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Add tests and fix MonomialBasis D3A3 instance
This commit is contained in:
sheaf
parent
cebfeb0b7a
commit
34c129d72a
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@ -205,10 +205,38 @@ executable inspect
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Math.Interval.Abstract
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build-depends:
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brush-strokes,
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data-reify
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brush-strokes
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, data-reify
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^>= 0.6.3
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test-suite tests
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import:
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common
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type:
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exitcode-stdio-1.0
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hs-source-dirs:
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src/test
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default-language:
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Haskell2010
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main-is:
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Main.hs
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build-depends:
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brush-strokes
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, falsify
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^>= 0.2
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, hspray
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^>= 0.1.3
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, tasty
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^>= 1.5
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, unordered-containers
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>= 0.2.15 && < 0.3
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benchmark cusps
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import:
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@ -4,10 +4,13 @@ constraints:
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acts -finitary,
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rounded-hw -pure-hs -c99 -avx512 +ghc-prim -x87-long-double
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tests: True
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allow-newer:
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acts:base, acts:deepseq,
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groups-generic:base,
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eigen:primitive,
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falsify:base, falsify:tasty,
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--package brush-strokes
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profiling: True
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@ -608,3 +608,34 @@ x2 = 𝕀 x2_lo x2_hi
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( b1 - a12 * x2 ) `extendedDivide` a11
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-}
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{-
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SMOKING GUN:
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> (f, fI) = brushStrokeFunctions $ ellipseBrushStroke (0,1) pi
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> (t, i, s) = mkBox (0.54, 0.55) 2 (0.5480, 0.5481)
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> _D32_dxdxdx $ dbrush $ eval fI (t,i,s)
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> [ℝ2 54187.61174031432 -11626.47655724034, ℝ2 55257.54384135226 -9759.09092706883]
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In Mathematica:
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FindMinimum[{D[b[vt, s, myPb0, myPb1][[1]], {vt, 3}] /. (vt -> t),
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0.54 <= t <= 0.55 && 0.548 <= s <= 0.5481}, {{t, 0.545}, {s,
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0.54805}}]
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> { -503.445, {t -> 0.54, s -> 0.548} }
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FindMaximum[{D[b[vt, s, myPb0, myPb1][[1]], {vt, 3}] /. (vt -> t),
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0.54 <= t <= 0.55 && 0.548 <= s <= 0.5481}, {{t, 0.545}, {s,
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0.54805}}]
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> { -480.086, {t -> 0.55, s -> 0.5481} }
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so the actual range is [-503.445,-480.086] but we have computed a range of
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[54187.61174031432, 55257.54384135226] which does not contain the actual range!
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-}
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{-
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Math.Ring.cos ( linearD @_ @3 (\i -> 𝕀 (getR1 $ inf i) (getR1 $ sup i)) (𝕀 (ℝ1 $ 0.548 * pi) (ℝ1 $ 0.5481 * pi)) :: D3𝔸1 ( 𝕀 Double ) )
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-}
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@ -140,8 +140,8 @@ boo x i y z
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ellipseTest :: StrokeDatum 3 AI
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ellipseTest =
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boo ( ellipseBrush ( Pt . Val ) scaleI ) 1
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( mkPoint ( ℝ2 0 0 ) 1.0111 1.0222 0 )
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( LineTo { curveEnd = NextPoint $ mkPoint ( ℝ2 100 0 ) 10.0333 10.0444 ( pi Prelude./ 2 )
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( mkPoint ( ℝ2 0 0 ) 10 25 0 )
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( LineTo { curveEnd = NextPoint $ mkPoint ( ℝ2 100 0 ) 15 40 pi
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, curveData = () } )
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where
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mkPoint :: ℝ 2 -> Double -> Double -> Double -> PointData ( ℝ 3 )
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@ -258,7 +258,7 @@ instance HasBézier 3 AI where
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( Cubic.bezier''' bez )
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--------------------------------------------------------------------------------
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-- Brushes (TODO copied from MetaBrush.Asset.Brushes)
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-- Brushes (TODO copied from Calligraphy.Brushes)
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κ :: Double
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κ = 0.5519150244935105707435627227925
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@ -304,13 +304,13 @@ ellipseBrush mkI scaleI =
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mkPt x y
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= let !x' = a `scaledBy` x
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!y' = b `scaledBy` y
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{-
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-- {-
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!c = cos phi
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!s = sin phi
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in ( x' * c - y' * s ) *^ e_x
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^+^ ( x' * s + y' * c ) *^ e_y
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-}
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-- {-
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-- -}
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{-
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!r = sqrt $ x' ^ 2 + y' ^ 2
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!arctgt = atan ( y' / x' )
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-- a and b are always strictly positive, so we can compute
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@ -326,7 +326,7 @@ ellipseBrush mkI scaleI =
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in
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( r * cos phi' ) *^ e_x
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^+^ ( r * sin phi' ) *^ e_y
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-- -}
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-}
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in circleSpline @AI @k @( ℝ 3 ) @( ℝ 2 ) mkPt
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where
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@ -244,7 +244,7 @@ chainRule1NQ zero_w sum_w scale_w df dg =
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]
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) ||]
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-- | The chain rule for a composition \( \mathbb{R}^n \to \mathbb{R} \to \mathbb{R} \)
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-- | The chain rule for a composition \( \mathbb{R}^n \to \mathbb{R}^1 \to \mathbb{R}^1 \)
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--
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-- (To be spliced in using Template Haskell.)
