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* @defgroup Bvec Bvec class
* @brief A block vector object.
*/
/**
* @file bvec.h
* @ingroup Bvec
* @brief Class Bvec: a block vector object.
* @author Michael Holst
* @note None
* @version $Id: bvec.h,v 1.40 2010/08/12 05:18:34 fetk Exp $
*
* @attention
* @verbatim
*
* MC = < Manifold Code >
* Copyright (C) 1994-- 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
*
* @endverbatim
*/
#ifndef _BVEC_H_
#define _BVEC_H_
#include <mc/mc_base.h>
#include <mc/vec.h>
#include <mc/bmat.h>
/**
* @ingroup Bvec
* @brief Contains public data members for Bvec class
* @author Michael Holst
*/
struct sBvec {
Vmem *vmem; /**< @brief the memory manager */
int iMadeVmem; /**< @brief did i make vmem or was it inherited */
char name[10]; /**< @brief character string name for this vector*/
int n; /**< @brief number of components in the vector */
double *u; /**< @brief the vector components */
int iMallocU; /**< @brief did i malloc u or was it passed in */
struct sBvec *coarse; /**< @brief next coarser object in the hierarchy */
struct sBvec *fine; /**< @brief next finer object in the hierarchy */
int numB; /**< @brief num vector blocks */
int numR[MAXV]; /**< @brief num of rows in each block vector */
Vec *VC[MAXV]; /**< @brief vector block substructure */
};
/**
* @brief Declaration of the Bvec class as the Bvec structure
* @ingroup Bvec
* @author Michael Holst
* @return None
*/
typedef struct sBvec Bvec;
/*
* ***************************************************************************
* Class Bvec: Inlineable methods (bvec.c)
* ***************************************************************************
*/
#if !defined(VINLINE_BAM)
/**
* @ingroup Bvec
* @brief Return the number of blocks.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return the number of blocks.
* @param thee pointer to the block vector
*/
VEXTERNC int Bvec_numB(Bvec *thee);
#else /* if defined(VINLINE_BAM) */
/**
* @ingroup Bvec
* @brief Return the number of blocks.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return the number of blocks.
* @param thee pointer to the block vector
*/
# define Bvec_numB(thee) ((thee)->numB)
#endif /* if !defined(VINLINE_BAM) */
/**
* @ingroup Bvec
* @brief The block vector constructor (data array malloc'd by us).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return Pointer to a newly allocated (empty) block vector
* @param vmem Memory management object
* @param name character string name for this vector
* @param pnumB num vector blocks
* @param pnumR num of rows in each block vector
*/
VEXTERNC Bvec* Bvec_ctor(Vmem *vmem,
const char *name, int pnumB, int pnumR[MAXV]);
/**
* @ingroup Bvec
* @brief The block vector constructor (data array passed in).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return Pointer to a newly allocated (empty) block vector
* @param vmem Memory management object
* @param name character string name for this vector
* @param pnumB num vector blocks
* @param pnumR num of rows in each block vector
* @param data the vector components
*/
VEXTERNC Bvec* Bvec_ctor2(Vmem *vmem,
const char *name, int pnumB, int pnumR[MAXV], double *data);
/**
* @ingroup Bvec
* @brief The vector constructor (data array malloc'd by us).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return Pointer to a newly allocated (empty) block vector
* @param vmem Memory management object
* @param name character string name for this vector
* @param length number of components in the vector
*/
VEXTERNC Bvec* Bvec_ctor3(Vmem *vmem,
const char *name, int length);
/**
* @ingroup Bvec
* @brief The vector constructor (data array malloc'd by us).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return Pointer to a newly allocated (empty) block vector
* @param vmem Memory management object
* @param name character string name for this vector
* @param length number of components in the vector
* @param data the vector components
*/
VEXTERNC Bvec* Bvec_ctor4(Vmem *vmem,
const char *name, int length, double *data);
/**
* @ingroup Bvec
* @brief The block vector destructor.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
*/
VEXTERNC void Bvec_dtor(Bvec **thee);
/**
* @ingroup Bvec
* @brief Create a set of vectors with duplicate attributes.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c) \n
* We actually do this using contiguous memory, i.e., each
* vector follows contiguously from the preceeding one.
