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 PetscFunctionBegin; 10 PetscCall(KSPSetWorkVecs(ksp, 9)); 11 PetscFunctionReturn(0); 12 } 13 14 PetscErrorCode KSPSolve_SYMMLQ(KSP ksp) { 15 PetscInt i; 16 PetscScalar alpha, beta, ibeta, betaold, beta1, ceta = 0, ceta_oold = 0.0, ceta_old = 0.0, ceta_bar; 17 PetscScalar c = 1.0, cold = 1.0, s = 0.0, sold = 0.0, coold, soold, rho0, rho1, rho2, rho3; 18 PetscScalar dp = 0.0; 19 PetscReal np = 0.0, s_prod; 20 Vec X, B, R, Z, U, V, W, UOLD, VOLD, Wbar; 21 Mat Amat, Pmat; 22 KSP_SYMMLQ *symmlq = (KSP_SYMMLQ *)ksp->data; 23 PetscBool diagonalscale; 24 25 PetscFunctionBegin; 26 PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale)); 27 PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name); 28 29 X = ksp->vec_sol; 30 B = ksp->vec_rhs; 31 R = ksp->work[0]; 32 Z = ksp->work[1]; 33 U = ksp->work[2]; 34 V = ksp->work[3]; 35 W = ksp->work[4]; 36 UOLD = ksp->work[5]; 37 VOLD = ksp->work[6]; 38 Wbar = ksp->work[7]; 39 40 PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat)); 41 42 ksp->its = 0; 43 44 PetscCall(VecSet(UOLD, 0.0)); /* u_old <- zeros; */ 45 PetscCall(VecCopy(UOLD, VOLD)); /* v_old <- u_old; */ 46 PetscCall(VecCopy(UOLD, W)); /* w <- u_old; */ 47 PetscCall(VecCopy(UOLD, Wbar)); /* w_bar <- u_old; */ 48 if (!ksp->guess_zero) { 49 PetscCall(KSP_MatMult(ksp, Amat, X, R)); /* r <- b - A*x */ 50 PetscCall(VecAYPX(R, -1.0, B)); 51 } else { 52 PetscCall(VecCopy(B, R)); /* r <- b (x is 0) */ 53 } 54 55 PetscCall(KSP_PCApply(ksp, R, Z)); /* z <- B*r */ 56 PetscCall(VecDot(R, Z, &dp)); /* dp = r'*z; */ 57 KSPCheckDot(ksp, dp); 58 if (PetscAbsScalar(dp) < symmlq->haptol) { 59 PetscCall(PetscInfo(ksp, "Detected happy breakdown %g tolerance %g\n", (double)PetscAbsScalar(dp), (double)symmlq->haptol)); 60 ksp->rnorm = 0.0; /* what should we really put here? */ 61 ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN; /* bugfix proposed by Lourens (lourens.vanzanen@shell.com) */ 62 PetscFunctionReturn(0); 63 } 64 65 #if !defined(PETSC_USE_COMPLEX) 66 if (dp < 0.0) { 67 ksp->reason = KSP_DIVERGED_INDEFINITE_PC; 68 PetscFunctionReturn(0); 69 } 70 #endif 71 dp = PetscSqrtScalar(dp); 72 beta = dp; /* beta <- sqrt(r'*z) */ 73 beta1 = beta; 74 s_prod = PetscAbsScalar(beta1); 75 76 PetscCall(VecCopy(R, V)); /* v <- r; */ 77 PetscCall(VecCopy(Z, U)); /* u <- z; */ 78 ibeta = 1.0 / beta; 79 PetscCall(VecScale(V, ibeta)); /* v <- ibeta*v; */ 80 PetscCall(VecScale(U, ibeta)); /* u <- ibeta*u; */ 81 PetscCall(VecCopy(U, Wbar)); /* w_bar <- u; */ 82 if (ksp->normtype != KSP_NORM_NONE) { 83 PetscCall(VecNorm(Z, NORM_2, &np)); /* np <- ||z|| */ 84 KSPCheckNorm(ksp, np); 85 } 86 PetscCall(KSPLogResidualHistory(ksp, np)); 87 PetscCall(KSPMonitor(ksp, 0, np)); 88 ksp->rnorm = np; 89 PetscCall((*ksp->converged)(ksp, 0, np, &ksp->reason, ksp->cnvP)); /* test for convergence */ 90 if (ksp->reason) PetscFunctionReturn(0); 91 92 i = 0; 93 ceta = 0.; 94 do { 95 ksp->its = i + 1; 96 97 /* Update */ 98 if (ksp->its > 1) { 99 PetscCall(VecCopy(V, VOLD)); /* v_old <- v; */ 100 PetscCall(VecCopy(U, UOLD)); /* u_old <- u; */ 101 102 PetscCall(VecCopy(R, V)); 