Namespace agregating IPSDK mathematical routines and classes. More...

Classes
class	AdaptiveGridPartition
	Class allowing to create an adaptive partition of data. More...

class	Affine2d
	Transformation class allowing to manage 2d affine transformations. More...

class	AnisotropicScale2d
	Transformation class allowing to manage 2d anisotropic scale transformations. More...

class	AnisotropicScale3d
	Transformation class allowing to manage 3d anisotropic scale transformations. More...

class	BaseCostFunction
	Base class for cost functions used during optimization process. More...

class	BaseDataPartition
	Base class for data partitioning. More...

class	BaseEstimator
	Base class for parametric estimation from data set. More...

class	BaseGaussianCurveEstimator
	Base class allowing to estimate gaussian curve parameters from a set of input data (based on Caruanas algorithm) More...

class	BaseGeometricTransform2d
	Base class for geometric transformation 2d management. More...

class	BaseGridPartition
	Base class for object allowing to create data partition based on grid. More...

class	BaseHistogram
	Base class for histogram data management. More...

class	BaseRobustEstimator
	Base class for parametric robust estimation from data set. More...

class	BipartitePartialMatch
	Algorithm allowing to solve a partial graph bipartite assigment problem. More...

class	EstimationConfig
	Configuration structure used for estimation management. More...

class	EstimationResults
	Structure allowing to encapsulate robust estimation results. More...

class	GaussianCurve2dEstimator
	Class allowing to estimate gaussian curve parameters from a set of input data. More...

class	GaussianCurve3dEstimator
	Class allowing to estimate gaussian curve parameters from a set of input data. More...

class	GaussianCurveNdEstimator
	Class allowing to estimate gaussian curve parameters from a set of input data. More...

class	Histogram
	Class allowing to encapsulated histogram data and to compute several associated indicators. More...

struct	HistogramExtrema
	structure allowing to encapsulate histogram extrema information More...

struct	HistogramGaussianCurveFit
	structure allowing to encapsulate gaussian curve fit information More...

class	IPSDKMathException
	Exception class for library IPSDKMath. More...

class	KernelKMeansCentroid
	Kernel centroid cluster representation. More...

class	KernelKMeansClustering
	Kernel implementation of KMeans algorithm. More...

class	KernelKMeansClusteringConfig
	Class allowing to encapsulated Kernel KMeans algorithm configuration. More...

class	KMeansClustering
	K-Means clustering algorithm with K-Means++ initialization. More...

class	KMeansClusteringConfig
	Class allowing to encapsulated KMeans algorithm configuration. More...

class	LinearKernel
	Linear function kernel. More...

class	LMSRobustEstimator
	Robust Least Mean Square estimatorThis algorithm do not request any threshold for model estimation. It has an outlier ratio upper bound at 50% (<50%) More...

class	MLESACRobustEstimator
	Robust Maximum Likelihood Estimation SAmple Consensus estimatorThis algorithm request a threshold value on residuals of model estimation. It has no outlier ratio upper bound. More...

class	MSACRobustEstimator
	Robust M-estimator SAmple Consensus estimatorThis algorithm request a threshold value on residuals of model estimation. It has no outlier ratio upper bound. More...

class	Munkres
	Implementation of munkres algorithm. More...

class	NonLinearSolver
	Class implementing a non linear solver based on Levenberg Marquardt algorithm. More...

struct	PhiTheta
	structure PhiTheta, containing the angles used for a spheric representation. Angles _phi and _theta are expressed in radians More...

class	Polynomial2dSurfaceEstimator
	Class allowing to estimate a second order polynomial 2d surface from a set of data such as $\left\{x_i, y_i, value_i=f(x_i, y_i)\right\}$ . More...

class	PolynomialKernel
	Polynomial function kernel. More...

class	RadialBasisKernel
	radial basis function kernel More...

class	RANSACRobustEstimator
	Robust RANdom SAmple Consensus estimatorThis algorithm request a threshold value on residuals of model estimation. It has no outlier ratio upper bound. More...

class	RegularGridPartition
	Class allowing to create a regular grid where each axis is divide into _nbBucketsByAxis sub range. More...

class	Rigid2d
	Transformation class allowing to manage 2d rigid transformations. More...

class	Scale2d
	Transformation class allowing to manage 2d scale transformations. More...

class	Scale3d
	Transformation class allowing to manage 3d scale transformations. More...

class	SigmoidKernel
	Sigmoid function kernel. More...

class	Similarity2d
	Transformation class allowing to manage 2d similarity transformations. More...

class	SpectralClustering
	Spectral clustering algorithm associated to a kernel kmeans clustering algorithm. More...

class	Transform2dFactory
	Factory used to handle geometric transformation 2d creation. More...

class	Transform3dFactory
	Factory used to handle geometric transformation 3d creation. More...

Typedefs
typedef boost::shared_ptr< BaseDataPartition >	DataPartitionPtr
	shared pointer to BaseDataPartition class

typedef boost::shared_ptr< const BaseDataPartition >	DataPartitionConstPtr
	shared pointer to const BaseDataPartition class

typedef Vector	DataType
	data type used for estimation

typedef Vector	ParameterType
	parameter type resulting from estimation

typedef Vector	ResidualsSet
	residuals type resulting from estimation

typedef std::vector< DataType >	DataSet
	collection of data associated to estimation

typedef std::vector< bool >	OutlierFlags
	collection of outliers flags

typedef boost::shared_ptr< BaseEstimator >	EstimatorPtr
	shared pointer to BaseEstimator class

typedef boost::shared_ptr< const BaseEstimator >	EstimatorConstPtr
	shared pointer to const BaseEstimator class

typedef boost::shared_ptr< BaseRobustEstimator >	RobustEstimatorPtr
	shared pointer to BaseRobustEstimator class

typedef boost::shared_ptr< const BaseRobustEstimator >	RobustEstimatorConstPtr
	shared pointer to const BaseRobustEstimator class

typedef CostFunctionPtr(*	CostFunCreator) (const DataSet &dataSet)

typedef std::vector< PhiTheta >	PhiThetaColl
	collection of phi theta data

typedef boost::numeric::ublas::unbounded_array< ipReal64 >	UnBoundedArray
	unbounded array type associated to library

typedef boost::numeric::ublas::vector< ipReal64 >	Vector
	vector type associated to library

typedef boost::numeric::ublas::bounded_vector< ipReal64, 2 >	Vector2d
	2d vector type associated to library

typedef boost::numeric::ublas::bounded_vector< ipReal64, 3 >	Vector3d
	3d vector type associated to library

typedef boost::numeric::ublas::bounded_vector< ipReal64, 4 >	Vector4d
	4d vector type associated to library

typedef boost::numeric::ublas::matrix< ipReal64 >	Matrix
	matrix type associated to library

typedef boost::numeric::ublas::bounded_matrix< ipReal64, 2, 2 >	Matrix2d
	2d matrix (2x2) type associated to library

typedef boost::numeric::ublas::bounded_matrix< ipReal64, 3, 3 >	Matrix3d
	3d matrix (3x3) type associated to library

typedef boost::numeric::ublas::bounded_matrix< ipReal64, 4, 4 >	Matrix4d
	4d matrix (4x4) type associated to library

typedef ProcessingResult< eOptStatus >	OptResult
	optimization result type

typedef boost::shared_ptr< BaseCostFunction >	CostFunctionPtr
	shared pointer to cost function

typedef boost::shared_ptr< const BaseCostFunction >	CostFunctionConstPtr
	shared pointer to const cost function

typedef std::pair< ipUInt64, ipUInt64 >	ExtremaRange
	index for dilated local extrema More...

typedef std::vector< ExtremaRange >	ExtremaRangeColl
	collection of indexes for dilated local extrema

typedef std::vector< HistogramExtrema >	HistogramExtremaColl
	collection of histogram extrema

typedef boost::shared_ptr< ipsdk::math::BaseHistogram >	HistogramPtr
	shared pointer to ipsdk::math::BaseHistogram

typedef boost::shared_ptr< const ipsdk::math::BaseHistogram >	HistogramConstPtr
	shared pointer to const ipsdk::math::BaseHistogram

Enumerations
enum	eClusteringMessage { eClusteringNotDone, eInvalidAccuracyThreshold, eInvalidClusterIndex, eInvalidMaxDictionarySize, eInvalidMinChangeRatio, eInvalidNbClusters, eInvalidPolynomialAlpha, eInvalidPolynomialBeta, eInvalidPolynomialDegree, eInvalidRBFSigma, eNullNbAttempts, eNullNbClusters, eNullNbIteration, eValidityIndexTypeNotYetSupported }
	Enumerate describing messages. More...

enum	eDataPartitionType { eDPT_Regular, eDPT_Adaptive }
	data partition type More...

enum	eEstimationMessage { eDataPartitionGenerationFailed, eDataPartitionNotInit, eDataSetAndOutlierFlagsSizeMismatch, eEstimationConfigNotInit, eEstimationFailedCantGetResults, eEstimationResultsNotInit, eEstimatorNotInit, eGridPartitionNotEnoughBuckets, eInvalidDataSize, eInvalidExpectedOutlierRatio, eInvalidGaussianSigma, eInvalidNbEstimParams, eInvalidOutlierRangeFactor, eInvalidOutlierThresholdFactor, eInvalidSubSetSize, eInvalidSuccessRatio, eNonLinearEstimationPassFailed, eNotEnoughData, eNullCostFunSharedPtr, eNullDataPartitionPtr, eNullDataSize, eNullEstimatorSharedPtr, eNullNbBucketsByAxis, eNullNbEstimParams, eNullNbMinRequestedData, eNullSubSetRequestedSize, eRegularGridPartitionInvalidRange, eResidualsFailure, eResidualsSetAndOutlierFlagsSizeMismatch, eResidualsSizeMismatch, eRobustEstimationFinalEstimationFailed, eRobustEstimationNoValidScore, eRobustEstimationNotDone, eRobustEstimationNotEnoughData, eRobustEstimationNotEnoughtSuccessfulRun, eRobustEstimatorNotInit, eUnsupportedRobustEstimatorType }

enum	eRobustEstimationType { eRET_NonRobust, eRET_LMS, eRET_RANSAC, eRET_MSAC, eRET_MLESAC }

enum	eTransform2dMessage { eInvalidNbParams, eTransformAlreadyRegistred, eTransformNotRegistred, eTransformationNotInvertible }
	Enumerate describing messages. More...

enum	eTransform3dMessage { eInvalidNbParams, eTransformAlreadyRegistred, eTransformNotRegistred, eTransformationNotInvertible }
	Enumerate describing messages. More...

enum	eGraphMessage { eAlgorithmNotInit, eAlgorithmNotResolved, eInvalidColumnIdx, eInvalidRowIdx, eNotColumnMajor, eNullMatrixSize }
	Enumerate describing messages. More...

