Common statistical functions. More...

Functions
static Type	milx::Math< Type >::Centroid (const vnl_vector< Type > &data)
	Compute the centroid (or the mean) of a data vector. More...

static vnl_vector< Type >	milx::Math< Type >::Centroid (const vnl_matrix< Type > &data)
	Compute the centroid (or the mean vector) of a data matrix. More...

static Type	milx::Math< Type >::CentroidSize (const vnl_matrix< Type > &data, const vnl_vector< Type > &centroid, bool norm=false)
	Compute the centroid size or scale for a series of points. More...

static vnl_vector< Type >	milx::Math< Type >::Centroid (vtkPoints *points)
	Compute the centroid (or the mean vector) of a data matrix. More...

static Type	milx::Math< Type >::CentroidSize (vtkPoints *points, const vnl_vector< Type > &centroid, bool norm=false)
	Compute the centroid size or scale for a series of points. More...

static vnl_matrix< Type >	milx::Math< Type >::CovarianceMatrix (vnl_vector< Type > sourceVector)
	Compute the covariance matrix from a vector. EXPERIMENTAL. More...

static vnl_matrix< Type >	milx::Math< Type >::CovarianceMatrix (vnl_vector< Type > sourceVector, vnl_vector< Type > targetVector)
	Compute the covariance matrix between two vectors. EXPERIMENTAL. More...

static vnl_matrix< Type >	milx::Math< Type >::CovarianceMatrix (const vnl_matrix< Type > &data, const vnl_vector< Type > &centroid)
	Compute the covariance matrix from a datamatrix. More...

static vnl_matrix< Type >	milx::Math< Type >::CovarianceMatrix (const vnl_matrix< Type > &data)
	Compute the covariance matrix from a datamatrix. More...

static vnl_matrix< Type >	milx::Math< Type >::CovarianceMatrix (vtkPoints *points, const vnl_vector< Type > &centroid)
	Compute the covariance matrix from a datamatrix. More...

static Type	milx::Math< Type >::MahalanobisDistance (const vnl_vector< Type > &source, const vnl_vector< Type > &target)
	Compute the Mahalanobis distance between two vectors with an unknown covariance matrix. EXPERIMENTAL. More...

static Type	milx::Math< Type >::MahalanobisDistance (const vnl_vector< Type > &target, const vnl_vector< Type > &mean, const vnl_matrix< Type > &invCovMatrix)
	Compute the Mahalanobis distance of a vector to a population. EXPERIMENTAL. More...

static Type	milx::Math< Type >::MahalanobisDistance (const vnl_vector< Type > &target, const vnl_vector< Type > &mean, const vnl_matrix< Type > &covMatrix, vnl_matrix< Type > &invCovMatrix)
	Compute the Mahalanobis distance of a vector to a population. EXPERIMENTAL. More...

Detailed Description

Common statistical functions.

Function Documentation

◆ Centroid() [1/3]

template<class Type >

Type milx::Math< Type >::Centroid ( const vnl_vector< Type > & data )

static

Compute the centroid (or the mean) of a data vector.

Sum

then average

Definition at line 177 of file milxMath.h.

◆ Centroid() [2/3]

template<class Type >

vnl_vector< Type > milx::Math< Type >::Centroid ( const vnl_matrix< Type > & data )

static

Compute the centroid (or the mean vector) of a data matrix.

Assumes that the rows contain the observations and the columns contain the variables

Sum

then average

Definition at line 190 of file milxMath.h.

◆ Centroid() [3/3]

template<class Type >

vnl_vector< Type > milx::Math< Type >::Centroid ( vtkPoints * points )

static

Compute the centroid (or the mean vector) of a data matrix.

Assumes that the data matrix rows contain the observations and the columns contain the variables Overloaded for points, which are common in vtkPolyData

Sum

then average

Definition at line 227 of file milxMath.h.

◆ CentroidSize() [1/2]

template<class Type >

Type milx::Math< Type >::CentroidSize	(	const vnl_matrix< Type > &	data,
		const vnl_vector< Type > &	centroid,
		bool	norm = `false`
	)

static

Compute the centroid size or scale for a series of points.

norm allows the scale to be average scale per point

Accumulate the squared distance from centroid

Norm and return

Definition at line 206 of file milxMath.h.

◆ CentroidSize() [2/2]

template<class Type >

Type milx::Math< Type >::CentroidSize	(	vtkPoints *	points,
		const vnl_vector< Type > &	centroid,
		bool	norm = `false`
	)

static

Compute the centroid size or scale for a series of points.

Overloaded for points, which are common in vtkPolyData norm allows the scale to be average scale per point

Accumulate the squared distance from centroid

Norm and return

Definition at line 244 of file milxMath.h.

◆ CovarianceMatrix() [1/5]

template<class Type >

vnl_matrix< Type > milx::Math< Type >::CovarianceMatrix ( vnl_vector< Type > sourceVector )

static

Compute the covariance matrix from a vector. EXPERIMENTAL.

