Actual source code: lmesolve.c

slepc-main 2024-11-09
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */
 10: /*
 11:    LME routines related to the solution process
 12: */

 14: #include <slepc/private/lmeimpl.h>
 15: #include <slepcblaslapack.h>

 17: /*@
 18:    LMESolve - Solves the linear matrix equation.

 20:    Collective

 22:    Input Parameter:
 23: .  lme - linear matrix equation solver context obtained from LMECreate()

 25:    Options Database Keys:
 26: +  -lme_view - print information about the solver used
 27: .  -lme_view_mat binary - save the matrix to the default binary viewer
 28: .  -lme_view_rhs binary - save right hand side to the default binary viewer
 29: .  -lme_view_solution binary - save computed solution to the default binary viewer
 30: -  -lme_converged_reason - print reason for convergence, and number of iterations

 32:    Notes:
 33:    The matrix coefficients are specified with LMESetCoefficients().
 34:    The right-hand side is specified with LMESetRHS().
 35:    The placeholder for the solution is specified with LMESetSolution().

 37:    Level: beginner

 39: .seealso: LMECreate(), LMESetUp(), LMEDestroy(), LMESetTolerances(), LMESetCoefficients(), LMESetRHS(), LMESetSolution()
 40: @*/
 41: PetscErrorCode LMESolve(LME lme)
 42: {
 43:   PetscFunctionBegin;

 46:   /* call setup */
 47:   PetscCall(LMESetUp(lme));
 48:   lme->its    = 0;
 49:   lme->errest = 0.0;

 51:   PetscCall(LMEViewFromOptions(lme,NULL,"-lme_view_pre"));

 53:   /* call solver */
 54:   PetscCheck(lme->ops->solve[lme->problem_type],PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"The specified solver does not support equation type %s",LMEProblemTypes[lme->problem_type]);
 55:   PetscCall(PetscLogEventBegin(LME_Solve,lme,0,0,0));
 56:   PetscUseTypeMethod(lme,solve[lme->problem_type]);
 57:   PetscCall(PetscLogEventEnd(LME_Solve,lme,0,0,0));

 59:   PetscCheck(lme->reason,PetscObjectComm((PetscObject)lme),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");

 61:   PetscCheck(!lme->errorifnotconverged || lme->reason>=0,PetscObjectComm((PetscObject)lme),PETSC_ERR_NOT_CONVERGED,"LMESolve has not converged");

 63:   /* various viewers */
 64:   PetscCall(LMEViewFromOptions(lme,NULL,"-lme_view"));
 65:   PetscCall(LMEConvergedReasonViewFromOptions(lme));
 66:   PetscCall(MatViewFromOptions(lme->A,(PetscObject)lme,"-lme_view_mat"));
 67:   PetscCall(MatViewFromOptions(lme->C,(PetscObject)lme,"-lme_view_rhs"));
 68:   PetscCall(MatViewFromOptions(lme->X,(PetscObject)lme,"-lme_view_solution"));
 69:   PetscFunctionReturn(PETSC_SUCCESS);
 70: }

 72: /*@
 73:    LMEGetIterationNumber - Gets the current iteration number. If the
 74:    call to LMESolve() is complete, then it returns the number of iterations
 75:    carried out by the solution method.

 77:    Not Collective

 79:    Input Parameter:
 80: .  lme - the linear matrix equation solver context

 82:    Output Parameter:
 83: .  its - number of iterations

 85:    Note:
 86:    During the i-th iteration this call returns i-1. If LMESolve() is
 87:    complete, then parameter "its" contains either the iteration number at
 88:    which convergence was successfully reached, or failure was detected.
 89:    Call LMEGetConvergedReason() to determine if the solver converged or
 90:    failed and why.

 92:    Level: intermediate

 94: .seealso: LMEGetConvergedReason(), LMESetTolerances()
 95: @*/
 96: PetscErrorCode LMEGetIterationNumber(LME lme,PetscInt *its)
 97: {
 98:   PetscFunctionBegin;
100:   PetscAssertPointer(its,2);
101:   *its = lme->its;
102:   PetscFunctionReturn(PETSC_SUCCESS);
103: }

105: /*@
106:    LMEGetConvergedReason - Gets the reason why the LMESolve() iteration was
107:    stopped.

