/****************************************************************** * * * File : spgmr.c * * Programmers : Scott D. Cohen and Alan C. Hindmarsh @ LLNL * * Last Modified : 1 September 1994 * *----------------------------------------------------------------* * This is the implementation file for the scaled preconditioned * * GMRES (SPGMR) iterative linear solver. * * * ******************************************************************/ #include #include #include "iterativ.h" #include "spgmr.h" #include "llnltyps.h" #include "vector.h" #include "llnlmath.h" #define ZERO RCONST(0.0) #define ONE RCONST(1.0) /*************** Private Helper Function Prototype *******************/ static void FreeVectorArray(N_Vector *A, int indMax); /* Implementation of Spgmr algorithm */ /*************** SpgmrMalloc *****************************************/ SpgmrMem SpgmrMalloc(integer N, int l_max, void *machEnv) { SpgmrMem mem; N_Vector *V, xcor, vtemp; real **Hes, *givens, *yg; int k, i; /* Check the input parameters */ if ((N <= 0) || (l_max <= 0)) return(NULL); /* Get memory for the Krylov basis vectors V[0], ..., V[l_max] */ V = (N_Vector *) malloc((l_max+1)*sizeof(N_Vector)); if (V == NULL) return(NULL); for (k=0; k <= l_max; k++) { V[k] = N_VNew(N, machEnv); if (V[k] == NULL) { FreeVectorArray(V, k-1); return(NULL); } } /* Get memory for the Hessenberg matrix Hes */ Hes = (real **) malloc((l_max+1)*sizeof(real *)); if (Hes == NULL) { FreeVectorArray(V, l_max); return(NULL); } for (k=0; k <= l_max; k++) { Hes[k] = (real *) malloc(l_max*sizeof(real)); if (Hes[k] == NULL) { for (i=0; i < k; i++) free(Hes[i]); FreeVectorArray(V, l_max); return(NULL); } } /* Get memory for Givens rotation components */ givens = (real *) malloc(2*l_max*sizeof(real)); if (givens == NULL) { for (i=0; i <= l_max; i++) free(Hes[i]); FreeVectorArray(V, l_max); return(NULL); } /* Get memory to hold the correction to z_tilde */ xcor = N_VNew(N, machEnv); if (xcor == NULL) { free(givens); for (i=0; i <= l_max; i++) free(Hes[i]); FreeVectorArray(V, l_max); return(NULL); } /* Get memory to hold SPGMR y and g vectors */ yg = (real *) malloc((l_max+1)*sizeof(real)); if (yg == NULL) { N_VFree(xcor); free(givens); for (i=0; i <= l_max; i++) free(Hes[i]); FreeVectorArray(V, l_max); return(NULL); } /* Get an array to hold a temporary vector */ vtemp = N_VNew(N, machEnv); if (vtemp == NULL) { free(yg); N_VFree(xcor); free(givens); for (i=0; i <= l_max; i++) free(Hes[i]); FreeVectorArray(V, l_max); return(NULL); } /* Get memory for an SpgmrMemRec containing SPGMR matrices and vectors */ mem = (SpgmrMem) malloc(sizeof(SpgmrMemRec)); if (mem == NULL) { N_VFree(vtemp); free(yg); N_VFree(xcor); free(givens); for (i=0; i <= l_max; i++) free(Hes[i]); FreeVectorArray(V, l_max); return(NULL); } /* Set the fields of mem */ mem->N = N; mem->l_max = l_max; mem->V = V; mem->Hes = Hes; mem->givens = givens; mem->xcor = xcor; mem->yg = yg; mem->vtemp = vtemp; /* Return the pointer to SPGMR memory */ return(mem); } /*************** SpgmrSolve ******************************************/ int SpgmrSolve(SpgmrMem mem, void *A_data, N_Vector x, N_Vector b, int pretype, int gstype, real delta, int max_restarts, void *P_data, N_Vector sx, N_Vector sb, ATimesFn atimes, PSolveFn psolve, real *res_norm, int *nli, int *nps) { N_Vector *V, xcor, vtemp; real **Hes, *givens, *yg; real s_r0_norm, beta, rotation_product, r_norm, s_product, rho; bool preOnLeft, preOnRight, scale_x, scale_b, converged; int i, j, k, l, l_plus_1, l_max, krydim, ier, ntries; if (mem == NULL) return(SPGMR_MEM_NULL); /* Make local copies of mem variables */ l_max = mem->l_max; V = mem->V; Hes = mem->Hes; givens = mem->givens; xcor = mem->xcor; yg = mem->yg; vtemp = mem->vtemp; *nli = *nps = 0; /* Initialize counters */ converged = FALSE; /* Initialize converged flag */ if (max_restarts < 0) max_restarts = 0; if ((pretype != LEFT) && (pretype != RIGHT) && (pretype != BOTH)) pretype = NONE; preOnLeft = ((pretype == LEFT) || (pretype == BOTH)); preOnRight = ((pretype == RIGHT) || (pretype == BOTH)); scale_x = (sx != NULL); scale_b = (sb != NULL); /* Set vtemp and V[0] to initial (unscaled) residual r_0 = b - A*x_0 */ if (N_VDotProd(x, x) == ZERO) { N_VScale(ONE, b, vtemp); } else { if (atimes(A_data, x, vtemp) != 0) return(SPGMR_ATIMES_FAIL); N_VLinearSum(ONE, b, -ONE, vtemp, vtemp); } N_VScale(ONE, vtemp, V[0]); /* Apply b-scaling to vtemp, get L2 norm of sb r_0, and return if small */ /* if (scale_b) N_VProd(sb, vtemp, vtemp); s_r0_norm = RSqrt(N_VDotProd(vtemp, vtemp)); if (s_r0_norm <= delta) return(SPGMR_SUCCESS); */ /* Apply left preconditioner and b-scaling to V[0] = r_0 */ if (preOnLeft) { ier = psolve(P_data, V[0], vtemp, LEFT); (*nps)++; if (ier != 0) return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC); } else { N_VScale(ONE, V[0], vtemp); } if (scale_b) { N_VProd(sb, vtemp, V[0]); } else { N_VScale(ONE, vtemp, V[0]); } /* Set r_norm = beta to L2 norm of V[0] = sb P1_inv r_0, and return if small */ *res_norm = r_norm = beta = RSqrt(N_VDotProd(V[0], V[0])); if (r_norm <= delta) return(SPGMR_SUCCESS); /* Set xcor = 0 */ N_VConst(ZERO, xcor); /* Begin outer iterations: up to (max_restarts + 1) attempts */ for (ntries = 0; ntries <= max_restarts; ntries++) { /* Initialize the Hessenberg matrix Hes and Givens rotation product. Normalize the initial vector V[0]. */ for (i=0; i <= l_max; i++) for (j=0; j < l_max; j++) Hes[i][j] = ZERO; rotation_product = ONE; N_VScale(ONE/r_norm, V[0], V[0]); /* Inner loop: generate Krylov sequence and Arnoldi basis */ for(l=0; l < l_max; l++) { (*nli)++; krydim = l_plus_1 = l + 1; /* Generate A-tilde V[l], where A-tilde = sb P1_inv A P2_inv sx_inv */ /* Apply x-scaling: vtemp = sx_inv V[l] */ if (scale_x) { N_VDiv(V[l], sx, vtemp); } else { N_VScale(ONE, V[l], vtemp); } /* Apply right precoditioner: vtemp = P2_inv sx_inv V[l] */ N_VScale(ONE, vtemp, V[l_plus_1]); if (preOnRight) { ier = psolve(P_data, V[l_plus_1], vtemp, RIGHT); (*nps)++; if (ier != 0) return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC); } /* Apply A: V[l+1] = A P2_inv sx_inv V[l] */ if (atimes(A_data, vtemp, V[l_plus_1] ) != 0) return(SPGMR_ATIMES_FAIL); /* Apply left preconditioning: vtemp = P1_inv A P2_inv sx_inv V[l] */ if (preOnLeft) { ier = psolve(P_data, V[l_plus_1], vtemp, LEFT); (*nps)++; if (ier != 0) return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC); } else { N_VScale(ONE, V[l_plus_1], vtemp); } /* Apply b-scaling: V[l+1] = sb P1_inv A P2_inv sx_inv V[l] */ if (scale_b) { N_VProd(sb, vtemp, V[l_plus_1]); } else { N_VScale(ONE, vtemp, V[l_plus_1]); } /* Orthogonalize