* @return None
* @param thee pointer to the block vector
* @param vecs the created block vector
* @param num the number of created vectors
*/
VEXTERNC void Bvec_createVectors(Bvec *thee, Bvec *vecs[], int num);
/**
* @ingroup Bvec
* @brief Destroy set of vectors previously created by Bvec_createVectors.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param vecs the created block vector
* @param num the number of created vectors
*/
VEXTERNC void Bvec_destroyVectors(Bvec *thee, Bvec *vecs[], int num);
/**
* @ingroup Bvec
* @brief Create a matrix from columns of vectors.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param vecs the created block vector
* @param num the number of created vectors
* @param mat Pointer to the sparse matrix
*/
VEXTERNC void Bvec_createVecMat(Bvec *thee, Bvec *vecs[], int num, Mat **mat);
/**
* @ingroup Bvec
* @brief Destroy matrix previously created by Bvec_createVecMat.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param vecs the created block vector
* @param num the number of created vectors
* @param mat Pointer to the sparse matrix
*/
VEXTERNC void Bvec_destroyVecMat(Bvec *thee, Bvec *vecs[], int num, Mat **mat);
/**
* @ingroup Bvec
* @brief Return the total number of rows.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return the total number of rows.
* @param thee pointer to the block vector
*/
VEXTERNC int Bvec_len(Bvec *thee);
/**
* @ingroup Bvec
* @brief Return a pointer to the total data array.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return a pointer to the total data arary
* @param thee pointer to the block vector
*/
VEXTERNC double* Bvec_addr(Bvec *thee);
/**
* @ingroup Bvec
* @brief Return value of component of vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return value of component of vector
* @param thee pointer to the block vector
* @param i index of the block vector
*/
VEXTERNC double Bvec_val(Bvec *thee, int i);
/**
* @ingroup Bvec
* @brief Set value of component of vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param i index of the block vector
* @param val value of the i-th component of the block vector
*/
VEXTERNC void Bvec_set(Bvec *thee, int i, double val);
/**
* @ingroup Bvec
* @brief 1-norm of a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return 1-norm of a block vector.
* @param thee pointer to the block vector
*/
VEXTERNC double Bvec_nrm1(Bvec *thee);
/**
* @ingroup Bvec
* @brief 2-norm of a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return 2-norm of a block vector
* @param thee pointer to the block vector
*/
VEXTERNC double Bvec_nrm2(Bvec *thee);
/**
* @ingroup Bvec
* @brief oo-norm of a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return oo-norm of a block vector.
* @param thee pointer to the block vector
*/
VEXTERNC double Bvec_nrm8(Bvec *thee);
/**
* @ingroup Bvec
* @brief 1-norm of the difference of two block vectors.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return 1-norm of the difference of two block vectors.
* @param thee pointer to the block vector
* @param v the source block vector
*/
VEXTERNC double Bvec_dif1(Bvec *thee, Bvec *v);
/**
* @ingroup Bvec
* @brief 2-norm of the difference of two block vectors.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return 2-norm of the difference of two block vectors.
* @param thee pointer to the block vector
* @param v the source block vector
*/
VEXTERNC double Bvec_dif2(Bvec *thee, Bvec *v);
/**
* @ingroup Bvec
* @brief oo-norm of the difference of two block vectors.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return oo-norm of the difference of two block vectors.
* @param thee pointer to the block vector
* @param v the source block vector
*/
VEXTERNC double Bvec_dif8(Bvec *thee, Bvec *v);
/**
* @ingroup Bvec
* @brief Dot product of two block vectors.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return Dot product of two block vectors.
* @param thee pointer to the block vector
* @param v the source block vector
*/
VEXTERNC double Bvec_dot(Bvec *thee, Bvec *v);
/**
* @ingroup Bvec
* @brief Initialize a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param val value to be initialized for the block vector
*/
VEXTERNC void Bvec_init(Bvec *thee, double val);
/**
* @ingroup Bvec
* @brief Scale a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param val value of the i-th component of the block vector
*/
VEXTERNC void Bvec_scal(Bvec *thee, double val);
/**
* @ingroup Bvec
* @brief Copy a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param v the source block vector
*/
VEXTERNC void Bvec_copy(Bvec *thee, Bvec *v);
/**
* @ingroup Bvec
* @brief Saxpy for a block vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param v the source block vector
* @param val coeficient for scaling the source block vector
*/
VEXTERNC void Bvec_axpy(Bvec *thee, Bvec *v, double val);
/**
* @ingroup Bvec
* @brief Print the block vector
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
*/
VEXTERNC void Bvec_print(Bvec *thee);
/**
* @ingroup Bvec
* @brief Print the block vector
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param fname the file name of the block vector
*/
VEXTERNC void Bvec_printSp(Bvec *thee, char *fname);
/**
* @ingroup Bvec
* @brief Apply inverse of diagonal to a vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param f source vector slot
*/
VEXTERNC void Bvec_diagScale(Bvec *thee, Bmat *A, Bvec *f);
/**
* @ingroup Bvec
* @brief Block matrix times vector.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param v the source block vector
* @param key index for different accumulation options
* @param part index for future use
*/
VEXTERNC void Bvec_matvec(Bvec *thee, Bmat *A, Bvec *v, int key, int part);
/**
* @ingroup Bvec
* @brief Generic smoothing operator (for a general YSMP-based matrix).
