whb.h File Reference

Class Whb: stabilized hierarchical basis library. More...

#include <mc/mc_base.h>
#include <mc/bam.h>

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Classes

struct sHBmat

struct HBmat Definition More...

struct sHBvec

struct HBvec Definition More...

struct sBchar

struct Bchar Definition More...

Typedefs

typedef struct sHBmat HBmat

Declaration of the HBmat class as the HBmat structure.

typedef struct sHBvec HBvec

Declaration of the HBvec class as the HBvec structure.

typedef struct sBchar Bchar

Declaration of the Bchar class as the Bchar structure.

Enumerations

enum HBMATtype {
ZERO_TYPE, AMIN_TYPE, ANOR_TYPE, GHB_TYPE,
GWM_TYPE
}

Class Whb: Parameters and datatypes.

Functions

void HBvec_hbVcyc (HBvec *dd, HBmat *Ahb, HBvec *rr, HBmat *Ghb, HBvec *ww, int key, int csolv)

Hierarchical Basis MG Vcycle (Bank, Dupont, and Yserentant).

void HBvec_initStructure (HBvec *thee, HBmat *Ahb)

Creates a chain of HBvec pointers to a Bvec.

void HBvec_killStructure (HBvec *thee)

Kills a chain of HBvec pointers.

void HBmat_initG (HBmat *thee, Bmat *Ppro, Bmat *Mlink, int meth)

Assembles the change of basis matrices for the HB Vcycle.

void HBmat_initA (HBmat *Ahb, HBmat *Ghb, Bmat *Alink)

Assembles the hierarchical matrix for the HB Vcycle.

void HBmat_killStructure (HBmat *thee)

Kills a chain of HBmat pointers.

void Bvec_hlmethod (Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut, int key, int flag, int itmax, double etol, int prec, int cycle, Bmat *P, Bmat *M, int meth)

Executes one of a number of hierarchical linear solvers.

void Bvec_hb (Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut, int key, int flag, int itmax, double etol, int meth, Bmat *Ppro, Bmat *M)

HBMG algorithm due to Bank, Dupont, and Yserentant.

void Bvec_hcg (Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut, int key, int flag, int itmax, double etol, int prec, Bmat *P, Bmat *M, Bvec *p, Bvec *ap, Bvec *bap, Bvec *po, Bvec *apo, Bvec *tp)

CG method with Bvec_hb as an optional preconditioner.

void Bvec_hbcg (Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut, int key, int flag, int itmax, double etol, int prec, Bmat *P, Bmat *M, Bvec *s, Bvec *p, Bvec *ap, Bvec *bap, Bvec *po, Bvec *apo, Bvec *q, Bvec *atq, Bvec *btatq, Bvec *qo, Bvec *atqo)

Bvec_hbcg with Bvec_hb as an optional preconditioner.

void HBmat_initMulti (HBmat **Ahb, HBmat **Ghb, Bmat *A, Bmat *M, Bmat *Ppro, int meth)

Assembles the hierarchical matrix structures for the HB Vcycle.

void HBmat_killMulti (HBmat **Ahb, HBmat **Ghb)

Destruct the hierarchical structures.

HBmat * HBmat_ctor (Vmem *vmem, const char *bname, int pnumB)

The HBmat constructor.

void HBmat_dtor (HBmat **thee)

The HBmat destructor.

HBvec * HBvec_ctor (Vmem *vmem, const char *bname, int pnumB)

The HBvec constructor.

void HBvec_dtor (HBvec **thee)

The HBvec destructor.

Bvec * Bvec_ctorPoint (Bvec *v, const char *name, int *ibase, int *numR)

Create a Bvec pointer to the tail of a Bvec.

void Bvec_dtorPoint (Bvec **thee)

The block vec pointer destructor.

Vec * Vec_ctorPoint (Vec *v, const char *name, int sep, int numR)

Create a Vec pointer to the tail of a Vec.

void Vec_dtorPoint (Vec **thee)

The vec pointer destructor.

