Add Mat6 and Mat7 synonyms.

[numerical-analysis.git] / src / FEM / R1.hs

diff --git a/src/FEM/R1.hs b/src/FEM/R1.hs
index 57e2412c83af938f736200bee0ce2b83299cff5f..ae7548a86d75d42311691c8bdcfa780384b3938c 100644 (file)
--- a/src/FEM/R1.hs
+++ b/src/FEM/R1.hs
@@ -281,22 +281,8 @@ big_Ns_matrix =
 --
 --   Examples:
 --
---   >>> import Linear.Matrix ( Col4, frobenius_norm, fromList )
---   >>> import Naturals ( N3, N4, N7 )
---
---   >>> let big_A = const (1::Double)
---   >>> let c x = sin x
---   >>> let f x = x*(sin x)
---   >>> let bdy = Left (Dirichlet (0,1::Double))
---   >>> let pde = PDE big_A c f bdy
---
---   >>> let i1 = (0.0,1/3)
---   >>> let i2 = (1/3,2/3)
---   >>> let i3 = (2/3,4/5)
---   >>> let i4 = (4/5,1.0)
---   >>> let mesh = fromList [[i1], [i2], [i3], [i4]] :: Col4 (Double,Double)
---   >>> let pvec = fromList [[2],[3],[2],[1]] :: Col4 Int
---   >>> let params = Params mesh pvec :: Params N4 N3 N7 Double
+--   >>> import Linear.Matrix ( Col7, frobenius_norm )
+--   >>> import FEM.R1.Example1 ( pde', params' )
 --
 --   >>> let f1 = [0.0418]
 --   >>> let f2 = [0.0805]
@@ -305,8 +291,8 @@ big_Ns_matrix =
 --   >>> let f5 = [-0.0332]
 --   >>> let f6 = [-0.0054]
 --   >>> let f7 = [-0.0267]
---   >>> let expected = fromList [f1,f2,f3,f4,f5,f6,f7] :: Col N7 Double
---   >>> let actual = big_F pde params
+--   >>> let expected = fromList [f1,f2,f3,f4,f5,f6,f7] :: Col7 Double
+--   >>> let actual = big_F pde' params'
 --   >>> frobenius_norm (actual - expected) < 1e-4
 --   True
 --
@@ -410,22 +396,8 @@ big_K_elem pde params _ k cur_K _ =
 --
 --   Examples:
 --
---   >>> import Linear.Matrix ( Col4, frobenius_norm, fromList )
---   >>> import Naturals ( N3, N4, N7 )
---
---   >>> let big_A = const (1::Double)
---   >>> let c x = sin x
---   >>> let f x = x*(sin x)
---   >>> let bdy = Left (Dirichlet (0,1::Double))
---   >>> let pde = PDE big_A c f bdy
---
---   >>> let i1 = (0.0,1/3)
---   >>> let i2 = (1/3,2/3)
---   >>> let i3 = (2/3,4/5)
---   >>> let i4 = (4/5,1.0)
---   >>> let mesh = fromList [[i1], [i2], [i3], [i4]] :: Col4 (Double,Double)
---   >>> let pvec = fromList [[2],[3],[2],[1]] :: Col4 Int
---   >>> let params = Params mesh pvec :: Params N4 N3 N7 Double
+--   >>> import Linear.Matrix ( Mat7, frobenius_norm )
+--   >>> import FEM.R1.Example1 ( pde', params' )
 --
 --   >>> let k1 = [6, -3, 0, 0, 0, 0, 0] :: [Double]
 --   >>> let k2 = [-3, 10.5, -7.5, 0, 0, 0, 0] :: [Double]
@@ -434,8 +406,8 @@ big_K_elem pde params _ k cur_K _ =
 --   >>> let k5 = [0, 0, 0, 0, 6, 0, 0] :: [Double]
 --   >>> let k6 = [0, 0, 0, 0, 0, 6, 0] :: [Double]
 --   >>> let k7 = [0, 0, 0, 0, 0, 0, 15] :: [Double]
---   >>> let expected = fromList [k1,k2,k3,k4,k5,k6,k7] :: Mat N7 N7 Double
---   >>> let actual = big_K pde params
+--   >>> let expected = fromList [k1,k2,k3,k4,k5,k6,k7] :: Mat7 Double
+--   >>> let actual = big_K pde' params'
 --   >>> frobenius_norm (actual - expected) < 1e-10
 --   True
