Stability | Experimental |
---|---|
Safe Haskell | None |
Language | Haskell98 |
Generic interface to Blas using safe foreign calls. Refer to the GHC documentation for more information regarding appropriate use of safe and unsafe foreign calls.
The functions here are named in a similar fashion to the original Blas interface, with
the type-dependent letter(s) removed. Some functions have been merged with
others to allow the interface to work on both real and complex numbers. If you can't a
particular function, try looking for its corresponding complex equivalent (e.g.
symv
is a special case of hemv
applied to real numbers).
Note: although complex versions of rot
and rotg
exist in many implementations,
they are not part of the official Blas standard and therefore not included here. If
you really need them, submit a ticket so we can try to come up with a solution.
The documentation here is still incomplete. Consult the official documentation for more information.
Notation:
⋅
denotes dot product (without any conjugation).*
denotes complex conjugation.⊤
denotes transpose.†
denotes conjugate transpose (Hermitian conjugate).
Conventions:
- All scalars are denoted with lowercase Greek letters
- All vectors are denoted with lowercase Latin letters and are assumed to be column vectors (unless transposed).
- All matrices are denoted with uppercase Latin letters.
Since: 0.1.1
- rotg :: Ptr Double -> Ptr Double -> Ptr Double -> Ptr Double -> IO ()
- rotmg :: Ptr Double -> Ptr Double -> Ptr Double -> Double -> Ptr Double -> IO ()
- rot :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Double -> IO ()
- rotm :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> IO ()
- swap :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- scal :: Int -> Double -> Ptr Double -> Int -> IO ()
- copy :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- axpy :: Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- dotu :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO Double
- dotc :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO Double
- dsdot :: Int -> Ptr Float -> Int -> Ptr Float -> Int -> IO Double
- nrm2 :: Int -> Ptr Double -> Int -> IO Double
- asum :: Int -> Ptr Double -> Int -> IO Double
- iamax :: Int -> Ptr Double -> Int -> IO Int
- gemv :: Order -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- gbmv :: Order -> Transpose -> Int -> Int -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- hemv :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- hbmv :: Order -> Uplo -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- hpmv :: Order -> Uplo -> Int -> Double -> Ptr Double -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- trmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- tbmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- tpmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Ptr Double -> Int -> IO ()
- trsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- tbsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- tpsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Ptr Double -> Int -> IO ()
- geru :: Order -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- gerc :: Order -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- her :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- hpr :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> IO ()
- her2 :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- hpr2 :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> IO ()
- gemm :: Order -> Transpose -> Transpose -> Int -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- symm :: Order -> Side -> Uplo -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- hemm :: Order -> Side -> Uplo -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- syrk :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- herk :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- syr2k :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- her2k :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO ()
- trmm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
- trsm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO ()
Level 1: vector-vector operations
Givens rotations
rotg :: Ptr Double -> Ptr Double -> Ptr Double -> Ptr Double -> IO () Source
Generate a Givens rotation. (Only available for real floating-point types.)
rotmg :: Ptr Double -> Ptr Double -> Ptr Double -> Double -> Ptr Double -> IO () Source
Generate a modified Givens rotation. (Only available for real floating-point types.)
rot :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Double -> IO () Source
Apply a Givens rotation. (Only available for real floating-point types.)
rotm :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> IO () Source
Apply a modified Givens rotation. (Only available for real floating-point types.)
Basic operations
swap :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Swap two vectors:
(x, y) ← (y, x)
copy :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Copy a vector into another vector:
y ← x
axpy :: Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Add a scalar-vector product to a vector.
y ← α x + y
dotu :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO Double Source
Calculate the bilinear dot product of two vectors:
x ⋅ y ≡ ∑[i] x[i] y[i]
dotc :: Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO Double Source
Calculate the sesquilinear dot product of two vectors.
x* ⋅ y ≡ ∑[i] x[i]* y[i]
dsdot :: Int -> Ptr Float -> Int -> Ptr Float -> Int -> IO Double Source
Calculate the dot product of two vectors with extended precision accumulation of the
intermediate results and return a double-precision result. (Only available in
the Double
module.)
Norm operations
nrm2 :: Int -> Ptr Double -> Int -> IO Double Source
Calculate the Euclidean (L²) norm of a vector:
‖x‖₂ ≡ √(∑[i] x[i]²)
asum :: Int -> Ptr Double -> Int -> IO Double Source
Calculate the Manhattan (L¹) norm, equal to the sum of the magnitudes of the elements:
‖x‖₁ = ∑[i] |x[i]|
iamax :: Int -> Ptr Double -> Int -> IO Int Source
Calculate the index of the element with the maximum magnitude (absolute value).