Bmat * Bmat_ctorPoint (Bmat *P, const char *name, int *ibase, int *numR)

Create a Bmat pointer to the tail of a Bmat.

void Bmat_dtorPoint (Bmat **thee)

The Bmat pointer destructor.

Mat * Mat_ctorPoint (Mat *P, const char *name, int ibase, int numR)

Create a Mat pointer to the tail of a Pro.

void Mat_dtorPoint (Mat **thee)

The Mat pointer destructor.

void HBmat_printSp (HBmat *thee, char *fname, int pflag)

Print an HBmat in MATLAB sparse form.

void Bmat_printDiriSp (Bmat *thee, char *fname, int pflag)

Print the Dirichlet info of a Bmat in MATLAB sparse form.

void Mat_printDiriSp (Mat *thee, char *fname, int pflag)

Print the Dirichlet info of a Bmat in MATLAB sparse form.

Mat * Bmat_AD (Bmat *thee, int p, int q)

Return the Mat structure AD.

void HBvec_matvec (HBvec *thee, HBmat *Gmat, int key, Bvec *work)

Special matrix-vector multiplication for HB.

double Bmat_lnDet (Bmat *thee)

Calculate the log of the determinant of a SPD Bmat matrix.

void BXLN_copyBmat (Bmat *thee, Bmat *Amat)

Create an BXLN copy of a Bmat.

void Bmat_copyBXLN (Bmat *thee, Bmat *Alink)

Produces a Bmat copy of a BXLN.

void BXLN_hbTriple (Bmat *thee, HBmat *G)

Produce the HB sparse triple matrix product:.

void BXLN_copyBlocks (Bmat *A, Bmat *A12, Bmat *A21, Bmat *A22)

Copies the A12, A21, and A22 blocks of a XLN, storing them in Mats of type COL, ROW, and DRC respectively.

void BXLN_shrinkLogical (Bmat *A, Bmat *A12, Bmat *A21)

Sets the sizes of the logical blocks inside a BXLN using the number of rows and cols in two different Bmats.

void HBmat_GHB2WMHB (HBmat *thee, Bmat *M)

Constructs G12/G22 for WMHB using Mhb and G21.

void XLN_hbTriple (Mat *thee, Mat *GL21, Mat *GL12, Mat *GL22, Mat *GR21, Mat *GR12, Mat *GR22)

Produce the HB sparse triple matrix product:.

void XLN_matmatContrib (Mat *thee, Mat *Ablock1, int ibase, int flag1, Mat *Ablock2, int jbase, int flag2)

Multiplies two Mat's contributing the result to an XLN.

void XLN_copySubblock (Mat *thee, Mat *Amat, int flag)

Copies the A12, A21, or A22 subblock of a XLN, storing it in a Mat of type COL, ROW, or DRC respectively.

void XLN_copyBlocks (Mat *Ablock, Mat *A12, Mat *A21, Mat *A22)

Copies the A12, A21, and A22 blocks of a XLN, storing them in Mats of type COL, ROW, and DRC respectively.

void XLN_shrinkLogical (Mat *A, Mat *A12, Mat *A21)

Sets the sizes of the logical blocks inside a XLN using the number of rows and cols in two different Mats.

void Mat_initGWMHB (Mat *G12, Mat *G22, Mat *G21, Mat *Mblock)

Constructs G12/G22 for WMHB using Mhb and G21.

void Bvec_submethod (Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut, int key, int flag, int itmax, double etol, int prec, int cycle, Bmat *P, int meth)

Executes one of a number of linear solvers.

void Bvec_fsmooth (Bvec *thee, Bmat *amat, Bvec *f, Bvec *w, int key, int ioflag, int meth, int adj, int itmax, Bchar *fc)

F-point smoothing operator.

Bchar * Bchar_ctor (Vmem *vmem, const char *name, int pnumB, int pnumR[MAXV])

The block character constructor.

void Bchar_dtor (Bchar **thee)

The block character destructor.

void Bchar_assem (Bchar *thee, int key, Bmat *Ppro)

Build a block list of F and C points.

void Bchar_assem2 (Bchar *thee, int key, Bmat *amat, Bmat *Ppro)

Build a block list of F and C points.

