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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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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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* 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::FDHessian(vector<double>& h){ |
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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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} |
