Actual source code: fnphi.c
slepc-3.18.1 2022-11-02
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: return 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: return 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: return 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: return 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: return 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: return 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: return 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: return 0;
205: }
207: PetscErrorCode FNSetFromOptions_Phi(FN fn,PetscOptionItems *PetscOptionsObject)
208: {
209: FN_PHI *ctx = (FN_PHI*)fn->data;
210: PetscInt k;
211: PetscBool flag;
213: PetscOptionsHeadBegin(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: PetscOptionsHeadEnd();
219: return 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: return 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: return 0;
240: }
242: SLEPC_EXTERN PetscErrorCode FNCreate_Phi(FN fn)
243: {
244: FN_PHI *ctx;
246: PetscNew(&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: return 0;
260: }