CDPL.Math Package Reference

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

Classes
class	ConstDGridExpression
	Represents the outcome of mathematical expressions/operations that result in a 3D grid. More...
class	ConstDHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	ConstDMatrixColumn
	Vector expression proxy that views a single column of an underlying matrix. More...
class	ConstDMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	ConstDMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	ConstDMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	ConstDMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	ConstDMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	ConstDQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	ConstDQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	ConstDVectorExpression
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	ConstDVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	ConstDVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	ConstDVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
class	ConstFGridExpression
	Represents the outcome of mathematical expressions/operations that result in a 3D grid. More...
class	ConstFHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	ConstFMatrixColumn
	Vector expression proxy that views a single column of an underlying matrix. More...
class	ConstFMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	ConstFMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	ConstFMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	ConstFMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	ConstFMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	ConstFQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	ConstFQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	ConstFVectorExpression
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	ConstFVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	ConstFVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	ConstFVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
class	ConstLHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	ConstLMatrixColumn
	Vector expression proxy that views a single column of an underlying matrix. More...
class	ConstLMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	ConstLMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	ConstLMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	ConstLMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	ConstLMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	ConstLQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	ConstLQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	ConstLVectorExpression
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	ConstLVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	ConstLVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	ConstLVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
class	ConstLowerTriangularDMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M. More...
class	ConstLowerTriangularFMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M. More...
class	ConstLowerTriangularLMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M. More...
class	ConstLowerTriangularULMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M. More...
class	ConstULHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	ConstULMatrixColumn
	Vector expression proxy that views a single column of an underlying matrix. More...
class	ConstULMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	ConstULMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	ConstULMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	ConstULMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	ConstULMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	ConstULQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	ConstULQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	ConstULVectorExpression
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	ConstULVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	ConstULVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	ConstULVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
class	ConstUnitLowerTriangularDMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitLowerTriangularFMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitLowerTriangularLMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitLowerTriangularULMatrixAdapter
	Matrix expression that exposes only the lower triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitUpperTriangularDMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitUpperTriangularFMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitUpperTriangularLMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUnitUpperTriangularULMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M with the diagonal elements set to one. More...
class	ConstUpperTriangularDMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M. More...
class	ConstUpperTriangularFMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M. More...
class	ConstUpperTriangularLMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M. More...
class	ConstUpperTriangularULMatrixAdapter
	Matrix expression that exposes only the upper triangular part of an underlying matrix M. More...
class	DGrid
	Unbounded dense grid storing floating-point values of type double. More...
class	DGridExpression
	Represents the outcome of mathematical expressions/operations that result in a 3D grid. More...
class	DHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	DIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type double. More...
class	DKabschAlgorithm
	Implementation of the Kabsch algorithm [KABA]. More...
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
	Vector expression proxy that views a single column of an underlying matrix. More...
class	DMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	DMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	DMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	DMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	DMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	DQuaternion
	General 4-component quaternion with component values of type double. More...
class	DQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	DQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	DRealQuaternion
	A memory-efficient pure-real quaternion with component values of type double. More...
class	DRegularSpatialGrid
	Unbounded dense regular spatial grid storing floating-point values of type double. More...
class	DRotationMatrix
	Rotation matrix holding floating-point values of type double. More...
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
	Scaling matrix holding floating-point values of type double. More...
class	DTranslationMatrix
	Translation matrix holding floating-point values of type double. More...
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
	Implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for solving unconstrained nonlinear optimization problems. More...
class	DVectorExpression
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	DVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	DVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	DVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
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
	A wrapper class for various types of callable objects. More...
class	DoubleDVectorFunctor
	A wrapper class for various types of callable objects. More...
class	DoubleVector2DArray2Functor
	A wrapper class for various types of callable objects. More...
class	DoubleVector2DArrayFunctor
	A wrapper class for various types of callable objects. More...
class	DoubleVector3DArray2Functor
	A wrapper class for various types of callable objects. More...
class	DoubleVector3DArrayFunctor
	A wrapper class for various types of callable objects. More...
class	FGrid
	Unbounded dense grid storing floating-point values of type float. More...
class	FGridExpression
	Represents the outcome of mathematical expressions/operations that result in a 3D grid. More...
class	FHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
class	FIdentityMatrix
	Memory-efficient immutable identity matrix with element values of type float. More...
class	FKabschAlgorithm
	Implementation of the Kabsch algorithm [KABA]. More...
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
	Vector expression proxy that views a single column of an underlying matrix. More...
class	FMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	FMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	FMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	FMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	FMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	FQuaternion
	General 4-component quaternion with component values of type float. More...
class	FQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	FQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	FRealQuaternion
	A memory-efficient pure-real quaternion with component values of type float. More...
class	FRegularSpatialGrid
	Unbounded dense regular spatial grid storing floating-point values of type float. More...
class	FRotationMatrix
	Rotation matrix holding floating-point values of type float. More...
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
	Scaling matrix holding floating-point values of type float. More...
class	FTranslationMatrix
	Translation matrix holding floating-point values of type float. More...
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
	Implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for solving unconstrained nonlinear optimization problems. More...
class	FVectorExpression
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	FVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	FVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	FVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
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
	A wrapper class for various types of callable objects. More...
class	FloatFVectorFunctor
	A wrapper class for various types of callable objects. More...
class	FloatVector2FArray2Functor
	A wrapper class for various types of callable objects. More...
class	FloatVector2FArrayFunctor
	A wrapper class for various types of callable objects. More...
class	FloatVector3FArray2Functor
	A wrapper class for various types of callable objects. More...
class	FloatVector3FArrayFunctor
	A wrapper class for various types of callable objects. More...
class	LHomogenousCoordsAdapter
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
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
	Vector expression proxy that views a single column of an underlying matrix. More...
class	LMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	LMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	LMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	LMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	LMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	LQuaternion
	General 4-component quaternion with component values of type long. More...
class	LQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	LQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	LRealQuaternion
	A memory-efficient pure-real quaternion with component values of type long. More...
class	LRotationMatrix
	Rotation matrix holding integer values of type long. More...
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
	Scaling matrix holding integer values of type long. More...
class	LTranslationMatrix
	Translation matrix holding integer values of type long. More...
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
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	LVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	LVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	LVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
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 triangular matrix adapters. More...
class	Matrix2D
	Bounded 2×2 matrix holding floating-point values of type double. More...
class	Matrix2F
	Bounded 2×2 matrix holding floating-point values of type float. More...
class	Matrix2L
	Bounded 2×2 matrix holding signed integers of type long. More...
class	Matrix2UL
	Bounded 2×2 matrix holding unsigned integers of type unsigned long. More...
class	Matrix3D
	Bounded 3×3 matrix holding floating-point values of type double. More...
class	Matrix3F
	Bounded 3×3 matrix holding floating-point values of type float. More...
class	Matrix3L
	Bounded 3×3 matrix holding signed integers of type long. More...
class	Matrix3UL
	Bounded 3×3 matrix holding unsigned integers of type unsigned long. More...
class	Matrix4D
	Bounded 4×4 matrix holding floating-point values of type double. More...
class	Matrix4F
	Bounded 4×4 matrix holding floating-point values of type float. More...
class	Matrix4L
	Bounded 4×4 matrix holding signed integers of type long. More...
class	Matrix4UL
	Bounded 4×4 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
	Vector expression that exposes a vector as its homogeneous-coordinate extension by appending an implicit 1 at the end. More...
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
	Vector expression proxy that views a single column of an underlying matrix. More...
class	ULMatrixExpression
	Represents the outcome of mathematical expressions/operations that result in a matrix. More...
class	ULMatrixRange
	Matrix expression proxy that views a contiguous rectangular subrange of an underlying matrix. More...
class	ULMatrixRow
	Vector expression proxy that views a single row of an underlying matrix. More...
class	ULMatrixSlice
	Matrix expression proxy that views a strided rectangular slice of an underlying matrix. More...
class	ULMatrixTranspose
	Mutable view adapter that exposes the transpose of a matrix M as a matrix expression ( \( (i, j) \to M(j, i) \)). More...
class	ULQuaternion
	General 4-component quaternion with component values of type unsigned long. More...
class	ULQuaternionExpression
	Represents the outcome of mathematical expressions/operations that result in a quaternion. More...
class	ULQuaternionVectorAdapter
	Adapter that exposes a quaternion as a 4-element vector expression (indices map to the components C1, C2, C3, C4). More...
class	ULRealQuaternion
	A memory-efficient pure-real quaternion with component values of type unsigned long. More...
class	ULRotationMatrix
	Rotation matrix holding unsigned integer values of type unsigned long. More...
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
	Scaling matrix holding unsigned integer values of type unsigned long. More...
class	ULTranslationMatrix
	Translation matrix holding unsigned integer values of type unsigned long. More...
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
	Represents the outcome of mathematical expressions/operations that result in a vector. More...
class	ULVectorQuaternionAdapter
	Quaternion expression that exposes a 4-element vector as a quaternion (component indices 0-3 map to C1-C4). More...
class	ULVectorRange
	Vector expression proxy that views a contiguous half-open subrange of an underlying vector. More...
class	ULVectorSlice
	Vector expression proxy that views a strided slice of an underlying vector. More...
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 triangular matrix adapters. More...
class	UnitUpper
	Tag selecting the unit-upper triangular view (zero below the diagonal, one on the diagonal) for triangular matrix adapters. More...
class	Upper
	Tag selecting the upper triangular view (entries strictly below the diagonal read as zero) for triangular matrix adapters. 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
	Kabsch algorithm [KABA] implementation that operates directly on vector array inputs. More...
class	Vector2DArrayBFGSMinimizer
	Implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for solving unconstrained nonlinear optimization problems. More...
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
	Kabsch algorithm [KABA] implementation that operates directly on vector array inputs. More...
class	Vector2FArrayBFGSMinimizer
	Implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for solving unconstrained nonlinear optimization problems. More...
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
	Kabsch algorithm [KABA] implementation that operates directly on vector array inputs. More...
class	Vector3DArrayBFGSMinimizer
	Implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for solving unconstrained nonlinear optimization problems. More...
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
	Kabsch algorithm [KABA] implementation that operates directly on vector array inputs. More...
class	Vector3FArrayBFGSMinimizer
	Implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for solving unconstrained nonlinear optimization problems. More...
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 (optionally clamped) cosine of the angle between the vector expressions e1 and e2. More...
float	angleCos (ConstFVectorExpression e1, ConstFVectorExpression e2, float sd, bool clamp=True)
	Returns the (optionally clamped) cosine of the angle between the vector expressions e1 and e2. More...
int	angleCos (ConstLVectorExpression e1, ConstLVectorExpression e2, int sd, bool clamp=True)
	Returns the (optionally clamped) cosine of the angle between the vector expressions e1 and e2. More...
int	angleCos (ConstULVectorExpression e1, ConstULVectorExpression e2, int sd, bool clamp=True)
	Returns the (optionally clamped) cosine of the angle between the vector expressions e1 and e2. More...
bool	calcCentroid (Vector2DArray va, Vector2D ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector2FArray va, Vector2F ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector2LArray va, Vector2L ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector2ULArray va, Vector2UL ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector3DArray va, Vector3D ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector3FArray va, Vector3F ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector3LArray va, Vector3L ctr)
	Calculates the centroid of the array elements. More...
bool	calcCentroid (Vector3ULArray va, Vector3UL ctr)
	Calculates the centroid of the array elements. More...
float	calcRMSD (Vector2DArray va1, Vector2DArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
float	calcRMSD (Vector2DArray va1, Vector2DArray va2, Matrix3D va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
float	calcRMSD (Vector2FArray va1, Vector2FArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
float	calcRMSD (Vector2FArray va1, Vector2FArray va2, Matrix3F va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
int	calcRMSD (Vector2LArray va1, Vector2LArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
int	calcRMSD (Vector2LArray va1, Vector2LArray va2, Matrix3L va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
int	calcRMSD (Vector2ULArray va1, Vector2ULArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
int	calcRMSD (Vector2ULArray va1, Vector2ULArray va2, Matrix3UL va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
float	calcRMSD (Vector3DArray va1, Vector3DArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
float	calcRMSD (Vector3DArray va1, Vector3DArray va2, Matrix4D va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
float	calcRMSD (Vector3FArray va1, Vector3FArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
float	calcRMSD (Vector3FArray va1, Vector3FArray va2, Matrix4F va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
int	calcRMSD (Vector3LArray va1, Vector3LArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
int	calcRMSD (Vector3LArray va1, Vector3LArray va2, Matrix4L va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
int	calcRMSD (Vector3ULArray va1, Vector3ULArray va2)
	Calculates the RMSD between the corresponding elements of va1 and va2. More...
int	calcRMSD (Vector3ULArray va1, Vector3ULArray va2, Matrix4UL va1_xform)
	Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1. More...
ConstDMatrixColumn	column (ConstDMatrixExpression ce, int j)
	Returns a constant matrix proxy viewing column j of ce. More...
ConstFMatrixColumn	column (ConstFMatrixExpression ce, int j)
	Returns a constant matrix proxy viewing column j of ce. More...
ConstLMatrixColumn	column (ConstLMatrixExpression ce, int j)
	Returns a constant matrix proxy viewing column j of ce. More...
ConstULMatrixColumn	column (ConstULMatrixExpression ce, int j)
	Returns a constant matrix proxy viewing column j of ce. More...
DMatrixColumn	column (DMatrixExpression me, int j)
	Returns a mutable matrix proxy viewing column j of me. More...
FMatrixColumn	column (FMatrixExpression me, int j)
	Returns a mutable matrix proxy viewing column j of me. More...
LMatrixColumn	column (LMatrixExpression me, int j)
	Returns a mutable matrix proxy viewing column j of me. More...
ULMatrixColumn	column (ULMatrixExpression me, int j)
	Returns a mutable matrix proxy viewing column j of me. More...
ConstDGridExpression	conj (ConstDGridExpression ge)
	Returns the element-wise complex conjugate of the grid expression ge (identity for real-valued grids). More...
ConstDMatrixExpression	conj (ConstDMatrixExpression me)
	Returns the element-wise complex conjugate of the matrix expression me (identity for real-valued matrices). More...
ConstDQuaternionExpression	conj (ConstDQuaternionExpression qe)
	Returns the quaternion conjugate of the quaternion expression qe (negates C2, C3, C4). More...
ConstDVectorExpression	conj (ConstDVectorExpression ve)
	Returns the element-wise complex conjugate of the vector expression ve (identity for real-valued vectors). More...
ConstFGridExpression	conj (ConstFGridExpression ge)
	Returns the element-wise complex conjugate of the grid expression ge (identity for real-valued grids). More...
ConstFMatrixExpression	conj (ConstFMatrixExpression me)
	Returns the element-wise complex conjugate of the matrix expression me (identity for real-valued matrices). More...
ConstFQuaternionExpression	conj (ConstFQuaternionExpression qe)
	Returns the quaternion conjugate of the quaternion expression qe (negates C2, C3, C4). More...
ConstFVectorExpression	conj (ConstFVectorExpression ve)
	Returns the element-wise complex conjugate of the vector expression ve (identity for real-valued vectors). More...
ConstLMatrixExpression	conj (ConstLMatrixExpression me)
	Returns the element-wise complex conjugate of the matrix expression me (identity for real-valued matrices). More...
ConstLQuaternionExpression	conj (ConstLQuaternionExpression qe)
	Returns the quaternion conjugate of the quaternion expression qe (negates C2, C3, C4). More...
ConstLVectorExpression	conj (ConstLVectorExpression ve)
	Returns the element-wise complex conjugate of the vector expression ve (identity for real-valued vectors). More...
ConstULMatrixExpression	conj (ConstULMatrixExpression me)
	Returns the element-wise complex conjugate of the matrix expression me (identity for real-valued matrices). More...
ConstULQuaternionExpression	conj (ConstULQuaternionExpression qe)
	Returns the quaternion conjugate of the quaternion expression qe (negates C2, C3, C4). More...
ConstULVectorExpression	conj (ConstULVectorExpression ve)
	Returns the element-wise complex conjugate of the vector expression ve (identity for real-valued vectors). More...
ConstDMatrixExpression	cross (ConstDVectorExpression e)
	Returns the cross-product (skew-symmetric) matrix corresponding to the 3D 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 3D 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 3D 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 3D vector expression e (such that cross(e) * v == crossProd(e, v)). More...
