1 2 #include <petsc-private/kspimpl.h> 3 4 typedef struct { 5 PetscReal haptol; 6 } KSP_SYMMLQ; 7 8 #undef __FUNCT__ 9 #define __FUNCT__ "KSPSetUp_SYMMLQ" 10 PetscErrorCode KSPSetUp_SYMMLQ(KSP ksp) 11 { 12 PetscErrorCode ierr; 13 14 PetscFunctionBegin; 15 ierr = KSPDefaultGetWork(ksp,9);CHKERRQ(ierr); 16 PetscFunctionReturn(0); 17 } 18 19 #undef __FUNCT__ 20 #define __FUNCT__ "KSPSolve_SYMMLQ" 21 PetscErrorCode KSPSolve_SYMMLQ(KSP ksp) 22 { 23 PetscErrorCode ierr; 24 PetscInt i; 25 PetscScalar alpha,beta,ibeta,betaold,beta1,ceta = 0,ceta_oold = 0.0, ceta_old = 0.0,ceta_bar; 26 PetscScalar c=1.0,cold=1.0,s=0.0,sold=0.0,coold,soold,rho0,rho1,rho2,rho3; 27 PetscScalar dp = 0.0; 28 PetscReal np,s_prod; 29 Vec X,B,R,Z,U,V,W,UOLD,VOLD,Wbar; 30 Mat Amat,Pmat; 31 MatStructure pflag; 32 KSP_SYMMLQ *symmlq = (KSP_SYMMLQ*)ksp->data; 33 PetscBool diagonalscale; 34 35 PetscFunctionBegin; 36 ierr = PCGetDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr); 37 if (diagonalscale) SETERRQ1(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name); 38 39 X = ksp->vec_sol; 40 B = ksp->vec_rhs; 41 R = ksp->work[0]; 42 Z = ksp->work[1]; 43 U = ksp->work[2]; 44 V = ksp->work[3]; 45 W = ksp->work[4]; 46 UOLD = ksp->work[5]; 47 VOLD = ksp->work[6]; 48 Wbar = ksp->work[7]; 49 50 ierr = PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);CHKERRQ(ierr); 51 52 ksp->its = 0; 53 54 ierr = VecSet(UOLD,0.0);CHKERRQ(ierr); /* u_old <- zeros; */ 55 ierr = VecCopy(UOLD,VOLD);CHKERRQ(ierr); /* v_old <- u_old; */ 56 ierr = VecCopy(UOLD,W);CHKERRQ(ierr); /* w <- u_old; */ 57 ierr = VecCopy(UOLD,Wbar);CHKERRQ(ierr); /* w_bar <- u_old; */ 58 if (!ksp->guess_zero) { 59 ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr); /* r <- b - A*x */ 60 ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr); 61 } else { 62 ierr = VecCopy(B,R);CHKERRQ(ierr); /* r <- b (x is 0) */ 63 } 64 65 ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- B*r */ 66 ierr = VecDot(R,Z,&dp);CHKERRQ(ierr); /* dp = r'*z; */ 67 if (PetscAbsScalar(dp) < symmlq->haptol) { 68 ierr = PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),symmlq->haptol);CHKERRQ(ierr); 69 ksp->rnorm = 0.0; /* what should we really put here? */ 70 ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN; /* bugfix proposed by Lourens (lourens.vanzanen@shell.com) */ 71 PetscFunctionReturn(0); 72 } 73 74 #if !defined(PETSC_USE_COMPLEX) 75 if (dp < 0.0) { 76 ksp->reason = KSP_DIVERGED_INDEFINITE_PC; 77 PetscFunctionReturn(0); 78 } 79 #endif 80 dp = PetscSqrtScalar(dp); 81 beta = dp; /* beta <- sqrt(r'*z) */ 82 beta1 = beta; 83 s_prod = PetscAbsScalar(beta1); 84 85 ierr = VecCopy(R,V);CHKERRQ(ierr); /* v <- r; */ 86 ierr = VecCopy(Z,U);CHKERRQ(ierr); /* u <- z; */ 87 ibeta = 1.0 / beta; 88 ierr = VecScale(V,ibeta);CHKERRQ(ierr); /* v <- ibeta*v; */ 89 ierr = VecScale(U,ibeta);CHKERRQ(ierr); /* u <- ibeta*u; */ 90 ierr = VecCopy(U,Wbar);CHKERRQ(ierr); /* w_bar <- u; */ 91 ierr = VecNorm(Z,NORM_2,&np);CHKERRQ(ierr); /* np <- ||z|| */ 92 KSPLogResidualHistory(ksp,np); 93 ierr = KSPMonitor(ksp,0,np);CHKERRQ(ierr); 94 ksp->rnorm = np; 95 ierr = (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP);CHKERRQ(ierr); /* test for convergence */ 96 if (ksp->reason) PetscFunctionReturn(0); 97 98 i = 0; ceta = 0.; 99 do { 100 ksp->its = i+1; 101 102 /* Update */ 103 if (ksp->its > 1) { 104 ierr = VecCopy(V,VOLD);CHKERRQ(ierr); /* v_old <- v; */ 105 ierr = VecCopy(U,UOLD);CHKERRQ(ierr); /* u_old <- u; */ 106 107 ierr = VecCopy(R,V);CHKERRQ(ierr); 108 ierr = VecScale(V,1.0/beta);CHKERRQ(ierr); /* v <- ibeta*r; */ 109 ierr = VecCopy(Z,U);CHKERRQ(ierr); 110 ierr = VecScale(U,1.0/beta);CHKERRQ(ierr); /* u <- ibeta*z; */ 111 112 ierr = VecCopy(Wbar,W);CHKERRQ(ierr); 113 ierr = VecScale(W,c);CHKERRQ(ierr); 114 ierr = VecAXPY(W,s,U);CHKERRQ(ierr); /* w <- c*w_bar + s*u; (w_k) */ 115 ierr = VecScale(Wbar,-s);CHKERRQ(ierr); 