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

Classes
class	ConstDGridExpression

class	ConstDHomogenousCoordsAdapter

class	ConstDMatrixColumn

class	ConstDMatrixExpression

class	ConstDMatrixRange

class	ConstDMatrixRow

class	ConstDMatrixSlice

class	ConstDMatrixTranspose

class	ConstDQuaternionExpression

class	ConstDQuaternionVectorAdapter

class	ConstDVectorExpression

class	ConstDVectorQuaternionAdapter

class	ConstDVectorRange

class	ConstDVectorSlice

class	ConstFGridExpression

class	ConstFHomogenousCoordsAdapter

class	ConstFMatrixColumn

class	ConstFMatrixExpression

class	ConstFMatrixRange

class	ConstFMatrixRow

class	ConstFMatrixSlice

class	ConstFMatrixTranspose

class	ConstFQuaternionExpression

class	ConstFQuaternionVectorAdapter

class	ConstFVectorExpression

class	ConstFVectorQuaternionAdapter

class	ConstFVectorRange

class	ConstFVectorSlice

class	ConstLHomogenousCoordsAdapter

class	ConstLMatrixColumn

class	ConstLMatrixExpression

class	ConstLMatrixRange

class	ConstLMatrixRow

class	ConstLMatrixSlice

class	ConstLMatrixTranspose

class	ConstLQuaternionExpression

class	ConstLQuaternionVectorAdapter

class	ConstLVectorExpression

class	ConstLVectorQuaternionAdapter

class	ConstLVectorRange

class	ConstLVectorSlice

class	ConstLowerTriangularDMatrixAdapter

class	ConstLowerTriangularFMatrixAdapter

class	ConstLowerTriangularLMatrixAdapter

class	ConstLowerTriangularULMatrixAdapter

class	ConstULHomogenousCoordsAdapter

class	ConstULMatrixColumn

class	ConstULMatrixExpression

class	ConstULMatrixRange

class	ConstULMatrixRow

class	ConstULMatrixSlice

class	ConstULMatrixTranspose

class	ConstULQuaternionExpression

class	ConstULQuaternionVectorAdapter

class	ConstULVectorExpression

class	ConstULVectorQuaternionAdapter

class	ConstULVectorRange

class	ConstULVectorSlice

class	ConstUnitLowerTriangularDMatrixAdapter

class	ConstUnitLowerTriangularFMatrixAdapter

class	ConstUnitLowerTriangularLMatrixAdapter

class	ConstUnitLowerTriangularULMatrixAdapter

class	ConstUnitUpperTriangularDMatrixAdapter

class	ConstUnitUpperTriangularFMatrixAdapter

class	ConstUnitUpperTriangularLMatrixAdapter

class	ConstUnitUpperTriangularULMatrixAdapter

class	ConstUpperTriangularDMatrixAdapter

class	ConstUpperTriangularFMatrixAdapter

class	ConstUpperTriangularLMatrixAdapter

class	ConstUpperTriangularULMatrixAdapter

class	DGrid
	An unbounded dense grid holding floating point values of type `double`. More...

class	DGridExpression

class	DHomogenousCoordsAdapter

class	DIdentityMatrix

class	DKabschAlgorithm

class	DMLRModel
	Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...

class	DMatrix
	An unbounded dense matrix holding floating point values of type `double`. More...

class	DMatrixColumn

class	DMatrixExpression

class	DMatrixRange

class	DMatrixRow

class	DMatrixSlice

class	DMatrixTranspose

class	DQuaternion

class	DQuaternionExpression

class	DQuaternionVectorAdapter

class	DRealQuaternion

class	DRegularSpatialGrid
	An unbounded dense regular grid in 3D space holding floating point values of type `double`. More...

class	DRotationMatrix

class	DScalarGrid

class	DScalarMatrix

class	DScalarVector

class	DScalingMatrix

class	DTranslationMatrix

class	DUnitVector

class	DVector
	An unbounded dense vector holding floating point values of type `double`. More...

class	DVectorBFGSMinimizer
	Fletcher's implementation of the BFGS method. More...

class	DVectorExpression

class	DVectorQuaternionAdapter

class	DVectorRange

class	DVectorSlice

class	DZeroGrid

class	DZeroMatrix

class	DZeroVector

class	DoubleDVector2Functor

class	DoubleDVectorFunctor

class	DoubleVector2DArray2Functor

class	DoubleVector2DArrayFunctor

class	DoubleVector3DArray2Functor

class	DoubleVector3DArrayFunctor

class	FGrid
	An unbounded dense grid holding floating point values of type `float`. More...

class	FGridExpression

class	FHomogenousCoordsAdapter

class	FIdentityMatrix

class	FKabschAlgorithm

class	FMLRModel
	Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...

class	FMatrix
	An unbounded dense matrix holding floating point values of type `float`. More...

class	FMatrixColumn

class	FMatrixExpression

class	FMatrixRange

class	FMatrixRow

class	FMatrixSlice

class	FMatrixTranspose

class	FQuaternion

class	FQuaternionExpression

class	FQuaternionVectorAdapter

class	FRealQuaternion

class	FRegularSpatialGrid
	An unbounded dense regular grid in 3D space holding floating point values of type `float`. More...

class	FRotationMatrix

class	FScalarGrid

class	FScalarMatrix

class	FScalarVector

class	FScalingMatrix

class	FTranslationMatrix

class	FUnitVector

class	FVector
	An unbounded dense vector holding floating point values of type `float`. More...

class	FVectorBFGSMinimizer
	Fletcher's implementation of the BFGS method. More...

class	FVectorExpression

class	FVectorQuaternionAdapter

class	FVectorRange

class	FVectorSlice

class	FZeroGrid

class	FZeroMatrix

class	FZeroVector

class	FloatFVector2Functor

class	FloatFVectorFunctor

class	FloatVector2FArray2Functor

class	FloatVector2FArrayFunctor

class	FloatVector3FArray2Functor

class	FloatVector3FArrayFunctor

class	LHomogenousCoordsAdapter

class	LIdentityMatrix

class	LMatrix
	An unbounded dense matrix holding signed integers of type `long`. More...

class	LMatrixColumn

class	LMatrixExpression

class	LMatrixRange

class	LMatrixRow

class	LMatrixSlice

class	LMatrixTranspose

class	LQuaternion

class	LQuaternionExpression

class	LQuaternionVectorAdapter

class	LRealQuaternion

class	LRotationMatrix

class	LScalarMatrix

class	LScalarVector

class	LScalingMatrix

class	LTranslationMatrix

class	LUnitVector

class	LVector
	An unbounded dense vector holding signed integers of type `long`. More...

class	LVectorExpression

class	LVectorQuaternionAdapter

class	LVectorRange

class	LVectorSlice

class	LZeroMatrix

class	LZeroVector

class	Lower

class	Matrix2D
	A bounded 2x2 matrix holding floating point values of type `double`. More...

class	Matrix2F
	A bounded 2x2 matrix holding floating point values of type `float`. More...

class	Matrix2L
	A bounded 2x2 matrix holding signed integers of type `long`. More...

class	Matrix2UL
	A bounded 2x2 matrix holding unsigned integers of type `unsigned long`. More...

class	Matrix3D
	A bounded 3x3 matrix holding floating point values of type `double`. More...

class	Matrix3F
	A bounded 3x3 matrix holding floating point values of type `float`. More...

class	Matrix3L
	A bounded 3x3 matrix holding signed integers of type `long`. More...

class	Matrix3UL
	A bounded 3x3 matrix holding unsigned integers of type `unsigned long`. More...

class	Matrix4D
	A bounded 4x4 matrix holding floating point values of type `double`. More...

class	Matrix4F
	A bounded 4x4 matrix holding floating point values of type `float`. More...

class	Matrix4L
	A bounded 4x4 matrix holding signed integers of type `long`. More...

class	Matrix4UL
	A bounded 4x4 matrix holding unsigned integers of type `unsigned long`. More...

class	Range

class	Slice

class	SparseDMatrix
	An unbounded sparse matrix holding floating point values of type `double`. More...

class	SparseDVector
	An unbounded sparse vector holding floating point values of type `double`. More...

class	SparseFMatrix
	An unbounded sparse matrix holding floating point values of type `float`. More...

class	SparseFVector
	An unbounded sparse vector holding floating point values of type `float`. More...

class	SparseLMatrix
	An unbounded sparse matrix holding signed integers of type `long`. More...

class	SparseLVector
	An unbounded sparse vector holding signed integers of type `long`. More...

class	SparseULMatrix
	An unbounded sparse matrix holding unsigned integers of type `unsigned long`. More...

class	SparseULVector
	An unbounded sparse vector holding unsigned integers of type `unsigned long`. More...

class	ULHomogenousCoordsAdapter

class	ULIdentityMatrix

class	ULMatrix
	An unbounded dense matrix holding unsigned integers of type `unsigned long`. More...

class	ULMatrixColumn

class	ULMatrixExpression

class	ULMatrixRange

class	ULMatrixRow

class	ULMatrixSlice

class	ULMatrixTranspose

class	ULQuaternion

class	ULQuaternionExpression

class	ULQuaternionVectorAdapter

class	ULRealQuaternion

class	ULRotationMatrix

class	ULScalarMatrix

class	ULScalarVector

class	ULScalingMatrix

class	ULTranslationMatrix

class	ULUnitVector

class	ULVector
	An unbounded dense vector holding unsigned integers of type `unsigned long`. More...

class	ULVectorExpression

class	ULVectorQuaternionAdapter

class	ULVectorRange

class	ULVectorSlice

class	ULZeroMatrix

class	ULZeroVector

class	UnitLower

class	UnitUpper

class	Upper

class	Vector2D
	A bounded 2 element vector holding floating point values of type `double`. More...

class	Vector2DArray
	An array of Math.Vector2D objects. More...

class	Vector2DArrayAlignmentCalculator

class	Vector2DArrayBFGSMinimizer

class	Vector2F
	A bounded 2 element vector holding floating point values of type `float`. More...

class	Vector2FArray
	An array of Math.Vector2F objects. More...

class	Vector2FArrayAlignmentCalculator

class	Vector2FArrayBFGSMinimizer

class	Vector2L
	A bounded 2 element vector holding signed integers of type `long`. More...

class	Vector2LArray
	An array of Math.Vector2L objects. More...

class	Vector2UL
	A bounded 2 element vector holding unsigned integers of type `unsigned long`. More...

class	Vector2ULArray
	An array of Math.Vector2UL objects. More...

class	Vector3D
	A bounded 3 element vector holding floating point values of type `double`. More...

class	Vector3DArray
	An array of Math.Vector3D objects. More...

class	Vector3DArrayAlignmentCalculator

class	Vector3DArrayBFGSMinimizer

class	Vector3F
	A bounded 3 element vector holding floating point values of type `float`. More...

class	Vector3FArray
	An array of Math.Vector3F objects. More...

class	Vector3FArrayAlignmentCalculator

class	Vector3FArrayBFGSMinimizer

class	Vector3L
	A bounded 3 element vector holding signed integers of type `long`. More...

class	Vector3LArray
	An array of Math.Vector3L objects. More...

class	Vector3UL
	A bounded 3 element vector holding unsigned integers of type `unsigned long`. More...

class	Vector3ULArray
	An array of Math.Vector3UL objects. More...

class	Vector4D
	A bounded 4 element vector holding floating point values of type `double`. More...

class	Vector4F
	A bounded 4 element vector holding floating point values of type `float`. More...

class	Vector4L
	A bounded 4 element vector holding signed integers of type `long`. More...

class	Vector4UL
	A bounded 4 element vector holding unsigned integers of type `unsigned long`. More...

class	Vector7D
	A bounded 7 element vector holding floating point values of type `double`. More...

