1 // Copyright (c) 1997-1999 Matra Datavision
2 // Copyright (c) 1999-2014 OPEN CASCADE SAS
4 // This file is part of Open CASCADE Technology software library.
6 // This library is free software; you can redistribute it and/or modify it under
7 // the terms of the GNU Lesser General Public License version 2.1 as published
8 // by the Free Software Foundation, with special exception defined in the file
9 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
10 // distribution for complete text of the license and disclaimer of any warranty.
12 // Alternatively, this file may be used under the terms of Open CASCADE
13 // commercial license or contractual agreement.
17 #include <math_Vector.hxx>
19 #include <PLib_JacobiPolynomial.hxx>
20 #include <PLib_JacobiPolynomial_0.hxx>
21 #include <Standard_ConstructionError.hxx>
22 #include <Standard_Type.hxx>
23 #include <TColStd_Array2OfReal.hxx>
25 IMPLEMENT_STANDARD_RTTIEXT(PLib_JacobiPolynomial,PLib_Base)
27 // The possible values for NbGaussPoints
28 const Standard_Integer NDEG8=8, NDEG10=10, NDEG15=15, NDEG20=20, NDEG25=25,
29 NDEG30=30, NDEG40=40, NDEG50=50, NDEG61=61;
31 const Standard_Integer UNDEFINED=-999;
33 //=======================================================================
34 //function : PLib_JacobiPolynomial
36 //=======================================================================
38 PLib_JacobiPolynomial::PLib_JacobiPolynomial (const Standard_Integer WorkDegree,
39 const GeomAbs_Shape ConstraintOrder)
41 myWorkDegree = WorkDegree;
43 switch (ConstraintOrder) {
44 case GeomAbs_C0: myNivConstr = 0; break;
45 case GeomAbs_C1: myNivConstr = 1; break;
46 case GeomAbs_C2: myNivConstr = 2; break;
48 Standard_ConstructionError::Raise("Invalid ConstraintOrder");
50 myDegree = myWorkDegree - 2*(myNivConstr+1);
52 Standard_ConstructionError::Raise("Invalid Degree");
55 //=======================================================================
58 //=======================================================================
60 void PLib_JacobiPolynomial::Points(const Standard_Integer NbGaussPoints,
61 TColStd_Array1OfReal& TabPoints) const
63 if ((NbGaussPoints != NDEG8 && NbGaussPoints != NDEG10 &&
64 NbGaussPoints != NDEG15 && NbGaussPoints != NDEG20 &&
65 NbGaussPoints != NDEG25 && NbGaussPoints != NDEG30 &&
66 NbGaussPoints != NDEG40 && NbGaussPoints != NDEG50 &&
67 NbGaussPoints != NDEG61) ||
68 NbGaussPoints <= myDegree)
69 Standard_ConstructionError::Raise("Invalid NbGaussPoints");
71 math_Vector DecreasingPoints(1,NbGaussPoints);
73 math::GaussPoints(NbGaussPoints,DecreasingPoints);
75 // TabPoints consist of only positive increasing values
76 for (Standard_Integer i=1; i<=NbGaussPoints/2; i++)
77 TabPoints(i) = DecreasingPoints(NbGaussPoints/2-i+1);
78 if (NbGaussPoints % 2 == 1)
81 TabPoints(0) = UNDEFINED;
84 //=======================================================================
87 //=======================================================================
89 void PLib_JacobiPolynomial::Weights(const Standard_Integer NbGaussPoints,
90 TColStd_Array2OfReal& TabWeights) const
94 Standard_Real const *pdb=NULL; // the current pointer to WeightsDB
95 switch (myNivConstr) {
96 case 0: pdb = WeightsDB_C0; break;
97 case 1: pdb = WeightsDB_C1; break;
98 case 2: pdb = WeightsDB_C2; break;
100 Standard_Integer infdg = 2*(myNivConstr+1);
101 if (NbGaussPoints > NDEG8) pdb += (NDEG8 *(NDEG8 -infdg)/2);
102 if (NbGaussPoints > NDEG10) pdb += (NDEG10*(NDEG10-infdg)/2);
103 if (NbGaussPoints > NDEG15) pdb += (((NDEG15-1)/2)*(NDEG15-infdg));
104 if (NbGaussPoints > NDEG20) pdb += (NDEG20*(NDEG20-infdg)/2);
105 if (NbGaussPoints > NDEG25) pdb += (((NDEG25-1)/2)*(NDEG25-infdg));
106 if (NbGaussPoints > NDEG30) pdb += (NDEG30*(NDEG30-infdg)/2);
107 if (NbGaussPoints > NDEG40) pdb += (NDEG40*(NDEG40-infdg)/2);
108 if (NbGaussPoints > NDEG50) pdb += (NDEG50*(NDEG50-infdg)/2);
110 // the copy of TabWeightsDB into TabWeights
111 for (j=0; j<=myDegree; j++) {
112 for (i=1; i<=NbGaussPoints/2; i++) {
113 TabWeights.SetValue(i,j,*pdb++);
117 if (NbGaussPoints % 2 == 1) {
118 // NbGaussPoints is odd - the values addition for 0.
