Actual source code: fnphi.c
slepc-3.21.1 2024-04-26
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: static 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: PetscFunctionBegin;
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: PetscFunctionReturn(PETSC_SUCCESS);
43: }
45: static 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];
51: PetscFunctionBegin;
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: PetscFunctionReturn(PETSC_SUCCESS);
59: }
61: static PetscErrorCode FNEvaluateFunctionMatVec_Phi(FN fn,Mat A,Vec v)
62: {
63: FN_PHI *ctx = (FN_PHI*)fn->data;
64: PetscInt i,j,m,n,nh;
65: PetscScalar *Ha,*va,sfactor=1.0;
66: const PetscScalar *Aa,*Fa;
68: PetscFunctionBegin;
69: PetscCall(MatGetSize(A,&m,NULL));
70: n = m+ctx->k;
71: if (ctx->H) {
72: PetscCall(MatGetSize(ctx->H,&nh,NULL));
73: if (n!=nh) {
74: PetscCall(MatDestroy(&ctx->H));
75: PetscCall(MatDestroy(&ctx->F));
76: }
77: }
78: if (!ctx->H) {
79: PetscCall(MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->H));
80: PetscCall(MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->F));
81: }
82: PetscCall(MatDenseGetArray(ctx->H,&Ha));
83: PetscCall(MatDenseGetArrayRead(A,&Aa));
84: for (j=0;j<m;j++) PetscCall(PetscArraycpy(Ha+j*n,Aa+j*m,m));
85: PetscCall(MatDenseRestoreArrayRead(A,&Aa));
86: if (ctx->k) {
87: for (j=0;j<m;j++) for (i=m;i<n;i++) Ha[i+j*n] = 0.0;
88: for (j=m;j<n;j++) for (i=0;i<n;i++) Ha[i+j*n] = 0.0;
89: Ha[0+m*n] = fn->alpha;
90: for (j=m+1;j<n;j++) Ha[j-1+j*n] = fn->alpha;
91: }
92: PetscCall(MatDenseRestoreArray(ctx->H,&Ha));
94: PetscCall(FNEvaluateFunctionMat_Exp_Higham(fn,ctx->H,ctx->F));
96: PetscCall(MatDenseGetArrayRead(ctx->F,&Fa));
97: PetscCall(VecGetArray(v,&va));
98: if (ctx->k) {
99: sfactor = PetscPowScalarInt(fn->alpha,-ctx->k);
100: for (i=0;i<m;i++) va[i] = sfactor*Fa[i+(n-1)*n];
101: } else {
102: for (i=0;i<m;i++) va[i] = sfactor*Fa[i+0*n];
103: }
104: PetscCall(VecRestoreArray(v,&va));
105: PetscCall(MatDenseRestoreArrayRead(ctx->F,&Fa));
106: PetscFunctionReturn(PETSC_SUCCESS);
107: }
109: static PetscErrorCode FNPhiSetIndex_Phi(FN fn,PetscInt k)
110: {
111: FN_PHI *ctx = (FN_PHI*)fn->data;
113: PetscFunctionBegin;
114: PetscCheck(k>=0,PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Index cannot be negative");
115: PetscCheck(k<=MAX_INDEX,PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Phi functions only implemented for k<=%d",MAX_INDEX);
116: if (k!=ctx->k) {
117: ctx->k = k;
118: PetscCall(MatDestroy(&ctx->H));
119: PetscCall(MatDestroy(&ctx->F));
120: }
121: PetscFunctionReturn(PETSC_SUCCESS);
122: }
124: /*@
125: FNPhiSetIndex - Sets the index of the phi-function.
127: Logically Collective
129: Input Parameters:
130: + fn - the math function context
131: - k - the index
133: Notes:
134: The phi-functions are defined as follows. The default is k=1.
135: .vb
136: phi_0(x) = exp(x)
137: phi_1(x) = (exp(x)-1)/x
138: phi_k(x) = (phi_{k-1}(x)-1/(k-1)!)/x
139: .ve
141: Level: intermediate
143: .seealso: FNPhiGetIndex()
144: @*/
145: PetscErrorCode FNPhiSetIndex(FN fn,PetscInt k)
146: {
147: PetscFunctionBegin;
150: PetscTryMethod(fn,"FNPhiSetIndex_C",(FN,PetscInt),(fn,k));
151: PetscFunctionReturn(PETSC_SUCCESS);
152: }
154: static PetscErrorCode FNPhiGetIndex_Phi(FN fn,PetscInt *k)
155: {
156: FN_PHI *ctx = (FN_PHI*)fn->data;
158: PetscFunctionBegin;
159: *k = ctx->k;
160: PetscFunctionReturn(PETSC_SUCCESS);
161: }
163: /*@
164: FNPhiGetIndex - Gets the index of the phi-function.