Detailed Description

Class Whb: stabilized hierarchical basis library.

Author:: Burak Aksoylu, Stephen Bond, and Michael Holst

Note:: None

Version:

Id: whb.h,v 1.20 2009/04/24 22:54:29 fetk Exp

Attention:

 *
 * MC = < Manifold Code >
 * Copyright (C) 1994--2008 Michael Holst
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 *
 *

Function Documentation

void BXLN_copyBlocks	(	Bmat *	A,
		Bmat *	A12,
		Bmat *	A21,
		Bmat *	A22
	)

Copies the A12, A21, and A22 blocks of a XLN, storing them in Mats of type COL, ROW, and DRC respectively.

Authors:: Burak Aksoylu and Stephen Bond 2002/01/26

Note:

Class Whb: Non-Inlineable methods (brcmat.c)

 *   Notes:  The logical position of eacg block is determined from the
 *           sizes of the other blocks.
 *
 *                    [   A11    |   A12   ]
 *                    [ sepxsep  | sepxn   ]
 *           A_hb  =  [----------|---------]  where numR = sep + n
 *                    [   A21    |   A22   ]
 *                    [   nxsep  |   nxn   ]
 *
 *           A12, A21, A22 must be passed w/ NULL_STATE blocks.
 *

Returns:: None

Parameters:

	A	Pointer to the Bmat object
	A12	Pointer to the Bmat object
	A21	Pointer to the Bmat object
	A22	Pointer to the Bmat object

void BXLN_copyBmat	(	Bmat *	thee,
		Bmat *	Amat
	)

Create an BXLN copy of a Bmat.

Author:: Stephen Bond 2002/01/28

Note:: Class Whb: Non-Inlineable methods (brcmat.c)
Only the upper triangular part of any symmetric part is copied.

Returns:: None

Parameters:

	thee	Pointer to the Bmat object
	Amat	Pointer to the Bmat object

void BXLN_hbTriple	(	Bmat *	thee,
		HBmat *	G
	)

Produce the HB sparse triple matrix product:.

 *           A(p,q)_hb = (I + G(p)') A(p,q) (I + G(q))
 *
 *                  = [  I     Gp21'    ] [ Apq11 Apq12 ] [  I      Gq12   ]
 *                    [ Gp12' (I+Gp22') ] [ Apq21 Apq22 ] [ Gq21  (I+Gq22) ]
 *

for every (p,q) block of A_hb.

Authors:: Stephen Bond and Burak Aksoylu 2002/01/26

Note:

Class Whb: Non-Inlineable methods (brcmat.c)

 *   Notes:  The G21, G22, and G12 blocks must be ROW, DRC, and COL
 *           formats respectively.  Any NULL blocks are treated as
 *           zero matrices.  If the subblock of the BXLN is of symmetric
 *           type, only the upper triangular portion is used/modified.
 *
 *           The matrix A is overwritten with the A11 result.
 *
 *  Method:  CASE 1: Heirarchical Basis (HB)
 *
 *           [A11 A12] += [ A12 Gq21 + Gp21'(A21 + A22 Gq21); Gp21'A22 ]
 *           [A21 A22]    [                        A22 Gq21 ;  0       ]
 *
 *           CASE 2: Wavelet Modified Heirarchical Basis (WMHB)
 *
 *   [A11 A12] += [ Gp21'(A21+A22*Gq21) + A12*Gq21 ; 0 ]
 *   [A21 A22]    [ Gp22'(A21+A22*Gq21) + A22*Gq21 ; 0 ]
 *
 *              + [ 0                   ; Gp21'(A22+A22*Gq22+A21*Gq12) ]
 *                [ Gp21'(A11+A12*Gq21) ; Gp22'(A22+A22*Gq22+A21*Gq12) ]
 *
 *              + [ 0 ; A11*Gq12 + A12*Gq22                                ]
 *                [ 0 ; A21*Gq12 + A22*Gq22 + Gp12'(A12+A12*Gq22+A11*Gq12) ]
 *

Returns:: None

Parameters:

	thee	Pointer to the Bmat object
	G	Pointer to the HBmat object

void BXLN_shrinkLogical	(	Bmat *	A,
		Bmat *	A12,
		Bmat *	A21
	)

Sets the sizes of the logical blocks inside a BXLN using the number of rows and cols in two different Bmats.

