/*******************************************************************
* *
* File : iterativ.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 header file contains declarations intended for use by *
* generic iterative solvers of Ax = b. The enumeration gives *
* symbolic names for the type of preconditioning to be used. *
* The function type declarations give the prototypes for the *
* functions to be called within an iterative linear solver, that *
* are responsible for *
* multiplying A by a given vector v (ATimesFn), and *
* solving the preconditioner equation Pz = r (PSolveFn). *
* *
*******************************************************************/
#ifdef __cplusplus /* wrapper to enable C++ usage */
extern "C" {
#endif
#ifndef _iterativ_h
#define _iterativ_h
#include "sundialstypes.h"
#include "nvector.h"
/******************************************************************
* *
* enum : types of preconditioning *
*----------------------------------------------------------------*
* NONE : The iterative linear solver should not use *
* preconditioning. *
* *
* LEFT : The iterative linear solver uses preconditioning on *
* the left only. *
* *
* RIGHT : The iterative linear solver uses preconditioning on *
* the right only. *
* *
* BOTH : The iterative linear solver uses preconditioning on *
* both the left and the right. *
* *
******************************************************************/
enum { NONE, LEFT, RIGHT, BOTH };
/******************************************************************
* *
* enum : types of Gram-Schmidt routines *
*----------------------------------------------------------------*
* MODIFIED_GS : The iterative solver uses the modified *
* Gram-Schmidt routine ModifiedGS listed in this *
* file. *
* *
* CLASSICAL_GS : The iterative solver uses the classical *
* Gram-Schmidt routine ClassicalGS listed in this *
* file. *
* *
******************************************************************/
enum { MODIFIED_GS, CLASSICAL_GS };
/******************************************************************
* *
* Type: ATimesFn *
*----------------------------------------------------------------*
* An ATimesFn multiplies Av and stores the result in z. The *
* caller is responsible for allocating memory for the z vector. *
* The parameter A_data is a pointer to any information about A *
* which the function needs in order to do its job. The vector v *
* is unchanged. An ATimesFn returns 0 if successful and a *
* non-zero value if unsuccessful. *
* *
******************************************************************/
typedef int (*ATimesFn)(void *A_data, N_Vector v, N_Vector z);
/******************************************************************
* *
* Type: PSolveFn *
*----------------------------------------------------------------*
* A PSolveFn solves the preconditioner equation Pz = r for the *
* vector z. The caller is responsible for allocating memory for *
* the z vector. The parameter P_data is a pointer to any *
* information about P which the function needs in order to do *
* its job. The parameter lr is input, and indicates whether P *
* is to be taken as the left preconditioner or the right *
* preconditioner: lr = 1 for left and lr = 2 for right. *
* If preconditioning is on one side only, lr can be ignored. *
* The vector r is unchanged. *
* A PSolveFn returns 0 if successful and a non-zero value if *
* unsuccessful. On a failure, a negative return value indicates *
* an unrecoverable condition, while a positive value indicates *
* a recoverable one, in which the calling routine may reattempt *
* the solution after updating preconditioner data. *
* *
******************************************************************/
typedef int (*PSolveFn)(void *P_data, N_Vector r, N_Vector z, int lr);
/******************************************************************
* *
* Function: ModifiedGS *
*----------------------------------------------------------------*
* ModifiedGS performs a modified Gram-Schmidt orthogonalization *
* of the N_Vector v[k] against the p unit N_Vectors at *
* v[k-1], v[k-2], ..., v[k-p]. *
* *
* v is an array of (k+1) N_Vectors v[i], i=0, 1, ..., k. *
* v[k-1], v[k-2], ..., v[k-p] are assumed to have L2-norm *
* equal to 1. *
* *
* h is the output k by k Hessenberg matrix of inner products. *
* This matrix must be allocated row-wise so that the (i,j)th *