Functions
ConstDGridExpression	elemProd (ConstDGridExpression e1, ConstDGridExpression e2)

ConstDGridExpression	imag (ConstDGridExpression e)

ConstDGridExpression	conj (ConstDGridExpression e)

ConstDGridExpression	real (ConstDGridExpression e)

ConstDGridExpression	herm (ConstDGridExpression e)

float	sum (ConstDGridExpression e)

bool	equals (ConstDGridExpression e1, ConstDGridExpression e2, float eps)

ConstDGridExpression	elemDiv (ConstDGridExpression e1, ConstDGridExpression e2)

float	norm1 (ConstDMatrixExpression e)

float	normFrob (ConstDMatrixExpression e)

ConstDMatrixExpression	elemProd (ConstDMatrixExpression e1, ConstDMatrixExpression e2)

ConstDVectorExpression	prod (ConstDMatrixExpression e1, ConstDVectorExpression e2)

DVectorExpression	prod (ConstDMatrixExpression e1, ConstDVectorExpression e2, DVectorExpression c)

ConstDMatrixExpression	prod (ConstDMatrixExpression e1, ConstDMatrixExpression e2)

DMatrixExpression	prod (ConstDMatrixExpression e1, ConstDMatrixExpression e2, DMatrixExpression c)

float	trace (ConstDMatrixExpression e)

ConstDMatrixSlice	slice (ConstDMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

ConstDMatrixRange	range (ConstDMatrixExpression e, Range r1, Range r2)

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

bool	luSubstitute (ConstDMatrixExpression e, DVectorExpression b)

bool	luSubstitute (ConstDMatrixExpression e, ConstULVectorExpression pv, DVectorExpression b)

bool	luSubstitute (ConstDMatrixExpression e, DMatrixExpression b)

bool	luSubstitute (ConstDMatrixExpression e, ConstULVectorExpression pv, DMatrixExpression b)

None	svSubstitute (ConstDMatrixExpression u, ConstDVectorExpression w, ConstDMatrixExpression v, ConstDVectorExpression b, DVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

None	svSubstitute (ConstDMatrixExpression u, ConstDVectorExpression w, ConstDMatrixExpression v, ConstDMatrixExpression b, DMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

float	normInf (ConstDMatrixExpression e)

ConstDMatrixExpression	imag (ConstDMatrixExpression e)

ConstUpperTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, Upper type)

ConstUnitUpperTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, UnitUpper type)

ConstLowerTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, Lower type)

ConstUnitLowerTriangularDMatrixAdapter	triang (ConstDMatrixExpression e, UnitLower type)

ConstDMatrixExpression	conj (ConstDMatrixExpression e)

ConstDMatrixExpression	real (ConstDMatrixExpression e)

ConstDMatrixExpression	herm (ConstDMatrixExpression e)

float	sum (ConstDMatrixExpression e)

ConstDMatrixColumn	column (ConstDMatrixExpression e, int i)

bool	solveUpper (ConstDMatrixExpression e1, DVectorExpression e2)

bool	solveUpper (ConstDMatrixExpression e1, DMatrixExpression e2)

bool	solveUnitUpper (ConstDMatrixExpression e1, DVectorExpression e2)

bool	solveUnitUpper (ConstDMatrixExpression e1, DMatrixExpression e2)

bool	solveLower (ConstDMatrixExpression e1, DVectorExpression e2)

bool	solveLower (ConstDMatrixExpression e1, DMatrixExpression e2)

bool	solveUnitLower (ConstDMatrixExpression e1, DVectorExpression e2)

bool	solveUnitLower (ConstDMatrixExpression e1, DMatrixExpression e2)

bool	equals (ConstDMatrixExpression e1, ConstDMatrixExpression e2, float eps)

ConstDMatrixTranspose	trans (ConstDMatrixExpression e)

float	det (ConstDMatrixExpression e)

bool	invert (ConstDMatrixExpression e, DMatrixExpression c)

ConstDMatrixExpression	elemDiv (ConstDMatrixExpression e1, ConstDMatrixExpression e2)

ConstDMatrixRow	row (ConstDMatrixExpression e, int i)

float	norm2 (ConstDQuaternionExpression e)

ConstDQuaternionVectorAdapter	vec (ConstDQuaternionExpression e)

ConstDQuaternionExpression	elemProd (ConstDQuaternionExpression e1, ConstDQuaternionExpression e2)

ConstDVectorExpression	rotate (ConstDQuaternionExpression e1, ConstDVectorExpression e2)

ConstDQuaternionExpression	conj (ConstDQuaternionExpression e)

float	real (ConstDQuaternionExpression e)

ConstDQuaternionExpression	unreal (ConstDQuaternionExpression e)

float	norm (ConstDQuaternionExpression e)

float	sum (ConstDQuaternionExpression e)

bool	equals (ConstDQuaternionExpression e1, ConstDQuaternionExpression e2, float eps)

ConstDQuaternionExpression	elemDiv (ConstDQuaternionExpression e1, ConstDQuaternionExpression e2)

ConstDQuaternionExpression	inv (ConstDQuaternionExpression e)

float	norm1 (ConstDVectorExpression e)

float	norm2 (ConstDVectorExpression e)

ConstDVectorExpression	elemProd (ConstDVectorExpression e1, ConstDVectorExpression e2)

float	innerProd (ConstDVectorExpression e1, ConstDVectorExpression e2)

ConstDMatrixExpression	outerProd (ConstDVectorExpression e1, ConstDVectorExpression e2)

ConstDVectorExpression	crossProd (ConstDVectorExpression e1, ConstDVectorExpression e2)

ConstDVectorExpression	prod (ConstDVectorExpression e1, ConstDMatrixExpression e2)

DVectorExpression	prod (ConstDVectorExpression e1, ConstDMatrixExpression e2, DVectorExpression c)

ConstDVectorSlice	slice (ConstDVectorExpression e, ast.Slice s)

ConstDVectorSlice	slice (ConstDVectorExpression e, int start, int stride, int size)

ConstDVectorRange	range (ConstDVectorExpression e, Range r)

ConstDVectorRange	range (ConstDVectorExpression e, int start, int stop)

float	normInf (ConstDVectorExpression e)

ConstDMatrixExpression	diag (ConstDVectorExpression e)

ConstDVectorExpression	imag (ConstDVectorExpression e)

ConstDHomogenousCoordsAdapter	homog (ConstDVectorExpression e)

float	length (ConstDVectorExpression e)

ConstDVectorExpression	conj (ConstDVectorExpression e)

ConstDVectorExpression	real (ConstDVectorExpression e)

ConstDVectorExpression	herm (ConstDVectorExpression e)

float	sum (ConstDVectorExpression e)

bool	equals (ConstDVectorExpression e1, ConstDVectorExpression e2, float eps)

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

ConstDMatrixExpression	cross (ConstDVectorExpression e)

ConstDVectorQuaternionAdapter	quat (ConstDVectorExpression e)

ConstDVectorExpression	elemDiv (ConstDVectorExpression e1, ConstDVectorExpression e2)

int	normInfIndex (ConstDVectorExpression e)

ConstFGridExpression	elemProd (ConstFGridExpression e1, ConstFGridExpression e2)

ConstFGridExpression	imag (ConstFGridExpression e)

ConstFGridExpression	conj (ConstFGridExpression e)

ConstFGridExpression	real (ConstFGridExpression e)

ConstFGridExpression	herm (ConstFGridExpression e)

float	sum (ConstFGridExpression e)

bool	equals (ConstFGridExpression e1, ConstFGridExpression e2, float eps)

ConstFGridExpression	elemDiv (ConstFGridExpression e1, ConstFGridExpression e2)

float	norm1 (ConstFMatrixExpression e)

float	normFrob (ConstFMatrixExpression e)

ConstFMatrixExpression	elemProd (ConstFMatrixExpression e1, ConstFMatrixExpression e2)

ConstFVectorExpression	prod (ConstFMatrixExpression e1, ConstFVectorExpression e2)

FVectorExpression	prod (ConstFMatrixExpression e1, ConstFVectorExpression e2, FVectorExpression c)

ConstFMatrixExpression	prod (ConstFMatrixExpression e1, ConstFMatrixExpression e2)

FMatrixExpression	prod (ConstFMatrixExpression e1, ConstFMatrixExpression e2, FMatrixExpression c)

float	trace (ConstFMatrixExpression e)

ConstFMatrixSlice	slice (ConstFMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

ConstFMatrixRange	range (ConstFMatrixExpression e, Range r1, Range r2)

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

bool	luSubstitute (ConstFMatrixExpression e, FVectorExpression b)

bool	luSubstitute (ConstFMatrixExpression e, ConstULVectorExpression pv, FVectorExpression b)

bool	luSubstitute (ConstFMatrixExpression e, FMatrixExpression b)

bool	luSubstitute (ConstFMatrixExpression e, ConstULVectorExpression pv, FMatrixExpression b)

None	svSubstitute (ConstFMatrixExpression u, ConstFVectorExpression w, ConstFMatrixExpression v, ConstFVectorExpression b, FVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

None	svSubstitute (ConstFMatrixExpression u, ConstFVectorExpression w, ConstFMatrixExpression v, ConstFMatrixExpression b, FMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

float	normInf (ConstFMatrixExpression e)

ConstFMatrixExpression	imag (ConstFMatrixExpression e)

ConstUpperTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, Upper type)

ConstUnitUpperTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, UnitUpper type)

ConstLowerTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, Lower type)

ConstUnitLowerTriangularFMatrixAdapter	triang (ConstFMatrixExpression e, UnitLower type)

ConstFMatrixExpression	conj (ConstFMatrixExpression e)

ConstFMatrixExpression	real (ConstFMatrixExpression e)

ConstFMatrixExpression	herm (ConstFMatrixExpression e)

float	sum (ConstFMatrixExpression e)

ConstFMatrixColumn	column (ConstFMatrixExpression e, int i)

bool	solveUpper (ConstFMatrixExpression e1, FVectorExpression e2)

bool	solveUpper (ConstFMatrixExpression e1, FMatrixExpression e2)

bool	solveUnitUpper (ConstFMatrixExpression e1, FVectorExpression e2)

bool	solveUnitUpper (ConstFMatrixExpression e1, FMatrixExpression e2)

bool	solveLower (ConstFMatrixExpression e1, FVectorExpression e2)

bool	solveLower (ConstFMatrixExpression e1, FMatrixExpression e2)

bool	solveUnitLower (ConstFMatrixExpression e1, FVectorExpression e2)

bool	solveUnitLower (ConstFMatrixExpression e1, FMatrixExpression e2)

bool	equals (ConstFMatrixExpression e1, ConstFMatrixExpression e2, float eps)

ConstFMatrixTranspose	trans (ConstFMatrixExpression e)

float	det (ConstFMatrixExpression e)

bool	invert (ConstFMatrixExpression e, FMatrixExpression c)

ConstFMatrixExpression	elemDiv (ConstFMatrixExpression e1, ConstFMatrixExpression e2)

ConstFMatrixRow	row (ConstFMatrixExpression e, int i)

float	norm2 (ConstFQuaternionExpression e)

ConstFQuaternionVectorAdapter	vec (ConstFQuaternionExpression e)

