Actual source code: cgne.c


  2: /*
  3:        cgimpl.h defines the simple data structured used to store information
  4:     related to the type of matrix (e.g. complex symmetric) being solved and
  5:     data used during the optional Lanczo process used to compute eigenvalues
  6: */
  7: #include <../src/ksp/ksp/impls/cg/cgimpl.h>
  8: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP, PetscReal *, PetscReal *);
  9: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP, PetscInt, PetscReal *, PetscReal *, PetscInt *);

 11: static PetscErrorCode KSPCGSetType_CGNE(KSP ksp, KSPCGType type)
 12: {
 13:   KSP_CG *cg = (KSP_CG *)ksp->data;

 15:   PetscFunctionBegin;
 16:   cg->type = type;
 17:   PetscFunctionReturn(PETSC_SUCCESS);
 18: }

 20: /*
 21:      KSPSetUp_CGNE - Sets up the workspace needed by the CGNE method.

 23:      IDENTICAL TO THE CG ONE EXCEPT for one extra work vector!
 24: */
 25: static PetscErrorCode KSPSetUp_CGNE(KSP ksp)
 26: {
 27:   KSP_CG  *cgP   = (KSP_CG *)ksp->data;
 28:   PetscInt maxit = ksp->max_it;

 30:   PetscFunctionBegin;
 31:   /* get work vectors needed by CGNE */
 32:   PetscCall(KSPSetWorkVecs(ksp, 4));

 34:   /*
 35:      If user requested computations of eigenvalues then allocate work
 36:      work space needed
 37:   */
 38:   if (ksp->calc_sings) {
 39:     /* get space to store tridiagonal matrix for Lanczos */
 40:     PetscCall(PetscMalloc4(maxit, &cgP->e, maxit, &cgP->d, maxit, &cgP->ee, maxit, &cgP->dd));

 42:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
 43:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
 44:   }
 45:   PetscFunctionReturn(PETSC_SUCCESS);
 46: }

 48: /*
 49:        KSPSolve_CGNE - This routine actually applies the conjugate gradient
 50:     method

 52:    Input Parameter:
 53: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
 54:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);

 56:     Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.

 58: */
 59: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
 60: {
 61:   PetscInt    i, stored_max_it, eigs;
 62:   PetscScalar dpi, a = 1.0, beta, betaold = 1.0, b = 0, *e = NULL, *d = NULL;
 63:   PetscReal   dp = 0.0;
 64:   Vec         X, B, Z, R, P, T;
 65:   KSP_CG     *cg;
 66:   Mat         Amat, Pmat;
 67:   PetscBool   diagonalscale, transpose_pc;

 69:   PetscFunctionBegin;
 70:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
 71:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);
 72:   PetscCall(PCApplyTransposeExists(ksp->pc, &transpose_pc));

 74:   cg            = (KSP_CG *)ksp->data;
 75:   eigs          = ksp->calc_sings;
 76:   stored_max_it = ksp->max_it;
 77:   X             = ksp->vec_sol;
 78:   B             = ksp->vec_rhs;
 79:   R             = ksp->work[0];
 80:   Z             = ksp->work[1];
 81:   P             = ksp->work[2];
 82:   T             = ksp->work[3];

 84: #define VecXDot(x, y, a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x, y, a) : VecTDot(x, y, a))

 86:   if (eigs) {
 87:     e    = cg->e;
 88:     d    = cg->d;
 89:     e[0] = 0.0;
 90:   }
 91:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));

 93:   ksp->its = 0;
 94:   PetscCall(KSP_MatMultTranspose(ksp, Amat, B, T));
 95:   if (!ksp->guess_zero) {
 96:     PetscCall(KSP_MatMult(ksp, Amat, X, P));
 97:     PetscCall(KSP_MatMultTranspose(ksp, Amat, P, R));
 98:     PetscCall(VecAYPX(R, -1.0, T));
 99:   } else {
100:     PetscCall(VecCopy(T, R)); /*     r <- b (x is 0) */
101:   }
102:   if (transpose_pc) {
103:     PetscCall(KSP_PCApplyTranspose(ksp, R, T));
104:   } else {
105:     PetscCall(KSP_PCApply(ksp, R, T));
106:   }
107:   PetscCall(KSP_PCApply(ksp, T, Z));

109:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
110:     PetscCall(VecNorm(Z, NORM_2, &dp)); /*    dp <- z'*z       */
111:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
112:     PetscCall(VecNorm(R, NORM_2, &dp)); /*    dp <- r'*r       */
113:   } else if (ksp->normtype == KSP_NORM_NATURAL) {
114:     PetscCall(VecXDot(Z, R, &beta));
115:     KSPCheckDot(ksp, beta);
116:     dp = PetscSqrtReal(PetscAbsScalar(beta));
117:   } else dp = 0.0;
118:   PetscCall(KSPLogResidualHistory(ksp, dp));
119:   PetscCall(KSPMonitor(ksp, 0, dp));
120:   ksp->rnorm = dp;
121:   PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP)); /* test for convergence */
122:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