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chainRuleN1Q :: forall du dr1 r
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@ -291,7 +291,7 @@ type instance Vars D𝔸0 = 0
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instance MonomialBasis D𝔸0 where
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monTabulate f =
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[|| let
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!_D0_v = $$( f $ Mon VZ )
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_D0_v = $$( f $ Mon VZ )
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in D0 { .. }
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||]
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@ -302,8 +302,8 @@ type instance Vars D1𝔸1 = 1
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instance MonomialBasis D1𝔸1 where
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monTabulate f =
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[|| let
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!_D11_v = $$( f $ Mon ( 0 `VS` VZ ) )
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!_D11_dx = T $$( f $ Mon ( 1 `VS` VZ ) )
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_D11_v = $$( f $ Mon ( 0 `VS` VZ ) )
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_D11_dx = T $$( f $ Mon ( 1 `VS` VZ ) )
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in D11 { .. }
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||]
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@ -316,9 +316,9 @@ type instance Vars D2𝔸1 = 1
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instance MonomialBasis D2𝔸1 where
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monTabulate f =
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[|| let
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!_D21_v = $$( f $ Mon ( 0 `VS` VZ ) )
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!_D21_dx = T $$( f $ Mon ( 1 `VS` VZ ) )
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!_D21_dxdx = T $$( f $ Mon ( 2 `VS` VZ ) )
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_D21_v = $$( f $ Mon ( 0 `VS` VZ ) )
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_D21_dx = T $$( f $ Mon ( 1 `VS` VZ ) )
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_D21_dxdx = T $$( f $ Mon ( 2 `VS` VZ ) )
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in D21 { .. }
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||]
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@ -332,10 +332,10 @@ type instance Vars D3𝔸1 = 1
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instance MonomialBasis D3𝔸1 where
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monTabulate f =
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[|| let
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!_D31_v = $$( f $ Mon ( 0 `VS` VZ ) )
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!_D31_dx = T $$( f $ Mon ( 1 `VS` VZ ) )
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!_D31_dxdx = T $$( f $ Mon ( 2 `VS` VZ ) )
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!_D31_dxdxdx = T $$( f $ Mon ( 3 `VS` VZ ) )
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_D31_v = $$( f $ Mon ( 0 `VS` VZ ) )
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_D31_dx = T $$( f $ Mon ( 1 `VS` VZ ) )
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_D31_dxdx = T $$( f $ Mon ( 2 `VS` VZ ) )
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_D31_dxdxdx = T $$( f $ Mon ( 3 `VS` VZ ) )
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in D31 { .. }
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||]
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@ -350,9 +350,9 @@ type instance Vars D1𝔸2 = 2
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instance MonomialBasis D1𝔸2 where
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monTabulate f =
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[|| let
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!_D12_v = $$( f $ Mon ( 0 `VS` 0 `VS` VZ ) )
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!_D12_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` VZ ) )
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!_D12_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` VZ ) )
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_D12_v = $$( f $ Mon ( 0 `VS` 0 `VS` VZ ) )
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_D12_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` VZ ) )
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_D12_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` VZ ) )
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in D12 { .. }
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||]
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@ -366,12 +366,12 @@ type instance Vars D2𝔸2 = 2
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instance MonomialBasis D2𝔸2 where
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monTabulate f =
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[|| let
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!_D22_v = $$( f $ Mon ( 0 `VS` 0 `VS` VZ ) )
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!_D22_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` VZ ) )
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!_D22_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` VZ ) )
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!_D22_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` VZ ) )
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!_D22_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` VZ ) )
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!_D22_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` VZ ) )
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_D22_v = $$( f $ Mon ( 0 `VS` 0 `VS` VZ ) )
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_D22_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` VZ ) )
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_D22_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` VZ ) )
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_D22_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` VZ ) )
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_D22_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` VZ ) )
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_D22_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` VZ ) )
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in D22 { .. }
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||]
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@ -388,16 +388,16 @@ type instance Vars D3𝔸2 = 2
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instance MonomialBasis D3𝔸2 where
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monTabulate f =
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[|| let
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!_D32_v = $$( f $ Mon ( 0 `VS` 0 `VS` VZ ) )
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!_D32_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` VZ ) )
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!_D32_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` VZ ) )
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!_D32_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` VZ ) )
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!_D32_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` VZ ) )
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!_D32_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` VZ ) )
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!_D32_dxdxdx = T $$( f $ Mon ( 3 `VS` 0 `VS` VZ ) )
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!_D32_dxdxdy = T $$( f $ Mon ( 2 `VS` 1 `VS` VZ ) )
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!_D32_dxdydy = T $$( f $ Mon ( 1 `VS` 2 `VS` VZ ) )
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!_D32_dydydy = T $$( f $ Mon ( 0 `VS` 3 `VS` VZ ) )
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_D32_v = $$( f $ Mon ( 0 `VS` 0 `VS` VZ ) )
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_D32_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` VZ ) )
