blas-hs-0.1.1.0: src/Blas/Specialized/Float/Safe.hs
-- This file is auto-generated. Do not edit directly.
-- |
-- Stability: Experimental
--
-- 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
-- <http://netlib.org/blas/#_blas_routines 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/
module Blas.Specialized.Float.Safe (
-- * Level 1: vector-vector operations
-- ** Givens rotations
rotg
, rotmg
, rot
, rotm
-- ** Basic operations
, swap
, scal
, copy
, axpy
, dotu
, dotc
, sdsdot
-- ** Norm operations
, nrm2
, asum
, iamax
-- * Level 2: matrix-vector operations
-- ** Multiplication
, gemv
, gbmv
, hemv
, hbmv
, hpmv
-- ** Triangular operations
, trmv
, tbmv
, tpmv
, trsv
, tbsv
, tpsv
-- ** Rank updates
, geru
, gerc
, her
, hpr
, her2
, hpr2
-- * Level 3: matrix-matrix operations
-- ** Multiplication
, gemm
, symm
, hemm
-- ** Rank updates
, syrk
, herk
, syr2k
, her2k
-- ** Triangular operations
, trmm
, trsm
) where
import Foreign (Ptr)
import Blas.Primitive.Types (Order, Transpose, Uplo, Diag, Side)
import qualified Blas.Primitive.Safe as C
-- | Generate a Givens rotation. (Only available for real floating-point types.)
rotg :: Ptr Float
-> Ptr Float
-> Ptr Float
-> Ptr Float
-> IO ()
rotg = C.srotg
-- | Generate a modified Givens rotation. (Only available for real floating-point
-- types.)
rotmg :: Ptr Float
-> Ptr Float
-> Ptr Float
-> Float
-> Ptr Float
-> IO ()
rotmg = C.srotmg
-- | Apply a Givens rotation. (Only available for real floating-point types.)
rot :: Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Float
-> IO ()
rot = C.srot
-- | Apply a modified Givens rotation. (Only available for real floating-point types.)
rotm :: Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> IO ()
rotm = C.srotm
-- | Swap two vectors:
--
-- > (x, y) ← (y, x)
swap :: Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
swap = C.sswap
-- | Multiply a vector by a scalar.
--
-- > x ← α x
scal :: Int
-> Float
-> Ptr Float
-> Int
-> IO ()
scal = C.sscal
-- | Copy a vector into another vector:
--
-- > y ← x
copy :: Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
copy = C.scopy
-- | Add a scalar-vector product to a vector.
--
-- > y ← α x + y
axpy :: Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
axpy = C.saxpy
-- | Calculate the bilinear dot product of two vectors:
--
-- > x ⋅ y ≡ ∑[i] x[i] y[i]
dotu :: Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO Float
dotu = C.sdot
-- | Calculate the sesquilinear dot product of two vectors.
--
-- > x* ⋅ y ≡ ∑[i] x[i]* y[i]
dotc :: Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO Float
dotc = C.sdot
-- | Calculate the dot product of two vectors with extended precision accumulation of the
-- intermediate results and add a scalar value to the result. (Only available for the
-- @'Float'@ type.)
sdsdot :: Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO Float
sdsdot = C.sdsdot
-- | Calculate the Euclidean (L²) norm of a vector:
--
-- > ‖x‖₂ ≡ √(∑[i] x[i]²)
nrm2 :: Int
-> Ptr Float
-> Int
-> IO Float
nrm2 = C.snrm2
-- | Calculate the Manhattan (L¹) norm, equal to the sum of the magnitudes of the elements:
--
-- > ‖x‖₁ = ∑[i] |x[i]|
asum :: Int
-> Ptr Float
-> Int
-> IO Float
asum = C.sasum
-- | Calculate the index of the element with the maximum magnitude (absolute value).
iamax :: Int
-> Ptr Float
-> Int
-> IO Int
iamax = C.isamax
-- | Perform a general matrix-vector update.
--
-- > y ← α T(A) x + β y
gemv :: Order
-> Transpose
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
gemv = C.sgemv
-- | Perform a general banded matrix-vector update.
--
-- > y ← α T(A) x + β y
gbmv :: Order
-> Transpose
-> Int
-> Int
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
gbmv = C.sgbmv
-- | Perform a hermitian matrix-vector update.
--
-- > y ← α A x + β y
hemv :: Order
-> Uplo
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
hemv = C.ssymv
-- | Perform a hermitian banded matrix-vector update.
--
-- > y ← α A x + β y
hbmv :: Order
-> Uplo
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
hbmv = C.ssbmv
-- | Perform a hermitian packed matrix-vector update.
--
-- > y ← α A x + β y
hpmv :: Order
-> Uplo
-> Int
-> Float
-> Ptr Float
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
hpmv = C.sspmv
-- | Multiply a triangular matrix by a vector.
--
-- > x ← T(A) x
trmv :: Order
-> Uplo
-> Transpose
-> Diag
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
trmv = C.strmv
-- | Multiply a triangular banded matrix by a vector.
--
-- > x ← T(A) x
tbmv :: Order
-> Uplo
-> Transpose
-> Diag
-> Int
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
tbmv = C.stbmv
-- | Multiply a triangular packed matrix by a vector.