ConstFQuaternionExpression	elemProd (ConstFQuaternionExpression e1, ConstFQuaternionExpression e2)

ConstFVectorExpression	rotate (ConstFQuaternionExpression e1, ConstFVectorExpression e2)

ConstFQuaternionExpression	conj (ConstFQuaternionExpression e)

float	real (ConstFQuaternionExpression e)

ConstFQuaternionExpression	unreal (ConstFQuaternionExpression e)

float	norm (ConstFQuaternionExpression e)

float	sum (ConstFQuaternionExpression e)

bool	equals (ConstFQuaternionExpression e1, ConstFQuaternionExpression e2, float eps)

ConstFQuaternionExpression	elemDiv (ConstFQuaternionExpression e1, ConstFQuaternionExpression e2)

ConstFQuaternionExpression	inv (ConstFQuaternionExpression e)

float	norm1 (ConstFVectorExpression e)

float	norm2 (ConstFVectorExpression e)

ConstFVectorExpression	elemProd (ConstFVectorExpression e1, ConstFVectorExpression e2)

float	innerProd (ConstFVectorExpression e1, ConstFVectorExpression e2)

ConstFMatrixExpression	outerProd (ConstFVectorExpression e1, ConstFVectorExpression e2)

ConstFVectorExpression	crossProd (ConstFVectorExpression e1, ConstFVectorExpression e2)

ConstFVectorExpression	prod (ConstFVectorExpression e1, ConstFMatrixExpression e2)

FVectorExpression	prod (ConstFVectorExpression e1, ConstFMatrixExpression e2, FVectorExpression c)

ConstFVectorSlice	slice (ConstFVectorExpression e, ast.Slice s)

ConstFVectorSlice	slice (ConstFVectorExpression e, int start, int stride, int size)

ConstFVectorRange	range (ConstFVectorExpression e, Range r)

ConstFVectorRange	range (ConstFVectorExpression e, int start, int stop)

float	normInf (ConstFVectorExpression e)

ConstFMatrixExpression	diag (ConstFVectorExpression e)

ConstFVectorExpression	imag (ConstFVectorExpression e)

ConstFHomogenousCoordsAdapter	homog (ConstFVectorExpression e)

float	length (ConstFVectorExpression e)

ConstFVectorExpression	conj (ConstFVectorExpression e)

ConstFVectorExpression	real (ConstFVectorExpression e)

ConstFVectorExpression	herm (ConstFVectorExpression e)

float	sum (ConstFVectorExpression e)

bool	equals (ConstFVectorExpression e1, ConstFVectorExpression e2, float eps)

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

ConstFMatrixExpression	cross (ConstFVectorExpression e)

ConstFVectorQuaternionAdapter	quat (ConstFVectorExpression e)

ConstFVectorExpression	elemDiv (ConstFVectorExpression e1, ConstFVectorExpression e2)

int	normInfIndex (ConstFVectorExpression e)

int	norm1 (ConstLMatrixExpression e)

int	normFrob (ConstLMatrixExpression e)

ConstLMatrixExpression	elemProd (ConstLMatrixExpression e1, ConstLMatrixExpression e2)

ConstLVectorExpression	prod (ConstLMatrixExpression e1, ConstLVectorExpression e2)

LVectorExpression	prod (ConstLMatrixExpression e1, ConstLVectorExpression e2, LVectorExpression c)

ConstLMatrixExpression	prod (ConstLMatrixExpression e1, ConstLMatrixExpression e2)

LMatrixExpression	prod (ConstLMatrixExpression e1, ConstLMatrixExpression e2, LMatrixExpression c)

int	trace (ConstLMatrixExpression e)

ConstLMatrixSlice	slice (ConstLMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

ConstLMatrixRange	range (ConstLMatrixExpression e, Range r1, Range r2)

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

bool	luSubstitute (ConstLMatrixExpression e, LVectorExpression b)

bool	luSubstitute (ConstLMatrixExpression e, ConstULVectorExpression pv, LVectorExpression b)

bool	luSubstitute (ConstLMatrixExpression e, LMatrixExpression b)

bool	luSubstitute (ConstLMatrixExpression e, ConstULVectorExpression pv, LMatrixExpression b)

None	svSubstitute (ConstLMatrixExpression u, ConstLVectorExpression w, ConstLMatrixExpression v, ConstLVectorExpression b, LVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

None	svSubstitute (ConstLMatrixExpression u, ConstLVectorExpression w, ConstLMatrixExpression v, ConstLMatrixExpression b, LMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

int	normInf (ConstLMatrixExpression e)

ConstLMatrixExpression	imag (ConstLMatrixExpression e)

ConstUpperTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, Upper type)

ConstUnitUpperTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, UnitUpper type)

ConstLowerTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, Lower type)

ConstUnitLowerTriangularLMatrixAdapter	triang (ConstLMatrixExpression e, UnitLower type)

ConstLMatrixExpression	conj (ConstLMatrixExpression e)

ConstLMatrixExpression	real (ConstLMatrixExpression e)

ConstLMatrixExpression	herm (ConstLMatrixExpression e)

int	sum (ConstLMatrixExpression e)

ConstLMatrixColumn	column (ConstLMatrixExpression e, int i)

bool	solveUpper (ConstLMatrixExpression e1, LVectorExpression e2)

bool	solveUpper (ConstLMatrixExpression e1, LMatrixExpression e2)

bool	solveUnitUpper (ConstLMatrixExpression e1, LVectorExpression e2)

bool	solveUnitUpper (ConstLMatrixExpression e1, LMatrixExpression e2)

bool	solveLower (ConstLMatrixExpression e1, LVectorExpression e2)

bool	solveLower (ConstLMatrixExpression e1, LMatrixExpression e2)

bool	solveUnitLower (ConstLMatrixExpression e1, LVectorExpression e2)

bool	solveUnitLower (ConstLMatrixExpression e1, LMatrixExpression e2)

bool	equals (ConstLMatrixExpression e1, ConstLMatrixExpression e2, int eps)

ConstLMatrixTranspose	trans (ConstLMatrixExpression e)

int	det (ConstLMatrixExpression e)

bool	invert (ConstLMatrixExpression e, LMatrixExpression c)

ConstLMatrixExpression	elemDiv (ConstLMatrixExpression e1, ConstLMatrixExpression e2)

ConstLMatrixRow	row (ConstLMatrixExpression e, int i)

int	norm2 (ConstLQuaternionExpression e)

ConstLQuaternionVectorAdapter	vec (ConstLQuaternionExpression e)

ConstLQuaternionExpression	elemProd (ConstLQuaternionExpression e1, ConstLQuaternionExpression e2)

ConstLVectorExpression	rotate (ConstLQuaternionExpression e1, ConstLVectorExpression e2)

ConstLQuaternionExpression	conj (ConstLQuaternionExpression e)

int	real (ConstLQuaternionExpression e)

ConstLQuaternionExpression	unreal (ConstLQuaternionExpression e)

int	norm (ConstLQuaternionExpression e)

int	sum (ConstLQuaternionExpression e)

bool	equals (ConstLQuaternionExpression e1, ConstLQuaternionExpression e2, int eps)

ConstLQuaternionExpression	elemDiv (ConstLQuaternionExpression e1, ConstLQuaternionExpression e2)

ConstLQuaternionExpression	inv (ConstLQuaternionExpression e)

int	norm1 (ConstLVectorExpression e)

int	norm2 (ConstLVectorExpression e)

ConstLVectorExpression	elemProd (ConstLVectorExpression e1, ConstLVectorExpression e2)

int	innerProd (ConstLVectorExpression e1, ConstLVectorExpression e2)

ConstLMatrixExpression	outerProd (ConstLVectorExpression e1, ConstLVectorExpression e2)

ConstLVectorExpression	crossProd (ConstLVectorExpression e1, ConstLVectorExpression e2)

ConstLVectorExpression	prod (ConstLVectorExpression e1, ConstLMatrixExpression e2)

LVectorExpression	prod (ConstLVectorExpression e1, ConstLMatrixExpression e2, LVectorExpression c)

ConstLVectorSlice	slice (ConstLVectorExpression e, ast.Slice s)

ConstLVectorSlice	slice (ConstLVectorExpression e, int start, int stride, int size)

ConstLVectorRange	range (ConstLVectorExpression e, Range r)

ConstLVectorRange	range (ConstLVectorExpression e, int start, int stop)

int	normInf (ConstLVectorExpression e)

ConstLMatrixExpression	diag (ConstLVectorExpression e)

ConstLVectorExpression	imag (ConstLVectorExpression e)

ConstLHomogenousCoordsAdapter	homog (ConstLVectorExpression e)

int	length (ConstLVectorExpression e)

ConstLVectorExpression	conj (ConstLVectorExpression e)

ConstLVectorExpression	real (ConstLVectorExpression e)

ConstLVectorExpression	herm (ConstLVectorExpression e)

int	sum (ConstLVectorExpression e)

bool	equals (ConstLVectorExpression e1, ConstLVectorExpression e2, int eps)

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

ConstLMatrixExpression	cross (ConstLVectorExpression e)

ConstLVectorQuaternionAdapter	quat (ConstLVectorExpression e)

ConstLVectorExpression	elemDiv (ConstLVectorExpression e1, ConstLVectorExpression e2)

int	normInfIndex (ConstLVectorExpression e)

int	norm1 (ConstULMatrixExpression e)

int	normFrob (ConstULMatrixExpression e)

ConstULMatrixExpression	elemProd (ConstULMatrixExpression e1, ConstULMatrixExpression e2)

ConstULVectorExpression	prod (ConstULMatrixExpression e1, ConstULVectorExpression e2)

ULVectorExpression	prod (ConstULMatrixExpression e1, ConstULVectorExpression e2, ULVectorExpression c)

ConstULMatrixExpression	prod (ConstULMatrixExpression e1, ConstULMatrixExpression e2)

ULMatrixExpression	prod (ConstULMatrixExpression e1, ConstULMatrixExpression e2, ULMatrixExpression c)

int	trace (ConstULMatrixExpression e)

ConstULMatrixSlice	slice (ConstULMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

ConstULMatrixRange	range (ConstULMatrixExpression e, Range r1, Range r2)

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

bool	luSubstitute (ConstULMatrixExpression e, ULVectorExpression b)

bool	luSubstitute (ConstULMatrixExpression e, ConstULVectorExpression pv, ULVectorExpression b)

bool	luSubstitute (ConstULMatrixExpression e, ULMatrixExpression b)

bool	luSubstitute (ConstULMatrixExpression e, ConstULVectorExpression pv, ULMatrixExpression b)

None	svSubstitute (ConstULMatrixExpression u, ConstULVectorExpression w, ConstULMatrixExpression v, ConstULVectorExpression b, ULVectorExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

None	svSubstitute (ConstULMatrixExpression u, ConstULVectorExpression w, ConstULMatrixExpression v, ConstULMatrixExpression b, ULMatrixExpression x)
	Solves \( A \cdot X = B \) for a matrix \( X \) where \( A \) is given by its Singular Value Decomposition [WSVD]. More...

int	normInf (ConstULMatrixExpression e)

ConstULMatrixExpression	imag (ConstULMatrixExpression e)

ConstUpperTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, Upper type)

ConstUnitUpperTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, UnitUpper type)

ConstLowerTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, Lower type)

ConstUnitLowerTriangularULMatrixAdapter	triang (ConstULMatrixExpression e, UnitLower type)

ConstULMatrixExpression	conj (ConstULMatrixExpression e)