Authors:: Burak Aksoylu and Stephen Bond 2002/01/26

Note:

Class Whb: Non-Inlineable methods (brcmat.c)

 *   Notes:  This method is used exclusively by HB methods to "replace"
 *           the matrix A with its A11 subblock.  The size of the A11
 *           sublock can be uniquely determined using the sizes of the A12
 *           and A21 sublocks:
 *
 *                 [   A11    |   A12   ]
 *                 [ sepxsep  | sepxn   ]
 *           A  =  [----------|---------]  where numR = sep + n
 *                 [   A21    |         ]
 *                 [   nxsep  |         ]
 *
 *           In the future, this routine may actually shrink the matrix,
 *           but for now it only sets the internal numR and numC arrays
 *           to reflect the size of the logical A11 block.
 *

Returns:: None

Parameters:

	A	Pointer to the Bmat object
	A12	Pointer to the Bmat object
	A21	Pointer to the Bmat object

void XLN_copyBlocks	(	Mat *	Ablock,
		Mat *	A12,
		Mat *	A21,
		Mat *	A22
	)

Copies the A12, A21, and A22 blocks of a XLN, storing them in Mats of type COL, ROW, and DRC respectively.

Authors:: Burak Aksoylu and Stephen Bond 2002/01/26

Note:

Class Whb: Non-Inlineable methods (rcmat.c)

 *   Notes:  The logical position of each block is determined from the
 *           sizes of the other blocks.
 *
 *                    [   A11    |   A12   ]
 *                    [ sepxsep  | sepxn   ]
 *           A_hb  =  [----------|---------]  where numR = sep + n
 *                    [   A21    |   A22   ]
 *                    [   nxsep  |   nxn   ]
 *
 *           A12, A21, A22 must be passed w/ NULL_STATE (i.e. after ctor).
 *

Returns:: None

Parameters:

	Ablock	Pointer to the Mat object
	A12	Pointer to the Mat object
	A21	Pointer to the Mat object
	A22	Pointer to the Mat object

void XLN_copySubblock	(	Mat *	thee,
		Mat *	Amat,
		int	flag
	)

Copies the A12, A21, or A22 subblock of a XLN, storing it in a Mat of type COL, ROW, or DRC respectively.

Authors:: Burak Aksoylu and Stephen Bond 2002/01/26

Note:

Class Whb: Non-Inlineable methods (rcmat.c)

 *   Notes:  The logical position of each block is determined from the
 *           sizes of the other blocks.
 *
 *                    [   A11    |   A12   ]
 *                    [ sepxsep  | sepxn   ]
 *           A_hb  =  [----------|---------]  where numR = sep + n
 *                    [   A21    |   A22   ]
 *                    [   nxsep  |   nxn   ]
 *
 *           The subblock must be passed w/ NULL_STATE (i.e. after ctor).
 *

Returns:: None

Parameters:

	thee	Pointer to the Mat object
	Amat	Pointer to the Mat object
	flag	index for different copy options

void XLN_hbTriple	(	Mat *	thee,
		Mat *	GL21,
		Mat *	GL12,
		Mat *	GL22,
		Mat *	GR21,
		Mat *	GR12,
		Mat *	GR22
	)

Produce the HB sparse triple matrix product:.

 *           A_hb = (I + GL') A (I + GR)
 *
 *                  = [  I     GL21'    ] [ A11 A12 ] [  I      GR12   ]
 *                    [ GL12' (I+GL22') ] [ A21 A22 ] [ GR21  (I+GR22) ]
 *

where GL/GR are the left/right change of basis matrices.

