Chemical Data Processing Library Python API - Version 1.1.1
Classes | Functions
CDPL.Math Package Reference

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

Classes

class  ConstDGridExpression
 
class  ConstDHomogenousCoordsAdapter
 
class  ConstDMatrixColumn
 
class  ConstDMatrixExpression
 
class  ConstDMatrixRange
 
class  ConstDMatrixRow
 
class  ConstDMatrixSlice
 
class  ConstDMatrixTranspose
 
class  ConstDQuaternionExpression
 
class  ConstDQuaternionVectorAdapter
 
class  ConstDVectorExpression
 
class  ConstDVectorQuaternionAdapter
 
class  ConstDVectorRange
 
class  ConstDVectorSlice
 
class  ConstFGridExpression
 
class  ConstFHomogenousCoordsAdapter
 
class  ConstFMatrixColumn
 
class  ConstFMatrixExpression
 
class  ConstFMatrixRange
 
class  ConstFMatrixRow
 
class  ConstFMatrixSlice
 
class  ConstFMatrixTranspose
 
class  ConstFQuaternionExpression
 
class  ConstFQuaternionVectorAdapter
 
class  ConstFVectorExpression
 
class  ConstFVectorQuaternionAdapter
 
class  ConstFVectorRange
 
class  ConstFVectorSlice
 
class  ConstLHomogenousCoordsAdapter
 
class  ConstLMatrixColumn
 
class  ConstLMatrixExpression
 
class  ConstLMatrixRange
 
class  ConstLMatrixRow
 
class  ConstLMatrixSlice
 
class  ConstLMatrixTranspose
 
class  ConstLowerTriangularDMatrixAdapter
 
class  ConstLowerTriangularFMatrixAdapter
 
class  ConstLowerTriangularLMatrixAdapter
 
class  ConstLowerTriangularULMatrixAdapter
 
class  ConstLQuaternionExpression
 
class  ConstLQuaternionVectorAdapter
 
class  ConstLVectorExpression
 
class  ConstLVectorQuaternionAdapter
 
class  ConstLVectorRange
 
class  ConstLVectorSlice
 
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  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  DMLRModel
 Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...
 
class  DoubleDVector2Functor
 
class  DoubleDVectorFunctor
 
class  DoubleVector2DArray2Functor
 
class  DoubleVector2DArrayFunctor
 
class  DoubleVector3DArray2Functor
 
class  DoubleVector3DArrayFunctor
 
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  FGrid
 An unbounded dense grid holding floating point values of type float. More...
 
class  FGridExpression
 
class  FHomogenousCoordsAdapter
 
class  FIdentityMatrix
 
class  FKabschAlgorithm
 
class  FloatFVector2Functor
 
class  FloatFVectorFunctor
 
class  FloatVector2FArray2Functor
 
class  FloatVector2FArrayFunctor
 
class  FloatVector3FArray2Functor
 
class  FloatVector3FArrayFunctor
 
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  FMLRModel
 Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...
 
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  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  Lower
 
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  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]

Parameters
e
Returns

◆ conj() [1/14]

Parameters
e
Returns

◆ real() [1/14]

Parameters
e
Returns

◆ herm() [1/10]

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]

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]

Parameters
e1
e2
Returns

◆ prod() [1/24]

Parameters
e1
e2
Returns

◆ prod() [2/24]

Parameters
e1
e2
c
Returns

◆ prod() [3/24]

Parameters
e1
e2
Returns

◆ prod() [4/24]

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]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ svSubstitute() [2/8]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ normInf() [1/8]

float CDPL.Math.normInf ( ConstDMatrixExpression  e)
Parameters
e
Returns

◆ imag() [2/10]

Parameters
e
Returns

◆ triang() [1/16]

Parameters
e
type
Returns

◆ triang() [2/16]

Parameters
e
type
Returns

◆ triang() [3/16]

Parameters
e
type
Returns

◆ triang() [4/16]

