Actual source code: cgne.c

petsc-dev 2014-08-28
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  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>       /*I "petscksp.h" I*/
  8: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
  9: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);

 13: static PetscErrorCode  KSPCGSetType_CGNE(KSP ksp,KSPCGType type)
 14: {
 15:   KSP_CG *cg = (KSP_CG*)ksp->data;

 18:   cg->type = type;
 19:   return(0);
 20: }


 23: /*
 24:      KSPSetUp_CGNE - Sets up the workspace needed by the CGNE method.

 26:      IDENTICAL TO THE CG ONE EXCEPT for one extra work vector!
 27: */
 30: PetscErrorCode KSPSetUp_CGNE(KSP ksp)
 31: {
 32:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
 34:   PetscInt       maxit = ksp->max_it;

 37:   /* get work vectors needed by CGNE */
 38:   KSPSetWorkVecs(ksp,4);

 40:   /*
 41:      If user requested computations of eigenvalues then allocate work
 42:      work space needed
 43:   */
 44:   if (ksp->calc_sings) {
 45:     /* get space to store tridiagonal matrix for Lanczos */
 46:     PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
 47:     PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));
 48:   }
 49:   return(0);
 50: }

 52: /*
 53:        KSPSolve_CGNE - This routine actually applies the conjugate gradient
 54:     method

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


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

 63: */
 66: PetscErrorCode  KSPSolve_CGNE(KSP ksp)
 67: {
 69:   PetscInt       i,stored_max_it,eigs;
 70:   PetscScalar    dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0;
 71:   PetscReal      dp = 0.0;
 72:   Vec            X,B,Z,R,P,T;
 73:   KSP_CG         *cg;
 74:   Mat            Amat,Pmat;
 75:   PetscBool      diagonalscale,transpose_pc;

 78:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
 79:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
 80:   PCApplyTransposeExists(ksp->pc,&transpose_pc);

 82:   cg            = (KSP_CG*)ksp->data;
 83:   eigs          = ksp->calc_sings;
 84:   stored_max_it = ksp->max_it;
 85:   X             = ksp->vec_sol;
 86:   B             = ksp->vec_rhs;
 87:   R             = ksp->work[0];
 88:   Z             = ksp->work[1];
 89:   P             = ksp->work[2];
 90:   T             = ksp->work[3];

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

 94:   if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
 95:   PCGetOperators(ksp->pc,&Amat,&Pmat);

 97:   ksp->its = 0;
 98:   MatMultTranspose(Amat,B,T);
 99:   if (!ksp->guess_zero) {
100:     KSP_MatMult(ksp,Amat,X,P);
101:     KSP_MatMultTranspose(ksp,Amat,P,R);
102:     VecAYPX(R,-1.0,T);
103:   } else {
104:     VecCopy(T,R);              /*     r <- b (x is 0) */
105:   }
106:   KSP_PCApply(ksp,R,T);
107:   if (transpose_pc) {
108:     KSP_PCApplyTranspose(ksp,T,Z);
109:   } else {
110:     KSP_PCApply(ksp,T,Z);
111:   }

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

127:   i = 0;
128:   do {
129:     ksp->its = i+1;
130:     VecXDot(Z,R,&beta); /*     beta <- r'z     */
131:     if (beta == 0.0) {
132:       ksp->reason = KSP_CONVERGED_ATOL;
133:       PetscInfo(ksp,"converged due to beta = 0\n");
134:       break;
135: #if !defined(PETSC_USE_COMPLEX)
136:     } else if (beta < 0.0) {
137:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
138:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
139:       break;
140: #endif
141:     }
142:     if (!i) {
143:       VecCopy(Z,P);          /*     p <- z          */
144:       b    = 0.0;
145:     } else {
146:       b = beta/betaold;
147:       if (eigs) {
148:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
149:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
150:       }
151:       VecAYPX(P,b,Z);     /*     p <- z + b* p   */
152:     }
153:     betaold = beta;
154:     MatMult(Amat,P,T);
155:     MatMultTranspose(Amat,T,Z);
156:     VecXDot(P,Z,&dpi);    /*     dpi <- z'p      */
157:     a       = beta/dpi;                            /*     a = beta/p'z    */
158:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
159:     VecAXPY(X,a,P);           /*     x <- x + ap     */
160:     VecAXPY(R,-a,Z);                       /*     r <- r - az     */
161:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
162:       KSP_PCApply(ksp,R,T);
163:       if (transpose_pc) {
164:         KSP_PCApplyTranspose(ksp,T,Z);
165:       } else {
166:         KSP_PCApply(ksp,T,Z);
167:       }
168:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
169:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
170:       VecNorm(R,NORM_2,&dp);
171:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
172:       dp = PetscSqrtReal(PetscAbsScalar(beta));
173:     } else {
174:       dp = 0.0;
175:     }
176:     ksp->rnorm = dp;
177:     KSPLogResidualHistory(ksp,dp);
178:     KSPMonitor(ksp,i+1,dp);
179:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
180:     if (ksp->reason) break;
181:     if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
182:       if (transpose_pc) {
183:         KSP_PCApplyTranspose(ksp,T,Z);
184:       } else {
185:         KSP_PCApply(ksp,T,Z);
186:       }
187:     }
188:     i++;
189:   } while (i<ksp->max_it);
190:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
191:   return(0);
192: }

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

198:     It must be wrapped in EXTERN_C_BEGIN to be dynamically linkable in C++
199: */

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

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


209:    Level: beginner

211:    Notes: eigenvalue computation routines will return information about the
212:           spectrum of A^t*A, rather than A.


215:    CGNE is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
216:    eigenvalues. A unitary matrix is a classic example where CGNE converges in one iteration, but GMRES and CGS need N
217:    iterations (see Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992). If you intend
218:    to solve least squares problems, use KSPLSQR.

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

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

227:    This only supports left preconditioning.

229:    This object is subclassed off of KSPCG

231: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
232:            KSPCGSetType(), KSPBICG

234: M*/

236: extern PetscErrorCode KSPDestroy_CG(KSP);
237: extern PetscErrorCode KSPReset_CG(KSP);
238: extern PetscErrorCode KSPView_CG(KSP,PetscViewer);
239: extern PetscErrorCode KSPSetFromOptions_CG(KSP);
240: PETSC_EXTERN PetscErrorCode KSPCGSetType_CG(KSP,KSPCGType);

244: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
245: {
247:   KSP_CG         *cg;

250:   PetscNewLog(ksp,&cg);
251: #if !defined(PETSC_USE_COMPLEX)
252:   cg->type = KSP_CG_SYMMETRIC;
253: #else
254:   cg->type = KSP_CG_HERMITIAN;
255: #endif
256:   ksp->data = (void*)cg;
257:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
258:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
259:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);

261:   /*
262:        Sets the functions that are associated with this data structure
263:        (in C++ this is the same as defining virtual functions)
264:   */
265:   ksp->ops->setup          = KSPSetUp_CGNE;
266:   ksp->ops->solve          = KSPSolve_CGNE;
267:   ksp->ops->destroy        = KSPDestroy_CG;
268:   ksp->ops->view           = KSPView_CG;
269:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
270:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
271:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

273:   /*
274:       Attach the function KSPCGSetType_CGNE() to this object. The routine
275:       KSPCGSetType() checks for this attached function and calls it if it finds
276:       it. (Sort of like a dynamic member function that can be added at run time
277:   */
278:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
279:   return(0);
280: }