/*******************************************************************
* File : spgmr.h *
* Programmers : Scott D. Cohen and Alan C. Hindmarsh @ LLNL *
* Version of : 26 June 2002 *
*-----------------------------------------------------------------*
* Copyright (c) 2002, The Regents of the University of California *
* Produced at the Lawrence Livermore National Laboratory *
* All rights reserved *
* For details, see sundials/shared/LICENSE *
*-----------------------------------------------------------------*
* This is the header file for the implementation of SPGMR Krylov *
* iterative linear solver. The SPGMR algorithm is based on the *
* Scaled Preconditioned GMRES (Generalized Minimal Residual) *
* method. *
* *
* The SPGMR algorithm solves a N by N linear system A x = b. *
* Preconditioning is allowed on the left, right, or both. *
* Scaling is allowed on both sides, and restarts are also allowed.*
* We denote the preconditioner and scaling matrices as follows: *
* P1 = left preconditioner *
* P2 = right preconditioner *
* S1 = diagonal matrix of scale factors for P1-inverse b *
* S2 = diagonal matrix of scale factors for P2 x *
* The matrices A, P1, and P2 are not required explicitly; only *
* routines that provide A, P1-inverse, and P2-inverse as *
* operators are required. *
* *
* In this notation, SPGMR applies the underlying GMRES method to *
* the equivalent transformed system *
* Abar xbar = bbar , where *
* Abar = S1 (P1-inverse) A (P2-inverse) (S2-inverse) , *
* bbar = S1 (P1-inverse) b , and xbar = S2 P2 x . *
* *
* The scaling matrices must be chosen so that vectors S1 *
* P1-inverse b and S2 P2 x have dimensionless components. *
* If preconditioning is done on the left only (P2 = I), by a *
* matrix P, then S2 must be a scaling for x, while S1 is a *
* scaling for P-inverse b, and so may also be taken as a scaling *
* for x. Similarly, if preconditioning is done on the right only *
* (P1 = I, P2 = P), then S1 must be a scaling for b, while S2 is *
* a scaling for P x, and may also be taken as a scaling for b. *
* *
* The stopping test for the SPGMR iterations is on the L2 norm of *
* the scaled preconditioned residual: *
* || bbar - Abar xbar ||_2 < delta *
* with an input test constant delta. *
* *
* The usage of this SPGMR solver involves supplying two routines *
* and making three calls. The user-supplied routines are *
* atimes (A_data, x, y) to compute y = A x, given x, *
* and *
* psolve (P_data, x, y, lr) *
* to solve P1 x = y or P2 x = y for x, given y. *
* The three user calls are: *
* mem = SpgmrMalloc(N, lmax, machEnv); *
* to initialize memory, *
* flag = SpgmrSolve(mem,A_data,x,b,..., *
* P_data,s1,s2,atimes,psolve,...); *
* to solve the system, and *
* SpgmrFree(mem); *
* to free the memory created by SpgmrMalloc. *
* Complete details for specifying atimes and psolve and for the *
* usage calls are given in the paragraphs below and in iterativ.h.*
* *
*******************************************************************/
#ifdef __cplusplus /* wrapper to enable C++ usage */
extern "C" {
#endif
#ifndef _spgmr_h
#define _spgmr_h
#include "sundialstypes.h"
#include "iterativ.h"
#include "nvector.h"
/******************************************************************
* *
* Types: SpgmrMemRec, SpgmrMem *
*----------------------------------------------------------------*
* SpgmrMem is a pointer to an SpgmrMemRec which contains *
* the memory needed by SpgmrSolve. The SpgmrMalloc routine *
* returns a pointer of type SpgmrMem which should then be passed *
* in subsequent calls to SpgmrSolve. The SpgmrFree routine frees *
* the memory allocated by SpgmrMalloc. *
* *
* N is the linear system size. *
* *
* l_max is the maximum Krylov dimension that SpgmrSolve will be *
* permitted to use. *
* *
* V is the array of Krylov basis vectors v_1, ..., v_(l_max+1), *
* stored in V[0], ..., V[l_max], where l_max is the second *
