Actual source code: fnphi.c
slepc-3.15.0 2021-03-31
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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: {
63: PetscErrorCode ierr;
64: FN_PHI *ctx = (FN_PHI*)fn->data;
65: PetscInt i,j,m,n,nh;
66: PetscScalar *Ha,*va,sfactor=1.0;
67: const PetscScalar *Aa,*Fa;
70: MatGetSize(A,&m,NULL);
71: n = m+ctx->k;
72: if (ctx->H) {
73: MatGetSize(ctx->H,&nh,NULL);
74: if (n!=nh) {
75: MatDestroy(&ctx->H);
76: MatDestroy(&ctx->F);
77: }
78: }
79: if (!ctx->H) {
80: MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->H);
81: MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->F);
82: }
83: MatDenseGetArray(ctx->H,&Ha);
84: MatDenseGetArrayRead(A,&Aa);
85: for (j=0;j<m;j++) {
86: PetscArraycpy(Ha+j*n,Aa+j*m,m);
87: }
88: MatDenseRestoreArrayRead(A,&Aa);
89: if (ctx->k) {
90: for (j=0;j<m;j++) for (i=m;i<n;i++) Ha[i+j*n] = 0.0;
91: for (j=m;j<n;j++) for (i=0;i<n;i++) Ha[i+j*n] = 0.0;
92: Ha[0+m*n] = fn->alpha;
93: for (j=m+1;j<n;j++) Ha[j-1+j*n] = fn->alpha;
94: }
95: MatDenseRestoreArray(ctx->H,&Ha);
97: FNEvaluateFunctionMat_Exp_Higham(fn,ctx->H,ctx->F);
99: MatDenseGetArrayRead(ctx->F,&Fa);
100: VecGetArray(v,&va);
101: if (ctx->k) {
102: sfactor = PetscPowScalarInt(fn->alpha,-ctx->k);
103: for (i=0;i<m;i++) va[i] = sfactor*Fa[i+(n-1)*n];
104: } else {
105: for (i=0;i<m;i++) va[i] = sfactor*Fa[i+0*n];
106: }
107: VecRestoreArray(v,&va);
108: MatDenseRestoreArrayRead(ctx->F,&Fa);
109: return(0);
110: }
112: static PetscErrorCode FNPhiSetIndex_Phi(FN fn,PetscInt k)
113: {
115: FN_PHI *ctx = (FN_PHI*)fn->data;
118: if (k<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Index cannot be negative");
119: if (k>MAX_INDEX) SETERRQ1(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Phi functions only implemented for k<=%d",MAX_INDEX);
120: if (k!=ctx->k) {
121: ctx->k = k;
122: MatDestroy(&ctx->H);
123: MatDestroy(&ctx->F);
124: }
125: return(0);
126: }
128: /*@
129: FNPhiSetIndex - Sets the index of the phi-function.
131: Logically Collective on fn
133: Input Parameters:
134: + fn - the math function context
135: - k - the index
137: Notes:
138: The phi-functions are defined as follows. The default is k=1.
139: .vb
140: phi_0(x) = exp(x)
141: phi_1(x) = (exp(x)-1)/x
142: phi_k(x) = (phi_{k-1}(x)-1/(k-1)!)/x
143: .ve
145: Level: intermediate
147: .seealso: FNPhiGetIndex()
148: @*/
149: PetscErrorCode FNPhiSetIndex(FN fn,PetscInt k)
150: {
156: PetscTryMethod(fn,"FNPhiSetIndex_C",(FN,PetscInt),(fn,k));
157: return(0);
158: }
160: static PetscErrorCode FNPhiGetIndex_Phi(FN fn,PetscInt *k)
161: {
162: FN_PHI *ctx = (FN_PHI*)fn->data;
165: *k = ctx->k;
166: return(0);
167: }
169: /*@
170: FNPhiGetIndex - Gets the index of the phi-function.