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_D32_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` VZ ) )
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_D32_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` VZ ) )
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_D32_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` VZ ) )
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_D32_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` VZ ) )
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_D32_dxdxdx = T $$( f $ Mon ( 3 `VS` 0 `VS` VZ ) )
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_D32_dxdxdy = T $$( f $ Mon ( 2 `VS` 1 `VS` VZ ) )
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_D32_dxdydy = T $$( f $ Mon ( 1 `VS` 2 `VS` VZ ) )
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_D32_dydydy = T $$( f $ Mon ( 0 `VS` 3 `VS` VZ ) )
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in D32 { .. } ||]
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monIndex d = \ case
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@ -435,16 +435,16 @@ type instance Vars D2𝔸3 = 3
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instance MonomialBasis D2𝔸3 where
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monTabulate f =
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[|| let
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!_D23_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D23_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D23_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` VZ ) )
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!_D23_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` VZ ) )
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!_D23_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D23_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` VZ ) )
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!_D23_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` VZ ) )
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!_D23_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` VZ ) )
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!_D23_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` VZ ) )
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!_D23_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` VZ ) )
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_D23_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` VZ ) )
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_D23_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` VZ ) )
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_D23_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` VZ ) )
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_D23_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` VZ ) )
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_D23_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` VZ ) )
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_D23_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` VZ ) )
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_D23_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` VZ ) )
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_D23_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` VZ ) )
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_D23_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` VZ ) )
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_D23_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` VZ ) )
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in D23 { .. }
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||]
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@ -466,26 +466,26 @@ type instance Vars D3𝔸3 = 3
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instance MonomialBasis D3𝔸3 where
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monTabulate f =
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[|| let
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!_D33_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D33_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D33_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` VZ ) )
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!_D33_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` VZ ) )
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!_D33_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D33_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` VZ ) )
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!_D33_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` VZ ) )
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!_D33_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` VZ ) )
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!_D33_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` VZ ) )
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!_D33_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` VZ ) )
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!_D33_dxdxdx = T $$( f $ Mon ( 3 `VS` 0 `VS` 0 `VS` VZ ) )
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!_D33_dxdxdy = T $$( f $ Mon ( 2 `VS` 1 `VS` 0 `VS` VZ ) )
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!_D33_dxdydy = T $$( f $ Mon ( 1 `VS` 2 `VS` 0 `VS` VZ ) )
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!_D33_dydydy = T $$( f $ Mon ( 0 `VS` 3 `VS` 0 `VS` VZ ) )
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!_D33_dxdxdz = T $$( f $ Mon ( 2 `VS` 0 `VS` 1 `VS` VZ ) )
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!_D33_dxdydz = T $$( f $ Mon ( 1 `VS` 1 `VS` 1 `VS` VZ ) )
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!_D33_dxdzdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 2 `VS` VZ ) )
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!_D33_dydydz = T $$( f $ Mon ( 0 `VS` 2 `VS` 1 `VS` VZ ) )
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!_D33_dydzdz = T $$( f $ Mon ( 0 `VS` 1 `VS` 2 `VS` VZ ) )
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!_D33_dzdzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 3 `VS` VZ ) )
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_D33_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` VZ ) )
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_D33_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` VZ ) )
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_D33_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` VZ ) )
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_D33_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` VZ ) )
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_D33_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` VZ ) )
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_D33_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` VZ ) )
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_D33_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` VZ ) )
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_D33_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` VZ ) )
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_D33_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` VZ ) )
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_D33_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` VZ ) )
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_D33_dxdxdx = T $$( f $ Mon ( 3 `VS` 0 `VS` 0 `VS` VZ ) )
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_D33_dxdxdy = T $$( f $ Mon ( 2 `VS` 1 `VS` 0 `VS` VZ ) )
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_D33_dxdydy = T $$( f $ Mon ( 1 `VS` 2 `VS` 0 `VS` VZ ) )
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_D33_dydydy = T $$( f $ Mon ( 0 `VS` 3 `VS` 0 `VS` VZ ) )
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_D33_dxdxdz = T $$( f $ Mon ( 2 `VS` 0 `VS` 1 `VS` VZ ) )
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_D33_dxdydz = T $$( f $ Mon ( 1 `VS` 1 `VS` 1 `VS` VZ ) )
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_D33_dxdzdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 2 `VS` VZ ) )
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_D33_dydydz = T $$( f $ Mon ( 0 `VS` 2 `VS` 1 `VS` VZ ) )