enum	eLinearAlgebraMessage { eColMatrixColMatrixSizeMismatch, eColMatrixRowMatrixSizeMismatch, eColMatrixVectorSizeMismatch, eExpectingSquareMatrix, eInvalidNbEigenValues, eMatrixMatrixSizeMismatch, eOneRankDeficientSystemExpected, eOverConstrainSystemExpected, eRowMatrixColMatrixSizeMismatch, eRowMatrixRowMatrixSizeMismatch, eRowMatrixVectorSizeMismatch, eUnknownLaPackError, eVectorMatrixSizeMismatch }
	Enumerate describing messages. More...

enum	eIPSDKMathMessage { eNullLineDirection, eObjectNotInit, eUnSupportedEntity, eThomsonNbPointsOutOfRange }
	Enumerate describing messages. More...

enum	eOptimizationMessage { eCostFunNotInit, eInvalidJacobianSize, eInvalidNbEquations, eInvalidNbParameters, eNonLinearSolverNotSolved, eNullCostFunction, eNullNbEquations, eNullNbParameters, eOptStatus0, eOptStatus1, eOptStatus2, eOptStatus3, eOptStatus4_1, eOptStatus4_2, eOptStatus5, eOptStatus6, eOptStatus7, eOptStatusM2, eOptStatusM3, eOptStatusM4, eOptStatusOther }
	Enumerate describing messages. More...

enum	eOptStatus { eOS_Succeeded, eOS_Warn, eOS_Failed }

enum	eTopHat1DExtremumType { eTH1DET_Center, eTH1DET_Begin, eTH1DET_End, eTH1DET_Extremum }
	Enumerate describing the extremum type to take into account for a 1D top-hat calculation. More...

enum	eExtremaType { eET_Minima, eET_Maxima }
	Enumerate allowing to define an extrema type. More...

enum	eExtremaBorderPolicy { eEBP_Keeped, eEBP_Skipped, eEBP_MakeRing }
	Enumerate allowing to describe border policy used during extrema extraction processing. More...

enum	eHistogramOutOfBoundsPolicy { eHOOBP_Ignored, eHOOBP_Nearest, eHOOBP_Dedicated, eHOOBP_DedicatedUpper }
	enumerate use to describe histogram policy used to process out of bounds data More...

enum	eStatisticsMessage { eCollSizeMismatch, eFailedToExportHistogram, eGaussianCurveInvalidEstimation, eGaussianCurveInvalidMatrixRank, eHistogramBoundsGlobalPolicyNotYetSuported, eHistogramInvalidBinIndex, eHistogramInvalidClassIndex, eHistogramInvalidQuantileValue, eHistogramNotInit, eHistogramPopulationSizeMismatch, eInvalidDilateFactor, eInvalidHistogramBinWidth, eInvalidHistogramBounds, eInvalidHistogramNbClasses, eInvalidHistogramNbClusters }
	Enumerate describing messages. More...

enum	eToolsMessage { ePolynomial2dSurfaceUndefined }

Functions
IPSDKMATH_API std::ostream &	operator<< (std::ostream &os, const EstimationConfig &config)
	output operator on EstimationConfig

IPSDKMATH_API std::ostream &	operator<< (std::ostream &os, const EstimationResults &results)
	output operator on EstimationResults

IPSDKMATH_API EstimationConfig	createNonRobustConfig ()
	function allowing to create a non robust estimation configuration

IPSDKMATH_API void	processEstimation (const EstimationConfig &config, const EstimatorPtr &pEstimator, const DataSet &inputDataSet, EstimationResults &results)
	function allowing to launch a robust estimation process More...

IPSDKMATH_API void	processEstimation (const EstimationConfig &config, const EstimatorPtr &pEstimator, const CostFunCreator &costFunCreator, const DataSet &inputDataSet, EstimationResults &results)
	function allowing to launch a robust estimation process completed with a non linear estimation More...

IPSDKMATH_API RobustEstimatorPtr	createRobustEstimator (const EstimationConfig &config, const EstimatorPtr &pEstimator)
	function allowing to create and initialize a robust estimator More...

IPSDKMATH_API ipReal64	computeRMS (const ResidualsSet &residualsSet)
	function allowing to compute root mean square from a collection of residuals

IPSDKMATH_API ipReal64	computeRMS (const ResidualsSet &residualsSet, const OutlierFlags &outlierFlags)
	function allowing to compute root mean square from a collection of residuals with associated outliers flag

IPSDKMATH_API DataSet	extractInliers (const DataSet &fullDataSet, const OutlierFlags &outlierFlags)
	function allowing to extract an inlier sub data set from a complete data set and a collection of outlier flags More...

IPSDKMATH_API ipUInt32	computeNbOutliers (const OutlierFlags &outlierFlags)
	function allowing to compute number of outliers into a collection of outlier flags

IPSDKMATH_API ipUInt32	computeNbInliers (const OutlierFlags &outlierFlags)
	function allowing to compute number of inliers into a collection of outlier flags

IPSDKMATH_API BoolResult	checkDataSize (const DataSet &dataSet, const ipUInt32 dataSize)
	function allowing to check data size among data set

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE void	cartesianToPolar (const TIn x, const TIn y, TOut &rho, TOut &theta)
	cartesian to polar convertion More...

IPSDKMATH_API bool	circleFromPoints (const ipReal64 x0, const ipReal64 y0, const ipReal64 x1, const ipReal64 y1, const ipReal64 x2, const ipReal64 y2, ipReal64 &xc, ipReal64 &yc, ipReal64 &radius)
	computation of circle parameters from three points More...

IPSDK_FORCEINLINE ipReal64	circlePerimeter (const ipReal64 radius)
	compute circle perimeter

IPSDK_FORCEINLINE ipReal64	circleArea (const ipReal64 radius)
	compute circle area

IPSDKMATH_API bool	convertEllipseFromQuadratic (const ipReal64 a11, const ipReal64 a12, const ipReal64 a22, const ipReal64 b1, const ipReal64 b2, const ipReal64 c, ipReal64 &cx, ipReal64 &cy, ipReal64 &theta, ipReal64 &a, ipReal64 &b)
	function allowing to convert from quadratic to standard representation of ellipse More...

IPSDKMATH_API bool	convertEllipseToQuadratic (const ipReal64 cx, const ipReal64 cy, const ipReal64 theta, const ipReal64 a, const ipReal64 b, ipReal64 &a11, ipReal64 &a12, ipReal64 &a22, ipReal64 &b1, ipReal64 &b2, ipReal64 &c)
	function allowing to convert from standard to quadratic representation of ellipse More...

IPSDKMATH_API ipReal64	ellipsePerimeterLowerBound (const ipReal64 a, const ipReal64 b)
	function allowing to compute lower bound value for an ellipse perimeter More...

IPSDKMATH_API ipReal64	ellipsePerimeterUpperBound (const ipReal64 a, const ipReal64 b)
	function allowing to compute upper bound value for an ellipse perimeter More...

IPSDKMATH_API ipReal64	ellipseArea (const ipReal64 a, const ipReal64 b)
	function allowing to compute ellipse area More...

IPSDKMATH_API ipReal64	ellipseExcentricity (const ipReal64 a, const ipReal64 b)
	function allowing to compute ellipse excentricity More...

IPSDKMATH_API bool	equivalentEllipse (const ipReal64 perimeter, const ipReal64 area, ipReal64 &a, ipReal64 &b)
	function allowing to compute equivalent ellipse for a given perimeter and area More...

IPSDKMATH_API ipReal64	ellipseRadius (const ipReal64 a, const ipReal64 b, const ipReal64 phi)
	function allowing to compute axis aligned ellipse 'radius' for a given angle phi More...

IPSDKMATH_API ipReal64	ellipseRadius (const ipReal64 a, const ipReal64 b, const ipReal64 ellipseOrient, const ipReal64 theta)
	function allowing to compute ellipse 'radius' for a given angle More...

IPSDKMATH_API void	ellipsePoint (const ipReal64 xc, const ipReal64 yc, const ipReal64 a, const ipReal64 b, const ipReal64 ellipseOrient, const ipReal64 theta, ipReal64 &ptX, ipReal64 &ptY)
	function allowing to compute ellipse boundary point for a given angle

IPSDKMATH_API bool	lineFromPoints (const ipReal64 x0, const ipReal64 y0, const ipReal64 x1, const ipReal64 y1, ipReal64 &rho, ipReal64 &theta)
	computation of line parameters from two points More...

template<typename T >
IPSDK_FORCEINLINE ipReal64	distance (const T x1, const T y1, const T x2, const T y2)
	Euclidian distance between 2d points.

template<typename T >
IPSDKMATH_API bool	segmentsIntersects (const T xSegStart0, const T ySegStart0, const T xSegEnd0, const T ySegEnd0, const T xSegStart1, const T ySegStart1, const T xSegEnd1, const T ySegEnd1)
	check whether two segments intersect

template<typename T >
IPSDK_FORCEINLINE ipReal64	normL2 (const T x, const T y)
	L2 norm of a 2d vector.

template<typename T >
IPSDK_FORCEINLINE T	scalarProduct (const T x1, const T y1, const T x2, const T y2)
	Scalar product of two 2d vectors.

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE void	cartesianToSpherical (const TIn x, const TIn y, const TIn z, TOut &rho, TOut &theta, TOut &phi)
	cartesian to spherical convertion More...

IPSDKMATH_API void	eulerToQuaternion (const ipReal64 chi, const ipReal64 beta, const ipReal64 alpha, ipReal64 &q0, ipReal64 &q1, ipReal64 &q2, ipReal64 &q3)
	Convertion from euler angles to a quaternion representation. More...

IPSDKMATH_API void	quaternionToEuler (const ipReal64 q0, const ipReal64 q1, const ipReal64 q2, const ipReal64 q3, ipReal64 &chi, ipReal64 &beta, ipReal64 &alpha)
	Convertion from quaternion representation to euler angles. More...

IPSDKMATH_API bool	convertEllipsoidFromQuadratic (const ipReal64 a11, const ipReal64 a12, const ipReal64 a13, const ipReal64 a22, const ipReal64 a23, const ipReal64 a33, const ipReal64 b1, const ipReal64 b2, const ipReal64 b3, const ipReal64 c0, ipReal64 &cx, ipReal64 &cy, ipReal64 &cz, ipReal64 &chi, ipReal64 &beta, ipReal64 &alpha, ipReal64 &a, ipReal64 &b, ipReal64 &c)
	function allowing to convert from quadratic to standard representation of ellipsoid More...

IPSDKMATH_API bool	convertEllipsoidToQuadratic (const ipReal64 cx, const ipReal64 cy, const ipReal64 cz, const ipReal64 chi, const ipReal64 beta, const ipReal64 alpha, const ipReal64 a, const ipReal64 b, const ipReal64 c, ipReal64 &a11, ipReal64 &a12, ipReal64 &a13, ipReal64 &a22, ipReal64 &a23, ipReal64 &a33, ipReal64 &b1, ipReal64 &b2, ipReal64 &b3, ipReal64 &c0)
	function allowing to convert from standard to quadratic representation of ellipsoid More...