Parameters
e
type
Returns

◆ conj() [2/14]

Parameters
e
Returns

◆ real() [2/14]

Parameters
e
Returns

◆ herm() [2/10]

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]

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]

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]

Parameters
e
Returns

◆ elemProd() [3/14]

Parameters
e1
e2
Returns

◆ rotate() [1/4]

Parameters
e1
e2
Returns

◆ conj() [3/14]

Parameters
e
Returns

◆ real() [3/14]

float CDPL.Math.real ( ConstDQuaternionExpression  e)
Parameters
e
Returns

◆ unreal() [1/4]

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]

Parameters
e1
e2
Returns

◆ inv() [1/4]

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]

Parameters
e1
e2
Returns

◆ innerProd() [1/4]

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

◆ outerProd() [1/4]

Parameters
e1
e2
Returns

◆ crossProd() [1/4]

Parameters
e1
e2
Returns

◆ prod() [5/24]

Parameters
e1
e2
Returns

◆ prod() [6/24]

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]

Parameters
e
Returns

◆ imag() [3/10]

Parameters
e
Returns

◆ homog() [1/8]

Parameters
e
Returns

◆ length() [1/4]

float CDPL.Math.length ( ConstDVectorExpression  e)
Parameters
e
Returns

◆ conj() [4/14]

Parameters
e
Returns

◆ real() [4/14]

Parameters
e
Returns

◆ herm() [3/10]

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]

Parameters
e
Returns

◆ quat() [1/16]

Parameters
e
Returns

◆ elemDiv() [4/14]

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]

Parameters
e
Returns

◆ conj() [5/14]

Parameters
e
Returns

◆ real() [5/14]

Parameters
e
Returns

◆ herm() [4/10]

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]

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]

Parameters
e1
e2
Returns

◆ prod() [7/24]

Parameters
e1
e2
Returns

◆ prod() [8/24]

Parameters
e1
e2
c
Returns

◆ prod() [9/24]

Parameters
e1
e2
Returns

◆ prod() [10/24]

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]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ svSubstitute() [4/8]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ normInf() [3/8]

float CDPL.Math.normInf ( ConstFMatrixExpression  e)
Parameters
e
Returns

◆ imag() [5/10]

Parameters
e
Returns

◆ triang() [5/16]

Parameters
e
type
Returns

◆ triang() [6/16]

Parameters
e
type
Returns

◆ triang() [7/16]

Parameters
e
type
Returns

◆ triang() [8/16]

Parameters
e
type
Returns

◆ conj() [6/14]

Parameters
e
Returns

◆ real() [6/14]

Parameters
e
Returns

◆ herm() [5/10]

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]

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]

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]

Parameters
e
Returns

◆ elemProd() [7/14]

Parameters
e1
e2
Returns

◆ rotate() [2/4]

Parameters
e1
e2
Returns

◆ conj() [7/14]

Parameters
e
Returns

◆ real() [7/14]

float CDPL.Math.real ( ConstFQuaternionExpression  e)
Parameters
e
Returns

◆ unreal() [2/4]

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]

Parameters
e1
e2
Returns

◆ inv() [2/4]

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]

Parameters
e1
e2
Returns

◆ innerProd() [2/4]

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

◆ outerProd() [2/4]

Parameters
e1
e2
Returns

◆ crossProd() [2/4]

Parameters
e1
e2
Returns

◆ prod() [11/24]

Parameters
e1
e2
Returns

◆ prod() [12/24]

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]

Parameters
e
Returns

◆ imag() [6/10]

Parameters
e
Returns

◆ homog() [2/8]

Parameters
e
Returns

◆ length() [2/4]

float CDPL.Math.length ( ConstFVectorExpression  e)
Parameters
e
Returns

◆ conj() [8/14]

Parameters
e
Returns

◆ real() [8/14]

Parameters
e
Returns

◆ herm() [6/10]

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]