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_D33_dydzdz = T $$( f $ Mon ( 0 `VS` 1 `VS` 2 `VS` VZ ) )
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_D33_dzdzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 3 `VS` VZ ) )
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in D33 { .. } ||]
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monIndex d = \ case
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@ -505,6 +505,7 @@ instance MonomialBasis D3𝔸3 where
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Mon ( 2 `VS` 0 `VS` 1 `VS` VZ ) -> [|| unT $ _D33_dxdxdz $$d ||]
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Mon ( 1 `VS` 1 `VS` 1 `VS` VZ ) -> [|| unT $ _D33_dxdydz $$d ||]
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Mon ( 1 `VS` 0 `VS` 2 `VS` VZ ) -> [|| unT $ _D33_dxdzdz $$d ||]
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Mon ( 0 `VS` 2 `VS` 1 `VS` VZ ) -> [|| unT $ _D33_dydydz $$d ||]
|
||||
Mon ( 0 `VS` 1 `VS` 2 `VS` VZ ) -> [|| unT $ _D33_dydzdz $$d ||]
|
||||
Mon ( 0 `VS` 0 `VS` 3 `VS` VZ ) -> [|| unT $ _D33_dzdzdz $$d ||]
|
||||
_ -> [|| _D33_v $$d ||]
|
||||
|
|
@ -514,11 +515,11 @@ type instance Vars D1𝔸4 = 4
|
|||
instance MonomialBasis D1𝔸4 where
|
||||
monTabulate f =
|
||||
[|| let
|
||||
!_D14_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D14_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D14_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D14_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D14_dw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D14_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D14_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D14_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D14_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D14_dw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
in D14 { .. } ||]
|
||||
|
||||
monIndex d = \ case
|
||||
|
|
@ -533,21 +534,21 @@ type instance Vars D2𝔸4 = 4
|
|||
instance MonomialBasis D2𝔸4 where
|
||||
monTabulate f =
|
||||
[|| let
|
||||
!_D24_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D24_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
!_D24_dxdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D24_dydw = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D24_dzdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
!_D24_dwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
_D24_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D24_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D24_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D24_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D24_dw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D24_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D24_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D24_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D24_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D24_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D24_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
_D24_dxdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D24_dydw = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D24_dzdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
_D24_dwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
in D24 { .. } ||]
|
||||
|
||||
monIndex d = \ case
|
||||
|
|
@ -573,41 +574,41 @@ type instance Vars D3𝔸4 = 4
|
|||
instance MonomialBasis D3𝔸4 where
|
||||
monTabulate f =
|
||||
[|| let
|
||||
!_D34_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dydw = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dzdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
!_D34_dxdxdx = T $$( f $ Mon ( 3 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdxdy = T $$( f $ Mon ( 2 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdydy = T $$( f $ Mon ( 1 `VS` 2 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dydydy = T $$( f $ Mon ( 0 `VS` 3 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdxdz = T $$( f $ Mon ( 2 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdydz = T $$( f $ Mon ( 1 `VS` 1 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdzdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dydydz = T $$( f $ Mon ( 0 `VS` 2 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dydzdz = T $$( f $ Mon ( 0 `VS` 1 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dzdzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 3 `VS` 0 `VS` VZ ) )
|
||||
!_D34_dxdxdw = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dxdydw = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dydydw = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dxdzdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dydzdw = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dzdzdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` 1 `VS` VZ ) )
|
||||
!_D34_dxdwdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
!_D34_dydwdw = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
!_D34_dzdwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 2 `VS` VZ ) )
|
||||
!_D34_dwdwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 3 `VS` VZ ) )
|
||||
_D34_v = $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dx = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dy = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dz = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D34_dw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D34_dxdx = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdy = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dydy = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D34_dydz = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D34_dzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D34_dydw = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D34_dzdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
_D34_dwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
_D34_dxdxdx = T $$( f $ Mon ( 3 `VS` 0 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdxdy = T $$( f $ Mon ( 2 `VS` 1 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdydy = T $$( f $ Mon ( 1 `VS` 2 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dydydy = T $$( f $ Mon ( 0 `VS` 3 `VS` 0 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdxdz = T $$( f $ Mon ( 2 `VS` 0 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdydz = T $$( f $ Mon ( 1 `VS` 1 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdzdz = T $$( f $ Mon ( 1 `VS` 0 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
_D34_dydydz = T $$( f $ Mon ( 0 `VS` 2 `VS` 1 `VS` 0 `VS` VZ ) )
|
||||
_D34_dydzdz = T $$( f $ Mon ( 0 `VS` 1 `VS` 2 `VS` 0 `VS` VZ ) )
|
||||
_D34_dzdzdz = T $$( f $ Mon ( 0 `VS` 0 `VS` 3 `VS` 0 `VS` VZ ) )
|
||||
_D34_dxdxdw = T $$( f $ Mon ( 2 `VS` 0 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D34_dxdydw = T $$( f $ Mon ( 1 `VS` 1 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D34_dydydw = T $$( f $ Mon ( 0 `VS` 2 `VS` 0 `VS` 1 `VS` VZ ) )
|
||||
_D34_dxdzdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
_D34_dydzdw = T $$( f $ Mon ( 0 `VS` 1 `VS` 1 `VS` 1 `VS` VZ ) )
|
||||
_D34_dzdzdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 2 `VS` 1 `VS` VZ ) )
|
||||
_D34_dxdwdw = T $$( f $ Mon ( 1 `VS` 0 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
_D34_dydwdw = T $$( f $ Mon ( 0 `VS` 1 `VS` 0 `VS` 2 `VS` VZ ) )
|
||||
_D34_dzdwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 1 `VS` 2 `VS` VZ ) )
|
||||
_D34_dwdwdw = T $$( f $ Mon ( 0 `VS` 0 `VS` 0 `VS` 3 `VS` VZ ) )
|
||||
in D34 { .. } ||]
|
||||
|
||||
monIndex d = \ case
|
||||
|
|
|
|||
|
|
@ -180,10 +180,10 @@ instance HasEnvelopeEquation 2 where
|
|||
-- ∂²c/∂s² = ∂²b/∂s²
|
||||
|
||||
envelopeEquation co ( D22 _ c_t c_s c_tt c_ts c_ss ) =
|
||||
let !ee = c_t × c_s
|
||||
!ee_t = c_tt × c_s + c_t × c_ts
|
||||
!ee_s = c_ts × c_s + c_t × c_ss
|
||||
!𝛿E𝛿sdcdt = ee_s *^ c_t ^-^ ee_t *^ c_s
|
||||
let ee = c_t × c_s
|
||||
ee_t = c_tt × c_s + c_t × c_ts
|
||||
ee_s = c_ts × c_s + c_t × c_ss
|
||||
𝛿E𝛿sdcdt = ee_s *^ c_t ^-^ ee_t *^ c_s
|
||||
-- TODO: we get c_t * c_t and c_s * c_s terms...
|
||||
-- These could be squares (better with interval arithmetic)?
