learn-physics 0.4.3 → 0.5

raw patch · 6 files changed

+130/−71 lines, 6 filesdep ~not-glossdep ~spatial-mathPVP ok

version bump matches the API change (PVP)

Dependency ranges changed: not-gloss, spatial-math

API changes (from Hackage documentation)

Files

• learn-physics.cabal +5/−5
• src/Physics/Learn.hs +15/−8
• src/Physics/Learn/Charge.hs +4/−4
• src/Physics/Learn/Curve.hs +38/−41
• src/Physics/Learn/Visual/VisTools.hs +13/−13
• src/Tests.hs +55/−0

@@ -1,5 +1,5 @@ Name:                learn-physics-Version:             0.4.3+Version:             0.5 Synopsis:            Haskell code for learning physics Description:         A library of functions for vector calculus,                      calculation of electric field, electric flux,@@ -11,8 +11,8 @@ Maintainer:          Scott N. Walck <walck@lvc.edu> Category:            Physics Build-type:          Simple-Cabal-version:       >=1.6-Tested-with:         GHC == 7.6.3+Cabal-version:       >=1.8+Tested-with:         GHC == 7.8.2 Library   Exposed-modules:     Physics.Learn.Charge                        Physics.Learn.Current@@ -36,8 +36,8 @@                        Physics.Learn.Visual.GlossTools   Build-depends:       base >= 4.2 && < 4.8,                        vector-space >= 0.8.4 && < 0.9,-                       not-gloss >= 0.5.0.4 && < 0.6,-                       spatial-math >= 0.1.7 && < 0.2,+                       not-gloss >= 0.6 && < 0.7,+                       spatial-math >= 0.2 && < 0.3,                        gloss >= 1.8 && < 1.9,                        gnuplot >= 0.5 && < 0.6   Hs-source-dirs:      src

@@ -121,8 +121,6 @@     , simpleLineIntegral     , dottedLineIntegral     , crossedLineIntegral-    , compositeSimpsonDottedLineIntegral-    , compositeSimpsonCrossedLineIntegral     -- ** Surfaces     , Surface(..)     , unitSphere@@ -162,9 +160,14 @@     , label     , postscript     , psFile+    -- ** Gloss library+    , polarToCart+    , cartToPolar+    , arrow+    , thickArrow     -- ** Vis library-    , xyzFromVec-    , xyzFromPos+    , v3FromVec+    , v3FromPos     , visVec     , oneVector     , displayVectorField@@ -249,8 +252,6 @@     , simpleLineIntegral     , dottedLineIntegral     , crossedLineIntegral-    , compositeSimpsonDottedLineIntegral-    , compositeSimpsonCrossedLineIntegral     ) import Physics.Learn.Surface     ( Surface(..)@@ -275,8 +276,8 @@     , volumeIntegral     ) import Physics.Learn.Visual.VisTools-    ( xyzFromVec-    , xyzFromPos+    ( v3FromVec+    , v3FromPos     , visVec     , oneVector     , displayVectorField@@ -325,4 +326,10 @@     ( label     , postscript     , psFile+    )+import Physics.Learn.Visual.GlossTools+    ( polarToCart+    , cartToPolar+    , arrow+    , thickArrow     )

