| 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 | Rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/fnimpl.h> /*I "slepcfn.h" I*/ | ||
| 15 | |||
| 16 | typedef struct { | ||
| 17 | PetscScalar *pcoeff; /* numerator coefficients */ | ||
| 18 | PetscInt np; /* length of array pcoeff, p(x) has degree np-1 */ | ||
| 19 | PetscScalar *qcoeff; /* denominator coefficients */ | ||
| 20 | PetscInt nq; /* length of array qcoeff, q(x) has degree nq-1 */ | ||
| 21 | } FN_RATIONAL; | ||
| 22 | |||
| 23 | 75443 | static PetscErrorCode FNEvaluateFunction_Rational(FN fn,PetscScalar x,PetscScalar *y) | |
| 24 | { | ||
| 25 | 75443 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 26 | 75443 | PetscInt i; | |
| 27 | 75443 | PetscScalar p,q; | |
| 28 | |||
| 29 |
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75443 | PetscFunctionBegin; |
| 30 |
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75443 | if (!ctx->np) p = 1.0; |
| 31 | else { | ||
| 32 | 75430 | p = ctx->pcoeff[0]; | |
| 33 |
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122770 | for (i=1;i<ctx->np;i++) |
| 34 | 47340 | p = ctx->pcoeff[i]+x*p; | |
| 35 | } | ||
| 36 |
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75443 | if (!ctx->nq) *y = p; |
| 37 | else { | ||
| 38 | 9701 | q = ctx->qcoeff[0]; | |
| 39 |
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20128 | for (i=1;i<ctx->nq;i++) |
| 40 | 10427 | q = ctx->qcoeff[i]+x*q; | |
| 41 |
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9701 | PetscCheck(q!=0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Function not defined in the requested value"); |
| 42 | 9701 | *y = p/q; | |
| 43 | } | ||
| 44 |
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18679 | PetscFunctionReturn(PETSC_SUCCESS); |
| 45 | } | ||
| 46 | |||
| 47 | /* | ||
| 48 | Horner evaluation of P=p(A) | ||
| 49 | d = degree of polynomial; coeff = coefficients of polynomial; W = workspace | ||
| 50 | */ | ||
| 51 | 12471 | static PetscErrorCode EvaluatePoly(Mat A,Mat P,Mat W,PetscInt d,PetscScalar *coeff) | |
| 52 | { | ||
| 53 | 12471 | PetscInt j; | |
| 54 | |||
| 55 |
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12471 | PetscFunctionBegin; |
| 56 |
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12471 | PetscCall(MatZeroEntries(P)); |
| 57 |
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12471 | if (!d) PetscCall(MatShift(P,1.0)); |
| 58 | else { | ||
| 59 |
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12471 | PetscCall(MatShift(P,coeff[0])); |
| 60 |
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21128 | for (j=1;j<d;j++) { |
| 61 |
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8657 | PetscCall(MatMatMult(P,A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&W)); |
| 62 |
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8657 | PetscCall(MatCopy(W,P,SAME_NONZERO_PATTERN)); |
| 63 |
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8657 | PetscCall(MatShift(P,coeff[j])); |
| 64 | } | ||
| 65 | } | ||
| 66 |
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3097 | PetscFunctionReturn(PETSC_SUCCESS); |
| 67 | } | ||
| 68 | |||
| 69 | 10191 | static PetscErrorCode FNEvaluateFunctionMat_Rational(FN fn,Mat A,Mat B) | |
| 70 | { | ||
| 71 | 10191 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 72 | 10191 | Mat P,Q,W,F; | |
| 73 | 10191 | PetscBool iscuda; | |
| 74 | |||
| 75 |
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10191 | PetscFunctionBegin; |
| 76 |
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10191 | if (A==B) PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&P)); |
| 77 | 10167 | else P = B; | |
| 78 |
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10191 | PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&W)); |
| 79 | |||
| 80 |
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10191 | PetscCall(EvaluatePoly(A,P,W,ctx->np,ctx->pcoeff)); |
| 81 |
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10191 | if (ctx->nq) { |
| 82 |
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2048 | PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Q)); |
| 83 |
