPL.Math.calcRMSD	(	Vector2ULArray	va1,
		Vector2ULArray	va2,
		Matrix3UL	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [9/16]

float CDPL.Math.calcRMSD	(	Vector3DArray	va1,
		Vector3DArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [10/16]

float CDPL.Math.calcRMSD	(	Vector3DArray	va1,
		Vector3DArray	va2,
		Matrix4D	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [11/16]

float CDPL.Math.calcRMSD	(	Vector3FArray	va1,
		Vector3FArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [12/16]

float CDPL.Math.calcRMSD	(	Vector3FArray	va1,
		Vector3FArray	va2,
		Matrix4F	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [13/16]

int CDPL.Math.calcRMSD	(	Vector3LArray	va1,
		Vector3LArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [14/16]

int CDPL.Math.calcRMSD	(	Vector3LArray	va1,
		Vector3LArray	va2,
		Matrix4L	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

calcRMSD() [15/16]

int CDPL.Math.calcRMSD	(	Vector3ULArray	va1,
		Vector3ULArray	va2
	)

Parameters

va1
va2

Returns

calcRMSD() [16/16]

int CDPL.Math.calcRMSD	(	Vector3ULArray	va1,
		Vector3ULArray	va2,
		Matrix4UL	va1_xform
	)

Parameters

va1
va2
va1_xform

Returns

column() [1/8]

ConstDMatrixColumn CDPL.Math.column	(	ConstDMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [2/8]

ConstFMatrixColumn CDPL.Math.column	(	ConstFMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [3/8]

ConstLMatrixColumn CDPL.Math.column	(	ConstLMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [4/8]

ConstULMatrixColumn CDPL.Math.column	(	ConstULMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [5/8]

DMatrixColumn CDPL.Math.column	(	DMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [6/8]

FMatrixColumn CDPL.Math.column	(	FMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [7/8]

LMatrixColumn CDPL.Math.column	(	LMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

column() [8/8]

ULMatrixColumn CDPL.Math.column	(	ULMatrixExpression	e,
		int	i
	)

Parameters

e
i

Returns

conj() [1/14]

ConstDGridExpression CDPL.Math.conj

(

ConstDGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [2/14]

ConstDMatrixExpression CDPL.Math.conj

(

ConstDMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [3/14]

ConstDQuaternionExpression CDPL.Math.conj

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [4/14]

ConstDVectorExpression CDPL.Math.conj

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [5/14]

ConstFGridExpression CDPL.Math.conj

(

ConstFGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [6/14]

ConstFMatrixExpression CDPL.Math.conj

(

ConstFMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [7/14]

ConstFQuaternionExpression CDPL.Math.conj

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [8/14]

ConstFVectorExpression CDPL.Math.conj

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [9/14]

ConstLMatrixExpression CDPL.Math.conj

(

ConstLMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [10/14]

ConstLQuaternionExpression CDPL.Math.conj

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [11/14]

ConstLVectorExpression CDPL.Math.conj

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [12/14]

ConstULMatrixExpression CDPL.Math.conj

(

ConstULMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [13/14]

ConstULQuaternionExpression CDPL.Math.conj

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

conj() [14/14]

ConstULVectorExpression CDPL.Math.conj

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

cross() [1/4]

ConstDMatrixExpression CDPL.Math.cross

(

ConstDVectorExpression

e

)

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

Parameters

e	The 3-vector expression.

Returns

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

cross() [2/4]

ConstFMatrixExpression CDPL.Math.cross

(

ConstFVectorExpression

e

)

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

Parameters

e	The 3-vector expression.

Returns

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

cross() [3/4]

ConstLMatrixExpression CDPL.Math.cross

(

ConstLVectorExpression

e

)

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

Parameters

e	The 3-vector expression.

Returns

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

cross() [4/4]

ConstULMatrixExpression CDPL.Math.cross

(

ConstULVectorExpression

e

)

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

Parameters

e	The 3-vector expression.

Returns

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

crossProd() [1/4]

ConstDVectorExpression CDPL.Math.crossProd	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2
	)

Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node.

Parameters

e1	The first 3-vector expression.
e2	The second 3-vector expression.

Returns

An expression-template node representing the cross product.

crossProd() [2/4]

ConstFVectorExpression CDPL.Math.crossProd	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2
	)

Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node.

Parameters

e1	The first 3-vector expression.
e2	The second 3-vector expression.

Returns

An expression-template node representing the cross product.

crossProd() [3/4]

ConstLVectorExpression CDPL.Math.crossProd	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2
	)

Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node.

Parameters

e1	The first 3-vector expression.
e2	The second 3-vector expression.

Returns

An expression-template node representing the cross product.

crossProd() [4/4]

ConstULVectorExpression CDPL.Math.crossProd	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2
	)

Returns the 3-vector cross product \( e_1 \times e_2 \) as an expression-template node.

Parameters

e1	The first 3-vector expression.
e2	The second 3-vector expression.

Returns

An expression-template node representing the cross product.

det() [1/4]

float CDPL.Math.det

(

ConstDMatrixExpression

e

)

Returns the determinant of the matrix expression e.

Parameters

e	The matrix expression.

Returns

The determinant of e.

det() [2/4]

float CDPL.Math.det

(

ConstFMatrixExpression

e

)

Returns the determinant of the matrix expression e.

Parameters

e	The matrix expression.

Returns

The determinant of e.

det() [3/4]

int CDPL.Math.det

(

ConstLMatrixExpression

e

)

Returns the determinant of the matrix expression e.

Parameters

e	The matrix expression.

Returns

The determinant of e.

det() [4/4]

int CDPL.Math.det

(

ConstULMatrixExpression

e

)

Returns the determinant of the matrix expression e.

Parameters

e	The matrix expression.

Returns

The determinant of e.

diag() [1/4]

ConstDMatrixExpression CDPL.Math.diag

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

An expression-template node representing the diagonal matrix.

diag() [2/4]

ConstFMatrixExpression CDPL.Math.diag

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

An expression-template node representing the diagonal matrix.

diag() [3/4]

ConstLMatrixExpression CDPL.Math.diag

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

An expression-template node representing the diagonal matrix.

diag() [4/4]

ConstULMatrixExpression CDPL.Math.diag

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

An expression-template node representing the diagonal matrix.

elemDiv() [1/14]

ConstDGridExpression CDPL.Math.elemDiv	(	ConstDGridExpression	e1,
		ConstDGridExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [2/14]

ConstDMatrixExpression CDPL.Math.elemDiv	(	ConstDMatrixExpression	e1,
		ConstDMatrixExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [3/14]

ConstDQuaternionExpression CDPL.Math.elemDiv	(	ConstDQuaternionExpression	e1,
		ConstDQuaternionExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [4/14]

ConstDVectorExpression CDPL.Math.elemDiv	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [5/14]

ConstFGridExpression CDPL.Math.elemDiv	(	ConstFGridExpression	e1,
		ConstFGridExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [6/14]

ConstFMatrixExpression CDPL.Math.elemDiv	(	ConstFMatrixExpression	e1,
		ConstFMatrixExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [7/14]

ConstFQuaternionExpression CDPL.Math.elemDiv	(	ConstFQuaternionExpression	e1,
		ConstFQuaternionExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [8/14]

ConstFVectorExpression CDPL.Math.elemDiv	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [9/14]

ConstLMatrixExpression CDPL.Math.elemDiv	(	ConstLMatrixExpression	e1,
		ConstLMatrixExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [10/14]

ConstLQuaternionExpression CDPL.Math.elemDiv	(	ConstLQuaternionExpression	e1,
		ConstLQuaternionExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [11/14]

ConstLVectorExpression CDPL.Math.elemDiv	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [12/14]

ConstULMatrixExpression CDPL.Math.elemDiv	(	ConstULMatrixExpression	e1,
		ConstULMatrixExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [13/14]

ConstULQuaternionExpression CDPL.Math.elemDiv	(	ConstULQuaternionExpression	e1,
		ConstULQuaternionExpression	e2
	)

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

Parameters

e1	The numerator vector expression.
e2	The denominator vector expression.

