| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
| 4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
| 5 | |||
| 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 | */ | ||
| 16 | |||
| 17 | #include <slepc/private/fnimpl.h> /*I "slepcfn.h" I*/ | ||
| 18 | |||
| 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; | ||
| 24 | |||
| 25 | #define MAX_INDEX 10 | ||
| 26 | |||
| 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 }; | ||
| 28 | |||
| 29 | 270 | static PetscErrorCode FNEvaluateFunction_Phi(FN fn,PetscScalar x,PetscScalar *y) | |
| 30 | { | ||
| 31 | 270 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 32 | 270 | PetscInt i; | |
| 33 | 270 | PetscScalar phi[MAX_INDEX+1]; | |
| 34 | |||
| 35 |
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270 | PetscFunctionBegin; |
| 36 |
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270 | if (x==0.0) *y = rfactorial[ctx->k]; |
| 37 | else { | ||
| 38 | 270 | phi[0] = PetscExpScalar(x); | |
| 39 |
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630 | for (i=1;i<=ctx->k;i++) phi[i] = (phi[i-1]-rfactorial[i-1])/x; |
| 40 | 270 | *y = phi[ctx->k]; | |
| 41 | } | ||
| 42 |
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270 | PetscFunctionReturn(PETSC_SUCCESS); |
| 43 | } | ||
| 44 | |||
| 45 | 30 | static PetscErrorCode FNEvaluateDerivative_Phi(FN fn,PetscScalar x,PetscScalar *y) | |
| 46 | { | ||
| 47 | 30 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 48 | 30 | PetscInt i; | |
| 49 | 30 | PetscScalar phi[MAX_INDEX+2]; | |
| 50 | |||
| 51 |
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30 | PetscFunctionBegin; |
| 52 |
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30 | if (x==0.0) *y = rfactorial[ctx->k+1]; |
| 53 | else { | ||
| 54 | 30 | phi[0] = PetscExpScalar(x); | |
| 55 |
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100 | for (i=1;i<=ctx->k+1;i++) phi[i] = (phi[i-1]-rfactorial[i-1])/x; |
| 56 | 30 | *y = phi[ctx->k] - phi[ctx->k+1]*(PetscReal)ctx->k; | |
| 57 | } | ||
| 58 |
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30 | PetscFunctionReturn(PETSC_SUCCESS); |
| 59 | } | ||
| 60 | |||
| 61 | 230 | static PetscErrorCode FNEvaluateFunctionMatVec_Phi(FN fn,Mat A,Vec v) | |
| 62 | { | ||
| 63 | 230 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 64 | 230 | PetscInt i,j,m,n,nh; | |
| 65 | 230 | PetscScalar *Ha,*va,sfactor=1.0; | |
| 66 | 230 | const PetscScalar *Aa,*Fa; | |
| 67 | |||
| 68 |
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230 | PetscFunctionBegin; |
| 69 |
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230 | PetscCall(MatGetSize(A,&m,NULL)); |
| 70 | 230 | n = m+ctx->k; | |
| 71 |
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230 | if (ctx->H) { |
| 72 |
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190 | PetscCall(MatGetSize(ctx->H,&nh,NULL)); |
| 73 |
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190 | if (n!=nh) { |
| 74 |
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190 | PetscCall(MatDestroy(&ctx->H)); |
| 75 |
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190 | PetscCall(MatDestroy(&ctx->F)); |
| 76 | } | ||
| 77 | } | ||
| 78 |
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230 | if (!ctx->H) { |
| 79 |
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230 | PetscCall(MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->H)); |
| 80 |
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230 | PetscCall(MatCreateDense(PETSC_COMM_SELF,n,n,n,n,NULL,&ctx->F)); |
| 81 | } | ||
| 82 |
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230 | PetscCall(MatDenseGetArray(ctx->H,&Ha)); |
| 83 |
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230 | PetscCall(MatDenseGetArrayRead(A,&Aa)); |
| 84 |
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15470 | for (j=0;j<m;j++) PetscCall(PetscArraycpy(Ha+j*n,Aa+j*m,m)); |
| 85 |
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230 | PetscCall(MatDenseRestoreArrayRead(A,&Aa)); |
| 86 |
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230 | if (ctx->k) { |
| 87 |
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30700 | for (j=0;j<m;j++) for (i=m;i<n;i++) Ha[i+j*n] = 0.0; |
| 88 |
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16080 | for (j=m;j<n;j++) for (i=0;i<n;i++) Ha[i+j*n] = 0.0; |
| 89 | 220 | Ha[0+m*n] = fn->alpha; | |
| 90 |
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240 | for (j=m+1;j<n;j++) Ha[j-1+j*n] = fn->alpha; |
| 91 | } | ||
| 92 |
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230 | PetscCall(MatDenseRestoreArray(ctx->H,&Ha)); |
| 93 | |||
| 94 |
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230 | PetscCall(FNEvaluateFunctionMat_Exp_Higham(fn,ctx->H,ctx->F)); |
| 95 | |||
| 96 |
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230 | PetscCall(MatDenseGetArrayRead(ctx->F,&Fa)); |
| 97 |
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230 | PetscCall(VecGetArray(v,&va)); |
| 98 |
