diff --git a/Src/Kernels/Taylor/FTaylorKernel_OptPreInd.hpp b/Src/Kernels/Taylor/FTaylorKernel_OptPreInd.hpp new file mode 100644 index 0000000000000000000000000000000000000000..cd5bbdf4c3f49d4aa2a3d07288265cdd4a8c4071 --- /dev/null +++ b/Src/Kernels/Taylor/FTaylorKernel_OptPreInd.hpp @@ -0,0 +1,930 @@ +// =================================================================================== +// Copyright ScalFmm 2011 INRIA, Olivier Coulaud, Bérenger Bramas, Matthias Messner +// olivier.coulaud@inria.fr, berenger.bramas@inria.fr +// This software is a computer program whose purpose is to compute the FMM. +// +// This software is governed by the CeCILL-C and LGPL licenses and +// abiding by the rules of distribution of free software. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public and CeCILL-C Licenses for more details. +// "http://www.cecill.info". +// "http://www.gnu.org/licenses". +// =================================================================================== +#ifndef FTAYLORKERNEL_HPP +#define FTAYLORKERNEL_HPP + +#include "../../Components/FAbstractKernels.hpp" +#include "../../Utils/FMemUtils.hpp" +#include "../../Utils/FDebug.hpp" +#include "../../Utils/FSmartPointer.hpp" +#include "../P2P/FP2P.hpp" + +/** + * @author Cyrille Piacibello + * @class FTaylorKernel + * + * @brief This kernel is an implementation of the different operators + * needed to compute the Fast Multipole Method using Taylor Expansion + * for the Far fields interaction. + */ + + +//TODO spécifier les arguments. +template< class CellClass, class ContainerClass, int P, int order> +class FTaylorKernel : public FAbstractKernels { + +private: + //Size of the multipole and local vectors + static const int SizeVector = ((P+1)*(P+2)*(P+3))*order/6; + + + //////////////////////////////////////////////////// + // Object Attributes + //////////////////////////////////////////////////// + const FReal boxWidth; //< the box width at leaf level + const int treeHeight; //< The height of the tree + const FReal widthAtLeafLevel; //< width of box at leaf level + const FReal widthAtLeafLevelDiv2; //< width of box at leaf leve div 2 + const FPoint boxCorner; //< position of the box corner + + //////////////////////////////////////////////////// + // PreComputed values + //////////////////////////////////////////////////// + FReal factorials[2*P+1]; //< This contains the factorial until P + FReal arrayDX[P+2],arrayDY[P+2],arrayDZ[P+2] ; //< Working arrays + static const int sizeDerivative = (2*P+1)*(P+1)*(2*P+3)/3; + FReal _PsiVector[sizeDerivative]; + FSmartPointer< FReal[343][sizeDerivative] > M2LpreComputedDerivatives; + FSmartPointer< int[SizeVector] > preComputedIndirections; + + FReal _coeffPoly[SizeVector];// _coeffNk[SizeVector] ; + + + //////////////////////////////////////////////////// + // Private method + //////////////////////////////////////////////////// + + /////////////////////////////////////////////////////// + // Precomputation + /////////////////////////////////////////////////////// + + /** Compute