ConstDVectorExpression	crossProd (ConstDVectorExpression e1, ConstDVectorExpression e2)
	Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object. More...
ConstFVectorExpression	crossProd (ConstFVectorExpression e1, ConstFVectorExpression e2)
	Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object. More...
ConstLVectorExpression	crossProd (ConstLVectorExpression e1, ConstLVectorExpression e2)
	Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object. More...
ConstULVectorExpression	crossProd (ConstULVectorExpression e1, ConstULVectorExpression e2)
	Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object. 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 ge1, ConstDGridExpression ge2)
	Returns the element-wise quotient of the grid expressions ge1 and ge2. More...
ConstDMatrixExpression	elemDiv (ConstDMatrixExpression me1, ConstDMatrixExpression me2)
	Returns the element-wise quotient of the matrix expressions me1 and me2. More...
ConstDQuaternionExpression	elemDiv (ConstDQuaternionExpression qe1, ConstDQuaternionExpression qe2)
	Returns the component-wise quotient of the quaternion expressions qe1 and qe2. More...
ConstDVectorExpression	elemDiv (ConstDVectorExpression ve1, ConstDVectorExpression ve2)
	Returns the element-wise quotient of the vector expressions ve1 and ve2. More...
ConstFGridExpression	elemDiv (ConstFGridExpression ge1, ConstFGridExpression ge2)
	Returns the element-wise quotient of the grid expressions ge1 and ge2. More...
ConstFMatrixExpression	elemDiv (ConstFMatrixExpression me1, ConstFMatrixExpression me2)
	Returns the element-wise quotient of the matrix expressions me1 and me2. More...
ConstFQuaternionExpression	elemDiv (ConstFQuaternionExpression qe1, ConstFQuaternionExpression qe2)
	Returns the component-wise quotient of the quaternion expressions qe1 and qe2. More...
ConstFVectorExpression	elemDiv (ConstFVectorExpression ve1, ConstFVectorExpression ve2)
	Returns the element-wise quotient of the vector expressions ve1 and ve2. More...
ConstLMatrixExpression	elemDiv (ConstLMatrixExpression me1, ConstLMatrixExpression me2)
	Returns the element-wise quotient of the matrix expressions me1 and me2. More...
ConstLQuaternionExpression	elemDiv (ConstLQuaternionExpression qe1, ConstLQuaternionExpression qe2)
	Returns the component-wise quotient of the quaternion expressions qe1 and qe2. More...
ConstLVectorExpression	elemDiv (ConstLVectorExpression ve1, ConstLVectorExpression ve2)
	Returns the element-wise quotient of the vector expressions ve1 and ve2. More...
ConstULMatrixExpression	elemDiv (ConstULMatrixExpression me1, ConstULMatrixExpression me2)
	Returns the element-wise quotient of the matrix expressions me1 and me2. More...
ConstULQuaternionExpression	elemDiv (ConstULQuaternionExpression qe1, ConstULQuaternionExpression qe2)
	Returns the component-wise quotient of the quaternion expressions qe1 and qe2. More...
ConstULVectorExpression	elemDiv (ConstULVectorExpression ve1, ConstULVectorExpression ve2)
	Returns the element-wise quotient of the vector expressions ve1 and ve2. More...
ConstDGridExpression	elemProd (ConstDGridExpression ge1, ConstDGridExpression ge2)
	Returns the element-wise product of the grid expressions ge1 and ge2 (Hadamard product). More...
ConstDMatrixExpression	elemProd (ConstDMatrixExpression me1, ConstDMatrixExpression me2)
	Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2. More...
ConstDQuaternionExpression	elemProd (ConstDQuaternionExpression qe1, ConstDQuaternionExpression qe2)
	Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2. More...
ConstDVectorExpression	elemProd (ConstDVectorExpression ve1, ConstDVectorExpression ve2)
	Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2. More...
ConstFGridExpression	elemProd (ConstFGridExpression ge1, ConstFGridExpression ge2)
	Returns the element-wise product of the grid expressions ge1 and ge2 (Hadamard product). More...
ConstFMatrixExpression	elemProd (ConstFMatrixExpression me1, ConstFMatrixExpression me2)
	Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2. More...
ConstFQuaternionExpression	elemProd (ConstFQuaternionExpression qe1, ConstFQuaternionExpression qe2)
	Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2. More...
ConstFVectorExpression	elemProd (ConstFVectorExpression ve1, ConstFVectorExpression ve2)
	Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2. More...
ConstLMatrixExpression	elemProd (ConstLMatrixExpression me1, ConstLMatrixExpression me2)
	Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2. More...
ConstLQuaternionExpression	elemProd (ConstLQuaternionExpression qe1, ConstLQuaternionExpression qe2)
	Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2. More...
ConstLVectorExpression	elemProd (ConstLVectorExpression ve1, ConstLVectorExpression ve2)
	Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2. More...
ConstULMatrixExpression	elemProd (ConstULMatrixExpression me1, ConstULMatrixExpression me2)
	Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2. More...
ConstULQuaternionExpression	elemProd (ConstULQuaternionExpression qe1, ConstULQuaternionExpression qe2)
	Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2. More...
ConstULVectorExpression	elemProd (ConstULVectorExpression ve1, ConstULVectorExpression ve2)
	Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2. More...
bool	equals (ConstDGridExpression ge1, ConstDGridExpression ge2, float eps)
	Tells whether the grid expressions ge1 and ge2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstDMatrixExpression me1, ConstDMatrixExpression me2, float eps)
	Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstDQuaternionExpression qe1, ConstDQuaternionExpression qe2, float eps)
	Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps. More...
bool	equals (ConstDVectorExpression ve1, ConstDVectorExpression ve2, float eps)
	Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFGridExpression ge1, ConstFGridExpression ge2, float eps)
	Tells whether the grid expressions ge1 and ge2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFMatrixExpression me1, ConstFMatrixExpression me2, float eps)
	Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstFQuaternionExpression qe1, ConstFQuaternionExpression qe2, float eps)
	Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps. More...
bool	equals (ConstFVectorExpression ve1, ConstFVectorExpression ve2, float eps)
	Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstLMatrixExpression me1, ConstLMatrixExpression me2, int eps)
	Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstLQuaternionExpression qe1, ConstLQuaternionExpression qe2, int eps)
	Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps. More...
bool	equals (ConstLVectorExpression ve1, ConstLVectorExpression ve2, int eps)
	Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstULMatrixExpression me1, ConstULMatrixExpression me2, int eps)
	Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps. More...
bool	equals (ConstULQuaternionExpression qe1, ConstULQuaternionExpression qe2, int eps)
	Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps. More...
bool	equals (ConstULVectorExpression ve1, ConstULVectorExpression ve2, int eps)
	Tells whether the vector expressions ve1 and ve2 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 \( Q(a, x) = 1 - P(a, x) \). 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 ge)
	Returns the Hermitian conjugate of the grid expression ge (alias of conj() for grids). More...
ConstDMatrixExpression	herm (ConstDMatrixExpression me)
	Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me. More...
ConstDVectorExpression	herm (ConstDVectorExpression ve)
	Returns the Hermitian conjugate of the vector expression ve (alias of conj() for vectors). More...
ConstFGridExpression	herm (ConstFGridExpression ge)
	Returns the Hermitian conjugate of the grid expression ge (alias of conj() for grids). More...
ConstFMatrixExpression	herm (ConstFMatrixExpression me)
	Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me. More...
ConstFVectorExpression	herm (ConstFVectorExpression ve)
	Returns the Hermitian conjugate of the vector expression ve (alias of conj() for vectors). More...
ConstLMatrixExpression	herm (ConstLMatrixExpression me)
	Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me. More...
ConstLVectorExpression	herm (ConstLVectorExpression ve)
	Returns the Hermitian conjugate of the vector expression ve (alias of conj() for vectors). More...
ConstULMatrixExpression	herm (ConstULMatrixExpression me)
	Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me. More...
ConstULVectorExpression	herm (ConstULVectorExpression ve)
	Returns the Hermitian conjugate of the vector expression ve (alias of conj() for vectors). More...
ConstDHomogenousCoordsAdapter	homog (ConstDVectorExpression ce)
	Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension. More...
ConstFHomogenousCoordsAdapter	homog (ConstFVectorExpression ce)
	Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension. More...
ConstLHomogenousCoordsAdapter	homog (ConstLVectorExpression ce)
	Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension. More...
ConstULHomogenousCoordsAdapter	homog (ConstULVectorExpression ce)
	Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension. More...
DHomogenousCoordsAdapter	homog (DVectorExpression me)
	Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension. More...
FHomogenousCoordsAdapter	homog (FVectorExpression me)
	Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension. More...
LHomogenousCoordsAdapter	homog (LVectorExpression me)
	Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension. More...
ULHomogenousCoordsAdapter	homog (ULVectorExpression me)
	Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension. More...
ConstDGridExpression	imag (ConstDGridExpression ge)
	Returns the element-wise imaginary part of the grid expression ge. More...
ConstDMatrixExpression	imag (ConstDMatrixExpression me)
	Returns the element-wise imaginary part of the matrix expression me. More...
ConstDVectorExpression	imag (ConstDVectorExpression ve)
	Returns the element-wise imaginary part of the vector expression ve. More...
ConstFGridExpression	imag (ConstFGridExpression ge)
	Returns the element-wise imaginary part of the grid expression ge. More...
ConstFMatrixExpression	imag (ConstFMatrixExpression me)
	Returns the element-wise imaginary part of the matrix expression me. More...
ConstFVectorExpression	imag (ConstFVectorExpression ve)
	Returns the element-wise imaginary part of the vector expression ve. More...
ConstLMatrixExpression	imag (ConstLMatrixExpression me)
	Returns the element-wise imaginary part of the matrix expression me. More...
ConstLVectorExpression	imag (ConstLVectorExpression ve)
	Returns the element-wise imaginary part of the vector expression ve. More...
ConstULMatrixExpression	imag (ConstULMatrixExpression me)
	Returns the element-wise imaginary part of the matrix expression me. More...
ConstULVectorExpression	imag (ConstULVectorExpression ve)
	Returns the element-wise imaginary part of the vector expression ve. 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 cell value of the regular spatial grid grid at the position pos. More...
float	interpolateTrilinear (FRegularSpatialGrid grid, Vector3F pos, bool local_pos)
	Returns the trilinearly interpolated cell value of the regular spatial grid grid at the position 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 a 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 a 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 a 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 a 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 [WLUD] of the matrix e without partial pivoting. More...
int	luDecompose (DMatrixExpression e, ULVectorExpression pv)
	Computes an in-place LU decomposition [WLUD] of the matrix e with partial (row) pivoting. More...
int	luDecompose (FMatrixExpression e)
	Computes an in-place LU decomposition [WLUD] of the matrix e without partial pivoting. More...
int	luDecompose (FMatrixExpression e, ULVectorExpression pv)
	Computes an in-place LU decomposition [WLUD] of the matrix e with partial (row) pivoting. More...
int	luDecompose (LMatrixExpression e)
	Computes an in-place LU decomposition [WLUD] of the matrix e without partial pivoting. More...
int	luDecompose (LMatrixExpression e, ULVectorExpression pv)
	Computes an in-place LU decomposition [WLUD] of the matrix e with partial (row) pivoting. More...
int	luDecompose (ULMatrixExpression e)
	Computes an in-place LU decomposition [WLUD] of the matrix e without partial pivoting. More...
int	luDecompose (ULMatrixExpression e, ULVectorExpression pv)
	Computes an in-place LU decomposition [WLUD] of the matrix e with partial (row) pivoting. More...
bool	luSubstitute (ConstDMatrixExpression lu, DVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstDMatrixExpression lu, ConstULVectorExpression pv, DVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstDMatrixExpression lu, DMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstDMatrixExpression lu, ConstULVectorExpression pv, DMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstFMatrixExpression lu, FVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstFMatrixExpression lu, ConstULVectorExpression pv, FVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstFMatrixExpression lu, FMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstFMatrixExpression lu, ConstULVectorExpression pv, FMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstLMatrixExpression lu, LVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstLMatrixExpression lu, ConstULVectorExpression pv, LVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstLMatrixExpression lu, LMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstLMatrixExpression lu, ConstULVectorExpression pv, LMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstULMatrixExpression lu, ULVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstULMatrixExpression lu, ConstULVectorExpression pv, ULVectorExpression bv)
	Solves \( LU\,x = b \) for bv in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
bool	luSubstitute (ConstULMatrixExpression lu, ULMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu (without pivoting). More...
bool	luSubstitute (ConstULMatrixExpression lu, ConstULVectorExpression pv, ULMatrixExpression bm)
	Solves \( LU\,X = B \) for the matrix bm in place, given the LU decomposition [WLUD] lu and pivot vector pv. More...
float	norm1 (ConstDMatrixExpression me)
	Returns the L1 (maximum absolute column sum) norm of the matrix expression me. More...
float	norm1 (ConstDVectorExpression ve)
	Returns the L1 norm of the vector expression ve ( \( \sum_i |ve(i)| \)). More...
float	norm1 (ConstFMatrixExpression me)
	Returns the L1 (maximum absolute column sum) norm of the matrix expression me. More...
float	norm1 (ConstFVectorExpression ve)
	Returns the L1 norm of the vector expression ve ( \( \sum_i |ve(i)| \)). More...
int	norm1 (ConstLMatrixExpression me)
	Returns the L1 (maximum absolute column sum) norm of the matrix expression me. More...
int	norm1 (ConstLVectorExpression ve)
	Returns the L1 norm of the vector expression ve ( \( \sum_i |ve(i)| \)). More...
int	norm1 (ConstULMatrixExpression me)
	Returns the L1 (maximum absolute column sum) norm of the matrix expression me. More...
int	norm1 (ConstULVectorExpression ve)
	Returns the L1 norm of the vector expression ve ( \( \sum_i |ve(i)| \)). More...
float	norm2 (ConstDQuaternionExpression qe)
	Returns the squared norm of the quaternion expression qe. More...
float	norm2 (ConstDVectorExpression ve)
	Returns the L2 (Euclidean) norm of the vector expression ve ( \( \sqrt{\sum_i |ve(i)|^2} \)). More...
float	norm2 (ConstFQuaternionExpression qe)
	Returns the squared norm of the quaternion expression qe. More...
float	norm2 (ConstFVectorExpression ve)
	Returns the L2 (Euclidean) norm of the vector expression ve ( \( \sqrt{\sum_i |ve(i)|^2} \)). More...
int	norm2 (ConstLQuaternionExpression qe)
	Returns the squared norm of the quaternion expression qe. More...
int	norm2 (ConstLVectorExpression ve)
	Returns the L2 (Euclidean) norm of the vector expression ve ( \( \sqrt{\sum_i |ve(i)|^2} \)). More...
int	norm2 (ConstULQuaternionExpression qe)
	Returns the squared norm of the quaternion expression qe. More...
int	norm2 (ConstULVectorExpression ve)
	Returns the L2 (Euclidean) norm of the vector expression ve ( \( \sqrt{\sum_i |ve(i)|^2} \)). 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 me)
	Returns the L∞ (maximum absolute row sum) norm of the matrix expression me. More...
float	normInf (ConstDVectorExpression ve)
	Returns the L∞ norm of the vector expression ve ( \( \max_i |ve(i)| \)). More...
float	normInf (ConstFMatrixExpression me)
	Returns the L∞ (maximum absolute row sum) norm of the matrix expression me. More...
float	normInf (ConstFVectorExpression ve)
	Returns the L∞ norm of the vector expression ve ( \( \max_i |ve(i)| \)). More...
int	normInf (ConstLMatrixExpression me)
	Returns the L∞ (maximum absolute row sum) norm of the matrix expression me. More...
int	normInf (ConstLVectorExpression ve)
	Returns the L∞ norm of the vector expression ve ( \( \max_i |ve(i)| \)). More...
int	normInf (ConstULMatrixExpression me)
	Returns the L∞ (maximum absolute row sum) norm of the matrix expression me. More...
int	normInf (ConstULVectorExpression ve)
	Returns the L∞ norm of the vector expression ve ( \( \max_i |ve(i)| \)). 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)
	Returns the i-th entry in the sequence of the first 10000 prime numbers (starting with 2). More...
ConstDVectorExpression	prod (ConstDMatrixExpression me, ConstDVectorExpression ve)
	Returns the matrix-vector product \( me \cdot ve \) as a vector expression. More...
DVectorExpression	prod (ConstDMatrixExpression me, ConstDVectorExpression ve, DVectorExpression c)
	Computes the matrix-vector product \( me \cdot ve \) 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. 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 ve, ConstDMatrixExpression me)
	Returns the vector-matrix product \( ve \cdot me \) as a vector expression. More...
DVectorExpression	prod (ConstDVectorExpression ve, ConstDMatrixExpression me, DVectorExpression c)
	Computes the vector-matrix product \( ve \cdot me \) and stores it in c. More...
ConstFVectorExpression	prod (ConstFMatrixExpression me, ConstFVectorExpression ve)
	Returns the matrix-vector product \( me \cdot ve \) as a vector expression. More...
FVectorExpression	prod (ConstFMatrixExpression me, ConstFVectorExpression ve, FVectorExpression c)
	Computes the matrix-vector product \( me \cdot ve \) 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. 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 ve, ConstFMatrixExpression me)
	Returns the vector-matrix product \( ve \cdot me \) as a vector expression. More...
FVectorExpression	prod (ConstFVectorExpression ve, ConstFMatrixExpression me, FVectorExpression c)
	Computes the vector-matrix product \( ve \cdot me \) and stores it in c. More...
ConstLVectorExpression	prod (ConstLMatrixExpression me, ConstLVectorExpression ve)
	Returns the matrix-vector product \( me \cdot ve \) as a vector expression. More...
LVectorExpression	prod (ConstLMatrixExpression me, ConstLVectorExpression ve, LVectorExpression c)
	Computes the matrix-vector product \( me \cdot ve \) 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. 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 ve, ConstLMatrixExpression me)
	Returns the vector-matrix product \( ve \cdot me \) as a vector expression. More...
LVectorExpression	prod (ConstLVectorExpression ve, ConstLMatrixExpression me, LVectorExpression c)
	Computes the vector-matrix product \( ve \cdot me \) and stores it in c. More...
ConstULVectorExpression	prod (ConstULMatrixExpression me, ConstULVectorExpression ve)
	Returns the matrix-vector product \( me \cdot ve \) as a vector expression. More...
ULVectorExpression	prod (ConstULMatrixExpression me, ConstULVectorExpression ve, ULVectorExpression c)
	Computes the matrix-vector product \( me \cdot ve \) 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. 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 ve, ConstULMatrixExpression me)
	Returns the vector-matrix product \( ve \cdot me \) as a vector expression. More...
ULVectorExpression	prod (ConstULVectorExpression ve, ConstULMatrixExpression me, ULVectorExpression c)
	Computes the vector-matrix product \( ve \cdot me \) 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 ce)
	Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion. More...
ConstFVectorQuaternionAdapter	quat (ConstFVectorExpression ce)
	Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion. More...
ConstLVectorQuaternionAdapter	quat (ConstLVectorExpression ce)
	Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion. More...
ConstULVectorQuaternionAdapter	quat (ConstULVectorExpression ce)
	Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion. More...
DVectorQuaternionAdapter	quat (DVectorExpression me)
	Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion. More...
FVectorQuaternionAdapter	quat (FVectorExpression me)
	Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion. More...
LVectorQuaternionAdapter	quat (LVectorExpression me)
	Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion. More...
ULVectorQuaternionAdapter	quat (ULVectorExpression me)
	Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion. More...
FRealQuaternion	quat (float t)
	Constructs a real quaternion from the scalar t (its real component). More...
FQuaternion	quat (float t1, float t2)
	Constructs a 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 quaternion from three scalar components (C1, C2, C3) — C4 is zero. More...
FQuaternion	quat (float t1, float t2, float t3, float t4)
	Constructs a quaternion from four scalar components (C1, C2, C3, C4). More...
LRealQuaternion	quat (int t)
	Constructs a real quaternion from the scalar t (its real component). More...
LQuaternion	quat (int t1, int t2)
	Constructs a 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 quaternion from three scalar components (C1, C2, C3) — C4 is zero. More...
LQuaternion	quat (int t1, int t2, int t3, int t4)
	Constructs a quaternion from four scalar components (C1, C2, C3, C4). More...
ConstDMatrixRange	range (ConstDMatrixExpression cme, Range r1, Range r2)
	Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme. More...
ConstDMatrixRange	range (ConstDMatrixExpression cme, int start1, int stop1, int start2, int stop2)
	Returns a constant matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of cme. More...
ConstDVectorRange	range (ConstDVectorExpression cve, Range r)
	Returns a constant vector proxy viewing the subrange r of cve. More...
ConstDVectorRange	range (ConstDVectorExpression cve, int start, int stop)
	Returns a constant vector proxy viewing the subrange [start, stop) of cve. More...
ConstFMatrixRange	range (ConstFMatrixExpression cme, Range r1, Range r2)
	Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme. More...
ConstFMatrixRange	range (ConstFMatrixExpression cme, int start1, int stop1, int start2, int stop2)
	Returns a constant matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of cme. More...
ConstFVectorRange	range (ConstFVectorExpression cve, Range r)
	Returns a constant vector proxy viewing the subrange r of cve. More...
ConstFVectorRange	range (ConstFVectorExpression cve, int start, int stop)
	Returns a constant vector proxy viewing the subrange [start, stop) of cve. More...
