Date: 2021-02-01T14:41:40+00:00

Actual source code: fnphi.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:    Phi functions
     12:       phi_0(x) = exp(x)
     13:       phi_1(x) = (exp(x)-1)/x
     14:       phi_k(x) = (phi_{k-1}(x)-1/(k-1)!)/x
     15: */

     17: #include <slepc/private/fnimpl.h>

     19: typedef struct {
     20:   PetscInt k;    /* index of the phi-function, defaults to k=1 */
     21:   Mat      H;    /* auxiliary matrix of order m+k */
     22:   Mat      F;    /* auxiliary matrix to store exp(H) */
     23: } FN_PHI;

     25: #define MAX_INDEX 10

     27: const static PetscReal rfactorial[MAX_INDEX+2] = { 1, 1, 0.5, 1.0/6, 1.0/24, 1.0/120, 1.0/720, 1.0/5040, 1.0/40320, 1.0/362880, 1.0/3628800, 1.0/39916800 };

     29: PetscErrorCode FNEvaluateFunction_Phi(FN fn,PetscScalar x,PetscScalar *y)
     30: {
     31:   FN_PHI      *ctx = (FN_PHI*)fn->data;
     32:   PetscInt    i;
     33:   PetscScalar phi[MAX_INDEX+1];

     36:   if (x==0.0) *y = rfactorial[ctx->k];
     37:   else {
     38:     phi[0] = PetscExpScalar(x);
     39:     for (i=1;i<=ctx->k;i++) phi[i] = (phi[i-1]-rfactorial[i-1])/x;
     40:     *y = phi[ctx->k];
     41:   }
     42:   return(0);
     43: }

     45: PetscErrorCode FNEvaluateDerivative_Phi(FN fn,PetscScalar x,PetscScalar *y)
     46: {
     47:   FN_PHI      *ctx = (FN_PHI*)fn->data;
     48:   PetscInt    i;
     49:   PetscScalar phi[MAX_INDEX+2];

     52:   if (x==0.0) *y = rfactorial[ctx->k+1];
     53:   else {
     54:     phi[0] = PetscExpScalar(x);
     55:     for (i=1;i<=ctx->k+1;i++) phi[i] = (phi[i-1]-rfactorial[i-1])/x;
     56:     *y = phi[ctx->k] - phi[ctx->k+1]*(PetscReal)ctx->k;
     57:   }
     58:   return(0);
     59: }

     61: PetscErrorCode FNEvaluateFunctionMatVec_Phi(FN fn,Mat A,Vec v)
     62: {
     64:   FN_PHI         *ctx = (FN_PHI*)fn->data;
     65:   PetscInt       i,j,m,n,nh;
     66:   PetscScalar    *Aa,*Ha,*Fa,*va,sfactor=1.0;

     69:   MatGetSize(A,&m,NULL);
     70:   n = m+ctx->k;
     71:   if (ctx->H) {
     72:     MatGetSize(ctx->H,&nh,NULL);
     73:     if (n!=nh) {
     74:       MatDestroy(&ctx->H);
     75:       MatDestroy(&ctx->F);
     76:     }
     77:   }
     78:   if (!ctx->H) {
     79:     MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->H);
     80:     MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->F);
     81:   }
     82:   MatDenseGetArray(ctx->H,&Ha);
     83:   MatDenseGetArray(A,&Aa);
     84:   for (j=0;j<m;j++) {
     85:     PetscArraycpy(Ha+j*n,Aa+j*m,m);
     86:   }
     87:   MatDenseRestoreArray(A,&Aa);
     88:   if (ctx->k) {
     89:     for (j=0;j<m;j++) for (i=m;i<n;i++) Ha[i+j*n] = 0.0;
     90:     for (j=m;j<n;j++) for (i=0;i<n;i++) Ha[i+j*n] = 0.0;
     91:     Ha[0+m*n] = fn->alpha;
     92:     for (j=m+1;j<n;j++) Ha[j-1+j*n] = fn->alpha;
     93:   }
     94:   MatDenseRestoreArray(ctx->H,&Ha);

     96:   FNEvaluateFunctionMat_Exp_Higham(fn,ctx->H,ctx->F);

     98:   MatDenseGetArray(ctx->F,&Fa);
     99:   VecGetArray(v,&va);
    100:   if (ctx->k) {
    101:     sfactor = PetscPowScalarInt(fn->alpha,-ctx->k);
    102:     for (i=0;i<m;i++) va[i] = sfactor*Fa[i+(n-1)*n];
    103:   } else {
    104:     for (i=0;i<m;i++) va[i] = sfactor*Fa[i+0*n];
    105:   }
    106:   VecRestoreArray(v,&va);
    107:   MatDenseRestoreArray(ctx->F,&Fa);
    108:   return(0);
    109: }

    111: static PetscErrorCode FNPhiSetIndex_Phi(FN fn,PetscInt k)
    112: {
    114:   FN_PHI         *ctx = (FN_PHI*)fn->data;

    117:   if (k<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Index cannot be negative");
    118:   if (k>MAX_INDEX) SETERRQ1(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Phi functions only implemented for k<=%d",MAX_INDEX);
    119:   if (k!=ctx->k) {
    120:     ctx->k = k;
    121:     MatDestroy(&ctx->H);
    122:     MatDestroy(&ctx->F);
    123:   }
    124:   return(0);
    125: }

    127: /*@
    128:    FNPhiSetIndex - Sets the index of the phi-function.