the factorial from 0 to P + * Then the data is accessible in factorials array: + * factorials[n] = n! with n <= P + */ + void precomputeFactorials(){ + factorials[0] = 1.0; + FReal fidx = 1.0; + for(int idx = 1 ; idx <= 2*P ; ++idx, ++fidx){ + factorials[idx] = fidx * factorials[idx-1]; + } + } + + + /** Return the position of a leaf from its tree coordinate */ + FPoint getLeafCenter(const FTreeCoordinate coordinate) const { + return FPoint( + FReal(coordinate.getX()) * widthAtLeafLevel + widthAtLeafLevelDiv2 + boxCorner.getX(), + FReal(coordinate.getY()) * widthAtLeafLevel + widthAtLeafLevelDiv2 + boxCorner.getY(), + FReal(coordinate.getZ()) * widthAtLeafLevel + widthAtLeafLevelDiv2 + boxCorner.getZ()); + } + + /** + * @brief Return the position of the center of a cell from its tree + * coordinate + * @param FTreeCoordinate + * @param inLevel the current level of Cell + */ + FPoint getCellCenter(const FTreeCoordinate coordinate, int inLevel) + { + + //Set the boxes width needed + FReal widthAtCurrentLevel = widthAtLeafLevel*FReal(1 << (treeHeight-(inLevel+1))); + FReal widthAtCurrentLevelDiv2 = widthAtCurrentLevel/FReal(2); + + //Get the coordinate + int a = coordinate.getX(); + int b = coordinate.getY(); + int c = coordinate.getZ(); + + //Set the center real coordinates from box corner and widths. + FReal X = boxCorner.getX() + FReal(a)*widthAtCurrentLevel + widthAtCurrentLevelDiv2; + FReal Y = boxCorner.getY() + FReal(b)*widthAtCurrentLevel + widthAtCurrentLevelDiv2; + FReal Z = boxCorner.getZ() + FReal(c)*widthAtCurrentLevel + widthAtCurrentLevelDiv2; + + FPoint cCenter = FPoint(X,Y,Z); + + return cCenter; + } + + + /** + * @brief Incrementation of powers in Taylor expansion + * Result : ...,[2,0,0],[1,1,0],[1,0,1],[0,2,0]... 3-tuple are sorted + * by size then alphabetical order. + */ + void incPowers(int * const FRestrict a, int *const FRestrict b, int *const FRestrict c) + { + int t = (*a)+(*b)+(*c); + if(t==0) + {a[0]=1;} + else{ if(t==a[0]) + {a[0]--; b[0]++;} + else{ if(t==c[0]) + {a[0]=t+1; c[0]=0;} + else{ if(b[0]!=0) + {b[0]--; c[0]++;} + else{ + b[0]=c[0]+1; + a[0]--; + c[0]=0; + } + } + } + } + } + + /** + * @brief Give the index of array from the corresponding 3-tuple + * powers. + */ + int powerToIdx(const int a,const int b,const int c) + { + int t,res,p = a+b+c; + res = p*(p+1)*(p+2)/6; + t = p - a; + res += t*(t+1)/2+c; + return res; + } + + /* Return the factorial of a number + */ + FReal fact(const int a){ + if(a<0) { + printf("fact :: Error factorial negative!! a=%d\n",a); + return FReal(0); + } + FReal result = 1; + for(int i = 1 ; i <= a ; ++i){ + result *= FReal(i); + } + return result; + } + + /* Return the product of factorial of 3 numbers + */ + FReal fact3int(const int a,const int b,const int c) + { + return ( factorials[a]*factorials[b]* factorials[c]) ; + } + + /* Return the combine of a paire of number + * \f[ C^{b}_{a} \f] + */ + FReal combin(const int& a, const int& b){ + if(apreComputedIndirections = new int[SizeVector][SizeVector]; + + int