Returns

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

elemDiv() [14/14]

ConstULVectorExpression CDPL.Math.elemDiv	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2
	)

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

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() [1/14]

ConstDGridExpression CDPL.Math.elemProd	(	ConstDGridExpression	e1,
		ConstDGridExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [2/14]

ConstDMatrixExpression CDPL.Math.elemProd	(	ConstDMatrixExpression	e1,
		ConstDMatrixExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [3/14]

ConstDQuaternionExpression CDPL.Math.elemProd	(	ConstDQuaternionExpression	e1,
		ConstDQuaternionExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [4/14]

ConstDVectorExpression CDPL.Math.elemProd	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [5/14]

ConstFGridExpression CDPL.Math.elemProd	(	ConstFGridExpression	e1,
		ConstFGridExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [6/14]

ConstFMatrixExpression CDPL.Math.elemProd	(	ConstFMatrixExpression	e1,
		ConstFMatrixExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [7/14]

ConstFQuaternionExpression CDPL.Math.elemProd	(	ConstFQuaternionExpression	e1,
		ConstFQuaternionExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [8/14]

ConstFVectorExpression CDPL.Math.elemProd	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [9/14]

ConstLMatrixExpression CDPL.Math.elemProd	(	ConstLMatrixExpression	e1,
		ConstLMatrixExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [10/14]

ConstLQuaternionExpression CDPL.Math.elemProd	(	ConstLQuaternionExpression	e1,
		ConstLQuaternionExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [11/14]

ConstLVectorExpression CDPL.Math.elemProd	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [12/14]

ConstULMatrixExpression CDPL.Math.elemProd	(	ConstULMatrixExpression	e1,
		ConstULMatrixExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [13/14]

ConstULQuaternionExpression CDPL.Math.elemProd	(	ConstULQuaternionExpression	e1,
		ConstULQuaternionExpression	e2
	)

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

Parameters

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

Returns

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

elemProd() [14/14]

ConstULVectorExpression CDPL.Math.elemProd	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2
	)

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

Parameters

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

Returns

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

equals() [1/14]

bool CDPL.Math.equals	(	ConstDGridExpression	e1,
		ConstDGridExpression	e2,
		float	eps
	)

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

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.

equals() [2/14]

bool CDPL.Math.equals	(	ConstDMatrixExpression	e1,
		ConstDMatrixExpression	e2,
		float	eps
	)

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

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.

equals() [3/14]

bool CDPL.Math.equals	(	ConstDQuaternionExpression	e1,
		ConstDQuaternionExpression	e2,
		float	eps
	)

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

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.

equals() [4/14]

bool CDPL.Math.equals	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2,
		float	eps
	)

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

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.

equals() [5/14]

bool CDPL.Math.equals	(	ConstFGridExpression	e1,
		ConstFGridExpression	e2,
		float	eps
	)

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

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.

equals() [6/14]

bool CDPL.Math.equals	(	ConstFMatrixExpression	e1,
		ConstFMatrixExpression	e2,
		float	eps
	)

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

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.

equals() [7/14]

bool CDPL.Math.equals	(	ConstFQuaternionExpression	e1,
		ConstFQuaternionExpression	e2,
		float	eps
	)

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

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.

equals() [8/14]

bool CDPL.Math.equals	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2,
		float	eps
	)

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

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.

equals() [9/14]

bool CDPL.Math.equals	(	ConstLMatrixExpression	e1,
		ConstLMatrixExpression	e2,
		int	eps
	)

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

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.

equals() [10/14]

bool CDPL.Math.equals	(	ConstLQuaternionExpression	e1,
		ConstLQuaternionExpression	e2,
		int	eps
	)

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

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.

equals() [11/14]

bool CDPL.Math.equals	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2,
		int	eps
	)

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

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.

equals() [12/14]

bool CDPL.Math.equals	(	ConstULMatrixExpression	e1,
		ConstULMatrixExpression	e2,
		int	eps
	)

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

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.

equals() [13/14]

bool CDPL.Math.equals	(	ConstULQuaternionExpression	e1,
		ConstULQuaternionExpression	e2,
		int	eps
	)

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

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.

equals() [14/14]

bool CDPL.Math.equals	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2,
		int	eps
	)

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

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.

factorial()

int CDPL.Math.factorial

(

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.

gammaQ()

float CDPL.Math.gammaQ	(	float	a,
		float	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()

float CDPL.Math.generalizedBell	(	float	x,
		float	a,
		float	b,
		float	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.

herm() [1/10]

ConstDGridExpression CDPL.Math.herm

(

ConstDGridExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [2/10]

ConstDMatrixExpression CDPL.Math.herm

(

ConstDMatrixExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [3/10]

ConstDVectorExpression CDPL.Math.herm

(

ConstDVectorExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [4/10]

ConstFGridExpression CDPL.Math.herm

(

ConstFGridExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [5/10]

ConstFMatrixExpression CDPL.Math.herm

(

ConstFMatrixExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [6/10]

ConstFVectorExpression CDPL.Math.herm

(

ConstFVectorExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [7/10]

ConstLMatrixExpression CDPL.Math.herm

(

ConstLMatrixExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [8/10]

ConstLVectorExpression CDPL.Math.herm

(

ConstLVectorExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [9/10]

ConstULMatrixExpression CDPL.Math.herm

(

ConstULMatrixExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

herm() [10/10]

ConstULVectorExpression CDPL.Math.herm

(

ConstULVectorExpression

e

)

Returns the Hermitian conjugate of the vector expression e (alias of conj() for vectors).

Parameters

e	The vector expression.

Returns

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

homog() [1/8]

ConstDHomogenousCoordsAdapter CDPL.Math.homog

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [2/8]

ConstFHomogenousCoordsAdapter CDPL.Math.homog

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [3/8]

ConstLHomogenousCoordsAdapter CDPL.Math.homog

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [4/8]

ConstULHomogenousCoordsAdapter CDPL.Math.homog

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [5/8]

DHomogenousCoordsAdapter CDPL.Math.homog

(

DVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [6/8]

FHomogenousCoordsAdapter CDPL.Math.homog

(

FVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [7/8]

LHomogenousCoordsAdapter CDPL.Math.homog

(

LVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

homog() [8/8]

ULHomogenousCoordsAdapter CDPL.Math.homog

(

ULVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant homogeneous-coordinates view of e.

imag() [1/10]

ConstDGridExpression CDPL.Math.imag

(

ConstDGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [2/10]

ConstDMatrixExpression CDPL.Math.imag

(

ConstDMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [3/10]

ConstDVectorExpression CDPL.Math.imag

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [4/10]

ConstFGridExpression CDPL.Math.imag

(

ConstFGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [5/10]

ConstFMatrixExpression CDPL.Math.imag

(

ConstFMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [6/10]

ConstFVectorExpression CDPL.Math.imag

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [7/10]

ConstLMatrixExpression CDPL.Math.imag

(

ConstLMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [8/10]

ConstLVectorExpression CDPL.Math.imag

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [9/10]

ConstULMatrixExpression CDPL.Math.imag

(

ConstULMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

imag() [10/10]

ConstULVectorExpression CDPL.Math.imag

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

innerProd() [1/4]

float CDPL.Math.innerProd	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2
	)

Returns the inner (dot) product of the vector expressions e1 and e2.