|
||||
in ( D12 ( co ee ) ( T $ co ee_t ) ( T $ co ee_s )
|
||||
|
|
@ -235,24 +235,24 @@ instance HasEnvelopeEquation 3 where
|
|||
( D32 _ c_t c_s
|
||||
c_tt c_ts c_ss
|
||||
c_ttt c_tts c_tss c_sss )
|
||||
= let !ee = c_t × c_s
|
||||
!ee_t = c_tt × c_s + c_t × c_ts
|
||||
!ee_s = c_ts × c_s + c_t × c_ss
|
||||
!ee_tt = c_ttt × c_s
|
||||
+ c_tt × c_ts * 2
|
||||
+ c_t × c_tts
|
||||
!ee_ts = c_tts × c_s
|
||||
+ c_tt × c_ss
|
||||
-- + c_ts × c_ts -- cancels out
|
||||
+ c_t × c_tss
|
||||
!ee_ss = c_tss × c_s
|
||||
+ c_ts × c_ss * 2
|
||||
+ c_t × c_sss
|
||||
!𝛿E𝛿sdcdt = ee_s *^ c_t ^-^ ee_t *^ c_s
|
||||
!𝛿E𝛿sdcdt_t = ee_ts *^ c_t ^+^ ee_s *^ c_tt
|
||||
^-^ ( ee_tt *^ c_s ^+^ ee_t *^ c_ts )
|
||||
!𝛿E𝛿sdcdt_s = ee_ss *^ c_t ^+^ ee_s *^ c_ts
|
||||
^-^ ( ee_ts *^ c_s ^+^ ee_t *^ c_ss )
|
||||
= let ee = c_t × c_s
|
||||
ee_t = c_tt × c_s + c_t × c_ts
|
||||
ee_s = c_ts × c_s + c_t × c_ss
|
||||
ee_tt = c_ttt × c_s
|
||||
+ c_tt × c_ts * 2
|
||||
+ c_t × c_tts
|
||||
ee_ts = c_tts × c_s
|
||||
+ c_tt × c_ss
|
||||
-- + c_ts × c_ts -- cancels out
|
||||
+ c_t × c_tss
|
||||
ee_ss = c_tss × c_s
|
||||
+ c_ts × c_ss * 2
|
||||
+ c_t × c_sss
|
||||
𝛿E𝛿sdcdt = ee_s *^ c_t ^-^ ee_t *^ c_s
|
||||
𝛿E𝛿sdcdt_t = ee_ts *^ c_t ^+^ ee_s *^ c_tt
|
||||
^-^ ( ee_tt *^ c_s ^+^ ee_t *^ c_ts )
|
||||
𝛿E𝛿sdcdt_s = ee_ss *^ c_t ^+^ ee_s *^ c_ts
|
||||
^-^ ( ee_ts *^ c_s ^+^ ee_t *^ c_ss )
|
||||
in ( D22
|
||||
( co ee )
|
||||
( T $ co ee_t ) ( T $ co ee_s )
|
||||
|
|
|
|||
|
|
@ -122,7 +122,9 @@ data Vec n a where
|
|||
-- can't be strict, otherwise we can't conveniently
|
||||
-- unsafeCoerce from lists
|
||||
|
||||
deriving stock instance Show a => Show ( Vec n a )
|
||||
--deriving stock instance Show a => Show ( Vec n a )
|
||||
instance Show a => Show ( Vec n a ) where
|
||||
showsPrec p v = showsPrec p ( unsafeCoerce v :: [ a ] )
|
||||
|
||||
deriving stock instance Functor ( Vec n )
|
||||
deriving stock instance Foldable ( Vec n )
|
||||
|
|
@ -137,9 +139,7 @@ instance Ord a => Ord ( Vec n a ) where
|
|||
|
||||
infixl 9 !
|
||||
(!) :: forall l a. Vec l a -> Fin l -> a
|
||||
VS a _ ! Fin 1 = a
|
||||
VS _ a ! Fin i = a ! Fin ( i - 1 )
|
||||
_ ! _ = error "impossible: Fin 0 is uninhabited"
|
||||
v ! Fin i = ( unsafeCoerce v :: [ a ] ) !! fromIntegral i
|
||||
|
||||
find :: forall l a. ( a -> Bool ) -> Vec l a -> MFin l
|
||||
find f v = MFin ( find_ 1 v )
|
||||
|
|
|
|||
319
brush-strokes/src/test/Main.hs
Normal file
319
brush-strokes/src/test/Main.hs
Normal file
|
|
@ -0,0 +1,319 @@
|
|||
{-# LANGUAGE AllowAmbiguousTypes #-}
|
||||
{-# LANGUAGE NumericUnderscores #-}
|
||||
{-# LANGUAGE ScopedTypeVariables #-}
|
||||
{-# LANGUAGE TemplateHaskell #-}
|
||||
|
||||
module Main (main) where
|
||||
|
||||
-- base
|
||||
import Prelude hiding
|
||||
( Num(..), (^) )
|
||||
import Data.Foldable
|
||||
( toList )
|
||||
import Data.List.NonEmpty
|
||||
( NonEmpty(..) )
|
||||
import Data.Maybe
|
||||
( catMaybes )
|
||||
import Data.Traversable
|
||||
( for )
|
||||
import Unsafe.Coerce
|
||||
( unsafeCoerce )
|
||||
|
||||
-- brush-strokes
|
||||
import Math.Algebra.Dual
|
||||
import Math.Linear
|
||||
import Math.Module
|
||||
import Math.Monomial
|
||||
( multiSubsetSum, multiSubsetsSum
|
||||
, MonomialBasis ( monTabulate, monIndex )
|
||||
)
|
||||
import Math.Ring
|
||||
|
||||
-- hspray
|
||||
import Math.Algebra.Hspray
|
||||
( Spray )
|
||||
import qualified Math.Algebra.Hspray as Spray
|
||||
|
||||
-- falsify
|
||||
import Test.Tasty.Falsify
|
||||
import qualified Test.Falsify.Generator as Falsify
|
||||
( Gen )
|
||||
import qualified Test.Falsify.Generator as Falsify.Gen
|
||||
import Test.Falsify.Predicate
|
||||
( (.$) )
|
||||
import qualified Test.Falsify.Predicate as Falsify.Prop
|
||||
import qualified Test.Falsify.Property as Falsify
|
||||
( Property
|
||||
, assert
|
||||
, discard
|
||||
, gen, genWith
|
||||
)
|
||||
import qualified Test.Falsify.Range as Falsify
|
||||
|
||||
-- tasty
|
