Stability | Experimental |
---|---|
Safe Haskell | Safe |
Language | Haskell98 |
Blas.Generic.Safe
Description
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.
Documentation
class (Floating a, Storable a) => Numeric a where #
Blas operations that are applicable to real and complex numbers.
Instances are defined for the 4 types supported by Blas: the single- and double-precision floating point types and their complex versions.
Minimal complete definition
swap, scal, copy, axpy, dotu, dotc, nrm2, asum, iamax, gemv, gbmv, hemv, hbmv, hpmv, trmv, tbmv, tpmv, trsv, tbsv, tpsv, geru, gerc, her, hpr, her2, hpr2, gemm, symm, hemm, syrk, herk, syr2k, her2k, trmm, trsm
Associated Types
Methods
swap :: Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Swap two vectors:
(x, y) ← (y, x)
scal :: Int -> a -> Ptr a -> Int -> IO () #
Multiply a vector by a scalar.
x ← α x
copy :: Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Copy a vector into another vector:
y ← x
axpy :: Int -> a -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Add a scalar-vector product to a vector.
y ← α x + y
dotu :: Int -> Ptr a -> Int -> Ptr a -> Int -> IO a #
Calculate the bilinear dot product of two vectors:
x ⋅ y ≡ ∑[i] x[i] y[i]
dotc :: Int -> Ptr a -> Int -> Ptr a -> Int -> IO a #
Calculate the sesquilinear dot product of two vectors.
x* ⋅ y ≡ ∑[i] x[i]* y[i]
nrm2 :: Int -> Ptr a -> Int -> IO (RealType a) #
Calculate the Euclidean (L²) norm of a vector:
‖x‖₂ ≡ √(∑[i] x[i]²)
asum :: Int -> Ptr a -> Int -> IO (RealType a) #
Calculate the Manhattan (L¹) norm, equal to the sum of the magnitudes of the elements:
‖x‖₁ = ∑[i] |x[i]|
iamax :: Int -> Ptr a -> Int -> IO Int #
Calculate the index of the element with the maximum magnitude (absolute value).
gemv :: Order -> Transpose -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
Perform a general matrix-vector update.
y ← α T(A) x + β y
gbmv :: Order -> Transpose -> Int -> Int -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
Perform a general banded matrix-vector update.
y ← α T(A) x + β y
hemv :: Order -> Uplo -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
Perform a hermitian matrix-vector update.
y ← α A x + β y
hbmv :: Order -> Uplo -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
Perform a hermitian banded matrix-vector update.
y ← α A x + β y
hpmv :: Order -> Uplo -> Int -> a -> Ptr a -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
Perform a hermitian packed matrix-vector update.
y ← α A x + β y
trmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Multiply a triangular matrix by a vector.
x ← T(A) x
tbmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Multiply a triangular banded matrix by a vector.
x ← T(A) x
tpmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr a -> Ptr a -> Int -> IO () #
Multiply a triangular packed matrix by a vector.
x ← T(A) x
trsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Multiply an inverse triangular matrix by a vector.
x ← T(A⁻¹) x
tbsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Multiply an inverse triangular banded matrix by a vector.
x ← T(A⁻¹) x
tpsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr a -> Ptr a -> Int -> IO () #
Multiply an inverse triangular packed matrix by a vector.
x ← T(A⁻¹) x
geru :: Order -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Perform an unconjugated rank-1 update of a general matrix.
A ← α x y⊤ + A
gerc :: Order -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Perform a conjugated rank-1 update of a general matrix.
A ← α x y† + A
her :: Order -> Uplo -> Int -> RealType a -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Perform a rank-1 update of a Hermitian matrix.
A ← α x y† + A
hpr :: Order -> Uplo -> Int -> RealType a -> Ptr a -> Int -> Ptr a -> IO () #
Perform a rank-1 update of a Hermitian packed matrix.
A ← α x y† + A
her2 :: Order -> Uplo -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Perform a rank-2 update of a Hermitian matrix.
A ← α x y† + y (α x)† + A
hpr2 :: Order -> Uplo -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> Ptr a -> IO () #
Perform a rank-2 update of a Hermitian packed matrix.
A ← α x y† + y (α x)† + A
Arguments
:: 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 |
-> a | Scaling factor |
-> Ptr a | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> Ptr a | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> a | Scaling factor |
-> Ptr a | 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
Arguments
:: Order | Layout of all the matrices. |
-> Side | Side that |
-> Uplo | The part of |
-> Int | Number of rows of |
-> Int | Number of columns of |
-> a | Scaling factor |
-> Ptr a | Pointer to a symmetric matrix |
-> Int | Stride of the major dimension of |
-> Ptr a | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> a | Scaling factor |
-> Ptr a | 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
Arguments
:: Order | Layout of all the matrices. |
-> Side | Side that |
-> Uplo | The part of |
-> Int | Number of rows of |
-> Int | Number of columns of |
-> a | Scaling factor |
-> Ptr a | Pointer to a Hermitian matrix |
-> Int | Stride of the major dimension of |
-> Ptr a | Pointer to a matrix |
-> Int | Stride of the major dimension of |
-> a | Scaling factor |
-> Ptr a | 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
syrk :: Order -> Uplo -> Transpose -> Int -> Int -> a -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
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 -> RealType a -> Ptr a -> Int -> RealType a -> Ptr a -> Int -> IO () #
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 -> a -> Ptr a -> Int -> Ptr a -> Int -> a -> Ptr a -> Int -> IO () #
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 -> a -> Ptr a -> Int -> Ptr a -> Int -> RealType a -> Ptr a -> Int -> IO () #
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
trmm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Perform a triangular matrix-matrix multiplication.
B ← α T(A) B or B ← α B T(A)
where A
is triangular.
trsm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> a -> Ptr a -> Int -> Ptr a -> Int -> IO () #
Perform an inverse triangular matrix-matrix multiplication.
B ← α T(A⁻¹) B or B ← α B T(A⁻¹)
where A
is triangular.
class Numeric a => RealNumeric a where #
Blas operations that are only applicable to real numbers.
Methods
rotg :: Ptr a -> Ptr a -> Ptr a -> Ptr a -> IO () #
Generate a Givens rotation. (Only available for real floating-point types.)
rotmg :: Ptr a -> Ptr a -> Ptr a -> a -> Ptr a -> IO () #
Generate a modified Givens rotation. (Only available for real floating-point types.)
rot :: Int -> Ptr a -> Int -> Ptr a -> Int -> a -> a -> IO () #
Apply a Givens rotation. (Only available for real floating-point types.)
rotm :: Int -> Ptr a -> Int -> Ptr a -> Int -> Ptr a -> IO () #
Apply a modified Givens rotation. (Only available for real floating-point types.)
Instances