Level 2: matrix-vector operations
Multiplication
gemv :: Order -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a general matrix-vector update.
y ← α T(A) x + β y
gbmv :: Order -> Transpose -> Int -> Int -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a general banded matrix-vector update.
y ← α T(A) x + β y
hemv :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a hermitian matrix-vector update.
y ← α A x + β y
hbmv :: Order -> Uplo -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a hermitian banded matrix-vector update.
y ← α A x + β y
hpmv :: Order -> Uplo -> Int -> Double -> Ptr Double -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a hermitian packed matrix-vector update.
y ← α A x + β y
Triangular operations
trmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Multiply a triangular matrix by a vector.
x ← T(A) x
tbmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Multiply a triangular banded matrix by a vector.
x ← T(A) x
tpmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Ptr Double -> Int -> IO () Source
Multiply a triangular packed matrix by a vector.
x ← T(A) x
trsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Multiply an inverse triangular matrix by a vector.
x ← T(A⁻¹) x
tbsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Multiply an inverse triangular banded matrix by a vector.
x ← T(A⁻¹) x
tpsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr Double -> Ptr Double -> Int -> IO () Source
Multiply an inverse triangular packed matrix by a vector.
x ← T(A⁻¹) x
Rank updates
geru :: Order -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Perform an unconjugated rank-1 update of a general matrix.
A ← α x y⊤ + A
gerc :: Order -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Perform a conjugated rank-1 update of a general matrix.
A ← α x y† + A
her :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Perform a rank-1 update of a Hermitian matrix.
A ← α x y† + A
hpr :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> IO () Source
Perform a rank-1 update of a Hermitian packed matrix.
A ← α x y† + A
her2 :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source
Perform a rank-2 update of a Hermitian matrix.
A ← α x y† + y (α x)† + A
hpr2 :: Order -> Uplo -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Ptr Double -> IO () Source
Perform a rank-2 update of a Hermitian packed matrix.
A ← α x y† + y (α x)† + A
Level 3: matrix-matrix operations
Multiplication
:: Order | Layout of all the matrices. |
-> Transpose | The operation |
-> Transpose | The operation |
-> Int | Number of rows of |
-> Int | Number of columns of |
-> Int | Number of columns of |
-> Double | Scaling factor |
-> Ptr Double | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> Ptr Double | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> Double | Scaling factor |
-> Ptr Double | Pointer to a mutable matrix |
-> Int | Stride of the major dimension of |
-> IO () |
Perform a general matrix-matrix update.
C ← α T(A) U(B) + β C
:: Order | Layout of all the matrices. |
-> Side | Side that |
-> Uplo | The part of |
-> Int | Number of rows of |
-> Int | Number of columns of |
-> Double | Scaling factor |
-> Ptr Double | Pointer to a symmetric matrix |
-> Int | Stride of the major dimension of |
-> Ptr Double | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> Double | Scaling factor |
-> Ptr Double | Pointer to a mutable matrix |
-> Int | Stride of the major dimension of |
-> IO () |
Perform a symmetric matrix-matrix update.
C ← α A B + β C or C ← α B A + β C
where A
is symmetric. The matrix A
must be in an unpacked format, although the
routine will only access half of it as specified by the
argument.Uplo
:: Order | Layout of all the matrices. |
-> Side | Side that |
-> Uplo | The part of |
-> Int | Number of rows of |
-> Int | Number of columns of |
-> Double | Scaling factor |
-> Ptr Double | Pointer to a Hermitian matrix |
-> Int | Stride of the major dimension of |
-> Ptr Double | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> Double | Scaling factor |
-> Ptr Double | Pointer to a mutable matrix |
-> Int | Stride of the major dimension of |
-> IO () |
Perform a Hermitian matrix-matrix update.
C ← α A B + β C or C ← α B A + β C
where A
is Hermitian. The matrix A
must be in an unpacked format, although the
routine will only access half of it as specified by the
argument.Uplo
Rank updates
syrk :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a symmetric rank-k update.
C ← α A A⊤ + β C or C ← α A⊤ A + β C
herk :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a Hermitian rank-k update.
C ← α A A† + β C or C ← α A† A + β C
syr2k :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a symmetric rank-2k update.
C ← α A B⊤ + α* B A⊤ + β C or C ← α A⊤ B + α* B⊤ A + β C
her2k :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> Double -> Ptr Double -> Int -> IO () Source
Perform a Hermitian rank-2k update.
C ← α A B† + α* B A† + β C or C ← α A† B + α* B† A + β C