Date: 2022-03-31T15:28:47+00:00

Actual source code: fnphi.c
slepc-3.17.0 2022-03-31
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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:    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: static const 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];

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

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

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

     59: PetscErrorCode FNEvaluateFunctionMatVec_Phi(FN fn,Mat A,Vec v)
     60: {
     61:   FN_PHI            *ctx = (FN_PHI*)fn->data;
     62:   PetscInt          i,j,m,n,nh;
     63:   PetscScalar       *Ha,*va,sfactor=1.0;
     64:   const PetscScalar *Aa,*Fa;

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

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

     93:   MatDenseGetArrayRead(ctx->F,&Fa);
     94:   VecGetArray(v,&va);
     95:   if (ctx->k) {
     96:     sfactor = PetscPowScalarInt(fn->alpha,-ctx->k);
     97:     for (i=0;i<m;i++) va[i] = sfactor*Fa[i+(n-1)*n];
     98:   } else {
     99:     for (i=0;i<m;i++) va[i] = sfactor*Fa[i+0*n];
    100:   }
    101:   VecRestoreArray(v,&va);
    102:   MatDenseRestoreArrayRead(ctx->F,&Fa);
    103:   PetscFunctionReturn(0);
    104: }

    106: static PetscErrorCode FNPhiSetIndex_Phi(FN fn,PetscInt k)
    107: {
    108:   FN_PHI         *ctx = (FN_PHI*)fn->data;

    112:   if (k!=ctx->k) {
    113:     ctx->k = k;
    114:     MatDestroy(&ctx->H);
    115:     MatDestroy(&ctx->F);
    116:   }
    117:   PetscFunctionReturn(0);
    118: }

    120: /*@
    121:    FNPhiSetIndex - Sets the index of the phi-function.

    123:    Logically Collective on fn

    125:    Input Parameters:
    126: +  fn - the math function context
    127: -  k  - the index

    129:    Notes:
    130:    The phi-functions are defined as follows. The default is k=1.
    131: .vb
    132:       phi_0(x) = exp(x)
    133:       phi_1(x) = (exp(x)-1)/x
    134:       phi_k(x) = (phi_{k-1}(x)-1/(k-1)!)/x
    135: .ve

    137:    Level: intermediate

    139: .seealso: FNPhiGetIndex()
    140: @*/
    141: PetscErrorCode FNPhiSetIndex(FN fn,PetscInt k)
    142: {
    145:   PetscTryMethod(fn,"FNPhiSetIndex_C",(FN,PetscInt),(fn,k));
    146:   PetscFunctionReturn(0);
    147: }

    149: static PetscErrorCode FNPhiGetIndex_Phi(FN fn,PetscInt *k)
    150: {
    151:   FN_PHI *ctx = (FN_PHI*)fn->data;

    153:   *k = ctx->k;
    154:   PetscFunctionReturn(0);
    155: }

    157: /*@
    158:    FNPhiGetIndex - Gets the index of the phi-function.

    160:    Not Collective

    162:    Input Parameter:
    163: .  fn - the math function context

    165:    Output Parameter:
    166: .  k  - the index

    168:    Level: intermediate

    170: .seealso: FNPhiSetIndex()
    171: @*/
    172: PetscErrorCode FNPhiGetIndex(FN fn,PetscInt *k)
    173: {
    176:   PetscUseMethod(fn,"FNPhiGetIndex_C",(FN,PetscInt*),(fn,k));
    177:   PetscFunctionReturn(0);
    178: }

    180: PetscErrorCode FNView_Phi(FN fn,PetscViewer viewer)
    181: {
    182:   FN_PHI         *ctx = (FN_PHI*)fn->data;
    183:   PetscBool      isascii;
    184:   char           str[50],strx[50];

    186:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    187:   if (isascii) {
    188:     PetscViewerASCIIPrintf(viewer,"  Phi_%" PetscInt_FMT ": ",ctx->k);
    189:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    190:     if (fn->beta!=(PetscScalar)1.0) {
    191:       SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE);
    192:       PetscViewerASCIIPrintf(viewer,"%s*",str);
    193:     }
    194:     if (fn->alpha==(PetscScalar)1.0) PetscSNPrintf(strx,sizeof(strx),"x");
    195:     else {
    196:       SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE);
    197:       PetscSNPrintf(strx,sizeof(strx),"(%s*x)",str);
    198:     }
    199:     if (!ctx->k) PetscViewerASCIIPrintf(viewer,"exp(%s)\n",strx);
    200:     else if (ctx->k==1) PetscViewerASCIIPrintf(viewer,"(exp(%s)-1)/%s\n",strx,strx);
    201:     else PetscViewerASCIIPrintf(viewer,"(phi_%" PetscInt_FMT "(%s)-1/%" PetscInt_FMT "!)/%s\n",ctx->k-1,strx,ctx->k-1,strx);
    202:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    203:   }
    204:   PetscFunctionReturn(0);
    205: }

    207: PetscErrorCode FNSetFromOptions_Phi(PetscOptionItems *PetscOptionsObject,FN fn)
    208: {
    209:   FN_PHI         *ctx = (FN_PHI*)fn->data;
    210:   PetscInt       k;
    211:   PetscBool      flag;

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

    215:     PetscOptionsInt("-fn_phi_index","Index of the phi-function","FNPhiSetIndex",ctx->k,&k,&flag);
    216:     if (flag) FNPhiSetIndex(fn,k);

    218:   PetscOptionsTail();
    219:   PetscFunctionReturn(0);
    220: }

    222: PetscErrorCode FNDuplicate_Phi(FN fn,MPI_Comm comm,FN *newfn)
    223: {
    224:   FN_PHI *ctx = (FN_PHI*)fn->data,*ctx2 = (FN_PHI*)(*newfn)->data;

    226:   ctx2->k = ctx->k;
    227:   PetscFunctionReturn(0);
    228: }

    230: PetscErrorCode FNDestroy_Phi(FN fn)
    231: {
    232:   FN_PHI         *ctx = (FN_PHI*)fn->data;

    234:   MatDestroy(&ctx->H);
    235:   MatDestroy(&ctx->F);
    236:   PetscFree(fn->data);
    237:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",NULL);
    238:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",NULL);
    239:   PetscFunctionReturn(0);
    240: }

    242: SLEPC_EXTERN PetscErrorCode FNCreate_Phi(FN fn)
    243: {
    244:   FN_PHI         *ctx;

    246:   PetscNewLog(fn,&ctx);
    247:   fn->data = (void*)ctx;
    248:   ctx->k   = 1;

    250:   fn->ops->evaluatefunction          = FNEvaluateFunction_Phi;
    251:   fn->ops->evaluatederivative        = FNEvaluateDerivative_Phi;
    252:   fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Phi;
    253:   fn->ops->setfromoptions            = FNSetFromOptions_Phi;
    254:   fn->ops->view                      = FNView_Phi;
    255:   fn->ops->duplicate                 = FNDuplicate_Phi;
    256:   fn->ops->destroy                   = FNDestroy_Phi;
    257:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",FNPhiSetIndex_Phi);
    258:   PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",FNPhiGetIndex_Phi);
    259:   PetscFunctionReturn(0);
    260: }