ConstULMatrixExpression	real (ConstULMatrixExpression e)

ConstULMatrixExpression	herm (ConstULMatrixExpression e)

int	sum (ConstULMatrixExpression e)

ConstULMatrixColumn	column (ConstULMatrixExpression e, int i)

bool	solveUpper (ConstULMatrixExpression e1, ULVectorExpression e2)

bool	solveUpper (ConstULMatrixExpression e1, ULMatrixExpression e2)

bool	solveUnitUpper (ConstULMatrixExpression e1, ULVectorExpression e2)

bool	solveUnitUpper (ConstULMatrixExpression e1, ULMatrixExpression e2)

bool	solveLower (ConstULMatrixExpression e1, ULVectorExpression e2)

bool	solveLower (ConstULMatrixExpression e1, ULMatrixExpression e2)

bool	solveUnitLower (ConstULMatrixExpression e1, ULVectorExpression e2)

bool	solveUnitLower (ConstULMatrixExpression e1, ULMatrixExpression e2)

bool	equals (ConstULMatrixExpression e1, ConstULMatrixExpression e2, int eps)

ConstULMatrixTranspose	trans (ConstULMatrixExpression e)

int	det (ConstULMatrixExpression e)

bool	invert (ConstULMatrixExpression e, ULMatrixExpression c)

ConstULMatrixExpression	elemDiv (ConstULMatrixExpression e1, ConstULMatrixExpression e2)

ConstULMatrixRow	row (ConstULMatrixExpression e, int i)

int	norm2 (ConstULQuaternionExpression e)

ConstULQuaternionVectorAdapter	vec (ConstULQuaternionExpression e)

ConstULQuaternionExpression	elemProd (ConstULQuaternionExpression e1, ConstULQuaternionExpression e2)

ConstULVectorExpression	rotate (ConstULQuaternionExpression e1, ConstULVectorExpression e2)

ConstULQuaternionExpression	conj (ConstULQuaternionExpression e)

int	real (ConstULQuaternionExpression e)

ConstULQuaternionExpression	unreal (ConstULQuaternionExpression e)

int	norm (ConstULQuaternionExpression e)

int	sum (ConstULQuaternionExpression e)

bool	equals (ConstULQuaternionExpression e1, ConstULQuaternionExpression e2, int eps)

ConstULQuaternionExpression	elemDiv (ConstULQuaternionExpression e1, ConstULQuaternionExpression e2)

ConstULQuaternionExpression	inv (ConstULQuaternionExpression e)

int	norm1 (ConstULVectorExpression e)

int	norm2 (ConstULVectorExpression e)

ConstULVectorExpression	elemProd (ConstULVectorExpression e1, ConstULVectorExpression e2)

int	innerProd (ConstULVectorExpression e1, ConstULVectorExpression e2)

ConstULMatrixExpression	outerProd (ConstULVectorExpression e1, ConstULVectorExpression e2)

ConstULVectorExpression	crossProd (ConstULVectorExpression e1, ConstULVectorExpression e2)

ConstULVectorExpression	prod (ConstULVectorExpression e1, ConstULMatrixExpression e2)

ULVectorExpression	prod (ConstULVectorExpression e1, ConstULMatrixExpression e2, ULVectorExpression c)

ConstULVectorSlice	slice (ConstULVectorExpression e, ast.Slice s)

ConstULVectorSlice	slice (ConstULVectorExpression e, int start, int stride, int size)

ConstULVectorRange	range (ConstULVectorExpression e, Range r)

ConstULVectorRange	range (ConstULVectorExpression e, int start, int stop)

int	normInf (ConstULVectorExpression e)

ConstULMatrixExpression	diag (ConstULVectorExpression e)

ConstULVectorExpression	imag (ConstULVectorExpression e)

ConstULHomogenousCoordsAdapter	homog (ConstULVectorExpression e)

int	length (ConstULVectorExpression e)

ConstULVectorExpression	conj (ConstULVectorExpression e)

ConstULVectorExpression	real (ConstULVectorExpression e)

ConstULVectorExpression	herm (ConstULVectorExpression e)

int	sum (ConstULVectorExpression e)

bool	equals (ConstULVectorExpression e1, ConstULVectorExpression e2, int eps)

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

ConstULMatrixExpression	cross (ConstULVectorExpression e)

ConstULVectorQuaternionAdapter	quat (ConstULVectorExpression e)

ConstULVectorExpression	elemDiv (ConstULVectorExpression e1, ConstULVectorExpression e2)

int	normInfIndex (ConstULVectorExpression e)

DMatrixSlice	slice (DMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

DMatrixRange	range (DMatrixExpression e, Range r1, Range r2)

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

int	luDecompose (DMatrixExpression e)

int	luDecompose (DMatrixExpression e, ULVectorExpression pv)

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	jacobiDiagonalize (DMatrixExpression a, DVectorExpression d, DMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...

DMatrixColumn	column (DMatrixExpression e, int i)

DMatrixTranspose	trans (DMatrixExpression e)

bool	invert (DMatrixExpression c)

DMatrixRow	row (DMatrixExpression e, int i)

float	interpolateTrilinear (DRegularSpatialGrid grid, Vector3D pos, bool local_pos)

DVectorSlice	slice (DVectorExpression e, ast.Slice s)

DVectorSlice	slice (DVectorExpression e, int start, int stride, int size)

DVectorRange	range (DVectorExpression e, Range r)

DVectorRange	range (DVectorExpression e, int start, int stop)

DHomogenousCoordsAdapter	homog (DVectorExpression e)

DVectorQuaternionAdapter	quat (DVectorExpression e)

FMatrixSlice	slice (FMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

FMatrixRange	range (FMatrixExpression e, Range r1, Range r2)

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

int	luDecompose (FMatrixExpression e)

int	luDecompose (FMatrixExpression e, ULVectorExpression pv)

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	jacobiDiagonalize (FMatrixExpression a, FVectorExpression d, FMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...

FMatrixColumn	column (FMatrixExpression e, int i)

FMatrixTranspose	trans (FMatrixExpression e)

bool	invert (FMatrixExpression c)

FMatrixRow	row (FMatrixExpression e, int i)

float	interpolateTrilinear (FRegularSpatialGrid grid, Vector3F pos, bool local_pos)

FVectorSlice	slice (FVectorExpression e, ast.Slice s)

FVectorSlice	slice (FVectorExpression e, int start, int stride, int size)

FVectorRange	range (FVectorExpression e, Range r)

FVectorRange	range (FVectorExpression e, int start, int stop)

FHomogenousCoordsAdapter	homog (FVectorExpression e)

FVectorQuaternionAdapter	quat (FVectorExpression e)

LMatrixSlice	slice (LMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

LMatrixRange	range (LMatrixExpression e, Range r1, Range r2)

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

int	luDecompose (LMatrixExpression e)

int	luDecompose (LMatrixExpression e, ULVectorExpression pv)

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	jacobiDiagonalize (LMatrixExpression a, LVectorExpression d, LMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...

LMatrixColumn	column (LMatrixExpression e, int i)

LMatrixTranspose	trans (LMatrixExpression e)

bool	invert (LMatrixExpression c)

LMatrixRow	row (LMatrixExpression e, int i)

LVectorSlice	slice (LVectorExpression e, ast.Slice s)

LVectorSlice	slice (LVectorExpression e, int start, int stride, int size)

LVectorRange	range (LVectorExpression e, Range r)

LVectorRange	range (LVectorExpression e, int start, int stop)

LHomogenousCoordsAdapter	homog (LVectorExpression e)

LVectorQuaternionAdapter	quat (LVectorExpression e)

ULMatrixSlice	slice (ULMatrixExpression e, ast.Slice s1, ast.Slice s2)

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

ULMatrixRange	range (ULMatrixExpression e, Range r1, Range r2)

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

int	luDecompose (ULMatrixExpression e)

int	luDecompose (ULMatrixExpression e, ULVectorExpression pv)

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...

bool	jacobiDiagonalize (ULMatrixExpression a, ULVectorExpression d, ULMatrixExpression v, int max_iter=50)
	Computes all eigenvalues and eigenvectors of a real symmetric matrix an using Jacobi's algorithm [WJACO ]. More...

ULMatrixColumn	column (ULMatrixExpression e, int i)

ULMatrixTranspose	trans (ULMatrixExpression e)

bool	invert (ULMatrixExpression c)

ULMatrixRow	row (ULMatrixExpression e, int i)

ULVectorSlice	slice (ULVectorExpression e, ast.Slice s)

ULVectorSlice	slice (ULVectorExpression e, int start, int stride, int size)

ULVectorRange	range (ULVectorExpression e, Range r)

ULVectorRange	range (ULVectorExpression e, int start, int stop)

ULHomogenousCoordsAdapter	homog (ULVectorExpression e)

ULVectorQuaternionAdapter	quat (ULVectorExpression e)

float	calcRMSD (Vector2DArray va1, Vector2DArray va2)

float	calcRMSD (Vector2DArray va1, Vector2DArray va2, Matrix3D va1_xform)

bool	calcCentroid (Vector2DArray va, Vector2D ctr)

None	transform (Vector2DArray va, Matrix2D xform)

None	transform (Vector2DArray va, Matrix3D xform)

float	calcRMSD (Vector2FArray va1, Vector2FArray va2)

float	calcRMSD (Vector2FArray va1, Vector2FArray va2, Matrix3F va1_xform)

bool	calcCentroid (Vector2FArray va, Vector2F ctr)

None	transform (Vector2FArray va, Matrix2F xform)

None	transform (Vector2FArray va, Matrix3F xform)

int	calcRMSD (Vector2LArray va1, Vector2LArray va2)

int	calcRMSD (Vector2LArray va1, Vector2LArray va2, Matrix3L va1_xform)

bool	calcCentroid (Vector2LArray va, Vector2L ctr)

None	transform (Vector2LArray va, Matrix2L xform)

None	transform (Vector2LArray va, Matrix3L xform)

int	calcRMSD (Vector2ULArray va1, Vector2ULArray va2)

int	calcRMSD (Vector2ULArray va1, Vector2ULArray va2, Matrix3UL va1_xform)

bool	calcCentroid (Vector2ULArray va, Vector2UL ctr)

None	transform (Vector2ULArray va, Matrix2UL xform)

None	transform (Vector2ULArray va, Matrix3UL xform)

float	calcRMSD (Vector3DArray va1, Vector3DArray va2)

float	calcRMSD (Vector3DArray va1, Vector3DArray va2, Matrix4D va1_xform)

bool	calcCentroid (Vector3DArray va, Vector3D ctr)

None	transform (Vector3DArray va, Matrix3D xform)

None	transform (Vector3DArray va, Matrix4D xform)

float	calcRMSD (Vector3FArray va1, Vector3FArray va2)

float	calcRMSD (Vector3FArray va1, Vector3FArray va2, Matrix4F va1_xform)

bool	calcCentroid (Vector3FArray va, Vector3F ctr)

None	transform (Vector3FArray va, Matrix3F xform)

None	transform (Vector3FArray va, Matrix4F xform)

int	calcRMSD (Vector3LArray va1, Vector3LArray va2)

int	calcRMSD (Vector3LArray va1, Vector3LArray va2, Matrix4L va1_xform)

bool	calcCentroid (Vector3LArray va, Vector3L ctr)

None	transform (Vector3LArray va, Matrix3L xform)

None	transform (Vector3LArray va, Matrix4L xform)

int	calcRMSD (Vector3ULArray va1, Vector3ULArray va2)

int	calcRMSD (Vector3ULArray va1, Vector3ULArray va2, Matrix4UL va1_xform)

bool	calcCentroid (Vector3ULArray va, Vector3UL ctr)

None	transform (Vector3ULArray va, Matrix3UL xform)

None	transform (Vector3ULArray va, Matrix4UL xform)

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

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

Vector2F	vec (float t1, float t2)

Vector3F	vec (float t1, float t2, float t3)

Vector4F	vec (float t1, float t2, float t3, float t4)

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

float	sign (float a, float b)
	Returns the magnitude of parameter a times the sign of parameter b. More...