IPSDKMATH_API ipReal64	ellipsoidArea (const ipReal64 a, const ipReal64 b, const ipReal64 c)
	function allowing to compute ellipsoid area More...

IPSDKMATH_API ipReal64	ellipsoidVolume (const ipReal64 a, const ipReal64 b, const ipReal64 c)
	function allowing to compute ellipsoid volume More...

IPSDKMATH_API ipReal64	ellipsoidExcentricity (const ipReal64 a, const ipReal64 b, const ipReal64 c)
	function allowing to compute ellipsoid excentricity More...

IPSDKMATH_API ipReal64	ellipsoidRadius (const ipReal64 a, const ipReal64 b, const ipReal64 c, const ipReal64 theta, const ipReal64 phi)
	function allowing to compute axis aligned ellipsoid 'radius' for a given orientation (see Points and vectors 3d representation) More...

IPSDKMATH_API ipReal64	ellipsoidRadius (const ipReal64 a, const ipReal64 b, const ipReal64 c, const Matrix3d &matRot, const ipReal64 theta, const ipReal64 phi)
	function allowing to compute ellipsoid 'radius' for a given orientation (see Points and vectors 3d representation) More...

IPSDKMATH_API void	ellipsoidPoint (const ipReal64 xc, const ipReal64 yc, const ipReal64 zc, const ipReal64 a, const ipReal64 b, const ipReal64 c, const Matrix3d &matRot, const ipReal64 theta, const ipReal64 phi, ipReal64 &ptX, ipReal64 &ptY, ipReal64 &ptZ)
	function allowing to compute ellipsoid boundary point for a given angle

IPSDKMATH_API bool	planFromPoints (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, ipReal64 &rho, ipReal64 &theta, ipReal64 &phi)
	computation of plan parameters from three points More...

template<typename T >
IPSDK_FORCEINLINE ipReal64	distance (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2)
	Euclidian distance between 3d points.

template<typename T >
IPSDKMATH_API bool	segmentsIntersects (const T xSegStart0, const T ySegStart0, const T zSegStart0, const T xSegEnd0, const T ySegEnd0, const T zSegEnd0, const T xSegStart1, const T ySegStart1, const T zSegStart1, const T xSegEnd1, const T ySegEnd1, const T zSegEnd1)
	check whether two segments intersect

IPSDKMATH_API bool	sphereFromPoints (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, const ipReal64 x3, const ipReal64 y3, const ipReal64 z3, ipReal64 &xc, ipReal64 &yc, ipReal64 &zc, ipReal64 &radius)
	computation of sphere parameters from four points More...

IPSDKMATH_API bool	sphereFromPoints (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, ipReal64 &xc, ipReal64 &yc, ipReal64 &zc, ipReal64 &radius)
	computation of sphere parameters from three points More...

IPSDK_FORCEINLINE ipReal64	sphereArea (const ipReal64 radius)
	compute sphere area

IPSDK_FORCEINLINE ipReal64	sphereVolume (const ipReal64 radius)
	compute sphere volume

IPSDKMATH_API ipReal64	tetrahedronArea (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, const ipReal64 x3, const ipReal64 y3, const ipReal64 z3)
	computation of tetrahedron area from its vertives coordinates

IPSDKMATH_API ipReal64	tetrahedronVolume (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, const ipReal64 x3, const ipReal64 y3, const ipReal64 z3)
	computation of tetrahedron volume from its vertives coordinates

IPSDKMATH_API ipReal64	tetrahedronSignedVolume (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, const ipReal64 x3, const ipReal64 y3, const ipReal64 z3)
	computation of tetrahedron signed volume from its vertives coordinates

IPSDKMATH_API ipReal64	tetrahedronSignedVolume (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2)
	computation of tetrahedron signed volume from its vertives coordinates (last vertice is supposed to be at origin)

IPSDKMATH_API void	tetrahedronInertia (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, ipReal64 &mxx, ipReal64 &mxy, ipReal64 &mxz, ipReal64 &myy, ipReal64 &myz, ipReal64 &mzz)
	computation of tetrahedron inertia tensor components (last vertice is supposed to be at origin)

IPSDK_FORCEINLINE ipReal64	trianglePerimeter (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2)
	computation of triangle perimeter from its vertives coordinates

IPSDK_FORCEINLINE ipReal64	triangleArea (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2)
	computation of triangle area from its vertives coordinates

IPSDK_FORCEINLINE void	triangleNormal (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, ipReal64 &nx, ipReal64 &ny, ipReal64 &nz)
	computation of triangle normal from its vertives coordinates More...

IPSDK_FORCEINLINE bool	triangleUnitNormal (const ipReal64 x0, const ipReal64 y0, const ipReal64 z0, const ipReal64 x1, const ipReal64 y1, const ipReal64 z1, const ipReal64 x2, const ipReal64 y2, const ipReal64 z2, ipReal64 &nx, ipReal64 &ny, ipReal64 &nz)
	computation of triangle unit normal from its vertives coordinates More...

template<typename T >
IPSDK_FORCEINLINE ipReal64	normL2 (const T x, const T y, const T z)
	L2 norm of a 3d vector.

template<typename T >
IPSDK_FORCEINLINE T	scalarProduct (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2)
	Scalar product of two 3d vectors.

template<typename T >
IPSDK_FORCEINLINE void	crossProduct (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2, T &xRes, T &yRes, T &zRes)
	Cross product of two 3d vectors.

IPSDK_FORCEINLINE ipReal64	modulo (const ipReal64 angle, const ipReal64 modulo)
	function allowing to compute modulo of an angle More...

IPSDK_FORCEINLINE ipReal64	centerModulo (const ipReal64 angle, const ipReal64 modulo)
	function allowing to compute centered modulo of an angle More...

IPSDK_FORCEINLINE ipReal64	det (const ipReal64 a11, const ipReal64 a12, const ipReal64 a21, const ipReal64 a22)
	computation of a 2x2 matrix determinant

IPSDK_FORCEINLINE ipReal64	det (const ipReal64 a11, const ipReal64 a12, const ipReal64 a13, const ipReal64 a21, const ipReal64 a22, const ipReal64 a23, const ipReal64 a31, const ipReal64 a32, const ipReal64 a33)
	computation of a 3x3 matrix determinant

IPSDK_FORCEINLINE bool	solveLinear (const ipReal64 a11, const ipReal64 a12, const ipReal64 b1, const ipReal64 a21, const ipReal64 a22, const ipReal64 b2, ipReal64 &x1, ipReal64 &x2)
	solve linear system of 2 equations with two unknowns (we solve linear system AX=B) More...

IPSDK_FORCEINLINE bool	solveLinear (const ipReal64 a11, const ipReal64 a12, const ipReal64 a13, const ipReal64 b1, const ipReal64 a21, const ipReal64 a22, const ipReal64 a23, const ipReal64 b2, const ipReal64 a31, const ipReal64 a32, const ipReal64 a33, const ipReal64 b3, ipReal64 &x1, ipReal64 &x2, ipReal64 &x3)
	solve linear system of 3 equations with three unknowns (we solve linear system AX=B) More...

IPSDK_FORCEINLINE bool	invertMatrix (ipReal64 &a11, ipReal64 &a12, ipReal64 &a21, ipReal64 &a22)
	inversion of a 2x2 matrix More...

IPSDKMATH_API bool	choleskyDecomposition (const Matrix &matA, Matrix &matU)
	decomposition of a nxn symetric positive definite matrix using cholesky decomposition More...

IPSDKMATH_API bool	choleskyInverse (Matrix &matA)
	in situ inversion of a nxn symetric positive definite matrix using cholesky decomposition method More...

IPSDKMATH_API bool	choleskyInverse (const Matrix &matA, Matrix &matInvA)
	inversion of a nxn symetric positive definite matrix using cholesky decomposition method More...

IPSDKMATH_API void	eigenDecomposition (const ipReal64 mXX, const ipReal64 mXY, const ipReal64 mYY, ipReal64 &lambdaMin, ipReal64 &lambdaMax, ipReal64 &theta)
	eigen decomposition of symetric 2x2 matrix $\begin{bmatrix} mXX & mXY \\ mXY & mYY \end{bmatrix}$ On output value are granted such that : More...

IPSDKMATH_API ipUInt32	eigenDecomposition (const Matrix &mat, Vector &eigenValues, Matrix &eigenVectors)
	eigen decomposition of symetric NxN matrix On output : More...

IPSDKMATH_API void	eigenPartialDecomposition (const Matrix &mat, Vector &eigenValues, Matrix &eigenVectors)
	eigen decomposition of symetric NxN matrix with search for only M greatest values On output : More...

IPSDK_FORCEINLINE ipReal64	comparable_distance (const ipsdk::math::Vector &v0, const ipsdk::math::Vector &v1)
	function allowing to compute comparable distance between two vectors More...

IPSDK_FORCEINLINE ipReal64	euclidian_distance (const ipsdk::math::Vector &v0, const ipsdk::math::Vector &v1)
	function allowing to compute euclidian distance between two vectors More...

template<typename ArrayType1 , typename ArrayType2 >
bool	equal (const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType1 > &mat1, const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType2 > &mat2)
	check for matrix equality

template<typename ArrayType1 , typename ArrayType2 >
bool	compare (const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType1 > &mat1, const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType2 > &mat2, const ipReal64 epsilonValue=NumericLimits< ipReal64 >::sqrt_epsilon())
	matrix comparison with tolerance on frobenius norm of difference

template<typename ArrayType1 , typename ArrayType2 >
bool	compareRelative (const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType1 > &mat1, const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType2 > &mat2, const ipReal64 epsilonValue=NumericLimits< ipReal64 >::sqrt_epsilon())

template<typename ArrayType1 , typename ArrayType2 >
bool	equal (const boost::numeric::ublas::vector< ipReal64, ArrayType1 > &vec1, const boost::numeric::ublas::vector< ipReal64, ArrayType2 > &vec2)
	check for vector equality

template<typename ArrayType1 , typename ArrayType2 >
bool	compare (const boost::numeric::ublas::vector< ipReal64, ArrayType1 > &vec1, const boost::numeric::ublas::vector< ipReal64, ArrayType2 > &vec2, const ipReal64 epsilonValue=NumericLimits< ipReal64 >::sqrt_epsilon())
	vector comparison with tolerance on euclidian norm of difference

template<typename ArrayType1 , typename ArrayType2 >
bool	compareRelative (const boost::numeric::ublas::vector< ipReal64, ArrayType1 > &vec1, const boost::numeric::ublas::vector< ipReal64, ArrayType2 > &vec2, const ipReal64 epsilonValue=NumericLimits< ipReal64 >::sqrt_epsilon())

IPSDKMATH_API bool	luSolve (const Matrix &matA, const Vector &vecB, Vector &vecX)
	linear system resolution using lu decomposition Solved system is : matA x VecX = vecB with More...