Parameters

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

Returns

\( \sum_i e_1(i) \cdot e_2(i) \).

innerProd() [2/4]

float CDPL.Math.innerProd	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2
	)

Returns the inner (dot) product of the vector expressions e1 and e2.

Parameters

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

Returns

\( \sum_i e_1(i) \cdot e_2(i) \).

innerProd() [3/4]

int CDPL.Math.innerProd	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2
	)

Returns the inner (dot) product of the vector expressions e1 and e2.

Parameters

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

Returns

\( \sum_i e_1(i) \cdot e_2(i) \).

innerProd() [4/4]

int CDPL.Math.innerProd	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2
	)

Returns the inner (dot) product of the vector expressions e1 and e2.

Parameters

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

Returns

\( \sum_i e_1(i) \cdot e_2(i) \).

interpolateTrilinear() [1/2]

float CDPL.Math.interpolateTrilinear	(	DRegularSpatialGrid	grid,
		Vector3D	pos,
		bool	local_pos
	)

Returns the trilinearly-interpolated value of grid at pos.

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).

interpolateTrilinear() [2/2]

float CDPL.Math.interpolateTrilinear	(	FRegularSpatialGrid	grid,
		Vector3F	pos,
		bool	local_pos
	)

Returns the trilinearly-interpolated value of grid at pos.

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).

inv() [1/4]

ConstDQuaternionExpression CDPL.Math.inv

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

inv() [2/4]

ConstFQuaternionExpression CDPL.Math.inv

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

inv() [3/4]

ConstLQuaternionExpression CDPL.Math.inv

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

inv() [4/4]

ConstULQuaternionExpression CDPL.Math.inv

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

invert() [1/8]

bool CDPL.Math.invert	(	ConstDMatrixExpression	e,
		DMatrixExpression	c
	)

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

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() [2/8]

bool CDPL.Math.invert	(	ConstFMatrixExpression	e,
		FMatrixExpression	c
	)

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

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() [3/8]

bool CDPL.Math.invert	(	ConstLMatrixExpression	e,
		LMatrixExpression	c
	)

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

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() [4/8]

bool CDPL.Math.invert	(	ConstULMatrixExpression	e,
		ULMatrixExpression	c
	)

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

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() [5/8]

bool CDPL.Math.invert

(

DMatrixExpression

c

)

Computes the inverse of the matrix container c in place.

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.

invert() [6/8]

bool CDPL.Math.invert

(

FMatrixExpression

c

)

Computes the inverse of the matrix container c in place.

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.

invert() [7/8]

bool CDPL.Math.invert

(

LMatrixExpression

c

)

Computes the inverse of the matrix container c in place.

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.

invert() [8/8]

bool CDPL.Math.invert

(

ULMatrixExpression

c

)

Computes the inverse of the matrix container c in place.

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.

jacobiDiagonalize() [1/4]

bool CDPL.Math.jacobiDiagonalize	(	DMatrixExpression	a,
		DVectorExpression	d,
		DMatrixExpression	v,
		int	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.

jacobiDiagonalize() [2/4]

bool CDPL.Math.jacobiDiagonalize	(	FMatrixExpression	a,
		FVectorExpression	d,
		FMatrixExpression	v,
		int	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.

jacobiDiagonalize() [3/4]

bool CDPL.Math.jacobiDiagonalize	(	LMatrixExpression	a,
		LVectorExpression	d,
		LMatrixExpression	v,
		int	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.

jacobiDiagonalize() [4/4]

bool CDPL.Math.jacobiDiagonalize	(	ULMatrixExpression	a,
		ULVectorExpression	d,
		ULMatrixExpression	v,
		int	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.

length() [1/4]

float CDPL.Math.length

(

ConstDVectorExpression

e

)

Returns the length (L2 norm) of the vector expression e (alias of norm2()).

Parameters

e	The vector expression.

Returns

The vector length.

length() [2/4]

float CDPL.Math.length

(

ConstFVectorExpression

e

)

Returns the length (L2 norm) of the vector expression e (alias of norm2()).

Parameters

e	The vector expression.

Returns

The vector length.

length() [3/4]

int CDPL.Math.length

(

ConstLVectorExpression

e

)

Returns the length (L2 norm) of the vector expression e (alias of norm2()).

Parameters

e	The vector expression.

Returns

The vector length.

length() [4/4]

int CDPL.Math.length

(

ConstULVectorExpression

e

)

Returns the length (L2 norm) of the vector expression e (alias of norm2()).

Parameters

e	The vector expression.

Returns

The vector length.

lnGamma()

float CDPL.Math.lnGamma

(

float

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.

luDecompose() [1/8]

int CDPL.Math.luDecompose

(

DMatrixExpression

e

)

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

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() [2/8]

int CDPL.Math.luDecompose	(	DMatrixExpression	e,
		ULVectorExpression	pv
	)

Parameters

e
pv

Returns

luDecompose() [3/8]

int CDPL.Math.luDecompose

(

FMatrixExpression

e

)

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

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() [4/8]

int CDPL.Math.luDecompose	(	FMatrixExpression	e,
		ULVectorExpression	pv
	)

Parameters

e
pv

Returns

luDecompose() [5/8]

int CDPL.Math.luDecompose

(

LMatrixExpression

e

)

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

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() [6/8]

int CDPL.Math.luDecompose	(	LMatrixExpression	e,
		ULVectorExpression	pv
	)

Parameters

e
pv

Returns

luDecompose() [7/8]

int CDPL.Math.luDecompose

(

ULMatrixExpression

e

)

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

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() [8/8]

int CDPL.Math.luDecompose	(	ULMatrixExpression	e,
		ULVectorExpression	pv
	)

Parameters

e
pv

Returns

luSubstitute() [1/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	e,
		DVectorExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [2/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	e,
		ConstULVectorExpression	pv,
		DVectorExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [3/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	e,
		DMatrixExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [4/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	e,
		ConstULVectorExpression	pv,
		DMatrixExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [5/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	e,
		FVectorExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [6/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	e,
		ConstULVectorExpression	pv,
		FVectorExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [7/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	e,
		FMatrixExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [8/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	e,
		ConstULVectorExpression	pv,
		FMatrixExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [9/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	e,
		LVectorExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [10/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	e,
		ConstULVectorExpression	pv,
		LVectorExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [11/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	e,
		LMatrixExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [12/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	e,
		ConstULVectorExpression	pv,
		LMatrixExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [13/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	e,
		ULVectorExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [14/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	e,
		ConstULVectorExpression	pv,
		ULVectorExpression	b
	)

Parameters

e
pv
b

Returns

luSubstitute() [15/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	e,
		ULMatrixExpression	b
	)

Parameters

e
b

Returns

luSubstitute() [16/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	e,
		ConstULVectorExpression	pv,
		ULMatrixExpression	b
	)