* @authors Michael Holst and Stephen Bond
* @note Class Bvec: Non-inlineable methods (bvec.c) \n
* meth==1, adj==0 : Forward Gauss-Seidel\n
* u = (D + L)^{-1}*(f - U*u)\n
* meth==1, adj==1 : Adjoint Gauss-Seidel\n
* u = (D + U)^{-1}*(f - L*u)\n
* meth==2 : Self-adjoint or Symmetric Gauss-Seidel\n
* Apply (meth==1, adj==0) then (meth==1, adj==1)
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param f source vector slot
* @param w the work block vector
* @param key smooth with A or A' (0=A, 1=A')
* @param ioflag debug output level (0=normal, 1=none, 2=lots, ... )
* @param meth smoother choice (0=jac, 1=gs, ... )
* @param adj adjoint choice (0=normal, 1=adjoint)
* @param itmax number of iterations to do (the maximum allowed)
* @param etol error tolerance (currently ignored)
* @param omega SOR parameter (currently ignored)
*/
VEXTERNC void Bvec_smooth(Bvec *thee, Bmat *A, Bvec *f, Bvec *w,
int key, int ioflag, int meth, int adj, int itmax, double etol,
double omega);
/**
* @ingroup Bvec
* @brief Apply boundary condition.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
* @param bmat the block sparse matrix
* @param key index for setting zeroes in the row/column components.
*/
VEXTERNC void Bvec_bnd(Bvec *thee, Bmat *bmat, int key);
/**
* @ingroup Bvec
* @brief Print the exact current malloc usage.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bvec.c)
* @return None
* @param thee pointer to the block vector
*/
VEXTERNC void Bvec_memChk(Bvec *thee);
/**
* @ingroup Bvec
* @brief Return the total number of rows.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return the total number of rows
* @param thee pointer to the block vector
*/
VEXTERNC int Bvec_numRT(Bvec *thee);
/**
* @ingroup Bvec
* @brief Return the size of a block.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return the size of a block
* @param thee pointer to the block vector
* @param i index of the block vector
*/
VEXTERNC int Bvec_numRB(Bvec *thee, int i);
/**
* @ingroup Bvec
* @brief Return a pointer to the data in a block.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return a pointer to the data in a block.
* @param thee pointer to the block vector
* @param i index of the block vector
*/
VEXTERNC double* Bvec_addrB(Bvec *thee, int i);
/**
* @ingroup Bvec
* @brief Return value of component of a vector.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return value of component of a vector.
* @param thee pointer to the block vector
* @param i index of the block vector
* @param which index of the component in the vector
*/
VEXTERNC double Bvec_valB(Bvec *thee, int i, int which);
/**
* @ingroup Bvec
* @brief Set value of component of a vector.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return None
* @param thee pointer to the block vector
* @param i index of the block vector
* @param which index of the component in the vector
* @param val value of the i-th component of the block vector
*/
VEXTERNC void Bvec_setB(Bvec *thee, int i, int which, double val);
/**
* @ingroup Bvec
* @brief Add value to component of a vector.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return None
* @param thee pointer to the block vector
* @param i index of the block vector
* @param which index of the component in the vector
* @param val value of the i-th component of the block vector
*/
VEXTERNC void Bvec_addToB(Bvec *thee, int i, int which, double val);
/**
* @ingroup Bvec
* @brief Initialize a particular block of a block vector.