IPSDKMATH_API bool	luInverse (Matrix &matA)
	in place inversion of a nxn squared matrix using lu decomposition method More...

IPSDKMATH_API bool	luInverse (const Matrix &matA, Matrix &matInvA)
	inversion of a nxn squared matrix using lu decomposition method With : More...

IPSDKMATH_API bool	upperTriangularInverse (Matrix &matA)
	inversion of a nxn upper triangular matrix More...

IPSDKMATH_API bool	lowerTriangularInverse (Matrix &matA)
	inversion of a nxn lower triangular matrix More...

IPSDKMATH_API bool	qrSolve (const Matrix &matA, const Vector &vecB, Vector &vecX)
	linear system resolution using qr decomposition method Solved system is : matA x VecX = vecB with More...

IPSDKMATH_API void	qrDecomposition (const Matrix &matA, Matrix &matQ, Matrix &matR)
	QR decomposition of mxn matrix Given mn = min(m,n), we have : More...

IPSDKMATH_API ipUInt32	svdSolve (const Matrix &matA, const Vector &vecB, Vector &vecX)
	over constrained linear system resolution using singular value decomposition method Solved system is : matA x vecX = vecB with More...

IPSDKMATH_API ipUInt32	svdSolve (const Matrix &matA, const Matrix &matB, Matrix &matX)
	over constrained linear system resolution using singular value decomposition method (case of multiple solved systems AX=B with shared matrix A) Solved system is : matA x matX = matB with More...

IPSDKMATH_API ipUInt32	svdSolve (const Matrix &matA, Vector &vecX)
	over constrained linear system resolution using singular value decomposition method Solved system is : matA x VecX = 0 with More...

IPSDKMATH_API void	svdDecomposition (const Matrix &matA, Matrix &matU, Vector &vecS, Matrix &matVt)
	singular value decomposition of mxn matrix Given mn = min(m,n), we have : More...

IPSDKMATH_API ipUInt32	svdInverse (const Matrix &matA, Matrix &matInvA)
	inversion of a mxn rectangular matrix with m >= n using singular value decomposition method. With : More...

IPSDKMATH_API const std::string &	getIPSDKMathLoggerName ()
	Recovery of logger name associated to library.

IPSDKMATH_API log4cplus::Logger &	getIPSDKMathLogger ()
	Recovery of logger associated to library.

IPSDKMATH_API const LogMessageManager &	getIPSDKMathLogMessageManager ()
	Recovery of message manager associated to library.

template<typename T >
IPSDKMATH_API ipUInt32	tophatThreshold1D (const std::vector< T > &vInBuf, const ipBool bBlack, const eTopHat1DExtremumType &extremumType, const ipReal32 calibratedHalfSize, const ipReal32 scale, const ipReal32 threshold, std::vector< ipInt32 > &vOutBuf)
	Compute the tophat threshold on a 1D signal stored in a std::vector and returns the number of detected extrama.

template<typename T >
IPSDKMATH_API std::vector< ipReal32 >	gaussianSmoothing1D (const std::vector< T > &vInBuf, const ipReal32 stdDev)
	Compute the Gaussian smoothing on a 1D signal stored in a std::vector.

IPSDKMATH_API ipUInt32	solveQuadratic (ipReal64 a, ipReal64 b, ipReal64 c, ipReal64 &x1, ipReal64 &x2)
	second order polynomial real roots search More...

template<typename T >
T	median (std::vector< T > &coll)
	function allowing to compute median of a collection More...

template<typename T >
IPSDKMATH_API ipReal64	mean (const std::vector< T > &coll)
	function allowing to compute mean for a vector

template<typename T >
IPSDKMATH_API ipReal64	variance (const std::vector< T > &coll)
	function allowing to compute variance for a vector

template<typename T >
IPSDKMATH_API ipReal64	stdDev (const std::vector< T > &coll)
	function allowing to compute standard deviation for a vector

template<typename T >
IPSDKMATH_API std::pair< ipReal64, ipReal64 >	meanAndVariance (const std::vector< T > &coll)
	function allowing to compute mean and variance for a vector

template<typename T >
IPSDKMATH_API ipReal64	correlation (const std::vector< T > &coll1, const std::vector< T > &coll2)
	function allowing to compute correlation between two vectors of data More...

template<typename T , typename IndexType >
IPSDKMATH_API void	findLocalStrictExtrema (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, const eExtremaType &extremaType, std::vector< IndexType > &extremaIdxColl)
	generic function allowing to search for local strict extrema into a collection of values More...

template<typename T , typename IndexType >
void	findLocalStrictMinima (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, std::vector< IndexType > &extremaIdxColl)
	generic function allowing to search for local strict minima into a collection of values More...

template<typename T , typename IndexType >
void	findLocalStrictMaxima (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, std::vector< IndexType > &extremaIdxColl)
	generic function allowing to search for local strict maxima into a collection of values More...

template<typename T >
IPSDKMATH_API void	findLocalDilatedExtrema (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, const eExtremaType &extremaType, const T &dilateFactor, ExtremaRangeColl &extremaRangeColl)
	generic function allowing to search for local 'dilated' extrema into a collection of values More...

template<typename T , typename IndexType >
IPSDKMATH_API void	findLocalExtrema (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, const eExtremaType &extremaType, std::vector< IndexType > &extremaIdxColl)
	function allowing to search for local extrema into a collection of values (this is the non strict extrema search version) More...

template<typename T , typename IndexType >
void	findLocalMinima (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, std::vector< IndexType > &extremaIdxColl)
	function allowing to search for local minima into a collection of values More...

template<typename T , typename IndexType >
void	findLocalMaxima (const std::vector< T > &inputColl, const eExtremaBorderPolicy &extremaBorderPolicy, std::vector< IndexType > &extremaIdxColl)
	function allowing to search for local maxima into a collection of values More...

template<typename ExtremaInfo , typename T >
IPSDKMATH_API void	filterExtrema (const eExtremaType &extremaType, const ipReal64 minDistance, const T extremaThresholdValue, boost::function< void(const ExtremaInfo &, ipReal64 &, T &)> extractExtremaCoordsWrapper, std::vector< ExtremaInfo > &extremaInfoColl)
	function allowing to filter a collection of extrema using a distance criterion More...

template<typename T , typename IndexType >
void	extractBasicExtremaCoords (const std::vector< T > &inputColl, const IndexType &dataIdx, ipReal64 &extremaLocation, T &extremaValue)

template<typename T >
IPSDKMATH_API void	extractBasicExtremaCoords (const std::vector< T > &inputColl, const ExtremaRange &extremaRange, ipReal64 &extremaLocation, T &extremaValue)
	basic function to retrieve extrema coordinates from an extrema range information More...

template<typename T , typename IndexType >
void	filterMinima (const std::vector< T > &inputColl, const ipReal64 minDistance, std::vector< IndexType > &extremaInfoColl)
	function allowing to filter a collection of minima using a distance criterion Extrema are first sorted in function of there value and then filtered using a distance criterion More...

template<typename T , typename IndexType >
void	filterMinima (const std::vector< T > &inputColl, const ipReal64 minDistance, const T extremaThresholdValue, std::vector< IndexType > &extremaInfoColl)
	function allowing to filter a collection of minima using a distance criterion and a value threshold Extrema are first sorted in function of there value and then filtered using a distance criterion More...

template<typename T , typename IndexType >
void	filterMaxima (const std::vector< T > &inputColl, const ipReal64 minDistance, std::vector< IndexType > &extremaInfoColl)
	function allowing to filter a collection of maxima using a distance criterion Extrema are first sorted in function of there value and then filtered using a distance criterion More...

template<typename T , typename IndexType >
void	filterMaxima (const std::vector< T > &inputColl, const ipReal64 minDistance, const T extremaThresholdValue, std::vector< IndexType > &extremaInfoColl)
	function allowing to filter a collection of maxima using a distance criterion and a value threshold Extrema are first sorted in function of there value and then filtered using a distance criterion More...

IPSDKMATH_API ipReal64	computeHistogramRange (const ipBool bDataIntegral, const ipReal64 firstHistoValue, const ipReal64 lastHistoValue)
	function allowing to compute range associated to an histogram More...

IPSDKMATH_API ipUInt32	computeHistogramNbClasses (const ipBool bDataIntegral, const ipReal64 firstHistoValue, const ipReal64 lastHistoValue, const ipReal64 binWidth)
	function allowing to compute number of classes associated to an histogram More...

IPSDKMATH_API ipReal64	computeHistogramBinWidth (const ipBool bDataIntegral, const ipReal64 firstHistoValue, const ipReal64 lastHistoValue, const ipUInt32 nbClasses)
	function allowing to compute bin width associated to an histogram More...

IPSDKMATH_API void	computeHistogramBoundsInfo (const ipUInt32 nbClasses, const eHistogramOutOfBoundsPolicy &outOfBoundsPolicy, ipUInt32 &lowerOutOfBoundsBinIdx, ipUInt32 &upperOutOfBoundsBinIdx, ipUInt32 &inBoundsBinOffset, ipUInt32 &nbBins)
	function allowing to deduce histogram bound policies from a global enumerate value More...

IPSDKMATH_API ipUInt32	computeHistogramNbBins (const ipUInt32 nbClasses, const eHistogramOutOfBoundsPolicy &outOfBoundsPolicy)
	function allowing to compute number of bins associated to an histogram

IPSDKMATH_API void	exportToCsv (const boost::filesystem::path &filePath, const ipsdk::math::BaseHistogram &histogram)
	function allowing to export histogram data to a csv file More...

IPSDKMATH_API bool	operator== (const ipsdk::math::HistogramExtrema &extrema1, const ipsdk::math::HistogramExtrema &extrema2)
	operator allowing to compare histogram extrema

IPSDKMATH_API std::ostream &	operator<< (std::ostream &os, const ipsdk::math::HistogramExtrema &extrema)
	operator allowing to write histogram extrema to a stream

IPSDKMATH_API std::ostream &	operator<< (std::ostream &os, const ipsdk::math::HistogramGaussianCurveFit &gaussianCurveFit)
	operator allowing to write histogram gaussian curve fit to a stream

IPSDKMATH_API std::ostream &	operator<< (std::ostream &os, const ipsdk::math::BaseHistogram &histogram)
	operator allowing to write histogram data to a stream

IPSDKMATH_API ipReal64	normalDistribution (const ipReal64 x, const ipReal64 stdDev, const ipReal64 mean=0)
	function allowing to compute normal distribution value More...

IPSDKMATH_API ipReal64	normalDistributionFirstDerivative (const ipReal64 x, const ipReal64 stdDev, const ipReal64 mean=0)
	function allowing to compute first derivative value for normal distribution More...

IPSDKMATH_API ipReal64	normalDistributionSecondDerivative (const ipReal64 x, const ipReal64 stdDev, const ipReal64 mean=0)
	function allowing to compute second derivative value for normal distribution More...