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2048 | PetscCall(EvaluatePoly(A,Q,W,ctx->nq,ctx->qcoeff)); |
| 84 |
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2048 | PetscCall(PetscObjectTypeCompare((PetscObject)A,MATSEQDENSECUDA,&iscuda)); |
| 85 |
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4072 | PetscCall(MatGetFactor(Q,iscuda?MATSOLVERCUDA:MATSOLVERPETSC,MAT_FACTOR_LU,&F)); |
| 86 |
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2048 | PetscCall(MatLUFactorSymbolic(F,Q,NULL,NULL,NULL)); |
| 87 |
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2048 | PetscCall(MatLUFactorNumeric(F,Q,NULL)); |
| 88 |
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2048 | PetscCall(MatMatSolve(F,P,P)); |
| 89 |
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2048 | PetscCall(MatDestroy(&F)); |
| 90 |
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2048 | PetscCall(MatDestroy(&Q)); |
| 91 | } | ||
| 92 | |||
| 93 |
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10191 | if (A==B) { |
| 94 |
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24 | PetscCall(MatCopy(P,B,SAME_NONZERO_PATTERN)); |
| 95 |
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24 | PetscCall(MatDestroy(&P)); |
| 96 | } | ||
| 97 |
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10191 | PetscCall(MatDestroy(&W)); |
| 98 |
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2539 | PetscFunctionReturn(PETSC_SUCCESS); |
| 99 | } | ||
| 100 | |||
| 101 | 208 | static PetscErrorCode FNEvaluateFunctionMatVec_Rational(FN fn,Mat A,Vec v) | |
| 102 | { | ||
| 103 | 208 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 104 | 208 | Mat P,Q,W,F; | |
| 105 | 208 | Vec b; | |
| 106 | 208 | PetscBool iscuda; | |
| 107 | |||
| 108 |
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208 | PetscFunctionBegin; |
| 109 |
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208 | PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&P)); |
| 110 |
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208 | PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&W)); |
| 111 | |||
| 112 |
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208 | PetscCall(EvaluatePoly(A,P,W,ctx->np,ctx->pcoeff)); |
| 113 |
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208 | if (ctx->nq) { |
| 114 |
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24 | PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Q)); |
| 115 |
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24 | PetscCall(EvaluatePoly(A,Q,W,ctx->nq,ctx->qcoeff)); |
| 116 |
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24 | PetscCall(PetscObjectTypeCompare((PetscObject)A,MATSEQDENSECUDA,&iscuda)); |
| 117 |
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40 | PetscCall(MatGetFactor(Q,iscuda?MATSOLVERCUDA:MATSOLVERPETSC,MAT_FACTOR_LU,&F)); |
| 118 |
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24 | PetscCall(MatLUFactorSymbolic(F,Q,NULL,NULL,NULL)); |
| 119 |
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24 | PetscCall(MatLUFactorNumeric(F,Q,NULL)); |
| 120 |
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24 | PetscCall(MatCreateVecs(P,&b,NULL)); |
| 121 |
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24 | PetscCall(MatGetColumnVector(P,b,0)); |
| 122 |
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24 | PetscCall(MatSolve(F,b,v)); |
| 123 |
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24 | PetscCall(VecDestroy(&b)); |
| 124 |
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24 | PetscCall(MatDestroy(&F)); |
| 125 |
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24 | PetscCall(MatDestroy(&Q)); |
| 126 |
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184 | } else PetscCall(MatGetColumnVector(P,v,0)); |
| 127 | |||
| 128 |
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208 | PetscCall(MatDestroy(&P)); |
| 129 |
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208 | PetscCall(MatDestroy(&W)); |
| 130 |
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48 | PetscFunctionReturn(PETSC_SUCCESS); |
| 131 | } | ||
| 132 | |||
| 133 | 27251 | static PetscErrorCode FNEvaluateDerivative_Rational(FN fn,PetscScalar x,PetscScalar *yp) | |
