CDPL.Math.FKabschAlgorithm Class Reference

Implementation of the Kabsch algorithm [KABA]. More...

Inheritance diagram for CDPL.Math.FKabschAlgorithm:

Public Member Functions
None	__init__ ()
	Contructs the FKabschAlgorithm instance.
None	__init__ (FKabschAlgorithm algo)
	Contructs a copy of the FKabschAlgorithm instance algo. More...
int	getObjectID ()
	Returns the numeric identifier (ID) of the wrapped C++ class instance. More...
FKabschAlgorithm	assign (FKabschAlgorithm algo)
	Replaces the current state with a copy of the state of the FKabschAlgorithm instance algo. More...
FMatrix	getTransform ()
	Returns the rigid-body transformation produced by the most recent successful align() call. More...
bool	align (ConstFMatrixExpression points, ConstFMatrixExpression ref_points, bool do_center=True, int max_svd_iter=0)
	Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD. More...
bool	align (ConstDMatrixExpression points, ConstDMatrixExpression ref_points, bool do_center=True, int max_svd_iter=0)
	Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD. More...
bool	align (ConstFMatrixExpression points, ConstFMatrixExpression ref_points, ConstFVectorExpression weights, bool do_center=True, int max_svd_iter=0)
	Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD. More...
bool	align (ConstDMatrixExpression points, ConstDMatrixExpression ref_points, ConstDVectorExpression weights, bool do_center=True, int max_svd_iter=0)
	Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD. More...

Properties
	objectID = property(getObjectID)
	transform = property(getTransform)

Detailed Description

Implementation of the Kabsch algorithm [KABA].

Finds the least Root Mean Square Distance between two sets of \( N \) points in \( D \) dimensions and the rigid transformation (i.e. translation and rotation) to employ in order to bring one set that close to the other.

Note that the points are paired, i.e. it is known which point in one set should be compared to a given point in the other set. It is possible to give weights to the points. Those weights are determined a priori and do not depend on the distances.

The convention is used that points are column vectors of the input matrices.

Constructor & Destructor Documentation

__init__()

None CDPL.Math.FKabschAlgorithm.__init__

(

FKabschAlgorithm

algo

)

Contructs a copy of the FKabschAlgorithm instance algo.

Parameters

algo	The FKabschAlgorithm instance to copy.

Member Function Documentation

getObjectID()

int CDPL.Math.FKabschAlgorithm.getObjectID

(

)

Returns the numeric identifier (ID) of the wrapped C++ class instance.

Different Python FKabschAlgorithm instances may reference the same underlying C++ class instance. The commonly used Python expression a is not b thus cannot tell reliably whether the two FKabschAlgorithm instances a and b reference different C++ objects. The numeric identifier returned by this method allows to correctly implement such an identity test via the simple expression a.getObjectID() != b.getObjectID().

Returns

The numeric ID of the internally referenced C++ class instance.

assign()

FKabschAlgorithm CDPL.Math.FKabschAlgorithm.assign

(

FKabschAlgorithm

algo

)

Replaces the current state with a copy of the state of the FKabschAlgorithm instance algo.

Parameters

algo	The FKabschAlgorithm instance to copy.

Returns

self.

getTransform()

FMatrix CDPL.Math.FKabschAlgorithm.getTransform

(

)

Returns the rigid-body transformation produced by the most recent successful align() call.

Returns

The (D+1)×(D+1) transformation matrix (homogeneous form).

align() [1/4]

bool CDPL.Math.FKabschAlgorithm.align	(	ConstFMatrixExpression	points,
		ConstFMatrixExpression	ref_points,
		bool	do_center = True,
		int	max_svd_iter = 0
	)

Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD.

Parameters

points	A D×N-matrix storing the points to align as column vectors.
ref_points	A D×N-matrix storing the reference points as column vectors.
do_center	True if centering of the data points needs to be performed, and False if not.
max_svd_iter	The maximum number of iterations to perform in the SV-decomposition, or 0 if no limit.

Returns

True if convergence in the internal SV-decomposition has been reached in max_svd_iter iterations, and False otherwise.

Precondition

points.getSize1() == ref_points.getSize1()

points.getSize2() == ref_points.getSize2()

Exceptions

Base.SizeError

if preconditions got violated.

align() [2/4]

bool CDPL.Math.FKabschAlgorithm.align	(	ConstDMatrixExpression	points,
		ConstDMatrixExpression	ref_points,
		bool	do_center = True,
		int	max_svd_iter = 0
	)

Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD.

Parameters

points	A D×N-matrix storing the points to align as column vectors.
ref_points	A D×N-matrix storing the reference points as column vectors.
do_center	True if centering of the data points needs to be performed, and False if not.
max_svd_iter	The maximum number of iterations to perform in the SV-decomposition, or 0 if no limit.

Returns

True if convergence in the internal SV-decomposition has been reached in max_svd_iter iterations, and False otherwise.

Precondition

points.getSize1() == ref_points.getSize1()

points.getSize2() == ref_points.getSize2()

Exceptions

Base.SizeError

if preconditions got violated.

align() [3/4]

bool CDPL.Math.FKabschAlgorithm.align	(	ConstFMatrixExpression	points,
		ConstFMatrixExpression	ref_points,
		ConstFVectorExpression	weights,
		bool	do_center = True,
		int	max_svd_iter = 0
	)

Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD.

Parameters

points	A D×N-matrix storing the points to align as column vectors.
ref_points	A D×N-matrix storing the reference points as column vectors.
weights	A \( N \)-dimensional vector storing the non-negative weights that are assigned to the points.
do_center	True if centering of the data points needs to be performed, and False if not.
max_svd_iter	The maximum number of iterations to perform in the SV-decomposition, or 0 if no limit.

Returns

True if convergence in the internal SV-decomposition has been reached in max_svd_iter iterations, and False otherwise.

Precondition

points.getSize1() == ref_points.getSize1()

points.getSize2() == ref_points.getSize2()

weights().getSize() == points.getSize2()

weights()(i) >= 0 && sum(weights) > 0

Exceptions

Base.SizeError

or Base.ValueError if preconditions got violated.

align() [4/4]

bool CDPL.Math.FKabschAlgorithm.align	(	ConstDMatrixExpression	points,
		ConstDMatrixExpression	ref_points,
		ConstDVectorExpression	weights,
		bool	do_center = True,
		int	max_svd_iter = 0
	)

Computes the rigid body transformation that aligns a set of \( N \) \( D \)-dimensional points points with a corresponding set of reference points ref_points at a minimum RMSD.

Parameters

points	A D×N-matrix storing the points to align as column vectors.
ref_points	A D×N-matrix storing the reference points as column vectors.
weights	A \( N \)-dimensional vector storing the non-negative weights that are assigned to the points.
do_center	True if centering of the data points needs to be performed, and False if not.
max_svd_iter	The maximum number of iterations to perform in the SV-decomposition, or 0 if no limit.

Returns

True if convergence in the internal SV-decomposition has been reached in max_svd_iter iterations, and False otherwise.

Precondition

points.getSize1() == ref_points.getSize1()

points.getSize2() == ref_points.getSize2()

weights().getSize() == points.getSize2()

weights()(i) >= 0 && sum(weights) > 0

Exceptions

Base.SizeError

or Base.ValueError if preconditions got violated.