ConstLMatrixRange	range (ConstLMatrixExpression cme, Range r1, Range r2)
	Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme. More...
ConstLMatrixRange	range (ConstLMatrixExpression cme, int start1, int stop1, int start2, int stop2)
	Returns a constant matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of cme. More...
ConstLVectorRange	range (ConstLVectorExpression cve, Range r)
	Returns a constant vector proxy viewing the subrange r of cve. More...
ConstLVectorRange	range (ConstLVectorExpression cve, int start, int stop)
	Returns a constant vector proxy viewing the subrange [start, stop) of cve. More...
ConstULMatrixRange	range (ConstULMatrixExpression cme, Range r1, Range r2)
	Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme. More...
ConstULMatrixRange	range (ConstULMatrixExpression cme, int start1, int stop1, int start2, int stop2)
	Returns a constant matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of cme. More...
ConstULVectorRange	range (ConstULVectorExpression cve, Range r)
	Returns a constant vector proxy viewing the subrange r of cve. More...
ConstULVectorRange	range (ConstULVectorExpression cve, int start, int stop)
	Returns a constant vector proxy viewing the subrange [start, stop) of cve. More...
DMatrixRange	range (DMatrixExpression mme, Range r1, Range r2)
	Returns a mutable matrix range proxy viewing the range of rows in r1 and columns in r2 of mme. More...
DMatrixRange	range (DMatrixExpression mme, int start1, int stop1, int start2, int stop2)
	Returns a mutable matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of mme. More...
DVectorRange	range (DVectorExpression mve, Range r)
	Returns a mutable vector proxy viewing the subrange r of mve. More...
DVectorRange	range (DVectorExpression mve, int start, int stop)
	Returns a mutable vector proxy viewing the subrange [start, stop) of mve. More...
FMatrixRange	range (FMatrixExpression mme, Range r1, Range r2)
	Returns a mutable matrix range proxy viewing the range of rows in r1 and columns in r2 of mme. More...
FMatrixRange	range (FMatrixExpression mme, int start1, int stop1, int start2, int stop2)
	Returns a mutable matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of mme. More...
FVectorRange	range (FVectorExpression mve, Range r)
	Returns a mutable vector proxy viewing the subrange r of mve. More...
FVectorRange	range (FVectorExpression mve, int start, int stop)
	Returns a mutable vector proxy viewing the subrange [start, stop) of mve. More...
LMatrixRange	range (LMatrixExpression mme, Range r1, Range r2)
	Returns a mutable matrix range proxy viewing the range of rows in r1 and columns in r2 of mme. More...
LMatrixRange	range (LMatrixExpression mme, int start1, int stop1, int start2, int stop2)
	Returns a mutable matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of mme. More...
LVectorRange	range (LVectorExpression mve, Range r)
	Returns a mutable vector proxy viewing the subrange r of mve. More...
LVectorRange	range (LVectorExpression mve, int start, int stop)
	Returns a mutable vector proxy viewing the subrange [start, stop) of mve. More...
ULMatrixRange	range (ULMatrixExpression mme, Range r1, Range r2)
	Returns a mutable matrix range proxy viewing the range of rows in r1 and columns in r2 of mme. More...
ULMatrixRange	range (ULMatrixExpression mme, int start1, int stop1, int start2, int stop2)
	Returns a mutable matrix proxy viewing the range of rows [start1, stop1) and columns [start2, stop2) of mme. More...
ULVectorRange	range (ULVectorExpression mve, Range r)
	Returns a mutable vector proxy viewing the subrange r of mve. More...
ULVectorRange	range (ULVectorExpression mve, int start, int stop)
	Returns a mutable vector proxy viewing the subrange [start, stop) of mve. More...
Range	range (int start, int stop)
	Convenience factory function for Math.Range with std::size_t indices. More...
ConstDGridExpression	real (ConstDGridExpression ge)
	Returns the element-wise real part of the grid expression ge. More...
ConstDMatrixExpression	real (ConstDMatrixExpression me)
	Returns the element-wise real part of the matrix expression me. More...
float	real (ConstDQuaternionExpression qe)
	Returns the real component (C1) of the quaternion expression qe. More...
ConstDVectorExpression	real (ConstDVectorExpression ve)
	Returns the element-wise real part of the vector expression ve. More...
ConstFGridExpression	real (ConstFGridExpression ge)
	Returns the element-wise real part of the grid expression ge. More...
ConstFMatrixExpression	real (ConstFMatrixExpression me)
	Returns the element-wise real part of the matrix expression me. More...
float	real (ConstFQuaternionExpression qe)
	Returns the real component (C1) of the quaternion expression qe. More...
ConstFVectorExpression	real (ConstFVectorExpression ve)
	Returns the element-wise real part of the vector expression ve. More...
ConstLMatrixExpression	real (ConstLMatrixExpression me)
	Returns the element-wise real part of the matrix expression me. More...
int	real (ConstLQuaternionExpression qe)
	Returns the real component (C1) of the quaternion expression qe. More...
ConstLVectorExpression	real (ConstLVectorExpression ve)
	Returns the element-wise real part of the vector expression ve. More...
ConstULMatrixExpression	real (ConstULMatrixExpression me)
	Returns the element-wise real part of the matrix expression me. More...
int	real (ConstULQuaternionExpression qe)
	Returns the real component (C1) of the quaternion expression qe. More...
ConstULVectorExpression	real (ConstULVectorExpression ve)
	Returns the element-wise real part of the vector expression ve. 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 ce, int i)
	Returns a constant matrix proxy viewing row i of ce. More...
ConstFMatrixRow	row (ConstFMatrixExpression ce, int i)
	Returns a constant matrix proxy viewing row i of ce. More...
ConstLMatrixRow	row (ConstLMatrixExpression ce, int i)
	Returns a constant matrix proxy viewing row i of ce. More...
ConstULMatrixRow	row (ConstULMatrixExpression ce, int i)
	Returns a constant matrix proxy viewing row i of ce. More...
DMatrixRow	row (DMatrixExpression me, int i)
	Returns a mutable matrix proxy viewing row i of me. More...
FMatrixRow	row (FMatrixExpression me, int i)
	Returns a mutable matrix proxy viewing row i of me. More...
LMatrixRow	row (LMatrixExpression me, int i)
	Returns a mutable matrix proxy viewing row i of me. More...
ULMatrixRow	row (ULMatrixExpression me, int i)
	Returns a mutable matrix proxy viewing row i of me. More...
float	sign (float a, float b)
	Returns the magnitude of parameter a times the sign of parameter b. More...
ConstDMatrixSlice	slice (ConstDMatrixExpression cme, Slice s1, Slice s2)
	Returns a constant matrix proxy viewing the strided rectangular slice (s1, s2) of cme. More...
ConstDMatrixSlice	slice (ConstDMatrixExpression cme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme. More...
ConstDVectorSlice	slice (ConstDVectorExpression cve, Slice s)
	Returns a constant vector proxy viewing the strided slice s of cve. More...
ConstDVectorSlice	slice (ConstDVectorExpression cve, int start, int stride, int size)
	Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve. More...
ConstFMatrixSlice	slice (ConstFMatrixExpression cme, Slice s1, Slice s2)
	Returns a constant matrix proxy viewing the strided rectangular slice (s1, s2) of cme. More...
ConstFMatrixSlice	slice (ConstFMatrixExpression cme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme. More...
ConstFVectorSlice	slice (ConstFVectorExpression cve, Slice s)
	Returns a constant vector proxy viewing the strided slice s of cve. More...
ConstFVectorSlice	slice (ConstFVectorExpression cve, int start, int stride, int size)
	Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve. More...
ConstLMatrixSlice	slice (ConstLMatrixExpression cme, Slice s1, Slice s2)
	Returns a constant matrix proxy viewing the strided rectangular slice (s1, s2) of cme. More...
ConstLMatrixSlice	slice (ConstLMatrixExpression cme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme. More...
ConstLVectorSlice	slice (ConstLVectorExpression cve, Slice s)
	Returns a constant vector proxy viewing the strided slice s of cve. More...
ConstLVectorSlice	slice (ConstLVectorExpression cve, int start, int stride, int size)
	Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve. More...
ConstULMatrixSlice	slice (ConstULMatrixExpression cme, Slice s1, Slice s2)
	Returns a constant matrix proxy viewing the strided rectangular slice (s1, s2) of cme. More...
ConstULMatrixSlice	slice (ConstULMatrixExpression cme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme. More...
ConstULVectorSlice	slice (ConstULVectorExpression cve, Slice s)
	Returns a constant vector proxy viewing the strided slice s of cve. More...
ConstULVectorSlice	slice (ConstULVectorExpression cve, int start, int stride, int size)
	Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve. More...
DMatrixSlice	slice (DMatrixExpression mme, Slice s1, Slice s2)
	Returns a mutable matrix slice proxy viewing the strided rectangular slice (s1, s2) of mme. More...
DMatrixSlice	slice (DMatrixExpression mme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme. More...
DVectorSlice	slice (DVectorExpression mve, Slice s)
	Returns a mutable vector proxy viewing the strided slice s of mve. More...
DVectorSlice	slice (DVectorExpression mve, int start, int stride, int size)
	Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve. More...
FMatrixSlice	slice (FMatrixExpression mme, Slice s1, Slice s2)
	Returns a mutable matrix slice proxy viewing the strided rectangular slice (s1, s2) of mme. More...
FMatrixSlice	slice (FMatrixExpression mme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme. More...
FVectorSlice	slice (FVectorExpression mve, Slice s)
	Returns a mutable vector proxy viewing the strided slice s of mve. More...
FVectorSlice	slice (FVectorExpression mve, int start, int stride, int size)
	Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve. More...
LMatrixSlice	slice (LMatrixExpression mme, Slice s1, Slice s2)
	Returns a mutable matrix slice proxy viewing the strided rectangular slice (s1, s2) of mme. More...
LMatrixSlice	slice (LMatrixExpression mme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme. More...
LVectorSlice	slice (LVectorExpression mve, Slice s)
	Returns a mutable vector proxy viewing the strided slice s of mve. More...
LVectorSlice	slice (LVectorExpression mve, int start, int stride, int size)
	Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve. More...
ULMatrixSlice	slice (ULMatrixExpression mme, Slice s1, Slice s2)
	Returns a mutable matrix slice proxy viewing the strided rectangular slice (s1, s2) of mme. More...
ULMatrixSlice	slice (ULMatrixExpression mme, int start1, int stride1, int size1, int start2, int stride2, int size2)
	Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme. More...
ULVectorSlice	slice (ULVectorExpression mve, Slice s)
	Returns a mutable vector proxy viewing the strided slice s of mve. More...
ULVectorSlice	slice (ULVectorExpression mve, int start, int stride, int size)
	Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve. More...
Slice	slice (int start, int stride, int size)
	Convenience factory function for Math.Slice with std::size_t indices and std::ptrdiff_t stride. More...
bool	solveLower (ConstDMatrixExpression l, DVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstDMatrixExpression l, DMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstFMatrixExpression l, FVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstFMatrixExpression l, FMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstLMatrixExpression l, LVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstLMatrixExpression l, LMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstULMatrixExpression l, ULVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveLower (ConstULMatrixExpression l, ULMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a lower-triangular matrix. More...
bool	solveUnitLower (ConstDMatrixExpression l, DVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a unit lower-triangular matrix (1 on the diagonal). More...
bool	solveUnitLower (ConstDMatrixExpression l, DMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstFMatrixExpression l, FVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a unit lower-triangular matrix (1 on the diagonal). More...
bool	solveUnitLower (ConstFMatrixExpression l, FMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstLMatrixExpression l, LVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a unit lower-triangular matrix (1 on the diagonal). More...
bool	solveUnitLower (ConstLMatrixExpression l, LMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a unit lower-triangular matrix. More...
bool	solveUnitLower (ConstULMatrixExpression l, ULVectorExpression bv)
	Solves \( L\,x = b \) in place by forward-substitution, where l is a unit lower-triangular matrix (1 on the diagonal). More...
bool	solveUnitLower (ConstULMatrixExpression l, ULMatrixExpression bm)
	Solves \( L\,X = B \) in place column-wise by forward-substitution, where l is a unit lower-triangular matrix. More...
bool	solveUnitUpper (ConstDMatrixExpression u, DVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is a unit upper-triangular matrix (1 on the diagonal). More...
bool	solveUnitUpper (ConstDMatrixExpression u, DMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstFMatrixExpression u, FVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is a unit upper-triangular matrix (1 on the diagonal). More...
bool	solveUnitUpper (ConstFMatrixExpression u, FMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstLMatrixExpression u, LVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is a unit upper-triangular matrix (1 on the diagonal). More...
bool	solveUnitUpper (ConstLMatrixExpression u, LMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is a unit upper-triangular matrix. More...
bool	solveUnitUpper (ConstULMatrixExpression u, ULVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is a unit upper-triangular matrix (1 on the diagonal). More...
bool	solveUnitUpper (ConstULMatrixExpression u, ULMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is a unit upper-triangular matrix. More...
bool	solveUpper (ConstDMatrixExpression u, DVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstDMatrixExpression u, DMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstFMatrixExpression u, FVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstFMatrixExpression u, FMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstLMatrixExpression u, LVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstLMatrixExpression u, LMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstULMatrixExpression u, ULVectorExpression bv)
	Solves \( U\,x = b \) in place by back-substitution, where u is an upper-triangular matrix. More...
bool	solveUpper (ConstULMatrixExpression u, ULMatrixExpression bm)
	Solves \( U\,X = B \) in place column-wise by back-substitution, where u is an upper-triangular matrix. More...
float	sum (ConstDGridExpression ge)
	Returns the sum of all elements of the grid expression ge. More...
float	sum (ConstDMatrixExpression me)
	Returns the sum of all elements of the matrix expression me. More...
float	sum (ConstDQuaternionExpression qe)
	Returns the sum of the four components of the quaternion expression qe. More...
float	sum (ConstDVectorExpression ve)
	Returns the sum of all elements of the vector expression ve. More...
float	sum (ConstFGridExpression ge)
	Returns the sum of all elements of the grid expression ge. More...
float	sum (ConstFMatrixExpression me)
	Returns the sum of all elements of the matrix expression me. More...
float	sum (ConstFQuaternionExpression qe)
	Returns the sum of the four components of the quaternion expression qe. More...
float	sum (ConstFVectorExpression ve)
	Returns the sum of all elements of the vector expression ve. More...
int	sum (ConstLMatrixExpression me)
	Returns the sum of all elements of the matrix expression me. More...
int	sum (ConstLQuaternionExpression qe)
	Returns the sum of the four components of the quaternion expression qe. More...
int	sum (ConstLVectorExpression ve)
	Returns the sum of all elements of the vector expression ve. More...
int	sum (ConstULMatrixExpression me)
	Returns the sum of all elements of the matrix expression me. More...
int	sum (ConstULQuaternionExpression qe)
	Returns the sum of the four components of the quaternion expression qe. More...
int	sum (ConstULVectorExpression ve)
	Returns the sum of all elements of the vector expression ve. More...
int	sum (object ge)
	Returns the sum of all elements of the grid expression ge. 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 vector \( X \) 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 vector \( X \) 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 vector \( X \) 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 vector \( X \) 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 vector \( X \) 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 vector \( X \) 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 vector \( X \) 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 vector \( X \) 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 ce)
	Returns a transposed view of the constant matrix expression ce. More...
ConstFMatrixTranspose	trans (ConstFMatrixExpression ce)
	Returns a transposed view of the constant matrix expression ce. More...
ConstLMatrixTranspose	trans (ConstLMatrixExpression ce)
	Returns a transposed view of the constant matrix expression ce. More...
ConstULMatrixTranspose	trans (ConstULMatrixExpression ce)
	Returns a transposed view of the constant matrix expression ce. More...
DMatrixTranspose	trans (DMatrixExpression me)
	Returns a transposed view of the mutable matrix expression me. More...
FMatrixTranspose	trans (FMatrixExpression me)
	Returns a transposed view of the mutable matrix expression me. More...
LMatrixTranspose	trans (LMatrixExpression me)
	Returns a transposed view of the mutable matrix expression me. More...
ULMatrixTranspose	trans (ULMatrixExpression me)
	Returns a transposed view of the mutable matrix expression me. More...
None	transform (Vector2DArray va, Matrix2D xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2DArray va, Matrix3D xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2FArray va, Matrix2F xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2FArray va, Matrix3F xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2LArray va, Matrix2L xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2LArray va, Matrix3L xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2ULArray va, Matrix2UL xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector2ULArray va, Matrix3UL xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3DArray va, Matrix3D xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3DArray va, Matrix4D xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3FArray va, Matrix3F xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3FArray va, Matrix4F xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3LArray va, Matrix3L xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3LArray va, Matrix4L xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3ULArray va, Matrix3UL xform)
	Transforms each vector in the array with the transformation matrix xform. More...
None	transform (Vector3ULArray va, Matrix4UL xform)
	Transforms each vector in the array with the transformation matrix xform. More...
ConstUpperTriangularDMatrixAdapter	triang (ConstDMatrixExpression ce, Upper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitUpperTriangularDMatrixAdapter	triang (ConstDMatrixExpression ce, UnitUpper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstLowerTriangularDMatrixAdapter	triang (ConstDMatrixExpression ce, Lower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitLowerTriangularDMatrixAdapter	triang (ConstDMatrixExpression ce, UnitLower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUpperTriangularFMatrixAdapter	triang (ConstFMatrixExpression ce, Upper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitUpperTriangularFMatrixAdapter	triang (ConstFMatrixExpression ce, UnitUpper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstLowerTriangularFMatrixAdapter	triang (ConstFMatrixExpression ce, Lower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitLowerTriangularFMatrixAdapter	triang (ConstFMatrixExpression ce, UnitLower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUpperTriangularLMatrixAdapter	triang (ConstLMatrixExpression ce, Upper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitUpperTriangularLMatrixAdapter	triang (ConstLMatrixExpression ce, UnitUpper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstLowerTriangularLMatrixAdapter	triang (ConstLMatrixExpression ce, Lower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitLowerTriangularLMatrixAdapter	triang (ConstLMatrixExpression ce, UnitLower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUpperTriangularULMatrixAdapter	triang (ConstULMatrixExpression ce, Upper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitUpperTriangularULMatrixAdapter	triang (ConstULMatrixExpression ce, UnitUpper type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstLowerTriangularULMatrixAdapter	triang (ConstULMatrixExpression ce, Lower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
ConstUnitLowerTriangularULMatrixAdapter	triang (ConstULMatrixExpression ce, UnitLower type)
	Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type. More...
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 ce)
	Returns a mutable quaternion adapter that exposes ce as 4-element vector expression. More...
ConstFQuaternionVectorAdapter	vec (ConstFQuaternionExpression ce)
	Returns a mutable quaternion adapter that exposes ce as 4-element vector expression. More...
ConstLQuaternionVectorAdapter	vec (ConstLQuaternionExpression ce)
	Returns a mutable quaternion adapter that exposes ce as 4-element vector expression. More...
ConstULQuaternionVectorAdapter	vec (ConstULQuaternionExpression ce)
	Returns a mutable quaternion adapter that exposes ce as 4-element vector expression. More...
DQuaternionVectorAdapter	vec (DQuaternionExpression me)
	Returns a mutable quaternion adapter that exposes me as 4-element vector expression. More...
FQuaternionVectorAdapter	vec (FQuaternionExpression me)
	Returns a mutable quaternion adapter that exposes me as 4-element vector expression. More...
LQuaternionVectorAdapter	vec (LQuaternionExpression me)
	Returns a mutable quaternion adapter that exposes me as 4-element vector expression. More...
ULQuaternionVectorAdapter	vec (ULQuaternionExpression me)
	Returns a mutable quaternion adapter that exposes me as 4-element vector expression. More...
Vector2F	vec (float t1, float t2)
	Constructs a vector of size 2 from the components t1 and t2. More...
Vector3F	vec (float t1, float t2, float t3)
	Constructs a vector of size 3 from the components t1, t2 and t3. More...
Vector4F	vec (float t1, float t2, float t3, float t4)
	Constructs a vector of size 4 from the components t1, t2, t3 and t4. More...
Vector2L	vec (int t1, int t2)
	Constructs a vector of size 2 from the components t1 and t2. More...
Vector3L	vec (int t1, int t2, int t3)
	Constructs a vector of size 3 from the components t1, t2 and t3. More...
Vector4L	vec (int t1, int t2, int t3, int t4)
	Constructs a vector 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 (optionally clamped) cosine of the angle between the vector expressions e1 and e2.