| 134 | { | ||
| 135 | 27251 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 136 | 27251 | PetscInt i; | |
| 137 | 27251 | PetscScalar p,q,pp,qp; | |
| 138 | |||
| 139 |
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27251 | PetscFunctionBegin; |
| 140 |
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27251 | if (!ctx->np) { |
| 141 | p = 1.0; | ||
| 142 | pp = 0.0; | ||
| 143 | } else { | ||
| 144 | 27238 | p = ctx->pcoeff[0]; | |
| 145 | 27238 | pp = 0.0; | |
| 146 |
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43820 | for (i=1;i<ctx->np;i++) { |
| 147 | 16582 | pp = p+x*pp; | |
| 148 | 16582 | p = ctx->pcoeff[i]+x*p; | |
| 149 | } | ||
| 150 | } | ||
| 151 |
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27251 | if (!ctx->nq) *yp = pp; |
| 152 | else { | ||
| 153 | 3556 | q = ctx->qcoeff[0]; | |
| 154 | 3556 | qp = 0.0; | |
| 155 |
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7158 | for (i=1;i<ctx->nq;i++) { |
| 156 | 3602 | qp = q+x*qp; | |
| 157 | 3602 | q = ctx->qcoeff[i]+x*q; | |
| 158 | } | ||
| 159 |
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3556 | PetscCheck(q!=0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Derivative not defined in the requested value"); |
| 160 | 3556 | *yp = (pp*q-p*qp)/(q*q); | |
| 161 | } | ||
| 162 |
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6648 | PetscFunctionReturn(PETSC_SUCCESS); |
| 163 | } | ||
| 164 | |||
| 165 | 197 | static PetscErrorCode FNView_Rational(FN fn,PetscViewer viewer) | |
| 166 | { | ||
| 167 | 197 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 168 | 197 | PetscBool isascii; | |
| 169 | 197 | PetscInt i; | |
| 170 | 197 | char str[50]; | |
| 171 | |||
| 172 |
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197 | PetscFunctionBegin; |
| 173 |
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197 | PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii)); |
| 174 |
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197 | if (isascii) { |
| 175 |
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197 | if (fn->alpha!=(PetscScalar)1.0 || fn->beta!=(PetscScalar)1.0) { |
| 176 |
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26 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_FALSE)); |
| 177 |
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26 | PetscCall(PetscViewerASCIIPrintf(viewer," scale factors: alpha=%s,",str)); |
| 178 |
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26 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 179 |
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26 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_FALSE)); |
| 180 |
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26 | PetscCall(PetscViewerASCIIPrintf(viewer," beta=%s\n",str)); |
| 181 |
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26 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 182 | } | ||
| 183 |
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197 | if (!ctx->nq) { |
| 184 |
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123 | if (!ctx->np) PetscCall(PetscViewerASCIIPrintf(viewer," constant: 1.0\n")); |
| 185 |
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123 | else if (ctx->np==1) { |
| 186 |
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45 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[0],PETSC_FALSE)); |
| 187 |
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45 | PetscCall(PetscViewerASCIIPrintf(viewer," constant: %s\n",str)); |
| 188 | } else { | ||
| 189 |
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78 | PetscCall(PetscViewerASCIIPrintf(viewer," polynomial: ")); |
| 190 |
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78 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 191 |
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215 | for (i=0;i<ctx->np-1;i++) { |
| 192 |
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137 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[i],PETSC_TRUE)); |
| 193 |
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137 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->np-i-1)); |
| 194 | } | ||
