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#include "NLModel.hpp"
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/**
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* calculate gradient using backward finite difference
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* df(Xk)/dXi = (f(Xk) - f(Xk - h*ei)) /h
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* where h is a small positive scalar and ei is the ith unit vector (ith column of the identity Matrix)
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* h can be used for all paritial derivatives, but in some cases, it is essential to use a different value
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* for each partial derivative
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*/
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vector<double> NLModel0::BackwardGrad(const vector<double>& x, double& fx, vector<double>& grad, const vector<double>& h){
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vector<double> tempX = x;
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vector<double> partialGrad;
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double fminus;
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double hi;
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for(int i = 0; i < ndim; i++){
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#ifndef IS_MPI
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hi = copysign(h[i], tempX[i]);
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//tempX[i] = x[i] + hi;
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tempX[i] -= hi;
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fminus = (*objfunc)(tempX);
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partialGrad[i] = (fx - fminus) / hi;
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//restore tempX to its original value
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tempX[i] += hi;
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#else
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if(procMappingArray[i] == myRank){
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hi = copysign(h[i], tempX[i]);
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tempX[i] -= hi;
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}
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fminus = (*objfunc)(tempX);
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if(procMappingArray[i] == myRank){
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partialGrad[i] = (fx - fminus) / hi;
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//restore tempX to its original value
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tempX[i] += hi;
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}
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#endif
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}
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return partialGrad;
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}
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/**
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* calculate gradient using forward finite difference
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* df(Xk)/dXi = (f(Xk+h*ei) - f(Xk)) /h
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* where h is a small positive scalar and ei is the ith unit vector (ith column of the identity Matrix)
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* h can be used for all paritial derivatives, but in some cases, it is essential to use a different value
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* for each partial derivative
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*/
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vector<double> NLModel0::ForwardGrad(const vector<double>& x, double& fx, vector<double>& grad, const vector<double>& h){
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vector<double> tempX = x;
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vector<double> partialGrad;
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double fplus;
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double hi;
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for(int i = 0; i < ndim; i++){
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#ifndef IS_MPI
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hi = copysign(h[i], tempX[i]);
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//tempX[i] = x[i] + hi;
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tempX[i] += hi;
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fplus = (*objfunc)(tempX);
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partialGrad[i] = (fplus - fx) / hi;
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//restore tempX to its original value
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tempX[i] -= hi;
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#else
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if(procMappingArray[i] == myRank){
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hi = copysign(h[i], tempX[i]);
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//tempX[i] = x[i] + hi;
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tempX[i] += hi;
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}
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fminus = (*objfunc)(tempX);
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if(procMappingArray[i] == myRank){
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partialGrad[i] = (fx - fminus) / hi;
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//restore tempX to its original value
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tempX[i] -= hi;
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}
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#endif
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}
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return partialGrad;
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}
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/**
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* calculate gradient using central finite difference
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* df(Xk)/dXi = (f(Xk+h*ei) - f(Xk - h*ei )) /h
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* where h is a small positive scalar and ei is the ith unit vector (ith column of the identity Matrix)
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* h can be used for all paritial derivatives, but in some cases, it is essential to use a different value
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* for each partial derivative
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*/
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vector<double> NLModel0::CentralGrad(const vector<double>& x, double& fx, vector<double>& grad, const vector<double>& h){
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vector<double> tempX = x;
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vector<double> partialGrad;
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double fplus, fminus;
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double hi;
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for(int i = 0; i < ndim; i++){
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#ifndef IS_MPI
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hi = copysign(h[i], tempX[i]);
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//tempX[i] = x[i] + hi
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tempX[i] += hi;
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fplus = (*objfunc)(tempX);
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//tempX[i] = x[i] -hi
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tempX[i] -= 2*hi;
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fminus = (*objfunc)(tempX);
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partialGrad[i] = (fplus + fminus) / (2*hi);
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//restore tempX to its original value
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tempX[i] += hi;
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#else
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if(procMappingArray[i] == myRank){
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hi = copysign(h[i], tempX[i]);
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//tempX[i] = x[i] + hi;
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tempX[i] += hi;
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}
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fplus = (*objfunc)(tempX);
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if(procMappingArray[i] == myRank){
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partialGrad[i] = (fx - fminus) / hi;
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//restore tempX to its original value
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tempX[i] -= 2*hi;
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}
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fminus = (*objfunc)(tempX);
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if(procMappingArray[i] == myRank){
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partialGrad[i] = (fx - fminus) / (2*hi);
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//restore tempX to its original value
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tempX[i] -= hi;
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}
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#endif
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}
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return partialGrad;
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}
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/**
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* calculate hessian using finite difference
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* d2f(Xk)/dxidxj = (df(Xk+h*ej)/dXi + df(Xk - h*ej)/dXi) /2h
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* where h is a small positive scalar and ei is the ith unit vector (ith column of the identity Matrix)
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*
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*/
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SymMatrix NLModel0::FiniteHessian(vector<double>& x, double fx, vector<double>& h){
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SymMatrix H(ndim);
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vector<double> tempX;
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vector<double> fi(ndim);
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vector<double> hi;
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double fij;
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tempX = x;
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//calculate f(X+ h*ei)
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for(int i = 0; i < ndim; i++){
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#ifndef IS_MPI
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hi[i] = copysign(h[i],tempX[i]);
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tempX[i] += hi[i];
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fi[i] = calcF(tempX);
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tempX[i] -= hi;
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#else
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if(procMappingArray[i] == myRank){
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hi[i] = copysign(h[i],tempX[i]);
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tempX[i] += hi[i];
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}
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fi[i] = calcF(tempX);
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if(procMappingArray[i] == myRank){
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tempX[i] -= hi[i];
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}
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#endif
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}
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#ifndef IS_MPI
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for(int i = 0; i < ndim; i++){
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tempX[i] += hi[i] * 2;
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fii = calcF(tempX);
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H(i,j) = ((fx - fi[i]) + (fii - fi[i])) / (hi[i]*hi[i]);
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tempX[i] -= hi[i];
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for(int j = i + 1; j < ndim; j++){
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tempX[j] += hi[j];
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fij = calcF(tempX);
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H(i,j) = ((f - fi[i]) + (fij - fi[j])) / (hi[i]*hi[j]);
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tempX[j] -= hi[j];
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}
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tempX[i] -= hi[i];
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}
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#else
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for(int i = 0; i < ndim; i++){
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if(procMappingArray[i] == myRank){
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tempX[i] += hi[i] * 2;
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}
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fii = calcF(tempX);
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H(i,j) = ((fx - fi[i]) + (fii - fi[i])) / (hi[i]*hi[i]);
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if(procMappingArray[i] == myRank){
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tempX[i] -= hi[i];
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}
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for(int j = i + 1; j < ndim; j++){
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if(procMappingArray[j] == myRank){
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tempX[j] += hi[j];
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}
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fij = calcF(tempX);
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H(i,j) = ((f - fi[i]) + (fij - fi[j])) / (hi[i]*hi[j]);
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if(procMappingArray[j] == myRank){
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tempX[j] -= hi[j];
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}
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}
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if(procMappingArray[i] == myRank){
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tempX[i] -= hi[i];
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}
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}
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#endif
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return H;
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}
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