blas-hs-0.1.1.0: Low-level Haskell bindings to Blas.

StabilityExperimental
Safe HaskellNone
LanguageHaskell98

Blas.Specialized.Double.Unsafe

Contents

Description

Generic interface to Blas using unsafe 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

Synopsis

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)

scal :: Int -> Double -> Ptr Double -> Int -> IO () Source

Multiply a vector by a scalar.

x ← α 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

gemm Source

Arguments

:: Order

Layout of all the matrices.

-> Transpose

The operation T to be applied to A.

-> Transpose

The operation U to be applied to B.

-> Int

Number of rows of T(A) and C.

-> Int

Number of columns of U(B) and C.

-> Int

Number of columns of T(A) and number of rows of U(B).

-> Double

Scaling factor α of the product.

-> Ptr Double

Pointer to a matrix A.

-> Int

Stride of the major dimension of A.

-> Ptr Double

Pointer to a matrix B.

-> Int

Stride of the major dimension of B.

-> Double

Scaling factor β of the original C.

-> Ptr Double

Pointer to a mutable matrix C.

-> Int

Stride of the major dimension of C.

-> IO () 

Perform a general matrix-matrix update.

C ← α T(A) U(B) + β C

symm Source

Arguments

:: Order

Layout of all the matrices.

-> Side

Side that A appears in the product.

-> Uplo

The part of A that is used.

-> Int

Number of rows of C.

-> Int

Number of columns of C.

-> Double

Scaling factor α of the product.

-> Ptr Double

Pointer to a symmetric matrix A.

-> Int

Stride of the major dimension of A.

-> Ptr Double

Pointer to a matrix B.

-> Int

Stride of the major dimension of B.

-> Double

Scaling factor α of the original C.

-> Ptr Double

Pointer to a mutable matrix C.

-> Int

Stride of the major dimension of C.

-> 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 Uplo argument.

hemm Source

Arguments

:: Order

Layout of all the matrices.

-> Side

Side that A appears in the product.

-> Uplo

The part of A that is used.

-> Int

Number of rows of C.

-> Int

Number of columns of C.

-> Double

Scaling factor α of the product.

-> Ptr Double

Pointer to a Hermitian matrix A.

-> Int

Stride of the major dimension of A.

-> Ptr Double

Pointer to a matrix B.

-> Int

Stride of the major dimension of B.

-> Double

Scaling factor α of the original C.

-> Ptr Double

Pointer to a mutable matrix C.

-> Int

Stride of the major dimension of C.

-> 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 Uplo argument.

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

Triangular operations

trmm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source

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 -> Double -> Ptr Double -> Int -> Ptr Double -> Int -> IO () Source

Perform an inverse triangular matrix-matrix multiplication.

B ← α T(A⁻¹) B    or    B ← α B T(A⁻¹)

where A is triangular.