-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | A native implementation of matrix operations.
--   
--   Matrix type and basic operations. Just a preliminary version without
--   too many features.
@package matrix
@version 0.1


-- | Matrix datatype an basic operations.
module Data.Matrix
data Matrix a

-- | Display a matrix as a <a>String</a>.
prettyMatrix :: Show a => Matrix a -> String

-- | Number of rows.
nrows :: Matrix a -> Int

-- | Number of columns.
ncols :: Matrix a -> Int

-- | The zero matrix of the given size.
zero :: Num a => Int -> Int -> Matrix a

-- | Identity matrix of the given order.
identity :: Num a => Int -> Matrix a

-- | Generate a matrix from a generator function.
matrix :: Int -> Int -> ((Int, Int) -> a) -> Matrix a

-- | Get an element of a matrix.
getElem :: Int -> Int -> Matrix a -> a

-- | Nice alias for <a>getElem</a>.
(!) :: Matrix a -> (Int, Int) -> a

-- | The transpose of a matrix.
transpose :: Matrix a -> Matrix a

-- | Extend a matrix to a given size adding zeroes. If the matrix already
--   has the required size, nothing happens.
extendTo :: Num a => Int -> Int -> Matrix a -> Matrix a

-- | Extract a submatrix.
submatrix :: Int -> Int -> Int -> Int -> Matrix a -> Matrix a

-- | Make a block-partition of a matrix using a given element as reference.
--   The element will stay in the bottom-right corner of the top-left
--   corner matrix.
--   
--   <pre>
--                   (             )   (      |      )
--                   (             )   ( ...  | ...  )
--                   (    x        )   (    x |      )
--   splitBlocks i j (             ) = (-------------) , where x = a_{i,j}
--                   (             )   (      |      )
--                   (             )   ( ...  | ...  )
--                   (             )   (      |      )
--   </pre>
--   
--   Note that some blocks can end up empty. We use the following notation
--   for these blocks:
--   
--   <pre>
--   ( TL | TR )
--   (---------)
--   ( BL | BR )
--   </pre>
--   
--   Where T = Top, B = Bottom, L = Left, R = Right.
--   
--   Implementation is done via slicing of vectors.
splitBlocks :: Int -> Int -> Matrix a -> (Matrix a, Matrix a, Matrix a, Matrix a)

-- | Horizontally join two matrices. Visually:
--   
--   <pre>
--   ( A ) &lt;|&gt; ( B ) = ( A | B )
--   </pre>
--   
--   Where both matrices <i>A</i> and <i>B</i> have the same number of
--   rows.
(<|>) :: Matrix a -> Matrix a -> Matrix a

-- | Vertically join two matrices. Visually:
--   
--   <pre>
--                     ( A )
--   ( A ) &lt;-&gt; ( B ) = ( - )
--                     ( B )
--   </pre>
--   
--   Where both matrices <i>A</i> and <i>B</i> have the same number of
--   columns.
(<->) :: Matrix a -> Matrix a -> Matrix a

-- | Join blocks of the form detailed in <a>splitBlocks</a>.
joinBlocks :: (Matrix a, Matrix a, Matrix a, Matrix a) -> Matrix a
instance Eq a => Eq (Matrix a)
instance Num a => Num (Matrix a)
instance Functor Matrix
instance NFData a => NFData (Matrix a)
instance Show a => Show (Matrix a)