manifolds 0.1.5.0 → 0.1.5.1

raw patch · 3 files changed

+38/−10 lines, 3 filesdep ~hmatrix

Dependency ranges changed: hmatrix

Files

• Data/LinearMap/HerMetric.hs +4/−4
• Data/Manifold/PseudoAffine.hs +32/−4
• manifolds.cabal +2/−2

@@ -267,27 +267,27 @@ eigenSpan :: (HasMetric v, Scalar v ~ ℝ) => HerMetric' v -> [v] eigenSpan (HerMetric' Nothing) = [] eigenSpan (HerMetric' (Just m)) = map fromPackedVector eigSpan- where (μs,vsm) = HMat.eigSH m -- TODO: replace with `eigSH'`, which is unchecked+ where (μs,vsm) = HMat.eigSH' m -- TODO: replace with `eigSH'`, which is unchecked                                -- (`HerMetric` is always Hermitian!)        eigSpan = zipWith (HMat.scale . sqrt) (HMat.toList μs) (HMat.toColumns vsm)  eigenSpan' :: (HasMetric v, Scalar v ~ ℝ) => HerMetric v -> [DualSpace v] eigenSpan' (HerMetric Nothing) = [] eigenSpan' (HerMetric (Just m)) = map fromPackedVector eigSpan- where (μs,vsm) = HMat.eigSH m -- TODO: replace with `eigSH'`, which is unchecked+ where (μs,vsm) = HMat.eigSH' m -- TODO: replace with `eigSH'`, which is unchecked                                -- (`HerMetric` is always Hermitian!)        eigSpan = zipWith (HMat.scale . sqrt) (HMat.toList μs) (HMat.toColumns vsm)  eigenCoSpan :: (HasMetric v, Scalar v ~ ℝ) => HerMetric' v -> [DualSpace v] eigenCoSpan (HerMetric' Nothing) = [] eigenCoSpan (HerMetric' (Just m)) = map fromPackedVector eigSpan- where (μs,vsm) = HMat.eigSH m -- TODO: replace with `eigSH'`, which is unchecked+ where (μs,vsm) = HMat.eigSH' m -- TODO: replace with `eigSH'`, which is unchecked                                -- (`HerMetric` is always Hermitian!)        eigSpan = zipWith (HMat.scale . recip . sqrt) (HMat.toList μs) (HMat.toColumns vsm) eigenCoSpan' :: (HasMetric v, Scalar v ~ ℝ) => HerMetric v -> [v] eigenCoSpan' (HerMetric Nothing) = [] eigenCoSpan' (HerMetric (Just m)) = map fromPackedVector eigSpan- where (μs,vsm) = HMat.eigSH m -- TODO: replace with `eigSH'`, which is unchecked+ where (μs,vsm) = HMat.eigSH' m -- TODO: replace with `eigSH'`, which is unchecked                                -- (`HerMetric` is always Hermitian!)        eigSpan = zipWith (HMat.scale . recip . sqrt) (HMat.toList μs) (HMat.toColumns vsm) 

@@ -50,7 +50,6 @@               Manifold             , Semimanifold(..)             , PseudoAffine(..)-            , Metric, Metric', euclideanMetric             -- * Regions within a manifold             , Region             -- * Hierarchy of manifold-categories@@ -60,7 +59,11 @@             , PWDiffable             -- ** Region-wise defined diff'able funcs             , RWDiffable-            -- * Helper constraints+            -- * Type definitions+            -- ** Metrics+            , Metric, Metric', euclideanMetric+            , RieMetric, RieMetric'+            -- ** Constraints             , RealDimension, AffineManifold             , LinearManifold             , WithField@@ -68,6 +71,7 @@             , EuclidSpace             -- * Misc             , palerp+            , discretisePath             ) where      @@ -221,9 +225,8 @@ class (PseudoAffine m, LinearManifold (Needle m), Interior m ~ m) => Manifold m instance (PseudoAffine m, LinearManifold (Needle m), Interior m ~ m) => Manifold m -type LocallyScalable s x = ( PseudoAffine x, (Needle x) ~ Needle x+type LocallyScalable s x = ( PseudoAffine x                            , HasMetric (Needle x)-                           , DualSpace (Needle x) ~ DualSpace (Needle x)                            , s ~ Scalar (Needle x) )  -- | Basically just an “updated” version of the 'VectorSpace' class.@@ -273,6 +276,12 @@ type Metric x = HerMetric (Needle x) type Metric' x = HerMetric' (Needle x) +-- | A Riemannian metric assigns each point on a manifold a scalar product on the tangent space.+--   Note that this association is /not/ continuous, because the charts/tangent spaces in the bundle+--   are a priori disjoint. However, for a proper Riemannian metric, all arising expressions+--   of scalar products from needles between points on the manifold ought to be differentiable.+type RieMetric x = x -> Metric x+type RieMetric' x = x -> Metric' x  -- | Interpolate between points, approximately linearly. For --   points that aren't close neighbours (i.e. lie in an almost@@ -287,6 +296,25 @@ palerp p1 p2 = case (fromInterior p2 :: x) .-~. p1 of   Option (Just v) -> return $ \t -> p1 .+~^ t *^ v   _ -> Hask.empty++++++discretisePath :: 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.+      -> 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)+ where traceFwd x₀ dir+         | abs x₀ > 1e+100  = [(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)   

@@ -1,7 +1,7 @@ Name:                manifolds-Version:             0.1.5.0+Version:             0.1.5.1 Category:            Math-Synopsis:            Working with manifolds in a direct, embedding-free way.+Synopsis:            Coordinate-free hypersurfaces Description:         Manifolds, a generalisation of the notion of “smooth curves” or surfaces,                      are topological spaces /locally homeomorphic to a vector space/. This gives                      rise to what is actually the most natural / mathematically elegant way of dealing