IPSDKMATH_API ipReal64	cumulativeNormalDistribution (const ipReal64 x, const ipReal64 stdDev, const ipReal64 mean=0)
	function allowing to approximate cumulative distribution function value for normal distribution More...

ipReal64	normalDistributionCoverage (const ipReal64 dist, const ipReal64 stdDev, const ipReal64 mean=0)
	function allowing to approximate normal distribution ratio coverage of values at a given distance away from the mean More...

IPSDK_FORCEINLINE ipReal64	linearInterpolation (const ipReal64 x, const ipReal64 f0, const ipReal64 f1)
	function allowing to compute linear interpolation between two values More...

IPSDK_FORCEINLINE ipReal64	biLinearInterpolation (const ipReal64 x, const ipReal64 y, const ipReal64 fX0Y0, const ipReal64 fX1Y0, const ipReal64 fX0Y1, const ipReal64 fX1Y1)
	function allowing to compute a bi linear interpolation More...

IPSDK_FORCEINLINE ipReal64	triLinearInterpolation (const ipReal64 x, const ipReal64 y, const ipReal64 z, const ipReal64 fX0Y0Z0, const ipReal64 fX1Y0Z0, const ipReal64 fX0Y1Z0, const ipReal64 fX1Y1Z0, const ipReal64 fX0Y0Z1, const ipReal64 fX1Y0Z1, const ipReal64 fX0Y1Z1, const ipReal64 fX1Y1Z1)
	function allowing to compute a tri linear interpolation More...

IPSDK_FORCEINLINE ipReal64	cubicInterpolation (const ipReal64 x, const ipReal64 fM1, const ipReal64 f0, const ipReal64 f1, const ipReal64 f2)
	function allowing to compute cubic interpolation between two values More...

IPSDK_FORCEINLINE ipReal64	biCubicInterpolation (const ipReal64 x, const ipReal64 y, const ipReal64 f[4][4])
	function allowing to compute a bi cubic interpolation More...

IPSDK_FORCEINLINE ipReal64	triCubicInterpolation (const ipReal64 x, const ipReal64 y, const ipReal64 z, const ipReal64 f[4][4][4])
	function allowing to compute a tri cubic interpolation More...

template<typename T >
IPSDKMATH_API void	sort (const T &x1, const T &x2, const T &x3, T &y1, T &y2, T &y3)
	function allowing to sort 3 numbers in ascending order More...

template<typename OutputType , typename InputType >
IPSDKMATH_API OutputType	round (const InputType value)
	function allowing to round number from a type to an other

template<typename OutputType , typename InputType >
IPSDKMATH_API OutputType	saturatedRound (const InputType value)
	function allowing to round number from a type to an other with overflow management

template<typename T >
IPSDKMATH_API boost::enable_if< typename boost::is_arithmetic< T >::type, bool >::type	compare (const T val1, const T val2, const T tolerance=NumericLimits< T >::sqrt_epsilon())
	function allowing to compare two values More...

template<typename T >
IPSDKMATH_API boost::enable_if< typename boost::is_arithmetic< T >::type, bool >::type	compare (const std::vector< T > &vec1, const std::vector< T > &vec2, const T tolerance=NumericLimits< T >::sqrt_epsilon())
	function allowing to compare two values More...

template<typename T >
IPSDKMATH_API boost::enable_if< typename boost::is_arithmetic< T >::type, bool >::type	compareRelative (const T val1, const T val2, const T tolerance=NumericLimits< T >::sqrt_epsilon())
	function allowing to compare two values More...

template<typename T >
IPSDKMATH_API boost::enable_if< typename boost::is_arithmetic< T >::type, bool >::type	compareRelative (const std::vector< T > &vec1, const std::vector< T > &vec2, const T tolerance=NumericLimits< T >::sqrt_epsilon())
	function allowing to compare two values More...


template<typename TOut , typename TIn >
IPSDK_FORCEINLINE TOut	polarToXCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta)
	polar to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE TOut	polarToYCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta)
	polar to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE void	polarToCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta, TOut &x, TOut &y)
	polar to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE void	polarToCartesian (const TIn rho, const TIn theta, TOut &x, TOut &y)
	polar to cartesian convertion More...


template<typename T >
IPSDK_FORCEINLINE void	angleToMatrix (const T cosTheta, const T sinTheta, T &rxx, T &rxy, T &ryx, T &ryy)
	Convertion from angle to rotation matrix. More...

template<typename T >
IPSDK_FORCEINLINE void	angleToMatrix (const T theta, T &rxx, T &rxy, T &ryx, T &ryy)
	Convertion from angle to rotation matrix. More...

IPSDK_FORCEINLINE Matrix2d	angleToMatrix (const ipReal64 theta)
	Convertion from angle to rotation matrix. More...


template<typename T >
IPSDK_FORCEINLINE void	matrixToAngle (const T rxx, const T rxy, T &theta)
	Convertion from rotation matrix to angle. More...

template<typename T >
IPSDK_FORCEINLINE void	matrixToAngle (const T rxx, const T rxy, const T ryx, const T ryy, T &theta)
	Convertion from rotation matrix to angle. More...

IPSDK_FORCEINLINE ipReal64	matrixToAngle (const Matrix2d &matRot)
	Convertion from rotation matrix to angle. More...


template<typename T >
IPSDK_FORCEINLINE void	rotate2d (const T xIn, const T yIn, const ipReal64 cosTheta, const ipReal64 sinTheta, T &xOut, T &yOut)
	rotation of a point using a rotation angle (rotation around origin) More...

template<typename T >
IPSDK_FORCEINLINE void	rotate2dInSitu (const ipReal64 cosTheta, const ipReal64 sinTheta, T &x, T &y)
	rotation of a point using a rotation angle (rotation around origin) More...

template<typename T >
IPSDK_FORCEINLINE void	rotate2d (const T xIn, const T yIn, const ipReal64 theta, T &xOut, T &yOut)
	rotation of a point using a rotation angle (rotation around origin) More...


template<typename T >
IPSDKMATH_API ipReal64	pointSegmentDistance (const T xPt, const T yPt, const T xSegStart, const T ySegStart, const T xSegEnd, const T ySegEnd)
	Euclidian distance between a point and a segment.

template<typename T >
IPSDKMATH_API ipReal64	pointSegmentDistance (const T xPt, const T yPt, const T xSegStart, const T ySegStart, const T xSegEnd, const T ySegEnd, ipReal64 &xMinDistPt, ipReal64 &yMinDistPtSeg)
	Euclidian distance between a point and a segment.


template<typename T >
IPSDKMATH_API ipReal64	segmentsDistance (const T xSegStart0, const T ySegStart0, const T xSegEnd0, const T ySegEnd0, const T xSegStart1, const T ySegStart1, const T xSegEnd1, const T ySegEnd1)
	Euclidian distance between two segments.

template<typename T >
IPSDKMATH_API ipReal64	segmentsDistance (const T xSegStart0, const T ySegStart0, const T xSegEnd0, const T ySegEnd0, const T xSegStart1, const T ySegStart1, const T xSegEnd1, const T ySegEnd1, ipReal64 &xMinDistPtSeg0, ipReal64 &yMinDistPtSeg0, ipReal64 &xMinDistPtSeg1, ipReal64 &yMinDistPtSeg1)
	Euclidian distance between two segments.


template<typename TOut , typename TIn >
IPSDK_FORCEINLINE TOut	sphericalToXCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta, const TIn cosPhi, const TIn sinPhi)
	spherical to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE TOut	sphericalToYCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta, const TIn cosPhi, const TIn sinPhi)
	spherical to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE TOut	sphericalToZCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta, const TIn cosPhi, const TIn sinPhi)
	spherical to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE void	sphericalToCartesian (const TIn rho, const TIn cosTheta, const TIn sinTheta, const TIn cosPhi, const TIn sinPhi, TOut &x, TOut &y, TOut &z)
	spherical to cartesian convertion More...

template<typename TOut , typename TIn >
IPSDK_FORCEINLINE void	sphericalToCartesian (const TIn rho, const TIn theta, const TIn phi, TOut &x, TOut &y, TOut &z)
	spherical to cartesian convertion More...


template<typename T >
IPSDK_FORCEINLINE void	eulerToMatrix (const T cosChi, const T sinChi, const T cosBeta, const T sinBeta, const T cosAlpha, const T sinAlpha, T &rxx, T &rxy, T &rxz, T &ryx, T &ryy, T &ryz, T &rzx, T &rzy, T &rzz)
	Convertion from euler angles to rotation matrix. More...

template<typename T >
IPSDK_FORCEINLINE void	eulerToMatrix (const T chi, const T beta, const T alpha, T &rxx, T &rxy, T &rxz, T &ryx, T &ryy, T &ryz, T &rzx, T &rzy, T &rzz)
	Convertion from euler angles to rotation matrix. More...

IPSDK_FORCEINLINE Matrix3d	eulerToMatrix (const ipReal64 chi, const ipReal64 beta, const ipReal64 alpha)
	Convertion from euler angles to rotation matrix. More...


template<typename T >
IPSDK_FORCEINLINE void	matrixToEuler (const T rxx, const T rxy, const T rxz, const T ryx, const T ryy, const T ryz, const T rzx, const T rzy, const T rzz, T &chi, T &beta, T &alpha)
	Convertion from rotation matrix to euler angles. More...

IPSDK_FORCEINLINE void	matrixToEuler (const Matrix3d &matRot, ipReal64 &chi, ipReal64 &beta, ipReal64 &alpha)
	Convertion from rotation matrix to euler angles. More...


template<typename T >
IPSDK_FORCEINLINE void	rotate3d (const T xIn, const T yIn, const T zIn, const ipReal64 rxx, const ipReal64 rxy, const ipReal64 rxz, const ipReal64 ryx, const ipReal64 ryy, const ipReal64 ryz, const ipReal64 rzx, const ipReal64 rzy, const ipReal64 rzz, T &xOut, T &yOut, T &zOut)
	rotation of a point using a rotation angle (rotation around origin) More...

template<typename T >
IPSDK_FORCEINLINE void	rotate3dInSitu (const ipReal64 rxx, const ipReal64 rxy, const ipReal64 rxz, const ipReal64 ryx, const ipReal64 ryy, const ipReal64 ryz, const ipReal64 rzx, const ipReal64 rzy, const ipReal64 rzz, T &x, T &y, T &z)
	rotation of a point using a rotation angle (rotation around origin) More...

template<typename T >
IPSDK_FORCEINLINE void	rotate3d (const T xIn, const T yIn, const T zIn, const ipReal64 cosChi, const ipReal64 sinChi, const ipReal64 cosBeta, const ipReal64 sinBeta, const ipReal64 cosAlpha, const ipReal64 sinAlpha, T &xOut, T &yOut, T &zOut)
	rotation of a point using a rotation angle (rotation around origin) More...

