LatticeCovering.c File Reference

Author:: Reinhard Prix Functions for covering metric parameter-spaces with a lattice.

#include <math.h>
#include <gsl/gsl_block.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_blas.h>
#include "LatticeCovering.h"

Include dependency graph for LatticeCovering.c:

Go to the source code of this file.

Defines

#define MIN(x, y)   ((x) < (y) ? (x) : (y))

#define MAX(x, y)   ((x) > (y) ? (x) : (y))

#define TRUE   (1==1)

#define FALSE   (1==0)

#define HAVE_INLINE   1

Functions

NRCSID (LATTICECOVERINGC,"$Id: LatticeCovering.c,v 1.4 2007/01/31 00:18:48 reinhard Exp $")

void LALLatticeCovering (LALStatus *status, REAL8VectorList **covering, REAL8 coveringRadius, const gsl_matrix *metric, const REAL8Vector *startPoint, BOOLEAN(*isInside)(const REAL8Vector *point), LatticeType latticeType)

Central function of this module: produce a lattice-covering of given lattice-type for the given parameter-space with constant metric.

void LALLatticeFill (LALStatus *status, REAL8VectorList **fillGrid, const gsl_matrix *generator, const REAL8Vector *startPoint, BOOLEAN(*isInside)(const REAL8Vector *point))

Fill the given parameter-space by a lattice defined by the specified generating matrix.

REAL8 XLALMetricScalarProduct (const gsl_vector *v1, const gsl_vector *v2, const gsl_matrix *gij)

Scalar product of two vectors with respect to the given metric $\vec{v}_1 \cdot \vec{v}_2 = g_{i j}\, v_1^i \,v_2^j$ .

int XLALFindCoveringGenerator (gsl_matrix **outmatrix, LatticeType type, REAL8 coveringRadius, const gsl_matrix *gij)

Construct the full-rank generating matrix of given type, for covering a space of given (constant) metric and a given covering Radius.

int XLALReduceGenerator2FullRank (gsl_matrix **outmatrix, const gsl_matrix *inmatrix)

"Reduce" a general (non-quadratic) generating matrix M with rank(M) <= cols(M) into a quadratic generator of full rank.

int XLALGetLatticeGenerator (gsl_matrix **outmatrix, UINT4 dimension, LatticeType type)

Return a (not necessarily quadratic) n-dimensional generating matrix for one of several possible lattices (currently possible: cubic or $A_n^*$ ).

REAL8VectorList * XLALREAL8VectorListAddEntry (REAL8VectorList *head, const REAL8Vector *entry)

Add a new element at the end of the list 'head', _copy_ the given entry there, and return pointer to the new list-entry.

void XLALREAL8VectorListDestroy (REAL8VectorList *head)

'List-destructor' for REAL8VectorList: free a complete list.

REAL8Vector * XLALgsl2LALmetric (const gsl_matrix *gmetric)

Translate a symmetric gsl_matrix into a 'LAL-encoded' REAL8Vector, using the index-convention l = a + b*(b+1) if a <= b, see PMETRIC_INDEX(a,b).

gsl_matrix * XLALmetric2gsl (const REAL8Vector *metric)

Convert a LAL-encoded metric (REAL8Vector) into a symmetric gsl_matrix.

Variables

INT4VectorList empty_INT4VectorList

REAL8VectorList empty_REAL8VectorList

Detailed Description

Author:: Reinhard Prix Functions for covering metric parameter-spaces with a lattice.

Date:: 2005

Id: LatticeCovering.c,v 1.4 2007/01/31 00:18:48 reinhard Exp

Todo:

iterative generation of lattice
optimize for speed

Definition in file LatticeCovering.c.

Define Documentation

#define MIN	(	x,
		y		)	((x) < (y) ? (x) : (y))

Definition at line 48 of file LatticeCovering.c.

#define MAX	(	x,
		y		)	((x) > (y) ? (x) : (y))

Definition at line 49 of file LatticeCovering.c.

#define TRUE (1==1)

Definition at line 51 of file LatticeCovering.c.

#define FALSE (1==0)

Definition at line 52 of file LatticeCovering.c.

#define HAVE_INLINE 1

Definition at line 55 of file LatticeCovering.c.

Function Documentation

NRCSID	(	LATTICECOVERINGC	,
		"$Id: LatticeCovering.	c,
		v 1.4 2007/01/31 00:18:48 reinhard Exp $"
	)

void LALLatticeCovering	(	LALStatus *	status,
		REAL8VectorList **	covering,
		REAL8	coveringRadius,
		const gsl_matrix *	metric,
		const REAL8Vector *	startPoint,
		BOOLEAN()(const REAL8Vector point)	isInside,
		LatticeType	latticeType
	)

Central function of this module: produce a lattice-covering of given lattice-type for the given parameter-space with constant metric.