Use with caution, this member computes the inter-component covariance matrix for the given vector

take outer product and add to matrix

Definition at line 310 of file milxMath.h.

◆ CovarianceMatrix() [2/5]

template<class Type >

vnl_matrix< Type > milx::Math< Type >::CovarianceMatrix	(	vnl_vector< Type >	sourceVector,
		vnl_vector< Type >	targetVector
	)

static

Compute the covariance matrix between two vectors. EXPERIMENTAL.

Use with caution, this member computes the inter-component covariance matrix for the given vectors

take outer product and add to matrix

Definition at line 323 of file milxMath.h.

◆ CovarianceMatrix() [3/5]

template<class Type >

vnl_matrix< Type > milx::Math< Type >::CovarianceMatrix	(	const vnl_matrix< Type > &	data,
		const vnl_vector< Type > &	centroid
	)

static

Compute the covariance matrix from a datamatrix.

Assumes that the data matrix rows contain the observations and the columns contain the variables. Centroid is removed from each row. The result is a nxn matrix where n is the number of variables The diagonal should contain the variances of the variables

Subtract centroid

take outer product and add to matrix

Definition at line 343 of file milxMath.h.

◆ CovarianceMatrix() [4/5]

template<class Type >

vnl_matrix< Type > milx::Math< Type >::CovarianceMatrix ( const vnl_matrix< Type > & data )

static

Compute the covariance matrix from a datamatrix.

Assumes that the data matrix rows contain the observations and the columns contain the variables. Centroid is assumed to have removed already. The result is a nxn matrix where n is the number of variables The diagonal should contain the variances of the variables

take outer product and add to matrix

Definition at line 371 of file milxMath.h.

◆ CovarianceMatrix() [5/5]

template<class Type >

vnl_matrix< Type > milx::Math< Type >::CovarianceMatrix	(	vtkPoints *	points,
		const vnl_vector< Type > &	centroid
	)

static

Compute the covariance matrix from a datamatrix.

Assumes that the data matrix rows contain the observations and the columns contain the variables. Centroid is removed from each row. The result is a nxn matrix where n is the number of variables The diagonal should contain the variances of the variables Overloaded for points, which are common in vtkPolyData

Subtract centroid

take outer product and add to matrix

Definition at line 393 of file milxMath.h.

◆ MahalanobisDistance() [1/3]

template<class Type >

Type milx::Math< Type >::MahalanobisDistance	(	const vnl_vector< Type > &	source,
		const vnl_vector< Type > &	target
	)

static

Compute the Mahalanobis distance between two vectors with an unknown covariance matrix. EXPERIMENTAL.

Mahalanobis distance takes into account the covariance between vectors in estimating the separation between them. Returns squared distance. This version assumes you do not know the covariance matrix, so an approximate one is constructed for matching purposes Vectors should be of the same length

Type 1 Computation (row wise)

Type 3 (column wise)

Type 4 (Cov Mat is 1x1)

Type 5

Type 6

Type 7

Definition at line 423 of file milxMath.h.

◆ MahalanobisDistance() [2/3]

template<class Type >

Type milx::Math< Type >::MahalanobisDistance	(	const vnl_vector< Type > &	target,
		const vnl_vector< Type > &	mean,
		const vnl_matrix< Type > &	invCovMatrix
	)

static

Compute the Mahalanobis distance of a vector to a population. EXPERIMENTAL.

Mahalanobis distance takes into account the covariance between the population and the vector in estimating the separation between them, so its more robust to outlyers. Returns squared distance. This version assumes you know the inverse covariance matrix of a population. The result of this member depends solely on the order of your covariance matrix

Definition at line 510 of file milxMath.h.

◆ MahalanobisDistance() [3/3]

template<class Type >

Type milx::Math< Type >::MahalanobisDistance	(	const vnl_vector< Type > &	target,
		const vnl_vector< Type > &	mean,
		const vnl_matrix< Type > &	covMatrix,
		vnl_matrix< Type > &	invCovMatrix
	)

static

Compute the Mahalanobis distance of a vector to a population. EXPERIMENTAL.

Mahalanobis distance takes into account the covariance between the population and the vector in estimating the separation between them, so its more robust to outlyers. Returns squared distance. This version assumes you know the covariance matrix of a population and the inverse covariance matrix is assigned to invCovMatrix The result of this member depends solely on the order of your covariance matrix

Definition at line 530 of file milxMath.h.

Functions

Detailed Description

Function Documentation

◆ Centroid() [1/3]

◆ Centroid() [2/3]

◆ Centroid() [3/3]

◆ CentroidSize() [1/2]

◆ CentroidSize() [2/2]

◆ CovarianceMatrix() [1/5]

◆ CovarianceMatrix() [2/5]

◆ CovarianceMatrix() [3/5]

◆ CovarianceMatrix() [4/5]

◆ CovarianceMatrix() [5/5]

◆ MahalanobisDistance() [1/3]

◆ MahalanobisDistance() [2/3]

◆ MahalanobisDistance() [3/3]