124:   i = 0;
125:   do {
126:     ksp->its = i + 1;
127:     PetscCall(VecXDot(Z, R, &beta)); /*     beta <- r'z     */
128:     KSPCheckDot(ksp, beta);
129:     if (beta == 0.0) {
130:       ksp->reason = KSP_CONVERGED_ATOL;
131:       PetscCall(PetscInfo(ksp, "converged due to beta = 0\n"));
132:       break;
133: #if !defined(PETSC_USE_COMPLEX)
134:     } else if (beta < 0.0) {
135:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
136:       PetscCall(PetscInfo(ksp, "diverging due to indefinite preconditioner\n"));
137:       break;
138: #endif
139:     }
140:     if (!i) {
141:       PetscCall(VecCopy(Z, P)); /*     p <- z          */
142:       b = 0.0;
143:     } else {
144:       b = beta / betaold;
145:       if (eigs) {
146:         PetscCheck(ksp->max_it == stored_max_it, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Can not change maxit AND calculate eigenvalues");
147:         e[i] = PetscSqrtReal(PetscAbsScalar(b)) / a;
148:       }
149:       PetscCall(VecAYPX(P, b, Z)); /*     p <- z + b* p   */
150:     }
151:     betaold = beta;
152:     PetscCall(KSP_MatMult(ksp, Amat, P, T));
153:     PetscCall(KSP_MatMultTranspose(ksp, Amat, T, Z));
154:     PetscCall(VecXDot(P, Z, &dpi)); /*     dpi <- z'p      */
155:     KSPCheckDot(ksp, dpi);
156:     a = beta / dpi; /*     a = beta/p'z    */
157:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b)) * e[i] + 1.0 / a;
158:     PetscCall(VecAXPY(X, a, P));  /*     x <- x + ap     */
159:     PetscCall(VecAXPY(R, -a, Z)); /*     r <- r - az     */
160:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
161:       if (transpose_pc) {
162:         PetscCall(KSP_PCApplyTranspose(ksp, R, T));
163:       } else {
164:         PetscCall(KSP_PCApply(ksp, R, T));
165:       }
166:       PetscCall(KSP_PCApply(ksp, T, Z));
167:       PetscCall(VecNorm(Z, NORM_2, &dp)); /*    dp <- z'*z       */
168:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
169:       PetscCall(VecNorm(R, NORM_2, &dp));
170:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
171:       dp = PetscSqrtReal(PetscAbsScalar(beta));
172:     } else dp = 0.0;
173:     ksp->rnorm = dp;
174:     PetscCall(KSPLogResidualHistory(ksp, dp));
175:     PetscCall(KSPMonitor(ksp, i + 1, dp));
176:     PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
177:     if (ksp->reason) break;
178:     if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
179:       if (transpose_pc) {
180:         PetscCall(KSP_PCApplyTranspose(ksp, R, T));
181:       } else {
182:         PetscCall(KSP_PCApply(ksp, R, T));
183:       }
184:       PetscCall(KSP_PCApply(ksp, T, Z));
185:     }
186:     i++;
187:   } while (i < ksp->max_it);
188:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
189:   PetscFunctionReturn(PETSC_SUCCESS);
190: }

192: /*
193:     KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
194:        function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)

196:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
197: */

199: /*MC
200:      KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
201:           without explicitly forming A^t*A

203:    Options Database Keys:
204: .   -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric

206:    Level: beginner

208:    Notes:
209:    Eigenvalue computation routines including `KSPSetComputeEigenvalues()` and `KSPComputeEigenvalues()` will return information about the
210:     spectrum of A^t*A, rather than A.

212:    `KSPCGNE` is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
213:    eigenvalues. A unitary matrix is a classic example where `KSPCGNE` converges in one iteration, but `KSPGMRES` and `KSPCGS` need N
214:    iterations, see [1]. If you intend to solve least squares problems, use `KSPLSQR`.

216:    This is NOT a different algorithm than used with `KSPCG`, it merely uses that algorithm with the
217:    matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.

219:    This method requires that one be able to apply the transpose of the preconditioner and operator
220:    as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
221:    the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?

223:    This only supports left preconditioning.

225:    Reference:
226: .   [1] -  Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992

228:    Developer Note:
229:    This object is subclassed off of `KSPCG`

231: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, 'KSPCG', `KSPLSQR', 'KSPCGLS`,
232:           `KSPCGSetType()`, `KSPBICG`, `KSPSetComputeEigenvalues()`, `KSPComputeEigenvalues()`
233: M*/

235: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
236: {
237:   KSP_CG *cg;

239:   PetscFunctionBegin;
240:   PetscCall(PetscNew(&cg));
241: #if !defined(PETSC_USE_COMPLEX)
242:   cg->type = KSP_CG_SYMMETRIC;
243: #else
244:   cg->type = KSP_CG_HERMITIAN;
245: #endif
246:   ksp->data = (void *)cg;
247:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
248:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2));
249:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));
250:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

252:   /*
253:        Sets the functions that are associated with this data structure
254:        (in C++ this is the same as defining virtual functions)
255:   */
256:   ksp->ops->setup          = KSPSetUp_CGNE;
257:   ksp->ops->solve          = KSPSolve_CGNE;
258:   ksp->ops->destroy        = KSPDestroy_CG;
259:   ksp->ops->view           = KSPView_CG;
260:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
261:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
262:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

264:   /*
265:       Attach the function KSPCGSetType_CGNE() to this object. The routine
266:       KSPCGSetType() checks for this attached function and calls it if it finds
267:       it. (Sort of like a dynamic member function that can be added at run time
268:   */
269:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetType_C", KSPCGSetType_CGNE));
270:   PetscFunctionReturn(PETSC_SUCCESS);
271: }