Parameters

e
pv
b

Returns

norm1() [1/8]

float CDPL.Math.norm1

(

ConstDMatrixExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [2/8]

float CDPL.Math.norm1

(

ConstDVectorExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [3/8]

float CDPL.Math.norm1

(

ConstFMatrixExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [4/8]

float CDPL.Math.norm1

(

ConstFVectorExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [5/8]

int CDPL.Math.norm1

(

ConstLMatrixExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [6/8]

int CDPL.Math.norm1

(

ConstLVectorExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [7/8]

int CDPL.Math.norm1

(

ConstULMatrixExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm1() [8/8]

int CDPL.Math.norm1

(

ConstULVectorExpression

e

)

Returns the L1 norm of the vector expression e ( \( \sum_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L1 norm.

norm2() [1/8]

float CDPL.Math.norm2

(

ConstDQuaternionExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [2/8]

float CDPL.Math.norm2

(

ConstDVectorExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [3/8]

float CDPL.Math.norm2

(

ConstFQuaternionExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [4/8]

float CDPL.Math.norm2

(

ConstFVectorExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [5/8]

int CDPL.Math.norm2

(

ConstLQuaternionExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [6/8]

int CDPL.Math.norm2

(

ConstLVectorExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [7/8]

int CDPL.Math.norm2

(

ConstULQuaternionExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm2() [8/8]

int CDPL.Math.norm2

(

ConstULVectorExpression

e

)

Returns the L2 (Euclidean) norm of the vector expression e ( \( \sqrt{\sum_i |e(i)|^2} \)).

Parameters

e	The vector expression.

Returns

The L2 norm.

norm() [1/4]

float CDPL.Math.norm

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

norm() [2/4]

float CDPL.Math.norm

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

norm() [3/4]

int CDPL.Math.norm

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

norm() [4/4]

int CDPL.Math.norm

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

normFrob() [1/4]

float CDPL.Math.normFrob

(

ConstDMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

The Frobenius norm of e.

normFrob() [2/4]

float CDPL.Math.normFrob

(

ConstFMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

The Frobenius norm of e.

normFrob() [3/4]

int CDPL.Math.normFrob

(

ConstLMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

The Frobenius norm of e.

normFrob() [4/4]

int CDPL.Math.normFrob

(

ConstULMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

The Frobenius norm of e.

normInf() [1/8]

float CDPL.Math.normInf

(

ConstDMatrixExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [2/8]

float CDPL.Math.normInf

(

ConstDVectorExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [3/8]

float CDPL.Math.normInf

(

ConstFMatrixExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [4/8]

float CDPL.Math.normInf

(

ConstFVectorExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [5/8]

int CDPL.Math.normInf

(

ConstLMatrixExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [6/8]

int CDPL.Math.normInf

(

ConstLVectorExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [7/8]

int CDPL.Math.normInf

(

ConstULMatrixExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInf() [8/8]

int CDPL.Math.normInf

(

ConstULVectorExpression

e

)

Returns the L∞ norm of the vector expression e ( \( \max_i |e(i)| \)).

Parameters

e	The vector expression.

Returns

The L∞ norm.

normInfIndex() [1/4]

int CDPL.Math.normInfIndex

(

ConstDVectorExpression

e

)

Returns the (first) index at which the vector expression e attains its L∞ norm.

Parameters

e	The vector expression.

Returns

The zero-based index of the element with the maximum absolute value.

normInfIndex() [2/4]

int CDPL.Math.normInfIndex

(

ConstFVectorExpression

e

)

Returns the (first) index at which the vector expression e attains its L∞ norm.

Parameters

e	The vector expression.

Returns

The zero-based index of the element with the maximum absolute value.

normInfIndex() [3/4]

int CDPL.Math.normInfIndex

(

ConstLVectorExpression

e

)

Returns the (first) index at which the vector expression e attains its L∞ norm.

Parameters

e	The vector expression.

Returns

The zero-based index of the element with the maximum absolute value.

normInfIndex() [4/4]

int CDPL.Math.normInfIndex

(

ConstULVectorExpression

e

)

Returns the (first) index at which the vector expression e attains its L∞ norm.

Parameters

e	The vector expression.

Returns

The zero-based index of the element with the maximum absolute value.

outerProd() [1/4]

ConstDMatrixExpression CDPL.Math.outerProd	(	ConstDVectorExpression	e1,
		ConstDVectorExpression	e2
	)

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

Parameters

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

Returns

An expression-template node representing the outer product.

outerProd() [2/4]

ConstFMatrixExpression CDPL.Math.outerProd	(	ConstFVectorExpression	e1,
		ConstFVectorExpression	e2
	)

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

Parameters

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

Returns

An expression-template node representing the outer product.

outerProd() [3/4]

ConstLMatrixExpression CDPL.Math.outerProd	(	ConstLVectorExpression	e1,
		ConstLVectorExpression	e2
	)

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

Parameters

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

Returns

An expression-template node representing the outer product.

outerProd() [4/4]

ConstULMatrixExpression CDPL.Math.outerProd	(	ConstULVectorExpression	e1,
		ConstULVectorExpression	e2
	)

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

Parameters

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

Returns

An expression-template node representing the outer product.

prime()

int CDPL.Math.prime

(

int

i

)

Parameters

i

Returns

prod() [1/24]

ConstDVectorExpression CDPL.Math.prod	(	ConstDMatrixExpression	e1,
		ConstDVectorExpression	e2
	)

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

Parameters

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

Returns

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

prod() [2/24]

DVectorExpression CDPL.Math.prod	(	ConstDMatrixExpression	e1,
		ConstDVectorExpression	e2,
		DVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [3/24]

ConstDMatrixExpression CDPL.Math.prod	(	ConstDMatrixExpression	e1,
		ConstDMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [4/24]

DMatrixExpression CDPL.Math.prod	(	ConstDMatrixExpression	e1,
		ConstDMatrixExpression	e2,
		DMatrixExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [5/24]

ConstDVectorExpression CDPL.Math.prod	(	ConstDVectorExpression	e1,
		ConstDMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [6/24]

DVectorExpression CDPL.Math.prod	(	ConstDVectorExpression	e1,
		ConstDMatrixExpression	e2,
		DVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [7/24]

ConstFVectorExpression CDPL.Math.prod	(	ConstFMatrixExpression	e1,
		ConstFVectorExpression	e2
	)

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

Parameters

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

Returns

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

prod() [8/24]

FVectorExpression CDPL.Math.prod	(	ConstFMatrixExpression	e1,
		ConstFVectorExpression	e2,
		FVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [9/24]

ConstFMatrixExpression CDPL.Math.prod	(	ConstFMatrixExpression	e1,
		ConstFMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [10/24]

FMatrixExpression CDPL.Math.prod	(	ConstFMatrixExpression	e1,
		ConstFMatrixExpression	e2,
		FMatrixExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [11/24]

ConstFVectorExpression CDPL.Math.prod	(	ConstFVectorExpression	e1,
		ConstFMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [12/24]

FVectorExpression CDPL.Math.prod	(	ConstFVectorExpression	e1,
		ConstFMatrixExpression	e2,
		FVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [13/24]

ConstLVectorExpression CDPL.Math.prod	(	ConstLMatrixExpression	e1,
		ConstLVectorExpression	e2
	)

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

Parameters

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

Returns

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

prod() [14/24]

