{-# OPTIONS_GHC -Wall #-} {-# LANGUAGE Safe #-} {- | Module : Physics.Learn.SimpleVec Copyright : (c) Scott N. Walck 2012-2018 License : BSD3 (see LICENSE) Maintainer : Scott N. Walck Stability : experimental Basic operations on the vector type 'Vec', such as vector addition and scalar multiplication. This module is simple in the sense that the operations on vectors all have simple, concrete types, without the need for type classes. This makes using and reasoning about vector operations easier for a person just learning Haskell. -} module Physics.Learn.SimpleVec ( Vec , R , xComp , yComp , zComp , vec , (^+^) , (^-^) , (*^) , (^*) , (^/) , (<.>) , (><) , magnitude , zeroV , negateV , sumV , iHat , jHat , kHat ) where import Physics.Learn.CommonVec ( Vec(..) , vec , iHat , jHat , kHat , (><) ) infixl 6 ^+^ infixl 6 ^-^ infixl 7 *^ infixl 7 ^* infixl 7 ^/ infixl 7 <.> type R = Double -- | The zero vector. zeroV :: Vec zeroV = vec 0 0 0 -- | The additive inverse of a vector. negateV :: Vec -> Vec negateV (Vec ax ay az) = Vec (-ax) (-ay) (-az) -- | Sum of a list of vectors. sumV :: [Vec] -> Vec sumV = foldr (^+^) zeroV -- | Vector addition. (^+^) :: Vec -> Vec -> Vec Vec ax ay az ^+^ Vec bx by bz = Vec (ax+bx) (ay+by) (az+bz) -- | Vector subtraction. (^-^) :: Vec -> Vec -> Vec Vec ax ay az ^-^ Vec bx by bz = Vec (ax-bx) (ay-by) (az-bz) -- | Scalar multiplication, where the scalar is on the left -- and the vector is on the right. (*^) :: R -> Vec -> Vec c *^ Vec ax ay az = Vec (c*ax) (c*ay) (c*az) -- | Scalar multiplication, where the scalar is on the right -- and the vector is on the left. (^*) :: Vec -> R -> Vec Vec ax ay az ^* c = Vec (c*ax) (c*ay) (c*az) -- | Division of a vector by a scalar. (^/) :: Vec -> R -> Vec Vec ax ay az ^/ c = Vec (ax/c) (ay/c) (az/c) -- | Dot product of two vectors. (<.>) :: Vec -> Vec -> R Vec ax ay az <.> Vec bx by bz = ax*bx + ay*by + az*bz -- | Magnitude of a vector. magnitude :: Vec -> R magnitude v = sqrt(v <.> v)