* entry is h[i][j]. The inner products (v[i],v[k]), *
* i=i0, i0+1, ..., k-1, are stored at h[i][k-1]. Here *
* i0=MAX(0,k-p). *
* *
* k is the index of the vector in the v array that needs to be *
* orthogonalized against previous vectors in the v array. *
* *
* p is the number of previous vectors in the v array against *
* which v[k] is to be orthogonalized. *
* *
* new_vk_norm is a pointer to memory allocated by the caller to *
* hold the Euclidean norm of the orthogonalized vector v[k]. *
* *
* If (k-p) < 0, then ModifiedGS uses p=k. The orthogonalized *
* v[k] is NOT normalized and is stored over the old v[k]. Once *
* the orthogonalization has been performed, the Euclidean norm *
* of v[k] is stored in (*new_vk_norm). *
* *
* ModifiedGS returns 0 to indicate success. It cannot fail. *
* *
******************************************************************/
int ModifiedGS(N_Vector *v, realtype **h, int k, int p,
realtype *new_vk_norm);
/******************************************************************
* *
* Function: ClassicalGS *
*----------------------------------------------------------------*
* ClassicalGS performs a classical Gram-Schmidt *
* orthogonalization of the N_Vector v[k] against the p unit *
* N_Vectors at v[k-1], v[k-2], ..., v[k-p]. The parameters v, h, *
* k, p, and new_vk_norm are as described in the documentation *
* for ModifiedGS. *
* *
* temp is an N_Vector which can be used as workspace by the *
* ClassicalGS routine. *
* *
* s is a length k array of realtype which can be used as *
* workspace by the ClassicalGS routine. *
* *
* ClassicalGS returns 0 to indicate success. It cannot fail. *
* *
******************************************************************/
int ClassicalGS(N_Vector *v, realtype **h, int k, int p,
realtype *new_vk_norm, N_Vector temp, realtype *s);
/******************************************************************
* *
* Function: QRfact *
*----------------------------------------------------------------*
* QRfact performs a QR factorization of the Hessenberg matrix H. *
* *
* n is the problem size; the matrix H is (n+1) by n. *
* *
* h is the (n+1) by n Hessenberg matrix H to be factored. It is *
* stored row-wise. *
* *
* q is an array of length 2*n containing the Givens rotations *
* computed by this function. A Givens rotation has the form: *
* | c -s | *
* | s c |. *
* The components of the Givens rotations are stored in q as *
* (c, s, c, s, ..., c, s). *
* *
* job is a control flag. If job==0, then a new QR factorization *
* is performed. If job!=0, then it is assumed that the first *
* n-1 columns of h have already been factored and only the last *
* column needs to be updated. *
* *
* QRfact returns 0 if successful. If a zero is encountered on *
* the diagonal of the triangular factor R, then QRfact returns *
* the equation number of the zero entry, where the equations are *
* numbered from 1, not 0. If QRsol is subsequently called in *
* this situation, it will return an error because it could not *
* divide by the zero diagonal entry. *
* *
******************************************************************/
int QRfact(int n, realtype **h, realtype *q, int job);
/******************************************************************
* *
* Function: QRsol *
*----------------------------------------------------------------*
* QRsol solves the linear least squares problem *
* *
* min (b - H*x, b - H*x), x in R^n, *
* *
* where H is a Hessenberg matrix, and b is in R^(n+1). *
* It uses the QR factors of H computed by QRfact. *
* *
* n is the problem size; the matrix H is (n+1) by n. *
* *
* h is a matrix (computed by QRfact) containing the upper *
* triangular factor R of the original Hessenberg matrix H. *
* *
* q is an array of length 2*n (computed by QRfact) containing *
* the Givens rotations used to factor H. *
* *
* b is the (n+1)-vector appearing in the least squares problem *
* above. *
* *
* On return, b contains the solution x of the least squares *
* problem, if QRsol was successful. *
* *
* QRsol returns a 0 if successful. Otherwise, a zero was *
* encountered on the diagonal of the triangular factor R. *
* In this case, QRsol returns the equation number (numbered *
* from 1, not 0) of the zero entry. *
* *
******************************************************************/
int QRsol(int n, realtype **h, realtype *q, realtype *b);
#endif
#ifdef __cplusplus
}
#endif