LVectorExpression CDPL.Math.prod	(	ConstLMatrixExpression	e1,
		ConstLVectorExpression	e2,
		LVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [15/24]

ConstLMatrixExpression CDPL.Math.prod	(	ConstLMatrixExpression	e1,
		ConstLMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [16/24]

LMatrixExpression CDPL.Math.prod	(	ConstLMatrixExpression	e1,
		ConstLMatrixExpression	e2,
		LMatrixExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [17/24]

ConstLVectorExpression CDPL.Math.prod	(	ConstLVectorExpression	e1,
		ConstLMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [18/24]

LVectorExpression CDPL.Math.prod	(	ConstLVectorExpression	e1,
		ConstLMatrixExpression	e2,
		LVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [19/24]

ConstULVectorExpression CDPL.Math.prod	(	ConstULMatrixExpression	e1,
		ConstULVectorExpression	e2
	)

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

Parameters

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

Returns

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

prod() [20/24]

ULVectorExpression CDPL.Math.prod	(	ConstULMatrixExpression	e1,
		ConstULVectorExpression	e2,
		ULVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [21/24]

ConstULMatrixExpression CDPL.Math.prod	(	ConstULMatrixExpression	e1,
		ConstULMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [22/24]

ULMatrixExpression CDPL.Math.prod	(	ConstULMatrixExpression	e1,
		ConstULMatrixExpression	e2,
		ULMatrixExpression	c
	)

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

Parameters

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

Returns

A reference to c.

prod() [23/24]

ConstULVectorExpression CDPL.Math.prod	(	ConstULVectorExpression	e1,
		ConstULMatrixExpression	e2
	)

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

Parameters

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

Returns

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

prod() [24/24]

ULVectorExpression CDPL.Math.prod	(	ConstULVectorExpression	e1,
		ConstULMatrixExpression	e2,
		ULVectorExpression	c
	)

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

Parameters

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

Returns

A reference to c.

pythag()

float CDPL.Math.pythag	(	float	a,
		float	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 \( \sqrt{a^2 + b^2} \).

quat() [1/16]

ConstDVectorQuaternionAdapter CDPL.Math.quat

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [2/16]

ConstFVectorQuaternionAdapter CDPL.Math.quat

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [3/16]

ConstLVectorQuaternionAdapter CDPL.Math.quat

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [4/16]

ConstULVectorQuaternionAdapter CDPL.Math.quat

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [5/16]

DVectorQuaternionAdapter CDPL.Math.quat

(

DVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [6/16]

FVectorQuaternionAdapter CDPL.Math.quat

(

FVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [7/16]

LVectorQuaternionAdapter CDPL.Math.quat

(

LVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [8/16]

ULVectorQuaternionAdapter CDPL.Math.quat

(

ULVectorExpression

e

)

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

Parameters

e	The vector expression to wrap.

Returns

A constant quaternion view of e.

quat() [9/16]

FRealQuaternion CDPL.Math.quat

(

float

t

)

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

Parameters

t	The real component.

Returns

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

quat() [10/16]

FQuaternion CDPL.Math.quat	(	float	t1,
		float	t2
	)

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

Parameters

t1	The C1 component.
t2	The C2 component.

Returns

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

quat() [11/16]

FQuaternion CDPL.Math.quat	(	float	t1,
		float	t2,
		float	t3
	)

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

Parameters

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

Returns

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

quat() [12/16]

FQuaternion CDPL.Math.quat	(	float	t1,
		float	t2,
		float	t3,
		float	t4
	)

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

Parameters

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

Returns

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

quat() [13/16]

LRealQuaternion CDPL.Math.quat

(

int

t

)

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

Parameters

t	The real component.

Returns

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

quat() [14/16]

LQuaternion CDPL.Math.quat	(	int	t1,
		int	t2
	)

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

Parameters

t1	The C1 component.
t2	The C2 component.

Returns

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

quat() [15/16]

LQuaternion CDPL.Math.quat	(	int	t1,
		int	t2,
		int	t3
	)

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

Parameters

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

Returns

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

quat() [16/16]

LQuaternion CDPL.Math.quat	(	int	t1,
		int	t2,
		int	t3,
		int	t4
	)

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

Parameters

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

Returns

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

range() [1/33]

ConstDMatrixRange CDPL.Math.range	(	ConstDMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [2/33]

ConstDMatrixRange CDPL.Math.range	(	ConstDMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [3/33]

ConstDVectorRange CDPL.Math.range	(	ConstDVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [4/33]

ConstDVectorRange CDPL.Math.range	(	ConstDVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [5/33]

ConstFMatrixRange CDPL.Math.range	(	ConstFMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [6/33]

ConstFMatrixRange CDPL.Math.range	(	ConstFMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [7/33]

ConstFVectorRange CDPL.Math.range	(	ConstFVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [8/33]

ConstFVectorRange CDPL.Math.range	(	ConstFVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [9/33]

ConstLMatrixRange CDPL.Math.range	(	ConstLMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [10/33]

ConstLMatrixRange CDPL.Math.range	(	ConstLMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [11/33]

ConstLVectorRange CDPL.Math.range	(	ConstLVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [12/33]

ConstLVectorRange CDPL.Math.range	(	ConstLVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [13/33]

ConstULMatrixRange CDPL.Math.range	(	ConstULMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [14/33]

ConstULMatrixRange CDPL.Math.range	(	ConstULMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [15/33]

ConstULVectorRange CDPL.Math.range	(	ConstULVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [16/33]

ConstULVectorRange CDPL.Math.range	(	ConstULVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [17/33]

DMatrixRange CDPL.Math.range	(	DMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [18/33]

DMatrixRange CDPL.Math.range	(	DMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [19/33]

DVectorRange CDPL.Math.range	(	DVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [20/33]

DVectorRange CDPL.Math.range	(	DVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [21/33]

FMatrixRange CDPL.Math.range	(	FMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [22/33]

FMatrixRange CDPL.Math.range	(	FMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [23/33]

FVectorRange CDPL.Math.range	(	FVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [24/33]

FVectorRange CDPL.Math.range	(	FVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [25/33]

LMatrixRange CDPL.Math.range	(	LMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [26/33]

LMatrixRange CDPL.Math.range	(	LMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [27/33]

LVectorRange CDPL.Math.range	(	LVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [28/33]

LVectorRange CDPL.Math.range	(	LVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [29/33]

ULMatrixRange CDPL.Math.range	(	ULMatrixExpression	e,
		Range	r1,
		Range	r2
	)

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

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() [30/33]

ULMatrixRange CDPL.Math.range	(	ULMatrixExpression	e,
		int	start1,
		int	stop1,
		int	start2,
		int	stop2
	)

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

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() [31/33]

ULVectorRange CDPL.Math.range	(	ULVectorExpression	e,
		Range	r
	)

Creates a constant Math.VectorRange view of the subrange r of the vector expression e.

Parameters

e	The vector expression.
r	The index range to view.

Returns

A constant range view of e.

range() [32/33]

ULVectorRange CDPL.Math.range	(	ULVectorExpression	e,
		int	start,
		int	stop
	)

Creates a constant Math.VectorRange view of the subrange [start, stop) of the vector expression e.

