Actual source code: agmresorthog.c

  1: #define PETSCKSP_DLL

  3: #include <../src/ksp/ksp/impls/gmres/agmres/agmresimpl.h>
  4: /*
  5:  *  This file implements the RODDEC algorithm : its purpose is to orthogonalize a set of vectors distributed across several processes. These processes are organized in a virtual ring.
  6:  * References : [1] Sidje, Roger B. Alternatives for parallel Krylov subspace basis computation. Numer. Linear Algebra Appl. 4 (1997), no. 4, 305-331
  7:  *
  8:  *
  9:  * initial author R. B. SIDJE,
 10:  * modified : G.-A Atenekeng-Kahou, 2008
 11:  * modified : D. NUENTSA WAKAM, 2011
 12:  *
 13:  */

 15: /*
 16:  * Take the processes that own the vectors and Organize them on a virtual ring.
 17:  */
 18: static PetscErrorCode KSPAGMRESRoddecGivens(PetscReal *, PetscReal *, PetscReal *, PetscInt);

 20: PetscErrorCode KSPAGMRESRoddecInitNeighboor(KSP ksp)
 21: {
 22:   MPI_Comm    comm;
 23:   KSP_AGMRES *agmres = (KSP_AGMRES *)(ksp->data);
 24:   PetscMPIInt First, Last, rank, size;

 26:   PetscObjectGetComm((PetscObject)agmres->vecs[0], &comm);
 27:   MPI_Comm_rank(comm, &rank);
 28:   MPI_Comm_size(comm, &size);
 29:   MPIU_Allreduce(&rank, &First, 1, MPI_INT, MPI_MIN, comm);
 30:   MPIU_Allreduce(&rank, &Last, 1, MPI_INT, MPI_MAX, comm);

 32:   if ((rank != Last) && (rank == 0)) {
 33:     agmres->Ileft  = rank - 1;
 34:     agmres->Iright = rank + 1;
 35:   } else {
 36:     if (rank == Last) {
 37:       agmres->Ileft  = rank - 1;
 38:       agmres->Iright = First;
 39:     } else {
 40:       {
 41:         agmres->Ileft  = Last;
 42:         agmres->Iright = rank + 1;
 43:       }
 44:     }
 45:   }
 46:   agmres->rank  = rank;
 47:   agmres->size  = size;
 48:   agmres->First = First;
 49:   agmres->Last  = Last;
 50:   return 0;
 51: }

 53: static PetscErrorCode KSPAGMRESRoddecGivens(PetscReal *c, PetscReal *s, PetscReal *r, PetscInt make_r)
 54: {
 55:   PetscReal a, b, t;

 57:   if (make_r == 1) {
 58:     a = *c;
 59:     b = *s;
 60:     if (b == 0.e0) {
 61:       *c = 1.e0;
 62:       *s = 0.e0;
 63:     } else {
 64:       if (PetscAbsReal(b) > PetscAbsReal(a)) {
 65:         t  = -a / b;
 66:         *s = 1.e0 / PetscSqrtReal(1.e0 + t * t);
 67:         *c = (*s) * t;
 68:       } else {
 69:         t  = -b / a;
 70:         *c = 1.e0 / PetscSqrtReal(1.e0 + t * t);
 71:         *s = (*c) * t;
 72:       }
 73:     }
 74:     if (*c == 0.e0) {
 75:       *r = 1.e0;
 76:     } else {
 77:       if (PetscAbsReal(*s) < PetscAbsReal(*c)) {
 78:         *r = PetscSign(*c) * (*s) / 2.e0;
 79:       } else {
 80:         *r = PetscSign(*s) * 2.e0 / (*c);
 81:       }
 82:     }
 83:   }