109:    Not Collective

111:    Input Parameter:
112: .  lme - the linear matrix equation solver context

114:    Output Parameter:
115: .  reason - negative value indicates diverged, positive value converged

117:    Notes:

119:    Possible values for reason are
120: +  LME_CONVERGED_TOL - converged up to tolerance
121: .  LME_DIVERGED_ITS - required more than max_it iterations to reach convergence
122: -  LME_DIVERGED_BREAKDOWN - generic breakdown in method

124:    Can only be called after the call to LMESolve() is complete.

126:    Level: intermediate

128: .seealso: LMESetTolerances(), LMESolve(), LMEConvergedReason, LMESetErrorIfNotConverged()
129: @*/
130: PetscErrorCode LMEGetConvergedReason(LME lme,LMEConvergedReason *reason)
131: {
132:   PetscFunctionBegin;
134:   PetscAssertPointer(reason,2);
135:   *reason = lme->reason;
136:   PetscFunctionReturn(PETSC_SUCCESS);
137: }

139: /*@
140:    LMEGetErrorEstimate - Returns the error estimate obtained during solve.

142:    Not Collective

144:    Input Parameter:
145: .  lme - linear matrix equation solver context

147:    Output Parameter:
148: .  errest - the error estimate

150:    Notes:
151:    This is the error estimated internally by the solver. The actual
152:    error bound can be computed with LMEComputeError(). Note that some
153:    solvers may not be able to provide an error estimate.

155:    Level: advanced

157: .seealso: LMEComputeError()
158: @*/
159: PetscErrorCode LMEGetErrorEstimate(LME lme,PetscReal *errest)
160: {
161:   PetscFunctionBegin;
163:   PetscAssertPointer(errest,2);
164:   *errest = lme->errest;
165:   PetscFunctionReturn(PETSC_SUCCESS);
166: }

168: /*
169:    LMEComputeResidualNorm_Lyapunov - Computes the Frobenius norm of the residual matrix
170:    associated with the Lyapunov equation.
171: */
172: static PetscErrorCode LMEComputeResidualNorm_Lyapunov(LME lme,PetscReal *norm)
173: {
174:   PetscInt          j,n,N,k,l,lda,ldb;
175:   PetscBLASInt      n_,N_,k_,l_,lda_,ldb_;
176:   PetscScalar       *Rarray,alpha=1.0,beta=0.0;
177:   const PetscScalar *A,*B;
178:   BV                W,AX,X1,C1;
179:   Mat               R,X1m,C1m;
180:   Vec               v,w;
181:   VecScatter        vscat;

183:   PetscFunctionBegin;
184:   PetscCall(MatLRCGetMats(lme->C,NULL,&C1m,NULL,NULL));
185:   PetscCall(MatLRCGetMats(lme->X,NULL,&X1m,NULL,NULL));
186:   PetscCall(BVCreateFromMat(C1m,&C1));
187:   PetscCall(BVSetFromOptions(C1));
188:   PetscCall(BVCreateFromMat(X1m,&X1));
189:   PetscCall(BVSetFromOptions(X1));
190:   PetscCall(BVGetSizes(X1,&n,&N,&k));
191:   PetscCall(BVGetSizes(C1,NULL,NULL,&l));
192:   PetscCall(PetscBLASIntCast(n,&n_));
193:   PetscCall(PetscBLASIntCast(N,&N_));
194:   PetscCall(PetscBLASIntCast(k,&k_));
195:   PetscCall(PetscBLASIntCast(l,&l_));

197:   /* create W to store a redundant copy of a BV in each process */
198:   PetscCall(BVCreate(PETSC_COMM_SELF,&W));
199:   PetscCall(BVSetSizes(W,N,N,k));
200:   PetscCall(BVSetFromOptions(W));
201:   PetscCall(BVGetColumn(X1,0,&v));
202:   PetscCall(VecScatterCreateToAll(v,&vscat,NULL));
203:   PetscCall(BVRestoreColumn(X1,0,&v));

205:   /* create AX to hold the product A*X1 */
206:   PetscCall(BVDuplicate(X1,&AX));
207:   PetscCall(BVMatMult(X1,lme->A,AX));

209:   /* create dense matrix to hold the residual R=C1*C1'+AX*X1'+X1*AX' */
210:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)lme),n,n,N,N,NULL,&R));