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.

range() [33/33]

Range CDPL.Math.range	(	int	start,
		int	stop
	)

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.

real() [1/14]

ConstDGridExpression CDPL.Math.real

(

ConstDGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [2/14]

ConstDMatrixExpression CDPL.Math.real

(

ConstDMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [3/14]

float CDPL.Math.real

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [4/14]

ConstDVectorExpression CDPL.Math.real

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [5/14]

ConstFGridExpression CDPL.Math.real

(

ConstFGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [6/14]

ConstFMatrixExpression CDPL.Math.real

(

ConstFMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [7/14]

float CDPL.Math.real

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [8/14]

ConstFVectorExpression CDPL.Math.real

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [9/14]

ConstLMatrixExpression CDPL.Math.real

(

ConstLMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [10/14]

int CDPL.Math.real

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [11/14]

ConstLVectorExpression CDPL.Math.real

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [12/14]

ConstULMatrixExpression CDPL.Math.real

(

ConstULMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [13/14]

int CDPL.Math.real

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

real() [14/14]

ConstULVectorExpression CDPL.Math.real

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

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

rotate() [1/4]

ConstDVectorExpression CDPL.Math.rotate	(	ConstDQuaternionExpression	e1,
		ConstDVectorExpression	e2
	)

Rotates the vector expression e2 by the quaternion expression e1.

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 \( e_1 \cdot e_2 \cdot e_1^{-1} \).

rotate() [2/4]

ConstFVectorExpression CDPL.Math.rotate	(	ConstFQuaternionExpression	e1,
		ConstFVectorExpression	e2
	)

Rotates the vector expression e2 by the quaternion expression e1.

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 \( e_1 \cdot e_2 \cdot e_1^{-1} \).

rotate() [3/4]

ConstLVectorExpression CDPL.Math.rotate	(	ConstLQuaternionExpression	e1,
		ConstLVectorExpression	e2
	)

Rotates the vector expression e2 by the quaternion expression e1.

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 \( e_1 \cdot e_2 \cdot e_1^{-1} \).

rotate() [4/4]

ConstULVectorExpression CDPL.Math.rotate	(	ConstULQuaternionExpression	e1,
		ConstULVectorExpression	e2
	)

Rotates the vector expression e2 by the quaternion expression e1.

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 \( e_1 \cdot e_2 \cdot e_1^{-1} \).

row() [1/8]

ConstDMatrixRow CDPL.Math.row	(	ConstDMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [2/8]

ConstFMatrixRow CDPL.Math.row	(	ConstFMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [3/8]

ConstLMatrixRow CDPL.Math.row	(	ConstLMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [4/8]

ConstULMatrixRow CDPL.Math.row	(	ConstULMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [5/8]

DMatrixRow CDPL.Math.row	(	DMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [6/8]

FMatrixRow CDPL.Math.row	(	FMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [7/8]

LMatrixRow CDPL.Math.row	(	LMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

row() [8/8]

ULMatrixRow CDPL.Math.row	(	ULMatrixExpression	e,
		int	i
	)

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

Parameters

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

Returns

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

sign()

float CDPL.Math.sign	(	float	a,
		float	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.

slice() [1/33]

ConstDMatrixSlice CDPL.Math.slice	(	ConstDMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [2/33]

ConstDMatrixSlice CDPL.Math.slice	(	ConstDMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [3/33]

ConstDVectorSlice CDPL.Math.slice	(	ConstDVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [4/33]

ConstDVectorSlice CDPL.Math.slice	(	ConstDVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [5/33]

ConstFMatrixSlice CDPL.Math.slice	(	ConstFMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [6/33]

ConstFMatrixSlice CDPL.Math.slice	(	ConstFMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [7/33]

ConstFVectorSlice CDPL.Math.slice	(	ConstFVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [8/33]

ConstFVectorSlice CDPL.Math.slice	(	ConstFVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [9/33]

ConstLMatrixSlice CDPL.Math.slice	(	ConstLMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [10/33]

ConstLMatrixSlice CDPL.Math.slice	(	ConstLMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [11/33]

ConstLVectorSlice CDPL.Math.slice	(	ConstLVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [12/33]

ConstLVectorSlice CDPL.Math.slice	(	ConstLVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [13/33]

ConstULMatrixSlice CDPL.Math.slice	(	ConstULMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [14/33]

ConstULMatrixSlice CDPL.Math.slice	(	ConstULMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [15/33]

ConstULVectorSlice CDPL.Math.slice	(	ConstULVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [16/33]

ConstULVectorSlice CDPL.Math.slice	(	ConstULVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [17/33]

DMatrixSlice CDPL.Math.slice	(	DMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [18/33]

DMatrixSlice CDPL.Math.slice	(	DMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [19/33]

DVectorSlice CDPL.Math.slice	(	DVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [20/33]

DVectorSlice CDPL.Math.slice	(	DVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [21/33]

FMatrixSlice CDPL.Math.slice	(	FMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [22/33]

FMatrixSlice CDPL.Math.slice	(	FMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [23/33]

FVectorSlice CDPL.Math.slice	(	FVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [24/33]

FVectorSlice CDPL.Math.slice	(	FVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [25/33]

LMatrixSlice CDPL.Math.slice	(	LMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [26/33]

LMatrixSlice CDPL.Math.slice	(	LMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [27/33]

LVectorSlice CDPL.Math.slice	(	LVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [28/33]

LVectorSlice CDPL.Math.slice	(	LVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [29/33]

ULMatrixSlice CDPL.Math.slice	(	ULMatrixExpression	e,
		Slice	s1,
		Slice	s2
	)

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

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() [30/33]

ULMatrixSlice CDPL.Math.slice	(	ULMatrixExpression	e,
		int	start1,
		int	stride1,
		int	size1,
		int	start2,
		int	stride2,
		int	size2
	)

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

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() [31/33]

ULVectorSlice CDPL.Math.slice	(	ULVectorExpression	e,
		Slice	s
	)

Creates a constant Math.VectorSlice view of the slice s of the vector expression e.

Parameters

e	The vector expression.
s	The (start, stride, size) slice to view.

Returns

A constant slice view of e.

slice() [32/33]

ULVectorSlice CDPL.Math.slice	(	ULVectorExpression	e,
		int	start,
		int	stride,
		int	size
	)

Creates a constant Math.VectorSlice view of the slice (start, stride, size) of the vector expression e.

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.

slice() [33/33]

Slice CDPL.Math.slice	(	int	start,
		int	stride,
		int	size
	)

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.

solveLower() [1/8]

bool CDPL.Math.solveLower	(	ConstDMatrixExpression	e1,
		DVectorExpression	e2
	)

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

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.

solveLower() [2/8]

bool CDPL.Math.solveLower	(	ConstDMatrixExpression	e1,
		DMatrixExpression	e2
	)

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

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.

solveLower() [3/8]

bool CDPL.Math.solveLower	(	ConstFMatrixExpression	e1,
		FVectorExpression	e2
	)

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

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.

solveLower() [4/8]

bool CDPL.Math.solveLower	(	ConstFMatrixExpression	e1,
		FMatrixExpression	e2
	)

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

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.

solveLower() [5/8]

bool CDPL.Math.solveLower	(	ConstLMatrixExpression	e1,
		LVectorExpression	e2
	)

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

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.

solveLower() [6/8]

bool CDPL.Math.solveLower	(	ConstLMatrixExpression	e1,
		LMatrixExpression	e2
	)

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

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.

solveLower() [7/8]

bool CDPL.Math.solveLower	(	ConstULMatrixExpression	e1,
		ULVectorExpression	e2
	)

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

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.