* parameter to SpgmrMalloc. Each v_i is a length N vector of *
* type N_Vector. (N is the first parameter to SpgmrMalloc and *
* represents the size of the linear system.) *
* *
* Hes is the (l_max+1) x l_max Hessenberg matrix. It is stored *
* row-wise so that the (i,j)th element is given by Hes[i][j]. *
* *
* givens is a length 2*l_max array which represents the *
* Givens rotation matrices that arise in the algorithm. The *
* Givens rotation matrices F_0, F_1, ..., F_j, where F_i is *
* *
* 1 *
* 1 *
* c_i -s_i <--- row i *
* s_i c_i *
* 1 *
* 1 *
* *
* are represented in the givens vector as *
* givens[0]=c_0, givens[1]=s_0, givens[2]=c_1, givens[3]=s_1, *
* ..., givens[2j]=c_j, givens[2j+1]=s_j. *
* *
* xcor is a length N vector (type N_Vector) which holds the *
* scaled, preconditioned correction to the initial guess. *
* *
* yg is a length (l_max+1) array of realtype used to hold "short"*
* vectors (e.g. y and g). *
* *
* vtemp is a length N vector (type N_Vector) used as temporary *
* vector storage during calculations. *
* *
******************************************************************/
typedef struct _SpgmrMemRec {
integertype N;
int l_max;
N_Vector *V;
realtype **Hes;
realtype *givens;
N_Vector xcor;
realtype *yg;
N_Vector vtemp;
} SpgmrMemRec, *SpgmrMem;
/******************************************************************
* *
* Function : SpgmrMalloc *
*----------------------------------------------------------------*
* SpgmrMalloc allocates the memory used by SpgmrSolve. It *
* returns a pointer of type SpgmrMem which the user of the *
* SPGMR package should pass to SpgmrSolve. The parameter N *
* is the size of the system to be solved by SpgmrSolve and l_max *
* is the maximum Krylov dimension that SpgmrSolve will be *
* permitted to use. The parameter machEnv is a pointer to *
* machine environment-specific information. This routine returns *
* NULL if there is a memory request failure. *
* *
******************************************************************/
SpgmrMem SpgmrMalloc(integertype N, int l_max, void *machEnv);
/******************************************************************
* *
* Function : SpgmrSolve *
*----------------------------------------------------------------*
* SpgmrSolve solves the linear system Ax = b using the SPGMR *
* method. The return values are given by the symbolic constants *
* below. The first SpgmrSolve parameter is a pointer to memory *
* allocated by a prior call to SpgmrMalloc. The system size N *
* passed in the call to SpgmrMalloc should be the same as the *
* length of all N_Vector arguments passed to SpgmrSolve. *
* *
* mem is the pointer returned by SpgmrMalloc to the structure *
* containing the memory needed by SpgmrSolve. *
* *
* A_data is a pointer to information about the coefficient *
* matrix A. This pointer is passed to the user-supplied function *
* atimes. *
* *
* x is the initial guess x_0 upon entry and the solution *
* N_Vector upon exit with return value SPGMR_SUCCESS or *
* SPGMR_RES_REDUCED. For all other return values, the output x *
* is undefined. *
* *
* b is the right hand side N_Vector. It is undisturbed by this *
* function. *
* *
* pretype is the type of preconditioning to be used. Its *
* legal possible values are enumerated in iterativ.h. These *
* values are NONE=0, LEFT=1, RIGHT=2, and BOTH=3. *
* *
* gstype is the type of Gram-Schmidt orthogonalization to be *
* used. Its legal values are enumerated in iterativ.h. These *
* values are MODIFIED_GS=0 and CLASSICAL_GS=1. *
* *
* delta is the tolerance on the L2 norm of the scaled, *
* preconditioned residual. On return with value SPGMR_SUCCESS, *
* this residual satisfies || s1 P1_inv (b - Ax) ||_2 <= delta. *
* *
* max_restarts is the maximum number of times the algorithm is *
* allowed to restart. *
* *
* P_data is a pointer to preconditioner information. This *
* pointer is passed to the user-supplied function psolve. *