212:   /* R=C1*C1' */
213:   PetscCall(MatDenseGetArrayWrite(R,&Rarray));
214:   for (j=0;j<l;j++) {
215:     PetscCall(BVGetColumn(C1,j,&v));
216:     PetscCall(BVGetColumn(W,j,&w));
217:     PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD));
218:     PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD));
219:     PetscCall(BVRestoreColumn(C1,j,&v));
220:     PetscCall(BVRestoreColumn(W,j,&w));
221:   }
222:   if (n) {
223:     PetscCall(BVGetArrayRead(C1,&A));
224:     PetscCall(BVGetLeadingDimension(C1,&lda));
225:     PetscCall(PetscBLASIntCast(lda,&lda_));
226:     PetscCall(BVGetArrayRead(W,&B));
227:     PetscCall(BVGetLeadingDimension(W,&ldb));
228:     PetscCall(PetscBLASIntCast(ldb,&ldb_));
229:     PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&l_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_));
230:     PetscCall(BVRestoreArrayRead(C1,&A));
231:     PetscCall(BVRestoreArrayRead(W,&B));
232:   }
233:   beta = 1.0;

235:   /* R+=AX*X1' */
236:   for (j=0;j<k;j++) {
237:     PetscCall(BVGetColumn(X1,j,&v));
238:     PetscCall(BVGetColumn(W,j,&w));
239:     PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD));
240:     PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD));
241:     PetscCall(BVRestoreColumn(X1,j,&v));
242:     PetscCall(BVRestoreColumn(W,j,&w));
243:   }
244:   if (n) {
245:     PetscCall(BVGetArrayRead(AX,&A));
246:     PetscCall(BVGetLeadingDimension(AX,&lda));
247:     PetscCall(PetscBLASIntCast(lda,&lda_));
248:     PetscCall(BVGetArrayRead(W,&B));
249:     PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_));
250:     PetscCall(BVRestoreArrayRead(AX,&A));
251:     PetscCall(BVRestoreArrayRead(W,&B));
252:   }

254:   /* R+=X1*AX' */
255:   for (j=0;j<k;j++) {
256:     PetscCall(BVGetColumn(AX,j,&v));
257:     PetscCall(BVGetColumn(W,j,&w));
258:     PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD));
259:     PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD));
260:     PetscCall(BVRestoreColumn(AX,j,&v));
261:     PetscCall(BVRestoreColumn(W,j,&w));
262:   }
263:   if (n) {
264:     PetscCall(BVGetArrayRead(X1,&A));
265:     PetscCall(BVGetLeadingDimension(AX,&lda));
266:     PetscCall(PetscBLASIntCast(lda,&lda_));
267:     PetscCall(BVGetArrayRead(W,&B));
268:     PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_));
269:     PetscCall(BVRestoreArrayRead(X1,&A));
270:     PetscCall(BVRestoreArrayRead(W,&B));
271:   }
272:   PetscCall(MatDenseRestoreArrayWrite(R,&Rarray));

274:   /* compute ||R||_F */
275:   PetscCall(MatNorm(R,NORM_FROBENIUS,norm));

277:   PetscCall(BVDestroy(&W));
278:   PetscCall(VecScatterDestroy(&vscat));
279:   PetscCall(BVDestroy(&AX));
280:   PetscCall(MatDestroy(&R));
281:   PetscCall(BVDestroy(&C1));
282:   PetscCall(BVDestroy(&X1));
283:   PetscFunctionReturn(PETSC_SUCCESS);
284: }

286: /*@
287:    LMEComputeError - Computes the error (based on the residual norm) associated
288:    with the last equation solved.

290:    Collective

292:    Input Parameter:
293: .  lme  - the linear matrix equation solver context

295:    Output Parameter:
296: .  error - the error

298:    Notes:
299:    This function is not scalable (in terms of memory or parallel communication),
300:    so it should not be called except in the case of small problem size. For
301:    large equations, use LMEGetErrorEstimate().

303:    Level: advanced

305: .seealso: LMESolve(), LMEGetErrorEstimate()
306: @*/
307: PetscErrorCode LMEComputeError(LME lme,PetscReal *error)
308: {
309:   PetscFunctionBegin;
311:   PetscAssertPointer(error,2);

313:   PetscCall(PetscLogEventBegin(LME_ComputeError,lme,0,0,0));
314:   /* compute residual norm */
315:   switch (lme->problem_type) {
316:     case LME_LYAPUNOV:
317:       PetscCall(LMEComputeResidualNorm_Lyapunov(lme,error));
318:       break;
319:     default:
320:       SETERRQ(PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"Not implemented for equation type %s",LMEProblemTypes[lme->problem_type]);
321:   }

323:   /* compute error */
324:   /* currently we only support absolute error, so just return the norm */
325:   PetscCall(PetscLogEventEnd(LME_ComputeError,lme,0,0,0));
326:   PetscFunctionReturn(PETSC_SUCCESS);
327: }