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return None
* @param thee pointer to the block vector
* @param i index of the block vector
* @param val value of the i-th component of the block vector
*/
VEXTERNC void Bvec_initB(Bvec *thee, int i, double val);
/**
* @ingroup Bvec
* @brief Log of abs value of entries of block vector, shifted by < val >
* @author Michael Holst
* @note BLOCK-ONLY STUFF
* @return None
* @param thee pointer to the block vector
* @param val value of the i-th component of the block vector
*/
VEXTERNC void Bvec_absLog(Bvec *thee, double val);
/**
* @ingroup Bvec
* @brief Executes one of a number of linear solvers.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bsolv.c)
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param f source vector slot
* @param r residual slot
* @param ut block NODAL analytical solution
* @param key index for different solution methods: 0=(Au=f), 1=(A'u=f)
* @param flag index for i/o control
* @param itmax number of iterations to do (the maximum allowed)
* @param etol error tolerance
* @param prec index for different preconditioners
* @param cycle index for symmetric/nonsymmetric multigrids
* @param P prolongation matrix maintained by aprx
* @param meth method choice (0=slu,1=mg,2=cg,3=bcg,4=pcg,5=pbcg)
*/
VEXTERNC void Bvec_lmethod(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);
/**
* @ingroup Bvec
* @brief Sparse LU direct solver (requires only a nonsingular A).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bsolv.c)
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param f source vector slot
* @param r residual slot
* @param ut block NODAL analytical solution
* @param key key ==0 --> Solve: A u = f\n
* key ==1 --> Solve: A' u = f
* @param flag Determines which "mode" we run in:\n
* flag==0,2 --> Normal: normal i/o\n
* flag==1,3 --> Silent: no i/o
*/
VEXTERNC void Bvec_slu(Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut,
int key, int flag);
/**
* @ingroup Bvec
* @brief MG algorithm front end (NOT recursively callable).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bsolv.c)\n
* We use P to build an algebraic multilevel hierarchy in
* A,u(thee),f,r,ut from the fine-level-only representations,
* and then make the first call to the recursively-callable
* core MG algorithm Bvec_mgCore().
* @return None
* @param thee solution slot
* @param A system matrix
* @param f source vector slot
* @param r residual slot
* @param ut true solution slot
* @param key just passed along to Bvec_mgCore()
* @param flag just passed along to Bvec_mgCore()
* @param itmax just passed along to Bvec_mgCore()
* @param etol just passed along to Bvec_mgCore()
* @param prec just passed along to Bvec_mgCore()
* @param cycle just passed along to Bvec_mgCore()
* @param P prolongation operators (linked list)
*/
VEXTERNC void Bvec_mg(Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut,
int key, int flag, int itmax, double etol, int prec, int cycle, Bmat *P);
/**
* @ingroup Bvec
* @brief Initialize the algebraic multilevel hierarchy for Bvec_mg
* @authors Michael Holst and Stephan Bond
* @note Class Bvec: Non-inlineable methods (bsolv.c)\n
* We use P to build an algebraic multilevel hierarchy in
* A,u(thee),f,r,ut from the fine-level-only representations.
* The vectors are created after the matrix to reduce the total
* memory usage since Bmat_galerkin uses temporary arrays.
* @return None
* @param thee solution slot
* @param A system matrix
* @param f source vector slot
* @param r residual slot
* @param P prolongation operators (linked list)
*/
VEXTERNC void Bvec_mgInit(Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bmat *P);
/**
* @ingroup Bvec
* @brief Destroy algebraic multilevel hierarchy created by Bvec_mgInit
* @authors Michael Holst and Stephan Bond
* @note Class Bvec: Non-inlineable methods (bsolv.c)\n
* Only the coarser level matrices and vectors are destructed.
* @return None
* @param thee solution slot
* @param A system matrix
* @param f source vector slot
* @param r residual slot
*/
VEXTERNC void Bvec_mgDestroy(Bvec *thee, Bmat *A, Bvec *f, Bvec *r);
/**
* @ingroup Bvec
* @brief CG method (ODIR algorithm, requires SPD operators A, B, and M).
* @authors Michael Holst and Stephan Bond
* @note Class Bvec: Non-inlineable methods (bsolv.c)\n
* @verbatim
* ODIR(M,B,A) (for Au=f, preconditioner B, inner-product M)
* ---------------------------------------------------------
*
* Given u^0
* r^0 = f - A u^0
* p^0 = B r^0 / ||B r^0||
* for i=0,1,2,....
