This module contains procedures and routines for finding the minimum-volume bounding ellipsoid partitioning of a given set of points by minimizing the volumes of the ellipsoids and comparing them against their parents. Monday 2:37 am, March 28, 2021, Dallas, TX Saturday 00:37 am, March 13, 2021, Dallas, TX Saturday 02:37 am, May 31, 2021, Dallas, TX Tuesday 2:13 am, March 10, 2021, Dallas, TX. More...

Data Types
type	KmeansTry_type

type	KvolTry_type

interface	partition_type
	The `partition_type` class. Partitions an input array `Point(nd,np)` with `nd` attributes and `np` observations (points). More...

type	ParTry_type

Functions/Subroutines
function	partition_typer (Point, nc, nt, nsim, nemax, minSize, stanEnabled, trimEnabled, kmeansRelTol, logExpansion, logShrinkage if MINVOL_ENABLED
	This function can serve as the constructor for `partition_type` while also performing the partitioning for the first time. Construct a hierarchical partitioning of the input `Point` using a combination of Kmeans, Kvolume, and density maximization algorithms. More...

subroutine	runPartition (Partition, Point, parentLogVolNormed)
	This procedure is a method of the class partition_type. Perform recursive clustering of the input `Point(nd,np)`. More...

PURE real(RK) function	getLogLikeFitness (count, logVolRatio)

real(RK) function, dimension(npmin:npmax)	getBiasCorrectionScaleFactorSq (nd, npmin, npmax)

subroutine	writePartition (Partition, fileUnit, Point)

Variables
character(*, SK), parameter	MODULE_NAME = "@pm_clusDensity"

real(RK), parameter	POSINF = +huge(0._RK) / 10

real(RK), parameter	NEGINF = -huge(0._RK) / 10

Detailed Description

This module contains procedures and routines for finding the minimum-volume bounding ellipsoid partitioning of a given set of points by minimizing the volumes of the ellipsoids and comparing them against their parents. Monday 2:37 am, March 28, 2021, Dallas, TX Saturday 00:37 am, March 13, 2021, Dallas, TX Saturday 02:37 am, May 31, 2021, Dallas, TX Tuesday 2:13 am, March 10, 2021, Dallas, TX.

Function/Subroutine Documentation

◆ getBiasCorrectionScaleFactorSq()

real(RK) function, dimension(npmin:npmax) pm_clusDensity::getBiasCorrectionScaleFactorSq	(	integer(IK), intent(in)	nd,
		integer(IK), intent(in)	npmin,
		integer(IK), intent(in)	npmax
	)

Warning: This function

Definition at line 928 of file pm_clusDensity.F90.

Referenced by pm_clusDensity::partition_type::partition_typer().

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◆ getLogLikeFitness()

PURE real(RK) function pm_clusDensity::getLogLikeFitness	(	integer(IK), intent(in)	count,
		real(RK)	logVolRatio
	)

Definition at line 907 of file pm_clusDensity.F90.

◆ partition_typer()

function pm_clusDensity::partition_typer	(	real(RK)	Point,
		integer(IK), intent(in), optional	nc,
		integer(IK), intent(in), optional	nt,
		integer(IK), intent(in), optional	nsim,
		integer(IK), intent(in), optional	nemax,
		integer(IK)	minSize,
		logical(LK)	stanEnabled,
		logical(LK)	trimEnabled,
		real(RK)	kmeansRelTol,
		real(RK)	logExpansion,
		real(RK)	logShrinkage,
			if,
			MINVOL_ENABLED
	)

This function can serve as the constructor for partition_type while also performing the partitioning for the first time. Construct a hierarchical partitioning of the input Point using a combination of Kmeans, Kvolume, and density maximization algorithms.