Authors:: Stephen Bond and Burak Aksoylu 2002/01/26

Note:

Class Whb: Non-Inlineable methods (rcmat.c)

 *   Notes:  The G21, G22, and G12 blocks must be ROW, DRC, and COL
 *           formats respectively.  Any NULL blocks are treated as
 *           zero matrices.  If the XLN is of symmetric type, only the
 *           upper triangular portion is used/modified.
 *
 *           The matrix A is overwritten with the A11 result.
 *
 *  Method:  CASE 1: Heirarchical Basis (HB)
 *
 *           [A11 A12] += [ A12 GL21 + GL21'(A21 + A22 GR21); GL21'A22 ]
 *           [A21 A22]    [                        A22 GR21 ;  0       ]
 *
 *           CASE 2: Wavelet Modified Heirarchical Basis (WMHB)
 *
 *   [A11 A12] += [ GL21'(A21+A22*GR21) + A12*GR21 ; 0 ]
 *   [A21 A22]    [ GL22'(A21+A22*GR21) + A22*GR21 ; 0 ]
 *
 *              + [ 0                   ; GL21'(A22+A22*GR22+A21*GR12) ]
 *                [ GL21'(A11+A12*GR21) ; GL22'(A22+A22*GR22+A21*GR12) ]
 *
 *              + [ 0 ; A11*GR12 + A12*GR22                                ]
 *                [ 0 ; A21*GR12 + A22*GR22 + GL12'(A12+A12*GR22+A11*GR12) ]
 *

Returns:: None

Parameters:

	thee	Pointer to the Mat object
	GL21	Pointer to the Mat object
	GL12	Pointer to the Mat object
	GL22	Pointer to the Mat object
	GR21	Pointer to the Mat object
	GR12	Pointer to the Mat object
	GR22	Pointer to the Mat object

void XLN_matmatContrib	(	Mat *	thee,
		Mat *	Ablock1,
		int	ibase,
		int	flag1,
		Mat *	Ablock2,
		int	jbase,
		int	flag2
	)

Multiplies two Mat's contributing the result to an XLN.

Author:: Stephen Bond

Note:: Class Whb: Non-Inlineable methods (rcmat.c)
The offset of the contrib is controlled by ibase, jbase. If flag1 (flag2) is nonzero, the first (second) matrix is applied using its transpose.
This routine is used by the WMHB method while forming the triple matrix product.

Returns:: None

Parameters:

	thee	Pointer to the Mat object
	Ablock1	Pointer to the Mat object
	ibase	pointer to size array
	flag1	index for transpose options
	Ablock2	Pointer to the Mat object
	jbase	pointer to size array
	flag2	index for transpose options

void XLN_shrinkLogical	(	Mat *	A,
		Mat *	A12,
		Mat *	A21
	)

Sets the sizes of the logical blocks inside a XLN using the number of rows and cols in two different Mats.

Authors:: Burak Aksoylu and Stephen Bond 2002/01/26

Note:

Class Whb: Non-Inlineable methods (rcmat.c)

 *   Notes:  This method is used exclusively by HB methods to "replace"
 *           the matrix A with its A11 subblock.  The size of the A11
 *           sublock can be uniquely determined using the sizes of the A12
 *           and A21 sublocks:
 *
 *                 [   A11    |   A12   ]
 *                 [ sepxsep  | sepxn   ]
 *           A  =  [----------|---------]  where numR = sep + n
 *                 [   A21    |         ]
 *                 [   nxsep  |         ]
 *
 *           In the future, this routine may actually shrink the matrix,
 *           but for now it only sets the internal numR and numC values
 *           to reflect the size of the logical A11 block.
 *

Returns:: None

Parameters:

	A	Pointer to the Mat object
	A12	Pointer to the Mat object
	A21	Pointer to the Mat object