solveLower() [8/8]

bool CDPL.Math.solveLower	(	ConstULMatrixExpression	e1,
		ULMatrixExpression	e2
	)

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

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() [1/8]

bool CDPL.Math.solveUnitLower	(	ConstDMatrixExpression	e1,
		DVectorExpression	e2
	)

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

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.

solveUnitLower() [2/8]

bool CDPL.Math.solveUnitLower	(	ConstDMatrixExpression	e1,
		DMatrixExpression	e2
	)

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

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.

solveUnitLower() [3/8]

bool CDPL.Math.solveUnitLower	(	ConstFMatrixExpression	e1,
		FVectorExpression	e2
	)

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

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.

solveUnitLower() [4/8]

bool CDPL.Math.solveUnitLower	(	ConstFMatrixExpression	e1,
		FMatrixExpression	e2
	)

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

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.

solveUnitLower() [5/8]

bool CDPL.Math.solveUnitLower	(	ConstLMatrixExpression	e1,
		LVectorExpression	e2
	)

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

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.

solveUnitLower() [6/8]

bool CDPL.Math.solveUnitLower	(	ConstLMatrixExpression	e1,
		LMatrixExpression	e2
	)

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

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.

solveUnitLower() [7/8]

bool CDPL.Math.solveUnitLower	(	ConstULMatrixExpression	e1,
		ULVectorExpression	e2
	)

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

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.

solveUnitLower() [8/8]

bool CDPL.Math.solveUnitLower	(	ConstULMatrixExpression	e1,
		ULMatrixExpression	e2
	)

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

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.

solveUnitUpper() [1/8]

bool CDPL.Math.solveUnitUpper	(	ConstDMatrixExpression	e1,
		DVectorExpression	e2
	)

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

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.

solveUnitUpper() [2/8]

bool CDPL.Math.solveUnitUpper	(	ConstDMatrixExpression	e1,
		DMatrixExpression	e2
	)

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

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.

solveUnitUpper() [3/8]

bool CDPL.Math.solveUnitUpper	(	ConstFMatrixExpression	e1,
		FVectorExpression	e2
	)

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

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.

solveUnitUpper() [4/8]

bool CDPL.Math.solveUnitUpper	(	ConstFMatrixExpression	e1,
		FMatrixExpression	e2
	)

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

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.

solveUnitUpper() [5/8]

bool CDPL.Math.solveUnitUpper	(	ConstLMatrixExpression	e1,
		LVectorExpression	e2
	)

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

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.

solveUnitUpper() [6/8]

bool CDPL.Math.solveUnitUpper	(	ConstLMatrixExpression	e1,
		LMatrixExpression	e2
	)

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

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.

solveUnitUpper() [7/8]

bool CDPL.Math.solveUnitUpper	(	ConstULMatrixExpression	e1,
		ULVectorExpression	e2
	)

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

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.

solveUnitUpper() [8/8]

bool CDPL.Math.solveUnitUpper	(	ConstULMatrixExpression	e1,
		ULMatrixExpression	e2
	)

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

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.

solveUpper() [1/8]

bool CDPL.Math.solveUpper	(	ConstDMatrixExpression	e1,
		DVectorExpression	e2
	)

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

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.

solveUpper() [2/8]

bool CDPL.Math.solveUpper	(	ConstDMatrixExpression	e1,
		DMatrixExpression	e2
	)

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

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.

solveUpper() [3/8]

bool CDPL.Math.solveUpper	(	ConstFMatrixExpression	e1,
		FVectorExpression	e2
	)

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

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.

solveUpper() [4/8]

bool CDPL.Math.solveUpper	(	ConstFMatrixExpression	e1,
		FMatrixExpression	e2
	)

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

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.

solveUpper() [5/8]

bool CDPL.Math.solveUpper	(	ConstLMatrixExpression	e1,
		LVectorExpression	e2
	)

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

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.

solveUpper() [6/8]

bool CDPL.Math.solveUpper	(	ConstLMatrixExpression	e1,
		LMatrixExpression	e2
	)

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

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.

solveUpper() [7/8]

bool CDPL.Math.solveUpper	(	ConstULMatrixExpression	e1,
		ULVectorExpression	e2
	)

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

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.

solveUpper() [8/8]

bool CDPL.Math.solveUpper	(	ConstULMatrixExpression	e1,
		ULMatrixExpression	e2
	)

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

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.

sum() [1/15]

float CDPL.Math.sum

(

ConstDGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [2/15]

float CDPL.Math.sum

(

ConstDMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [3/15]

float CDPL.Math.sum

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [4/15]

float CDPL.Math.sum

(

ConstDVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [5/15]

float CDPL.Math.sum

(

ConstFGridExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [6/15]

float CDPL.Math.sum

(

ConstFMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [7/15]

float CDPL.Math.sum

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [8/15]

float CDPL.Math.sum

(

ConstFVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [9/15]

int CDPL.Math.sum

(

ConstLMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [10/15]

int CDPL.Math.sum

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [11/15]

int CDPL.Math.sum

(

ConstLVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [12/15]

int CDPL.Math.sum

(

ConstULMatrixExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [13/15]

int CDPL.Math.sum

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [14/15]

int CDPL.Math.sum

(

ConstULVectorExpression

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

sum() [15/15]

int CDPL.Math.sum

(

object

e

)

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

Parameters

e	The vector expression.

Returns

\( \sum_i e(i) \).

svDecompose() [1/4]

bool CDPL.Math.svDecompose	(	DMatrixExpression	a,
		DVectorExpression	w,
		DMatrixExpression	v,
		int	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.

svDecompose() [2/4]

bool CDPL.Math.svDecompose	(	FMatrixExpression	a,
		FVectorExpression	w,
		FMatrixExpression	v,
		int	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.

svDecompose() [3/4]

bool CDPL.Math.svDecompose	(	LMatrixExpression	a,
		LVectorExpression	w,
		LMatrixExpression	v,
		int	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.

svDecompose() [4/4]

bool CDPL.Math.svDecompose	(	ULMatrixExpression	a,
		ULVectorExpression	w,
		ULMatrixExpression	v,
		int	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() [1/8]

None CDPL.Math.svSubstitute	(	ConstDMatrixExpression	u,
		ConstDVectorExpression	w,
		ConstDMatrixExpression	v,
		ConstDVectorExpression	b,
		DVectorExpression	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()

svSubstitute() [2/8]

None CDPL.Math.svSubstitute	(	ConstDMatrixExpression	u,
		ConstDVectorExpression	w,
		ConstDMatrixExpression	v,
		ConstDMatrixExpression	b,
		DMatrixExpression	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()

svSubstitute() [3/8]

None CDPL.Math.svSubstitute	(	ConstFMatrixExpression	u,
		ConstFVectorExpression	w,
		ConstFMatrixExpression	v,
		ConstFVectorExpression	b,
		FVectorExpression	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()

svSubstitute() [4/8]

None CDPL.Math.svSubstitute	(	ConstFMatrixExpression	u,
		ConstFVectorExpression	w,
		ConstFMatrixExpression	v,
		ConstFMatrixExpression	b,
		FMatrixExpression	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()

svSubstitute() [5/8]

None CDPL.Math.svSubstitute	(	ConstLMatrixExpression	u,
		ConstLVectorExpression	w,
		ConstLMatrixExpression	v,
		ConstLVectorExpression	b,
		LVectorExpression	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()

svSubstitute() [6/8]

None CDPL.Math.svSubstitute	(	ConstLMatrixExpression	u,
		ConstLVectorExpression	w,
		ConstLMatrixExpression	v,
		ConstLMatrixExpression	b,
		LMatrixExpression	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()

svSubstitute() [7/8]

None CDPL.Math.svSubstitute	(	ConstULMatrixExpression	u,
		ConstULVectorExpression	w,
		ConstULMatrixExpression	v,
		ConstULVectorExpression	b,
		ULVectorExpression	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()

svSubstitute() [8/8]

None CDPL.Math.svSubstitute	(	ConstULMatrixExpression	u,
		ConstULVectorExpression	w,
		ConstULMatrixExpression	v,
		ConstULMatrixExpression	b,
		ULMatrixExpression	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()

trace() [1/4]

float CDPL.Math.trace

(

ConstDMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

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

trace() [2/4]

float CDPL.Math.trace

(

ConstFMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

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

trace() [3/4]

int CDPL.Math.trace

(

ConstLMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

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

trace() [4/4]

int CDPL.Math.trace

(

ConstULMatrixExpression

e

)

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

Parameters

e	The matrix expression.