al=0,bl=0,cl=0; + int alpha; + //Loop over first index + for(int k=0; k= 0 ; --am) + { + alpha = ord-am; + if ( alpha ==1 ) { + for( int i=0 ; i <=1 ; (++i, ++j) ) + { + preComputedIndirections[k][j] = powerToIdx(al+am,bl+1-i,cl+i); + } + } + else { + for( int bm=ord-am ; bm >= 0 ; --bm, ++j) + { + preComputedIndirections[k][j] = powerToIdx(al+am,bl+bm,cl+(ord-am-bm)); + } + } + } + } + incPowers(&al,&bl,&cl); + } + } + + /* Precomputation of all the derivatives that will be needed for the + * computation of M2L translations : + * + * Derivatives depends only on the distance between cells, so for + * each level, and each possible relative positions (343), we + * compute all the values needed. + */ + void preComputeDerivative() + { + //Allocation of the memory needed + M2LpreComputedDerivatives = new FReal[treeHeight][343][sizeDerivative]; + // This is the width of a box at each level + FReal boxWidthAtLevel = widthAtLeafLevel; + // from leaf level to the root + for(int idxLevel = treeHeight-1 ; idxLevel > 0 ; --idxLevel){ + // we compute all possibilities + for(int idxX = -3 ; idxX <= 3 ; ++idxX ){ + for(int idxY = -3 ; idxY <= 3 ; ++idxY ){ + for(int idxZ = -3 ; idxZ <= 3 ; ++idxZ ){ + // if this is not a neighbour + if( idxX < -1 || 1 < idxX || idxY < -1 || 1 < idxY || idxZ < -1 || 1 < idxZ ){ + //Compute the relative position + const FPoint relativePosition( -FReal(idxX)*boxWidthAtLevel, + -FReal(idxY)*boxWidthAtLevel, + -FReal(idxZ)*boxWidthAtLevel); + // this is the position in the index system from 0 to 343 + const int position = ((( (idxX+3) * 7) + (idxY+3))) * 7 + idxZ + 3; + initDerivative(relativePosition.getX(),relativePosition.getY(),relativePosition.getZ(),M2LpreComputedDerivatives[idxLevel][position]); + computeFullDerivative(relativePosition.getX(),relativePosition.getY(),relativePosition.getZ(),M2LpreComputedDerivatives[idxLevel][position]); + } + } + } + } + boxWidthAtLevel *= FReal(2); + } + } + + /** @brief Init the derivative array for using of following formula + * from "A cartesian tree-code for screened coulomb interactions" + * + * @todo METTRE les fonctions pour intialiser la recurrence. \f$x_i\f$ ?? \f$x_i\f$ ?? + * @todo LA formule ci-dessous n'utilise pas k! + */ + + void initDerivative(const FReal & dx ,const FReal & dy ,const FReal & dz , FReal * tab) + { + FReal R2 = dx*dx+dy*dy+dz*dz; + tab[0]=FReal(1)/FMath::Sqrt(R2); + FReal R3 = tab[0]/(R2); + tab[1]= -dx*R3; //Derivative in (1,0,0) il doit y avoir un - + tab[2]= -dy*R3; //Derivative in (0,1,0) + tab[3]= -dz*R3; //Derivative in (0,0,1) + FReal R5 = R3/R2; + tab[4] = FReal(3)*dx*dx*R5-R3; //Derivative in (2,0,0) + tab[5] = FReal(3)*dx*dy*R5; //Derivative in (1,1,0) + tab[6] = FReal(3)*dx*dz*R5; //Derivative in (1,0,1) + tab[7] = FReal(3)*dy*dy*R5-R3; //Derivative in (0,2,0) + tab[8] = FReal(3)*dy*dz*R5; //Derivative in (0,1,1) + tab[9] = FReal(3)*dz*dz*R5-R3; //Derivative in (0,0,2) + } + + /** @brief Compute and store the derivative for a given tuple. + * Derivative are used for the M2L + * + *\f[ + * \Psi_{\mathbf{k}}^{c} \left [\left |\mathbf{k}\right |\times \left | + * \mathbf{x}_i-\mathbf{x}_c\right |^2 \right ]\ + * = (2\times \left |{\mathbf{k}}\right |-1) + * \sum_{j=0}^{3}\left [ k_j (x_{i_j}-x_{c_j}) + * \Psi_{\mathbf{k}-e_j,i}^{c}\right ]\ + * -(\left |\mathbf{k}\right |-1) \sum_{j=0}^{3}\left + * [ k_j(k_j-1) \Psi_{\mathbf{k}-2 e_j,i}^{c} \right] + * \f] + * where \f$ \mathbf{k} = (k_1,k_2,k_3) \f$ + */ + void computeFullDerivative( FReal dx, FReal dy, FReal dz, // Distance from distant center to local center + FReal * yetComputed) + { + + initDerivative(dx,dy,dz,yetComputed); + FReal dist2 = dx*dx+dy*dy+dz*dz; + int idxTarget; //Index of current yetComputed entry + int idxSrc1, idxSrc2, idxSrc3, //Indexes of needed yetComputed entries + idxSrc4, idxSrc5, idxSrc6; + int a=0,b=0,c=0; //Powers of expansions + + for(c=3 ; c<=2*P ; ++c){ + //Computation of derivatives Psi_{0,0,c} + // |x-y|^2 * Psi_{0,0,c} + (2*c-1) * dz *Psi_{0,0,c-1} + (c-1)^2 * Psi_{0,0,c-2} = 0 + idxTarget = powerToIdx(0,0,c); + idxSrc1 = powerToIdx(0,0,c-1); + idxSrc2 = powerToIdx(0,0,c-2); + yetComputed[idxTarget] = -(FReal(2*c-1)*dz*yetComputed[idxSrc1] + FReal((c-1)*(c-1))*yetComputed[idxSrc2])/dist2; + } + b=1; + for(c=2 ; c<=2*P-1 ; ++c){ + //Computation of derivatives Psi_{0,1,c} + // |x-y|^2 * Psi_{0,1,c} + (2*c) * dz *Psi_{0,1,c-1} + c*(c-1) * Psi_{0,1,c-2} + dy*Psi_{0,0,c} = 0 + idxTarget = powerToIdx(0,1,c); + idxSrc1 = powerToIdx(0,1,c-1); + idxSrc2 = powerToIdx(0,1,c-2); + idxSrc3 = powerToIdx(0,0,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2]+ dy*yetComputed[idxSrc3])/dist2; + } + b=2; + for(c=1 ; c<= 2*P-b ; ++c){ + //Computation of derivatives Psi_{0,2,c} + //|x-y|^2 * Psi_{0,2,c} + (2*c) * dz *Psi_{0,2,c-1} + (c*(c-1)) * Psi_{0,2,c-2} + 3*dy * Psi_{0,1,c} + Psi_{0,0,c} = 0 + idxTarget = powerToIdx(0,2,c); + idxSrc1 = powerToIdx(0,2,c-1); + idxSrc2 = powerToIdx(0,2,c-2); + idxSrc3 = powerToIdx(0,1,c); + idxSrc4 = powerToIdx(0,0,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2] + + FReal(3)*dy*yetComputed[idxSrc3] + yetComputed[idxSrc4])/dist2; + } + for(b=3 ; b<= 2*P ; ++b){ + //Computation of derivatives Psi_{0,b,0} + // |x-y|^2 * Psi_{0,b,0} + (2*b-1) * dy *Psi_{0,b-1,0} + (b-1)^2 * Psi_{0,b-2,c} = 0 + idxTarget = powerToIdx(0,b,0); + idxSrc1 = powerToIdx(0,b-1,0); + idxSrc2 = powerToIdx(0,b-2,0); + yetComputed[idxTarget] = -(FReal(2*b-1)*dy*yetComputed[idxSrc1] + FReal((b-1)*(b-1))*yetComputed[idxSrc2])/dist2; + for(c=1 ; c<= 2*P-b ; ++c) { + //Computation of derivatives Psi_{0,b,c} + //|x-y|^2*Psi_{0,b,c} + (2*c)*dz*Psi_{0,b,c-1} + (c*(c-1))*Psi_{0,b,c-2} + (2*b-1)*dy*Psi_{0,b-1,c} + (b-1)^2 * Psi_{0,b-2,c} = 0 + idxTarget = powerToIdx(0,b,c); + idxSrc1 = powerToIdx(0,b,c-1); + idxSrc2 = powerToIdx(0,b,c-2); + idxSrc3 = powerToIdx(0,b-1,c); + idxSrc4 = powerToIdx(0,b-2,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2] + + FReal(2*b-1)*dy*yetComputed[idxSrc3] + FReal((b-1)*(b-1))*yetComputed[idxSrc4])/dist2; + } + } + a=1; + b=0; + for(c=2 ; c<= 2*P-1 ; ++c){ + //Computation of derivatives Psi_{1,0,c} + //|x-y|^2 * Psi_{1,0,c} + (2*c)*dz*Psi_{1,0,c-1} + c*(c-1)*Psi_{1,0,c-2} + dx*Psi_{0,0,c} + idxTarget = powerToIdx(1,0,c); + idxSrc1 = powerToIdx(1,0,c-1); + idxSrc2 = powerToIdx(1,0,c-2); + idxSrc3 = powerToIdx(0,0,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2] + dx*yetComputed[idxSrc3])/dist2; + } + b=1; + //Computation of derivatives Psi_{1,1,1} + //|x-y|^2 * Psi_{1,1,1} + 2*dz*Psi_{1,1,0} + 2*dy*Psi_{1,0,1} + dx*Psi_{0,1,1} + idxTarget = powerToIdx(1,1,1); + idxSrc1 = powerToIdx(1,1,0); + idxSrc2 = powerToIdx(1,0,1); + idxSrc3 = powerToIdx(0,1,1); + yetComputed[idxTarget] = -(FReal(2)*dz*yetComputed[idxSrc1] + FReal(2)*dy*yetComputed[idxSrc2] + dx*yetComputed[idxSrc3])/dist2; + for(c=2 ; c<= 2*P-2 ; ++c){ + //Computation of derivatives Psi_{1,1,c} + //|x-y|^2 * Psi_{1,1,c} + (2*c)*dz*Psi_{1,1,c-1} + c*(c-1)*Psi_{1,1,c-2} + 2*dy*Psi_{1,0,c} + dx*Psi_{0,1,c} + idxTarget = powerToIdx(1,1,c); + idxSrc1 = powerToIdx(1,1,c-1); + idxSrc2 = powerToIdx(1,1,c-2); + idxSrc3 = powerToIdx(1,0,c); + idxSrc4 = powerToIdx(0,1,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2] + + FReal(2)*dy*yetComputed[idxSrc3]+ dx*yetComputed[idxSrc4])/dist2; + } + for(b=2 ; b<= 2*P-a ; ++b){ + for(c=0 ; c<= 2*P-b-1 ; ++c){ + //Computation of derivatives Psi_{1,b,c} + //|x-y|^2 * Psi_{1,b,c} + (2*b)*dy*Psi_{1,b-1,c} + b*(b-1)*Psi_{1,b-2,c} + (2*c)*dz*Psi_{1,b,c-1} + c*(c-1)*Psi_{1,b,c-2} + dx*Psi_{0,b,c} + idxTarget = powerToIdx(1,b,c); + idxSrc1 = powerToIdx(1,b-1,c); + idxSrc2 = powerToIdx(1,b-2,c); + idxSrc3 = powerToIdx(1,b,c-1); + idxSrc4 = powerToIdx(1,b,c-2); + idxSrc5 = powerToIdx(0,b,c); + yetComputed[idxTarget] = -(FReal(2*b)*dy*yetComputed[idxSrc1] + FReal(b*(b-1))*yetComputed[idxSrc2] + + FReal(2*c)*dz*yetComputed[idxSrc3]+ FReal(c*(c-1))*yetComputed[idxSrc4] + + dx*yetComputed[idxSrc5])/dist2; + } + } + for(a=2 ; a<=2*P ; ++a){ + //Computation of derivatives Psi_{a,0,0} + // |x-y|^2 * Psi_{a,0,0} + (2*a-1) * dx *Psi_{a-1,0,0} + (a-1)^2 * Psi_{a-2,0,0} = 0 + idxTarget = powerToIdx(a,0,0); + idxSrc1 = powerToIdx(a-1,0,0); + idxSrc2 = powerToIdx(a-2,0,0); + yetComputed[idxTarget] = -(FReal(2*a-1)*dx*yetComputed[idxSrc1] + FReal((a-1)*(a-1))*yetComputed[idxSrc2])/dist2; + if(a <= 2*P-1){ + //Computation of derivatives Psi_{a,0,1} + // |x-y|^2 * Psi_{a,0,1} + 2*dz*Psi_{a,0,0} + (2*a-1)*dx*Psi_{a-1,0,1} + (a-1)^2*Psi_{a-2,0,1} = 0 + idxSrc1 = idxTarget; + idxTarget = powerToIdx(a,0,1); + idxSrc2 = powerToIdx(a-1,0,1); + idxSrc3 = powerToIdx(a-2,0,1); + yetComputed[idxTarget] = -(FReal(2)*dz*yetComputed[idxSrc1] + FReal(2*a-1)*dx*yetComputed[idxSrc2] + FReal((a-1)*(a-1))*yetComputed[idxSrc3])/dist2; + //Computation of derivatives Psi_{a,1,0} + // |x-y|^2 * Psi_{a,1,0} + 2*dy*Psi_{a,0,0} + (2*a-1)*dx*Psi_{a-1,1,0} + (a-1)^2*Psi_{a-2,1,0} = 0 + idxTarget = powerToIdx(a,1,0); + idxSrc2 = powerToIdx(a-1,1,0); + idxSrc3 = powerToIdx(a-2,1,0); + yetComputed[idxTarget] = -(FReal(2)*dy*yetComputed[idxSrc1] + FReal(2*a-1)*dx*yetComputed[idxSrc2] + FReal((a-1)*(a-1))*yetComputed[idxSrc3])/dist2; + if(a <= 2*P-2){ + b=0; + for(c=2 ; c <= 2*P-a ; ++c){ + //Computation of derivatives Psi_{a,0,c} + // |x-y|^2 * Psi_{a,0,c} + 2*c*dz*Psi_{a,0,c-1} + c*(c-1)*Psi_{a,0,c-2} + (2*a-1)*dx*Psi_{a-1,0,c} + (a-1)^2*Psi_{a-2,0,c} = 0 + idxTarget = powerToIdx(a,0,c); + idxSrc1 = powerToIdx(a,0,c-1); + idxSrc2 = powerToIdx(a,0,c-2); + idxSrc3 = powerToIdx(a-1,0,c); + idxSrc4 = powerToIdx(a-2,0,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2] + + FReal(2*a-1)*dx*yetComputed[idxSrc3] + FReal((a-1)*(a-1))*yetComputed[idxSrc4])/dist2; + } + b=1; + for(c=1 ; c <= 2*P-a-1 ; ++c){ + //Computation of derivatives Psi_{a,1,c} + // |x-y|^2 * Psi_{a,1,c} + 2*c*dz*Psi_{a,1,c-1} + c*(c-1)*Psi_{a,1,c-2} + 2*a*dx*Psi_{a-1,1,c} + a*(a-1)*Psi_{a-2,1,c} + dy*Psi_{a,0,c}= 0 + idxTarget = powerToIdx(a,1,c); + idxSrc1 = powerToIdx(a,1,c-1); + idxSrc2 = powerToIdx(a,1,c-2); + idxSrc3 = powerToIdx(a-1,1,c); + idxSrc4 = powerToIdx(a-2,1,c); + idxSrc5 = powerToIdx(a,0,c); + yetComputed[idxTarget] = -(FReal(2*c)*dz*yetComputed[idxSrc1] + FReal(c*(c-1))*yetComputed[idxSrc2] + + FReal(2*a)*dx*yetComputed[idxSrc3] + FReal(a*(a-1))*yetComputed[idxSrc4] + + dy*yetComputed[idxSrc5])/dist2; + } + for(b=2 ; b <= 2*P-a ; ++b){ + //Computation of derivatives Psi_{a,b,0} + // |x-y|^2 * Psi_{a,b,0} + 2*b*dy*Psi_{a,b-1,0} + b*(b-1)*Psi_{a,b-2,0} + (2*a-1)*dx*Psi_{a-1,b,0} + (a-1)^2*Psi_{a-2,b,0} = 0 + idxTarget = powerToIdx(a,b,0); + idxSrc1 = powerToIdx(a,b-1,0); + idxSrc2 = powerToIdx(a,b-2,0); + idxSrc3 = powerToIdx(a-1,b,0); + idxSrc4 = powerToIdx(a-2,b,0); + yetComputed[idxTarget] = -(FReal(2*b)*dy*yetComputed[idxSrc1] + FReal(b*(b-1))*yetComputed[idxSrc2] + + FReal(2*a-1)*dx*yetComputed[idxSrc3] + FReal((a-1)*(a-1))*yetComputed[idxSrc4])/dist2; + if(a+b < 2*P){ + //Computation of derivatives Psi_{a,b,1} + // |x-y|^2 * Psi_{a,b,1} + 2*b*dy*Psi_{a,b-1,1} + b*(b-1)*Psi_{a,b-2,1} + 2*a*dx*Psi_{a-1,b,1} + a*(a-1)*Psi_{a-2,b,1} + dz*Psi_{a,b,0}= 0 + idxTarget = powerToIdx(a,b,1); + idxSrc1 = powerToIdx(a,b-1,1); + idxSrc2 = powerToIdx(a,b-2,1); + idxSrc3 = powerToIdx(a-1,b,1); + idxSrc4 = powerToIdx(a-2,b,1); + idxSrc5 = powerToIdx(a,b,0); + yetComputed[idxTarget] = -(FReal(2*b)*dy*yetComputed[idxSrc1] + FReal(b*(b-1))*yetComputed[idxSrc2] + + FReal(2*a)*dx*yetComputed[idxSrc3] + FReal(a*(a-1))*yetComputed[idxSrc4] + + dz*yetComputed[idxSrc5])/dist2; + } + for(c=2 ; c <= 2*P-b-a ; ++c){ + //Computation of derivatives Psi_{a,b,c} with a >= 2 + // |x-y|^2*Psi_{a,b,c} + (2*a-1)*dx*Psi_{a-1,b,c} + a*(a-2)*Psi_{a-2,b,c} + 2*b*dy*Psi_{a,b-1,c} + b*(b-1)*Psi_{a,b-2,c} + // + 2*c*dz*Psi_{a,b,c-1}} = 0 + idxTarget = powerToIdx(a,b,c); + idxSrc1 = powerToIdx(a-1,b,c); + idxSrc2 = powerToIdx(a,b-1,c); + idxSrc3 = powerToIdx(a,b,c-1); + idxSrc4 = powerToIdx(a-2,b,c); + idxSrc5 = powerToIdx(a,b-2,c); + idxSrc6 = powerToIdx(a,b,c-2); + yetComputed[idxTarget] = -(FReal(2*a-1)*dx*yetComputed[idxSrc1] + FReal((a-1)*(a-1))*yetComputed[idxSrc4] + + FReal(2*b)*dy*yetComputed[idxSrc2] + FReal(b*(b-1))*yetComputed[idxSrc5] + + FReal(2*c)*dz*yetComputed[idxSrc3] + FReal(c*(c-1))*yetComputed[idxSrc6])/dist2; + } + } + } + } + } + } + + + ///////////////////////////////// + ///////// Public Methods //////// + ///////////////////////////////// + +public: + + /*Constructor, need system information*/ + FTaylorKernel(const int inTreeHeight, const FReal inBoxWidth, const FPoint& inBoxCenter) : + boxWidth(inBoxWidth), + treeHeight(inTreeHeight), + widthAtLeafLevel(inBoxWidth/FReal(1 << (inTreeHeight-1))), + widthAtLeafLevelDiv2(widthAtLeafLevel/2), + boxCorner(inBoxCenter.getX()-(inBoxWidth/2),inBoxCenter.getY()-(inBoxWidth/2),inBoxCenter.getZ()-(inBoxWidth/2)) + { + FReal facto; + this->precomputeFactorials() ; + // int a = 0, b = 0, c = 0; + for(int i=0 , a = 0, b = 0, c = 0; i(fact3int(a,b,c)); + //_coeffPoly[i] = static_cast(factorials[a+b+c])/(facto*facto); + _coeffPoly[i] = FReal(1.0)/(facto); + //_coeffNk[i] = static_cast(factorials[a+b+c])/facto; +#ifdef OC + // _coeffPoly[i] = static_cast(factorials[a+b+c])/facto; + //_coeffPoly[i] = static_cast(factorials[a+b+c])/(facto*facto); + +#endif + // std::cout << " i a b c " <incPowers(&a,&b,&c); //inc powers of expansion + } + this->preComputeDerivative(); + this->preComputeIndirection(); + + //Use it for verifying size of datas used. + //printf("Size of datas : \n Sizeof(FReal) = %d\n, SizeVector = %d\n, SizeDerivative = %d\n",sizeof(FReal(0)),SizeVector,sizeDerivative); + } + + /* Default destructor + */ + virtual ~FTaylorKernel(){ + + } + + /**P2M + * @brief Fill the Multipole with the field created by the cell + * particles. + * + * Formula : + * \f[ + * M_{k} = \frac{|k|!}{k! k!} \sum_{j=0}^{N}{ q_j (x_c-x_j)^{k}} + * \f] + * where \f$x_c\f$ is the centre of the cell and \f$x_j\f$ the \f$j^{th}\f$ particles and \f$q_j\f$ its charge and \f$N\f$ the particle number. + */ + void P2M(CellClass* const pole, + const ContainerClass* const particles) + { + //Copying cell center position once and for all + const FPoint& cellCenter = getLeafCenter(pole->getCoordinate()); + + FReal * FRestrict multipole = pole->getMultipole(); + FMemUtils::memset(multipole,0,SizeVector*sizeof(FReal(0.0))); + + FReal multipole2[SizeVector] ; + + int nbPart = particles->getNbParticles(), i; + const FReal* const * positions = particles->getPositions(); + const FReal* posX = positions[0]; + const FReal* posY = positions[1]; + const FReal* posZ = positions[2]; + + const FReal* phyValue = particles->getPhysicalValues(); + // + // Iterating over Particles + // + FReal xc = cellCenter.getX(), yc = cellCenter.getY(), zc = cellCenter.getZ() ; + FReal dx[3] ; + for(int idPart=0 ; idPartgetCoordinate(),inLevel); + FReal * FRestrict mult = pole->getMultipole(); + + //Iteration over the eight children + int idxChild; + FReal coeff; + for(idxChild=0 ; idxChild<8 ; ++idxChild) + { + if(child[idxChild]){ + // + const FPoint& childCenter = getCellCenter(child[idxChild]->getCoordinate(),inLevel+1); + const FReal * FRestrict multChild = child[idxChild]->getMultipole(); + + //Set