103 PetscCall(VecScale(V, 1.0 / beta)); /* v <- ibeta*r; */ 104 PetscCall(VecCopy(Z, U)); 105 PetscCall(VecScale(U, 1.0 / beta)); /* u <- ibeta*z; */ 106 107 PetscCall(VecCopy(Wbar, W)); 108 PetscCall(VecScale(W, c)); 109 PetscCall(VecAXPY(W, s, U)); /* w <- c*w_bar + s*u; (w_k) */ 110 PetscCall(VecScale(Wbar, -s)); 111 PetscCall(VecAXPY(Wbar, c, U)); /* w_bar <- -s*w_bar + c*u; (w_bar_(k+1)) */ 112 PetscCall(VecAXPY(X, ceta, W)); /* x <- x + ceta * w; (xL_k) */ 113 114 ceta_oold = ceta_old; 115 ceta_old = ceta; 116 } 117 118 /* Lanczos */ 119 PetscCall(KSP_MatMult(ksp, Amat, U, R)); /* r <- Amat*u; */ 120 PetscCall(VecDot(U, R, &alpha)); /* alpha <- u'*r; */ 121 PetscCall(KSP_PCApply(ksp, R, Z)); /* z <- B*r; */ 122 123 PetscCall(VecAXPY(R, -alpha, V)); /* r <- r - alpha* v; */ 124 PetscCall(VecAXPY(Z, -alpha, U)); /* z <- z - alpha* u; */ 125 PetscCall(VecAXPY(R, -beta, VOLD)); /* r <- r - beta * v_old; */ 126 PetscCall(VecAXPY(Z, -beta, UOLD)); /* z <- z - beta * u_old; */ 127 betaold = beta; /* beta_k */ 128 PetscCall(VecDot(R, Z, &dp)); /* dp <- r'*z; */ 129 KSPCheckDot(ksp, dp); 130 if (PetscAbsScalar(dp) < symmlq->haptol) { 131 PetscCall(PetscInfo(ksp, "Detected happy breakdown %g tolerance %g\n", (double)PetscAbsScalar(dp), (double)symmlq->haptol)); 132 dp = 0.0; 133 } 134 135 #if !defined(PETSC_USE_COMPLEX) 136 if (dp < 0.0) { 137 ksp->reason = KSP_DIVERGED_INDEFINITE_PC; 138 break; 139 } 140 #endif 141 beta = PetscSqrtScalar(dp); /* beta = sqrt(dp); */ 142 143 /* QR factorization */ 144 coold = cold; 145 cold = c; 146 soold = sold; 147 sold = s; 148 rho0 = cold * alpha - coold * sold * betaold; /* gamma_bar */ 149 rho1 = PetscSqrtScalar(rho0 * rho0 + beta * beta); /* gamma */ 150 rho2 = sold * alpha + coold * cold * betaold; /* delta */ 151 rho3 = soold * betaold; /* epsilon */ 152 153 /* Givens rotation: [c -s; s c] (different from the Reference!) */ 154 c = rho0 / rho1; 155 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 PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm)); 167 PetscCall(KSPMonitor(ksp, i + 1, ksp->rnorm)); 168 PetscCall((*ksp->converged)(ksp, i + 1, ksp->rnorm, &ksp->reason, ksp->cnvP)); /* 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 PetscCall(VecAXPY(X, ceta_bar, Wbar)); /* 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`, `KSP` 200 M*/ 201 PETSC_EXTERN PetscErrorCode KSPCreate_SYMMLQ(KSP ksp) { 202 KSP_SYMMLQ *symmlq; 203 204 PetscFunctionBegin; 205 PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3)); 206 PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1)); 207 208 PetscCall(PetscNew(&symmlq)); 209 symmlq->haptol = 1.e-18; 210 ksp->data = (void *)symmlq; 211 212 /* 213 Sets the functions that are associated with this data structure 214 (in C++ this is the same as defining virtual functions) 215 */ 216 ksp->ops->setup = KSPSetUp_SYMMLQ; 217 ksp->ops->solve = KSPSolve_SYMMLQ; 218 ksp->ops->destroy = KSPDestroyDefault; 219 ksp->ops->setfromoptions = NULL; 220 ksp->ops->buildsolution = KSPBuildSolutionDefault; 221 ksp->ops->buildresidual = KSPBuildResidualDefault; 222 PetscFunctionReturn(0); 223 } 224