||||
import qualified Test.Tasty as Tasty
|
||||
|
||||
-- unordered-containers
|
||||
import qualified Data.HashMap.Lazy as HashMap
|
||||
|
||||
--------------------------------------------------------------------------------
|
||||
|
||||
|
||||
main :: IO ()
|
||||
main =
|
||||
Tasty.defaultMain $
|
||||
Tasty.testGroup "brush-strokes property tests"
|
||||
[ Tasty.testGroup "Automatic differentiation"
|
||||
[ Tasty.testGroup "Monomial basis"
|
||||
[ testProperty "Round trip D33" testMonomialBasisD33
|
||||
]
|
||||
, Tasty.testGroup "Monomials"
|
||||
[ Tasty.testGroup "multiSubsetSum"
|
||||
[ testProperty "multiSubsetSum valid" testMultiSubsetSumValid
|
||||
, testProperty "multiSubsetSum exhaustive" testMultiSubsetSumExhaustive
|
||||
]
|
||||
-- , Tasty.testGroup "multiSubsetsSum"
|
||||
-- [ testProperty "multiSubsetsSum exhaustive" testMultiSubsetsSumExhaustive
|
||||
-- ]
|
||||
]
|
||||
, Tasty.testGroup "chainRule1NQ"
|
||||
[ testProperty "chainRule1NQ_1" testChainRule1NQ_1
|
||||
, testProperty "chainRule1NQ_2" testChainRule1NQ_2
|
||||
, testProperty "chainRule1NQ_3" testChainRule1NQ_3
|
||||
]
|
||||
]
|
||||
]
|
||||
|
||||
-- | Check that the 'multiSubsetSum' function returns valid answers, i.e.
|
||||
-- all returned multisubsets have the desired size and sum.
|
||||
testMultiSubsetSumValid :: Falsify.Property ()
|
||||
testMultiSubsetSumValid = do
|
||||
rg <- Falsify.genWith (\ rg -> Just $ "range = " ++ show rg ) $ Falsify.Gen.inRange $ Falsify.between ( 1, 6 )
|
||||
sz <- Falsify.genWith (\ sz -> Just $ "size = " ++ show sz ) $ Falsify.Gen.inRange $ Falsify.between ( 0, 20 )
|
||||
tot <- Falsify.genWith (\ tot -> Just $ "tot = " ++ show tot) $ Falsify.Gen.inRange $ Falsify.between ( sz, sz * rg )
|
||||
let range = [ 1 .. rg ]
|
||||
mss = multiSubsetSum sz tot range
|
||||
case mss of
|
||||
[] -> Falsify.discard
|
||||
r:rs -> do
|
||||
ms <- Falsify.gen $ Falsify.Gen.elem ( r :| rs )
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.eq
|
||||
.$ ("(sz, tot)", (sz, tot) )
|
||||
.$ ("computed (sz, tot)", (size ms, total ms))
|
||||
where
|
||||
size, total :: [ ( Word, Word ) ] -> Word
|
||||
size [] = 0
|
||||
size ((_,n):ins) = n + size ins
|
||||
total [] = 0
|
||||
total ((i,n):ins) = i * n + total ins
|
||||
|
||||
-- | Check that the 'multiSubsetSum' function returns all multisubsets of
|
||||
-- the given set, by generating a random multisubset, computing its size, and
|
||||
-- checking it belongs to the output of the 'multiSubsetSum' function.
|
||||
testMultiSubsetSumExhaustive :: Falsify.Property ()
|
||||
testMultiSubsetSumExhaustive = do
|
||||
rg <- Falsify.genWith (\ rg -> Just $ "range = " ++ show rg) $ Falsify.Gen.inRange $ Falsify.between ( 1, 6 )
|
||||
sz <- Falsify.genWith (\ sz -> Just $ "size = " ++ show sz) $ Falsify.Gen.inRange $ Falsify.between ( 0, 10 )
|
||||
let range = [ 1 .. rg ]
|
||||
(multiSubset, tot) <- Falsify.genWith (\ ms -> Just $ "multisubset = " ++ show ms) $ genMultiSubset range sz
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.elem
|
||||
.$ ("all multisubsets", multiSubsetSum sz tot range )
|
||||
.$ ("random multisubset", multiSubset)
|
||||
|
||||
genMultiSubset :: [ Word ] -> Word -> Falsify.Gen ( [ ( Word, Word ) ] , Word )
|
||||
genMultiSubset [i] sz =
|
||||
return $
|
||||
if sz == 0
|
||||
then ( [], 0 )
|
||||
else ( [ ( i, sz ) ], i * sz )
|
||||
genMultiSubset (i:is) sz = do
|
||||
nb <- Falsify.Gen.inRange $ Falsify.between ( 0, sz )
|
||||
(rest, tot) <- genMultiSubset is ( sz - nb )
|
||||
return $ ( if nb == 0 then rest else ( i, nb ) : rest, tot + nb * i )
|
||||
genMultiSubset [] _ = error "impossible"
|
||||
|
||||
coerceVec1 :: [ a ] -> Vec n a
|
||||
coerceVec1 = unsafeCoerce
|
||||
|
||||
coerceVec2 :: Vec n a -> [ a ]
|
||||
coerceVec2 = toList
|
||||
|
||||
-- | Check that the 'multiSubsetSums' function returns all collections of
|
||||
-- multisubsets of the given set (see 'testMultiSubsetSumExhaustive').