V[l+1] against previous V[i]: V[l+1] = w_tilde. */ if (gstype == CLASSICAL_GS) { if (ClassicalGS(V, Hes, l_plus_1, l_max, &(Hes[l_plus_1][l]), vtemp, yg) != 0) return(SPGMR_GS_FAIL); } else { if (ModifiedGS(V, Hes, l_plus_1, l_max, &(Hes[l_plus_1][l])) != 0) return(SPGMR_GS_FAIL); } /* Update the QR factorization of Hes */ if(QRfact(krydim, Hes, givens, l) != 0 ) return(SPGMR_QRFACT_FAIL); /* Update residual norm estimate; break if convergence test passes */ rotation_product *= givens[2*l+1]; if ((*res_norm = rho = ABS(rotation_product*r_norm)) <= delta) { converged = TRUE; break; } /* Normalize V[l+1] with norm value from the Gram-Schmidt */ N_VScale(ONE/Hes[l_plus_1][l], V[l_plus_1], V[l_plus_1]); } /* Inner loop is done. Compute the new correction vector xcor */ /* Construct g, then solve for y */ yg[0] = r_norm; for (i=1; i <= krydim; i++) yg[i]=ZERO; if (QRsol(krydim, Hes, givens, yg) != 0) return(SPGMR_QRSOL_FAIL); /* Add correction vector V_l y to xcor */ for (k=0; k < krydim; k++) N_VLinearSum(yg[k], V[k], ONE, xcor, xcor); /* If converged, construct the final solution vector x */ if (converged) { /* Apply x-scaling and right precond.: vtemp = P2_inv sx_inv xcor */ if (scale_x) N_VDiv(xcor, sx, xcor); if (preOnRight) { ier = psolve(P_data, xcor, vtemp, RIGHT); (*nps)++; if (ier != 0) return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC); } else { N_VScale(ONE, xcor, vtemp); } /* Add correction to initial x to get final solution x, and return */ N_VLinearSum(ONE, x, ONE, vtemp, x); return(SPGMR_SUCCESS); } /* Not yet converged; if allowed, prepare for restart */ if (ntries == max_restarts) break; /* Construct last column of Q in yg */ s_product = ONE; for (i=krydim; i > 0; i--) { yg[i] = s_product*givens[2*i-2]; s_product *= givens[2*i-1]; } yg[0] = s_product; /* Scale r_norm and yg */ r_norm *= s_product; for (i=0; i <= krydim; i++) yg[i] *= r_norm; r_norm = ABS(r_norm); /* Multiply yg by V_(krydim+1) to get last residual vector; restart */ N_VScale(yg[0], V[0], V[0]); for( k=1; k <= krydim; k++) N_VLinearSum(yg[k], V[k], ONE, V[0], V[0]); } /* Failed to converge, even after allowed restarts. If the residual norm was reduced below its initial value, compute and return x anyway. Otherwise return failure flag. */ if (rho < beta) { /* Apply the x-scaling and right precond.: vtemp = P2_inv sx_inv xcor */ if (scale_x) N_VDiv(xcor, sx, xcor); if (preOnRight) { ier = psolve(P_data, xcor, vtemp, RIGHT); (*nps)++; if (ier != 0) return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC); } else { N_VScale(ONE, xcor, vtemp); } /* Add vtemp to initial x to get final solution x, and return */ N_VLinearSum(ONE, x, ONE, vtemp, x); return(SPGMR_RES_REDUCED); } return(SPGMR_CONV_FAIL); } /*************** SpgmrFree *******************************************/ void SpgmrFree(SpgmrMem mem) { int i, l_max; real **Hes; if (mem == NULL) return; l_max = mem->l_max; Hes = mem->Hes; FreeVectorArray(mem->V, l_max); for (i=0; i <= l_max; i++) free(Hes[i]); free(Hes); free(mem->givens); N_VFree(mem->xcor); free(mem->yg); N_VFree(mem->vtemp); free(mem); } /*************** Private Helper Function: FreeVectorArray ************/ static void FreeVectorArray(N_Vector *A, int indMax) { int j; for (j=0; j <= indMax; j++) N_VFree(A[j]); free(A); }