{-# language GADTs, TypeOperators #-}
{-# language TypeFamilies #-}
module Data.Dim where

import Data.Vector.Unboxed as V


-- * Dimension metadata

data family Dim a
data instance Dim (Dd i)
data instance Dim (Sd i)

-- | To define a /dense/ dimension we only need the dimensionality parameter
newtype Dd i = Dd { dDim :: i } deriving (Eq, Show)

-- | To define a /sparse/ dimension we need a cumulative array, an index array and a dimensionality parameter
data Sd i = Sd {
      -- | Cumulative array (# nonzero entries per degree of freedom). Not all storage formats (e.g. COO for rank-2 tensors) need this information.
      sCml :: Maybe (V.Vector i)
      -- | Index array (indices of nonzero entries)
    , sIdx :: V.Vector i
      -- | Size of the tensor along this dimension
    , sDim :: i }
  deriving (Eq, Show)

-- | A tensor dimension can be either dense or sparse.
--
-- Example: the CSR format is /dense/ in the first index (rows) and /sparse/ in the second index (columns)

dim :: Either (Dd c) (Sd c) -> c
dim = either dDim sDim