172: Not Collective
174: Input Parameter:
175: . fn - the math function context
177: Output Parameter:
178: . k - the index
180: Level: intermediate
182: .seealso: FNPhiSetIndex()
183: @*/
184: PetscErrorCode FNPhiGetIndex(FN fn,PetscInt *k)
185: {
191: PetscUseMethod(fn,"FNPhiGetIndex_C",(FN,PetscInt*),(fn,k));
192: return(0);
193: }
195: PetscErrorCode FNView_Phi(FN fn,PetscViewer viewer)
196: {
198: FN_PHI *ctx = (FN_PHI*)fn->data;
199: PetscBool isascii;
200: char str[50],strx[50];
203: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
204: if (isascii) {
205: PetscViewerASCIIPrintf(viewer," Phi_%D: ",ctx->k);
206: PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
207: if (fn->beta!=(PetscScalar)1.0) {
208: SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE);
209: PetscViewerASCIIPrintf(viewer,"%s*",str);
210: }
211: if (fn->alpha==(PetscScalar)1.0) {
212: PetscSNPrintf(strx,sizeof(strx),"x");
213: } else {
214: SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE);
215: PetscSNPrintf(strx,sizeof(strx),"(%s*x)",str);
216: }
217: if (!ctx->k) {
218: PetscViewerASCIIPrintf(viewer,"exp(%s)\n",strx);
219: } else if (ctx->k==1) {
220: PetscViewerASCIIPrintf(viewer,"(exp(%s)-1)/%s\n",strx,strx);
221: } else {
222: PetscViewerASCIIPrintf(viewer,"(phi_%D(%s)-1/%D!)/%s\n",ctx->k-1,strx,ctx->k-1,strx);
223: }
224: PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
225: }
226: return(0);
227: }
229: PetscErrorCode FNSetFromOptions_Phi(PetscOptionItems *PetscOptionsObject,FN fn)
230: {
232: FN_PHI *ctx = (FN_PHI*)fn->data;
233: PetscInt k;
234: PetscBool flag;
237: PetscOptionsHead(PetscOptionsObject,"FN Phi Options");
239: PetscOptionsInt("-fn_phi_index","Index of the phi-function","FNPhiSetIndex",ctx->k,&k,&flag);
240: if (flag) { FNPhiSetIndex(fn,k); }
242: PetscOptionsTail();
243: return(0);
244: }
246: PetscErrorCode FNDuplicate_Phi(FN fn,MPI_Comm comm,FN *newfn)
247: {
248: FN_PHI *ctx = (FN_PHI*)fn->data,*ctx2 = (FN_PHI*)(*newfn)->data;
251: ctx2->k = ctx->k;
252: return(0);
253: }
255: PetscErrorCode FNDestroy_Phi(FN fn)
256: {
258: FN_PHI *ctx = (FN_PHI*)fn->data;
261: MatDestroy(&ctx->H);
262: MatDestroy(&ctx->F);
263: PetscFree(fn->data);
264: PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",NULL);
265: PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",NULL);
266: return(0);
267: }
269: SLEPC_EXTERN PetscErrorCode FNCreate_Phi(FN fn)
270: {
272: FN_PHI *ctx;
275: PetscNewLog(fn,&ctx);
276: fn->data = (void*)ctx;
277: ctx->k = 1;
279: fn->ops->evaluatefunction = FNEvaluateFunction_Phi;
280: fn->ops->evaluatederivative = FNEvaluateDerivative_Phi;
281: fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Phi;
282: fn->ops->setfromoptions = FNSetFromOptions_Phi;
283: fn->ops->view = FNView_Phi;
284: fn->ops->duplicate = FNDuplicate_Phi;
285: fn->ops->destroy = FNDestroy_Phi;
286: PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",FNPhiSetIndex_Phi);
287: PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",FNPhiGetIndex_Phi);
288: return(0);
289: }