116 ierr = VecAXPY(Wbar,c,U);CHKERRQ(ierr); /* w_bar <- -s*w_bar + c*u; (w_bar_(k+1)) */ 117 ierr = VecAXPY(X,ceta,W);CHKERRQ(ierr); /* x <- x + ceta * w; (xL_k) */ 118 119 ceta_oold = ceta_old; 120 ceta_old = ceta; 121 } 122 123 /* Lanczos */ 124 ierr = KSP_MatMult(ksp,Amat,U,R);CHKERRQ(ierr); /* r <- Amat*u; */ 125 ierr = VecDot(U,R,&alpha);CHKERRQ(ierr); /* alpha <- u'*r; */ 126 ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- B*r; */ 127 128 ierr = VecAXPY(R,-alpha,V);CHKERRQ(ierr); /* r <- r - alpha* v; */ 129 ierr = VecAXPY(Z,-alpha,U);CHKERRQ(ierr); /* z <- z - alpha* u; */ 130 ierr = VecAXPY(R,-beta,VOLD);CHKERRQ(ierr); /* r <- r - beta * v_old; */ 131 ierr = VecAXPY(Z,-beta,UOLD);CHKERRQ(ierr); /* z <- z - beta * u_old; */ 132 betaold = beta; /* beta_k */ 133 ierr = VecDot(R,Z,&dp);CHKERRQ(ierr); /* dp <- r'*z; */ 134 if (PetscAbsScalar(dp) < symmlq->haptol) { 135 ierr = PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),symmlq->haptol);CHKERRQ(ierr); 136 dp = 0.0; 137 } 138 139 #if !defined(PETSC_USE_COMPLEX) 140 if (dp < 0.0) { 141 ksp->reason = KSP_DIVERGED_INDEFINITE_PC; 142 break; 143 } 144 #endif 145 beta = PetscSqrtScalar(dp); /* beta = sqrt(dp); */ 146 147 /* QR factorization */ 148 coold = cold; cold = c; soold = sold; sold = s; 149 rho0 = cold * alpha - coold * sold * betaold; /* gamma_bar */ 150 rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta); /* gamma */ 151 rho2 = sold * alpha + coold * cold * betaold; /* delta */ 152 rho3 = soold * betaold; /* epsilon */ 153 154 /* Givens rotation: [c -s; s c] (different from the Reference!) */ 155 c = rho0 / rho1; s = beta / rho1; 156 157 if (ksp->its==1) { 158 ceta = beta1/rho1; 159 } else { 160 ceta = -(rho2*ceta_old + rho3*ceta_oold)/rho1; 161 } 162 163 s_prod = s_prod*PetscAbsScalar(s); 164 if (c == 0.0) { 165 np = s_prod*1.e16; 166 } else { 167 np = s_prod/PetscAbsScalar(c); /* residual norm for xc_k (CGNORM) */ 168 } 169 ksp->rnorm = np; 170 KSPLogResidualHistory(ksp,np); 171 ierr = KSPMonitor(ksp,i+1,np);CHKERRQ(ierr); 172 ierr = (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP);CHKERRQ(ierr); /* test for convergence */ 173 if (ksp->reason) break; 174 i++; 175 } while (i<ksp->max_it); 176 177 /* move to the CG point: xc_(k+1) */ 178 if (c == 0.0) { 179 ceta_bar = ceta*1.e15; 180 } else { 181 ceta_bar = ceta/c; 182 } 183 ierr = VecAXPY(X,ceta_bar,Wbar);CHKERRQ(ierr); /* x <- x + ceta_bar*w_bar */ 184 185 if (i >= ksp->max_it) { 186 ksp->reason = KSP_DIVERGED_ITS; 187 } 188 PetscFunctionReturn(0); 189 } 190 191 /*MC 192 KSPSYMMLQ - This code implements the SYMMLQ method. 193 194 Options Database Keys: 195 . see KSPSolve() 196 197 Level: beginner 198 199 Notes: The operator and the preconditioner must be symmetric for this method. The 200 preconditioner must be POSITIVE-DEFINITE. 201 202 Supports only left preconditioning. 203 204 Reference: Paige & Saunders, 1975. 205 206 .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP 207 M*/ 208 EXTERN_C_BEGIN 209 #undef __FUNCT__ 210 #define __FUNCT__ "KSPCreate_SYMMLQ" 211 PetscErrorCode KSPCreate_SYMMLQ(KSP ksp) 212 { 213 KSP_SYMMLQ *symmlq; 214 PetscErrorCode ierr; 215 216 PetscFunctionBegin; 217 ierr = KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);CHKERRQ(ierr); 218 ierr = PetscNewLog(ksp,KSP_SYMMLQ,&symmlq);CHKERRQ(ierr); 219 symmlq->haptol = 1.e-18; 220 ksp->data = (void*)symmlq; 221 222 /* 223 Sets the functions that are associated with this data structure 224 (in C++ this is the same as defining virtual functions) 225 */ 226 ksp->ops->setup = KSPSetUp_SYMMLQ; 227 ksp->ops->solve = KSPSolve_SYMMLQ; 228 ksp->ops->destroy = KSPDefaultDestroy; 229 ksp->ops->setfromoptions = 0; 230 ksp->ops->buildsolution = KSPDefaultBuildSolution; 231 ksp->ops->buildresidual = KSPDefaultBuildResidual; 232 PetscFunctionReturn(0); 233 } 234 EXTERN_C_END 235 236 237 238 239 240