For optimal covering, use latticeType=0, namely the An* lattice, which is the best known covering-lattice up to dimension 23, see [CS99]

Algorithm:

1) use XLALFindCoveringGenerator() to get the generator of the given lattice.

2) use it to LALLatticeFill() the space.

Parameters:

covering	[out] final covering-grid
coveringRadius	[in] covering radius
metric	[in] constant metric
startPoint	[in] start-point in the covering-region
isInside	[in] boundary-condition

Definition at line 103 of file LatticeCovering.c.

void LALLatticeFill	(	LALStatus *	status,
		REAL8VectorList **	fillGrid,
		const gsl_matrix *	generator,
		const REAL8Vector *	startPoint,
		BOOLEAN()(const REAL8Vector point)	isInside
	)

Fill the given parameter-space by a lattice defined by the specified generating matrix.

Note1:: The input generating-matrix (generator) must already be scaled correctly to the required covering radius, also, it needs to be in canonical full-rank square matrix form.

Note2:: As always in this module, the generating matrix contains the lattice-vectors as rows

Parameters:

fillGrid	[out] fillGrid final fill-grid (physical points)
generator	[in] SQUARE generating matrix for lattice
startPoint	[in] physical startpoint for filling
isInside	[in] boundary-condition

Definition at line 167 of file LatticeCovering.c.

REAL8 XLALMetricScalarProduct	(	const gsl_vector *	v1,
		const gsl_vector *	v2,
		const gsl_matrix *	gij
	)

Scalar product of two vectors with respect to the given metric $\vec{v}_1 \cdot \vec{v}_2 = g_{i j}\, v_1^i \,v_2^j$ .

Definition at line 405 of file LatticeCovering.c.

int XLALFindCoveringGenerator	(	gsl_matrix **	outmatrix,
		LatticeType	type,
		REAL8	coveringRadius,
		const gsl_matrix *	gij
	)

Construct the full-rank generating matrix of given type, for covering a space of given (constant) metric and a given covering Radius.

Note1:: the returned generator is a square matrix, with lattice-vectors in the matrix-rows (as always in this module!)

Note2:: the memory for 'outmatrix' is allocated here with gsl_matrix_alloc() and needs to be free by the caller via gsl_matrix_free()

Algorithm:

1) get the (generally non-square) generating matrix for the lattice
2) reduce it to a full-rank square generating matrix by expressing the lattice vectors in the basis of their spanned space
3) translate the basis-vectors to the coordinates cooresponding to the given metric
4) scale the generating matrix to the given covering radius

Parameters:

outmatrix	[out] generating matrix for covering lattice
type	[in] type of lattice
coveringRadius	[in] desired covering radius
gij	[in] (constant) metric of covering space

Definition at line 591 of file LatticeCovering.c.

int XLALReduceGenerator2FullRank	(	gsl_matrix **	outmatrix,
		const gsl_matrix *	inmatrix
	)

"Reduce" a general (non-quadratic) generating matrix M with rank(M) <= cols(M) into a quadratic generator of full rank.

The input matrix can have columns >= rows, the rows reprenting the lattice vectors. This algorithm simply proceeds by constructing an (Euclidean!) orthonormal basis out of the lattice vectors (using GramSchmidt), and then expressing the lattice-vectors in this new basis.

Note:: the memory for 'outmatrix' is allocated in here via gsl_matrix_alloc() and has to be free'ed by the caller via gsl_matrix_free() !

Parameters:

outmatrix	[out] full-rank square generating matrix
inmatrix	[in] generating matrix (cols >= rows)

Definition at line 691 of file LatticeCovering.c.

int XLALGetLatticeGenerator	(	gsl_matrix **	outmatrix,
		UINT4	dimension,
		LatticeType	type
	)

Return a (not necessarily quadratic) n-dimensional generating matrix for one of several possible lattices (currently possible: cubic or $A_n^*$ ).

See [CS99] for the definition and properties of these lattices.

Note1:: Because these lattices are intended for covering, we scale them so that their covering-radius is unity. This allows the user to later-on scale these easily to any desired covering-radius without having to know anything about the lattice... (Remembering that if you scale the generator of a lattice by , then the covering radius R scales as )

Note2:: The memory for 'outmatrix' is allocated in here via gsl_matrix_alloc() and has to be free'ed by the caller via gsl_matrix_free() !

Parameters:

outmatrix	[out] generating matrix
dimension	[in] number of dimensions
type	[in] type of lattice

Definition at line 795 of file LatticeCovering.c.