| 195 |
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78 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[ctx->np-1],PETSC_TRUE)); |
| 196 |
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78 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s\n",str)); |
| 197 |
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78 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 198 | } | ||
| 199 |
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74 | } else if (!ctx->np) { |
| 200 |
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13 | PetscCall(PetscViewerASCIIPrintf(viewer," inverse polynomial: 1 / (")); |
| 201 |
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13 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 202 |
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39 | for (i=0;i<ctx->nq-1;i++) { |
| 203 |
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26 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[i],PETSC_TRUE)); |
| 204 |
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26 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->nq-i-1)); |
| 205 | } | ||
| 206 |
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13 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[ctx->nq-1],PETSC_TRUE)); |
| 207 |
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13 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s)\n",str)); |
| 208 |
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13 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 209 | } else { | ||
| 210 |
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61 | PetscCall(PetscViewerASCIIPrintf(viewer," rational function: (")); |
| 211 |
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61 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
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122 | for (i=0;i<ctx->np-1;i++) { |
| 213 |
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61 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[i],PETSC_TRUE)); |
| 214 |
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61 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->np-i-1)); |
| 215 | } | ||
| 216 |
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61 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[ctx->np-1],PETSC_TRUE)); |
| 217 |
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61 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s) / (",str)); |
| 218 |
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183 | for (i=0;i<ctx->nq-1;i++) { |
| 219 |
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122 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[i],PETSC_TRUE)); |
| 220 |
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122 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->nq-i-1)); |
| 221 | } | ||
| 222 |
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61 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[ctx->nq-1],PETSC_TRUE)); |
| 223 |
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61 | PetscCall(PetscViewerASCIIPrintf(viewer,"%s)\n",str)); |
| 224 |
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61 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 225 | } | ||
| 226 | } | ||
| 227 |
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38 | PetscFunctionReturn(PETSC_SUCCESS); |
| 228 | } | ||
| 229 | |||
| 230 | 1822 | static PetscErrorCode FNRationalSetNumerator_Rational(FN fn,PetscInt np,PetscScalar *pcoeff) | |
| 231 | { | ||
| 232 | 1822 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 233 | 1822 | PetscInt i; | |
| 234 | |||
| 235 |
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1822 | PetscFunctionBegin; |
| 236 |
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1822 | PetscCheck(np>=0,PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Argument np cannot be negative"); |
| 237 | 1822 | ctx->np = np; | |
| 238 |
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1822 | PetscCall(PetscFree(ctx->pcoeff)); |
| 239 |
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1822 | if (np) { |
| 240 |
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1809 | PetscCall(PetscMalloc1(np,&ctx->pcoeff)); |