template<typename T >
IPSDK_FORCEINLINE void	rotate3dInSitu (const ipReal64 cosChi, const ipReal64 sinChi, const ipReal64 cosBeta, const ipReal64 sinBeta, const ipReal64 cosAlpha, const ipReal64 sinAlpha, T &x, T &y, T &z)
	rotation of a point using a rotation angle (rotation around origin) More...

template<typename T >
IPSDK_FORCEINLINE void	rotate3d (const T xIn, const T yIn, const T zIn, const ipReal64 chi, const ipReal64 beta, const ipReal64 alpha, T &xOut, T &yOut, T &zOut)
	rotation of a point using a rotation angle (rotation around origin) More...


template<typename T >
IPSDKMATH_API ipReal64	pointSegmentDistance (const T xPt, const T yPt, const T zPt, const T xSegStart, const T ySegStart, const T zSegStart, const T xSegEnd, const T ySegEnd, const T zSegEnd)
	Euclidian distance between a point and a segment.

template<typename T >
IPSDKMATH_API ipReal64	pointSegmentDistance (const T xPt, const T yPt, const T zPt, const T xSegStart, const T ySegStart, const T zSegStart, const T xSegEnd, const T ySegEnd, const T zSegEnd, ipReal64 &xMinDistPt, ipReal64 &yMinDistPtSeg, ipReal64 &zMinDistPtSeg)
	Euclidian distance between a point and a segment.


template<typename T >
IPSDKMATH_API ipReal64	segmentsDistance (const T xSegStart0, const T ySegStart0, const T zSegStart0, const T xSegEnd0, const T ySegEnd0, const T zSegEnd0, const T xSegStart1, const T ySegStart1, const T zSegStart1, const T xSegEnd1, const T ySegEnd1, const T zSegEnd1)
	Euclidian distance between two segments.

template<typename T >
IPSDKMATH_API ipReal64	segmentsDistance (const T xSegStart0, const T ySegStart0, const T zSegStart0, const T xSegEnd0, const T ySegEnd0, const T zSegEnd0, const T xSegStart1, const T ySegStart1, const T zSegStart1, const T xSegEnd1, const T ySegEnd1, const T zSegEnd1, ipReal64 &xMinDistPtSeg0, ipReal64 &yMinDistPtSeg0, ipReal64 &zMinDistPtSeg0, ipReal64 &xMinDistPtSeg1, ipReal64 &yMinDistPtSeg1, ipReal64 &zMinDistPtSeg1)
	Euclidian distance between two segments.


IPSDK_FORCEINLINE ipReal64	degToRad (const ipReal64 angle)
	convertion functions between radians and degrees

IPSDK_FORCEINLINE ipReal64	radToDeg (const ipReal64 angle)
	convertion functions between radians and degrees


template<typename T >
IPSDKMATH_API void	eigenDecomposition (const T mXX, const T mXY, const T mXZ, const T mYY, const T mYZ, const T mZZ, T &lambdaMin, T &lambdaInter, T &lambdaMax, T &vMinX, T &vMinY, T &vMinZ, T &vInterX, T &vInterY, T &vInterZ, T &vMaxX, T &vMaxY, T &vMaxZ)
	eigen decomposition of symetric 3x3 matrix $\begin{bmatrix} mXX & mXY & mXZ \\ mXY & mYY & mYZ \\ mXZ & mYZ & mZZ \end{bmatrix}$ On output value are granted such that : More...

template<typename T >
IPSDKMATH_API void	eigenDecomposition (const T mXX, const T mXY, const T mXZ, const T mYY, const T mYZ, const T mZZ, T &lambdaMin, T &lambdaInter, T &lambdaMax, T &chi, T &beta, T &alpha)
	eigen decomposition of symetric 3x3 matrix $\begin{bmatrix} mXX & mXY & mXZ \\ mXY & mYY & mYZ \\ mXZ & mYZ & mZZ \end{bmatrix}$ On output value are granted such that : More...


template<typename ArrayType >
std::vector< ipReal64 >	fromUBlas (const boost::numeric::ublas::vector< ipReal64, ArrayType > &inputVector)
	convert a math Vector from and to an std vector

template<typename ArrayType >
void	fromUBlas (const boost::numeric::ublas::vector< ipReal64, ArrayType > &inputVector, std::vector< ipReal64 > &outputVector)
	convert a math Vector from and to an std vector

IPSDKMATH_API ipsdk::math::Vector	toUBlas (const std::vector< ipReal64 > &inputVector)
	convert a math Vector from and to an std vector

IPSDKMATH_API void	toUBlas (const std::vector< ipReal64 > &inputVector, ipsdk::math::Vector &outputVector)
	convert a math Vector from and to an std vector


template<typename ArrayType >
std::vector< ipReal64 >	fromUBlas (const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType > &inputMatrix)
	convert a math Matrix from and to an std vector

template<typename ArrayType >
void	fromUBlas (const boost::numeric::ublas::matrix< ipReal64, boost::numeric::ublas::row_major, ArrayType > &inputMatrix, std::vector< ipReal64 > &outputVector)
	convert a math Matrix from and to an std vector

IPSDKMATH_API ipsdk::math::Matrix	toUBlas (const std::vector< ipReal64 > &inputVector, const ipUInt32 sizeX, const ipUInt32 sizeY)
	convert a math Matrix from and to an std vector

IPSDKMATH_API void	toUBlas (const std::vector< ipReal64 > &inputVector, ipsdk::math::Matrix &outputMatrix)
	convert a math Matrix from and to an std vector


template<typename IteratorType >
void	extractMinMax (const IteratorType &iterBegin, const IteratorType &iterEnd, typename std::iterator_traits< IteratorType >::value_type &minValue, typename std::iterator_traits< IteratorType >::value_type &maxValue)
	function allowing to compute minimum and maximum value for a collection

template<typename ContainerType >
void	extractMinMax (const ContainerType &coll, typename ContainerType::value_type &minValue, typename ContainerType::value_type &maxValue)
	function allowing to compute minimum and maximum value for a collection

Detailed Description

Namespace agregating IPSDK mathematical routines and classes.

Typedef Documentation

◆ CostFunCreator

typedef CostFunctionPtr(* ipsdk::math::CostFunCreator) (const DataSet &dataSet)

function allowing to initialize a cost function used for non linear processing given a dataset

◆ ExtremaRange

typedef std::pair<ipUInt64, ipUInt64> ipsdk::math::ExtremaRange

index for dilated local extrema

An extrema can span over several contiguous data (ie. a range). It is represented by a pair containing its starting index and its length

Enumeration Type Documentation

◆ eClusteringMessage

enum ipsdk::math::eClusteringMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eClusteringNotDone	Proceed to clustering before use.
eInvalidAccuracyThreshold	Invalid accuracy threshold value f, should be strictly positive.
eInvalidClusterIndex	Invalid cluster index {d} while clustering operation count d clusters.
eInvalidMaxDictionarySize	Invalid maximum dictionary size, should not be null.
eInvalidMinChangeRatio	Invalid minimum change ratio f, should be in [0, 1[.
eInvalidNbClusters	Number of clusters {d} should not be greater than number of input data {d}.
eInvalidPolynomialAlpha	Invalid polynomial kernel alpha value f, should be strictly positive.
eInvalidPolynomialBeta	Invalid polynomial kernel beta value f, should be positive.
eInvalidPolynomialDegree	Invalid polynomial kernel degree f, should be strictly positive.
eInvalidRBFSigma	Invalid sigma value f for radial basis function, should be strictly positive.
eNullNbAttempts	Number of attempts parameter should not be null.
eNullNbClusters	Target number of clusters should not be null.
eNullNbIteration	Number of iterations parameter should not be null.
eValidityIndexTypeNotYetSupported	Clustering validity index s is not yet supported.

◆ eDataPartitionType

enum ipsdk::math::eDataPartitionType

data partition type

Note: This object is associated to a strong enumerate definition

See also: IPSDK_Enum

Enumerator
eDPT_Regular	Regular partition type (each axis is divide with constant bucket size)
eDPT_Adaptive	Adaptive partition type (axis are divide using non constant bucket size with respect to a 'by axis' histogram of population)

◆ eEstimationMessage

enum ipsdk::math::eEstimationMessage

Enumerator
eDataPartitionGenerationFailed	Failed to generate a sub set of data using data partition.
eDataPartitionNotInit	Data partition has not been initialized.
eDataSetAndOutlierFlagsSizeMismatch	Data set collection size d mismatch with outlier flags collection size d.
eEstimationConfigNotInit	Estimation configuration has not been initialized.
eEstimationFailedCantGetResults	Can't get results from a failed estimation.
eEstimationResultsNotInit	Estimation results have not been initialized.
eEstimatorNotInit	Estimator has not been initialized.
eGridPartitionNotEnoughBuckets	Not enough buckets d generated to ensure requested sub sets size d.
eInvalidDataSize	Invalid data size d into data set, expecting data with size d.
eInvalidExpectedOutlierRatio	Invalid expected outlier ratio value f, should be in [0, d[.
eInvalidGaussianSigma	Input gaussian sigma value {f} should be strictly positive.
eInvalidNbEstimParams	Invalid number of estimated parameters d, expecting d number of estimated parameters.
eInvalidOutlierRangeFactor	Input outlier range factor value {f} should be strictly greater than outlier threshold factor {f}.
eInvalidOutlierThresholdFactor	Input outlier threshold factor value {f} should be strictly positive.
eInvalidSubSetSize	Invalid data sub set size d, exepection sub set with size d.
eInvalidSuccessRatio	Invalid success ratio value f, should be in ]0, 1[.
eNonLinearEstimationPassFailed	Non linear estimation pass failed s.
eNotEnoughData	Data set with size d do no contains enough data to ensure processing (needs at least d data)
eNullCostFunSharedPtr	Cost function shared pointer should not be null for estimation.
eNullDataPartitionPtr	Data partition shared pointer should not be null.
eNullDataSize	Data size should not be null.
eNullEstimatorSharedPtr	Estimator shared pointer should not be null for robust estimator initialization.
eNullNbBucketsByAxis	Number of buckets by axis should not be null.
eNullNbEstimParams	Number of estimated parameters should not be null.
eNullNbMinRequestedData	Minimun number of requested data should not be null.
eNullSubSetRequestedSize	Sub set requested size should not be null.
eRegularGridPartitionInvalidRange	Data range [f, f] is not sufficient to ensure regular grid bucket partitioning.
eResidualsFailure	Residuals computation failed while estimation was successful s.
eResidualsSetAndOutlierFlagsSizeMismatch	Residuals set collection size d mismatch with outlier flags collection size d.
eResidualsSizeMismatch	Residuals collection size d mismatch with data set size d.
eRobustEstimationFinalEstimationFailed	Robust estimation final estimation failed s.
eRobustEstimationNoValidScore	Robust estimation failed, no valid estimation score computed, outlier threshold may be to high.
eRobustEstimationNotDone	Robust estimation has not been proceeded, can't retrieve results.
eRobustEstimationNotEnoughData	Not enough data d to ensure robust estimation (need at least d data)
eRobustEstimationNotEnoughtSuccessfulRun	Robust estimation failed after d runs (with d successful runs), while expecting d successful runs.
eRobustEstimatorNotInit	Robust estimator has not been initialized.
eUnsupportedRobustEstimatorType	Robust estimator s is not yet supported.