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 (optionally clamped) cosine of the angle between the vector expressions e1 and e2.

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 (optionally clamped) cosine of the angle between the vector expressions e1 and e2.

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 (optionally clamped) cosine of the angle between the vector expressions e1 and e2.

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
	)

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [2/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [3/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [4/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [5/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [6/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [7/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcCentroid() [8/8]

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

Calculates the centroid of the array elements.

Parameters

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

Returns

True if the array is not empty, and False otherwise.

calcRMSD() [1/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [2/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [3/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [4/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [5/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [6/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [7/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [8/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [9/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [10/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [11/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [12/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [13/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [14/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

calcRMSD() [15/16]

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

Calculates the RMSD between the corresponding elements of va1 and va2.

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

Parameters

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

Returns

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

calcRMSD() [16/16]

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

Calculates the RMSD between corresponding elements of va1 and va2 after applying the homogeneous transformation va1_xform to the elements of va1.

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

Parameters

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

Returns

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

column() [1/8]

ConstDMatrixColumn CDPL.Math.column	(	ConstDMatrixExpression	ce,
		int	j
	)

Returns a constant matrix proxy viewing column j of ce.

Parameters

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

Returns

A proxy object referring to column j of ce.

column() [2/8]

ConstFMatrixColumn CDPL.Math.column	(	ConstFMatrixExpression	ce,
		int	j
	)

Returns a constant matrix proxy viewing column j of ce.

Parameters

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

Returns

A proxy object referring to column j of ce.

column() [3/8]

ConstLMatrixColumn CDPL.Math.column	(	ConstLMatrixExpression	ce,
		int	j
	)

Returns a constant matrix proxy viewing column j of ce.

Parameters

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

Returns

A proxy object referring to column j of ce.

column() [4/8]

ConstULMatrixColumn CDPL.Math.column	(	ConstULMatrixExpression	ce,
		int	j
	)

Returns a constant matrix proxy viewing column j of ce.