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230 | if (ctx->k) { |
| 99 | 220 | sfactor = PetscPowScalarInt(fn->alpha,-ctx->k); | |
| 100 |
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15600 | for (i=0;i<m;i++) va[i] = sfactor*Fa[i+(n-1)*n]; |
| 101 | } else { | ||
| 102 |
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90 | for (i=0;i<m;i++) va[i] = sfactor*Fa[i+0*n]; |
| 103 | } | ||
| 104 |
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230 | PetscCall(VecRestoreArray(v,&va)); |
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230 | PetscCall(MatDenseRestoreArrayRead(ctx->F,&Fa)); |
| 106 |
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46 | PetscFunctionReturn(PETSC_SUCCESS); |
| 107 | } | ||
| 108 | |||
| 109 | 30 | static PetscErrorCode FNPhiSetIndex_Phi(FN fn,PetscInt k) | |
| 110 | { | ||
| 111 | 30 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 112 | |||
| 113 |
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30 | PetscFunctionBegin; |
| 114 |
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30 | PetscCheck(k>=0,PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Index cannot be negative"); |
| 115 |
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30 | PetscCheck(k<=MAX_INDEX,PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Phi functions only implemented for k<=%d",MAX_INDEX); |
| 116 |
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30 | if (k!=ctx->k) { |
| 117 | 20 | ctx->k = k; | |
| 118 |
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20 | PetscCall(MatDestroy(&ctx->H)); |
| 119 |
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20 | PetscCall(MatDestroy(&ctx->F)); |
| 120 | } | ||
| 121 |
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6 | PetscFunctionReturn(PETSC_SUCCESS); |
| 122 | } | ||
| 123 | |||
| 124 | /*@ | ||
| 125 | FNPhiSetIndex - Sets the index of the phi-function. | ||
| 126 | |||
| 127 | Logically Collective | ||
| 128 | |||
| 129 | Input Parameters: | ||
| 130 | + fn - the math function context | ||
| 131 | - k - the index | ||
| 132 | |||
| 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 | ||
| 140 | |||
| 141 | Level: intermediate | ||
| 142 | |||
| 143 | .seealso: FNPhiGetIndex() | ||
| 144 | @*/ | ||
| 145 | 30 | PetscErrorCode FNPhiSetIndex(FN fn,PetscInt k) | |
| 146 | { | ||
| 147 |
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30 | PetscFunctionBegin; |
| 148 |
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30 | PetscValidHeaderSpecific(fn,FN_CLASSID,1); |
| 149 |
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30 | PetscValidLogicalCollectiveInt(fn,k,2); |
| 150 |
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30 | PetscTryMethod(fn,"FNPhiSetIndex_C",(FN,PetscInt),(fn,k)); |
| 151 |
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30 | PetscFunctionReturn(PETSC_SUCCESS); |
| 152 | } | ||
| 153 | |||
| 154 | 10 | static PetscErrorCode FNPhiGetIndex_Phi(FN fn,PetscInt *k) | |
| 155 | { | ||
| 156 | 10 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 157 | |||
| 158 |
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10 | PetscFunctionBegin; |
| 159 | 10 | *k = ctx->k; | |
| 160 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 161 | } | ||
| 162 | |||
| 163 | /*@ | ||
| 164 | FNPhiGetIndex - Gets the index of the phi-function. | ||
| 165 | |||
| 166 | Not Collective | ||
| 167 | |||
| 168 | Input Parameter: | ||
| 169 | . fn - the math function context | ||
| 170 | |||
| 171 | Output Parameter: | ||
| 172 | . k - the index | ||
| 173 | |||
| 174 | Level: intermediate | ||
| 175 | |||
| 176 | .seealso: FNPhiSetIndex() | ||
| 177 | @*/ | ||
| 178 | 10 | PetscErrorCode FNPhiGetIndex(FN fn,PetscInt *k) | |
| 179 | { | ||
| 180 |
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10 | PetscFunctionBegin; |
| 181 |
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10 | PetscValidHeaderSpecific(fn,FN_CLASSID,1); |
| 182 |
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10 | PetscAssertPointer(k,2); |
| 183 |
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10 | PetscUseMethod(fn,"FNPhiGetIndex_C",(FN,PetscInt*),(fn,k)); |
| 184 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 185 | } | ||
| 186 | |||
| 187 | 30 | static PetscErrorCode FNView_Phi(FN fn,PetscViewer viewer) | |
| 188 | { | ||
| 189 | 30 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 190 | 30 | PetscBool isascii; | |
| 191 | 30 | char str[50],strx[50]; | |
| 192 | |||
| 193 |
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30 | PetscFunctionBegin; |
| 194 |
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30 | PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii)); |
| 195 |
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30 | if (isascii) { |
| 196 |
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30 | PetscCall(PetscViewerASCIIPrintf(viewer," phi_%" PetscInt_FMT ": ",ctx->k)); |
| 197 |
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30 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 198 |