 85:   if (*r == 1.e0) {
 86:     *c = 0.e0;
 87:     *s = 1.e0;
 88:   } else {
 89:     if (PetscAbsReal(*r) < 1.e0) {
 90:       *s = 2.e0 * (*r);
 91:       *c = PetscSqrtReal(1.e0 - (*s) * (*s));
 92:     } else {
 93:       *c = 2.e0 / (*r);
 94:       *s = PetscSqrtReal(1.e0 - (*c) * (*c));
 95:     }
 96:   }
 97:   return 0;
 98: }

100: /*
101:  * Compute the QR factorization of the Krylov basis vectors
102:  * Input :
103:  *  - the vectors are available in agmres->vecs (alias VEC_V)
104:  *  - nvec :  the number of vectors
105:  * Output :
106:  *  - agmres->Qloc : product of elementary reflectors for the QR of the (local part) of the vectors.
107:  *  - agmres->sgn :  Sign of the rotations
108:  *  - agmres->tloc : scalar factors of the elementary reflectors.

110:  */
111: PetscErrorCode KSPAGMRESRoddec(KSP ksp, PetscInt nvec)
112: {
113:   KSP_AGMRES  *agmres = (KSP_AGMRES *)ksp->data;
114:   MPI_Comm     comm;
115:   PetscScalar *Qloc    = agmres->Qloc;
116:   PetscScalar *sgn     = agmres->sgn;
117:   PetscScalar *tloc    = agmres->tloc;
118:   PetscReal   *wbufptr = agmres->wbufptr;
119:   PetscMPIInt  rank    = agmres->rank;
120:   PetscMPIInt  First   = agmres->First;
121:   PetscMPIInt  Last    = agmres->Last;
122:   PetscBLASInt pas, len, bnloc, bpos;
123:   PetscInt     nloc, d, i, j, k;
124:   PetscInt     pos;
125:   PetscReal    c, s, rho, Ajj, val, tt, old;
126:   PetscScalar *col;
127:   MPI_Status   status;
128:   PetscBLASInt N = MAXKSPSIZE + 1;