@@ -77,7 +77,7 @@ totalCharge :: ChargeDistribution -> Charge totalCharge (PointCharge q _)       = q totalCharge (LineCharge lambda c)   = simpleLineIntegral 1000 lambda c-totalCharge (SurfaceCharge sigma s) = surfaceIntegral 100 100 sigma s+totalCharge (SurfaceCharge sigma s) = surfaceIntegral 200 200 sigma s totalCharge (VolumeCharge rho v)    = volumeIntegral 50 50 50 rho v totalCharge (MultipleCharges ds)           = sum [totalCharge d | d <- ds] @@ -122,7 +122,7 @@     -> Surface         -- ^ geometry of the surface charge     -> VectorField     -- ^ electric field (in V/m) eFieldFromSurfaceCharge sigma s r-    = k *^ surfaceIntegral 100 100 integrand s+    = k *^ surfaceIntegral 200 200 integrand s       where         k = 9e9  -- 1 / (4 * pi * epsilon0)         integrand r' = sigma r' *^ d ^/ magnitude d ** 3@@ -160,7 +160,7 @@  -- | The electric flux through a surface produced by a charge distribution. electricFlux :: Surface -> ChargeDistribution -> Double-electricFlux surf dist = dottedSurfaceIntegral 100 100 (eField dist) surf+electricFlux surf dist = dottedSurfaceIntegral 200 200 (eField dist) surf  ------------------------ -- Electric Potential --@@ -209,7 +209,7 @@     -> Surface         -- ^ geometry of the surface charge     -> ScalarField     -- ^ electric potential ePotFromSurfaceCharge sigma s r-    = k *^ surfaceIntegral 100 100 integrand s+    = k *^ surfaceIntegral 200 200 integrand s       where         k = 9e9  -- 1 / (4 * pi * epsilon0)         integrand r' = sigma r' / magnitude d