* *
* s1 is an N_Vector of positive scale factors for P1-inv b, where*
* P1 is the left preconditioner. (Not tested for positivity.) *
* Pass NULL if no scaling on P1-inv b is required. *
* *
* s2 is an N_Vector of positive scale factors for P2 x, where *
* P2 is the right preconditioner. (Not tested for positivity.) *
* Pass NULL if no scaling on P2 x is required. *
* *
* atimes is the user-supplied function which performs the *
* operation of multiplying A by a given vector. Its description *
* is given in iterativ.h. *
* *
* psolve is the user-supplied function which solves a *
* preconditioner system Pz = r, where P is P1 or P2. Its full *
* description is given in iterativ.h. The psolve function will *
* not be called if pretype is NONE; in that case, the user *
* should pass NULL for psolve. *
* *
* res_norm is a pointer to the L2 norm of the scaled, *
* preconditioned residual. On return with value SPGMR_SUCCESS or *
* SPGMR_RES_REDUCED, (*res_norm) contains the value *
* || s1 P1_inv (b - Ax) ||_2 for the computed solution x. *
* For all other return values, (*res_norm) is undefined. The *
* caller is responsible for allocating the memory (*res_norm) *
* to be filled in by SpgmrSolve. *
* *
* nli is a pointer to the number of linear iterations done in *
* the execution of SpgmrSolve. The caller is responsible for *
* allocating the memory (*nli) to be filled in by SpgmrSolve. *
* *
* nps is a pointer to the number of calls made to psolve during *
* the execution of SpgmrSolve. The caller is responsible for *
* allocating the memory (*nps) to be filled in by SpgmrSolve. *
* *
* Note.. Repeated calls can be made to SpgmrSolve with varying *
* input arguments. If, however, the problem size N or the *
* maximum Krylov dimension l_max changes, then a call to *
* SpgmrMalloc must be made to obtain new memory for SpgmrSolve *
* to use. *
* *
******************************************************************/
int SpgmrSolve(SpgmrMem mem, void *A_data, N_Vector x, N_Vector b,
int pretype, int gstype, realtype delta,
int max_restarts, void *P_data, N_Vector s1,
N_Vector s2, ATimesFn atimes, PSolveFn psolve,
realtype *res_norm, int *nli, int *nps);
/* Return values for SpgmrSolve */
#define SPGMR_SUCCESS 0 /* Converged */
#define SPGMR_RES_REDUCED 1 /* Did not converge, but reduced
norm of residual */
#define SPGMR_CONV_FAIL 2 /* Failed to converge */
#define SPGMR_QRFACT_FAIL 3 /* QRfact found singular matrix */
#define SPGMR_PSOLVE_FAIL_REC 4 /* psolve failed recoverably */
#define SPGMR_MEM_NULL -1 /* mem argument is NULL */
#define SPGMR_ATIMES_FAIL -2 /* atimes returned failure flag */
#define SPGMR_PSOLVE_FAIL_UNREC -3 /* psolve failed unrecoverably */
#define SPGMR_GS_FAIL -4 /* Gram-Schmidt routine
returned failure flag */
#define SPGMR_QRSOL_FAIL -5 /* QRsol found singular R */
/******************************************************************
* *
* Function : SpgmrFree *
*----------------------------------------------------------------*
* SpgmrMalloc frees the memory allocated by SpgmrMalloc. It is *
* illegal to use the pointer mem after a call to SpgmrFree. *
* *
******************************************************************/
void SpgmrFree(SpgmrMem mem);
/******************************************************************
* Macro: SPGMR_VTEMP *
* *
*----------------------------------------------------------------*
* This macro provides access to the work vector vtemp in the *
* memory block of the SPGMR module. The argument mem is the *
* memory pointer returned by SpgmrMalloc, of type SpgmrMem, *
* and the macro value is of type N_Vector. *
* On a return from SpgmrSolve with *nli = 0, this vector *
* contains the scaled preconditioned initial residual, *
* s1 * P1_inverse * (b - A x_0). *
******************************************************************/
#define SPGMR_VTEMP(mem) (mem->vtemp)
#endif
#ifdef __cplusplus
}
#endif