init_dynamic_lno Subroutine

  subroutine init_dynamic_lno(this, input_shape, verbose)
    !! Initialise parameter storage and output buffers for the layer
    implicit none

    ! Arguments
    class(dynamic_lno_layer_type), intent(inout) :: this
    !! Layer instance to initialise
    integer, dimension(:), intent(in) :: input_shape
    !! Input shape used to infer num_inputs
    integer, optional, intent(in) :: verbose
    !! Verbosity level

    ! Local variables
    integer :: num_inputs, k
    !! Effective fan-in size and pole index
    integer :: verbose_ = 0
    !! Effective verbosity level

    if(present(verbose)) verbose_ = verbose

    !---------------------------------------------------------------------------
    ! Set shapes
    !---------------------------------------------------------------------------
    if(.not.allocated(this%input_shape)) call this%set_shape(input_shape)
    this%num_inputs = this%input_shape(1)
    this%output_shape = [this%num_outputs]
    this%num_params = this%get_num_params()


    !---------------------------------------------------------------------------
    ! Allocate learnable parameters
    !
    ! params(1): mu  learnable poles        [num_modes]
    ! params(2): beta learnable residues    [num_modes]
    ! params(3): W   local bypass weights   [num_outputs x num_inputs]
    ! params(4): b   bias                   [num_outputs]  (optional)
    !---------------------------------------------------------------------------
    allocate(this%weight_shape(2,3))
    this%weight_shape(:,1) = [ this%num_modes, 1 ]
    this%weight_shape(:,2) = [ this%num_modes, 1 ]
    this%weight_shape(:,3) = [ this%num_outputs, this%num_inputs ]

    if(this%use_bias)then
       this%bias_shape = [ this%num_outputs ]
       allocate(this%params(4))
    else
       allocate(this%params(3))
    end if

    ! mu: learnable poles
    call this%params(1)%allocate([this%num_modes, 1, 1])
    call this%params(1)%set_requires_grad(.true.)
    this%params(1)%fix_pointer = .true.
    this%params(1)%is_sample_dependent = .false.
    this%params(1)%is_temporary = .false.

    ! beta: learnable residues
    call this%params(2)%allocate([this%num_modes, 1, 1])
    call this%params(2)%set_requires_grad(.true.)
    this%params(2)%fix_pointer = .true.
    this%params(2)%is_sample_dependent = .false.
    this%params(2)%is_temporary = .false.

    ! W: local bypass weights
    call this%params(3)%allocate([this%num_outputs, this%num_inputs, 1])
    call this%params(3)%set_requires_grad(.true.)
    this%params(3)%fix_pointer = .true.
    this%params(3)%is_sample_dependent = .false.
    this%params(3)%is_temporary = .false.

    num_inputs = this%num_inputs
    if(this%use_bias)then
       num_inputs = this%num_inputs + 1
       call this%params(4)%allocate([this%bias_shape, 1])
       call this%params(4)%set_requires_grad(.true.)
       this%params(4)%fix_pointer = .true.
       this%params(4)%is_sample_dependent = .false.
       this%params(4)%is_temporary = .false.
    end if


    !---------------------------------------------------------------------------
    ! Initialise learnable parameters
    !
    ! Poles: mu_n = n*pi (matches original fixed Laplace frequencies, gives
    !         the same initial spectral basis as the prior fixed construction)
    ! Residues: kernel initialiser (small random values)
    ! W: kernel initialiser
    ! b: bias initialiser
    !---------------------------------------------------------------------------
    do k = 1, this%num_modes
       this%params(1)%val(k, 1) = real(k, real32) * pi
    end do
    call this%kernel_init%initialise( &
         this%params(2)%val(:,1), &
         fan_in = this%num_modes, fan_out = this%num_modes, &
         spacing = [ this%num_modes ] &
    )
    call this%kernel_init%initialise( &
         this%params(3)%val(:,1), &
         fan_in = num_inputs, fan_out = this%num_outputs, &
         spacing = [ this%num_outputs ] &
    )
    if(this%use_bias)then
       call this%bias_init%initialise( &
            this%params(4)%val(:,1), &
            fan_in = num_inputs, fan_out = this%num_outputs &
       )
    end if


    !---------------------------------------------------------------------------
    ! Allocate output arrays
    !---------------------------------------------------------------------------
    if(allocated(this%output)) deallocate(this%output)
    allocate(this%output(1,1))
    if(this%z(1)%allocated) call this%z(1)%deallocate()

  end subroutine init_dynamic_lno