@@ -28,6 +28,8 @@     , simpleLineIntegral     , dottedLineIntegral     , crossedLineIntegral+    , compositeTrapezoidDottedLineIntegral+    , compositeTrapezoidCrossedLineIntegral     , compositeSimpsonDottedLineIntegral     , compositeSimpsonCrossedLineIntegral     )@@ -68,12 +70,32 @@                    }  -- | A dotted line integral.+--   Convenience function for 'compositeSimpsonDottedLineIntegral'. dottedLineIntegral+    :: Int          -- ^ number of half-intervals+                    --   (one less than the number of function evaluations)+    -> VectorField  -- ^ vector field+    -> Curve        -- ^ curve to integrate over+    -> Double       -- ^ scalar result+dottedLineIntegral = compositeSimpsonDottedLineIntegral++-- | Calculates integral vf x dl over curve.+--   Convenience function for 'compositeSimpsonCrossedLineIntegral'.+crossedLineIntegral+    :: Int          -- ^ number of half-intervals+                    --   (one less than the number of function evaluations)+    -> VectorField  -- ^ vector field+    -> Curve        -- ^ curve to integrate over+    -> Vec          -- ^ vector result+crossedLineIntegral = compositeSimpsonCrossedLineIntegral++-- | A dotted line integral, performed in an unsophisticated way.+compositeTrapezoidDottedLineIntegral     :: Int          -- ^ number of intervals     -> VectorField  -- ^ vector field     -> Curve        -- ^ curve to integrate over     -> Double       -- ^ scalar result-dottedLineIntegral n vf (Curve f a b)+compositeTrapezoidDottedLineIntegral n vf (Curve f a b)     = sum $ zipWith (<.>) aveVecs dls       where         dt = (b - a) / fromIntegral n@@ -82,13 +104,13 @@         aveVecs = zipWith average vecs (tail vecs)         dls = zipWith displacement pts (tail pts) --- | Calculates integral vf x dl over curve.-crossedLineIntegral+-- | Calculates integral vf x dl over curve in an unsophisticated way.+compositeTrapezoidCrossedLineIntegral     :: Int          -- ^ number of intervals     -> VectorField  -- ^ vector field     -> Curve        -- ^ curve to integrate over     -> Vec          -- ^ vector result-crossedLineIntegral n vf (Curve f a b)+compositeTrapezoidCrossedLineIntegral n vf (Curve f a b)     = sumV $ zipWith (><) aveVecs dls       where         dt = (b - a) / fromIntegral n@@ -113,35 +135,6 @@         aveVecs = zipWith average vecs (tail vecs)         dls = zipWith displacement pts (tail pts) -{--lineIntegral :: (InnerSpace v, Scalar v ~ Double) => Double-             -> (Vec -> v)-             -> Curve-             -> v-lineIntegral tol field (Curve f a b)-    = let ca = f a-          cb = f b-          fielda = field ca-          fieldb = field cb-          val = average fielda fieldb ^* magnitude (cb ^-^ ca)-      in evalInterval tol 1 20 field (Curve f a b) ca cb fielda fieldb val--evalInterval :: (InnerSpace v, Scalar v ~ Double) => Double -> Int -> Int-             -> (Vec -> v) -> Curve -> Vec -> Vec -> v -> v -> v -> v-evalInterval tol level maxlevel field (Curve f a b) ca cb fielda fieldb val-    = let t = (a + b) / 2-          ct = f t-          fieldt = field ct-          vall = average fielda fieldt ^* magnitude (ct ^-^ ca)-          valr = average fieldt fieldb ^* magnitude (cb ^-^ ct)-          newval = vall ^+^ valr-      in if magnitude (newval ^-^ val) < tol then-             newval-         else-             evalInterval (tol/2) (level+1) maxlevel field (Curve f a t) ca ct fielda fieldt vall ^+^-             evalInterval (tol/2) (level+1) maxlevel field (Curve f t b) ct cb fieldt fieldb valr--}- -- | Reparametrize a curve from 0 to 1. normalizeCurve :: Curve -> Curve normalizeCurve (Curve f a b)@@ -227,10 +220,12 @@ --   Quadratic approximation to curve. --   Composite strategy. --   Dotted line integral.-compositeSimpsonDottedLineIntegral :: Int -- ^ number of half-intervals (one less than the number of function evaluations-                                   -> VectorField  -- ^ vector field-                                   -> Curve        -- ^ curve to integrate over-                                   -> Double       -- ^ scalar result+compositeSimpsonDottedLineIntegral+    :: Int          -- ^ number of half-intervals+                    --   (one less than the number of function evaluations)+    -> VectorField  -- ^ vector field+    -> Curve        -- ^ curve to integrate over+    -> Double       -- ^ scalar result compositeSimpsonDottedLineIntegral n vf (Curve c a b)     = let nEven = 2 * div n 2           dt = (b - a) / fromIntegral nEven@@ -259,10 +254,12 @@ --   Quadratic approximation to curve. --   Composite strategy. --   Crossed line integral.-compositeSimpsonCrossedLineIntegral :: Int -- ^ number of half-intervals (one less than the number of function evaluations-                                    -> VectorField  -- ^ vector field-                                    -> Curve        -- ^ curve to integrate over-                                    -> Vec          -- ^ vector result+compositeSimpsonCrossedLineIntegral+    :: Int          -- ^ number of half-intervals+                    --   (one less than the number of function evaluations)+    -> VectorField  -- ^ vector field+    -> Curve        -- ^ curve to integrate over+    -> Vec          -- ^ vector result compositeSimpsonCrossedLineIntegral n vf (Curve c a b)     = let nEven = 2 * div n 2           dt = (b - a) / fromIntegral nEven