130:   PetscObjectGetComm((PetscObject)ksp, &comm);
131:   PetscLogEventBegin(KSP_AGMRESRoddec, ksp, 0, 0, 0);
132:   PetscArrayzero(agmres->Rloc, N * N);
133:   /* check input arguments */
135:   VecGetLocalSize(VEC_V(0), &nloc);
136:   PetscBLASIntCast(nloc, &bnloc);
138:   pas = 1;
139:   /* Copy the vectors of the basis */
140:   for (j = 0; j < nvec; j++) {
141:     VecGetArray(VEC_V(j), &col);
142:     PetscCallBLAS("BLAScopy", BLAScopy_(&bnloc, col, &pas, &Qloc[j * nloc], &pas));
143:     VecRestoreArray(VEC_V(j), &col);
144:   }
145:   /* Each process performs a local QR on its own block */
146:   for (j = 0; j < nvec; j++) {
147:     len = nloc - j;
148:     Ajj = Qloc[j * nloc + j];
149:     PetscCallBLAS("BLASnrm2", rho = -PetscSign(Ajj) * BLASnrm2_(&len, &(Qloc[j * nloc + j]), &pas));
150:     if (rho == 0.0) tloc[j] = 0.0;
151:     else {
152:       tloc[j] = (Ajj - rho) / rho;
153:       len     = len - 1;
154:       val     = 1.0 / (Ajj - rho);
155:       PetscCallBLAS("BLASscal", BLASscal_(&len, &val, &(Qloc[j * nloc + j + 1]), &pas));
156:       Qloc[j * nloc + j] = 1.0;
157:       len                = len + 1;
158:       for (k = j + 1; k < nvec; k++) {
159:         PetscCallBLAS("BLASdot", tt = tloc[j] * BLASdot_(&len, &(Qloc[j * nloc + j]), &pas, &(Qloc[k * nloc + j]), &pas));
160:         PetscCallBLAS("BLASaxpy", BLASaxpy_(&len, &tt, &(Qloc[j * nloc + j]), &pas, &(Qloc[k * nloc + j]), &pas));
161:       }
162:       Qloc[j * nloc + j] = rho;
163:     }
164:   }
165:   /* annihilate undesirable Rloc, diagonal by diagonal*/
166:   for (d = 0; d < nvec; d++) {
167:     len = nvec - d;
168:     if (rank == First) {
169:       PetscCallBLAS("BLAScopy", BLAScopy_(&len, &(Qloc[d * nloc + d]), &bnloc, &(wbufptr[d]), &pas));
170:       MPI_Send(&(wbufptr[d]), len, MPIU_SCALAR, rank + 1, agmres->tag, comm);
171:     } else {
172:       MPI_Recv(&(wbufptr[d]), len, MPIU_SCALAR, rank - 1, agmres->tag, comm, &status);
173:       /* Elimination of Rloc(1,d)*/
174:       c = wbufptr[d];
175:       s = Qloc[d * nloc];
176:       KSPAGMRESRoddecGivens(&c, &s, &rho, 1);
177:       /* Apply Givens Rotation*/
178:       for (k = d; k < nvec; k++) {
179:         old            = wbufptr[k];
180:         wbufptr[k]     = c * old - s * Qloc[k * nloc];
181:         Qloc[k * nloc] = s * old + c * Qloc[k * nloc];
182:       }
183:       Qloc[d * nloc] = rho;
184:       if (rank != Last) MPI_Send(&(wbufptr[d]), len, MPIU_SCALAR, rank + 1, agmres->tag, comm);
185:       /* zero-out the d-th diagonal of Rloc ...*/
186:       for (j = d + 1; j < nvec; j++) {
187:         /* elimination of Rloc[i][j]*/
188:         i = j - d;
189:         c = Qloc[j * nloc + i - 1];
190:         s = Qloc[j * nloc + i];
191:         KSPAGMRESRoddecGivens(&c, &s, &rho, 1);
192:         for (k = j; k < nvec; k++) {
193:           old                    = Qloc[k * nloc + i - 1];
194:           Qloc[k * nloc + i - 1] = c * old - s * Qloc[k * nloc + i];
195:           Qloc[k * nloc + i]     = s * old + c * Qloc[k * nloc + i];
196:         }
197:         Qloc[j * nloc + i] = rho;
198:       }
199:       if (rank == Last) {
200:         PetscCallBLAS("BLAScopy", BLAScopy_(&len, &(wbufptr[d]), &pas, RLOC(d, d), &N));
201:         for (k = d + 1; k < nvec; k++) *RLOC(k, d) = 0.0;
202:       }
203:     }
204:   }

206:   if (rank == Last) {
207:     for (d = 0; d < nvec; d++) {
208:       pos = nvec - d;
209:       PetscBLASIntCast(pos, &bpos);
210:       sgn[d] = PetscSign(*RLOC(d, d));
211:       PetscCallBLAS("BLASscal", BLASscal_(&bpos, &(sgn[d]), RLOC(d, d), &N));
212:     }
213:   }
214:   /* BroadCast Rloc to all other processes
215:    * NWD : should not be needed
216:    */
217:   MPI_Bcast(agmres->Rloc, N * N, MPIU_SCALAR, Last, comm);
218:   PetscLogEventEnd(KSP_AGMRESRoddec, ksp, 0, 0, 0);
219:   return 0;
220: }