the distance between centers of cells + dx = cellCenter.getX() - childCenter.getX(); + dy = cellCenter.getY() - childCenter.getY(); + dz = cellCenter.getZ() - childCenter.getZ(); + + // Precompute the arrays of dx^i + arrayDX[0] = 1.0 ; + arrayDY[0] = 1.0 ; + arrayDZ[0] = 1.0 ; + for (int i = 1 ; i <= P ; ++i) { + arrayDX[i] = dx * arrayDX[i-1] ; + arrayDY[i] = dy * arrayDY[i-1] ; + arrayDZ[i] = dz * arrayDZ[i-1] ; + } + + a=0; + b=0; + c=0; + //FReal value ; + FReal value; + //Iteration over parent multipole array + for(int idxMult = 0 ; idxMultgetLocal(); + //index for distant neighbors + int idxNeigh; + FReal tmp1; + int * ind; + FReal * psiVector; + const FReal * multipole; + //Loop over all the possible neighbors + for(idxNeigh=0 ; idxNeigh<343 ; ++idxNeigh){ + //Need to test if current neighbor is one of the interaction list + if(distantNeighbors[idxNeigh]){ + + //Try with preComputed values for derivatives + psiVector = M2LpreComputedDerivatives[inLevel][idxNeigh]; + + multipole = distantNeighbors[idxNeigh]->getMultipole(); + //Iteration over Multipole / Local + //Iterating over local array : n + for(int i=0 ; ipreComputedIndirections[i]; + tmp1 = FReal(0); + + //Iterating over multipole array + for (int j=0 ; jgetCoordinate(),inLevel); + + // Get father local expansion + const FReal* FRestrict fatherExpansion = fatherCell->getLocal() ; + int idxFatherLoc; //index of Father local expansion to be read. + FReal dx, dy, dz, coeff; + int ap, bp, cp, af, bf, cf; //Indexes of expansion for father and child. + // + // For all children + for(int idxChild = 0 ; idxChild < 8 ; ++idxChild){ + // if child exists + if(childCell[idxChild]){ + + FReal* FRestrict childExpansion = childCell[idxChild]->getLocal() ; + const FPoint& childCenter = getCellCenter(childCell[idxChild]->getCoordinate(),inLevel+1); + + //Set the distance between centers of cells + // Child - father + dx = childCenter.getX()-locCenter.getX(); + dy = childCenter.getY()-locCenter.getY(); + dz = childCenter.getZ()-locCenter.getZ(); + // Precompute the arrays of dx^i + arrayDX[0] = 1.0 ; + arrayDY[0] = 1.0 ; + arrayDZ[0] = 1.0 ; + for (int i = 1 ; i <= P ; ++i) { + arrayDX[i] = dx * arrayDX[i-1] ; + arrayDY[i] = dy * arrayDY[i-1] ; + arrayDZ[i] = dz * arrayDZ[i-1] ; + } + // + //iterator over child's local expansion (to be filled) + af=0; bf=0; cf=0; + for(int k=0 ; kgetCoordinate()); + //Iterator over particles + int nbPart = particles->getNbParticles(); + + // + //Iteration over Local array + // + const FReal * iterLocal = local->getLocal(); + const FReal * const * positions = particles->getPositions(); + const FReal * posX = positions[0]; + const FReal * posY = positions[1]; + const FReal * posZ = positions[2]; + + FReal * forceX = particles->getForcesX(); + FReal * forceY = particles->getForcesY(); + FReal * forceZ = particles->getForcesZ(); + + FReal * targetsPotentials = particles->getPotentials(); + + FReal * phyValues = particles->getPhysicalValues(); + + //Iteration over particles + for(int i=0 ; i