blas-0.7: TODO

One great way to help is just to use the library, and give me feedback from
your experience.  What do you like?  What don't you like?  What is fast?
What is slow?  This stuff is really important for me to know.

If you are interested in hacking on the library, there is tons of work to do.
Here is a partial list.  Let me know what you would like to work on, and I can
give you some guidance on the best way to approach the task.

Small projects
--------------

* Write tests.  Look at the HPC output (from `make hpc` in the `tests` 
  directory), to find what functions are not being tested.

* Write benchmarks, especially ones that allow comparisons with C or Fortran.  
  The LU decomposition [on my blog][] is a good starting point.
  [on my blog]:http://quantile95.com/2008/10/31/ann-blas-bindings-for-haskell-version-06

* Write a tutorial or blog post about the library.

* The tests for solving triangular systems fail when an ill-conditioned 
  matrix gets generated.  I have investigated some of the failing cases
  in R, and have determined this isn't a bug.  Ideally, we should only
  test with well-conditioned systems. 

* Put better checks in swapElem for WriteTensor.

* Better error reporting.  Change the "check" functions in BLAS.Internal
  to be like "checkIsSquare".

* The ReadTensor/WriteTensor functions for Banded matrices are
  really terrible.  Re-write these to be more efficient.

* Add getSum/sum.  Put in re-write rules from scale and add to axpy.  Here
  is the old code and re-write rules (from version 0.4):
 
   <pre><code>
    unsafeGetSum :: (BLAS1 e) => 
        e -> DVector s n e -> e -> DVector t n e -> IO (DVector r n e)
    unsafeGetSum 1 x beta y
        | beta /= 1 = unsafeGetSum beta y 1 x
    unsafeGetSum alpha x beta y
        | isConj x = do
            s <- unsafeGetSum (E.conj alpha) (conj x) (E.conj beta) (conj y)
            return (conj s)
        | otherwise = do
            s <- newCopy y
            scaleBy beta (unsafeThaw s)
            axpy alpha x (unsafeThaw s)
            return (unsafeCoerce s)

    {-# RULES
      "scale/plus"   forall k l x y. plus (scale k x) (scale l y) = add k x l y
      "scale1/plus"  forall k x y.   plus (scale k x) y = add k x 1 y
      "scale2/plus"  forall k x y.   plus x (scale k y) = add 1 x k y
      
      "scale/minus"  forall k l x y. minus (scale k x) (scale l y) = 
                                         add k x (-l) y
      "scale1/minus" forall k x y.   minus (scale k x) y = add k x (-1) y
      "scale2/minus" forall k x y.   minus x (scale k y) = add 1 x (-k) y
      #-}
  </pre></code>

Medium projects
---------------

* Looking at the HPC output, there are a few important code paths that 
  aren't getting covered by the tests.  Specifically in the following 
  functions: gemm, hemv, hemm, hbmm, trmv, trmm, etc.  These functions
  are in Data.Matrix.Banded.IOBase and Data.Matrix.Dense.Base.
  It is impossible to test these code paths using pure code.  You need to
  use STMatrix and STVector.  I suggest stealing "Mondaic.hs" from
  QuickCheck2 for this purpose.  

* There do not yet exist bindings for `ger`, `syr`, etc.  Add them.  The
  bindings should only be for mutable types, and should have names like
  `rank1UpdateMatrix`, `rankKUpdateHermMatrix`, etc.

* I haven't really tested it, but probably the library doesn't build on
  Windows.  See if it is possible to build the library on windows.  If
  not, figure out how to do so.  This may involve using something other
  than autoconf on windows.

* Provide custum `unsafeGetRow`/`unsafeGetCol` functions for Herm Matrix,
  Tri Matrix, etc. rather than using matrix multiplication, which is what
  the default instance does.

* Provide Read/Write Tensor instances for Herm Matrix, Tri Matrix, 
  Herm Banded, etc.

* Write tests for STBanded.  The easiest way to do this is to mimic what is
  done in the STMatrix tests.

* Add getDenseMatrix/toDenseMatrix to MMatrix/IMatrix.  Ideally put in
  customized versions for all 6 matrix types.

* Optimization: Add `isRealType :: e -> Bool` and specilize hemm.

* Add functions for arithmetic on banded matrices, and provide a `Num`
  instance for Banded.

* Right now BLAS.h, double.c, zomplex.c, Double.hs, Zomplex.hs, and
  BLAS.Level{1,2,3}.hs are all (somewhat tediously) generated by hand.
  It would be nice to have a script that automatically generates them
  from a standard "cblas.h" header file.  Ideally, the script would also
  work for "clapack.h".  This would be *really* useful for the upcoming
  LAPACK bindings.  It's a chance to play around with Language.C for
  anyone who is interested.


Big Projects
------------

* Support for packed storage of symmetric and triangular matrices.  
  Add a Data.Matrix.Packed class with a heirarchy similar to 
  Data.Matrix.Banded. Provide MMatrix/IMatrix instances for 
  Tri Packed and Herm Packed.

* Data.Matrix.Dense.Base is really, really ugly.  Unfortunately, I didn't
  figure out the best way to write these functions until after I had 
  written all of the dense matrix ones.  The cleaner approach is the one
  followed in Data.Matrix.Banded.{IOBase,Base}, where all of the functions
  are determined in terms of IO types (instead of using the general type
  classes).  Reorganize Data.Matrix.Dense.{Base,IOBase,STBase} to mimic
  the style of Data.Matrix.Banded.

Notes
-----

* There is one remaining functional dependency in `Shaped x i | x -> i`.  We
  cannot get rid of it since GHC 6.10.1 has not yet implemented equality
  constraints in superclass contexts, which are required for MatrixShaped.
  When GHC implements this feature, get rid of this last remaining
  dependency.