Actual source code: cgne.c

petsc-3.4.4 2014-03-13
  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,PetscScalar,&cgP->e,maxit+1,PetscScalar,&cgP->d,maxit+1,PetscReal,&cgP->ee,maxit+1,PetscReal,&cgP->dd);
 47:     PetscLogObjectMemory(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:   MatStructure   pflag;
 76:   PetscBool      diagonalscale,transpose_pc;

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

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

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

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

 98:   ksp->its = 0;
 99:   MatMultTranspose(Amat,B,T);
100:   if (!ksp->guess_zero) {
101:     KSP_MatMult(ksp,Amat,X,P);
102:     KSP_MatMultTranspose(ksp,Amat,P,R);
103:     VecAYPX(R,-1.0,T);
104:   } else {
105:     VecCopy(T,R);              /*     r <- b (x is 0) */
106:   }
107:   KSP_PCApply(ksp,R,T);
108:   if (transpose_pc) {
109:     KSP_PCApplyTranspose(ksp,T,Z);
110:   } else {
111:     KSP_PCApply(ksp,T,Z);
112:   }

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

128:   i = 0;
129:   do {
130:     ksp->its = i+1;
131:     VecXDot(Z,R,&beta); /*     beta <- r'z     */
132:     if (beta == 0.0) {
133:       ksp->reason = KSP_CONVERGED_ATOL;
134:       PetscInfo(ksp,"converged due to beta = 0\n");
135:       break;
136: #if !defined(PETSC_USE_COMPLEX)
137:     } else if (beta < 0.0) {
138:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
139:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
140:       break;
141: #endif
142:     }
143:     if (!i) {
144:       VecCopy(Z,P);          /*     p <- z          */
145:       b    = 0.0;
146:     } else {
147:       b = beta/betaold;
148:       if (eigs) {
149:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
150:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
151:       }
152:       VecAYPX(P,b,Z);     /*     p <- z + b* p   */
153:     }
154:     betaold = beta;
155:     MatMult(Amat,P,T);
156:     MatMultTranspose(Amat,T,Z);
157:     VecXDot(P,Z,&dpi);    /*     dpi <- z'p      */
158:     a       = beta/dpi;                            /*     a = beta/p'z    */
159:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
160:     VecAXPY(X,a,P);           /*     x <- x + ap     */
161:     VecAXPY(R,-a,Z);                       /*     r <- r - az     */
162:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
163:       KSP_PCApply(ksp,R,T);
164:       if (transpose_pc) {
165:         KSP_PCApplyTranspose(ksp,T,Z);
166:       } else {
167:         KSP_PCApply(ksp,T,Z);
168:       }
169:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
170:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
171:       VecNorm(R,NORM_2,&dp);
172:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
173:       dp = PetscSqrtReal(PetscAbsScalar(beta));
174:     } else {
175:       dp = 0.0;
176:     }
177:     ksp->rnorm = dp;
178:     KSPLogResidualHistory(ksp,dp);
179:     KSPMonitor(ksp,i+1,dp);
180:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
181:     if (ksp->reason) break;
182:     if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
183:       if (transpose_pc) {
184:         KSP_PCApplyTranspose(ksp,T,Z);
185:       } else {
186:         KSP_PCApply(ksp,T,Z);
187:       }
188:     }
189:     i++;
190:   } while (i<ksp->max_it);
191:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
192:   return(0);
193: }

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

199:     It must be wrapped in EXTERN_C_BEGIN to be dynamically linkable in C++
200: */

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

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


210:    Level: beginner

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


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

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

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

228:    This only supports left preconditioning.

230:    This object is subclassed off of KSPCG

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

235: M*/

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

245: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
246: {
248:   KSP_CG         *cg;

251:   PetscNewLog(ksp,KSP_CG,&cg);
252: #if !defined(PETSC_USE_COMPLEX)
253:   cg->type = KSP_CG_SYMMETRIC;
254: #else
255:   cg->type = KSP_CG_HERMITIAN;
256: #endif
257:   ksp->data = (void*)cg;
258:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
259:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
260:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,1);

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

274:   /*
275:       Attach the function KSPCGSetType_CGNE() to this object. The routine
276:       KSPCGSetType() checks for this attached function and calls it if it finds
277:       it. (Sort of like a dynamic member function that can be added at run time
278:   */
279:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
280:   return(0);
281: }