Returns

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

trans() [1/8]

ConstDMatrixTranspose CDPL.Math.trans

(

ConstDMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [2/8]

ConstFMatrixTranspose CDPL.Math.trans

(

ConstFMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [3/8]

ConstLMatrixTranspose CDPL.Math.trans

(

ConstLMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [4/8]

ConstULMatrixTranspose CDPL.Math.trans

(

ConstULMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [5/8]

DMatrixTranspose CDPL.Math.trans

(

DMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [6/8]

FMatrixTranspose CDPL.Math.trans

(

FMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [7/8]

LMatrixTranspose CDPL.Math.trans

(

LMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

trans() [8/8]

ULMatrixTranspose CDPL.Math.trans

(

ULMatrixExpression

e

)

Returns the transpose of the mutable vector expression e (the identity for vectors — provided for matrix-API symmetry).

Parameters

e	The vector expression.

Returns

A reference to e.

transform() [1/16]

None CDPL.Math.transform	(	Vector2DArray	va,
		Matrix2D	xform
	)

Parameters

va
xform

transform() [2/16]

None CDPL.Math.transform	(	Vector2DArray	va,
		Matrix3D	xform
	)

Parameters

va
xform

transform() [3/16]

None CDPL.Math.transform	(	Vector2FArray	va,
		Matrix2F	xform
	)

Parameters

va
xform

transform() [4/16]

None CDPL.Math.transform	(	Vector2FArray	va,
		Matrix3F	xform
	)

Parameters

va
xform

transform() [5/16]

None CDPL.Math.transform	(	Vector2LArray	va,
		Matrix2L	xform
	)

Parameters

va
xform

transform() [6/16]

None CDPL.Math.transform	(	Vector2LArray	va,
		Matrix3L	xform
	)

Parameters

va
xform

transform() [7/16]

None CDPL.Math.transform	(	Vector2ULArray	va,
		Matrix2UL	xform
	)

Parameters

va
xform

transform() [8/16]

None CDPL.Math.transform	(	Vector2ULArray	va,
		Matrix3UL	xform
	)

Parameters

va
xform

transform() [9/16]

None CDPL.Math.transform	(	Vector3DArray	va,
		Matrix3D	xform
	)

Parameters

va
xform

transform() [10/16]

None CDPL.Math.transform	(	Vector3DArray	va,
		Matrix4D	xform
	)

Parameters

va
xform

transform() [11/16]

None CDPL.Math.transform	(	Vector3FArray	va,
		Matrix3F	xform
	)

Parameters

va
xform

transform() [12/16]

None CDPL.Math.transform	(	Vector3FArray	va,
		Matrix4F	xform
	)

Parameters

va
xform

transform() [13/16]

None CDPL.Math.transform	(	Vector3LArray	va,
		Matrix3L	xform
	)

Parameters

va
xform

transform() [14/16]

None CDPL.Math.transform	(	Vector3LArray	va,
		Matrix4L	xform
	)

Parameters

va
xform

transform() [15/16]

None CDPL.Math.transform	(	Vector3ULArray	va,
		Matrix3UL	xform
	)

Parameters

va
xform

transform() [16/16]

None CDPL.Math.transform	(	Vector3ULArray	va,
		Matrix4UL	xform
	)

Parameters

va
xform

triang() [1/16]

ConstUpperTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

triang() [2/16]

ConstUnitUpperTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

triang() [3/16]

ConstLowerTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

triang() [4/16]

ConstUnitLowerTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

triang() [5/16]

ConstUpperTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

triang() [6/16]

ConstUnitUpperTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

triang() [7/16]

ConstLowerTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

triang() [8/16]

ConstUnitLowerTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

triang() [9/16]

ConstUpperTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

triang() [10/16]

ConstUnitUpperTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

triang() [11/16]

ConstLowerTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

triang() [12/16]

ConstUnitLowerTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

triang() [13/16]

ConstUpperTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

triang() [14/16]

ConstUnitUpperTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

triang() [15/16]

ConstLowerTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

triang() [16/16]

ConstUnitLowerTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

unreal() [1/4]

ConstDQuaternionExpression CDPL.Math.unreal

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

unreal() [2/4]

ConstFQuaternionExpression CDPL.Math.unreal

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

unreal() [3/4]

ConstLQuaternionExpression CDPL.Math.unreal

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

unreal() [4/4]

ConstULQuaternionExpression CDPL.Math.unreal

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The quaternion expression.

Returns

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

vec() [1/10]

ConstDQuaternionVectorAdapter CDPL.Math.vec

(

ConstDQuaternionExpression

e

)

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

Parameters

e	The quaternion expression to wrap.

Returns

A constant 4-element vector view of e.

vec() [2/10]

ConstFQuaternionVectorAdapter CDPL.Math.vec

(

ConstFQuaternionExpression

e

)

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

Parameters

e	The quaternion expression to wrap.

Returns

A constant 4-element vector view of e.

vec() [3/10]

ConstLQuaternionVectorAdapter CDPL.Math.vec

(

ConstLQuaternionExpression

e

)

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

Parameters

e	The quaternion expression to wrap.

Returns

A constant 4-element vector view of e.

vec() [4/10]

ConstULQuaternionVectorAdapter CDPL.Math.vec

(

ConstULQuaternionExpression

e

)

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

Parameters

e	The quaternion expression to wrap.

Returns

A constant 4-element vector view of e.

vec() [5/10]

Vector2F CDPL.Math.vec	(	float	t1,
		float	t2
	)

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

Parameters

t1	The first component.
t2	The second component.

Returns

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

vec() [6/10]

Vector3F CDPL.Math.vec	(	float	t1,
		float	t2,
		float	t3
	)

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

Parameters

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

Returns

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

vec() [7/10]

Vector4F CDPL.Math.vec	(	float	t1,
		float	t2,
		float	t3,
		float	t4
	)

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

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).

vec() [8/10]

Vector2L CDPL.Math.vec	(	int	t1,
		int	t2
	)

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

Parameters

t1	The first component.
t2	The second component.

Returns

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

vec() [9/10]

Vector3L CDPL.Math.vec	(	int	t1,
		int	t2,
		int	t3
	)

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

Parameters

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

Returns

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

vec() [10/10]

Vector4L CDPL.Math.vec	(	int	t1,
		int	t2,
		int	t3,
		int	t4
	)

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

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).