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{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE GADTs #-}
{- |
Module : Numeric.HMatrix.Static.Complex
Copyright : (c) Alberto Ruiz 2006-14
License : BSD3
Stability : experimental
-}
module Numeric.Complex(
C, M,
vec2, vec3, vec4, (&), (#),
vect,
Her, her, 𝑖,
) where
import GHC.TypeLits
import Numeric.LinearAlgebra.Util(ℂ,iC)
import qualified Numeric.LinearAlgebra.HMatrix as LA
import Numeric.LinearAlgebra.Static
𝑖 :: Sized ℂ s c => s
𝑖 = konst iC
newtype Her n = Her (M n n)
her :: KnownNat n => M n n -> Her n
her m = Her $ (m + LA.tr m)/2
infixl 4 &
(&) :: forall n . KnownNat n
=> C n -> ℂ -> C (n+1)
u & x = u # (mkC (LA.scalar x) :: C 1)
infixl 4 #
(#) :: forall n m . (KnownNat n, KnownNat m)
=> C n -> C m -> C (n+m)
(C u) # (C v) = C (vconcat u v)
vec2 :: ℂ -> ℂ -> C 2
vec2 a b = C (gvec2 a b)
vec3 :: ℂ -> ℂ -> ℂ -> C 3
vec3 a b c = C (gvec3 a b c)
vec4 :: ℂ -> ℂ -> ℂ -> ℂ -> C 4
vec4 a b c d = C (gvec4 a b c d)
vect :: forall n . KnownNat n => [ℂ] -> C n
vect xs = C (gvect "C" xs)
|