* alpha_i = <M e^i, p^i> / <M p^i, p^i>
* u^{i+1} = u^i + alpha_i p^i
* r^{i+1} = r^i - alpha_i A p^i
* gamma_i = <M B A p^i, p^i> / <M p^i, p^i>
* sigma_i = <M B A p^i, p^{i-1}> / <M p^{i-1}, p^{i-1}>
* v = B A p^i - gamma_i p^i - sigma_i p^{i-1}
* p^{i+1} = v / ||v||
* end for
*
* CG=ODIR(M=A,B=B,A=A)
* --------------------
*
* Given u^0
* r^0 = f - A u^0
* p^0 = B r^0 / ||B r^0||
* for i=0,1,2,....
* alpha_i = <r^i, p^i> / <A p^i, p^i>
* u^{i+1} = u^i + alpha_i p^i
* r^{i+1} = r^i - alpha_i A p^i
* gamma_i = <B A p^i, A p^i> / <A p^i, p^i>
* sigma_i = <B A p^i, A p^{i-1}> / <A p^{i-1}, p^{i-1}>
* v = B A p^i - gamma_i p^i - sigma_i p^{i-1}
* p^{i+1} = v / ||v||
* end for
* @endverbatim
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param f source vector slot
* @param r residual slot
* @param ut block NODAL analytical solution
* @param key index for different solution methods: 0=(Au=f), 1=(A'u=f)
* @param flag 0 --> Normal: check itmax, error tolerance; normal i/o\n
* 1 --> Silent: check only itmax; no i/o\n
* 2 --> Subcycle: check itmax, error tolerance; subcycle i/o\n
* 3 --> Subcycle: check itmax, error tolerance; no i/o
* @param itmax number of iterations to do (the maximum allowed)
* @param etol error tolerance
* @param prec index for different preconditioners
* @param cycle index for symmetric/nonsymmetric multigrids
* @param P prolongation matrix maintained by aprx
* @param p the block vector p
* @param ap another block vector ap
* @param bap third block vector bap
* @param po the block vector po
* @param apo the block vector apo
* @param tp temporary block vector tp
*/
VEXTERNC void Bvec_cg(Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut,
int key, int flag, int itmax, double etol, int prec, int cycle, Bmat *P,
Bvec *p, Bvec *ap, Bvec *bap, Bvec *po, Bvec *apo, Bvec *tp);
/**
* @ingroup Bvec
* @brief BCG method (pure bi-orthogonal extension of CG).
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bsolv.c)\n
* This is a pure Petrov-Galerkin formulation of the
* ODIR implementation of CG, and reduces to (exactly)
* the ODIR implementation of CG in the case of a
* symmetric (possibly indefinite) system matrix A and a
* symmetric (possibly indefinite) preconditioner B.
* (However, the operation count of BCG is rougly double
* that of CG.)
* @verbatim
* PG-ODIR(M,B,A) (for Au=f, preconditioner B, inner-product M)
* ------------------------------------------------------------
*
* Given u^0
* r^0 = f - A u^0
* s^0 = f - A' u^0
* p^0 = B r^0 / ||B r^0||
* q^0 = B's^0 / ||B's^0||
* for i=0,1,2,....
* alpha_i = <M e^i, q^i> / <M p^i, q^i>
* u^{i+1} = u^i + alpha_i p^i
* r^{i+1} = r^i - alpha_i A p^i
* gamma_i = <M B A p^i, q^i> / <M p^i, q^i>
* sigma_i = <M B A p^i, q^{i-1}> / <M p^{i-1}, q^{i-1}>
* delta_i = <M B A p^{i-1}, q^i> / <M p^{i-1}, q^{i-1}>
* v = B A p^i - gamma_i p^i - sigma_i p^{i-1}
* w = B'A' q^i - gamma_i q^i - delta_i q^{i-1}
* p^{i+1} = v / ||v||
* q^{i+1} = w / ||w||
* end for
*
* BCG=PG-ODIR(M=A,B=B,A=A)
* ------------------------
* Given u^0
* r^0 = f - A u^0
* s^0 = f - A' u^0
* p^0 = B r^0 / ||B r^0||
* q^0 = B's^0 / ||B's^0||
* for i=0,1,2,....
