statespace_mapped#

A model declared as a map from parameters to entries of the system matrices, for models written without Fortran code. The Python package’s MappedModel builds on it.

The representation holds every fixed entry and the initialization. The map says which entries the parameters set:

  • entries: parameter k sets \(X(i, j, t) = c\,\psi_k\), for X one of Z, H, T, R, Q, c, d (codes 2-8, as SS_ARR_* in the C interface) and t = 0 for every time slice;

  • covariance blocks: parameters \(k, \dots, k + q - 1\), \(q = d(d+1)/2\), are the lower triangle, by columns, of a d × d block of H or Q starting at row and column offset.

Transform groups map consecutive parameters to the optimizer’s scale:

kind

value

transform

MAP_NONE

0

none

MAP_POSITIVE

1

\(\exp(2x)\) (DK §7.3.2)

MAP_INTERVAL

2

\(m + h x / \sqrt{1 + x^2}\) onto (lo, hi)

MAP_STATIONARY

3

stationary AR coefficients (Monahan 1984)

MAP_INVERTIBLE

4

invertible MA coefficients

MAP_COV

5

Cholesky factor with log diagonal (covariance blocks)

Parameters in no group are unconstrained. Since update only overwrites the mapped entries, the fixed entries are set once.

mapped_model_t#

type, extends(ssm_model_t) :: mapped_model_t
  type(map_entry_t), allocatable :: entries(:)
  type(map_block_t), allocatable :: blocks(:)
  type(map_group_t), allocatable :: groups(:)
  real(dp), allocatable :: start(:)
  character(len=32), allocatable :: names(:)
contains
  procedure :: add_entry, add_block, add_group
end type

subroutine add_entry(self, param, array, i, j, t, coef)
subroutine add_block(self, array, offset, dim, first)     ! also adds a MAP_COV group
subroutine add_group(self, kind, first, last, lo, hi)

map_entry_t, map_block_t and map_group_t hold these declarations.

mapped_model#

function mapped_model(rep, k) result(model)
  type(ssm_rep_t), intent(in) :: rep
  integer, intent(in) :: k
  type(mapped_model_t) :: model

A mapped model with k parameters over a copy of rep; start values 0.1 and names param1, ... until set.

Example#

The local level model:

type(mapped_model_t) :: model
rep = ssm_rep(y, m=1, r=1)
rep%Z = 1.0_dp; rep%T = 1.0_dp
call rep%initialize_diffuse()
model = mapped_model(rep, 2)
call model%add_entry(1, 3, 1, 1, 0, 1.0_dp)          ! H(1, 1) = params(1)
call model%add_entry(2, 6, 1, 1, 0, 1.0_dp)          ! Q(1, 1) = params(2)
call model%add_group(MAP_POSITIVE, 1, 2, 0.0_dp, 0.0_dp)