Parameters

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

Returns

A proxy object referring to column j of ce.

column() [5/8]

DMatrixColumn CDPL.Math.column	(	DMatrixExpression	me,
		int	j
	)

Returns a mutable matrix proxy viewing column j of me.

Parameters

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

Returns

A proxy object referring to column j of me.

column() [6/8]

FMatrixColumn CDPL.Math.column	(	FMatrixExpression	me,
		int	j
	)

Returns a mutable matrix proxy viewing column j of me.

Parameters

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

Returns

A proxy object referring to column j of me.

column() [7/8]

LMatrixColumn CDPL.Math.column	(	LMatrixExpression	me,
		int	j
	)

Returns a mutable matrix proxy viewing column j of me.

Parameters

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

Returns

A proxy object referring to column j of me.

column() [8/8]

ULMatrixColumn CDPL.Math.column	(	ULMatrixExpression	me,
		int	j
	)

Returns a mutable matrix proxy viewing column j of me.

Parameters

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

Returns

A proxy object referring to column j of me.

conj() [1/14]

ConstDGridExpression CDPL.Math.conj

(

ConstDGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing \( \overline{ge} \).

conj() [2/14]

ConstDMatrixExpression CDPL.Math.conj

(

ConstDMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me} \).

conj() [3/14]

ConstDQuaternionExpression CDPL.Math.conj

(

ConstDQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

An expression object representing \( \overline{qe} \).

conj() [4/14]

ConstDVectorExpression CDPL.Math.conj

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

conj() [5/14]

ConstFGridExpression CDPL.Math.conj

(

ConstFGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing \( \overline{ge} \).

conj() [6/14]

ConstFMatrixExpression CDPL.Math.conj

(

ConstFMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me} \).

conj() [7/14]

ConstFQuaternionExpression CDPL.Math.conj

(

ConstFQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

An expression object representing \( \overline{qe} \).

conj() [8/14]

ConstFVectorExpression CDPL.Math.conj

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

conj() [9/14]

ConstLMatrixExpression CDPL.Math.conj

(

ConstLMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me} \).

conj() [10/14]

ConstLQuaternionExpression CDPL.Math.conj

(

ConstLQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

An expression object representing \( \overline{qe} \).

conj() [11/14]

ConstLVectorExpression CDPL.Math.conj

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

conj() [12/14]

ConstULMatrixExpression CDPL.Math.conj

(

ConstULMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me} \).

conj() [13/14]

ConstULQuaternionExpression CDPL.Math.conj

(

ConstULQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

An expression object representing \( \overline{qe} \).

conj() [14/14]

ConstULVectorExpression CDPL.Math.conj

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

cross() [1/4]

ConstDMatrixExpression CDPL.Math.cross

(

ConstDVectorExpression

e

)

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

Parameters

e	The 3D vector expression.

Returns

An expression object representing the skew-symmetric matrix.

cross() [2/4]

ConstFMatrixExpression CDPL.Math.cross

(

ConstFVectorExpression

e

)

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

Parameters

e	The 3D vector expression.

Returns

An expression object representing the skew-symmetric matrix.

cross() [3/4]

ConstLMatrixExpression CDPL.Math.cross

(

ConstLVectorExpression

e

)

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

Parameters

e	The 3D vector expression.

Returns

An expression object representing the skew-symmetric matrix.

cross() [4/4]

ConstULMatrixExpression CDPL.Math.cross

(

ConstULVectorExpression

e

)

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

Parameters

e	The 3D vector expression.

Returns

An expression object representing the skew-symmetric matrix.

crossProd() [1/4]

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

Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object.

Parameters

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

Returns

An expression object representing the cross product.

crossProd() [2/4]

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

Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object.

Parameters

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

Returns

An expression object representing the cross product.

crossProd() [3/4]

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

Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object.

Parameters

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

Returns

An expression object representing the cross product.

crossProd() [4/4]

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

Returns the 3D vector cross product \( e_1 \times e_2 \) as an expression object.

Parameters

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

Returns

An expression object 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 object 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 object 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 object 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 object representing the diagonal matrix.

elemDiv() [1/14]

ConstDGridExpression CDPL.Math.elemDiv	(	ConstDGridExpression	ge1,
		ConstDGridExpression	ge2
	)

Returns the element-wise quotient of the grid expressions ge1 and ge2.

Parameters

ge1	The numerator grid expression.
ge2	The denominator grid expression.

Returns

An expression object representing the element-wise quotient \( ge_1 / ge_2 \).

elemDiv() [2/14]

ConstDMatrixExpression CDPL.Math.elemDiv	(	ConstDMatrixExpression	me1,
		ConstDMatrixExpression	me2
	)

Returns the element-wise quotient of the matrix expressions me1 and me2.

Parameters

me1	The numerator matrix expression.
me2	The denominator matrix expression.

Returns

An expression object representing the element-wise quotient \( me_1 / me_2 \).

elemDiv() [3/14]

ConstDQuaternionExpression CDPL.Math.elemDiv	(	ConstDQuaternionExpression	qe1,
		ConstDQuaternionExpression	qe2
	)

Returns the component-wise quotient of the quaternion expressions qe1 and qe2.

Parameters

qe1	The numerator quaternion expression.
qe2	The denominator quaternion expression.

Returns

An expression object representing the component-wise quotient \( qe_1 / qe_2 \).

elemDiv() [4/14]

ConstDVectorExpression CDPL.Math.elemDiv	(	ConstDVectorExpression	ve1,
		ConstDVectorExpression	ve2
	)

Returns the element-wise quotient of the vector expressions ve1 and ve2.

Parameters

ve1	The numerator vector expression.
ve2	The denominator vector expression.

Returns

An expression object representing the element-wise quotient \( ve_1 / ve_2 \).

elemDiv() [5/14]

ConstFGridExpression CDPL.Math.elemDiv	(	ConstFGridExpression	ge1,
		ConstFGridExpression	ge2
	)

Returns the element-wise quotient of the grid expressions ge1 and ge2.

Parameters

ge1	The numerator grid expression.
ge2	The denominator grid expression.

Returns

An expression object representing the element-wise quotient \( ge_1 / ge_2 \).

elemDiv() [6/14]

ConstFMatrixExpression CDPL.Math.elemDiv	(	ConstFMatrixExpression	me1,
		ConstFMatrixExpression	me2
	)

Returns the element-wise quotient of the matrix expressions me1 and me2.

Parameters

me1	The numerator matrix expression.
me2	The denominator matrix expression.

Returns

An expression object representing the element-wise quotient \( me_1 / me_2 \).

elemDiv() [7/14]

ConstFQuaternionExpression CDPL.Math.elemDiv	(	ConstFQuaternionExpression	qe1,
		ConstFQuaternionExpression	qe2
	)

Returns the component-wise quotient of the quaternion expressions qe1 and qe2.

Parameters

qe1	The numerator quaternion expression.
qe2	The denominator quaternion expression.

Returns

An expression object representing the component-wise quotient \( qe_1 / qe_2 \).

elemDiv() [8/14]

ConstFVectorExpression CDPL.Math.elemDiv	(	ConstFVectorExpression	ve1,
		ConstFVectorExpression	ve2
	)

Returns the element-wise quotient of the vector expressions ve1 and ve2.

Parameters

ve1	The numerator vector expression.
ve2	The denominator vector expression.

Returns

An expression object representing the element-wise quotient \( ve_1 / ve_2 \).

elemDiv() [9/14]

ConstLMatrixExpression CDPL.Math.elemDiv	(	ConstLMatrixExpression	me1,
		ConstLMatrixExpression	me2
	)

Returns the element-wise quotient of the matrix expressions me1 and me2.

Parameters

me1	The numerator matrix expression.
me2	The denominator matrix expression.

Returns

An expression object representing the element-wise quotient \( me_1 / me_2 \).

elemDiv() [10/14]

ConstLQuaternionExpression CDPL.Math.elemDiv	(	ConstLQuaternionExpression	qe1,
		ConstLQuaternionExpression	qe2
	)

Returns the component-wise quotient of the quaternion expressions qe1 and qe2.

Parameters

qe1	The numerator quaternion expression.
qe2	The denominator quaternion expression.

Returns

An expression object representing the component-wise quotient \( qe_1 / qe_2 \).

elemDiv() [11/14]

ConstLVectorExpression CDPL.Math.elemDiv	(	ConstLVectorExpression	ve1,
		ConstLVectorExpression	ve2
	)

Returns the element-wise quotient of the vector expressions ve1 and ve2.

Parameters

ve1	The numerator vector expression.
ve2	The denominator vector expression.

Returns

An expression object representing the element-wise quotient \( ve_1 / ve_2 \).

elemDiv() [12/14]

ConstULMatrixExpression CDPL.Math.elemDiv	(	ConstULMatrixExpression	me1,
		ConstULMatrixExpression	me2
	)

Returns the element-wise quotient of the matrix expressions me1 and me2.

Parameters

me1	The numerator matrix expression.
me2	The denominator matrix expression.

Returns

An expression object representing the element-wise quotient \( me_1 / me_2 \).

elemDiv() [13/14]

ConstULQuaternionExpression CDPL.Math.elemDiv	(	ConstULQuaternionExpression	qe1,
		ConstULQuaternionExpression	qe2
	)

Returns the component-wise quotient of the quaternion expressions qe1 and qe2.

Parameters

qe1	The numerator quaternion expression.
qe2	The denominator quaternion expression.

Returns

An expression object representing the component-wise quotient \( qe_1 / qe_2 \).

elemDiv() [14/14]

ConstULVectorExpression CDPL.Math.elemDiv	(	ConstULVectorExpression	ve1,
		ConstULVectorExpression	ve2
	)

Returns the element-wise quotient of the vector expressions ve1 and ve2.

Parameters

ve1	The numerator vector expression.
ve2	The denominator vector expression.

Returns

An expression object representing the element-wise quotient \( ve_1 / ve_2 \).

elemProd() [1/14]

ConstDGridExpression CDPL.Math.elemProd	(	ConstDGridExpression	ge1,
		ConstDGridExpression	ge2
	)

Returns the element-wise product of the grid expressions ge1 and ge2 (Hadamard product).

Parameters

ge1	The first grid expression.
ge2	The second grid expression.

Returns

An expression object representing the element-wise product \( ge_1 \odot ge_2 \).

elemProd() [2/14]

ConstDMatrixExpression CDPL.Math.elemProd	(	ConstDMatrixExpression	me1,
		ConstDMatrixExpression	me2
	)

Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2.

Parameters

me1	The first matrix expression.
me2	The second matrix expression.

Returns

An expression object representing the element-wise product \( me_1 \odot me_2 \).

elemProd() [3/14]

ConstDQuaternionExpression CDPL.Math.elemProd	(	ConstDQuaternionExpression	qe1,
		ConstDQuaternionExpression	qe2
	)

Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.

Returns

An expression object representing the component-wise product \( qe_1 \odot qe_2 \).

elemProd() [4/14]

ConstDVectorExpression CDPL.Math.elemProd	(	ConstDVectorExpression	ve1,
		ConstDVectorExpression	ve2
	)

Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2.

Parameters

ve1	The first vector expression.
ve2	The second vector expression.

Returns

An expression object representing the element-wise product \( ve_1 \odot ve_2 \).

elemProd() [5/14]

ConstFGridExpression CDPL.Math.elemProd	(	ConstFGridExpression	ge1,
		ConstFGridExpression	ge2
	)

Returns the element-wise product of the grid expressions ge1 and ge2 (Hadamard product).

Parameters

ge1	The first grid expression.
ge2	The second grid expression.

Returns

An expression object representing the element-wise product \( ge_1 \odot ge_2 \).

elemProd() [6/14]

ConstFMatrixExpression CDPL.Math.elemProd	(	ConstFMatrixExpression	me1,
		ConstFMatrixExpression	me2
	)

Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2.

Parameters

me1	The first matrix expression.
me2	The second matrix expression.

Returns

An expression object representing the element-wise product \( me_1 \odot me_2 \).

elemProd() [7/14]

ConstFQuaternionExpression CDPL.Math.elemProd	(	ConstFQuaternionExpression	qe1,
		ConstFQuaternionExpression	qe2
	)

Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.

Returns

An expression object representing the component-wise product \( qe_1 \odot qe_2 \).

elemProd() [8/14]

ConstFVectorExpression CDPL.Math.elemProd	(	ConstFVectorExpression	ve1,
		ConstFVectorExpression	ve2
	)

Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2.

Parameters

ve1	The first vector expression.
ve2	The second vector expression.

Returns

An expression object representing the element-wise product \( ve_1 \odot ve_2 \).

elemProd() [9/14]

ConstLMatrixExpression CDPL.Math.elemProd	(	ConstLMatrixExpression	me1,
		ConstLMatrixExpression	me2
	)

Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2.

Parameters

me1	The first matrix expression.
me2	The second matrix expression.

Returns

An expression object representing the element-wise product \( me_1 \odot me_2 \).

elemProd() [10/14]

ConstLQuaternionExpression CDPL.Math.elemProd	(	ConstLQuaternionExpression	qe1,
		ConstLQuaternionExpression	qe2
	)

Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.

Returns

An expression object representing the component-wise product \( qe_1 \odot qe_2 \).

elemProd() [11/14]

ConstLVectorExpression CDPL.Math.elemProd	(	ConstLVectorExpression	ve1,
		ConstLVectorExpression	ve2
	)

Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2.

Parameters

ve1	The first vector expression.
ve2	The second vector expression.

Returns

An expression object representing the element-wise product \( ve_1 \odot ve_2 \).

elemProd() [12/14]

ConstULMatrixExpression CDPL.Math.elemProd	(	ConstULMatrixExpression	me1,
		ConstULMatrixExpression	me2
	)

Returns the element-wise product (Hadamard product) of the matrix expressions me1 and me2.

Parameters

me1	The first matrix expression.
me2	The second matrix expression.

Returns

An expression object representing the element-wise product \( me_1 \odot me_2 \).

elemProd() [13/14]

ConstULQuaternionExpression CDPL.Math.elemProd	(	ConstULQuaternionExpression	qe1,
		ConstULQuaternionExpression	qe2
	)

Returns the component-wise product (Hadamard product) of the quaternion expressions qe1 and qe2.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.

Returns

An expression object representing the component-wise product \( qe_1 \odot qe_2 \).

elemProd() [14/14]

ConstULVectorExpression CDPL.Math.elemProd	(	ConstULVectorExpression	ve1,
		ConstULVectorExpression	ve2
	)

Returns the element-wise product (Hadamard product) of the vector expressions ve1 and ve2.

Parameters

ve1	The first vector expression.
ve2	The second vector expression.

Returns

An expression object representing the element-wise product \( ve_1 \odot ve_2 \).

equals() [1/14]

bool CDPL.Math.equals	(	ConstDGridExpression	ge1,
		ConstDGridExpression	ge2,
		float	eps
	)

Tells whether the grid expressions ge1 and ge2 agree element-wise within the absolute tolerance eps.

Parameters

ge1	The first grid expression.
ge2	The second grid 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	me1,
		ConstDMatrixExpression	me2,
		float	eps
	)

Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps.

Parameters

me1	The first matrix expression.
me2	The second matrix 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	qe1,
		ConstDQuaternionExpression	qe2,
		float	eps
	)

Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.
eps	The non-negative absolute tolerance.

