assert(GetColumnsOfMatrix(input.GetInitialConditionMatrix(), 1).size()==input.GetDimension()); //Assert that the dimension of the initial conditions is the same as the system dimension
}
/**
* \brief Method allowing the implementation of Adam-Bashforth method 2 steps.
* This method is one of the several definition of the virtual inherited method.
* There are no arguments as all information needed are stored and are accessible in the input object.
* @return Void return as the solution is stored in the solution object.
*/
void BashforthSecondStep::SolveVectorialODE() {
vector<double> tmp1 = GetColumnsOfMatrix(input->GetInitialConditionMatrix(), 0); //tmp1 is a temporary vector that takes the solution vector (i-2) at each iteration.
vector<double> tmp2 = GetColumnsOfMatrix(input->GetInitialConditionMatrix(), 1); //tmp2 is a temporary vector that takes the solution vector (i-1) at each iteration.
vector<double> tmp_solution = tmp1; //Definition of the temporary vector storing for each step the solution
solution->ModifySolutionByColumns(tmp1, 0); //Definition of the initial solution with the initial condition
if(1%input->GetWriteOutputTimestep()==0.0) solution->ModifySolutionByColumns(tmp2, 1); //Write output every WriteOutputTimestep.
vector<double> past_solution1 = GetColumnsOfMatrix(input->GetFunctionMatrix(),0);//Vector (i-1) at each iteration storing the function defining the system
const double timestep = input->GetTimestep(); //Get the timestep and store it
const double overall_timestep = input->GetNumberSteps(); //Get the overall number of timestep we will do and store it
int position_to_write = 2; //Integer defining the position of the column of solution matrix where output is written.
for (int i = 2; i < overall_timestep; ++i) { //Solve the system for a fixed number of time steps.
const vector<double> &past_solution2 = past_solution1; //Past_solution2 takes the value (i-2) at each iteration of the vector containing the function defining the system.
past_solution1 = GetColumnsOfMatrix(input->GetFunctionMatrix(), i-1); //Past_solution1 takes the value (i-1) at each iteration of the vector containing the function defining the system.
tmp_solution = SubtractTwoVector(SubtractTwoVector(AddTwoVector(AddTwoVector(MultiplyWithVectorByRight(Multiply(input->GetCoefficientMatrix(), timestep*1.5),tmp1),(MultiplyVectorAndScalar(tmp1,1.0))),MultiplyVectorAndScalar(past_solution1,(1.5*timestep))),MultiplyWithVectorByRight(input->GetCoefficientMatrix(),MultiplyVectorAndScalar(tmp2,(0.5*timestep)))),MultiplyVectorAndScalar(past_solution2,(timestep*0.5))); //Apply the definition of the Adam-Bashforth method 1 step : https://en.wikipedia.org/wiki/Linear_multistep_method#Adams%E2%80%93Bashforth_methods
if (i%input->GetWriteOutputTimestep()==0.0){ //Write output for each print time step