* alpha_i = <r^i, q^i> / <A p^i, q^i>
* u^{i+1} = u^i + alpha_i p^i
* r^{i+1} = r^i - alpha_i A p^i
* gamma_i = <B A p^i, A' q^i> / <A p^i, q^i>
* sigma_i = <B A p^i, A' q^{i-1}> / <A p^{i-1}, q^{i-1}>
* delta_i = <A p^{i-1}, B'A' q^i> / <A p^{i-1}, q^{i-1}>
* v = B A p^i - gamma_i p^i - sigma_i p^{i-1}
* w = B'A' q^i - gamma_i q^i - delta_i q^{i-1}
* p^{i+1} = v / ||v||
* q^{i+1} = w / ||w||
* end for
* @endverbatim
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param f source vector slot
* @param r residual slot
* @param ut block NODAL analytical solution
* @param key smooth with A or A' (0=A, 1=A')
* @param flag determines which "mode" we run in:\n
* 0 --> Normal: check itmax, error tolerance; normal i/o\n
* 1 --> Silent: check only itmax; no i/o\n
* 2 --> Subcycle: check itmax, error tolerance; subcycle i/o\n
* 3 --> Subcycle: check itmax, error tolerance; no i/o
* @param itmax number of iterations to do (the maximum allowed)
* @param etol error tolerance
* @param prec index for different preconditioners
* @param cycle index for symmetric/nonsymmetric multigrids
* @param P prolongation matrix maintained by aprx
* @param s residual block vector s: f - A'u
* @param p the block vector p
* @param ap another block vector ap
* @param bap third block vector bap
* @param po the block vector po
* @param apo the block vector apo
* @param q the block vector q
* @param atq the block vector atq
* @param btatq the block vector btatq
* @param qo the block vector qo
* @param atqo the block vector atqo
*/
VEXTERNC void Bvec_bcg(Bvec *thee, Bmat *A, Bvec *f, Bvec *r, Bvec *ut,
int key, int flag, int itmax, double etol, int prec, int cycle, Bmat *P,
Bvec *s,
Bvec *p, Bvec *ap, Bvec *bap, Bvec *po, Bvec *apo,
Bvec *q, Bvec *atq, Bvec *btatq, Bvec *qo, Bvec *atqo);
/**
* @ingroup Bvec
* @brief Calculate the eigenvector corresponding to the second smallest
* eigenvalue of the given (symmetric adjacency) matrix.
* @author Michael Holst
* @note Class Bvec: Non-inlineable methods (bsolv.c)\n\n
* We make the following assumptions about the matrix A, which
* are valid when A is the adjaceny matrix of a simplex mesh
* (e.g., the laplace operator for the dual mesh): \n\n
* (1) A is symmetric positive semi-definite\n
* (2) A is singular with null space of dimension 1\n
* (3) A has a unique smallest eigenvalue "0" and a
* corresponding unique (up to constant multiplier)
* eigenvector (or null vector) representing the set of
* constant vectors.\n\n
* Note that since A is symmetric, it has a complete set of
* orthonormal eigenvectors. \n\n
* The algorithm we employ here is a simple inverse iteration
* (or Rayleigh quotient iteration) which pulls out the
* second smallest eigenvalue (the smallest positive eigenvalue)
* and the corresponding eigenvector. The algorithm simply
* does a sequence of inexact inverse iterations, while
* repeatedly orthogonalizing the computed eigenvector against
* the unique null vector of constants. The inverse step
* damps out all eigendirections other than the smallest, and
* the orthgonalizing step removes the smallest eigen direction.\n\n
* On convergence (change in eigenvector meets a tolerance) then
* we generate the corresponding eigenvalue with a final
* Rayleigh quotient.
* @return None
* @param thee pointer to the block vector
* @param A system matrix
* @param litmax number of iterations to do (the maximum allowed)
* @param letol error tolerance
* @param lambda Point to the eigenvalue
* @param key smooth with A or A' (0=A, 1=A')
* @param flag determines which "mode" we run in:\n
* 0 --> Normal: check itmax, error tolerance; normal i/o\n
* 1 --> Silent: check only itmax; no i/o\n
* 2 --> Subcycle: check itmax, error tolerance; subcycle i/o\n
* 3 --> Subcycle: check itmax, error tolerance; no i/o
* @param itmax number of iterations to do (the maximum allowed)
* @param etol error tolerance
*/
VEXTERNC void Bvec_eig(Bvec *thee, Bmat *A,
int litmax, double letol, double *lambda,
int key, int flag, int itmax, double etol);
#endif /* _BVEC_H_ */
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