| 241 |
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4743 | for (i=0;i<np;i++) ctx->pcoeff[i] = pcoeff[i]; |
| 242 | } | ||
| 243 |
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439 | PetscFunctionReturn(PETSC_SUCCESS); |
| 244 | } | ||
| 245 | |||
| 246 | /*@ | ||
| 247 | FNRationalSetNumerator - Sets the parameters defining the numerator of the | ||
| 248 | rational function. | ||
| 249 | |||
| 250 | Logically Collective | ||
| 251 | |||
| 252 | Input Parameters: | ||
| 253 | + fn - the math function context | ||
| 254 | . np - number of coefficients | ||
| 255 | - pcoeff - coefficients (array of scalar values) | ||
| 256 | |||
| 257 | Notes: | ||
| 258 | Let the rational function be $f(x) = p(x)/q(x)$, where $p(x)$ and $q(x)$ are | ||
| 259 | polynomials. This function provides the coefficients of the numerator $p(x)$. | ||
| 260 | Hence, $p(x)$ is of degree `np-1`. If `np` is zero, or this function is not | ||
| 261 | called, then the numerator is assumed to be $p(x)=1$. | ||
| 262 | |||
| 263 | In polynomials, high order coefficients are stored in the first positions | ||
| 264 | of the array, e.g., to represent $x^2-3$ use `{1,0,-3}`. | ||
| 265 | |||
| 266 | Level: intermediate | ||
| 267 | |||
| 268 | .seealso: [](sec:fn), `FNRATIONAL`, `FNRationalSetDenominator()`, `FNRationalGetNumerator()` | ||
| 269 | @*/ | ||
| 270 | 1822 | PetscErrorCode FNRationalSetNumerator(FN fn,PetscInt np,PetscScalar pcoeff[]) | |
| 271 | { | ||
| 272 |
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1822 | PetscFunctionBegin; |
| 273 |
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1822 | PetscValidHeaderSpecific(fn,FN_CLASSID,1); |
| 274 |
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1822 | PetscValidLogicalCollectiveInt(fn,np,2); |
| 275 |
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1822 | if (np) PetscAssertPointer(pcoeff,3); |
| 276 |
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1822 | PetscTryMethod(fn,"FNRationalSetNumerator_C",(FN,PetscInt,PetscScalar*),(fn,np,pcoeff)); |
| 277 |
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1822 | PetscFunctionReturn(PETSC_SUCCESS); |
| 278 | } | ||
| 279 | |||
| 280 | 13 | static PetscErrorCode FNRationalGetNumerator_Rational(FN fn,PetscInt *np,PetscScalar *pcoeff[]) | |
| 281 | { | ||
| 282 | 13 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 283 | 13 | PetscInt i; | |
| 284 | |||
| 285 |
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13 | PetscFunctionBegin; |
| 286 |
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13 | if (np) *np = ctx->np; |
| 287 |
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13 | if (pcoeff) { |
| 288 |
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13 | if (!ctx->np) *pcoeff = NULL; |
| 289 | else { | ||
| 290 |
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13 | PetscCall(PetscMalloc1(ctx->np,pcoeff)); |
| 291 |
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39 | for (i=0;i<ctx->np;i++) (*pcoeff)[i] = ctx->pcoeff[i]; |
| 292 | } | ||
| 293 | } | ||
| 294 |
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2 | PetscFunctionReturn(PETSC_SUCCESS); |
| 295 | } | ||
| 296 | |||
| 297 | /*@C | ||
| 298 | FNRationalGetNumerator - Gets the parameters that define the numerator of the | ||
| 299 | rational function. | ||
| 300 | |||
| 301 | Not Collective | ||
| 302 | |||
| 303 | Input Parameter: | ||
| 304 | . fn - the math function context | ||
| 305 | |||
| 306 | Output Parameters: | ||
| 307 | + np - number of coefficients | ||
| 308 | - pcoeff - coefficients (array of scalar values, length `np`) | ||
| 309 | |||
| 310 | Notes: | ||
| 311 | The values passed by user with `FNRationalSetNumerator()` are returned (or | ||
| 312 | `NULL` pointers otherwise). | ||
| 313 | The `pcoeff` array should be freed by the user when no longer needed. | ||
| 314 | |||
| 315 | Level: intermediate | ||
| 316 | |||
| 317 | .seealso: [](sec:fn), `FNRATIONAL`, `FNRationalSetNumerator()` | ||
| 318 | @*/ | ||
| 319 | 13 | PetscErrorCode FNRationalGetNumerator(FN fn,PetscInt *np,PetscScalar *pcoeff[]) PeNS | |
| 320 | { | ||
| 321 |