Classes
struct	sHBmat
	struct HBmat Definition More...
struct	sHBvec
	struct HBvec Definition More...
struct	sBchar
	struct Bchar Definition More...
Typedefs
typedef struct sHBmat	HBmat
	Declaration of the HBmat class as the HBmat structure.
typedef struct sHBvec	HBvec
	Declaration of the HBvec class as the HBvec structure.
typedef struct sBchar	Bchar
	Declaration of the Bchar class as the Bchar structure.
Enumerations
enum	HBMATtype { ZERO_TYPE, AMIN_TYPE, ANOR_TYPE, GHB_TYPE, GWM_TYPE }
	Class Whb: Parameters and datatypes.
Functions
void	HBvec_hbVcyc (HBvec dd, HBmat Ahb, HBvec rr, HBmat Ghb, HBvec *ww, int key, int csolv)
	Hierarchical Basis MG Vcycle (Bank, Dupont, and Yserentant).
void	HBvec_initStructure (HBvec thee, HBmat Ahb)
	Creates a chain of HBvec pointers to a Bvec.
void	HBvec_killStructure (HBvec *thee)
	Kills a chain of HBvec pointers.
void	HBmat_initG (HBmat thee, Bmat Ppro, Bmat *Mlink, int meth)
	Assembles the change of basis matrices for the HB Vcycle.
void	HBmat_initA (HBmat Ahb, HBmat Ghb, Bmat *Alink)
	Assembles the hierarchical matrix for the HB Vcycle.
void	HBmat_killStructure (HBmat *thee)
	Kills a chain of HBmat pointers.
void	Bvec_hlmethod (Bvec thee, Bmat A, Bvec f, Bvec r, Bvec ut, int key, int flag, int itmax, double etol, int prec, int cycle, Bmat P, Bmat *M, int meth)
	Executes one of a number of hierarchical linear solvers.
void	Bvec_hb (Bvec thee, Bmat A, Bvec f, Bvec r, Bvec ut, int key, int flag, int itmax, double etol, int meth, Bmat Ppro, Bmat *M)
	HBMG algorithm due to Bank, Dupont, and Yserentant.
void	Bvec_hcg (Bvec thee, Bmat A, Bvec f, Bvec r, Bvec ut, int key, int flag, int itmax, double etol, int prec, Bmat P, Bmat M, Bvec p, Bvec ap, Bvec bap, Bvec po, Bvec apo, Bvec *tp)
	CG method with Bvec_hb as an optional preconditioner.
void	Bvec_hbcg (Bvec thee, Bmat A, Bvec f, Bvec r, Bvec ut, int key, int flag, int itmax, double etol, int prec, Bmat P, Bmat M, Bvec s, Bvec p, Bvec ap, Bvec bap, Bvec po, Bvec apo, Bvec q, Bvec atq, Bvec btatq, Bvec qo, Bvec atqo)
	Bvec_hbcg with Bvec_hb as an optional preconditioner.
void	HBmat_initMulti (HBmat Ahb, HBmat Ghb, Bmat A, Bmat M, Bmat *Ppro, int meth)
	Assembles the hierarchical matrix structures for the HB Vcycle.
void	HBmat_killMulti (HBmat Ahb, HBmat Ghb)
	Destruct the hierarchical structures.
HBmat *	HBmat_ctor (Vmem vmem, const char bname, int pnumB)
	The HBmat constructor.
void	HBmat_dtor (HBmat **thee)
	The HBmat destructor.
HBvec *	HBvec_ctor (Vmem vmem, const char bname, int pnumB)
	The HBvec constructor.
void	HBvec_dtor (HBvec **thee)
	The HBvec destructor.
Bvec *	Bvec_ctorPoint (Bvec v, const char name, int ibase, int numR)
	Create a Bvec pointer to the tail of a Bvec.
void	Bvec_dtorPoint (Bvec **thee)
	The block vec pointer destructor.
Vec *	Vec_ctorPoint (Vec v, const char name, int sep, int numR)
	Create a Vec pointer to the tail of a Vec.
void	Vec_dtorPoint (Vec **thee)
	The vec pointer destructor.
Bmat *	Bmat_ctorPoint (Bmat P, const char name, int ibase, int numR)
	Create a Bmat pointer to the tail of a Bmat.
