manifolds 0.1.5.1 → 0.1.5.2

raw patch · 3 files changed

+99/−11 lines, 3 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• Data/LinearMap/HerMetric.hs +6/−3
• Data/Manifold/PseudoAffine.hs +92/−7
• manifolds.cabal +1/−1

@@ -28,7 +28,7 @@   -- * One-dimensional axes and product spaces   , factoriseMetric, factoriseMetric'   , productMetric, productMetric'-  , metricAsLength, metric'AsLength+  , metricAsLength, metricFromLength, metric'AsLength   -- * Utility for metrics   , transformMetric, transformMetric'   , dualiseMetric, dualiseMetric'@@ -214,7 +214,7 @@ transformMetric :: (HasMetric v, HasMetric w, Scalar v ~ Scalar w)            => (w :-* v) -> HerMetric v -> HerMetric w transformMetric _ (HerMetric Nothing) = HerMetric Nothing-transformMetric t (HerMetric (Just m)) = matrixMetric $ HMat.tr tmat HMat.<> m HMat.<> tmat+transformMetric t (HerMetric (Just m)) = matrixMetric $ tmat HMat.<> m HMat.<> HMat.tr tmat  where tmat = asPackedMatrix t  transformMetric' :: ( HasMetric v, HasMetric w, Scalar v ~ Scalar w )@@ -515,8 +515,11 @@ metricAsLength :: HerMetric ℝ -> ℝ metricAsLength = recip . (`metric`1) +metricFromLength :: ℝ -> HerMetric ℝ+metricFromLength = projector . recip+ metric'AsLength :: HerMetric' ℝ -> ℝ-metric'AsLength = recip . (`metric'`1)+metric'AsLength = recip . (`metric'`1)  -- do we really want `recip` here?   spanHilbertSubspace :: ∀ s v w

