Method refineHessian

SRC/reliability/analysis/hessianApproximation/Hessian.cpp:764–962

}

int Hessian::refineHessian(int time, int colOfHessian)
{
	Vector column(sizeOfHessian);
	
	double tol = perturbTol;
	int ii = colOfHessian;
	int success =-1;
	int kk=0;
	static Vector grad_1(sizeOfHessian);
	static Vector grad_2(sizeOfHessian);
	static Vector grad_3(sizeOfHessian);
	
	Vector u = *designPointUSpace;

	/*
	theProbabilityTransformation->set_u(u);
	int result = theProbabilityTransformation->transform_u_to_x_andComputeJacobian();
	if (result < 0) {
		opserr << "Hessian::formHessianByFDM - " << endln
			<< " could not transform from u to x." << endln;
		return -1;
	}
	Matrix jacobian_x_u = theProbabilityTransformation->getJacobian_x_u();
	*/
	Matrix jacobian_x_u;
	int result = theProbabilityTransformation->getJacobian_x_to_u(jacobian_x_u);
	if (result < 0) {
		opserr << "Hessian::formHessianByFDM - " << endln
			<< " could not transform from u to x." << endln;
		return -1;
	}

	double u_1, u_2, u_3;

    u_1 =u(ii);
	grad_1.addVector(0.0, *standSens,1.0);
	
	//u_2 = u(ii)*tol;
	//grad_2=g(u_2);

	Vector gradientOfgFunction(sizeOfHessian );

    double u_save = u(ii);

	if (fabs(u(ii))<1.0e-10) { 
		opserr<<"Warning: u("<<ii<<") is "<<u(ii)<<"!!!!"<<endln;
	    u(ii)=-tol/100.0;
	}
	else u(ii) = u(ii)*(1.0-tol);
	
	u_2=u(ii);
		
    opserr<<"re-perturbation to get hessian, ii:"<<ii<<". u_2:"<<u_2<<endln;
	

    /*
	theProbabilityTransformation->set_u(u);
	result = theProbabilityTransformation->transform_u_to_x_andComputeJacobian();