Parameters
e
Returns

◆ quat() [2/16]

Parameters
e
Returns

◆ elemDiv() [8/14]

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]

Parameters
e1
e2
Returns

◆ prod() [13/24]

Parameters
e1
e2
Returns

◆ prod() [14/24]

Parameters
e1
e2
c
Returns

◆ prod() [15/24]

Parameters
e1
e2
Returns

◆ prod() [16/24]

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]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ svSubstitute() [6/8]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ normInf() [5/8]

int CDPL.Math.normInf ( ConstLMatrixExpression  e)
Parameters
e
Returns

◆ imag() [7/10]

Parameters
e
Returns

◆ triang() [9/16]

Parameters
e
type
Returns

◆ triang() [10/16]

Parameters
e
type
Returns

◆ triang() [11/16]

Parameters
e
type
Returns

◆ triang() [12/16]

Parameters
e
type
Returns

◆ conj() [9/14]

Parameters
e
Returns

◆ real() [9/14]

Parameters
e
Returns

◆ herm() [7/10]

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]

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]

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]

Parameters
e
Returns

◆ elemProd() [10/14]

Parameters
e1
e2
Returns

◆ rotate() [3/4]

Parameters
e1
e2
Returns

◆ conj() [10/14]

Parameters
e
Returns

◆ real() [10/14]

int CDPL.Math.real ( ConstLQuaternionExpression  e)
Parameters
e
Returns

◆ unreal() [3/4]

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]

Parameters
e1
e2
Returns

◆ inv() [3/4]

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]

Parameters
e1
e2
Returns

◆ innerProd() [3/4]

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

◆ outerProd() [3/4]

Parameters
e1
e2
Returns

◆ crossProd() [3/4]

Parameters
e1
e2
Returns

◆ prod() [17/24]

Parameters
e1
e2
Returns

◆ prod() [18/24]

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]

Parameters
e
Returns

◆ imag() [8/10]

Parameters
e
Returns

◆ homog() [3/8]

Parameters
e
Returns

◆ length() [3/4]

int CDPL.Math.length ( ConstLVectorExpression  e)
Parameters
e
Returns

◆ conj() [11/14]

Parameters
e
Returns

◆ real() [11/14]

Parameters
e
Returns

◆ herm() [8/10]

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]

Parameters
e
Returns

◆ quat() [3/16]

Parameters
e
Returns

◆ elemDiv() [11/14]

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]

Parameters
e1
e2
Returns

◆ prod() [19/24]

Parameters
e1
e2
Returns

◆ prod() [20/24]

Parameters
e1
e2
c
Returns

◆ prod() [21/24]

Parameters
e1
e2
Returns

◆ prod() [22/24]

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]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ svSubstitute() [8/8]

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
uThe \( M \times N \)-dimensional matrix \( U \).
wThe \( N \)-dimensional vector \( W \) holding the singular values of \( A \).
vThe \( N \times N \)-dimensional matrix \( V \).
bThe \( M \times P \)-dimensional right-hand side matrix \( B \).
xThe \( N \times P \)-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.SizeErrorif preconditions are violated.
See also
svDecomposition()

◆ normInf() [7/8]

int CDPL.Math.normInf ( ConstULMatrixExpression  e)
Parameters
e
Returns

◆ imag() [9/10]

Parameters
e
Returns

◆ triang() [13/16]

Parameters
e
type
Returns

◆ triang() [14/16]

Parameters
e
type
Returns

◆ triang() [15/16]

Parameters
e
type
Returns

◆ triang() [16/16]

Parameters
e
type
Returns

◆ conj() [12/14]

Parameters
e
Returns

◆ real() [12/14]

Parameters
e
Returns

◆ herm() [9/10]

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]

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]

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]

Parameters
e
Returns

◆ elemProd() [13/14]

Parameters
e1
e2
Returns

◆ rotate() [4/4]

Parameters
e1
e2
Returns

◆ conj() [13/14]