166: Not Collective
168: Input Parameter:
169: . fn - the math function context
171: Output Parameter:
172: . k - the index
174: Level: intermediate
176: .seealso: FNPhiSetIndex()
177: @*/
178: PetscErrorCode FNPhiGetIndex(FN fn,PetscInt *k)
179: {
180: PetscFunctionBegin;
182: PetscAssertPointer(k,2);
183: PetscUseMethod(fn,"FNPhiGetIndex_C",(FN,PetscInt*),(fn,k));
184: PetscFunctionReturn(PETSC_SUCCESS);
185: }
187: static PetscErrorCode FNView_Phi(FN fn,PetscViewer viewer)
188: {
189: FN_PHI *ctx = (FN_PHI*)fn->data;
190: PetscBool isascii;
191: char str[50],strx[50];
193: PetscFunctionBegin;
194: PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
195: if (isascii) {
196: PetscCall(PetscViewerASCIIPrintf(viewer," phi_%" PetscInt_FMT ": ",ctx->k));
197: PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
198: if (fn->beta!=(PetscScalar)1.0) {
199: PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE));
200: PetscCall(PetscViewerASCIIPrintf(viewer,"%s*",str));
201: }
202: if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscSNPrintf(strx,sizeof(strx),"x"));
203: else {
204: PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE));
205: PetscCall(PetscSNPrintf(strx,sizeof(strx),"(%s*x)",str));
206: }
207: if (!ctx->k) PetscCall(PetscViewerASCIIPrintf(viewer,"exp(%s)\n",strx));
208: else if (ctx->k==1) PetscCall(PetscViewerASCIIPrintf(viewer,"(exp(%s)-1)/%s\n",strx,strx));
209: else PetscCall(PetscViewerASCIIPrintf(viewer,"(phi_%" PetscInt_FMT "(%s)-1/%" PetscInt_FMT "!)/%s\n",ctx->k-1,strx,ctx->k-1,strx));
210: PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
211: }
212: PetscFunctionReturn(PETSC_SUCCESS);
213: }
215: static PetscErrorCode FNSetFromOptions_Phi(FN fn,PetscOptionItems *PetscOptionsObject)
216: {
217: FN_PHI *ctx = (FN_PHI*)fn->data;
218: PetscInt k;
219: PetscBool flag;
221: PetscFunctionBegin;
222: PetscOptionsHeadBegin(PetscOptionsObject,"FN Phi Options");
224: PetscCall(PetscOptionsInt("-fn_phi_index","Index of the phi-function","FNPhiSetIndex",ctx->k,&k,&flag));
225: if (flag) PetscCall(FNPhiSetIndex(fn,k));
227: PetscOptionsHeadEnd();
228: PetscFunctionReturn(PETSC_SUCCESS);
229: }
231: static PetscErrorCode FNDuplicate_Phi(FN fn,MPI_Comm comm,FN *newfn)
232: {
233: FN_PHI *ctx = (FN_PHI*)fn->data,*ctx2 = (FN_PHI*)(*newfn)->data;
235: PetscFunctionBegin;
236: ctx2->k = ctx->k;
237: PetscFunctionReturn(PETSC_SUCCESS);
238: }
240: static PetscErrorCode FNDestroy_Phi(FN fn)
241: {
242: FN_PHI *ctx = (FN_PHI*)fn->data;
244: PetscFunctionBegin;
245: PetscCall(MatDestroy(&ctx->H));
246: PetscCall(MatDestroy(&ctx->F));
247: PetscCall(PetscFree(fn->data));
248: PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",NULL));
249: PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",NULL));
250: PetscFunctionReturn(PETSC_SUCCESS);
251: }
253: SLEPC_EXTERN PetscErrorCode FNCreate_Phi(FN fn)
254: {
255: FN_PHI *ctx;
257: PetscFunctionBegin;
258: PetscCall(PetscNew(&ctx));
259: fn->data = (void*)ctx;
260: ctx->k = 1;
262: fn->ops->evaluatefunction = FNEvaluateFunction_Phi;
263: fn->ops->evaluatederivative = FNEvaluateDerivative_Phi;
264: fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Phi;
265: fn->ops->setfromoptions = FNSetFromOptions_Phi;
266: fn->ops->view = FNView_Phi;
267: fn->ops->duplicate = FNDuplicate_Phi;
268: fn->ops->destroy = FNDestroy_Phi;
269: PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",FNPhiSetIndex_Phi));
270: PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",FNPhiGetIndex_Phi));
271: PetscFunctionReturn(PETSC_SUCCESS);
272: }