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