119 Standard_Real const *pdb0=NULL; // the current pointer to WeightsDB0
120 switch (myNivConstr) {
121 case 0: pdb0 = WeightsDB0_C0; break;
122 case 1: pdb0 = WeightsDB0_C1; break;
123 case 2: pdb0 = WeightsDB0_C2; break;
126 if (NbGaussPoints > NDEG15) pdb0 += ((NDEG15-1-infdg)/2 + 1);
127 if (NbGaussPoints > NDEG25) pdb0 += ((NDEG25-1-infdg)/2 + 1);
129 // the copy of TabWeightsDB0 into TabWeights
130 for (j=0; j<=myDegree; j+=2)
131 TabWeights.SetValue(0,j,*pdb0++);
132 for (j=1; j<=myDegree; j+=2)
133 TabWeights.SetValue(0,j,0.);
136 for (j=0; j<=myDegree; j++) {
137 TabWeights.SetValue(0,j,UNDEFINED);
142 //=======================================================================
143 //function : MaxValue
145 //=======================================================================
147 void PLib_JacobiPolynomial::MaxValue(TColStd_Array1OfReal& TabMax) const
149 Standard_Real const *pdb=NULL; // the pointer to MaxValues
150 switch (myNivConstr) {
151 case 0: pdb = MaxValuesDB_C0; break;
152 case 1: pdb = MaxValuesDB_C1; break;
153 case 2: pdb = MaxValuesDB_C2; break;
155 for (Standard_Integer i=TabMax.Lower(); i <= TabMax.Upper(); i++) {
156 TabMax.SetValue(i,*pdb++);
160 //=======================================================================
161 //function : MaxError
163 //=======================================================================
165 Standard_Real PLib_JacobiPolynomial::MaxError(const Standard_Integer Dimension,
166 Standard_Real& JacCoeff,
167 const Standard_Integer NewDegree) const
169 Standard_Integer i,idim,ibeg,icut;
171 math_Vector MaxErrDim(1,Dimension,0.);
173 TColStd_Array1OfReal TabMax(0, myDegree+1);
176 ibeg = 2*(myNivConstr+1);
177 icut = Max (ibeg, NewDegree+1);
178 Standard_Real * JacArray = &JacCoeff;
179 for (idim=1; idim<=Dimension; idim++) {
180 for (i=icut; i<=myWorkDegree; i++) {
181 MaxErrDim(idim) += Abs(JacArray[i*Dimension+idim-1]) * TabMax(i-ibeg);
184 Standard_Real MaxErr = MaxErrDim.Norm();
188 //=======================================================================
189 //function : ReduceDegree
191 //=======================================================================
193 void PLib_JacobiPolynomial::ReduceDegree(const Standard_Integer Dimension,
194 const Standard_Integer MaxDegree,
195 const Standard_Real Tol,
196 Standard_Real& JacCoeff,
197 Standard_Integer& NewDegree,
198 Standard_Real& MaxError) const
200 Standard_Integer i,idim,icut, ia = 2*(myNivConstr+1)-1;
201 Standard_Real Bid,Eps1,Error;
203 math_Vector MaxErrDim(1,Dimension,0.);
210 TColStd_Array1OfReal TabMax(0, myDegree+1);
212 Standard_Real * JacArray = &JacCoeff;
213 for (i=myWorkDegree; i>=icut; i--) {
214 for (idim=1; idim<=Dimension; idim++) {
215 MaxErrDim(idim) += Abs(JacArray[i*Dimension+idim-1]) * TabMax(i-icut);
217 Error = MaxErrDim.Norm();
218 if (Error > Tol && i <= MaxDegree) {
228 for (i=ia; i>=1; i--) {
230 for (idim=1; idim<=Dimension; idim++) {
231 Bid += Abs(JacArray[i*Dimension+idim-1]);
241 //=======================================================================
242 //function : AverageError
244 //=======================================================================
246 Standard_Real PLib_JacobiPolynomial::AverageError(const Standard_Integer Dimension,
247 Standard_Real& JacCoeff,