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13 | PetscFunctionBegin; |
| 322 |
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13 | PetscValidHeaderSpecific(fn,FN_CLASSID,1); |
| 323 |
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13 | PetscUseMethod(fn,"FNRationalGetNumerator_C",(FN,PetscInt*,PetscScalar**),(fn,np,pcoeff)); |
| 324 |
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13 | PetscFunctionReturn(PETSC_SUCCESS); |
| 325 | } | ||
| 326 | |||
| 327 | 284 | static PetscErrorCode FNRationalSetDenominator_Rational(FN fn,PetscInt nq,PetscScalar *qcoeff) | |
| 328 | { | ||
| 329 | 284 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 330 | 284 | PetscInt i; | |
| 331 | |||
| 332 |
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284 | PetscFunctionBegin; |
| 333 |
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284 | PetscCheck(nq>=0,PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Argument nq cannot be negative"); |
| 334 | 284 | ctx->nq = nq; | |
| 335 |
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284 | PetscCall(PetscFree(ctx->qcoeff)); |
| 336 |
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284 | if (nq) { |
| 337 |
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271 | PetscCall(PetscMalloc1(nq,&ctx->qcoeff)); |
| 338 |
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887 | for (i=0;i<nq;i++) ctx->qcoeff[i] = qcoeff[i]; |
| 339 | } | ||
| 340 |
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65 | PetscFunctionReturn(PETSC_SUCCESS); |
| 341 | } | ||
| 342 | |||
| 343 | /*@ | ||
| 344 | FNRationalSetDenominator - Sets the parameters defining the denominator of the | ||
| 345 | rational function. | ||
| 346 | |||
| 347 | Logically Collective | ||
| 348 | |||
| 349 | Input Parameters: | ||
| 350 | + fn - the math function context | ||
| 351 | . nq - number of coefficients | ||
| 352 | - qcoeff - coefficients (array of scalar values) | ||
| 353 | |||
| 354 | Notes: | ||
| 355 | Let the rational function be $f(x) = p(x)/q(x)$, where $p(x)$ and $q(x)$ are | ||
| 356 | polynomials. This function provides the coefficients of the denominator $q(x)$. | ||
| 357 | Hence, $q(x)$ is of degree `nq-1`. If `nq` is zero, or this function is not | ||
| 358 | called, then the function is assumed to be polynomial, $f(x) = p(x)$. | ||
| 359 | |||
| 360 | In polynomials, high order coefficients are stored in the first positions | ||
| 361 | of the array, e.g., to represent $x^2-3$ use `{1,0,-3}`. | ||
| 362 | |||
| 363 | Level: intermediate | ||
| 364 | |||
| 365 | .seealso: [](sec:fn), `FNRATIONAL`, `FNRationalSetNumerator()`, `FNRationalGetDenominator()` | ||
| 366 | @*/ | ||
| 367 | 284 | PetscErrorCode FNRationalSetDenominator(FN fn,PetscInt nq,PetscScalar qcoeff[]) | |
| 368 | { | ||
| 369 |
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284 | PetscFunctionBegin; |
| 370 |
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284 | PetscValidHeaderSpecific(fn,FN_CLASSID,1); |
| 371 |
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284 | PetscValidLogicalCollectiveInt(fn,nq,2); |
| 372 |
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284 | if (nq) PetscAssertPointer(qcoeff,3); |
| 373 |
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284 | PetscTryMethod(fn,"FNRationalSetDenominator_C",(FN,PetscInt,PetscScalar*),(fn,nq,qcoeff)); |
| 374 |
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284 | PetscFunctionReturn(PETSC_SUCCESS); |
| 375 | } | ||
| 376 | |||
| 377 | 93 | static PetscErrorCode FNRationalGetDenominator_Rational(FN fn,PetscInt *nq,PetscScalar *qcoeff[]) | |
| 378 | { | ||
| 379 | 93 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 380 | 93 | PetscInt i; | |
| 381 | |||
| 382 |
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93 | PetscFunctionBegin; |
| 383 |
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93 | if (nq) *nq = ctx->nq; |
| 384 |
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93 | if (qcoeff) { |
| 385 |
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93 | if (!ctx->nq) *qcoeff = NULL; |
| 386 | else { | ||
| 387 |
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37 | PetscCall(PetscMalloc1(ctx->nq,qcoeff)); |