@@ -3,8 +3,8 @@ -- | Some tools related to the not-gloss 3D graphics and animation library.  module Physics.Learn.Visual.VisTools-    ( xyzFromVec-    , xyzFromPos+    ( v3FromVec+    , v3FromPos     , visVec     , oneVector     , displayVectorField@@ -13,7 +13,7 @@     where  import SpatialMath-    ( Xyz(..)+    ( V3(..)     , Euler(..)     ) import Vis@@ -37,17 +37,17 @@     ( Curve(..)     ) --- | Make an 'Xyz' object from a 'Vec'.-xyzFromVec :: Vec -> Xyz Double-xyzFromVec v = Xyz x y z+-- | Make a 'V3' object from a 'Vec'.+v3FromVec :: Vec -> V3 Double+v3FromVec v = V3 x y z     where       x = xComp v       y = yComp v       z = zComp v --- | Make an 'Xyz' object from a 'Position'.-xyzFromPos :: Position -> Xyz Double-xyzFromPos r = Xyz x y z+-- | Make a 'V3' object from a 'Position'.+v3FromPos :: Position -> V3 Double+v3FromPos r = V3 x y z     where       (x,y,z) = cartesianCoordinates r @@ -58,16 +58,16 @@                    -> VectorField       -- ^ vector field to display                    -> VisObject Double  -- ^ the displayable object displayVectorField col unitsPerMeter samplePts field-    = VisObjects [Trans (xyzFromPos r) $ visVec col (e ^/ unitsPerMeter) | r <- samplePts, let e = field r]+    = VisObjects [Trans (v3FromPos r) $ visVec col (e ^/ unitsPerMeter) | r <- samplePts, let e = field r]  -- | A displayable VisObject for a curve. curveObject :: Color -> Curve -> VisObject Double curveObject color (Curve f a b)-    = Line' [(xyzFromPos (f t), color) | t <- [a,a+(b-a)/1000..b]]+    = Line' [(v3FromPos (f t), color) | t <- [a,a+(b-a)/1000..b]]  -- | Place a vector at a particular position. oneVector :: Color -> Position -> Vec -> VisObject Double-oneVector c r v = Trans (xyzFromPos r) $ visVec c v+oneVector c r v = Trans (v3FromPos r) $ visVec c v  data Cart = Cart Double Double Double             deriving (Show)@@ -85,7 +85,7 @@  -- | A VisObject arrow from a vector visVec :: Color -> Vec -> VisObject Double-visVec c v = rotZ phi $ rotY theta $ Arrow (r,20*r) (Xyz 0 0 1) c+visVec c v = rotZ phi $ rotY theta $ Arrow (r,20*r) (V3 0 0 1) c     where       x = xComp v       y = yComp v

@@ -0,0 +1,55 @@+{-# OPTIONS_GHC -Wall #-}++module Main where++import Physics.Learn+import Test.QuickCheck++propGaussLaw1 :: (Double,Double,Double) -> Bool+propGaussLaw1 (x,y,z) = abs (eFlux - q/epsilon0) < 0.01+    where+      eFlux = fluxThroughLargeCenteredSphere (x,y,z) q+      epsilon0 = 1 / (4 * pi * 9e9)+      q = epsilon0++fluxThroughLargeCenteredSphere :: (Double,Double,Double) -> Double -> Double+fluxThroughLargeCenteredSphere (x,y,z) q+    = electricFlux (centeredSphere radius) (PointCharge q (cart x y z))+      where+        radius = 2 * sqrt(x*x + y*y + z*z) + 1++currentLoop :: Double -> Current -> CurrentDistribution+currentLoop radius i+    = LineCurrent i (Curve (\phi -> cyl radius phi 0) 0 (2*pi))++amperianLoop :: Double -> Curve+amperianLoop radius+    = Curve (\t -> cart (radius + radius * sin t) 0 (radius * cos t)) 0 (2*pi)++magCirculation :: Double -> Current -> Double+magCirculation radius i+    = dottedLineIntegral 20+      (bFieldFromCurrentLoop i (Curve (\phi -> cyl radius phi 0) 0 (2*pi)))+      (amperianLoop radius)++bFieldFromCurrentLoop :: Current -> Curve -> VectorField+bFieldFromCurrentLoop i c r+    = k *^ crossedLineIntegral 20 integrand c+      where+        k = 1e-7  -- mu0 / (4 * pi)+        integrand r' = (-i) *^ d ^/ magnitude d ** 3+            where+              d = displacement r' r++propAmpere1 :: Double -> Property+propAmpere1 radius+    = radius > 0 ==> abs (magCirculation radius i - 4*pi*1e-7 * i) < 0.01+      where+        i = 1 / (4*pi*1e-7)++main :: IO ()+main = putStrLn "Gauss's law test:" >>+       quickCheck propGaussLaw1 >>+       putStrLn "Ampere's law test:" >>+       quickCheck propAmpere1+