FRealQuaternion	quat (float t)

FQuaternion	quat (float t1, float t2)

FQuaternion	quat (float t1, float t2, float t3)

FQuaternion	quat (float t1, float t2, float t3, float t4)

Vector2L	vec (int t1, int t2)

Vector3L	vec (int t1, int t2, int t3)

Vector4L	vec (int t1, int t2, int t3, int t4)

ast.Slice	slice (int start, int stride, int size)

Range	range (int start, int stop)

int	prime (int i)

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

LRealQuaternion	quat (int t)

LQuaternion	quat (int t1, int t2)

LQuaternion	quat (int t1, int t2, int t3)

LQuaternion	quat (int t1, int t2, int t3, int t4)

int	sum (object e)

Detailed Description

Contains classes and functions related to mathematics.

Function Documentation

◆ elemProd() [1/14]

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

Parameters

e1
e2

Returns

◆ imag() [1/10]

ConstDGridExpression CDPL.Math.imag ( ConstDGridExpression e )

Parameters

e

Returns

◆ conj() [1/14]

ConstDGridExpression CDPL.Math.conj ( ConstDGridExpression e )

Parameters

e

Returns

◆ real() [1/14]

ConstDGridExpression CDPL.Math.real ( ConstDGridExpression e )

Parameters

e

Returns

◆ herm() [1/10]

ConstDGridExpression CDPL.Math.herm ( ConstDGridExpression e )

Parameters

e

Returns

◆ sum() [1/15]

float CDPL.Math.sum ( ConstDGridExpression e )

Parameters

e

Returns

◆ equals() [1/14]

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

Parameters

e1
e2
eps

Returns

◆ elemDiv() [1/14]

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

Parameters

e1
e2

Returns

◆ norm1() [1/8]

float CDPL.Math.norm1 ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ normFrob() [1/4]

float CDPL.Math.normFrob ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ elemProd() [2/14]

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

Parameters

e1
e2

Returns

◆ prod() [1/24]

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

Parameters

e1
e2

Returns

◆ prod() [2/24]

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

Parameters

e1
e2
c

Returns

◆ prod() [3/24]

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

Parameters

e1
e2

Returns

◆ prod() [4/24]

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

Parameters

e1
e2
c

Returns

◆ trace() [1/4]

float CDPL.Math.trace ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ slice() [1/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [2/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [1/33]

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

Parameters

e
r1
r2

Returns

◆ range() [2/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luSubstitute() [1/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [2/16]

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

Parameters

e
pv
b

Returns

◆ luSubstitute() [3/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [4/16]

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

Parameters

e
pv
b

Returns

◆ svSubstitute() [1/8]

None CDPL.Math.svSubstitute	(	ConstDMatrixExpression	u,
		ConstDVectorExpression	w,
		ConstDMatrixExpression	v,
		ConstDVectorExpression	b,
		DVectorExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ svSubstitute() [2/8]

None CDPL.Math.svSubstitute	(	ConstDMatrixExpression	u,
		ConstDVectorExpression	w,
		ConstDMatrixExpression	v,
		ConstDMatrixExpression	b,
		DMatrixExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ normInf() [1/8]

float CDPL.Math.normInf ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ imag() [2/10]

ConstDMatrixExpression CDPL.Math.imag ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ triang() [1/16]

ConstUpperTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

◆ triang() [2/16]

ConstUnitUpperTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

◆ triang() [3/16]

ConstLowerTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

◆ triang() [4/16]

ConstUnitLowerTriangularDMatrixAdapter CDPL.Math.triang	(	ConstDMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

◆ conj() [2/14]

ConstDMatrixExpression CDPL.Math.conj ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ real() [2/14]

ConstDMatrixExpression CDPL.Math.real ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ herm() [2/10]

ConstDMatrixExpression CDPL.Math.herm ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ sum() [2/15]

float CDPL.Math.sum ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ column() [1/8]

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

Parameters

e
i

Returns

◆ solveUpper() [1/8]

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

Parameters

e1
e2

Returns

◆ solveUpper() [2/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [1/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [2/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [1/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [2/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [1/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [2/8]

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

Parameters

e1
e2

Returns

◆ equals() [2/14]

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

Parameters

e1
e2
eps

Returns

◆ trans() [1/8]

ConstDMatrixTranspose CDPL.Math.trans ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ det() [1/4]

float CDPL.Math.det ( ConstDMatrixExpression e )

Parameters

e

Returns

◆ invert() [1/8]

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

Parameters

e
c

Returns

◆ elemDiv() [2/14]

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

Parameters

e1
e2

Returns

◆ row() [1/8]

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

Parameters

e
i

Returns

◆ norm2() [1/8]

float CDPL.Math.norm2 ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ vec() [1/10]

ConstDQuaternionVectorAdapter CDPL.Math.vec ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ elemProd() [3/14]

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

Parameters

e1
e2

Returns

◆ rotate() [1/4]

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

Parameters

e1
e2

Returns

◆ conj() [3/14]

ConstDQuaternionExpression CDPL.Math.conj ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ real() [3/14]

float CDPL.Math.real ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ unreal() [1/4]

ConstDQuaternionExpression CDPL.Math.unreal ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ norm() [1/4]

float CDPL.Math.norm ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ sum() [3/15]

float CDPL.Math.sum ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ equals() [3/14]

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

Parameters

e1
e2
eps

Returns

◆ elemDiv() [3/14]

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

Parameters

e1
e2

Returns

◆ inv() [1/4]

ConstDQuaternionExpression CDPL.Math.inv ( ConstDQuaternionExpression e )

Parameters

e

Returns

◆ norm1() [2/8]

float CDPL.Math.norm1 ( ConstDVectorExpression e )

Parameters

e

Returns

◆ norm2() [2/8]

float CDPL.Math.norm2 ( ConstDVectorExpression e )

Parameters

e

Returns

◆ elemProd() [4/14]

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

Parameters

e1
e2

Returns

◆ innerProd() [1/4]

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

Parameters

e1
e2

Returns

◆ outerProd() [1/4]

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

Parameters

e1
e2

Returns

◆ crossProd() [1/4]

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

Parameters

e1
e2

Returns

◆ prod() [5/24]

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

Parameters

e1
e2

Returns

◆ prod() [6/24]

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

Parameters

e1
e2
c

Returns

◆ slice() [3/33]

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

Parameters

e
s

Returns

◆ slice() [4/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [3/33]

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

Parameters

e
r

Returns

◆ range() [4/33]

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

Parameters

e
start
stop

Returns

◆ normInf() [2/8]

float CDPL.Math.normInf ( ConstDVectorExpression e )

Parameters

e

Returns

◆ diag() [1/4]

ConstDMatrixExpression CDPL.Math.diag ( ConstDVectorExpression e )

Parameters

e

Returns

◆ imag() [3/10]

ConstDVectorExpression CDPL.Math.imag ( ConstDVectorExpression e )

Parameters

e

Returns

◆ homog() [1/8]

ConstDHomogenousCoordsAdapter CDPL.Math.homog ( ConstDVectorExpression e )

Parameters

e

Returns

◆ length() [1/4]

float CDPL.Math.length ( ConstDVectorExpression e )

Parameters

e

Returns

◆ conj() [4/14]

ConstDVectorExpression CDPL.Math.conj ( ConstDVectorExpression e )

Parameters

e

Returns

◆ real() [4/14]

ConstDVectorExpression CDPL.Math.real ( ConstDVectorExpression e )

Parameters

e

Returns

◆ herm() [3/10]

ConstDVectorExpression CDPL.Math.herm ( ConstDVectorExpression e )

Parameters

e

Returns

◆ sum() [4/15]

float CDPL.Math.sum ( ConstDVectorExpression e )

Parameters

e

Returns

◆ equals() [4/14]

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

Parameters

e1
e2
eps

Returns

◆ angleCos() [1/4]

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

Parameters

e1
e2
sd
clamp

Returns

◆ cross() [1/4]

ConstDMatrixExpression CDPL.Math.cross ( ConstDVectorExpression e )

Parameters

e

Returns

◆ quat() [1/16]

ConstDVectorQuaternionAdapter CDPL.Math.quat ( ConstDVectorExpression e )

Parameters

e

Returns

◆ elemDiv() [4/14]

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

Parameters

e1
e2

Returns

◆ normInfIndex() [1/4]

int CDPL.Math.normInfIndex ( ConstDVectorExpression e )

Parameters

e

Returns

◆ elemProd() [5/14]

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

Parameters

e1
e2

Returns

◆ imag() [4/10]

ConstFGridExpression CDPL.Math.imag ( ConstFGridExpression e )

Parameters

e

Returns

◆ conj() [5/14]

ConstFGridExpression CDPL.Math.conj ( ConstFGridExpression e )

Parameters

e

Returns

◆ real() [5/14]

ConstFGridExpression CDPL.Math.real ( ConstFGridExpression e )

Parameters

e

Returns

◆ herm() [4/10]

ConstFGridExpression CDPL.Math.herm ( ConstFGridExpression e )

Parameters

e

Returns

◆ sum() [5/15]

float CDPL.Math.sum ( ConstFGridExpression e )

Parameters

e

Returns

◆ equals() [5/14]

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

Parameters

e1
e2
eps

Returns

◆ elemDiv() [5/14]

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

Parameters

e1
e2

Returns

◆ norm1() [3/8]

float CDPL.Math.norm1 ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ normFrob() [2/4]

float CDPL.Math.normFrob ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ elemProd() [6/14]

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

Parameters

e1
e2

Returns

◆ prod() [7/24]

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

Parameters

e1
e2

Returns

◆ prod() [8/24]

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

Parameters

e1
e2
c

Returns

◆ prod() [9/24]

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

Parameters

e1
e2

Returns

◆ prod() [10/24]

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

Parameters

e1
e2
c

Returns

◆ trace() [2/4]

float CDPL.Math.trace ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ slice() [5/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [6/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [5/33]

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

Parameters

e
r1
r2

Returns

◆ range() [6/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luSubstitute() [5/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [6/16]

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

Parameters

e
pv
b

Returns

◆ luSubstitute() [7/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [8/16]

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

Parameters

e
pv
b

Returns

◆ svSubstitute() [3/8]

None CDPL.Math.svSubstitute	(	ConstFMatrixExpression	u,
		ConstFVectorExpression	w,
		ConstFMatrixExpression	v,
		ConstFVectorExpression	b,
		FVectorExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ svSubstitute() [4/8]

None CDPL.Math.svSubstitute	(	ConstFMatrixExpression	u,
		ConstFVectorExpression	w,
		ConstFMatrixExpression	v,
		ConstFMatrixExpression	b,
		FMatrixExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ normInf() [3/8]

float CDPL.Math.normInf ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ imag() [5/10]

ConstFMatrixExpression CDPL.Math.imag ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ triang() [5/16]

ConstUpperTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

◆ triang() [6/16]

ConstUnitUpperTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

◆ triang() [7/16]

ConstLowerTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

◆ triang() [8/16]

ConstUnitLowerTriangularFMatrixAdapter CDPL.Math.triang	(	ConstFMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

◆ conj() [6/14]

ConstFMatrixExpression CDPL.Math.conj ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ real() [6/14]

ConstFMatrixExpression CDPL.Math.real ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ herm() [5/10]

ConstFMatrixExpression CDPL.Math.herm ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ sum() [6/15]

float CDPL.Math.sum ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ column() [2/8]

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

Parameters

e
i

Returns

◆ solveUpper() [3/8]

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

Parameters

e1
e2

Returns

◆ solveUpper() [4/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [3/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [4/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [3/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [4/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [3/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [4/8]

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

Parameters

e1
e2

Returns

◆ equals() [6/14]

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

Parameters

e1
e2
eps

Returns

◆ trans() [2/8]

ConstFMatrixTranspose CDPL.Math.trans ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ det() [2/4]

float CDPL.Math.det ( ConstFMatrixExpression e )

Parameters

e

Returns

◆ invert() [2/8]

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

Parameters

e
c

Returns

◆ elemDiv() [6/14]

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

Parameters

e1
e2

Returns

◆ row() [2/8]

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

Parameters

e
i

Returns

◆ norm2() [3/8]

float CDPL.Math.norm2 ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ vec() [2/10]

ConstFQuaternionVectorAdapter CDPL.Math.vec ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ elemProd() [7/14]

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

Parameters

e1
e2

Returns

◆ rotate() [2/4]

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

Parameters

e1
e2

Returns

◆ conj() [7/14]

ConstFQuaternionExpression CDPL.Math.conj ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ real() [7/14]

float CDPL.Math.real ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ unreal() [2/4]

ConstFQuaternionExpression CDPL.Math.unreal ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ norm() [2/4]

float CDPL.Math.norm ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ sum() [7/15]

float CDPL.Math.sum ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ equals() [7/14]

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

Parameters

e1
e2
eps

Returns

◆ elemDiv() [7/14]

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

Parameters

e1
e2

Returns

◆ inv() [2/4]

ConstFQuaternionExpression CDPL.Math.inv ( ConstFQuaternionExpression e )

Parameters

e

Returns

◆ norm1() [4/8]

float CDPL.Math.norm1 ( ConstFVectorExpression e )

Parameters

e

Returns

◆ norm2() [4/8]

float CDPL.Math.norm2 ( ConstFVectorExpression e )

Parameters

e

Returns

◆ elemProd() [8/14]

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

Parameters

e1
e2

Returns

◆ innerProd() [2/4]

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

Parameters

e1
e2

Returns

◆ outerProd() [2/4]

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

Parameters

e1
e2

Returns

◆ crossProd() [2/4]

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

Parameters

e1
e2

Returns

◆ prod() [11/24]

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

Parameters

e1
e2

Returns

◆ prod() [12/24]

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

Parameters

e1
e2
c

Returns

◆ slice() [7/33]

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

Parameters

e
s

Returns

◆ slice() [8/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [7/33]

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

Parameters

e
r

Returns

◆ range() [8/33]

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

Parameters

e
start
stop

Returns

◆ normInf() [4/8]

float CDPL.Math.normInf ( ConstFVectorExpression e )

Parameters

e

Returns

◆ diag() [2/4]

ConstFMatrixExpression CDPL.Math.diag ( ConstFVectorExpression e )

Parameters

e

Returns

◆ imag() [6/10]

ConstFVectorExpression CDPL.Math.imag ( ConstFVectorExpression e )

Parameters

e

Returns

◆ homog() [2/8]

ConstFHomogenousCoordsAdapter CDPL.Math.homog ( ConstFVectorExpression e )

Parameters

e

Returns

◆ length() [2/4]

float CDPL.Math.length ( ConstFVectorExpression e )

Parameters

e

Returns

◆ conj() [8/14]

ConstFVectorExpression CDPL.Math.conj ( ConstFVectorExpression e )

Parameters

e

Returns

◆ real() [8/14]

ConstFVectorExpression CDPL.Math.real ( ConstFVectorExpression e )

Parameters

e

Returns

◆ herm() [6/10]

ConstFVectorExpression CDPL.Math.herm ( ConstFVectorExpression e )

Parameters

e

Returns

◆ sum() [8/15]

float CDPL.Math.sum ( ConstFVectorExpression e )

Parameters

e

Returns

◆ equals() [8/14]

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

Parameters

e1
e2
eps

Returns

◆ angleCos() [2/4]

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

Parameters

e1
e2
sd
clamp

Returns

◆ cross() [2/4]

ConstFMatrixExpression CDPL.Math.cross ( ConstFVectorExpression e )

Parameters

e

Returns

◆ quat() [2/16]

ConstFVectorQuaternionAdapter CDPL.Math.quat ( ConstFVectorExpression e )

Parameters

e

Returns

◆ elemDiv() [8/14]

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

Parameters

e1
e2

Returns

◆ normInfIndex() [2/4]

int CDPL.Math.normInfIndex ( ConstFVectorExpression e )

Parameters

e

Returns

◆ norm1() [5/8]

int CDPL.Math.norm1 ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ normFrob() [3/4]

int CDPL.Math.normFrob ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ elemProd() [9/14]

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

Parameters

e1
e2

Returns

◆ prod() [13/24]

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

Parameters

e1
e2

Returns

◆ prod() [14/24]

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

Parameters

e1
e2
c

Returns

◆ prod() [15/24]

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

Parameters

e1
e2

Returns

◆ prod() [16/24]

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

Parameters

e1
e2
c

Returns

◆ trace() [3/4]

int CDPL.Math.trace ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ slice() [9/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [10/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [9/33]

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

Parameters

e
r1
r2

Returns

◆ range() [10/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luSubstitute() [9/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [10/16]

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

Parameters

e
pv
b

Returns

◆ luSubstitute() [11/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [12/16]

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

Parameters

e
pv
b

Returns

◆ svSubstitute() [5/8]

None CDPL.Math.svSubstitute	(	ConstLMatrixExpression	u,
		ConstLVectorExpression	w,
		ConstLMatrixExpression	v,
		ConstLVectorExpression	b,
		LVectorExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ svSubstitute() [6/8]

None CDPL.Math.svSubstitute	(	ConstLMatrixExpression	u,
		ConstLVectorExpression	w,
		ConstLMatrixExpression	v,
		ConstLMatrixExpression	b,
		LMatrixExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ normInf() [5/8]

int CDPL.Math.normInf ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ imag() [7/10]

ConstLMatrixExpression CDPL.Math.imag ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ triang() [9/16]

ConstUpperTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

◆ triang() [10/16]

ConstUnitUpperTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

◆ triang() [11/16]

ConstLowerTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

◆ triang() [12/16]

ConstUnitLowerTriangularLMatrixAdapter CDPL.Math.triang	(	ConstLMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

◆ conj() [9/14]

ConstLMatrixExpression CDPL.Math.conj ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ real() [9/14]

ConstLMatrixExpression CDPL.Math.real ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ herm() [7/10]

ConstLMatrixExpression CDPL.Math.herm ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ sum() [9/15]

int CDPL.Math.sum ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ column() [3/8]

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

Parameters

e
i

Returns

◆ solveUpper() [5/8]

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

Parameters

e1
e2

Returns

◆ solveUpper() [6/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [5/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [6/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [5/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [6/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [5/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [6/8]

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

Parameters

e1
e2

Returns

◆ equals() [9/14]

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

Parameters

e1
e2
eps

Returns

◆ trans() [3/8]

ConstLMatrixTranspose CDPL.Math.trans ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ det() [3/4]

int CDPL.Math.det ( ConstLMatrixExpression e )

Parameters

e

Returns

◆ invert() [3/8]

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

Parameters

e
c

Returns

◆ elemDiv() [9/14]

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

Parameters

e1
e2

Returns

◆ row() [3/8]

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

Parameters

e
i

Returns

◆ norm2() [5/8]

int CDPL.Math.norm2 ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ vec() [3/10]

ConstLQuaternionVectorAdapter CDPL.Math.vec ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ elemProd() [10/14]

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

Parameters

e1
e2

Returns

◆ rotate() [3/4]

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

Parameters

e1
e2

Returns

◆ conj() [10/14]

ConstLQuaternionExpression CDPL.Math.conj ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ real() [10/14]

int CDPL.Math.real ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ unreal() [3/4]

ConstLQuaternionExpression CDPL.Math.unreal ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ norm() [3/4]

int CDPL.Math.norm ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ sum() [10/15]

int CDPL.Math.sum ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ equals() [10/14]

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

Parameters

e1
e2
eps

Returns

◆ elemDiv() [10/14]

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

Parameters

e1
e2

Returns

◆ inv() [3/4]

ConstLQuaternionExpression CDPL.Math.inv ( ConstLQuaternionExpression e )

Parameters

e

Returns

◆ norm1() [6/8]

int CDPL.Math.norm1 ( ConstLVectorExpression e )

Parameters

e

Returns

◆ norm2() [6/8]

int CDPL.Math.norm2 ( ConstLVectorExpression e )

Parameters

e

Returns

◆ elemProd() [11/14]

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

Parameters

e1
e2

Returns

◆ innerProd() [3/4]

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

Parameters

e1
e2

Returns

◆ outerProd() [3/4]

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

Parameters

e1
e2

Returns

◆ crossProd() [3/4]

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

Parameters

e1
e2

Returns

◆ prod() [17/24]

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

Parameters

e1
e2

Returns

◆ prod() [18/24]

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

Parameters

e1
e2
c

Returns

◆ slice() [11/33]

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

Parameters

e
s

Returns

◆ slice() [12/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [11/33]

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

Parameters

e
r

Returns

◆ range() [12/33]

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

Parameters

e
start
stop

Returns

◆ normInf() [6/8]

int CDPL.Math.normInf ( ConstLVectorExpression e )

Parameters

e

Returns

◆ diag() [3/4]

ConstLMatrixExpression CDPL.Math.diag ( ConstLVectorExpression e )

Parameters

e

Returns

◆ imag() [8/10]

ConstLVectorExpression CDPL.Math.imag ( ConstLVectorExpression e )

Parameters

e

Returns

◆ homog() [3/8]

ConstLHomogenousCoordsAdapter CDPL.Math.homog ( ConstLVectorExpression e )

Parameters

e

Returns

◆ length() [3/4]

int CDPL.Math.length ( ConstLVectorExpression e )

Parameters

e

Returns

◆ conj() [11/14]

ConstLVectorExpression CDPL.Math.conj ( ConstLVectorExpression e )

Parameters

e

Returns

◆ real() [11/14]

ConstLVectorExpression CDPL.Math.real ( ConstLVectorExpression e )

Parameters

e

Returns

◆ herm() [8/10]

ConstLVectorExpression CDPL.Math.herm ( ConstLVectorExpression e )

Parameters

e

Returns

◆ sum() [11/15]

int CDPL.Math.sum ( ConstLVectorExpression e )

Parameters

e

Returns

◆ equals() [11/14]

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

Parameters

e1
e2
eps

Returns

◆ angleCos() [3/4]

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

Parameters

e1
e2
sd
clamp

Returns

◆ cross() [3/4]

ConstLMatrixExpression CDPL.Math.cross ( ConstLVectorExpression e )

Parameters

e

Returns

◆ quat() [3/16]

ConstLVectorQuaternionAdapter CDPL.Math.quat ( ConstLVectorExpression e )