|
||||
testMultiSubsetsSumExhaustive :: Falsify.Property ()
|
||||
testMultiSubsetsSumExhaustive = do
|
||||
rg <- Falsify.genWith (\ rg -> Just $ "range = " ++ show rg) $ Falsify.Gen.inRange $ Falsify.between ( 1, 5 )
|
||||
let range = [ 1 .. rg ]
|
||||
n <- Falsify.genWith (\ n -> Just $ "n = " ++ show n ) $ Falsify.Gen.inRange $ Falsify.between ( 1, 10 )
|
||||
multiSubsets <- for ( [ 0 .. n - 1 ] :: [ Word ] ) \ i -> do
|
||||
sz <- Falsify.gen $ Falsify.Gen.inRange $ Falsify.between ( 0, 5 )
|
||||
( ms, tot ) <- Falsify.genWith ( \ ms -> Just $ "ms_" ++ show i ++ " = " ++ show ms ) $ genMultiSubset range sz
|
||||
return ( ms, sz, tot )
|
||||
let mss = map ( \ (ms, _,_) -> ms ) multiSubsets
|
||||
szs = map ( \ (_,sz,_) -> sz) multiSubsets
|
||||
tot = sum $ map ( \(_,_,t) -> t) multiSubsets
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.elem
|
||||
.$ ("all multisubsets", map coerceVec2 $ multiSubsetsSum range tot $ coerceVec1 szs )
|
||||
.$ ("random multisubset", mss)
|
||||
|
||||
|
||||
testRoundTrip
|
||||
:: ( Show a, Eq a )
|
||||
=> Falsify.Gen a
|
||||
-> ( a -> a )
|
||||
-> Falsify.Property ()
|
||||
testRoundTrip g roundTrip = do
|
||||
d <- Falsify.gen g
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.eq
|
||||
.$ ("value", d )
|
||||
.$ ("round tripped", roundTrip d )
|
||||
|
||||
testMonomialBasisD33 :: Falsify.Property ()
|
||||
testMonomialBasisD33 =
|
||||
testRoundTrip genD33 \ d -> $$( monTabulate \ mon -> monIndex [|| d ||] mon )
|
||||
where
|
||||
genD33 :: Falsify.Gen ( D3𝔸3 Double )
|
||||
genD33 =
|
||||
D33 <$> (unT <$> g)
|
||||
<*> g <*> g <*> g
|
||||
<*> g <*> g <*> g <*> g <*> g <*> g
|
||||
<*> g <*> g <*> g <*> g <*> g <*> g <*> g <*> g <*> g <*> g
|
||||
|
||||
g :: Falsify.Gen ( T Double )
|
||||
g = T . fromIntegral <$> Falsify.Gen.inRange ( Falsify.withOrigin ( -100, 100 ) ( 0 :: Int ) )
|
||||
|
||||
-- | Test the Faà di Bruno formula on polynomials, with a composition
|
||||
-- \( g(f_1(x), f_2(x), .., f_n(x)) \).
|
||||
testChainRule1NQ_1 :: Falsify.Property ()
|
||||
testChainRule1NQ_1 = do
|
||||
f <- genSpray "f" 1
|
||||
g <- genSpray "g" 1
|
||||
let gof_spray = Spray.composeSpray g [f]
|
||||
gof_chain =
|
||||
chain @_ @3 @( ℝ 1 ) ( ℝ1 <$> fromSpray @3 @( ℝ 1 ) f ) ( fromSpray @3 @( ℝ 1 ) g )
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.eq
|
||||
.$ ("direct", fromSpray @3 @( ℝ 1 ) gof_spray )
|
||||
.$ ("chain rule", gof_chain )
|
||||
|
||||
-- | Test the Faà di Bruno formula on polynomials, with a composition
|
||||
-- \( g(f_1(x), f_2(x), .., f_n(x)) \).
|
||||
testChainRule1NQ_2 :: Falsify.Property ()
|
||||
testChainRule1NQ_2 = do
|
||||
f1 <- genSpray "f1" 1
|
||||
f2 <- genSpray "f2" 1
|
||||
g <- genSpray "g" 2
|
||||
let gof_spray = Spray.composeSpray g [f1, f2]
|
||||
f = ℝ2 <$> fromSpray @3 @( ℝ 1 ) f1
|
||||
<*> fromSpray @3 @( ℝ 1 ) f2
|
||||
gof_chain =
|
||||
chain @_ @3 @( ℝ 2 ) f ( fromSpray @3 @( ℝ 2 ) g )
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.eq
|
||||
.$ ("direct", fromSpray @3 @( ℝ 1 ) gof_spray )
|
||||
.$ ("chain rule", gof_chain )
|
||||
|
||||
-- | Test the Faà di Bruno formula on polynomials, with a composition
|
||||
-- \( g(f_1(x), f_2(x), .., f_n(x)) \).