248 const Standard_Integer NewDegree)
251 Standard_Integer i,idim, icut = Max (2*(myNivConstr+1)+1, NewDegree+1);
252 Standard_Real BidJ, AverageErr = 0.;
253 Standard_Real * JacArray = &JacCoeff;
254 for (idim=1; idim<=Dimension; idim++) {
255 for (i=icut; i<=myDegree; i++) {
256 BidJ = JacArray[i*Dimension+idim-1];
257 AverageErr += BidJ*BidJ;
260 AverageErr = sqrt(AverageErr/2);
264 //=======================================================================
265 //function :ToCoefficients
267 //=======================================================================
269 void PLib_JacobiPolynomial::ToCoefficients(const Standard_Integer Dimension,
270 const Standard_Integer Degree,
271 const TColStd_Array1OfReal& JacCoeff,
272 TColStd_Array1OfReal& Coefficients) const
274 const Standard_Integer MAXM=31;
275 Standard_Integer i,iptt,j,idim, ii, jj;
276 Standard_Real const *pTr=NULL; // the pointer to TransMatrix
278 Standard_Integer ibegJC=JacCoeff.Lower(), ibegC=Coefficients.Lower();
280 switch (myNivConstr) {
281 case 0: pTr = &TransMatrix_C0[0][0]; break;
282 case 1: pTr = &TransMatrix_C1[0][0]; break;
283 case 2: pTr = &TransMatrix_C2[0][0]; break;
285 // the conversation for even elements of JacCoeff
286 for (i=0; i<=Degree/2; i++) {
287 iptt = i*MAXM-(i+1)*i/2;
288 for (idim=1; idim<=Dimension; idim++) {
290 for (j=i; j<=Degree/2; j++) {
291 Bid += (*(pTr+iptt+j)) * JacCoeff(2*j*Dimension+idim-1);
293 Coefficients.SetValue(2*i*Dimension+idim-1, Bid);
297 if (Degree == 0) return;
299 // the conversation for odd elements of JacCoeff
300 pTr += MAXM*(MAXM+1)/2;
301 for (i=0; i<=(Degree-1)/2; i++) {
302 iptt = i*MAXM-(i+1)*i/2;
303 ii = ibegC+(2*i+1)*Dimension;
304 for (idim=1; idim<=Dimension; idim++, ii++) {
306 jj = ibegJC+(2*i+1)*Dimension+idim-1;
307 for (j=i; j<=(Degree-1)/2; j++, jj+=2*Dimension) {
308 Bid += (*(pTr+iptt+j)) * JacCoeff(jj);
310 Coefficients(ii) = Bid;
315 //=======================================================================
317 //purpose : common part of D0,D1,D2,D3 (FORTRAN subroutine MPOJAC)
318 //=======================================================================
320 void PLib_JacobiPolynomial::D0123(const Standard_Integer NDeriv,
321 const Standard_Real U,
322 TColStd_Array1OfReal& BasisValue,
323 TColStd_Array1OfReal& BasisD1,
324 TColStd_Array1OfReal& BasisD2,
325 TColStd_Array1OfReal& BasisD3)
327 Standard_Integer i,j, HermitNivConstr = 2*(myNivConstr+1);
328 Standard_Real Aux1,Aux2;
330 if (myTNorm.IsNull()) {
332 // Inizialization of myTNorm,myCofA,myCofB,myDenom
334 myTNorm = new TColStd_HArray1OfReal(0,myDegree);
335 for (i=0; i<=myDegree; i++) {
337 for (j=1; j<=HermitNivConstr; j++) {
338 Aux2 *= ((Standard_Real)(i+HermitNivConstr+j)/(Standard_Real)(i+j));
340 myTNorm->SetValue(i, Sqrt (Aux2 * (2*i+2*HermitNivConstr+1) /
341 (Pow (2,2*HermitNivConstr+1))));
345 myCofA = new TColStd_HArray1OfReal(0,myDegree);
346 myCofB = new TColStd_HArray1OfReal(0,myDegree);
347 myDenom = new TColStd_HArray1OfReal(0,myDegree);
348 for (i=2; i<=myDegree; i++) {
349 Aux1 = HermitNivConstr+i-1;
351 myCofA ->SetValue(i, Aux2*(Aux2+1)*(Aux2+2));
352 myCofB ->SetValue(i, -2. *(Aux2+2) * Aux1* Aux1);
353 myDenom->SetValue(i, 1./(2. * i * ( i-1 + 2*HermitNivConstr+1) * Aux2));
