Data.Array.Accelerate.Numeric.LinearAlgebra

Types

class (Elt a, Num a) => Numeric a

Minimal complete definition

numericR

Instances

Numeric Double

Methods

numericR :: NumericR Double

Numeric Float

Methods

numericR :: NumericR Float

Numeric (Complex Double)

Methods

numericR :: NumericR (Complex Double)

Numeric (Complex Float)

Methods

numericR :: NumericR (Complex Float)

type Scalar e = Array DIM0 e

Scalars arrays hold a single element

type Vector e = Array DIM1 e

Vectors are one-dimensional arrays

type Matrix e = Array DIM2 e

Matrices as dense two-dimensional arrays in row-major ordering

Products

Vector-vector

(<.>) :: Numeric e => Acc (Vector e) -> Acc (Vector e) -> Acc (Scalar e) infixr 8

An infix synonym for dotu.

>>> let a = fromList (Z:.4) [1..]
>>> let b = fromList (Z:.4) [-2,0,1,1]
>>> a <.> b
Scalar Z [5.0]

>>> let c = fromList (Z:.2) [1:+1, 1:+0]
>>> let d = fromList (Z:.2) [1:+0, 1:+(-1)]
>>> c <.> d
Scalar Z [2.0 :+ 0.0]

(><) :: Numeric e => Acc (Vector e) -> Acc (Vector e) -> Acc (Matrix e) infixr 8

Outer product of two vectors

>>> let a = fromList (Z :. 3) [1,2,3]
>>> let b = fromList (Z :. 3) [5,2,3]
>>> a >< b
 Matrix (Z :. 3 :. 3)
   [  5.0, 2.0, 3.0
   , 10.0, 4.0, 6.0
   , 15.0, 6.0, 9.0 ]

Matrix-vector

(#>) :: Numeric e => Acc (Matrix e) -> Acc (Vector e) -> Acc (Vector e) infixr 8

Dense matrix-vector product

>>> let m = fromList (Z :. 2 :. 3) [1..]
>>> m
Matrix (Z :. 2 :. 3)
 [ 1.0, 2.0, 3.0
 , 4.0, 5.0, 6.0 ]

>>> let x = fromList (Z :. 3) [10,20,30]

>>> m #> x
Vector (Z :. 2) [140.0,320.0]

See gemv for a more general version of this operation.

(<#) :: Numeric e => Acc (Vector e) -> Acc (Matrix e) -> Acc (Vector e) infixr 8

Dense vector-matrix product

>>> let m = fromList (Z :. 2 :. 3) [1..]
>>> m
Matrix (Z :. 2 :. 3)
 [1.0,2.0,3.0,
  4.0,5.0,6.0]

>>> let v = fromList (Z :. 2) [5,10]

>>> v <# m
Vector (Z :. 3) [45.0,60.0,75.0]

See gemv for a more general version of this operation.

Matrix-matrix

(<>) :: Numeric e => Acc (Matrix e) -> Acc (Matrix e) -> Acc (Matrix e) infixr 8

Dense matrix-matrix product

>>> let a = fromList (Z :. 3 :. 5) [1..]
>>> a
Matrix (Z:.3:.5)
 [  1.0,  2.0,  3.0,  4.0,  5.0
 ,  6.0,  7.0,  8.0,  9.0, 10.0
 , 11.0, 12.0, 13.0, 14.0, 15.0 ]

>>> let b = fromList (Z :. 5 :. 2) [1,3, 0,2, -1,5, 7,7, 6,0]
>>> b
Matrix (Z :. 5 :. 2)
 [  1.0, 3.0
 ,  0.0, 2.0
 , -1.0, 5.0
 ,  7.0, 7.0
 ,  6.0, 0.0 ]

>>> a <> b
Matrix (Z :. 3 :. 2)
 [  56.0,  50.0
 , 121.0, 135.0
 , 186.0, 220.0 ]

See gemm for a more general version of this operation.

Diagonal

identity :: Num e => Exp Int -> Acc (Matrix e)

Create a square identity matrix of the given dimension

diagonal :: Num e => Acc (Vector e) -> Acc (Matrix e)

Create a square matrix with the given diagonal