222: /*
223:  *  Computes Out <-- Q * In where Q is the orthogonal matrix from AGMRESRoddec
224:  *  Input
225:  *   - Qloc, sgn, tloc, nvec (see AGMRESRoddec above)
226:  *   - In : input vector (size nvec)
227:  *  Output :
228:  *   - Out : Petsc vector (distributed as the basis vectors)
229:  */
230: PetscErrorCode KSPAGMRESRodvec(KSP ksp, PetscInt nvec, PetscScalar *In, Vec Out)
231: {
232:   KSP_AGMRES  *agmres = (KSP_AGMRES *)ksp->data;
233:   MPI_Comm     comm;
234:   PetscScalar *Qloc  = agmres->Qloc;
235:   PetscScalar *sgn   = agmres->sgn;
236:   PetscScalar *tloc  = agmres->tloc;
237:   PetscMPIInt  rank  = agmres->rank;
238:   PetscMPIInt  First = agmres->First, Last = agmres->Last;
239:   PetscMPIInt  Iright = agmres->Iright, Ileft = agmres->Ileft;
240:   PetscScalar *y, *zloc;
241:   PetscInt     nloc, d, len, i, j;
242:   PetscBLASInt bnvec, pas, blen;
243:   PetscInt     dpt;
244:   PetscReal    c, s, rho, zp, zq, yd = 0.0, tt;
245:   MPI_Status   status;

247:   PetscBLASIntCast(nvec, &bnvec);
248:   PetscObjectGetComm((PetscObject)ksp, &comm);
249:   pas = 1;
250:   VecGetLocalSize(VEC_V(0), &nloc);
251:   PetscMalloc1(nvec, &y);
252:   PetscArraycpy(y, In, nvec);
253:   VecGetArray(Out, &zloc);

255:   if (rank == Last) {
256:     for (i = 0; i < nvec; i++) y[i] = sgn[i] * y[i];
257:   }
258:   for (i = 0; i < nloc; i++) zloc[i] = 0.0;
259:   if (agmres->size == 1) PetscCallBLAS("BLAScopy", BLAScopy_(&bnvec, y, &pas, &(zloc[0]), &pas));
260:   else {
261:     for (d = nvec - 1; d >= 0; d--) {
262:       if (rank == First) {
263:         MPI_Recv(&(zloc[d]), 1, MPIU_SCALAR, Iright, agmres->tag, comm, &status);
264:       } else {
265:         for (j = nvec - 1; j >= d + 1; j--) {
266:           i = j - d;
267:           KSPAGMRESRoddecGivens(&c, &s, &(Qloc[j * nloc + i]), 0);
268:           zp          = zloc[i - 1];
269:           zq          = zloc[i];
270:           zloc[i - 1] = c * zp + s * zq;
271:           zloc[i]     = -s * zp + c * zq;
272:         }
273:         KSPAGMRESRoddecGivens(&c, &s, &(Qloc[d * nloc]), 0);
274:         if (rank == Last) {
275:           zp      = y[d];
276:           zq      = zloc[0];
277:           y[d]    = c * zp + s * zq;
278:           zloc[0] = -s * zp + c * zq;
279:           MPI_Send(&(y[d]), 1, MPIU_SCALAR, Ileft, agmres->tag, comm);
280:         } else {
281:           MPI_Recv(&yd, 1, MPIU_SCALAR, Iright, agmres->tag, comm, &status);
282:           zp      = yd;
283:           zq      = zloc[0];
284:           yd      = c * zp + s * zq;
285:           zloc[0] = -s * zp + c * zq;
286:           MPI_Send(&yd, 1, MPIU_SCALAR, Ileft, agmres->tag, comm);
287:         }
288:       }
289:     }
290:   }
291:   for (j = nvec - 1; j >= 0; j--) {
292:     dpt = j * nloc + j;
293:     if (tloc[j] != 0.0) {
294:       len = nloc - j;
295:       PetscBLASIntCast(len, &blen);
296:       rho       = Qloc[dpt];
297:       Qloc[dpt] = 1.0;
298:       tt        = tloc[j] * (BLASdot_(&blen, &(Qloc[dpt]), &pas, &(zloc[j]), &pas));
299:       PetscCallBLAS("BLASaxpy", BLASaxpy_(&blen, &tt, &(Qloc[dpt]), &pas, &(zloc[j]), &pas));
300:       Qloc[dpt] = rho;
301:     }
302:   }
303:   VecRestoreArray(Out, &zloc);
304:   PetscFree(y);
305:   return 0;
306: }