358 // --- Positionements triviaux -----
359 Standard_Integer ibeg0 = BasisValue.Lower();
360 Standard_Integer ibeg1 = BasisD1.Lower();
361 Standard_Integer ibeg2 = BasisD2.Lower();
362 Standard_Integer ibeg3 = BasisD3.Lower();
363 Standard_Integer i0, i1, i2, i3;
367 BasisValue(ibeg0+0) = 1.;
369 BasisD1(ibeg1+0) = 0.;
371 BasisD2(ibeg2+0) = 0.;
373 BasisD3(ibeg3+0) = 0.;
378 BasisValue(ibeg0+0) = 1.;
379 Aux1 = HermitNivConstr+1;
380 BasisValue(ibeg0+1) = Aux1 * U;
382 BasisD1(ibeg1+0) = 0.;
383 BasisD1(ibeg1+1) = Aux1;
385 BasisD2(ibeg2+0) = 0.;
386 BasisD2(ibeg2+1) = 0.;
388 BasisD3(ibeg3+0) = 0.;
389 BasisD3(ibeg3+1) = 0.;
396 // --- Positionement par reccurence
399 Standard_Real * BV = &BasisValue(ibeg0);
400 Standard_Real * CofA = &myCofA->ChangeValue(0);
401 Standard_Real * CofB = &myCofB->ChangeValue(0);
402 Standard_Real * Denom = &myDenom->ChangeValue(0);
403 for (i=2; i<=myDegree; i++) {
404 BV[i] = (CofA[i]*U*BV[i-1] + CofB[i]*BV[i-2])*Denom[i];
409 Standard_Real CofA, CofB, Denom;
410 for (i=2; i<=myDegree; i++) {
413 CofA = myCofA->Value(i);
414 CofB = myCofB->Value(i);
415 Denom = myDenom->Value(i);
417 BasisValue(i0) = (CofA * U * BasisValue(i0-1) +
418 CofB * BasisValue(i0-2)) * Denom;
419 BasisD1(i1) = (CofA * (U * BasisD1(i1-1) + BasisValue(i0-1)) +
420 CofB * BasisD1(i1-2)) * Denom;
423 BasisD2(i2) = ( CofA * (U*BasisD2(i2-1) + 2*BasisD1(i1-1)) +
424 CofB*BasisD2(i2-2)) * Denom;
427 BasisD3(i3) = (CofA * (U*BasisD3(i3-1) + 3*BasisD2(i2-1)) +
428 CofB*BasisD3(i3-2)) * Denom;
437 Standard_Real * BV = &BasisValue(ibeg0);
438 Standard_Real * TNorm = &myTNorm->ChangeValue(0);
439 for (i=0; i<=myDegree; i++)
444 for (i=0; i<=myDegree; i++) {
445 TNorm = myTNorm->Value(i);
446 BasisValue(i+ibeg0) *= TNorm;
447 BasisD1(i+ibeg1) *= TNorm;
449 BasisD2(i+ibeg2) *= TNorm;
450 if (NDeriv >= 3) BasisD3(i+ibeg3) *= TNorm;
456 //=======================================================================
459 //=======================================================================
461 void PLib_JacobiPolynomial::D0(const Standard_Real U,
462 TColStd_Array1OfReal& BasisValue)
464 D0123(0,U,BasisValue,BasisValue,BasisValue,BasisValue);
467 //=======================================================================
470 //=======================================================================
472 void PLib_JacobiPolynomial::D1(const Standard_Real U,
473 TColStd_Array1OfReal& BasisValue,
474 TColStd_Array1OfReal& BasisD1)
476 D0123(1,U,BasisValue,BasisD1,BasisD1,BasisD1);
479 //=======================================================================
482 //=======================================================================
484 void PLib_JacobiPolynomial::D2(const Standard_Real U,
485 TColStd_Array1OfReal& BasisValue,
486 TColStd_Array1OfReal& BasisD1,
487 TColStd_Array1OfReal& BasisD2)
489 D0123(2,U,BasisValue,BasisD1,BasisD2,BasisD2);
492 //=======================================================================
495 //=======================================================================
497 void PLib_JacobiPolynomial::D3(const Standard_Real U,
498 TColStd_Array1OfReal& BasisValue,
499 TColStd_Array1OfReal& BasisD1,
500 TColStd_Array1OfReal& BasisD2,
501 TColStd_Array1OfReal& BasisD3)
503 D0123(3,U,BasisValue,BasisD1,BasisD2,BasisD3);