diff --git a/learn-physics.cabal b/learn-physics.cabal --- a/learn-physics.cabal +++ b/learn-physics.cabal @@ -1,5 +1,5 @@ Name: learn-physics -Version: 0.3.1 +Version: 0.4 Synopsis: Haskell code for learning physics Description: A library of functions for vector calculus, calculation of electric field, electric flux, @@ -31,11 +31,13 @@ Physics.Learn.RootFinding Physics.Learn.Mechanics Physics.Learn + Physics.Learn.Visual.PlotTools Physics.Learn.Visual.VisTools Build-depends: base >= 4.2 && < 4.8, vector-space >= 0.8.4 && < 0.9, not-gloss >= 0.5.0.4 && < 0.7, - spatial-math >= 0.1.7 && < 0.3 + spatial-math >= 0.1.7 && < 0.3, + gnuplot >= 0.5 && < 0.6 Hs-source-dirs: src Source-repository head diff --git a/src/Physics/Learn.hs b/src/Physics/Learn.hs --- a/src/Physics/Learn.hs +++ b/src/Physics/Learn.hs @@ -145,13 +145,23 @@ , shiftVolume -- ** Volume Integral , volumeIntegral - -- * Utilities + -- * Differential Equations , StateSpace(..) --- , (.-^) --- , Time + , (.-^) + , Time + , DifferentialEquation + , InitialValueProblem + , EvolutionMethod + , SolutionMethod + , stepSolution + , eulerMethod , rungeKutta4 , integrateSystem -- * Visualization + -- ** Plotting + , label + , postscript + , psFile -- ** Vis library , xyzFromVec , xyzFromPos @@ -274,8 +284,14 @@ ) import Physics.Learn.StateSpace ( StateSpace(..) --- , (.-^) --- , Time + , (.-^) + , Time + , DifferentialEquation + , InitialValueProblem + , EvolutionMethod + , SolutionMethod + , stepSolution + , eulerMethod ) import Physics.Learn.RungeKutta ( rungeKutta4 @@ -304,4 +320,9 @@ , ManyParticleAccelerationFunction , manyParticleStateDeriv , manyParticleRungeKuttaStep + ) +import Physics.Learn.Visual.PlotTools + ( label + , postscript + , psFile ) diff --git a/src/Physics/Learn/Curve.hs b/src/Physics/Learn/Curve.hs --- a/src/Physics/Learn/Curve.hs +++ b/src/Physics/Learn/Curve.hs @@ -62,9 +62,9 @@ ) -- | 'Curve' is a parametrized function into three-space, an initial limit, and a final limit. -data Curve = Curve { curveFunc :: (Double -> Position) -- ^ function from one parameter into space - , startingCurveParam :: Double -- ^ starting value of the parameter - , endingCurveParam :: Double -- ^ ending value of the parameter +data Curve = Curve { curveFunc :: Double -> Position -- ^ function from one parameter into space + , startingCurveParam :: Double -- ^ starting value of the parameter + , endingCurveParam :: Double -- ^ ending value of the parameter } -- | A dotted line integral. diff --git a/src/Physics/Learn/Mechanics.hs b/src/Physics/Learn/Mechanics.hs --- a/src/Physics/Learn/Mechanics.hs +++ b/src/Physics/Learn/Mechanics.hs @@ -49,7 +49,7 @@ import Physics.Learn.StateSpace ( StateSpace(..) , Diff - , TimeDerivative + , DifferentialEquation ) import Physics.Learn.RungeKutta ( rungeKutta4 @@ -91,7 +91,7 @@ -- | Time derivative of state for a single particle -- with a constant mass. simpleStateDeriv :: SimpleAccelerationFunction -- ^ acceleration function for the particle - -> TimeDerivative SimpleState -- ^ derivatives as a function of state + -> DifferentialEquation SimpleState -- ^ differential equation simpleStateDeriv a (t, r, v) = (1, v, a(t, r, v)) -- | Single Runge-Kutta step @@ -144,7 +144,7 @@ -- | Time derivative of state for a single particle -- with a constant mass. oneParticleStateDeriv :: OneParticleAccelerationFunction -- ^ acceleration function for the particle - -> TimeDerivative OneParticleSystemState -- ^ derivatives as a function of state + -> DifferentialEquation OneParticleSystemState -- ^ differential equation oneParticleStateDeriv a st@(_t, St _r v) = (1, DSt v (a st)) -- | Single Runge-Kutta step @@ -178,7 +178,7 @@ -- | Time derivative of state for two particles -- with constant mass. twoParticleStateDeriv :: TwoParticleAccelerationFunction -- ^ acceleration function for two particles - -> TimeDerivative TwoParticleSystemState -- ^ derivatives as a function of state + -> DifferentialEquation TwoParticleSystemState -- ^ differential equation twoParticleStateDeriv af2 st2@(_t, St _r1 v1, St _r2 v2) = (1, DSt v1 a1, DSt v2 a2) where (a1,a2) = af2 st2 @@ -206,7 +206,7 @@ -- | Time derivative of state for many particles -- with constant mass. manyParticleStateDeriv :: ManyParticleAccelerationFunction -- ^ acceleration function for many particles - -> TimeDerivative ManyParticleSystemState -- ^ derivatives as a function of state + -> DifferentialEquation ManyParticleSystemState -- ^ differential equation manyParticleStateDeriv af st@(_t, sts) = (1, [DSt v a | (v,a) <- zip vs as]) where vs = map velocity sts diff --git a/src/Physics/Learn/StateSpace.hs b/src/Physics/Learn/StateSpace.hs --- a/src/Physics/Learn/StateSpace.hs +++ b/src/Physics/Learn/StateSpace.hs @@ -12,7 +12,7 @@ A 'StateSpace' is an affine space where the associated vector space has scalars that are instances of 'Fractional'. If p is an instance of 'StateSpace', then the associated vectorspace -'Diff' p is intended to represent the space of time derivatives +'Diff' p is intended to represent the space of (time) derivatives of paths in p. 