Actual source code: cgs.c

```  1: /*
2:     Note that for the complex numbers version, the VecDot() arguments
3:     within the code MUST remain in the order given for correct computation
4:     of inner products.
5: */
6: #include <petsc/private/kspimpl.h>

8: static PetscErrorCode KSPSetUp_CGS(KSP ksp)
9: {
10:   PetscFunctionBegin;
11:   PetscCall(KSPSetWorkVecs(ksp, 7));
12:   PetscFunctionReturn(PETSC_SUCCESS);
13: }

15: static PetscErrorCode KSPSolve_CGS(KSP ksp)
16: {
17:   PetscInt    i;
18:   PetscScalar rho, rhoold, a, s, b;
19:   Vec         X, B, V, P, R, RP, T, Q, U, AUQ;
20:   PetscReal   dp = 0.0;
21:   PetscBool   diagonalscale;

23:   PetscFunctionBegin;
24:   /* not sure what residual norm it does use, should use for right preconditioning */

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);

29:   X   = ksp->vec_sol;
30:   B   = ksp->vec_rhs;
31:   R   = ksp->work[0];
32:   RP  = ksp->work[1];
33:   V   = ksp->work[2];
34:   T   = ksp->work[3];
35:   Q   = ksp->work[4];
36:   P   = ksp->work[5];
37:   U   = ksp->work[6];
38:   AUQ = V;

40:   /* Compute initial preconditioned residual */
41:   PetscCall(KSPInitialResidual(ksp, X, V, T, R, B));

43:   /* Test for nothing to do */
44:   if (ksp->normtype != KSP_NORM_NONE) {
45:     PetscCall(VecNorm(R, NORM_2, &dp));
46:     KSPCheckNorm(ksp, dp);
47:     if (ksp->normtype == KSP_NORM_NATURAL) dp *= dp;
48:   } else dp = 0.0;

50:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
51:   ksp->its   = 0;
52:   ksp->rnorm = dp;
53:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
54:   PetscCall(KSPLogResidualHistory(ksp, dp));
55:   PetscCall(KSPMonitor(ksp, 0, dp));
56:   PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP));
57:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

59:   /* Make the initial Rp == R */
60:   PetscCall(VecCopy(R, RP));
61:   /*  added for Fidap */
62:   /* Penalize Startup - Isaac Hasbani Trick for CGS
63:      Since most initial conditions result in a mostly 0 residual,
64:      we change all the 0 values in the vector RP to the maximum.
65:   */
66:   if (ksp->normtype == KSP_NORM_NATURAL) {
67:     PetscReal    vr0max;
68:     PetscScalar *tmp_RP = NULL;
69:     PetscInt     numnp = 0, *max_pos = NULL;
70:     PetscCall(VecMax(RP, max_pos, &vr0max));
71:     PetscCall(VecGetArray(RP, &tmp_RP));
72:     PetscCall(VecGetLocalSize(RP, &numnp));
73:     for (i = 0; i < numnp; i++) {
74:       if (tmp_RP[i] == 0.0) tmp_RP[i] = vr0max;
75:     }
76:     PetscCall(VecRestoreArray(RP, &tmp_RP));
77:   }
78:   /*  end of addition for Fidap */

80:   /* Set the initial conditions */
81:   PetscCall(VecDot(R, RP, &rhoold)); /* rhoold = (r,rp)      */
82:   PetscCall(VecCopy(R, U));
83:   PetscCall(VecCopy(R, P));
84:   PetscCall(KSP_PCApplyBAorAB(ksp, P, V, T));

86:   i = 0;
87:   do {
88:     PetscCall(VecDot(V, RP, &s)); /* s <- (v,rp)          */
89:     KSPCheckDot(ksp, s);
90:     a = rhoold / s;                    /* a <- rho / s         */
91:     PetscCall(VecWAXPY(Q, -a, V, U));  /* q <- u - a v         */
92:     PetscCall(VecWAXPY(T, 1.0, U, Q)); /* t <- u + q           */
93:     PetscCall(VecAXPY(X, a, T));       /* x <- x + a (u + q)   */
94:     PetscCall(KSP_PCApplyBAorAB(ksp, T, AUQ, U));
95:     PetscCall(VecAXPY(R, -a, AUQ)); /* r <- r - a K (u + q) */
96:     PetscCall(VecDot(R, RP, &rho)); /* rho <- (r,rp)        */
97:     KSPCheckDot(ksp, rho);
98:     if (ksp->normtype == KSP_NORM_NATURAL) {
99:       dp = PetscAbsScalar(rho);
100:     } else if (ksp->normtype != KSP_NORM_NONE) {
101:       PetscCall(VecNorm(R, NORM_2, &dp));
102:       KSPCheckNorm(ksp, dp);
103:     } else dp = 0.0;

105:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
106:     ksp->its++;
107:     ksp->rnorm = dp;
108:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
109:     PetscCall(KSPLogResidualHistory(ksp, dp));
110:     PetscCall(KSPMonitor(ksp, i + 1, dp));
111:     PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
112:     if (ksp->reason) break;

114:     b = rho / rhoold;                /* b <- rho / rhoold    */
115:     PetscCall(VecWAXPY(U, b, Q, R)); /* u <- r + b q         */
116:     PetscCall(VecAXPY(Q, b, P));
117:     PetscCall(VecWAXPY(P, b, Q, U));            /* p <- u + b(q + b p)  */
118:     PetscCall(KSP_PCApplyBAorAB(ksp, P, V, Q)); /* v <- K p    */
119:     rhoold = rho;
120:     i++;
121:   } while (i < ksp->max_it);
122:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;

124:   PetscCall(KSPUnwindPreconditioner(ksp, X, T));
125:   PetscFunctionReturn(PETSC_SUCCESS);
126: }

128: /*MC
129:      KSPCGS - This code implements the CGS (Conjugate Gradient Squared) method {cite}`so:89`.

131:    Level: beginner

133:    Notes:
134:    Does not require a symmetric matrix. Does not apply transpose of the matrix.

136:    Supports left and right preconditioning, but not symmetric.

138:    Developer Note:
139:    Has this weird support for doing the convergence test with the natural norm, I assume this works only with
140:    no preconditioning and symmetric positive definite operator.

142: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPBCGS`, `KSPSetPCSide()`
143: M*/
144: PETSC_EXTERN PetscErrorCode KSPCreate_CGS(KSP ksp)
145: {
146:   PetscFunctionBegin;
147:   ksp->data = (void *)0;

149:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
150:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
151:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));
152:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_RIGHT, 2));
153:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));
154:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

156:   ksp->ops->setup          = KSPSetUp_CGS;
157:   ksp->ops->solve          = KSPSolve_CGS;
158:   ksp->ops->destroy        = KSPDestroyDefault;
159:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
160:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
161:   ksp->ops->setfromoptions = NULL;
162:   ksp->ops->view           = NULL;
163:   PetscFunctionReturn(PETSC_SUCCESS);
164: }
```