Actual source code: fnphi.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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>      /*I "slepcfn.h" I*/

 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:     PetscMemcpy(Ha+j*n,Aa+j*m,m*sizeof(PetscScalar));
 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,50,fn->beta,PETSC_TRUE);
208:       PetscViewerASCIIPrintf(viewer,"%s*",str);
209:     }
210:     if (fn->alpha==(PetscScalar)1.0) {
211:       PetscSNPrintf(strx,50,"x");
212:     } else {
213:       SlepcSNPrintfScalar(str,50,fn->alpha,PETSC_TRUE);
214:       PetscSNPrintf(strx,50,"(%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: }