Returns

True if all four components agree within eps, and False otherwise.

equals() [4/14]

bool CDPL.Math.equals	(	ConstDVectorExpression	ve1,
		ConstDVectorExpression	ve2,
		float	eps
	)

Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps.

Parameters

ve1	The first vector expression.
ve2	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	ge1,
		ConstFGridExpression	ge2,
		float	eps
	)

Tells whether the grid expressions ge1 and ge2 agree element-wise within the absolute tolerance eps.

Parameters

ge1	The first grid expression.
ge2	The second grid 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	me1,
		ConstFMatrixExpression	me2,
		float	eps
	)

Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps.

Parameters

me1	The first matrix expression.
me2	The second matrix 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	qe1,
		ConstFQuaternionExpression	qe2,
		float	eps
	)

Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.
eps	The non-negative absolute tolerance.

Returns

True if all four components agree within eps, and False otherwise.

equals() [8/14]

bool CDPL.Math.equals	(	ConstFVectorExpression	ve1,
		ConstFVectorExpression	ve2,
		float	eps
	)

Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps.

Parameters

ve1	The first vector expression.
ve2	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	me1,
		ConstLMatrixExpression	me2,
		int	eps
	)

Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps.

Parameters

me1	The first matrix expression.
me2	The second matrix 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	qe1,
		ConstLQuaternionExpression	qe2,
		int	eps
	)

Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.
eps	The non-negative absolute tolerance.

Returns

True if all four components agree within eps, and False otherwise.

equals() [11/14]

bool CDPL.Math.equals	(	ConstLVectorExpression	ve1,
		ConstLVectorExpression	ve2,
		int	eps
	)

Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps.

Parameters

ve1	The first vector expression.
ve2	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	me1,
		ConstULMatrixExpression	me2,
		int	eps
	)

Tells whether the matrix expressions me1 and me2 agree element-wise within the absolute tolerance eps.

Parameters

me1	The first matrix expression.
me2	The second matrix 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	qe1,
		ConstULQuaternionExpression	qe2,
		int	eps
	)

Tells whether the quaternion expressions qe1 and qe2 agree component-wise within the absolute tolerance eps.

Parameters

qe1	The first quaternion expression.
qe2	The second quaternion expression.
eps	The non-negative absolute tolerance.

Returns

True if all four components agree within eps, and False otherwise.

equals() [14/14]

bool CDPL.Math.equals	(	ConstULVectorExpression	ve1,
		ConstULVectorExpression	ve2,
		int	eps
	)

Tells whether the vector expressions ve1 and ve2 agree element-wise within the absolute tolerance eps.

Parameters

ve1	The first vector expression.
ve2	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 \( Q(a, x) = 1 - P(a, x) \).

Parameters

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

Returns

The computed value of the incomplete gamma function.

See also

[NRIC]

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

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing \( \overline{ge} \).

herm() [2/10]

ConstDMatrixExpression CDPL.Math.herm

(

ConstDMatrixExpression

me

)

Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me.

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me^T} \).

herm() [3/10]

ConstDVectorExpression CDPL.Math.herm

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

herm() [4/10]

ConstFGridExpression CDPL.Math.herm

(

ConstFGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing \( \overline{ge} \).

herm() [5/10]

ConstFMatrixExpression CDPL.Math.herm

(

ConstFMatrixExpression

me

)

Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me.

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me^T} \).

herm() [6/10]

ConstFVectorExpression CDPL.Math.herm

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

herm() [7/10]

ConstLMatrixExpression CDPL.Math.herm

(

ConstLMatrixExpression

me

)

Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me.

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me^T} \).

herm() [8/10]

ConstLVectorExpression CDPL.Math.herm

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

herm() [9/10]

ConstULMatrixExpression CDPL.Math.herm

(

ConstULMatrixExpression

me

)

Returns the Hermitian conjugate (conjugate transpose) of the matrix expression me.

Parameters

me	The matrix expression.

Returns

An expression object representing \( \overline{me^T} \).

herm() [10/10]

ConstULVectorExpression CDPL.Math.herm

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing \( \overline{ve} \).

homog() [1/8]

ConstDHomogenousCoordsAdapter CDPL.Math.homog

(

ConstDVectorExpression

ce

)

Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as its homogeneous-coordinate extension.

homog() [2/8]

ConstFHomogenousCoordsAdapter CDPL.Math.homog

(

ConstFVectorExpression

ce

)

Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as its homogeneous-coordinate extension.

homog() [3/8]

ConstLHomogenousCoordsAdapter CDPL.Math.homog

(

ConstLVectorExpression

ce

)

Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as its homogeneous-coordinate extension.

homog() [4/8]

ConstULHomogenousCoordsAdapter CDPL.Math.homog

(

ConstULVectorExpression

ce

)

Returns a constant vector adapter that exposes ce as its homogeneous-coordinate extension.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as its homogeneous-coordinate extension.

homog() [5/8]

DHomogenousCoordsAdapter CDPL.Math.homog

(

DVectorExpression

me

)

Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as its homogeneous-coordinate extension.

homog() [6/8]

FHomogenousCoordsAdapter CDPL.Math.homog

(

FVectorExpression

me

)

Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as its homogeneous-coordinate extension.

homog() [7/8]

LHomogenousCoordsAdapter CDPL.Math.homog

(

LVectorExpression

me

)

Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as its homogeneous-coordinate extension.

homog() [8/8]

ULHomogenousCoordsAdapter CDPL.Math.homog

(

ULVectorExpression

me

)

Returns a mutable vector adapter that exposes me as its homogeneous-coordinate extension.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as its homogeneous-coordinate extension.

imag() [1/10]

ConstDGridExpression CDPL.Math.imag

(

ConstDGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing the imaginary part of ge.

imag() [2/10]

ConstDMatrixExpression CDPL.Math.imag

(

ConstDMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the imaginary part of me.

imag() [3/10]

ConstDVectorExpression CDPL.Math.imag

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the imaginary part of ve.

imag() [4/10]

ConstFGridExpression CDPL.Math.imag

(

ConstFGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing the imaginary part of ge.

imag() [5/10]

ConstFMatrixExpression CDPL.Math.imag

(

ConstFMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the imaginary part of me.

imag() [6/10]

ConstFVectorExpression CDPL.Math.imag

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the imaginary part of ve.

imag() [7/10]

ConstLMatrixExpression CDPL.Math.imag

(

ConstLMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the imaginary part of me.

imag() [8/10]

ConstLVectorExpression CDPL.Math.imag

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the imaginary part of ve.

imag() [9/10]

ConstULMatrixExpression CDPL.Math.imag

(

ConstULMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the imaginary part of me.

imag() [10/10]

ConstULVectorExpression CDPL.Math.imag

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the imaginary part of ve.

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 cell value of the regular spatial grid grid at the position pos.

Parameters

grid	The regular spatial grid.
pos	The query position.
local_pos	If True, pos specifies local grid coordinates and world coordinates otherwise.

Returns

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

interpolateTrilinear() [2/2]

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

Returns the trilinearly interpolated cell value of the regular spatial grid grid at the position pos.

Parameters

grid	The regular spatial grid.
pos	The query position.
local_pos	If True, pos specifies local grid coordinates and world coordinates otherwise.

Returns

The trilinearly interpolated grid cell value at pos (zero if the 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 object 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 object 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 object 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 object 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 a 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 a 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 a 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 a 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 of e.

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 of e.

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 of e.

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 of e.

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.

See also

[NRIC]

luDecompose() [1/8]

int CDPL.Math.luDecompose

(

DMatrixExpression

e

)

Computes an in-place LU decomposition [WLUD] 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
	)

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

Parameters

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

Returns

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

luDecompose() [3/8]

int CDPL.Math.luDecompose

(

FMatrixExpression

e

)

Computes an in-place LU decomposition [WLUD] 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
	)

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

Parameters

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

Returns

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

luDecompose() [5/8]

int CDPL.Math.luDecompose

(

LMatrixExpression

e

)

Computes an in-place LU decomposition [WLUD] 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
	)

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

Parameters

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

Returns

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

luDecompose() [7/8]

int CDPL.Math.luDecompose

(

ULMatrixExpression

e

)

Computes an in-place LU decomposition [WLUD] 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
	)

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

Parameters

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

Returns

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

luSubstitute() [1/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	lu,
		DVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [2/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	lu,
		ConstULVectorExpression	pv,
		DVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [3/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	lu,
		DMatrixExpression	bm
	)

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

Parameters

lu	The LU decomposition.
bm	The right-hand side matrix \( B \), overwritten with the solution.

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [4/16]

bool CDPL.Math.luSubstitute	(	ConstDMatrixExpression	lu,
		ConstULVectorExpression	pv,
		DMatrixExpression	bm
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [5/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	lu,
		FVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [6/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	lu,
		ConstULVectorExpression	pv,
		FVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [7/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	lu,
		FMatrixExpression	bm
	)

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

Parameters

lu	The LU decomposition.
bm	The right-hand side matrix \( B \), overwritten with the solution.

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [8/16]

bool CDPL.Math.luSubstitute	(	ConstFMatrixExpression	lu,
		ConstULVectorExpression	pv,
		FMatrixExpression	bm
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [9/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	lu,
		LVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [10/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	lu,
		ConstULVectorExpression	pv,
		LVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [11/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	lu,
		LMatrixExpression	bm
	)

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

Parameters

lu	The LU decomposition.
bm	The right-hand side matrix \( B \), overwritten with the solution.

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [12/16]

bool CDPL.Math.luSubstitute	(	ConstLMatrixExpression	lu,
		ConstULVectorExpression	pv,
		LMatrixExpression	bm
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [13/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	lu,
		ULVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [14/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	lu,
		ConstULVectorExpression	pv,
		ULVectorExpression	bv
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [15/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	lu,
		ULMatrixExpression	bm
	)

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

Parameters

lu	The LU decomposition.
bm	The right-hand side matrix \( B \), overwritten with the solution.

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

luSubstitute() [16/16]

bool CDPL.Math.luSubstitute	(	ConstULMatrixExpression	lu,
		ConstULVectorExpression	pv,
		ULMatrixExpression	bm
	)

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

Parameters

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

Returns

True if the back-substitution succeeded, and False if a zero pivot was encountered.

norm1() [1/8]

float CDPL.Math.norm1

(

ConstDMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L1 norm of me.

norm1() [2/8]

float CDPL.Math.norm1

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L1 norm of ve.

norm1() [3/8]

float CDPL.Math.norm1

(

ConstFMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L1 norm of me.

norm1() [4/8]

float CDPL.Math.norm1

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L1 norm of ve.

norm1() [5/8]

int CDPL.Math.norm1

(

ConstLMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L1 norm of me.

norm1() [6/8]

int CDPL.Math.norm1

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L1 norm of ve.

norm1() [7/8]

int CDPL.Math.norm1

(

ConstULMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L1 norm of me.

norm1() [8/8]

int CDPL.Math.norm1

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L1 norm of ve.

norm2() [1/8]

float CDPL.Math.norm2

(

ConstDQuaternionExpression

qe

)

Returns the squared norm of the quaternion expression qe.

Parameters

qe	The quaternion expression.

Returns

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

norm2() [2/8]

float CDPL.Math.norm2

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L2 norm of ve.

norm2() [3/8]

float CDPL.Math.norm2

(

ConstFQuaternionExpression

qe

)

Returns the squared norm of the quaternion expression qe.

Parameters

qe	The quaternion expression.

Returns

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

norm2() [4/8]

float CDPL.Math.norm2

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L2 norm of ve.

norm2() [5/8]

int CDPL.Math.norm2

(

ConstLQuaternionExpression

qe

)

Returns the squared norm of the quaternion expression qe.

Parameters

qe	The quaternion expression.

Returns

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

norm2() [6/8]

int CDPL.Math.norm2

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L2 norm of ve.

norm2() [7/8]

int CDPL.Math.norm2

(

ConstULQuaternionExpression

qe

)

Returns the squared norm of the quaternion expression qe.

Parameters

qe	The quaternion expression.

Returns

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

norm2() [8/8]

int CDPL.Math.norm2

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L2 norm of ve.

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

me

)

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

Parameters

me	The matrix expression.

Returns

The L∞ norm of me.

normInf() [2/8]

float CDPL.Math.normInf

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L∞ norm of ve.

normInf() [3/8]

float CDPL.Math.normInf

(

ConstFMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L∞ norm of me.

normInf() [4/8]

float CDPL.Math.normInf

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L∞ norm of ve.

normInf() [5/8]

int CDPL.Math.normInf

(

ConstLMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L∞ norm of me.

normInf() [6/8]

int CDPL.Math.normInf

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L∞ norm of ve.

normInf() [7/8]

int CDPL.Math.normInf

(

ConstULMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

The L∞ norm of me.

normInf() [8/8]

int CDPL.Math.normInf

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

The L∞ norm of ve.

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 object 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 object 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 object 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 object representing the outer product.

prime()

int CDPL.Math.prime

(

int

i

)

Returns the i-th entry in the sequence of the first 10000 prime numbers (starting with 2).

Parameters

i	The zero-based prime number index.

Returns

The prime number at index i.

Exceptions

RuntimeError

if i ≥ 10000.

prod() [1/24]

ConstDVectorExpression CDPL.Math.prod	(	ConstDMatrixExpression	me,
		ConstDVectorExpression	ve
	)

Returns the matrix-vector product \( me \cdot ve \) as a vector expression.

Parameters

me	The matrix expression.
ve	The vector expression.

Returns

An expression object representing \( me \cdot ve \).

prod() [2/24]

DVectorExpression CDPL.Math.prod	(	ConstDMatrixExpression	me,
		ConstDVectorExpression	ve,
		DVectorExpression	c
	)

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

Parameters

me	The matrix expression.
ve	The vector expression.
c	The output vector container receiving the result.

Returns

The output container 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.

Parameters

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

Returns

An expression object 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

The output container c.

prod() [5/24]

ConstDVectorExpression CDPL.Math.prod	(	ConstDVectorExpression	ve,
		ConstDMatrixExpression	me
	)

Returns the vector-matrix product \( ve \cdot me \) as a vector expression.

Parameters

ve	The vector expression.
me	The matrix expression.

Returns

An expression object representing \( ve \cdot me \).

prod() [6/24]

DVectorExpression CDPL.Math.prod	(	ConstDVectorExpression	ve,
		ConstDMatrixExpression	me,
		DVectorExpression	c
	)

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

Parameters

ve	The vector expression.
me	The matrix expression.
c	The output vector container receiving the result.

Returns

The output container c.

prod() [7/24]

ConstFVectorExpression CDPL.Math.prod	(	ConstFMatrixExpression	me,
		ConstFVectorExpression	ve
	)

Returns the matrix-vector product \( me \cdot ve \) as a vector expression.

Parameters

me	The matrix expression.
ve	The vector expression.

Returns

An expression object representing \( me \cdot ve \).

prod() [8/24]

FVectorExpression CDPL.Math.prod	(	ConstFMatrixExpression	me,
		ConstFVectorExpression	ve,
		FVectorExpression	c
	)

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

Parameters

me	The matrix expression.
ve	The vector expression.
c	The output vector container receiving the result.