Parameters

[in]	Point	: An array of size `(nd = #dimensions, np = #observations)` containing the input set of points to partition.
[in]	nc	: The number of clusters at each level of partitioning (optional, default = `2`).
[in]	nt	: The number of Kmeans clustering tries before choosing the optimal clustering among all (optional, default = `1`).
[in]	nsim	: The number of Monte Carlo simulation tries to estimate the sum of volumes of partitions excluding overlaps (optional, default = `0`).
[in]	nemax	: The maximum number of partitions to be expected or identified in the input `Point` (optional, default = `max(nc, 1 + np / (nd + 1))`).
[in]	minSize	: The minimum allowed size of a partition, that is, the minimum allowed number of points in a partition (optional, default = `0`).
[in]	stanEnabled	: A logical value, indicating weather `Point` should be standardized prior to each Kmeans clustering (optional, default = `.true.`).
[in]	trimEnabled	: A logical value, indicating weather all allocatable components have been trimmed to the minimum size (optional, default = `.false.`).
[in]	kmeansRelTol	: The relative tolerance below which the Kmeans clustering is assumed to have converged (optional, default = `1.e-4`).
[in]	logExpansion	: The factor by which the expected volumes of the bounding ellipsoids are enlarged before any comparisons are made for further sub-partitioning (optional, default = `0.`).
[in]	logShrinkage	: The logarithm of the factor by which the sum of the volumes of the children bounds must be smaller than their parents to warrant further sub-partitioning (optional, default = `0.`).
[in]	inclusionFraction	: The fraction of non-member points that are inside the partition, to be used in estimating of the true volumes of the partitions (optional, default = `1.`).
[in]	parentLogVolNormed	: The logarithm of the volume of the input set of points normalized to the volume of the unit `nd`-ball (optional, default = `-infinity`).
[in]	mahalSqWeightExponent	: The exponent with which the density of the partitions are exponentiated to be used as the Mahalanobis distance weights (optional, default = `0.`).
[in]	kmeansNumFailMax	: The maximum number of times Kmeans clustering is allowed to fail (optional, default = `10`).
[in]	kmeansNumRecursionMax	: The maximum number of times Kmeans clustering is allowed to refine the cluster centers via the algorithm of Lloyd (optional, default = `300`).
[in]	kvolumeNumRecursionMax	: The maximum number of times Kvolume algorithm is run to minimize the partition volumes at a given partitioning level (optional, default = `3`).

Warning: On output, Point will be reordered.; When trimEnabled = .false., only the first 1:ne elements of all allocatable arrays contain meaningful information. As such, the rest of the trailing elements must be properly ignored when using the allocatable Partition components. For example, upon exit, only PartitionLogVolNormed(1 : Partitionne) contain meaningful information.; When trimEnabled = .true., all allocatable arrays will be trimmed from size nemax to the size ne. In such a case, calling the method Partitiontun() after constructing the Partition object for the first time will likely lead to segmentation fault error.

Remarks: When nsim = 0, the effective sum of volumes will be computed and used assuming that no partitions overlap. This is essentially equivalent to summing over all partition volumes.; If no input value if provided for parentLogVolNormed, both parentLogVolNormed and pointLogVolNormed will (must) be set to NEGINF.

Author:: Amir Shahmoradi, April 03, 2017, 2:16 AM, ICES, University of Texas at Austin

Definition at line 220 of file pm_clusDensity.F90.

◆ runPartition()

subroutine pm_clusDensity::runPartition	(	class(partition_type)	Partition,
		real(RK)	Point,
		real(RK)	parentLogVolNormed
	)

This procedure is a method of the class partition_type. Perform recursive clustering of the input Point(nd,np).

Parameters

[in,out]	Partition	: An object of class partition_type that contains the partitioning configuration on input and the partition on output.
[in,out]	Point	: An array of size `(nd,np)` containing the input set of points to partition.

Warning: On input, nemax must be always larger than or equal to nc.; On output, Point will be reordered.

Definition at line 360 of file pm_clusDensity.F90.

◆ writePartition()

subroutine pm_clusDensity::writePartition	(	class(partition_type)	Partition,
		integer(IK)	fileUnit,
		real(RK)	Point
	)

Definition at line 978 of file pm_clusDensity.F90.

Variable Documentation

◆ MODULE_NAME

character(*, SK), parameter pm_clusDensity::MODULE_NAME = "@pm_clusDensity"

Definition at line 70 of file pm_clusDensity.F90.

◆ NEGINF

real(RK), parameter pm_clusDensity::NEGINF = -huge(0._RK) / 10

Definition at line 72 of file pm_clusDensity.F90.

◆ POSINF

real(RK), parameter pm_clusDensity::POSINF = +huge(0._RK) / 10

Definition at line 71 of file pm_clusDensity.F90.

Data Types

Functions/Subroutines

Variables