Parameters
e
Returns

◆ real() [13/14]

int CDPL.Math.real ( ConstULQuaternionExpression  e)
Parameters
e
Returns

◆ unreal() [4/4]

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]

Parameters
e1
e2
Returns

◆ inv() [4/4]

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]

Parameters
e1
e2
Returns

◆ innerProd() [4/4]

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

◆ outerProd() [4/4]

Parameters
e1
e2
Returns

◆ crossProd() [4/4]

Parameters
e1
e2
Returns

◆ prod() [23/24]

Parameters
e1
e2
Returns

◆ prod() [24/24]

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]

Parameters
e
Returns

◆ imag() [10/10]

Parameters
e
Returns

◆ homog() [4/8]

Parameters
e
Returns

◆ length() [4/4]

int CDPL.Math.length ( ConstULVectorExpression  e)
Parameters
e
Returns

◆ conj() [14/14]

Parameters
e
Returns

◆ real() [14/14]

Parameters
e
Returns

◆ herm() [10/10]

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]

Parameters
e
Returns

◆ quat() [4/16]

Parameters
e
Returns

◆ elemDiv() [14/14]

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
aThe decomposed \( M \times N \)-matrix \( A \) which will be replaced by \( U \) on output.
wThe \( N \)-dimensional output vector \( W \) holding the singular values.
vThe \( N \times N \)-dimensional output matrix \( V \).
max_iterThe 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.SizeErrorif 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
aThe real symmetric matrix for which to compute eigenvalues and eigenvectors.
dThe output vector which will contain the eigenvalues of a.
vThe matrix whose columns will contain the normalized eigenvectors of a.
max_iterThe 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.SizeErrorif 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]

Parameters
e
Returns

◆ quat() [5/16]

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
aThe decomposed \( M \times N \)-matrix \( A \) which will be replaced by \( U \) on output.
wThe \( N \)-dimensional output vector \( W \) holding the singular values.
vThe \( N \times N \)-dimensional output matrix \( V \).
max_iterThe 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.SizeErrorif 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
aThe real symmetric matrix for which to compute eigenvalues and eigenvectors.
dThe output vector which will contain the eigenvalues of a.
vThe matrix whose columns will contain the normalized eigenvectors of a.
max_iterThe 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.SizeErrorif 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]

Parameters
e
Returns

◆ quat() [6/16]

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
aThe decomposed \( M \times N \)-matrix \( A \) which will be replaced by \( U \) on output.
wThe \( N \)-dimensional output vector \( W \) holding the singular values.
vThe \( N \times N \)-dimensional output matrix \( V \).
max_iterThe 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.SizeErrorif 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
aThe real symmetric matrix for which to compute eigenvalues and eigenvectors.
dThe output vector which will contain the eigenvalues of a.
vThe matrix whose columns will contain the normalized eigenvectors of a.
max_iterThe 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.SizeErrorif 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]

Parameters
e
Returns

◆ quat() [7/16]

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
aThe decomposed \( M \times N \)-matrix \( A \) which will be replaced by \( U \) on output.
wThe \( N \)-dimensional output vector \( W \) holding the singular values.
vThe \( N \times N \)-dimensional output matrix \( V \).
max_iterThe 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.SizeErrorif 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
aThe real symmetric matrix for which to compute eigenvalues and eigenvectors.
dThe output vector which will contain the eigenvalues of a.
vThe matrix whose columns will contain the normalized eigenvectors of a.
max_iterThe 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.SizeErrorif 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]

Parameters
e
Returns

◆ quat() [8/16]

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
aThe function argument a.
xThe 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
zThe 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
aThe variable a.
bThe 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
xThe generalized bell function argument
aControls the width of the curve at \(f(x) = 0.5 \).
bControls the slope of the curve at \( x = c - a \) and \( x = c + a \).
cLocates 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
aThe parameter a.
bThe 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
nThe 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