'StateSpace' is very similar to Conal Elliott's 'AffineSpace'. @@ -22,7 +22,12 @@ ( StateSpace(..) , (.-^) , Time - , TimeDerivative + , DifferentialEquation + , InitialValueProblem + , EvolutionMethod + , SolutionMethod + , stepSolution + , eulerMethod ) where @@ -31,7 +36,6 @@ ) import Data.VectorSpace ( VectorSpace(..) --- , Scalar ) import Physics.Learn.Position ( Position @@ -40,17 +44,19 @@ ) import Physics.Learn.CarrotVec ( Vec --- , (^+^) + , (^*) , (^-^) ) infixl 6 .+^, .-^ infix 6 .-. --- | A 'StateSpace' has an associated vector space, the vectors of which --- can be multiplied or divided by scalars. --- An example would be the set of positions of a particle. --- Position is not a vector, but displacement (difference in position) is a vector. +-- | An instance of 'StateSpace' is a data type that can serve as the state +-- of some system. Alternatively, a 'StateSpace' is a collection of dependent +-- variables for a differential equation. +-- A 'StateSpace' has an associated vector space for the (time) derivatives +-- of the state. The associated vector space is a linearized version of +-- the 'StateSpace'. class (VectorSpace (Diff p), Fractional (Scalar (Diff p))) => StateSpace p where -- | Associated vector space type Diff p @@ -76,6 +82,7 @@ (.-.) = (^-^) (.+^) = (^+^) +-- | Position is not a vector, but displacement (difference in position) is a vector. instance StateSpace Position where type Diff Position = Vec (.-.) = flip displacement @@ -109,10 +116,37 @@ (.-.) = zipWith (.-.) (.+^) = zipWith (.+^) --- | The time derivative of a state is an element of the associated vector space. -type TimeDerivative state = state -> Diff state +-- | A differential equation expresses how the dependent variables (state) +-- change with the independent variable (time). +-- A differential equation is specified by giving the (time) derivative +-- of the state as a function of the state. +-- The (time) derivative of a state is an element of the associated vector space. +type DifferentialEquation state = state -> Diff state -{- -class HasTimeDerivative state where - timeDeriv :: state -> Diff state --} +-- | An initial value problem is a differential equation along with an initial state. +type InitialValueProblem state = (DifferentialEquation state, state) + +-- | A (numerical) solution method is a way of converting +-- an initial value problem into a list of states (a solution). +-- The list of states need not be equally spaced in time. +type SolutionMethod state = InitialValueProblem state -> [state] + +-- | An evolution method is a way of approximating the state +-- after advancing a finite interval in the independent +-- variable (time) from a given state. +type EvolutionMethod state + = DifferentialEquation state -- ^ differential equation + -> Time state -- ^ time interval + -> state -- ^ initial state + -> state -- ^ evolved state + +-- | Given an evolution method and a time step, return the solution method +-- which applies the evolution method repeatedly with with given time step. +-- The solution method returned will produce an infinite list of states. +stepSolution :: EvolutionMethod state -> Time state -> SolutionMethod state +stepSolution ev dt (de, ic) = iterate (ev de dt) ic + +-- | The Euler method is the simplest evolution method. +-- It increments the state by the derivative times the time step. +eulerMethod :: StateSpace state => EvolutionMethod state +eulerMethod de dt st = st .+^ de st ^* dt diff --git a/src/Physics/Learn/Visual/PlotTools.hs b/src/Physics/Learn/Visual/PlotTools.hs new file mode 100644 --- /dev/null +++ b/src/Physics/Learn/Visual/PlotTools.hs @@ -0,0 +1,57 @@ +{-# OPTIONS_GHC -Wall #-} + +{- | +Module : Physics.Learn.Visual.PlotTools +Copyright : (c) Scott N. Walck 2011-2014 +License : BSD3 (see LICENSE) +Maintainer : Scott N. Walck +Stability : experimental + +This module contains helping functions for using Gnuplot. +-} + +module Physics.Learn.Visual.PlotTools + ( label + , postscript + , psFile + , examplePlot1 + , examplePlot2 + ) + where + +import Graphics.Gnuplot.Simple + ( Attribute(..) + , plotFunc + ) + +-- | An 'Attribute' with a given label at a given position. +label :: String -> (Double,Double) -> Attribute +label name (x,y) + = Custom "label" [show name ++ " at " ++ show x ++ "," ++ show y] + +-- | An 'Attribute' that requests postscript output. +postscript :: Attribute +postscript = Custom "term" ["postscript"] + +-- | An 'Attribute' giving the postscript file name. +psFile :: FilePath -> Attribute +psFile file = Custom "output" [show file] + +-- | An example of the use of 'label'. See the source code. +examplePlot1 :: IO () +examplePlot1 = plotFunc [Title "Cosine Wave" + ,XLabel "Time (ms)" + ,YLabel "Velocity" + ,label "Albert Einstein" (2,0.8) + ] [0,0.01..10::Double] cos + +-- | An example of the use of 'postscript' and 'psFile'. See the source code. +examplePlot2 :: IO () +examplePlot2 = plotFunc [Title "Cosine Wave" + ,XLabel "Time (ms)" + ,YLabel "Velocity of Car" + ,label "Albert Einstein" (2,0.8) + ,postscript + ,psFile "post1.ps" + ] [0,0.01..10::Double] cos +