Returns

The output container 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.

Parameters

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

Returns

An expression object 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

The output container c.

prod() [11/24]

ConstFVectorExpression CDPL.Math.prod	(	ConstFVectorExpression	ve,
		ConstFMatrixExpression	me
	)

Returns the vector-matrix product \( ve \cdot me \) as a vector expression.

Parameters

ve	The vector expression.
me	The matrix expression.

Returns

An expression object representing \( ve \cdot me \).

prod() [12/24]

FVectorExpression CDPL.Math.prod	(	ConstFVectorExpression	ve,
		ConstFMatrixExpression	me,
		FVectorExpression	c
	)

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

Parameters

ve	The vector expression.
me	The matrix expression.
c	The output vector container receiving the result.

Returns

The output container c.

prod() [13/24]

ConstLVectorExpression CDPL.Math.prod	(	ConstLMatrixExpression	me,
		ConstLVectorExpression	ve
	)

Returns the matrix-vector product \( me \cdot ve \) as a vector expression.

Parameters

me	The matrix expression.
ve	The vector expression.

Returns

An expression object representing \( me \cdot ve \).

prod() [14/24]

LVectorExpression CDPL.Math.prod	(	ConstLMatrixExpression	me,
		ConstLVectorExpression	ve,
		LVectorExpression	c
	)

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

Parameters

me	The matrix expression.
ve	The vector expression.
c	The output vector container receiving the result.

Returns

The output container 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.

Parameters

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

Returns

An expression object 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

The output container c.

prod() [17/24]

ConstLVectorExpression CDPL.Math.prod	(	ConstLVectorExpression	ve,
		ConstLMatrixExpression	me
	)

Returns the vector-matrix product \( ve \cdot me \) as a vector expression.

Parameters

ve	The vector expression.
me	The matrix expression.

Returns

An expression object representing \( ve \cdot me \).

prod() [18/24]

LVectorExpression CDPL.Math.prod	(	ConstLVectorExpression	ve,
		ConstLMatrixExpression	me,
		LVectorExpression	c
	)

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

Parameters

ve	The vector expression.
me	The matrix expression.
c	The output vector container receiving the result.

Returns

The output container c.

prod() [19/24]

ConstULVectorExpression CDPL.Math.prod	(	ConstULMatrixExpression	me,
		ConstULVectorExpression	ve
	)

Returns the matrix-vector product \( me \cdot ve \) as a vector expression.

Parameters

me	The matrix expression.
ve	The vector expression.

Returns

An expression object representing \( me \cdot ve \).

prod() [20/24]

ULVectorExpression CDPL.Math.prod	(	ConstULMatrixExpression	me,
		ConstULVectorExpression	ve,
		ULVectorExpression	c
	)

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

Parameters

me	The matrix expression.
ve	The vector expression.
c	The output vector container receiving the result.

Returns

The output container 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.

Parameters

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

Returns

An expression object 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

The output container c.

prod() [23/24]

ConstULVectorExpression CDPL.Math.prod	(	ConstULVectorExpression	ve,
		ConstULMatrixExpression	me
	)

Returns the vector-matrix product \( ve \cdot me \) as a vector expression.

Parameters

ve	The vector expression.
me	The matrix expression.

Returns

An expression object representing \( ve \cdot me \).

prod() [24/24]

ULVectorExpression CDPL.Math.prod	(	ConstULVectorExpression	ve,
		ConstULMatrixExpression	me,
		ULVectorExpression	c
	)

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

Parameters

ve	The vector expression.
me	The matrix expression.
c	The output vector container receiving the result.

Returns

The output container 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

ce

)

Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as quaternion.

quat() [2/16]

ConstFVectorQuaternionAdapter CDPL.Math.quat

(

ConstFVectorExpression

ce

)

Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as quaternion.

quat() [3/16]

ConstLVectorQuaternionAdapter CDPL.Math.quat

(

ConstLVectorExpression

ce

)

Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as quaternion.

quat() [4/16]

ConstULVectorQuaternionAdapter CDPL.Math.quat

(

ConstULVectorExpression

ce

)

Returns a constant vector adapter that exposes the 4-element vector expression ce as quaternion.

Parameters

ce	The vector expression to wrap.

Returns

An adapter object exposing ce as quaternion.

quat() [5/16]

DVectorQuaternionAdapter CDPL.Math.quat

(

DVectorExpression

me

)

Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as quaternion.

quat() [6/16]

FVectorQuaternionAdapter CDPL.Math.quat

(

FVectorExpression

me

)

Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as quaternion.

quat() [7/16]

LVectorQuaternionAdapter CDPL.Math.quat

(

LVectorExpression

me

)

Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as quaternion.

quat() [8/16]

ULVectorQuaternionAdapter CDPL.Math.quat

(

ULVectorExpression

me

)

Returns a mutable vector adapter that exposes the 4-element vector expression me as quaternion.

Parameters

me	The vector expression to wrap.

Returns

An adapter object exposing me as quaternion.

quat() [9/16]

FRealQuaternion CDPL.Math.quat

(

float

t

)

Constructs a real quaternion 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 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 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 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 real quaternion 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 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 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 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	cme,
		Range	r1,
		Range	r2
	)

Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme.

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of cme.

range() [2/33]

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

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

Parameters

cme	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 proxy object referring to the specified rectangular subrange of cme.

range() [3/33]

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

Returns a constant vector proxy viewing the subrange r of cve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of cve.

range() [4/33]

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

Returns a constant vector proxy viewing the subrange [start, stop) of cve.

Parameters

cve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of cve.

range() [5/33]

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

Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme.

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of cme.

range() [6/33]

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

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

Parameters

cme	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 proxy object referring to the specified rectangular subrange of cme.

range() [7/33]

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

Returns a constant vector proxy viewing the subrange r of cve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of cve.

range() [8/33]

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

Returns a constant vector proxy viewing the subrange [start, stop) of cve.

Parameters

cve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of cve.

range() [9/33]

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

Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme.

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of cme.

range() [10/33]

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

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

Parameters

cme	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 proxy object referring to the specified rectangular subrange of cme.

range() [11/33]

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

Returns a constant vector proxy viewing the subrange r of cve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of cve.

range() [12/33]

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

Returns a constant vector proxy viewing the subrange [start, stop) of cve.

Parameters

cve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of cve.

range() [13/33]

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

Returns a constant matrix proxy viewing the range of rows in r1 and columns in r2 of cme.

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of cme.

range() [14/33]

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

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

Parameters

cme	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 proxy object referring to the specified rectangular subrange of cme.

range() [15/33]

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

Returns a constant vector proxy viewing the subrange r of cve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of cve.

range() [16/33]

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

Returns a constant vector proxy viewing the subrange [start, stop) of cve.

Parameters

cve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of cve.

range() [17/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of mme.

range() [18/33]

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

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

Parameters

mme	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 proxy object referring to the specified rectangular subrange of mme.

range() [19/33]

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

Returns a mutable vector proxy viewing the subrange r of mve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of mve.

range() [20/33]

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

Returns a mutable vector proxy viewing the subrange [start, stop) of mve.

Parameters

mve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of mve.

range() [21/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of mme.

range() [22/33]

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

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

Parameters

mme	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 proxy object referring to the specified rectangular subrange of mme.

range() [23/33]

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

Returns a mutable vector proxy viewing the subrange r of mve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of mve.

range() [24/33]

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

Returns a mutable vector proxy viewing the subrange [start, stop) of mve.

Parameters

mve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of mve.

range() [25/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of mme.

range() [26/33]

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

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

Parameters

mme	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 proxy object referring to the specified rectangular subrange of mme.

range() [27/33]

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

Returns a mutable vector proxy viewing the subrange r of mve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of mve.

range() [28/33]

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

Returns a mutable vector proxy viewing the subrange [start, stop) of mve.

Parameters

mve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of mve.

range() [29/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified rectangular subrange of mme.

range() [30/33]

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

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

Parameters

mme	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 proxy object referring to the specified rectangular subrange of mme.

range() [31/33]

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

Returns a mutable vector proxy viewing the subrange r of mve.

Parameters

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

Returns

A proxy object referring to the specified subbrange of mve.

range() [32/33]

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

Returns a mutable vector proxy viewing the subrange [start, stop) of mve.

Parameters

mve	The vector expression.
start	The (inclusive) start index of the range.
stop	The (exclusive) end index of the range.

Returns

A proxy object referring to the specified subbrange of mve.

range() [33/33]

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

Convenience factory function 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

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing the real part of ge.

real() [2/14]

ConstDMatrixExpression CDPL.Math.real

(

ConstDMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the real part of me.

real() [3/14]

float CDPL.Math.real

(

ConstDQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

real() [4/14]

ConstDVectorExpression CDPL.Math.real

(

ConstDVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the real part of ve.

real() [5/14]

ConstFGridExpression CDPL.Math.real

(

ConstFGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

An expression object representing the real part of ge.

real() [6/14]

ConstFMatrixExpression CDPL.Math.real

(

ConstFMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the real part of me.

real() [7/14]

float CDPL.Math.real

(

ConstFQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

real() [8/14]

ConstFVectorExpression CDPL.Math.real

(

ConstFVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the real part of ve.

real() [9/14]

ConstLMatrixExpression CDPL.Math.real

(

ConstLMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the real part of me.

real() [10/14]

int CDPL.Math.real

(

ConstLQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

real() [11/14]

ConstLVectorExpression CDPL.Math.real

(

ConstLVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the real part of ve.

real() [12/14]

ConstULMatrixExpression CDPL.Math.real

(

ConstULMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

An expression object representing the real part of me.

real() [13/14]

int CDPL.Math.real

(

ConstULQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

real() [14/14]

ConstULVectorExpression CDPL.Math.real

(

ConstULVectorExpression

ve

)

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

Parameters

ve	The vector expression.

Returns

An expression object representing the real part of ve.

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 object representing the rotated 3D 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 object representing the rotated 3D 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 object representing the rotated 3D 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 object representing the rotated 3D vector \( e_1 \cdot e_2 \cdot e_1^{-1} \).

row() [1/8]

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

Returns a constant matrix proxy viewing row i of ce.

Parameters

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

Returns

A proxy object referring to row i of ce.

row() [2/8]

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

Returns a constant matrix proxy viewing row i of ce.

Parameters

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

Returns

A proxy object referring to row i of ce.

row() [3/8]

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

Returns a constant matrix proxy viewing row i of ce.

Parameters

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

Returns

A proxy object referring to row i of ce.

row() [4/8]

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

Returns a constant matrix proxy viewing row i of ce.

Parameters

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

Returns

A proxy object referring to row i of ce.

row() [5/8]

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

Returns a mutable matrix proxy viewing row i of me.

Parameters

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

Returns

A proxy object referring to row i of me.

row() [6/8]

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

Returns a mutable matrix proxy viewing row i of me.

Parameters

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

Returns

A proxy object referring to row i of me.

row() [7/8]

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

Returns a mutable matrix proxy viewing row i of me.

Parameters

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

Returns

A proxy object referring to row i of me.

row() [8/8]

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

Returns a mutable matrix proxy viewing row i of me.

Parameters

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

Returns

A proxy object referring to row i of me.

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	cme,
		Slice	s1,
		Slice	s2
	)

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of cme.

slice() [2/33]

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

Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme.

Parameters

cme	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 proxy object referring to the specified strided rectangular slice of cme.

slice() [3/33]

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

Returns a constant vector proxy viewing the strided slice s of cve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of cve.

slice() [4/33]

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

Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve.

Parameters

cve	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 proxy object referring to the specified strided slice of cve.

slice() [5/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of cme.

slice() [6/33]

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

Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme.

Parameters

cme	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 proxy object referring to the specified strided rectangular slice of cme.

slice() [7/33]

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

Returns a constant vector proxy viewing the strided slice s of cve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of cve.

slice() [8/33]

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

Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve.

Parameters

cve	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 proxy object referring to the specified strided slice of cve.

slice() [9/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of cme.

slice() [10/33]

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

Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme.

Parameters

cme	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 proxy object referring to the specified strided rectangular slice of cme.

slice() [11/33]

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

Returns a constant vector proxy viewing the strided slice s of cve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of cve.

slice() [12/33]

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

Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve.

Parameters

cve	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 proxy object referring to the specified strided slice of cve.

slice() [13/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of cme.

slice() [14/33]

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

Returns a constant matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of cme.

Parameters

cme	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 proxy object referring to the specified strided rectangular slice of cme.

slice() [15/33]

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

Returns a constant vector proxy viewing the strided slice s of cve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of cve.

slice() [16/33]

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

Returns a constant vector proxy viewing the strided slice (start, stride, size) of cve.

Parameters

cve	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 proxy object referring to the specified strided slice of cve.

slice() [17/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of mme.

slice() [18/33]

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

Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme.

Parameters

mme	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 proxy object referring to the specified strided rectangular slice of mme.

slice() [19/33]

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

Returns a mutable vector proxy viewing the strided slice s of mve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of mve.

slice() [20/33]

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

Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve.

Parameters

mve	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 proxy object referring to the specified strided slice of mve.

slice() [21/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of mme.

slice() [22/33]

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

Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme.

Parameters

mme	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 proxy object referring to the specified strided rectangular slice of mme.

slice() [23/33]

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

Returns a mutable vector proxy viewing the strided slice s of mve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of mve.

slice() [24/33]

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

Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve.

Parameters

mve	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 proxy object referring to the specified strided slice of mve.

slice() [25/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of mme.

slice() [26/33]

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

Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme.

Parameters

mme	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 proxy object referring to the specified strided rectangular slice of mme.

slice() [27/33]

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

Returns a mutable vector proxy viewing the strided slice s of mve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of mve.

slice() [28/33]

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

Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve.

Parameters

mve	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 proxy object referring to the specified strided slice of mve.

slice() [29/33]

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

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

Parameters

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

Returns

A proxy object referring to the specified strided rectangular slice of mme.

slice() [30/33]

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

Returns a mutable matrix proxy viewing the strided rectangular slice specified by rows (start1, stride1, size1) and columns (start2, stride2, size2) of mme.

Parameters

mme	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 proxy object referring to the specified strided rectangular slice of mme.

slice() [31/33]

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

Returns a mutable vector proxy viewing the strided slice s of mve.

Parameters

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

Returns

A proxy object referring to the specified strided slice of mve.

slice() [32/33]

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

Returns a mutable vector proxy viewing the strided slice (start, stride, size) of mve.