Parameters

e

Returns

◆ elemDiv() [11/14]

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

Parameters

e1
e2

Returns

◆ normInfIndex() [3/4]

int CDPL.Math.normInfIndex ( ConstLVectorExpression e )

Parameters

e

Returns

◆ norm1() [7/8]

int CDPL.Math.norm1 ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ normFrob() [4/4]

int CDPL.Math.normFrob ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ elemProd() [12/14]

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

Parameters

e1
e2

Returns

◆ prod() [19/24]

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

Parameters

e1
e2

Returns

◆ prod() [20/24]

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

Parameters

e1
e2
c

Returns

◆ prod() [21/24]

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

Parameters

e1
e2

Returns

◆ prod() [22/24]

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

Parameters

e1
e2
c

Returns

◆ trace() [4/4]

int CDPL.Math.trace ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ slice() [13/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [14/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [13/33]

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

Parameters

e
r1
r2

Returns

◆ range() [14/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luSubstitute() [13/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [14/16]

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

Parameters

e
pv
b

Returns

◆ luSubstitute() [15/16]

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

Parameters

e
b

Returns

◆ luSubstitute() [16/16]

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

Parameters

e
pv
b

Returns

◆ svSubstitute() [7/8]

None CDPL.Math.svSubstitute	(	ConstULMatrixExpression	u,
		ConstULVectorExpression	w,
		ConstULMatrixExpression	v,
		ConstULVectorExpression	b,
		ULVectorExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ svSubstitute() [8/8]

None CDPL.Math.svSubstitute	(	ConstULMatrixExpression	u,
		ConstULVectorExpression	w,
		ConstULMatrixExpression	v,
		ConstULMatrixExpression	b,
		ULMatrixExpression	x
	)

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

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

Parameters

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

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

Exceptions

Base.SizeError if preconditions are violated.

See also: svDecomposition()

◆ normInf() [7/8]

int CDPL.Math.normInf ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ imag() [9/10]

ConstULMatrixExpression CDPL.Math.imag ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ triang() [13/16]

ConstUpperTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		Upper	type
	)

Parameters

e
type

Returns

◆ triang() [14/16]

ConstUnitUpperTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		UnitUpper	type
	)

Parameters

e
type

Returns

◆ triang() [15/16]

ConstLowerTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		Lower	type
	)

Parameters

e
type

Returns

◆ triang() [16/16]

ConstUnitLowerTriangularULMatrixAdapter CDPL.Math.triang	(	ConstULMatrixExpression	e,
		UnitLower	type
	)

Parameters

e
type

Returns

◆ conj() [12/14]

ConstULMatrixExpression CDPL.Math.conj ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ real() [12/14]

ConstULMatrixExpression CDPL.Math.real ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ herm() [9/10]

ConstULMatrixExpression CDPL.Math.herm ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ sum() [12/15]

int CDPL.Math.sum ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ column() [4/8]

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

Parameters

e
i

Returns

◆ solveUpper() [7/8]

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

Parameters

e1
e2

Returns

◆ solveUpper() [8/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [7/8]

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

Parameters

e1
e2

Returns

◆ solveUnitUpper() [8/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [7/8]

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

Parameters

e1
e2

Returns

◆ solveLower() [8/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [7/8]

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

Parameters

e1
e2

Returns

◆ solveUnitLower() [8/8]

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

Parameters

e1
e2

Returns

◆ equals() [12/14]

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

Parameters

e1
e2
eps

Returns

◆ trans() [4/8]

ConstULMatrixTranspose CDPL.Math.trans ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ det() [4/4]

int CDPL.Math.det ( ConstULMatrixExpression e )

Parameters

e

Returns

◆ invert() [4/8]

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

Parameters

e
c

Returns

◆ elemDiv() [12/14]

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

Parameters

e1
e2

Returns

◆ row() [4/8]

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

Parameters

e
i

Returns

◆ norm2() [7/8]

int CDPL.Math.norm2 ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ vec() [4/10]

ConstULQuaternionVectorAdapter CDPL.Math.vec ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ elemProd() [13/14]

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

Parameters

e1
e2

Returns

◆ rotate() [4/4]

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

Parameters

e1
e2

Returns

◆ conj() [13/14]

ConstULQuaternionExpression CDPL.Math.conj ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ real() [13/14]

int CDPL.Math.real ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ unreal() [4/4]

ConstULQuaternionExpression CDPL.Math.unreal ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ norm() [4/4]

int CDPL.Math.norm ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ sum() [13/15]

int CDPL.Math.sum ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ equals() [13/14]

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

Parameters

e1
e2
eps

Returns

◆ elemDiv() [13/14]

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

Parameters

e1
e2

Returns

◆ inv() [4/4]

ConstULQuaternionExpression CDPL.Math.inv ( ConstULQuaternionExpression e )

Parameters

e

Returns

◆ norm1() [8/8]

int CDPL.Math.norm1 ( ConstULVectorExpression e )

Parameters

e

Returns

◆ norm2() [8/8]

int CDPL.Math.norm2 ( ConstULVectorExpression e )

Parameters

e

Returns

◆ elemProd() [14/14]

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

Parameters

e1
e2

Returns

◆ innerProd() [4/4]

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

Parameters

e1
e2

Returns

◆ outerProd() [4/4]

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

Parameters

e1
e2

Returns

◆ crossProd() [4/4]

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

Parameters

e1
e2

Returns

◆ prod() [23/24]

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

Parameters

e1
e2

Returns

◆ prod() [24/24]

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

Parameters

e1
e2
c

Returns

◆ slice() [15/33]

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

Parameters

e
s

Returns

◆ slice() [16/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [15/33]

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

Parameters

e
r

Returns

◆ range() [16/33]

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

Parameters

e
start
stop

Returns

◆ normInf() [8/8]

int CDPL.Math.normInf ( ConstULVectorExpression e )

Parameters

e

Returns

◆ diag() [4/4]

ConstULMatrixExpression CDPL.Math.diag ( ConstULVectorExpression e )

Parameters

e

Returns

◆ imag() [10/10]

ConstULVectorExpression CDPL.Math.imag ( ConstULVectorExpression e )

Parameters

e

Returns

◆ homog() [4/8]

ConstULHomogenousCoordsAdapter CDPL.Math.homog ( ConstULVectorExpression e )

Parameters

e

Returns

◆ length() [4/4]

int CDPL.Math.length ( ConstULVectorExpression e )

Parameters

e

Returns

◆ conj() [14/14]

ConstULVectorExpression CDPL.Math.conj ( ConstULVectorExpression e )

Parameters

e

Returns

◆ real() [14/14]

ConstULVectorExpression CDPL.Math.real ( ConstULVectorExpression e )

Parameters

e

Returns

◆ herm() [10/10]

ConstULVectorExpression CDPL.Math.herm ( ConstULVectorExpression e )

Parameters

e

Returns

◆ sum() [14/15]

int CDPL.Math.sum ( ConstULVectorExpression e )

Parameters

e

Returns

◆ equals() [14/14]

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

Parameters

e1
e2
eps

Returns

◆ angleCos() [4/4]

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

Parameters

e1
e2
sd
clamp

Returns

◆ cross() [4/4]

ConstULMatrixExpression CDPL.Math.cross ( ConstULVectorExpression e )

Parameters

e

Returns

◆ quat() [4/16]

ConstULVectorQuaternionAdapter CDPL.Math.quat ( ConstULVectorExpression e )

Parameters

e

Returns

◆ elemDiv() [14/14]

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

Parameters

e1
e2

Returns

◆ normInfIndex() [4/4]

int CDPL.Math.normInfIndex ( ConstULVectorExpression e )

Parameters

e

Returns

◆ slice() [17/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [18/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [17/33]

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

Parameters

e
r1
r2

Returns

◆ range() [18/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luDecompose() [1/8]

int CDPL.Math.luDecompose ( DMatrixExpression e )

Parameters

e

Returns

◆ luDecompose() [2/8]

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

Parameters

e
pv

Returns

◆ 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.

◆ jacobiDiagonalize() [1/4]

bool CDPL.Math.jacobiDiagonalize	(	DMatrixExpression	a,
		DVectorExpression	d,
		DMatrixExpression	v,
		int	max_iter = `50`
	)

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

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

Parameters

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

Returns: True if a is a non-empty symmetric matrix and convergence has been reached in max_iter iterations, and False otherwise.

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

Exceptions

Base.SizeError if preconditions are violated.

◆ column() [5/8]

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

Parameters

e
i

Returns

◆ trans() [5/8]

DMatrixTranspose CDPL.Math.trans ( DMatrixExpression e )

Parameters

e

Returns

◆ invert() [5/8]

bool CDPL.Math.invert ( DMatrixExpression c )

Parameters

c

Returns

◆ row() [5/8]

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

Parameters

e
i

Returns

◆ interpolateTrilinear() [1/2]

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

Parameters

grid
pos
local_pos

Returns

◆ slice() [19/33]

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

Parameters

e
s

Returns

◆ slice() [20/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [19/33]

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

Parameters

e
r

Returns

◆ range() [20/33]

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

Parameters

e
start
stop

Returns

◆ homog() [5/8]

DHomogenousCoordsAdapter CDPL.Math.homog ( DVectorExpression e )

Parameters

e

Returns

◆ quat() [5/16]

DVectorQuaternionAdapter CDPL.Math.quat ( DVectorExpression e )

Parameters

e

Returns

◆ slice() [21/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [22/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [21/33]

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

Parameters

e
r1
r2

Returns

◆ range() [22/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luDecompose() [3/8]

int CDPL.Math.luDecompose ( FMatrixExpression e )

Parameters

e

Returns

◆ luDecompose() [4/8]

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

Parameters

e
pv

Returns

◆ 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.

◆ jacobiDiagonalize() [2/4]

bool CDPL.Math.jacobiDiagonalize	(	FMatrixExpression	a,
		FVectorExpression	d,
		FMatrixExpression	v,
		int	max_iter = `50`
	)

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

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

Parameters

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

Returns: True if a is a non-empty symmetric matrix and convergence has been reached in max_iter iterations, and False otherwise.

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

Exceptions

Base.SizeError if preconditions are violated.

◆ column() [6/8]

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

Parameters

e
i

Returns

◆ trans() [6/8]

FMatrixTranspose CDPL.Math.trans ( FMatrixExpression e )

Parameters

e

Returns

◆ invert() [6/8]

bool CDPL.Math.invert ( FMatrixExpression c )

Parameters

c

Returns

◆ row() [6/8]

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

Parameters

e
i

Returns

◆ interpolateTrilinear() [2/2]

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

Parameters

grid
pos
local_pos

Returns

◆ slice() [23/33]

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

Parameters

e
s

Returns

◆ slice() [24/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [23/33]

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

Parameters

e
r

Returns

◆ range() [24/33]

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

Parameters

e
start
stop

Returns

◆ homog() [6/8]

FHomogenousCoordsAdapter CDPL.Math.homog ( FVectorExpression e )

Parameters

e

Returns

◆ quat() [6/16]

FVectorQuaternionAdapter CDPL.Math.quat ( FVectorExpression e )

Parameters

e

Returns

◆ slice() [25/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [26/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [25/33]

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

Parameters

e
r1
r2

Returns

◆ range() [26/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luDecompose() [5/8]

int CDPL.Math.luDecompose ( LMatrixExpression e )

Parameters

e

Returns

◆ luDecompose() [6/8]

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

Parameters

e
pv

Returns

◆ 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.