◆ eRobustEstimationType

enum ipsdk::math::eRobustEstimationType

Enumerator
eRET_NonRobust	Non robust estimation is used.
eRET_LMS	Least Median of square robust estimation.
eRET_RANSAC	RANdom SAmple Consensus robust estimation.
eRET_MSAC	M-estimator SAmple Consensus robust estimation.
eRET_MLESAC	Maximum Likelihood Estimation SAmple Consensus robust estimation.

◆ eTransform2dMessage

enum ipsdk::math::eTransform2dMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eInvalidNbParams	Number of parameters d is not valid for transformation type s, expecting d parameters.
eTransformAlreadyRegistred	Geometric transformation s has already been registred.
eTransformNotRegistred	Geometric transformation s has not been registred.
eTransformationNotInvertible	Transformation cannot be inverted.

◆ eTransform3dMessage

enum ipsdk::math::eTransform3dMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eInvalidNbParams	Number of parameters d is not valid for transformation type s, expecting d parameters.
eTransformAlreadyRegistred	Geometric transformation s has already been registred.
eTransformNotRegistred	Geometric transformation s has not been registred.
eTransformationNotInvertible	Transformation cannot be inverted.

◆ eGraphMessage

enum ipsdk::math::eGraphMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eAlgorithmNotInit	Algorithm has not been initialized.
eAlgorithmNotResolved	Algorithm has not been resolved, can't access associated results.
eInvalidColumnIdx	Column index d is not valid given total number of matrix columns d.
eInvalidRowIdx	Row index d is not valid given total number of matrix rows d.
eNotColumnMajor	Matrix should be column major for munkres processing while input number of rows is d and number of columns is d.
eNullMatrixSize	Matrix size should not be null for munkres algorithm.

◆ eLinearAlgebraMessage

enum ipsdk::math::eLinearAlgebraMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eColMatrixColMatrixSizeMismatch	Matrix col size d mismatch with matrix col size d.
eColMatrixRowMatrixSizeMismatch	Matrix col size d mismatch with matrix row size d.
eColMatrixVectorSizeMismatch	Matrix col size d mismatch with vector size d.
eExpectingSquareMatrix	Algorithm expects a square matrix while matrix size is {d, d}.
eInvalidNbEigenValues	Number of searched eigen values {d} can't be greater than input matrix size {d}.
eMatrixMatrixSizeMismatch	Matrix size {d, d} mismatch with matrix size {d, d}.
eOneRankDeficientSystemExpected	Expecting at least a one rank deficient linear system while d equations for d variables on input.
eOverConstrainSystemExpected	Invalid input matrix size {d, d}, expecting over constrained system.
eRowMatrixColMatrixSizeMismatch	Matrix row size d mismatch with matrix col size d.
eRowMatrixRowMatrixSizeMismatch	Matrix row size d mismatch with matrix row size d.
eRowMatrixVectorSizeMismatch	Matrix row size d mismatch with vector size d.
eUnknownLaPackError	LaPack repport an error during execution.
eVectorMatrixSizeMismatch	Input vector size d mismatch with output matrix global size d (sx=d, sy=d)

◆ eIPSDKMathMessage

enum ipsdk::math::eIPSDKMathMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eNullLineDirection	Invalid line direction, should not be null.
eObjectNotInit	Object has not been initialized, can't use it.
eUnSupportedEntity	Geometric processing doesn't support entity.
eThomsonNbPointsOutOfRange	Number of points passed as argument is out of range (should be between 1 and 400)

◆ eOptimizationMessage

enum ipsdk::math::eOptimizationMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eCostFunNotInit	Cost function has not been initialized.
eInvalidJacobianSize	Invalid input jacobian matrix size {d, d}, while expecting d parameters and d equations.
eInvalidNbEquations	Input equations vector with size d is invalid regards to expected number of equations s.
eInvalidNbParameters	Input parameter vector with size d is invalid regards to expected number of parameters s.
eNonLinearSolverNotSolved	Non linear solver has not been successfully executed.
eNullCostFunction	Input cost function shared pointer should not be null.
eNullNbEquations	Number of equations should not be null.
eNullNbParameters	Number of parameters should not be null.
eOptStatus0	Improper input parameters.
eOptStatus1	Algorithm estimates that the relative error in the sum of squares is at most tol.
eOptStatus2	Algorithm estimates that the relative error between x and the solution is at most tol.
eOptStatus3	Algorithm estimates that the relative error in the sum of squares and between x and the solution is at most tol.
eOptStatus4_1	Null residuals on last iteration.
eOptStatus4_2	Fvec is orthogonal to the columns of the jacobian to machine precision.
eOptStatus5	Number of calls to fcn has reached or exceeded max number of iterations.
eOptStatus6	Tol is too small. no further reduction in the sum of squares is possible.
eOptStatus7	Tol is too small. no further improvement in the approximate solution x is possible.
eOptStatusM2	Function evaluation failed with following reason s.
eOptStatusM3	Jacobian evaluation failed with following reason s.
eOptStatusM4	Unexpected input parameters for minpack function wrapper.
eOptStatusOther	Algorithm ended for an unknown reason.

◆ eOptStatus

enum ipsdk::math::eOptStatus

Enumerator
eOS_Succeeded	Optimization has been successfully executed.
eOS_Warn	Optimization has been executed with warnings.
eOS_Failed	No successful optimization has been executed.

◆ eTopHat1DExtremumType

enum ipsdk::math::eTopHat1DExtremumType

Enumerate describing the extremum type to take into account for a 1D top-hat calculation.

Note: This object is associated to a strong enumerate definition

See also: IPSDK_Enum

Enumerator
eTH1DET_Center	Use the center element of the area detected by the top-hay.
eTH1DET_Begin	Use the first element of the area detected by the top-hay.
eTH1DET_End	Use the last element of the area detected by the top-hay.
eTH1DET_Extremum	Take into account the local extrema.

◆ eExtremaType

enum ipsdk::math::eExtremaType

Enumerate allowing to define an extrema type.

Note: This object is associated to a strong enumerate definition

See also: IPSDK_Enum

Enumerator
eET_Minima	Minima extrema.
eET_Maxima	Maxima extrema.

◆ eExtremaBorderPolicy

enum ipsdk::math::eExtremaBorderPolicy

Enumerate allowing to describe border policy used during extrema extraction processing.

Note: This object is associated to a strong enumerate definition

See also: IPSDK_Enum

Enumerator
eEBP_Keeped	Extremal border values are keeped on output.
eEBP_Skipped	Extremal border values are skipped on output.
eEBP_MakeRing	Input data are considered as a ring collection Last and first elements are proceeded as adjacent data (for example this can be the case on angular values)

◆ eHistogramOutOfBoundsPolicy

enum ipsdk::math::eHistogramOutOfBoundsPolicy

enumerate use to describe histogram policy used to process out of bounds data

Note: This object is associated to a strong enumerate definition

See also: IPSDK_Enum

Enumerator
eHOOBP_Ignored	Data with values not in [firstHistoValue, lastHistoValue] are ignored.
eHOOBP_Nearest	Data with values :
eHOOBP_Dedicated	lower than firstHistoValue are aggregated with value firstHistoValue- greater than lastHistoValue are aggregated with value lastHistoValue Data with values :
eHOOBP_DedicatedUpper	lower than firstHistoValue are aggregated to a dedicated first bin- greater than lastHistoValue are aggregated to a dedicated last bin Data with values :

◆ eStatisticsMessage

enum ipsdk::math::eStatisticsMessage

Enumerate describing messages.

Note: This enumerate is associated to a message map

See also: IPSDK_Message_Map

Enumerator
eCollSizeMismatch	Input collections size should be the same (first collection size is d while second collection size is d)
eFailedToExportHistogram	Failed to export histogram to file s.
eGaussianCurveInvalidEstimation	Gaussian curve estimation leads to an invalid solution for estimated parameters.
eGaussianCurveInvalidMatrixRank	Invalid matrix rank d for gaussian curve estimation, expecting a full matrix rank [d].
eHistogramBoundsGlobalPolicyNotYetSuported	Histogram global bounds policy s is not yet supported.
eHistogramInvalidBinIndex	Histogram bin index d is not valid for histogram with d bins.
eHistogramInvalidClassIndex	Histogram class index d is not valid for histogram with d classes.
eHistogramInvalidQuantileValue	Invalid quantile value f, should be in [0, 1].
eHistogramNotInit	Histogram class has not been initialized.
eHistogramPopulationSizeMismatch	Histogram population with expected size d mismatch from provided collection size d.
eInvalidDilateFactor	Dilate factor should be positive.
eInvalidHistogramBinWidth	Histogram bin width f should be greater than zero.
eInvalidHistogramBounds	First histogram value f should be greater than last one f.
eInvalidHistogramNbClasses	Histogram number of classes should not be null.
eInvalidHistogramNbClusters	Number of clusters {d} should not be greater than number of used histogram bins {d}.

◆ eToolsMessage

enum ipsdk::math::eToolsMessage

Enumerator
ePolynomial2dSurfaceUndefined	Polynomial 2d surface is not well defined by input data, can't estimate it.

Function Documentation

◆ createRobustEstimator()

IPSDKMATH_API RobustEstimatorPtr ipsdk::math::createRobustEstimator	(	const EstimationConfig &	config,
		const EstimatorPtr &	pEstimator
	)

function allowing to create and initialize a robust estimator

Exceptions

ipsdk::math::IPSDKMathException	if pEstimator.get() == 0 \|\| pEstimator->isInit() == false
ipsdk::math::IPSDKMathException	if config.isInit() == false

◆ extractInliers()

IPSDKMATH_API DataSet ipsdk::math::extractInliers	(	const DataSet &	fullDataSet,
		const OutlierFlags &	outlierFlags
	)

function allowing to extract an inlier sub data set from a complete data set and a collection of outlier flags

Exceptions

ipsdk::math::IPSDKMathException if fullDataSet.size() != outlierFlags.size()

◆ polarToXCartesian()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE TOut ipsdk::math::polarToXCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta
	)

polar to cartesian convertion

For more informations report to Points and vectors 2d representation

◆ polarToYCartesian()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE TOut ipsdk::math::polarToYCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta
	)

polar to cartesian convertion

For more informations report to Points and vectors 2d representation

◆ polarToCartesian() [1/2]

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE void ipsdk::math::polarToCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta,
		TOut &	x,
		TOut &	y
	)

polar to cartesian convertion

For more informations report to Points and vectors 2d representation

◆ polarToCartesian() [2/2]

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE void ipsdk::math::polarToCartesian	(	const TIn	rho,
		const TIn	theta,
		TOut &	x,
		TOut &	y
	)

polar to cartesian convertion

For more informations report to Points and vectors 2d representation

◆ cartesianToPolar()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE void ipsdk::math::cartesianToPolar	(	const TIn	x,
		const TIn	y,
		TOut &	rho,
		TOut &	theta
	)

cartesian to polar convertion

For more informations report to Points and vectors 2d representation

◆ angleToMatrix() [1/3]

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::angleToMatrix	(	const T	cosTheta,
		const T	sinTheta,
		T &	rxx,
		T &	rxy,
		T &	ryx,
		T &	ryy
	)

Convertion from angle to rotation matrix.