--
-- > x ← T(A) x
tpmv :: Order
-> Uplo
-> Transpose
-> Diag
-> Int
-> Ptr Float
-> Ptr Float
-> Int
-> IO ()
tpmv = C.stpmv
-- | Multiply an inverse triangular matrix by a vector.
--
-- > x ← T(A⁻¹) x
trsv :: Order
-> Uplo
-> Transpose
-> Diag
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
trsv = C.strsv
-- | Multiply an inverse triangular banded matrix by a vector.
--
-- > x ← T(A⁻¹) x
tbsv :: Order
-> Uplo
-> Transpose
-> Diag
-> Int
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
tbsv = C.stbsv
-- | Multiply an inverse triangular packed matrix by a vector.
--
-- > x ← T(A⁻¹) x
tpsv :: Order
-> Uplo
-> Transpose
-> Diag
-> Int
-> Ptr Float
-> Ptr Float
-> Int
-> IO ()
tpsv = C.stpsv
-- | Perform an unconjugated rank-1 update of a general matrix.
--
-- > A ← α x y⊤ + A
geru :: Order
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
geru = C.sger
-- | Perform a conjugated rank-1 update of a general matrix.
--
-- > A ← α x y† + A
gerc :: Order
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
gerc = C.sger
-- | Perform a rank-1 update of a Hermitian matrix.
--
-- > A ← α x y† + A
her :: Order
-> Uplo
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
her = C.ssyr
-- | Perform a rank-1 update of a Hermitian packed matrix.
--
-- > A ← α x y† + A
hpr :: Order
-> Uplo
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> IO ()
hpr = C.sspr
-- | Perform a rank-2 update of a Hermitian matrix.
--
-- > A ← α x y† + y (α x)† + A
her2 :: Order
-> Uplo
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
her2 = C.ssyr2
-- | Perform a rank-2 update of a Hermitian packed matrix.
--
-- > A ← α x y† + y (α x)† + A
hpr2 :: Order
-> Uplo
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Ptr Float
-> IO ()
hpr2 = C.sspr2
-- | Perform a general matrix-matrix update.
--
-- > C ← α T(A) U(B) + β C
gemm :: 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)@.
-> Float -- ^ Scaling factor @α@ of the product.
-> Ptr Float -- ^ Pointer to a matrix @A@.
-> Int -- ^ Stride of the major dimension of @A@.
-> Ptr Float -- ^ Pointer to a matrix @B@.
-> Int -- ^ Stride of the major dimension of @B@.
-> Float -- ^ Scaling factor @β@ of the original @C@.
-> Ptr Float -- ^ Pointer to a mutable matrix @C@.
-> Int -- ^ Stride of the major dimension of @C@.
-> IO ()
gemm = C.sgemm
-- | 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.
symm :: 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@.
-> Float -- ^ Scaling factor @α@ of the product.
-> Ptr Float -- ^ Pointer to a symmetric matrix @A@.
-> Int -- ^ Stride of the major dimension of @A@.
-> Ptr Float -- ^ Pointer to a matrix @B@.
-> Int -- ^ Stride of the major dimension of @B@.
-> Float -- ^ Scaling factor @α@ of the original @C@.
-> Ptr Float -- ^ Pointer to a mutable matrix @C@.
-> Int -- ^ Stride of the major dimension of @C@.
-> IO ()
symm = C.ssymm
-- | 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.
hemm :: 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@.
-> Float -- ^ Scaling factor @α@ of the product.
-> Ptr Float -- ^ Pointer to a Hermitian matrix @A@.
-> Int -- ^ Stride of the major dimension of @A@.
-> Ptr Float -- ^ Pointer to a matrix @B@.
-> Int -- ^ Stride of the major dimension of @B@.
-> Float -- ^ Scaling factor @α@ of the original @C@.
-> Ptr Float -- ^ Pointer to a mutable matrix @C@.
-> Int -- ^ Stride of the major dimension of @C@.
-> IO ()
hemm = C.ssymm
-- | Perform a symmetric rank-k update.
--
-- > C ← α A A⊤ + β C or C ← α A⊤ A + β C
syrk :: Order
-> Uplo
-> Transpose
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
syrk = C.ssyrk
-- | Perform a Hermitian rank-k update.
--
-- > C ← α A A† + β C or C ← α A† A + β C
herk :: Order
-> Uplo
-> Transpose
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
herk = C.ssyrk
-- | 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
syr2k :: Order
-> Uplo
-> Transpose
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
syr2k = C.ssyr2k
-- | 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
her2k :: Order
-> Uplo
-> Transpose
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> Float
-> Ptr Float
-> Int
-> IO ()
her2k = C.ssyr2k
-- | Perform a triangular matrix-matrix multiplication.
--
-- > B ← α T(A) B or B ← α B T(A)
--
-- where @A@ is triangular.
trmm :: Order
-> Side
-> Uplo
-> Transpose
-> Diag
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
trmm = C.strmm
-- | Perform an inverse triangular matrix-matrix multiplication.
--
-- > B ← α T(A⁻¹) B or B ← α B T(A⁻¹)
--
-- where @A@ is triangular.
trsm :: Order
-> Side
-> Uplo
-> Transpose
-> Diag
-> Int
-> Int
-> Float
-> Ptr Float
-> Int
-> Ptr Float
-> Int
-> IO ()
trsm = C.strsm