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1. module Data.Matrix

   Matrix datatype and operations. Every provided example has been tested. Run cabal test for further tests.

2. data Matrix a

   matrix	Data.Matrix

   Type of matrices. Elements can be of any type. Rows and columns are indexed starting by 1. This means that, if m :: Matrix a and i,j :: Int, then m ! (i,j) is the element in the i-th row and j-th column of m.

3. forceMatrix :: Matrix a -> Matrix a

   matrix	Data.Matrix

   O(rows*cols). Similar to force. It copies the matrix content dropping any extra memory. Useful when using submatrix from a big matrix.

4. getMatrixAsVector :: Matrix a -> Vector a

   matrix	Data.Matrix

   O(rows*cols). Transform a Matrix to a Vector of size rows*cols. This is equivalent to get all the rows of the matrix using getRow and then append them, but far more efficient.

5. matrix :: Int -> Int -> ((Int, Int) -> a) -> Matrix a

   matrix	Data.Matrix

   O(rows*cols). Generate a matrix from a generator function. Example of usage:

   (  1  0 -1 -2 )
   (  3  2  1  0 )
   (  5  4  3  2 )
   matrix 4 4 $ \(i,j) -> 2*i - j = (  7  6  5  4 )
   

6. minorMatrix :: Int -> Int -> Matrix a -> Matrix a

   matrix	Data.Matrix

   O(rows*cols). Remove a row and a column from a matrix. Example:

   ( 1 2 3 )
   ( 4 5 6 )   ( 1 3 )
   minorMatrix 2 2 ( 7 8 9 ) = ( 7 9 )
   

7. multStrassenMixed :: Num a => Matrix a -> Matrix a -> Matrix a

   matrix	Data.Matrix

   Mixed Strassen's matrix multiplication.

8. permMatrix :: Num a => Int -> Int -> Int -> Matrix a

   matrix	Data.Matrix

   O(rows*cols). Permutation matrix.

   permMatrix n i j =
   i     j       n
   1 ( 1 0 ... 0 ... 0 ... 0 0 )
   2 ( 0 1 ... 0 ... 0 ... 0 0 )
   (     ...   ...   ...     )
   i ( 0 0 ... 0 ... 1 ... 0 0 )
   (     ...   ...   ...     )
   j ( 0 0 ... 1 ... 0 ... 0 0 )
   (     ...   ...   ...     )
   ( 0 0 ... 0 ... 0 ... 1 0 )
   n ( 0 0 ... 0 ... 0 ... 0 1 )
   

   When i == j it reduces to identity n.

9. prettyMatrix :: Show a => Matrix a -> String

   matrix	Data.Matrix

   Display a matrix as a String using the Show instance of its elements.

10. scaleMatrix :: Num a => a -> Matrix a -> Matrix a

    matrix	Data.Matrix

    Scale a matrix by a given factor. Example:

    ( 1 2 3 )   (  2  4  6 )
    ( 4 5 6 )   (  8 10 12 )
    scaleMatrix 2 ( 7 8 9 ) = ( 14 16 18 )
    

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