Date: 2021-02-01T14:42:22+00:00

Actual source code: lmesolve.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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 on lme

     22:    Input Parameters:
     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: {

     48:   /* call setup */
     49:   LMESetUp(lme);
     50:   lme->its    = 0;
     51:   lme->errest = 0.0;

     53:   LMEViewFromOptions(lme,NULL,"-lme_view_pre");

     55:   /* call solver */
     56:   if (!lme->ops->solve[lme->problem_type]) SETERRQ1(PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"The specified solver does not support equation type %s",LMEProblemTypes[lme->problem_type]);
     57:   PetscLogEventBegin(LME_Solve,lme,0,0,0);
     58:   (*lme->ops->solve[lme->problem_type])(lme);
     59:   PetscLogEventEnd(LME_Solve,lme,0,0,0);

     61:   if (!lme->reason) SETERRQ(PetscObjectComm((PetscObject)lme),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");

     63:   if (lme->errorifnotconverged && lme->reason < 0) SETERRQ(PetscObjectComm((PetscObject)lme),PETSC_ERR_NOT_CONVERGED,"LMESolve has not converged");

     65:   /* various viewers */
     66:   LMEViewFromOptions(lme,NULL,"-lme_view");
     67:   LMEConvergedReasonViewFromOptions(lme);
     68:   MatViewFromOptions(lme->A,(PetscObject)lme,"-lme_view_mat");
     69:   MatViewFromOptions(lme->C,(PetscObject)lme,"-lme_view_rhs");
     70:   MatViewFromOptions(lme->X,(PetscObject)lme,"-lme_view_solution");
     71:   return(0);
     72: }

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

     79:    Not Collective

     81:    Input Parameter:
     82: .  lme - the linear matrix equation solver context

     84:    Output Parameter:
     85: .  its - number of iterations

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

     94:    Level: intermediate

     96: .seealso: LMEGetConvergedReason(), LMESetTolerances()
     97: @*/
     98: PetscErrorCode LMEGetIterationNumber(LME lme,PetscInt *its)
     99: {
    103:   *its = lme->its;
    104:   return(0);
    105: }

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

    111:    Not Collective

    113:    Input Parameter:
    114: .  lme - the linear matrix equation solver context

    116:    Output Parameter:
    117: .  reason - negative value indicates diverged, positive value converged

    119:    Notes:

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

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

    128:    Level: intermediate

    130: .seealso: LMESetTolerances(), LMESolve(), LMEConvergedReason, LMESetErrorIfNotConverged()
    131: @*/
    132: PetscErrorCode LMEGetConvergedReason(LME lme,LMEConvergedReason *reason)
    133: {
    137:   *reason = lme->reason;
    138:   return(0);
    139: }

    141: /*@
    142:    LMEGetErrorEstimate - Returns the error estimate obtained during solve.

    144:    Not Collective

    146:    Input Parameter:
    147: .  lme - linear matrix equation solver context

    149:    Output Parameter:
    150: .  errest - the error estimate

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

    157:    Level: advanced

    159: .seealso: LMEComputeError()
    160: @*/
    161: PetscErrorCode LMEGetErrorEstimate(LME lme,PetscReal *errest)
    162: {
    166:   *errest = lme->errest;
    167:   return(0);
    168: }

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

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

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

    208:   /* create AX to hold the product A*X1 */
    209:   BVDuplicate(X1,&AX);
    210:   BVMatMult(X1,lme->A,AX);

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

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

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

    251:   /* R+=X1*AX' */
    252:   for (j=0;j<k;j++) {
    253:     BVGetColumn(AX,j,&v);
    254:     BVGetColumn(W,j,&w);
    255:     VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD);
    256:     VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD);
    257:     BVRestoreColumn(AX,j,&v);
    258:     BVRestoreColumn(W,j,&w);
    259:   }
    260:   if (n) {
    261:     BVGetArrayRead(X1,&A);
    262:     BVGetArrayRead(W,&B);
    263:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&n_,(PetscScalar*)B,&N_,&beta,Rarray,&n_));
    264:     BVRestoreArrayRead(X1,&A);
    265:     BVRestoreArrayRead(W,&B);
    266:   }
    267:   MatDenseRestoreArray(R,&Rarray);

    269:   /* compute ||R||_F */
    270:   MatAssemblyBegin(R,MAT_FINAL_ASSEMBLY);
    271:   MatAssemblyEnd(R,MAT_FINAL_ASSEMBLY);
    272:   MatNorm(R,NORM_FROBENIUS,norm);

    274:   BVDestroy(&W);
    275:   VecScatterDestroy(&vscat);
    276:   BVDestroy(&AX);
    277:   MatDestroy(&R);
    278:   BVDestroy(&C1);
    279:   BVDestroy(&X1);
    280:   return(0);
    281: }

    283: /*@
    284:    LMEComputeError - Computes the error (based on the residual norm) associated
    285:    with the last equation solved.

    287:    Collective on lme

    289:    Input Parameter:
    290: .  lme  - the linear matrix equation solver context

    292:    Output Parameter:
    293: .  error - the error

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

    300:    Level: advanced

    302: .seealso: LMESolve(), LMEGetErrorEstimate()
    303: @*/
    304: PetscErrorCode LMEComputeError(LME lme,PetscReal *error)
    305: {

    312:   PetscLogEventBegin(LME_ComputeError,lme,0,0,0);
    313:   /* compute residual norm */
    314:   switch (lme->problem_type) {
    315:     case LME_LYAPUNOV:
    316:       LMEComputeResidualNorm_Lyapunov(lme,error);
    317:       break;
    318:     default:
    319:       SETERRQ1(PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"Not implemented for equation type %s",LMEProblemTypes[lme->problem_type]);
    320:   }

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