Safe Haskell  None 

The BLAS
module provides a fully general
yet type safe BLAS API.
When in doubt about the semantics of an operation, consult your system's BLAS api documentation, or just read the documentation for the Intel MKL BLAS distribution
A few basic notes about how to invoke BLAS routines.
Many BLAS operations take one or more arguments of type Transpose
.
Tranpose
has the following different constructors, which tell BLAS
routines what transformation to implicitly apply to an input matrix mat
with dimension n x m
.

NoTranspose
leaves the matrixmat
as is. 
Transpose
treats themat
as being implicitly transposed, with dimensionm x n
. Entrymat(i,j)
being treated as actually being the entrymat(j,i)
. For Real matrices this is also the matrix adjoint operation. ieTranpose(mat)(i,j)=mat(j,i)

ConjNoTranspose
will implicitly conjugatemat
, which is a no op for Real (Float
orDouble
) matrices, but for 'Complex Float' and 'Complex Double' matrices, a given matrix entrymat(i,j)==x
will be treated as actually being:+
yconjugate(mat)(i,j)=y
.:+
x 
ConjTranpose
will implicitly transpose and conjugate the input matrix. ConjugateTranpose acts as matrix adjoint for both real and complex matrices.
The *gemm operations work as follows (using sgemm
as an example):

'sgemm trLeft trRight alpha beta left right result'
, wheretrLeft
andtrRight
are values of typeTranspose
that respectively act on the matricesleft
andright
.  the generalized matrix computation thusly formed can be viewed as being
result = alpha * trLeft(left) * trRight(right) + beta * result
the *gemv operations are akin to the *gemm operations, but with right
and result
being vectors rather than matrices.
the *trsv operations solve for x
in the equation A x = y
given A
and y
.
The MatUpLo
argument determines if the matrix should be treated as upper or
lower triangular and MatDiag
determines if the triangular solver should treat
the diagonal of the matrix as being all 1's or not. A general pattern of invocation
would be
.
A key detail to note is that the input vector is ALSO the result vector,
ie strsv
matuplo tranposeMatA matdiag matrixA xVectorstrsv
and friends updates the vector place.
Documentation
type GemvFun el orient s m = Transpose > el > el > MDenseMatrix s orient el > MDenseVector s Direct el > MDenseVector s Direct el > m ()Source
type GemmFun el orient s m = Transpose > Transpose > el > el > MDenseMatrix s orient el > MDenseMatrix s orient el > MDenseMatrix s orient el > m ()Source
type TrsvFun el orient s m = MatUpLo > Transpose > MatDiag > MDenseMatrix s orient el > MDenseVector s Direct el > m ()Source