For more informations report to Rotations 2d

◆ angleToMatrix() [2/3]

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::angleToMatrix	(	const T	theta,
		T &	rxx,
		T &	rxy,
		T &	ryx,
		T &	ryy
	)

Convertion from angle to rotation matrix.

For more informations report to Rotations 2d

◆ angleToMatrix() [3/3]

IPSDK_FORCEINLINE Matrix2d ipsdk::math::angleToMatrix ( const ipReal64 theta )

Convertion from angle to rotation matrix.

For more informations report to Rotations 2d

◆ matrixToAngle() [1/3]

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::matrixToAngle	(	const T	rxx,
		const T	rxy,
		T &	theta
	)

Convertion from rotation matrix to angle.

Note: On ouput theta belongs to interval ]-Pi, Pi]

For more informations report to Rotations 2d

◆ matrixToAngle() [2/3]

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::matrixToAngle	(	const T	rxx,
		const T	rxy,
		const T	ryx,
		const T	ryy,
		T &	theta
	)

Convertion from rotation matrix to angle.

Note: On ouput theta belongs to interval ]-Pi, Pi]

For more informations report to Rotations 2d

◆ matrixToAngle() [3/3]

IPSDK_FORCEINLINE ipReal64 ipsdk::math::matrixToAngle ( const Matrix2d & matRot )

Convertion from rotation matrix to angle.

Note: On ouput theta belongs to interval ]-Pi, Pi]

For more informations report to Rotations 2d

◆ rotate2d() [1/2]

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::rotate2d	(	const T	xIn,
		const T	yIn,
		const ipReal64	cosTheta,
		const ipReal64	sinTheta,
		T &	xOut,
		T &	yOut
	)

rotation of a point using a rotation angle (rotation around origin)

For more informations report to Rotations 2d

◆ rotate2dInSitu()

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::rotate2dInSitu	(	const ipReal64	cosTheta,
		const ipReal64	sinTheta,
		T &	x,
		T &	y
	)

rotation of a point using a rotation angle (rotation around origin)

For more informations report to Rotations 2d

◆ rotate2d() [2/2]

template<typename T >

IPSDK_FORCEINLINE void ipsdk::math::rotate2d	(	const T	xIn,
		const T	yIn,
		const ipReal64	theta,
		T &	xOut,
		T &	yOut
	)

rotation of a point using a rotation angle (rotation around origin)

For more informations report to Rotations 2d

◆ circleFromPoints()

IPSDKMATH_API bool ipsdk::math::circleFromPoints	(	const ipReal64	x0,
		const ipReal64	y0,
		const ipReal64	x1,
		const ipReal64	y1,
		const ipReal64	x2,
		const ipReal64	y2,
		ipReal64 &	xc,
		ipReal64 &	yc,
		ipReal64 &	radius
	)

computation of circle parameters from three points

Returns: false if points are aligned

◆ convertEllipseFromQuadratic()

IPSDKMATH_API bool ipsdk::math::convertEllipseFromQuadratic	(	const ipReal64	a11,
		const ipReal64	a12,
		const ipReal64	a22,
		const ipReal64	b1,
		const ipReal64	b2,
		const ipReal64	c,
		ipReal64 &	cx,
		ipReal64 &	cy,
		ipReal64 &	theta,
		ipReal64 &	a,
		ipReal64 &	b
	)

function allowing to convert from quadratic to standard representation of ellipse

Given a quadratic representation of ellipse given by equation $a_{11}x^2+2a_{12}xy+a_{22}y^2+b_{1}x+b_{2}y+c = 0$ , function computes standard ellipse parameters used in matrix equation $(X-C)^tRDR^t(X-C)=0$ . With :

$X=\left(\begin{matrix}x\\y\end{matrix}\right)$
$C=\left(\begin{matrix}c_x\\c_y\end{matrix}\right)$ ellipse center coordinates
a rotation matrix defined by angle $\theta$ which give the orientation of ellipse major axis (with $\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]$ ) See Rotations 2d for more informations on 2d orientations
$D=\left(\begin{matrix}\frac{1}{a^2} 0\\0 \frac{1}{b^2}\end{matrix}\right)$ given ( and respectivelly semimajor and semiminor axis of the ellipse
Returns
false if input quadratic parameters do not correspond to an ellipse (quadratic equation only match an ellipse if $a_{11}a_{22}-a_{12}^2>0$ )

◆ convertEllipseToQuadratic()

IPSDKMATH_API bool ipsdk::math::convertEllipseToQuadratic	(	const ipReal64	cx,
		const ipReal64	cy,
		const ipReal64	theta,
		const ipReal64	a,
		const ipReal64	b,
		ipReal64 &	a11,
		ipReal64 &	a12,
		ipReal64 &	a22,
		ipReal64 &	b1,
		ipReal64 &	b2,
		ipReal64 &	c
	)

function allowing to convert from standard to quadratic representation of ellipse

Given a standard ellipse parameters used in matrix equation $(X-C)^tRDR^t(X-C)=0$ . With :

$X=\left(\begin{matrix}x\\y\end{matrix}\right)$
$C=\left(\begin{matrix}c_x\\c_y\end{matrix}\right)$ ellipse center coordinates
a rotation matrix defined by angle $\theta$ which give the orientation of ellipse major axis (with $\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]$ ) See Rotations 2d for more informations on 2d orientations
$D=\left(\begin{matrix}\frac{1}{a^2} 0\\0 \frac{1}{b^2}\end{matrix}\right)$ given ( and respectivelly semimajor and semiminor axis of the ellipse

Function computes a quadratic representation of ellipse given by equation $a_{11}x^2+2a_{12}xy+a_{22}y^2+b_{1}x+b_{2}y+c = 0$

Returns: false if input standard parameters do not correspond to an ellipse (ie if or if )

◆ ellipsePerimeterLowerBound()

IPSDKMATH_API ipReal64 ipsdk::math::ellipsePerimeterLowerBound	(	const ipReal64	a,
		const ipReal64	b
	)

function allowing to compute lower bound value for an ellipse perimeter

Ellipse perimeter lower bound is given by $4\sqrt{a^2+b^2}$

See also: https://en.wikipedia.org/wiki/Ellipse

◆ ellipsePerimeterUpperBound()

IPSDKMATH_API ipReal64 ipsdk::math::ellipsePerimeterUpperBound	(	const ipReal64	a,
		const ipReal64	b
	)

function allowing to compute upper bound value for an ellipse perimeter

Ellipse perimeter upper bound is given by $\pi\sqrt{2(a^2+b^2)}$

Note: This value can also be used as an approximate value for ellipse perimeter

See also: https://en.wikipedia.org/wiki/Ellipse

◆ ellipseArea()

IPSDKMATH_API ipReal64 ipsdk::math::ellipseArea	(	const ipReal64	a,
		const ipReal64	b
	)

function allowing to compute ellipse area

Ellipse area is given by $\pi a b$

◆ ellipseExcentricity()

IPSDKMATH_API ipReal64 ipsdk::math::ellipseExcentricity	(	const ipReal64	a,
		const ipReal64	b
	)

function allowing to compute ellipse excentricity

Ellipse excentricity is given by $\frac{\sqrt{A^2-B^2}}{A}$ with $A=max(a, b)$ and $C=min(a, b)$

Returns: 0 if

◆ equivalentEllipse()

IPSDKMATH_API bool ipsdk::math::equivalentEllipse	(	const ipReal64	perimeter,
		const ipReal64	area,
		ipReal64 &	a,
		ipReal64 &	b
	)

function allowing to compute equivalent ellipse for a given perimeter and area

Returns: false in case of failure

◆ ellipseRadius() [1/2]

IPSDKMATH_API ipReal64 ipsdk::math::ellipseRadius	(	const ipReal64	a,
		const ipReal64	b,
		const ipReal64	phi
	)

function allowing to compute axis aligned ellipse 'radius' for a given angle phi

Returns: 0 if a<=0 || b<=0

◆ ellipseRadius() [2/2]

IPSDKMATH_API ipReal64 ipsdk::math::ellipseRadius	(	const ipReal64	a,
		const ipReal64	b,
		const ipReal64	ellipseOrient,
		const ipReal64	theta
	)

function allowing to compute ellipse 'radius' for a given angle

Returns: 0 if a<=0 || b<=0

◆ lineFromPoints()

IPSDKMATH_API bool ipsdk::math::lineFromPoints	(	const ipReal64	x0,
		const ipReal64	y0,
		const ipReal64	x1,
		const ipReal64	y1,
		ipReal64 &	rho,
		ipReal64 &	theta
	)

computation of line parameters from two points

Returns: false if points are equal

◆ sphericalToXCartesian()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE TOut ipsdk::math::sphericalToXCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta,
		const TIn	cosPhi,
		const TIn	sinPhi
	)

spherical to cartesian convertion

For more informations report to Points and vectors 3d representation

◆ sphericalToYCartesian()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE TOut ipsdk::math::sphericalToYCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta,
		const TIn	cosPhi,
		const TIn	sinPhi
	)

spherical to cartesian convertion

For more informations report to Points and vectors 3d representation

◆ sphericalToZCartesian()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE TOut ipsdk::math::sphericalToZCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta,
		const TIn	cosPhi,
		const TIn	sinPhi
	)

spherical to cartesian convertion

For more informations report to Points and vectors 3d representation

◆ sphericalToCartesian() [1/2]

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE void ipsdk::math::sphericalToCartesian	(	const TIn	rho,
		const TIn	cosTheta,
		const TIn	sinTheta,
		const TIn	cosPhi,
		const TIn	sinPhi,
		TOut &	x,
		TOut &	y,
		TOut &	z
	)

spherical to cartesian convertion

For more informations report to Points and vectors 3d representation

◆ sphericalToCartesian() [2/2]

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE void ipsdk::math::sphericalToCartesian	(	const TIn	rho,
		const TIn	theta,
		const TIn	phi,
		TOut &	x,
		TOut &	y,
		TOut &	z
	)

spherical to cartesian convertion

For more informations report to Points and vectors 3d representation

◆ cartesianToSpherical()

template<typename TOut , typename TIn >

IPSDK_FORCEINLINE void ipsdk::math::cartesianToSpherical	(	const TIn	x,
		const TIn	y,
		const TIn	z,
		TOut &	rho,
		TOut &	theta,
		TOut &	phi
	)

cartesian to spherical convertion

For more informations report to Points and vectors 3d representation