| 388 |
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124 | for (i=0;i<ctx->nq;i++) (*qcoeff)[i] = ctx->qcoeff[i]; |
| 389 | } | ||
| 390 | } | ||
| 391 |
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22 | PetscFunctionReturn(PETSC_SUCCESS); |
| 392 | } | ||
| 393 | |||
| 394 | /*@C | ||
| 395 | FNRationalGetDenominator - Gets the parameters that define the denominator of the | ||
| 396 | rational function. | ||
| 397 | |||
| 398 | Not Collective | ||
| 399 | |||
| 400 | Input Parameter: | ||
| 401 | . fn - the math function context | ||
| 402 | |||
| 403 | Output Parameters: | ||
| 404 | + nq - number of coefficients | ||
| 405 | - qcoeff - coefficients (array of scalar values, length `nq`) | ||
| 406 | |||
| 407 | Notes: | ||
| 408 | The values passed by user with `FNRationalSetDenominator()` are returned (or a | ||
| 409 | `NULL` pointer otherwise). | ||
| 410 | The `qcoeff` array should be freed by the user when no longer needed. | ||
| 411 | |||
| 412 | Level: intermediate | ||
| 413 | |||
| 414 | .seealso: [](sec:fn), `FNRATIONAL`, `FNRationalSetDenominator()` | ||
| 415 | @*/ | ||
| 416 | 93 | PetscErrorCode FNRationalGetDenominator(FN fn,PetscInt *nq,PetscScalar *qcoeff[]) PeNS | |
| 417 | { | ||
| 418 |
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93 | PetscFunctionBegin; |
| 419 |
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93 | PetscValidHeaderSpecific(fn,FN_CLASSID,1); |
| 420 |
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93 | PetscUseMethod(fn,"FNRationalGetDenominator_C",(FN,PetscInt*,PetscScalar**),(fn,nq,qcoeff)); |
| 421 |
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93 | PetscFunctionReturn(PETSC_SUCCESS); |
| 422 | } | ||
| 423 | |||
| 424 | 1705 | static PetscErrorCode FNSetFromOptions_Rational(FN fn,PetscOptionItems PetscOptionsObject) | |
| 425 | { | ||
| 426 | #define PARMAX 10 | ||
| 427 | 1705 | PetscScalar array[PARMAX]; | |
| 428 | 1705 | PetscInt i,k; | |
| 429 | 1705 | PetscBool flg; | |
| 430 | |||
| 431 |
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1705 | PetscFunctionBegin; |
| 432 |
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1705 | PetscOptionsHeadBegin(PetscOptionsObject,"FN Rational Options"); |
| 433 | |||
| 434 | 1705 | k = PARMAX; | |
| 435 |
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18755 | for (i=0;i<k;i++) array[i] = 0; |
| 436 |
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1705 | PetscCall(PetscOptionsScalarArray("-fn_rational_numerator","Numerator coefficients (one or more scalar values separated with a comma without spaces)","FNRationalSetNumerator",array,&k,&flg)); |
| 437 |
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1705 | if (flg) PetscCall(FNRationalSetNumerator(fn,k,array)); |
| 438 | |||
| 439 | 1705 | k = PARMAX; | |
| 440 |
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18755 | for (i=0;i<k;i++) array[i] = 0; |
| 441 |
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1705 | PetscCall(PetscOptionsScalarArray("-fn_rational_denominator","Denominator coefficients (one or more scalar values separated with a comma without spaces)","FNRationalSetDenominator",array,&k,&flg)); |
| 442 |
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1705 | if (flg) PetscCall(FNRationalSetDenominator(fn,k,array)); |
| 443 | |||
| 444 |
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1705 | PetscOptionsHeadEnd(); |
| 445 |
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411 | PetscFunctionReturn(PETSC_SUCCESS); |
| 446 | } | ||
| 447 | |||
| 448 | 232 | static PetscErrorCode FNDuplicate_Rational(FN fn,MPI_Comm comm,FN *newfn) | |
| 449 | { | ||
| 450 | 232 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data,*ctx2 = (FN_RATIONAL*)(*newfn)->data; | |
| 451 | 232 | PetscInt i; | |
| 452 | |||
| 453 |
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232 | PetscFunctionBegin; |
| 454 | 232 | ctx2->np = ctx->np; | |
| 455 |
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232 | if (ctx->np) { |
| 456 |
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232 | PetscCall(PetscMalloc1(ctx->np,&ctx2->pcoeff)); |
| 457 |