REAL8VectorList* XLALREAL8VectorListAddEntry	(	REAL8VectorList *	head,
		const REAL8Vector *	entry
	)

Add a new element at the end of the list 'head', _copy_ the given entry there, and return pointer to the new list-entry.

Note:: This function is rather permissive in that it takes the vector-dimension from the new entry 'el', without requiring this to be equal to the dimension of the other list-entries...

Definition at line 939 of file LatticeCovering.c.

void XLALREAL8VectorListDestroy ( REAL8VectorList * head )

'List-destructor' for REAL8VectorList: free a complete list.

Note:: 'head' will be freed too, so make sure not to pass a non-freeable head (like an automatic variabe)

Definition at line 1063 of file LatticeCovering.c.

REAL8Vector* XLALgsl2LALmetric ( const gsl_matrix * gmetric )

Translate a symmetric gsl_matrix into a 'LAL-encoded' REAL8Vector, using the index-convention l = a + b*(b+1) if a <= b, see PMETRIC_INDEX(a,b).

Definition at line 1150 of file LatticeCovering.c.

gsl_matrix* XLALmetric2gsl ( const REAL8Vector * metric )

Convert a LAL-encoded metric (REAL8Vector) into a symmetric gsl_matrix.

Definition at line 1184 of file LatticeCovering.c.

Variable Documentation

INT4VectorList empty_INT4VectorList

Definition at line 62 of file LatticeCovering.c.

REAL8VectorList empty_REAL8VectorList

Definition at line 63 of file LatticeCovering.c.

Generated on Sat Aug 30 03:13:59 2008 for LAL by

1.5.2


Defines
#define	MIN(x, y) ((x) < (y) ? (x) : (y))
#define	MAX(x, y) ((x) > (y) ? (x) : (y))
#define	TRUE (1==1)
#define	FALSE (1==0)
#define	HAVE_INLINE 1
Functions
	NRCSID (LATTICECOVERINGC,"$Id: LatticeCovering.c,v 1.4 2007/01/31 00:18:48 reinhard Exp $")
void	LALLatticeCovering (LALStatus status, REAL8VectorList covering, REAL8 coveringRadius, const gsl_matrix metric, const REAL8Vector startPoint, BOOLEAN(isInside)(const REAL8Vector *point), LatticeType latticeType)
	Central function of this module: produce a lattice-covering of given lattice-type for the given parameter-space with constant metric.
void	LALLatticeFill (LALStatus status, REAL8VectorList fillGrid, const gsl_matrix generator, const REAL8Vector startPoint, BOOLEAN(isInside)(const REAL8Vector *point))
	Fill the given parameter-space by a lattice defined by the specified generating matrix.
REAL8	XLALMetricScalarProduct (const gsl_vector v1, const gsl_vector v2, const gsl_matrix *gij)
	Scalar product of two vectors with respect to the given metric $\vec{v}_1 \cdot \vec{v}_2 = g_{i j}\, v_1^i \,v_2^j$ .
int	XLALFindCoveringGenerator (gsl_matrix *outmatrix, LatticeType type, REAL8 coveringRadius, const gsl_matrix gij)
	Construct the full-rank generating matrix of given type, for covering a space of given (constant) metric and a given covering Radius.
int	XLALReduceGenerator2FullRank (gsl_matrix *outmatrix, const gsl_matrix inmatrix)
	"Reduce" a general (non-quadratic) generating matrix M with rank(M) <= cols(M) into a quadratic generator of full rank.
int	XLALGetLatticeGenerator (gsl_matrix **outmatrix, UINT4 dimension, LatticeType type)
	Return a (not necessarily quadratic) n-dimensional generating matrix for one of several possible lattices (currently possible: cubic or ).
REAL8VectorList *	XLALREAL8VectorListAddEntry (REAL8VectorList head, const REAL8Vector entry)
	Add a new element at the end of the list 'head', _copy_ the given entry there, and return pointer to the new list-entry.
void	XLALREAL8VectorListDestroy (REAL8VectorList *head)
	'List-destructor' for REAL8VectorList: free a complete list.
REAL8Vector *	XLALgsl2LALmetric (const gsl_matrix *gmetric)
	Translate a symmetric gsl_matrix into a 'LAL-encoded' REAL8Vector, using the index-convention l = a + b*(b+1) if a <= b, see PMETRIC_INDEX(a,b).
gsl_matrix *	XLALmetric2gsl (const REAL8Vector *metric)
	Convert a LAL-encoded metric (REAL8Vector) into a symmetric gsl_matrix.
Variables
INT4VectorList	empty_INT4VectorList
REAL8VectorList	empty_REAL8VectorList