void	Bmat_dtorPoint (Bmat **thee)
	The Bmat pointer destructor.
Mat *	Mat_ctorPoint (Mat P, const char name, int ibase, int numR)
	Create a Mat pointer to the tail of a Pro.
void	Mat_dtorPoint (Mat **thee)
	The Mat pointer destructor.
void	HBmat_printSp (HBmat thee, char fname, int pflag)
	Print an HBmat in MATLAB sparse form.
void	Bmat_printDiriSp (Bmat thee, char fname, int pflag)
	Print the Dirichlet info of a Bmat in MATLAB sparse form.
void	Mat_printDiriSp (Mat thee, char fname, int pflag)
	Print the Dirichlet info of a Bmat in MATLAB sparse form.
Mat *	Bmat_AD (Bmat *thee, int p, int q)
	Return the Mat structure AD.
void	HBvec_matvec (HBvec thee, HBmat Gmat, int key, Bvec *work)
	Special matrix-vector multiplication for HB.
double	Bmat_lnDet (Bmat *thee)
	Calculate the log of the determinant of a SPD Bmat matrix.
void	BXLN_copyBmat (Bmat thee, Bmat Amat)
	Create an BXLN copy of a Bmat.
void	Bmat_copyBXLN (Bmat thee, Bmat Alink)
	Produces a Bmat copy of a BXLN.
void	BXLN_hbTriple (Bmat thee, HBmat G)
	Produce the HB sparse triple matrix product:.
void	BXLN_copyBlocks (Bmat A, Bmat A12, Bmat A21, Bmat A22)
	Copies the A12, A21, and A22 blocks of a XLN, storing them in Mats of type COL, ROW, and DRC respectively.
void	BXLN_shrinkLogical (Bmat A, Bmat A12, Bmat *A21)
	Sets the sizes of the logical blocks inside a BXLN using the number of rows and cols in two different Bmats.
void	HBmat_GHB2WMHB (HBmat thee, Bmat M)
	Constructs G12/G22 for WMHB using Mhb and G21.
void	XLN_hbTriple (Mat thee, Mat GL21, Mat GL12, Mat GL22, Mat GR21, Mat GR12, Mat *GR22)
	Produce the HB sparse triple matrix product:.
void	XLN_matmatContrib (Mat thee, Mat Ablock1, int ibase, int flag1, Mat *Ablock2, int jbase, int flag2)
	Multiplies two Mat's contributing the result to an XLN.
void	XLN_copySubblock (Mat thee, Mat Amat, int flag)
	Copies the A12, A21, or A22 subblock of a XLN, storing it in a Mat of type COL, ROW, or DRC respectively.
void	XLN_copyBlocks (Mat Ablock, Mat A12, Mat A21, Mat A22)
	Copies the A12, A21, and A22 blocks of a XLN, storing them in Mats of type COL, ROW, and DRC respectively.
void	XLN_shrinkLogical (Mat A, Mat A12, Mat *A21)
	Sets the sizes of the logical blocks inside a XLN using the number of rows and cols in two different Mats.
void	Mat_initGWMHB (Mat G12, Mat G22, Mat G21, Mat Mblock)
	Constructs G12/G22 for WMHB using Mhb and G21.
void	Bvec_submethod (Bvec thee, Bmat A, Bvec f, Bvec r, Bvec ut, int key, int flag, int itmax, double etol, int prec, int cycle, Bmat P, int meth)
	Executes one of a number of linear solvers.
void	Bvec_fsmooth (Bvec thee, Bmat amat, Bvec f, Bvec w, int key, int ioflag, int meth, int adj, int itmax, Bchar *fc)
	F-point smoothing operator.
Bchar *	Bchar_ctor (Vmem vmem, const char name, int pnumB, int pnumR[MAXV])
	The block character constructor.
void	Bchar_dtor (Bchar **thee)
	The block character destructor.
void	Bchar_assem (Bchar thee, int key, Bmat Ppro)
	Build a block list of F and C points.
void	Bchar_assem2 (Bchar thee, int key, Bmat amat, Bmat *Ppro)
	Build a block list of F and C points.