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30 | if (fn->beta!=(PetscScalar)1.0) { |
| 199 |
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10 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE)); |
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10 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s*",str)); |
| 201 | } | ||
| 202 |
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30 | if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscSNPrintf(strx,sizeof(strx),"x")); |
| 203 | else { | ||
| 204 |
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10 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE)); |
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10 | PetscCall(PetscSNPrintf(strx,sizeof(strx),"(%s*x)",str)); |
| 206 | } | ||
| 207 |
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30 | if (!ctx->k) PetscCall(PetscViewerASCIIPrintf(viewer,"exp(%s)\n",strx)); |
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20 | else if (ctx->k==1) PetscCall(PetscViewerASCIIPrintf(viewer,"(exp(%s)-1)/%s\n",strx,strx)); |
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10 | else PetscCall(PetscViewerASCIIPrintf(viewer,"(phi_%" PetscInt_FMT "(%s)-1/%" PetscInt_FMT "!)/%s\n",ctx->k-1,strx,ctx->k-1,strx)); |
| 210 |
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30 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 211 | } | ||
| 212 |
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6 | PetscFunctionReturn(PETSC_SUCCESS); |
| 213 | } | ||
| 214 | |||
| 215 | 20 | static PetscErrorCode FNSetFromOptions_Phi(FN fn,PetscOptionItems PetscOptionsObject) | |
| 216 | { | ||
| 217 | 20 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 218 | 20 | PetscInt k; | |
| 219 | 20 | PetscBool flag; | |
| 220 | |||
| 221 |
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20 | PetscFunctionBegin; |
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20 | PetscOptionsHeadBegin(PetscOptionsObject,"FN Phi Options"); |
| 223 | |||
| 224 |
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20 | PetscCall(PetscOptionsInt("-fn_phi_index","Index of the phi-function","FNPhiSetIndex",ctx->k,&k,&flag)); |
| 225 |
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20 | if (flag) PetscCall(FNPhiSetIndex(fn,k)); |
| 226 | |||
| 227 |
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20 | PetscOptionsHeadEnd(); |
| 228 |
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4 | PetscFunctionReturn(PETSC_SUCCESS); |
| 229 | } | ||
| 230 | |||
| 231 | 10 | static PetscErrorCode FNDuplicate_Phi(FN fn,MPI_Comm comm,FN *newfn) | |
| 232 | { | ||
| 233 | 10 | FN_PHI *ctx = (FN_PHI*)fn->data,*ctx2 = (FN_PHI*)(*newfn)->data; | |
| 234 | |||
| 235 |
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10 | PetscFunctionBegin; |
| 236 | 10 | ctx2->k = ctx->k; | |
| 237 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 238 | } | ||
| 239 | |||
| 240 | 50 | static PetscErrorCode FNDestroy_Phi(FN fn) | |
| 241 | { | ||
| 242 | 50 | FN_PHI *ctx = (FN_PHI*)fn->data; | |
| 243 | |||
| 244 |
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50 | PetscFunctionBegin; |
| 245 |
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50 | PetscCall(MatDestroy(&ctx->H)); |
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50 | PetscCall(MatDestroy(&ctx->F)); |
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50 | PetscCall(PetscFree(fn->data)); |
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50 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",NULL)); |
| 249 |
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50 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",NULL)); |
| 250 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 251 | } | ||
| 252 | |||
| 253 | 50 | SLEPC_EXTERN PetscErrorCode FNCreate_Phi(FN fn) | |
| 254 | { | ||
| 255 | 50 | FN_PHI *ctx; | |
| 256 | |||
| 257 |
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50 | PetscFunctionBegin; |
| 258 |
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50 | PetscCall(PetscNew(&ctx)); |
| 259 | 50 | fn->data = (void*)ctx; | |
| 260 | 50 | ctx->k = 1; | |
| 261 | |||
| 262 | 50 | fn->ops->evaluatefunction = FNEvaluateFunction_Phi; | |
| 263 | 50 | fn->ops->evaluatederivative = FNEvaluateDerivative_Phi; | |
| 264 | 50 | fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Phi; | |
| 265 | 50 | fn->ops->setfromoptions = FNSetFromOptions_Phi; | |
| 266 | 50 | fn->ops->view = FNView_Phi; | |
| 267 | 50 | fn->ops->duplicate = FNDuplicate_Phi; | |
| 268 | 50 | fn->ops->destroy = FNDestroy_Phi; | |
| 269 |
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50 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiSetIndex_C",FNPhiSetIndex_Phi)); |
| 270 |
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50 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNPhiGetIndex_C",FNPhiGetIndex_Phi)); |
| 271 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 272 | } | ||
| 273 |