Parameters

mve	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 proxy object referring to the specified strided slice of mve.

slice() [33/33]

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

Convenience factory function 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	l,
		DVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveLower() [2/8]

bool CDPL.Math.solveLower	(	ConstDMatrixExpression	l,
		DMatrixExpression	bm
	)

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

Parameters

l	The lower-triangular coefficient matrix.
bm	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	l,
		FVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveLower() [4/8]

bool CDPL.Math.solveLower	(	ConstFMatrixExpression	l,
		FMatrixExpression	bm
	)

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

Parameters

l	The lower-triangular coefficient matrix.
bm	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	l,
		LVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveLower() [6/8]

bool CDPL.Math.solveLower	(	ConstLMatrixExpression	l,
		LMatrixExpression	bm
	)

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

Parameters

l	The lower-triangular coefficient matrix.
bm	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	l,
		ULVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveLower() [8/8]

bool CDPL.Math.solveLower	(	ConstULMatrixExpression	l,
		ULMatrixExpression	bm
	)

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

Parameters

l	The lower-triangular coefficient matrix.
bm	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	l,
		DVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitLower() [2/8]

bool CDPL.Math.solveUnitLower	(	ConstDMatrixExpression	l,
		DMatrixExpression	bm
	)

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

Parameters

l	The unit lower-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	l,
		FVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitLower() [4/8]

bool CDPL.Math.solveUnitLower	(	ConstFMatrixExpression	l,
		FMatrixExpression	bm
	)

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

Parameters

l	The unit lower-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	l,
		LVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitLower() [6/8]

bool CDPL.Math.solveUnitLower	(	ConstLMatrixExpression	l,
		LMatrixExpression	bm
	)

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

Parameters

l	The unit lower-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	l,
		ULVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitLower() [8/8]

bool CDPL.Math.solveUnitLower	(	ConstULMatrixExpression	l,
		ULMatrixExpression	bm
	)

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

Parameters

l	The unit lower-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	u,
		DVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitUpper() [2/8]

bool CDPL.Math.solveUnitUpper	(	ConstDMatrixExpression	u,
		DMatrixExpression	bm
	)

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

Parameters

u	The unit upper-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	u,
		FVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitUpper() [4/8]

bool CDPL.Math.solveUnitUpper	(	ConstFMatrixExpression	u,
		FMatrixExpression	bm
	)

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

Parameters

u	The unit upper-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	u,
		LVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitUpper() [6/8]

bool CDPL.Math.solveUnitUpper	(	ConstLMatrixExpression	u,
		LMatrixExpression	bm
	)

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

Parameters

u	The unit upper-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	u,
		ULVectorExpression	bv
	)

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

Parameters

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

Returns

True if the substitution succeeded, and False if the system is not square or dimensions do not match.

solveUnitUpper() [8/8]

bool CDPL.Math.solveUnitUpper	(	ConstULMatrixExpression	u,
		ULMatrixExpression	bm
	)

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

Parameters

u	The unit upper-triangular coefficient matrix (diagonal entries are taken as 1).
bm	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	u,
		DVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveUpper() [2/8]

bool CDPL.Math.solveUpper	(	ConstDMatrixExpression	u,
		DMatrixExpression	bm
	)

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

Parameters

u	The upper-triangular coefficient matrix.
bm	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	u,
		FVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveUpper() [4/8]

bool CDPL.Math.solveUpper	(	ConstFMatrixExpression	u,
		FMatrixExpression	bm
	)

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

Parameters

u	The upper-triangular coefficient matrix.
bm	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	u,
		LVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveUpper() [6/8]

bool CDPL.Math.solveUpper	(	ConstLMatrixExpression	u,
		LMatrixExpression	bm
	)

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

Parameters

u	The upper-triangular coefficient matrix.
bm	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	u,
		ULVectorExpression	bv
	)

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

Parameters

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

Returns

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

solveUpper() [8/8]

bool CDPL.Math.solveUpper	(	ConstULMatrixExpression	u,
		ULMatrixExpression	bm
	)

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

Parameters

u	The upper-triangular coefficient matrix.
bm	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

ge

)

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

Parameters

ge	The grid expression.

Returns

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

sum() [2/15]

float CDPL.Math.sum

(

ConstDMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

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

sum() [3/15]

float CDPL.Math.sum

(

ConstDQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

sum() [4/15]

float CDPL.Math.sum

(

ConstDVectorExpression

ve

)

Returns the sum of all elements of the vector expression ve.

Parameters

ve	The vector expression.

Returns

\( \sum_i ve(i) \).

sum() [5/15]

float CDPL.Math.sum

(

ConstFGridExpression

ge

)

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

Parameters

ge	The grid expression.

Returns

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

sum() [6/15]

float CDPL.Math.sum

(

ConstFMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

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

sum() [7/15]

float CDPL.Math.sum

(

ConstFQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

sum() [8/15]

float CDPL.Math.sum

(

ConstFVectorExpression

ve

)

Returns the sum of all elements of the vector expression ve.

Parameters

ve	The vector expression.

Returns

\( \sum_i ve(i) \).

sum() [9/15]

int CDPL.Math.sum

(

ConstLMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

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

sum() [10/15]

int CDPL.Math.sum

(

ConstLQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

sum() [11/15]

int CDPL.Math.sum

(

ConstLVectorExpression

ve

)

Returns the sum of all elements of the vector expression ve.

Parameters

ve	The vector expression.

Returns

\( \sum_i ve(i) \).

sum() [12/15]

int CDPL.Math.sum

(

ConstULMatrixExpression

me

)

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

Parameters

me	The matrix expression.

Returns

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

sum() [13/15]

int CDPL.Math.sum

(

ConstULQuaternionExpression

qe

)

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

Parameters

qe	The quaternion expression.

Returns

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

sum() [14/15]

int CDPL.Math.sum

(

ConstULVectorExpression

ve

)

Returns the sum of all elements of the vector expression ve.

Parameters

ve	The vector expression.

Returns

\( \sum_i ve(i) \).

sum() [15/15]

int CDPL.Math.sum

(

object

ge

)

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

Parameters

ge	The grid expression.

Returns

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

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 vector \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD].

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [2/8]

None CDPL.Math.svSubstitute	(	ConstDMatrixExpression	u,
		ConstDVectorExpression	w,
		ConstDMatrixExpression	v,
		ConstDMatrixExpression	b,
		DMatrixExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [3/8]

None CDPL.Math.svSubstitute	(	ConstFMatrixExpression	u,
		ConstFVectorExpression	w,
		ConstFMatrixExpression	v,
		ConstFVectorExpression	b,
		FVectorExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [4/8]

None CDPL.Math.svSubstitute	(	ConstFMatrixExpression	u,
		ConstFVectorExpression	w,
		ConstFMatrixExpression	v,
		ConstFMatrixExpression	b,
		FMatrixExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [5/8]

None CDPL.Math.svSubstitute	(	ConstLMatrixExpression	u,
		ConstLVectorExpression	w,
		ConstLMatrixExpression	v,
		ConstLVectorExpression	b,
		LVectorExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [6/8]

None CDPL.Math.svSubstitute	(	ConstLMatrixExpression	u,
		ConstLVectorExpression	w,
		ConstLMatrixExpression	v,
		ConstLMatrixExpression	b,
		LMatrixExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [7/8]

None CDPL.Math.svSubstitute	(	ConstULMatrixExpression	u,
		ConstULVectorExpression	w,
		ConstULMatrixExpression	v,
		ConstULVectorExpression	b,
		ULVectorExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

svSubstitute() [8/8]

None CDPL.Math.svSubstitute	(	ConstULMatrixExpression	u,
		ConstULVectorExpression	w,
		ConstULMatrixExpression	v,
		ConstULMatrixExpression	b,
		ULMatrixExpression	x
	)

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

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

Parameters

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

Precondition

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

See also

svDecomposition()

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

ce

)

Returns a transposed view of the constant matrix expression ce.

Parameters

ce	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of ce.

trans() [2/8]

ConstFMatrixTranspose CDPL.Math.trans

(

ConstFMatrixExpression

ce

)

Returns a transposed view of the constant matrix expression ce.

Parameters

ce	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of ce.

trans() [3/8]

ConstLMatrixTranspose CDPL.Math.trans

(

ConstLMatrixExpression

ce

)

Returns a transposed view of the constant matrix expression ce.

Parameters

ce	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of ce.

trans() [4/8]

ConstULMatrixTranspose CDPL.Math.trans

(

ConstULMatrixExpression

ce

)

Returns a transposed view of the constant matrix expression ce.

Parameters

ce	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of ce.

trans() [5/8]

DMatrixTranspose CDPL.Math.trans

(

DMatrixExpression

me

)

Returns a transposed view of the mutable matrix expression me.

Parameters

me	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of me.

trans() [6/8]

FMatrixTranspose CDPL.Math.trans

(

FMatrixExpression

me

)

Returns a transposed view of the mutable matrix expression me.

Parameters

me	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of me.

trans() [7/8]

LMatrixTranspose CDPL.Math.trans

(

LMatrixExpression

me

)

Returns a transposed view of the mutable matrix expression me.

Parameters

me	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of me.

trans() [8/8]

ULMatrixTranspose CDPL.Math.trans

(

ULMatrixExpression

me

)

Returns a transposed view of the mutable matrix expression me.

Parameters

me	The matrix expression to transpose.

Returns

A matrix wrapper object representing the transpose of me.

transform() [1/16]

None CDPL.Math.transform	(	Vector2DArray	va,
		Matrix2D	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [2/16]

None CDPL.Math.transform	(	Vector2DArray	va,
		Matrix3D	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [3/16]

None CDPL.Math.transform	(	Vector2FArray	va,
		Matrix2F	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [4/16]

None CDPL.Math.transform	(	Vector2FArray	va,
		Matrix3F	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [5/16]

None CDPL.Math.transform	(	Vector2LArray	va,
		Matrix2L	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [6/16]

None CDPL.Math.transform	(	Vector2LArray	va,
		Matrix3L	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [7/16]

None CDPL.Math.transform	(	Vector2ULArray	va,
		Matrix2UL	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [8/16]

None CDPL.Math.transform	(	Vector2ULArray	va,
		Matrix3UL	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [9/16]

None CDPL.Math.transform	(	Vector3DArray	va,
		Matrix3D	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [10/16]

None CDPL.Math.transform	(	Vector3DArray	va,
		Matrix4D	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [11/16]

None CDPL.Math.transform	(	Vector3FArray	va,
		Matrix3F	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [12/16]

None CDPL.Math.transform	(	Vector3FArray	va,
		Matrix4F	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [13/16]

None CDPL.Math.transform	(	Vector3LArray	va,
		Matrix3L	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [14/16]

None CDPL.Math.transform	(	Vector3LArray	va,
		Matrix4L	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [15/16]

None CDPL.Math.transform	(	Vector3ULArray	va,
		Matrix3UL	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

transform() [16/16]

None CDPL.Math.transform	(	Vector3ULArray	va,
		Matrix4UL	xform
	)

Transforms each vector in the array with the transformation matrix xform.

Parameters

va	The vectors to transform.
xform	The transformation matrix.

triang() [1/16]

ConstUpperTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	ce,
		Upper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [2/16]

ConstUnitUpperTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	ce,
		UnitUpper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [3/16]

ConstLowerTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	ce,
		Lower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [4/16]

ConstUnitLowerTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	ce,
		UnitLower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [5/16]

ConstUpperTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	ce,
		Upper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [6/16]

ConstUnitUpperTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	ce,
		UnitUpper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [7/16]

ConstLowerTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	ce,
		Lower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [8/16]

ConstUnitLowerTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	ce,
		UnitLower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [9/16]

ConstUpperTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	ce,
		Upper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [10/16]

ConstUnitUpperTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	ce,
		UnitUpper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [11/16]

ConstLowerTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	ce,
		Lower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [12/16]

ConstUnitLowerTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	ce,
		UnitLower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [13/16]

ConstUpperTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	ce,
		Upper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [14/16]

ConstUnitUpperTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	ce,
		UnitUpper	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [15/16]

ConstLowerTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	ce,
		Lower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

triang() [16/16]

ConstUnitLowerTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	ce,
		UnitLower	type
	)

Returns a constant matrix adapter that exposes a triangular part of ce according to the policy type.

Parameters

ce	The matrix expression to wrap.
type	The triangular-view selection policy

Returns

An adapter object exposing a triangular part of ce according to the selected policy.

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 object 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 object 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 object 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 object representing the unreal part of e.

vec() [1/14]

ConstDQuaternionVectorAdapter CDPL.Math.vec

(

ConstDQuaternionExpression

ce

)

Returns a mutable quaternion adapter that exposes ce as 4-element vector expression.

Parameters

ce	The quaternion expression to wrap.

Returns

An adapter object exposing ce as 4-element vector expression.

vec() [2/14]

ConstFQuaternionVectorAdapter CDPL.Math.vec

(

ConstFQuaternionExpression

ce

)

Returns a mutable quaternion adapter that exposes ce as 4-element vector expression.

Parameters

ce	The quaternion expression to wrap.

Returns

An adapter object exposing ce as 4-element vector expression.

vec() [3/14]

ConstLQuaternionVectorAdapter CDPL.Math.vec

(

ConstLQuaternionExpression

ce

)

Returns a mutable quaternion adapter that exposes ce as 4-element vector expression.

Parameters

ce	The quaternion expression to wrap.

Returns

An adapter object exposing ce as 4-element vector expression.

vec() [4/14]

ConstULQuaternionVectorAdapter CDPL.Math.vec

(

ConstULQuaternionExpression

ce

)

Returns a mutable quaternion adapter that exposes ce as 4-element vector expression.

Parameters

ce	The quaternion expression to wrap.

Returns

An adapter object exposing ce as 4-element vector expression.

vec() [5/14]

DQuaternionVectorAdapter CDPL.Math.vec

(

DQuaternionExpression

me

)

Returns a mutable quaternion adapter that exposes me as 4-element vector expression.

Parameters

me	The quaternion expression to wrap.

Returns

An adapter object exposing me as 4-element vector expression.

vec() [6/14]

FQuaternionVectorAdapter CDPL.Math.vec

(

FQuaternionExpression

me

)

Returns a mutable quaternion adapter that exposes me as 4-element vector expression.

Parameters

me	The quaternion expression to wrap.

Returns

An adapter object exposing me as 4-element vector expression.

vec() [7/14]

LQuaternionVectorAdapter CDPL.Math.vec

(

LQuaternionExpression

me

)

Returns a mutable quaternion adapter that exposes me as 4-element vector expression.

Parameters

me	The quaternion expression to wrap.

Returns

An adapter object exposing me as 4-element vector expression.

vec() [8/14]

ULQuaternionVectorAdapter CDPL.Math.vec

(

ULQuaternionExpression

me

)

Returns a mutable quaternion adapter that exposes me as 4-element vector expression.

Parameters

me	The quaternion expression to wrap.

Returns

An adapter object exposing me as 4-element vector expression.

vec() [9/14]

Vector2F CDPL.Math.vec	(	float	t1,
		float	t2
	)

Constructs a vector 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() [10/14]

Vector3F CDPL.Math.vec	(	float	t1,
		float	t2,
		float	t3
	)

Constructs a vector 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() [11/14]

Vector4F CDPL.Math.vec	(	float	t1,
		float	t2,
		float	t3,
		float	t4
	)

Constructs a vector 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() [12/14]

Vector2L CDPL.Math.vec	(	int	t1,
		int	t2
	)

Constructs a vector 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() [13/14]

Vector3L CDPL.Math.vec	(	int	t1,
		int	t2,
		int	t3
	)

Constructs a vector 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() [14/14]

Vector4L CDPL.Math.vec	(	int	t1,
		int	t2,
		int	t3,
		int	t4
	)

Constructs a vector 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).