init_spectrum Subroutine

  subroutine init_spectrum(n_gauss, params, dim_v, line, amp_fact_init, sig_init, maxiter, m, iprint)
    !! Initialization of the mean sprectrum with N Gaussian
    implicit none
    
    integer, intent(in) :: n_gauss !! number of Gaussian
    integer, intent(in) :: dim_v !! dimension along v axis
    integer, intent(in) :: maxiter !! Max number of iteration
    integer, intent(in) :: m !! number of corrections used in the limited memory matrix by LBFGS-B
    integer, intent(in) :: iprint !! print option

    real(xp), intent(in), dimension(dim_v) :: line !! spectrum
    real(xp), intent(in) :: amp_fact_init !! times max amplitude of additional Gaussian
    real(xp), intent(in) :: sig_init !! dispersion of additional Gaussian

    real(xp), intent(inout), dimension(3*n_gauss)  :: params !! params to optimize

    integer :: i, j, k, p
    real(xp), dimension(:), allocatable :: lb, ub
    real(xp), dimension(dim_v) :: model, residual
    real(xp), dimension(:), allocatable :: x
    
    do i=1, n_gauss
       allocate(lb(3*i), ub(3*i))
       model = 0._xp
       residual = 0._xp
       lb = 0._xp; ub=0._xp
       
       call init_bounds(line, i, dim_v, lb, ub)

       do j=1, i
          do k=1, dim_v
             model(k) = model(k) + gaussian(k, params(1+(3*(j-1))), params(2+(3*(j-1))), params(3+(3*(j-1))))
          end do
       enddo

       residual = model - line
       
       allocate(x(3*i))
       x = 0._xp
       
       do p=1, 3*(i-1)
          x(p) = params(p);
       end do
       
       x(2+(3*(i-1))) = minloc(residual, dim_v)
       x(1+(3*(i-1))) = line(int(x(2+(3*(i-1))))) * amp_fact_init
       x(3+(3*(i-1))) = sig_init;
       
       call minimize_spec(3*i, m, x, lb, ub, line, dim_v, i, maxiter, iprint)
       
       do p=1, 3*i   
          params(p) = x(p);
       end do
       
       deallocate(x)
       deallocate(lb, ub)
    enddo
  end subroutine init_spectrum