◆ jacobiDiagonalize() [3/4]

bool CDPL.Math.jacobiDiagonalize	(	LMatrixExpression	a,
		LVectorExpression	d,
		LMatrixExpression	v,
		int	max_iter = `50`
	)

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

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

Parameters

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

Returns: True if a is a non-empty symmetric matrix and convergence has been reached in max_iter iterations, and False otherwise.

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

Exceptions

Base.SizeError if preconditions are violated.

◆ column() [7/8]

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

Parameters

e
i

Returns

◆ trans() [7/8]

LMatrixTranspose CDPL.Math.trans ( LMatrixExpression e )

Parameters

e

Returns

◆ invert() [7/8]

bool CDPL.Math.invert ( LMatrixExpression c )

Parameters

c

Returns

◆ row() [7/8]

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

Parameters

e
i

Returns

◆ slice() [27/33]

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

Parameters

e
s

Returns

◆ slice() [28/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [27/33]

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

Parameters

e
r

Returns

◆ range() [28/33]

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

Parameters

e
start
stop

Returns

◆ homog() [7/8]

LHomogenousCoordsAdapter CDPL.Math.homog ( LVectorExpression e )

Parameters

e

Returns

◆ quat() [7/16]

LVectorQuaternionAdapter CDPL.Math.quat ( LVectorExpression e )

Parameters

e

Returns

◆ slice() [29/33]

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

Parameters

e
s1
s2

Returns

◆ slice() [30/33]

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

Parameters

e
start1
stride1
size1
start2
stride2
size2

Returns

◆ range() [29/33]

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

Parameters

e
r1
r2

Returns

◆ range() [30/33]

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

Parameters

e
start1
stop1
start2
stop2

Returns

◆ luDecompose() [7/8]

int CDPL.Math.luDecompose ( ULMatrixExpression e )

Parameters

e

Returns

◆ luDecompose() [8/8]

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

Parameters

e
pv

Returns

◆ 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.

◆ jacobiDiagonalize() [4/4]

bool CDPL.Math.jacobiDiagonalize	(	ULMatrixExpression	a,
		ULVectorExpression	d,
		ULMatrixExpression	v,
		int	max_iter = `50`
	)

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

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

Parameters

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

Returns: True if a is a non-empty symmetric matrix and convergence has been reached in max_iter iterations, and False otherwise.

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

Exceptions

Base.SizeError if preconditions are violated.

◆ column() [8/8]

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

Parameters

e
i

Returns

◆ trans() [8/8]

ULMatrixTranspose CDPL.Math.trans ( ULMatrixExpression e )

Parameters

e

Returns

◆ invert() [8/8]

bool CDPL.Math.invert ( ULMatrixExpression c )

Parameters

c

Returns

◆ row() [8/8]

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

Parameters

e
i

Returns

◆ slice() [31/33]

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

Parameters

e
s

Returns

◆ slice() [32/33]

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

Parameters

e
start
stride
size

Returns

◆ range() [31/33]

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

Parameters

e
r

Returns

◆ range() [32/33]

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

Parameters

e
start
stop

Returns

◆ homog() [8/8]

ULHomogenousCoordsAdapter CDPL.Math.homog ( ULVectorExpression e )

Parameters

e

Returns

◆ quat() [8/16]

ULVectorQuaternionAdapter CDPL.Math.quat ( ULVectorExpression e )

Parameters

e

Returns

◆ calcRMSD() [1/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [2/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [1/8]

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

Parameters

va
ctr

Returns

◆ transform() [1/16]

None CDPL.Math.transform	(	Vector2DArray	va,
		Matrix2D	xform
	)

Parameters

va
xform

◆ transform() [2/16]

None CDPL.Math.transform	(	Vector2DArray	va,
		Matrix3D	xform
	)

Parameters

va
xform

◆ calcRMSD() [3/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [4/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [2/8]

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

Parameters

va
ctr

Returns

◆ transform() [3/16]

None CDPL.Math.transform	(	Vector2FArray	va,
		Matrix2F	xform
	)

Parameters

va
xform

◆ transform() [4/16]

None CDPL.Math.transform	(	Vector2FArray	va,
		Matrix3F	xform
	)

Parameters

va
xform

◆ calcRMSD() [5/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [6/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [3/8]

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

Parameters

va
ctr

Returns

◆ transform() [5/16]

None CDPL.Math.transform	(	Vector2LArray	va,
		Matrix2L	xform
	)

Parameters

va
xform

◆ transform() [6/16]

None CDPL.Math.transform	(	Vector2LArray	va,
		Matrix3L	xform
	)

Parameters

va
xform

◆ calcRMSD() [7/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [8/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [4/8]

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

Parameters

va
ctr

Returns

◆ transform() [7/16]

None CDPL.Math.transform	(	Vector2ULArray	va,
		Matrix2UL	xform
	)

Parameters

va
xform

◆ transform() [8/16]

None CDPL.Math.transform	(	Vector2ULArray	va,
		Matrix3UL	xform
	)

Parameters

va
xform

◆ calcRMSD() [9/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [10/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [5/8]

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

Parameters

va
ctr

Returns

◆ transform() [9/16]

None CDPL.Math.transform	(	Vector3DArray	va,
		Matrix3D	xform
	)

Parameters

va
xform

◆ transform() [10/16]

None CDPL.Math.transform	(	Vector3DArray	va,
		Matrix4D	xform
	)

Parameters

va
xform

◆ calcRMSD() [11/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [12/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [6/8]

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

Parameters

va
ctr

Returns

◆ transform() [11/16]

None CDPL.Math.transform	(	Vector3FArray	va,
		Matrix3F	xform
	)

Parameters

va
xform

◆ transform() [12/16]

None CDPL.Math.transform	(	Vector3FArray	va,
		Matrix4F	xform
	)

Parameters

va
xform

◆ calcRMSD() [13/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [14/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [7/8]

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

Parameters

va
ctr

Returns

◆ transform() [13/16]

None CDPL.Math.transform	(	Vector3LArray	va,
		Matrix3L	xform
	)

Parameters

va
xform

◆ transform() [14/16]

None CDPL.Math.transform	(	Vector3LArray	va,
		Matrix4L	xform
	)

Parameters

va
xform

◆ calcRMSD() [15/16]

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

Parameters

va1
va2

Returns

◆ calcRMSD() [16/16]

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

Parameters

va1
va2
va1_xform

Returns

◆ calcCentroid() [8/8]

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

Parameters

va
ctr

Returns

◆ transform() [15/16]

None CDPL.Math.transform	(	Vector3ULArray	va,
		Matrix3UL	xform
	)

Parameters

va
xform

◆ transform() [16/16]

None CDPL.Math.transform	(	Vector3ULArray	va,
		Matrix4UL	xform
	)

Parameters

va
xform

◆ gammaQ()

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

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

Parameters

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

Returns: The computed value of the incomplete gamma function.

◆ 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.

◆ vec() [5/10]

Vector2F CDPL.Math.vec	(	float	t1,
		float	t2
	)

Parameters

t1
t2

Returns

◆ vec() [6/10]

Vector3F CDPL.Math.vec	(	float	t1,
		float	t2,
		float	t3
	)

Parameters

t1
t2
t3

Returns

◆ vec() [7/10]

Vector4F CDPL.Math.vec	(	float	t1,
		float	t2,
		float	t3,
		float	t4
	)

Parameters

t1
t2
t3
t4

Returns

◆ 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 \( \sqrt{a^2 + b^2} \).

◆ 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.

◆ 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.

◆ quat() [9/16]

FRealQuaternion CDPL.Math.quat ( float t )

Parameters

t

Returns

◆ quat() [10/16]

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

Parameters

t1
t2

Returns

◆ quat() [11/16]

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

Parameters

t1
t2
t3

Returns

◆ quat() [12/16]

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

Parameters

t1
t2
t3
t4

Returns

◆ vec() [8/10]

Vector2L CDPL.Math.vec	(	int	t1,
		int	t2
	)

Parameters

t1
t2

Returns

◆ vec() [9/10]

Vector3L CDPL.Math.vec	(	int	t1,
		int	t2,
		int	t3
	)

Parameters

t1
t2
t3

Returns

◆ vec() [10/10]

Vector4L CDPL.Math.vec	(	int	t1,
		int	t2,
		int	t3,
		int	t4
	)

Parameters

t1
t2
t3
t4

Returns

◆ slice() [33/33]

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

Parameters

start
stride
size

Returns

◆ range() [33/33]

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

Parameters

start
stop

Returns

◆ prime()

int CDPL.Math.prime ( int i )

Parameters

i

Returns

◆ 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.

◆ quat() [13/16]

LRealQuaternion CDPL.Math.quat ( int t )

Parameters

t

Returns

◆ quat() [14/16]

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

Parameters

t1
t2

Returns

◆ quat() [15/16]

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

Parameters

t1
t2
t3

Returns

◆ quat() [16/16]

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

Parameters

t1
t2
t3
t4

Returns

◆ sum() [15/15]

int CDPL.Math.sum ( object e )

Parameters

e

Returns

Classes

Functions

Detailed Description

Function Documentation

◆ elemProd() [1/14]

◆ imag() [1/10]

◆ conj() [1/14]

◆ real() [1/14]

◆ herm() [1/10]

◆ sum() [1/15]

◆ equals() [1/14]

◆ elemDiv() [1/14]

◆ norm1() [1/8]

◆ normFrob() [1/4]

◆ elemProd() [2/14]

◆ prod() [1/24]

◆ prod() [2/24]

◆ prod() [3/24]

◆ prod() [4/24]

◆ trace() [1/4]

◆ slice() [1/33]

◆ slice() [2/33]

◆ range() [1/33]

◆ range() [2/33]

◆ luSubstitute() [1/16]

◆ luSubstitute() [2/16]

◆ luSubstitute() [3/16]

◆ luSubstitute() [4/16]

◆ svSubstitute() [1/8]

◆ svSubstitute() [2/8]

◆ normInf() [1/8]

◆ imag() [2/10]

◆ triang() [1/16]

◆ triang() [2/16]

◆ triang() [3/16]

◆ triang() [4/16]

◆ conj() [2/14]

◆ real() [2/14]

◆ herm() [2/10]

◆ sum() [2/15]

◆ column() [1/8]

◆ solveUpper() [1/8]

◆ solveUpper() [2/8]

◆ solveUnitUpper() [1/8]

◆ solveUnitUpper() [2/8]

◆ solveLower() [1/8]

◆ solveLower() [2/8]

◆ solveUnitLower() [1/8]

◆ solveUnitLower() [2/8]

◆ equals() [2/14]

◆ trans() [1/8]

◆ det() [1/4]

◆ invert() [1/8]

◆ elemDiv() [2/14]

◆ row() [1/8]

◆ norm2() [1/8]

◆ vec() [1/10]

◆ elemProd() [3/14]

◆ rotate() [1/4]

◆ conj() [3/14]

◆ real() [3/14]

◆ unreal() [1/4]

◆ norm() [1/4]

◆ sum() [3/15]

◆ equals() [3/14]

◆ elemDiv() [3/14]

◆ inv() [1/4]

◆ norm1() [2/8]

◆ norm2() [2/8]

◆ elemProd() [4/14]

◆ innerProd() [1/4]

◆ outerProd() [1/4]

◆ crossProd() [1/4]

◆ prod() [5/24]

◆ prod() [6/24]

◆ slice() [3/33]

◆ slice() [4/33]

◆ range() [3/33]

◆ range() [4/33]

◆ normInf() [2/8]