    130:    Logically Collective on fn

    132:    Input Parameters:
    133: +  fn - the math function context
    134: -  k  - the index

    136:    Notes:
    137:    The phi-functions are defined as follows. The default is k=1.
    138: .vb
    139:       phi_0(x) = exp(x)
    140:       phi_1(x) = (exp(x)-1)/x
    141:       phi_k(x) = (phi_{k-1}(x)-1/(k-1)!)/x
    142: .ve

    144:    Level: intermediate

    146: .seealso: FNPhiGetIndex()
    147: @*/
    148: PetscErrorCode FNPhiSetIndex(FN fn,PetscInt k)
    149: {

    155:   PetscTryMethod(fn,"FNPhiSetIndex_C",(FN,PetscInt),(fn,k));
    156:   return(0);
    157: }

    159: static PetscErrorCode FNPhiGetIndex_Phi(FN fn,PetscInt *k)
    160: {
    161:   FN_PHI *ctx = (FN_PHI*)fn->data;

    164:   *k = ctx->k;
    165:   return(0);
    166: }

    168: /*@
    169:    FNPhiGetIndex - Gets the index of the phi-function.

    171:    Not Collective

    173:    Input Parameter:
    174: .  fn - the math function context

    176:    Output Parameter:
    177: .  k  - the index

    179:    Level: intermediate

    181: .seealso: FNPhiSetIndex()
    182: @*/
    183: PetscErrorCode FNPhiGetIndex(FN fn,PetscInt *k)
    184: {

    190:   PetscUseMethod(fn,"FNPhiGetIndex_C",(FN,PetscInt*),(fn,k));
    191:   return(0);
    192: }

    194: PetscErrorCode FNView_Phi(FN fn,PetscViewer viewer)
    195: {
    197:   FN_PHI         *ctx = (FN_PHI*)fn->data;
    198:   PetscBool      isascii;
    199:   char           str[50],strx[50];

    202:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    203:   if (isascii) {
    204:     PetscViewerASCIIPrintf(viewer,"  Phi_%D: ",ctx->k);
    205:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    206:     if (fn->beta!=(PetscScalar)1.0) {
    207:       SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE);
    208:       PetscViewerASCIIPrintf(viewer,"%s*",str);
    209:     }
    210:     if (fn->alpha==(PetscScalar)1.0) {
    211:       PetscSNPrintf(strx,sizeof(strx),"x");
    212:     } else {
    213:       SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE);
    214:       PetscSNPrintf(strx,sizeof(strx),"(%s*x)",str);
    215:     }
    216:     if (!ctx->k) {
    217:       PetscViewerASCIIPrintf(viewer,"exp(%s)\n",strx);
    218:     } else if (ctx->k==1) {
    219:       PetscViewerASCIIPrintf(viewer,"(exp(%s)-1)/%s\n",strx,strx);
    220:     } else {
    221:       PetscViewerASCIIPrintf(viewer,"(phi_%D(%s)-1/%D!)/%s\n",ctx->k-1,strx,ctx->k-1,strx);
    222:     }
    223:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    224:   }
    225:   return(0);
    226: }

    228: PetscErrorCode FNSetFromOptions_Phi(PetscOptionItems *PetscOptionsObject,FN fn)
    229: {
    231:   FN_PHI         *ctx = (FN_PHI*)fn->data;
    232:   PetscInt       k;
    233:   PetscBool      flag;

    236:   PetscOptionsHead(PetscOptionsObject,"FN Phi Options");

    238:     PetscOptionsInt("-fn_phi_index","Index of the phi-function","FNPhiSetIndex",ctx->k,&k,&flag);
    239:     if (flag) { FNPhiSetIndex(fn,k); }

    241:   PetscOptionsTail();
    242:   return(0);
    243: }

    245: PetscErrorCode FNDuplicate_Phi(FN fn,MPI_Comm comm,FN *newfn)
    246: {
    247:   FN_PHI *ctx = (FN_PHI*)fn->data,*ctx2 = (FN_PHI*)(*newfn)->data;

    250:   ctx2->k = ctx->k;
    251:   return(0);
    252: }

    254: PetscErrorCode FNDestroy_Phi(FN fn)
    255: {
    257:   FN_PHI         *ctx = (FN_PHI*)fn->data;

    260:   MatDestroy(&ctx->H);
    261:   MatDestroy(&ctx->F);
    262:   PetscFree(fn->data);
    263:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",NULL);
    264:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",NULL);
    265:   return(0);
    266: }

    268: SLEPC_EXTERN PetscErrorCode FNCreate_Phi(FN fn)
    269: {
    271:   FN_PHI         *ctx;

    274:   PetscNewLog(fn,&ctx);
    275:   fn->data = (void*)ctx;
    276:   ctx->k   = 1;

    278:   fn->ops->evaluatefunction          = FNEvaluateFunction_Phi;
    279:   fn->ops->evaluatederivative        = FNEvaluateDerivative_Phi;
    280:   fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Phi;
    281:   fn->ops->setfromoptions            = FNSetFromOptions_Phi;
    282:   fn->ops->view                      = FNView_Phi;
    283:   fn->ops->duplicate                 = FNDuplicate_Phi;
    284:   fn->ops->destroy                   = FNDestroy_Phi;
    285:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",FNPhiSetIndex_Phi);
    286:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",FNPhiGetIndex_Phi);
    287:   return(0);
    288: }