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652 | for (i=0;i<ctx->np;i++) ctx2->pcoeff[i] = ctx->pcoeff[i]; |
| 458 | } | ||
| 459 | 232 | ctx2->nq = ctx->nq; | |
| 460 |
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232 | if (ctx->nq) { |
| 461 |
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84 | PetscCall(PetscMalloc1(ctx->nq,&ctx2->qcoeff)); |
| 462 |
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272 | for (i=0;i<ctx->nq;i++) ctx2->qcoeff[i] = ctx->qcoeff[i]; |
| 463 | } | ||
| 464 |
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56 | PetscFunctionReturn(PETSC_SUCCESS); |
| 465 | } | ||
| 466 | |||
| 467 | 2037 | static PetscErrorCode FNDestroy_Rational(FN fn) | |
| 468 | { | ||
| 469 | 2037 | FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data; | |
| 470 | |||
| 471 |
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2037 | PetscFunctionBegin; |
| 472 |
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2037 | PetscCall(PetscFree(ctx->pcoeff)); |
| 473 |
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2037 | PetscCall(PetscFree(ctx->qcoeff)); |
| 474 |
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2037 | PetscCall(PetscFree(fn->data)); |
| 475 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",NULL)); |
| 476 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",NULL)); |
| 477 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",NULL)); |
| 478 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",NULL)); |
| 479 |
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491 | PetscFunctionReturn(PETSC_SUCCESS); |
| 480 | } | ||
| 481 | |||
| 482 | /*MC | ||
| 483 | FNRATIONAL - FNRATIONAL = "rational" - A rational function $f(x)=p(x)/q(x)$, | ||
| 484 | where the coefficients of the $p(x)$ and $q(x)$ polynomials are specified with | ||
| 485 | `FNRationalSetNumerator()` and `FNRationalSetDenominator()`, respectively. | ||
| 486 | |||
| 487 | Level: beginner | ||
| 488 | |||
| 489 | Notes: | ||
| 490 | The function will behave as a polynomial if only the numerator is given. | ||
| 491 | |||
| 492 | When working with matrix functions, the rational function should rather be | ||
| 493 | interpreted as $f(x)=q(x)^{-1}p(x)$. | ||
| 494 | |||
| 495 | .seealso: [](sec:fn), `FN`, `FNType`, `FNSetType()`, `FNRationalSetNumerator()`, `FNRationalSetDenominator()` | ||
| 496 | M*/ | ||
| 497 | |||
| 498 | 2037 | SLEPC_EXTERN PetscErrorCode FNCreate_Rational(FN fn) | |
| 499 | { | ||
| 500 | 2037 | FN_RATIONAL *ctx; | |
| 501 | |||
| 502 |
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2037 | PetscFunctionBegin; |
| 503 |
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2037 | PetscCall(PetscNew(&ctx)); |
| 504 | 2037 | fn->data = (void*)ctx; | |
| 505 | |||
| 506 | 2037 | fn->ops->evaluatefunction = FNEvaluateFunction_Rational; | |
| 507 | 2037 | fn->ops->evaluatederivative = FNEvaluateDerivative_Rational; | |
| 508 | 2037 | fn->ops->evaluatefunctionmat[0] = FNEvaluateFunctionMat_Rational; | |
| 509 | 2037 | fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Rational; | |
| 510 | #if defined(PETSC_HAVE_CUDA) | ||
| 511 | 527 | fn->ops->evaluatefunctionmatcuda[0] = FNEvaluateFunctionMat_Rational; | |
| 512 | 527 | fn->ops->evaluatefunctionmatveccuda[0] = FNEvaluateFunctionMatVec_Rational; | |
| 513 | #endif | ||
| 514 | 2037 | fn->ops->setfromoptions = FNSetFromOptions_Rational; | |
| 515 | 2037 | fn->ops->view = FNView_Rational; | |
| 516 | 2037 | fn->ops->duplicate = FNDuplicate_Rational; | |
| 517 | 2037 | fn->ops->destroy = FNDestroy_Rational; | |
| 518 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",FNRationalSetNumerator_Rational)); |
| 519 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",FNRationalGetNumerator_Rational)); |
| 520 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",FNRationalSetDenominator_Rational)); |
| 521 |
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2037 | PetscCall(PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",FNRationalGetDenominator_Rational)); |
| 522 |
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491 | PetscFunctionReturn(PETSC_SUCCESS); |
| 523 | } | ||
| 524 |