|
||||
testChainRule1NQ_3 :: Falsify.Property ()
|
||||
testChainRule1NQ_3 = do
|
||||
f1 <- genSpray "f1" 1
|
||||
f2 <- genSpray "f2" 1
|
||||
f3 <- genSpray "f3" 1
|
||||
g <- genSpray "g" 3
|
||||
let gof_spray = Spray.composeSpray g [f1, f2, f3]
|
||||
f = ℝ3 <$> fromSpray @3 @( ℝ 1 ) f1
|
||||
<*> fromSpray @3 @( ℝ 1 ) f2
|
||||
<*> fromSpray @3 @( ℝ 1 ) f3
|
||||
gof_chain =
|
||||
chain @_ @3 @( ℝ 3 ) f ( fromSpray @3 @( ℝ 3 ) g )
|
||||
Falsify.assert
|
||||
$ Falsify.Prop.eq
|
||||
.$ ("direct", fromSpray @3 @( ℝ 1 ) gof_spray )
|
||||
.$ ("chain rule", gof_chain )
|
||||
|
||||
class FromSpray v where
|
||||
varFn :: Int -> v
|
||||
linFn :: v -> Int -> Double
|
||||
|
||||
instance FromSpray ( ℝ 1 ) where
|
||||
varFn = \case
|
||||
0 -> ℝ1 1
|
||||
i -> error $ "fromSpray in 1d but variable " ++ show i
|
||||
linFn ( ℝ1 x ) = \case
|
||||
0 -> x
|
||||
i -> error $ "fromSpray in 1d but variable " ++ show i
|
||||
instance FromSpray ( ℝ 2 ) where
|
||||
varFn = \case
|
||||
0 -> ℝ2 1 0
|
||||
1 -> ℝ2 0 1
|
||||
i -> error $ "fromSpray in 2d but variable " ++ show i
|
||||
linFn ( ℝ2 x y ) = \case
|
||||
0 -> x
|
||||
1 -> y
|
||||
i -> error $ "fromSpray in 2d but variable " ++ show i
|
||||
instance FromSpray ( ℝ 3 ) where
|
||||
varFn = \case
|
||||
0 -> ℝ3 1 0 0
|
||||
1 -> ℝ3 0 1 0
|
||||
2 -> ℝ3 0 0 1
|
||||
i -> error $ "fromSpray in 3d but variable " ++ show i
|
||||
linFn ( ℝ3 x y z ) = \case
|
||||
0 -> x
|
||||
1 -> y
|
||||
2 -> z
|
||||
i -> error $ "fromSpray in 3d but variable " ++ show i
|
||||
|
||||
genSpray :: String -> Word -> Falsify.Property ( Spray Double )
|
||||
genSpray lbl nbVars = Falsify.genWith (\ p -> Just $ lbl ++ " = " ++ Spray.prettySpray show "x" p) $ do
|
||||
deg <- Falsify.Gen.inRange $ Falsify.between ( 0, 10 )
|
||||
let mons = allMonomials deg nbVars
|
||||
coeffs <-
|
||||
for mons $ \ mon -> do
|
||||
if all (== 0) mon
|
||||
then return Nothing
|
||||
else do
|
||||
nonZero <- Falsify.Gen.bool False
|
||||
if nonZero
|
||||
then return Nothing
|
||||
else do
|
||||
-- Just use (small) integral values in tests for now,
|
||||
-- to avoid errors arising from rounding.
|
||||
c <- Falsify.Gen.inRange $ Falsify.withOrigin ( -100, 100 ) ( 0 :: Int )
|
||||
return $ Just ( map fromIntegral mon, fromIntegral c )
|
||||
return $ Spray.fromList $ catMaybes coeffs
|
||||
|
||||
allMonomials :: Word -> Word -> [ [ Word ] ]
|
||||
allMonomials k _ | k < 0 = []
|
||||
allMonomials _ 0 = [ [] ]
|
||||
allMonomials 0 n = [ replicate ( fromIntegral n ) 0 ]
|
||||
allMonomials k n = [ i : is | i <- reverse [ 0 .. k ], is <- allMonomials ( k - i ) ( n - 1 ) ]
|
||||
|
||||
-- | Convert a multivariate polynomial from the @hspray@ library to the dual algebra.
|
||||
fromSpray
|
||||
:: forall k v
|
||||
. ( HasChainRule Double k v
|
||||
, Module Double (T v)
|
||||
, Applicative ( D k v )
|
||||
, Ring ( D k v Double )
|
||||
, FromSpray v
|
||||
)
|
||||
=> Spray Double
|
||||
-> D k v Double
|
||||
fromSpray coeffs = HashMap.foldlWithKey' addMonomial ( konst @Double @k @v $ HashMap.lookupDefault 0 (Spray.Powers mempty 0) coeffs ) coeffs
|
||||
where
|
||||
addMonomial :: D k v Double -> Spray.Powers -> Double -> D k v Double
|
||||
addMonomial a xs c = a + monomial c ( toList $ Spray.exponents xs )
|
||||
monomial :: Double -> [ Int ] -> D k v Double
|
||||
monomial _ [] = konst @Double @k @v 0
|
||||
monomial c is = fmap ( c * ) $ go 0 is
|
||||
go :: Int -> [ Int ] -> D k v Double
|
||||
go _ [] = konst @Double @k @v 1
|
||||
go d (i : is) = pow d i * go ( d + 1 ) is
|
||||
pow :: Int -> Int -> D k v Double
|
||||
pow _ 0 = konst @Double @k @v 1
|
||||
pow d i = linearD @Double @k @v ( \ x -> linFn @v x d ) ( unT origin :: v ) ^ ( fromIntegral i )
|
||||
Loading…
Reference in a new issue