@@ -52,6 +52,7 @@             , PseudoAffine(..)             -- * Regions within a manifold             , Region+            , smoothIndicator             -- * Hierarchy of manifold-categories             -- ** Everywhere differentiable functions             , Differentiable@@ -71,7 +72,11 @@             , EuclidSpace             -- * Misc             , palerp-            , discretisePath+            , discretisePathIn+            , discretisePathSegs+            , continuousIntervals+            , regionOfContinuityAround+            , analyseLocalBehaviour             ) where      @@ -301,23 +306,103 @@   -discretisePath :: WithField ℝ Manifold x+discretisePathIn :: WithField ℝ Manifold x       => Int                    -- ^ Limit the number of steps taken in either direction. Note this will not cap the resolution but /length/ of the discretised path.+      -> Region ℝ ℝ             -- ^ Parameter interval of interest       -> RieMetric x            -- ^ Inaccuracy allowance /ε/.       -> (Differentiable ℝ ℝ x) -- ^ Path specification.       -> [(ℝ,x)]                -- ^ Trail of points along the path, such that a linear interpolation deviates nowhere by more as /ε/.-discretisePath nLim m (Differentiable f)-         = reverse (tail . take nLim $ traceFwd 0 (-1)) ++ take nLim (traceFwd 0 1)+discretisePathIn nLim (Region xm rLim) m (Differentiable f)+         = reverse (tail . take nLim $ traceFwd xm (-1)) ++ take nLim (traceFwd xm 1)  where traceFwd x₀ dir-         | abs x₀ > 1e+100  = [(x₀, fx₀)]-         | otherwise        = (x₀, fx₀) : traceFwd xn dir+         | rnfn x₀ < 0        = []+         | abs x₀ > hugeℝVal  = [(x₀, fx₀)] +         | otherwise          = (x₀, fx₀) : traceFwd xn dir         where (fx₀, _, δx²) = f x₀               εx = m fx₀               χ = metric (δx² εx) 1               xn = x₀ + dir * min (abs x₀+1) (recip χ)+       rnfn = case rLim of+                GlobalRegion -> const 1+                PreRegion (Differentiable pmbf) -> pmbf >>> \(q,_,_)->q+                       +discretisePathSegs :: WithField ℝ Manifold x+      => Int              -- ^ Maximum number of path segments and/or points per segment.+      -> RieMetric x      -- ^ Inaccuracy allowance /ε/.+      -> RWDiffable ℝ ℝ x -- ^ Path specification.+      -> [[(ℝ,x)]]        -- ^ Trail of points along the path, such that a linear interpolation deviates nowhere by more as /ε/.+discretisePathSegs nLim m (RWDiffable f) = jumpsFwd nLim 0 (True,True)+ where jumpsFwd nLim' x₀ (goL,goR)+         | abs x₀ > hugeℝVal      = []+         | Option Nothing <- fq₀  = error "`discretisePathSegs` not yet implemented for partial functions outside of a null set."+         | xr < -hugeℝVal+          || xr < hugeℝVal        = [pseg]+         | not goL                = pseg : jumpR+         | not goR                = pseg : jumpL+         | otherwise              = pseg : (zip jumpL jumpR >>= \(l,r)->[l,r])+        where (r₀, fq₀) = f x₀+              Option (Just lf) = fq₀+              pseg = first (subtract x₀) <$>+                  discretisePathIn nLim' (Region x₀ r₀) m (lf . actuallyAffine x₀ idL)+              ((xl,_):(xpl,_):_) = pseg+              ((xr,_):(xpr,_):_) = reverse pseg+              jumpR = jumpsFwd (nLim'-1) (xr*2-xpr) (False,goR)+              jumpL = jumpsFwd (nLim'-1) (xl*2-xpl) (goL,False)+              +             +continuousIntervals :: RWDiffable ℝ ℝ x -> (ℝ,ℝ) -> [(ℝ,ℝ)]+continuousIntervals (RWDiffable f) (xl,xr) = enter xl+ where enter x₀ = case f x₀ of +                    (GlobalRegion, _) -> [(xl,xr)]+                    (PreRegion r₀, _) -> exit r₀ x₀+        where exit :: Differentiable ℝ ℝ ℝ -> ℝ -> [(ℝ,ℝ)]+              exit (Differentiable r) x+               | x > xr           = [(x₀,xr)]+               | y' > 0          = exit (Differentiable r)+                                        (x + metricAsLength (δ (metricFromLength y)))+               | -y/y' < 1e-10   = (x₀,x) : enter (x + min 1e-100 (abs x * 1e-8))+               | otherwise       = exit (Differentiable r) xn+               where (y, y'm, δ) = r x+                     xn = bisBack $ x - y/y'+                      where bisBack xq+                              | ybm > 0    = xbm+                              | otherwise  = bisBack xbm+                             where (ybm, _, _) = r xbm+                                   xbm = (xq*9 + x)/10+                     y' = lapply y'm 1+              +analyseLocalBehaviour ::+    RWDiffable ℝ ℝ ℝ+ -> ℝ                      -- ^ /x/₀ value.+ -> Option ( (ℝ,ℝ)+           , ℝ->Option ℝ ) -- ^ /f/ /x/₀, derivative (i.e. Taylor-1-coefficient),+                           --   and reverse propagation of /O/ (/δ/²) bound.+analyseLocalBehaviour (RWDiffable f) x₀ = case f x₀ of+       (_, Option Nothing) -> Hask.empty+       (_, Option (Just (Differentiable fd))) -> return $+              let (fx, j, δf) = fd x₀+                  epsprop ε+                    | ε>0  = case metric (δf $ metricFromLength ε) 1 of+                               0  -> Hask.empty+                               δ' -> return $ recip δ'+                    | otherwise  = pure 0+              in ((fx, lapply j 1), epsprop) +-- | Represent a 'Region' by a smooth function which is positive within the region,+--   and crosses zero at the boundary.+smoothIndicator :: LocallyScalable ℝ q => Region ℝ q -> Differentiable ℝ q ℝ+smoothIndicator (Region _ GlobalRegion) = const 1+smoothIndicator (Region _ (PreRegion r)) = r +regionOfContinuityAround :: RWDiffable ℝ q x -> q -> Region ℝ q+regionOfContinuityAround (RWDiffable f) q = Region q . fst . f $ q+              +++hugeℝVal :: ℝ+hugeℝVal = 1e+100+ #define deriveAffine(t)          \ instance Semimanifold (t) where { \   type Needle (t) = Diff (t);      \@@ -515,7 +600,7 @@  dev_ε_δ :: RealDimension a                 => (a -> a) -> LinDevPropag a a-dev_ε_δ f d = let ε = 1 / metric d 1 in projector $ 1 / sqrt (f ε)+dev_ε_δ f d = let ε = 1 / metric d 1 in projector $ 1 / f ε  -- | The category of differentiable functions between manifolds over scalar @s@. --   

@@ -1,5 +1,5 @@ Name:                manifolds-Version:             0.1.5.1+Version:             0.1.5.2 Category:            Math Synopsis:            Coordinate-free hypersurfaces Description:         Manifolds, a generalisation of the notion of “smooth curves” or surfaces,