 --
@@ -489,22 +461,8 @@ big_M_elem pde params _ k cur_M _ =
 --
 --   Examples:
 --
---   >>> import Linear.Matrix ( Col4, frobenius_norm, fromList )
---   >>> import Naturals ( N3, N4, N7 )
---
---   >>> let big_A = const (1::Double)
---   >>> let c x = sin x
---   >>> let f x = x*(sin x)
---   >>> let bdy = Left (Dirichlet (0,1::Double))
---   >>> let pde = PDE big_A c f bdy
---
---   >>> let i1 = (0.0,1/3)
---   >>> let i2 = (1/3,2/3)
---   >>> let i3 = (2/3,4/5)
---   >>> let i4 = (4/5,1.0)
---   >>> let mesh = fromList [[i1], [i2], [i3], [i4]] :: Col4 (Double,Double)
---   >>> let pvec = fromList [[2],[3],[2],[1]] :: Col4 Int
---   >>> let params = Params mesh pvec :: Params N4 N3 N7 Double
+--   >>> import Linear.Matrix ( Mat7, frobenius_norm )
+--   >>> import FEM.R1.Example1 ( pde', params' )
 --
 --   >>> let m1 = [0.0723,0.0266,0,-0.0135,-0.0305,0.0058,0] :: [Double]
 --   >>> let m2 = [0.0266,0.0897,0.0149,0,-0.0345,-0.0109,-0.0179] :: [Double]
@@ -514,8 +472,8 @@ big_M_elem pde params _ k cur_M _ =
 --   >>> let m6 = [0.0058,-0.0109,0,0,0.0018,0.0076,0] :: [Double]
 --   >>> let m7 = [0,-0.0179,-0.0185,0,0,0,0.0178] :: [Double]
 --
---   >>> let expected = fromList [m1,m2,m3,m4,m5,m6,m7] :: Mat N7 N7 Double
---   >>> let actual = big_M pde params
+--   >>> let expected = fromList [m1,m2,m3,m4,m5,m6,m7] :: Mat7 Double
+--   >>> let actual = big_M pde' params'
 --   >>> frobenius_norm (actual - expected) < 1e-3
 --   True
 --
@@ -536,22 +494,8 @@ big_M pde params =
 --
 --   Examples:
 --
---   >>> import Linear.Matrix ( Col4, Col7, frobenius_norm, fromList )
---   >>> import Naturals ( N3, N4, N7 )
---
---   >>> let big_A = const (1::Double)
---   >>> let c x = sin x
---   >>> let f x = x*(sin x)
---   >>> let bdy = Left (Dirichlet (0,1::Double))
---   >>> let pde = PDE big_A c f bdy
---
---   >>> let i1 = (0.0,1/3)
---   >>> let i2 = (1/3,2/3)
---   >>> let i3 = (2/3,4/5)
---   >>> let i4 = (4/5,1.0)
---   >>> let mesh = fromList [[i1], [i2], [i3], [i4]] :: Col4 (Double,Double)
---   >>> let pvec = fromList [[2],[3],[2],[1]] :: Col4 Int
---   >>> let params = Params mesh pvec :: Params N4 N3 N7 Double
+--   >>> import Linear.Matrix ( Col7, frobenius_norm )
+--   >>> import FEM.R1.Example1 ( pde', params' )
 --
 --   >>> let c1 = [0.02366220347687] :: [Double]
 --   >>> let c2 = [0.03431630082636] :: [Double]
@@ -560,8 +504,9 @@ big_M pde params =
 --   >>> let c5 = [-0.00518637005151] :: [Double]
 --   >>> let c6 = [-0.00085028505337] :: [Double]
 --   >>> let c7 = [-0.00170478210110] :: [Double]
+--   >>>
 --   >>> let expected = fromList [c1,c2,c3,c4,c5,c6,c7] :: Col7 Double
---   >>> let actual = coefficients pde params
+--   >>> let actual = coefficients pde' params'
 --   >>> frobenius_norm (actual - expected) < 1e-8
 --   True
 --
@@ -599,7 +544,7 @@ solution pde params =
     mesh_with_ptr_rows = zip2 (mesh params) (rows2 ptr)
 
     make_local_coeffs :: (Interval a, Row (S n) Int) -> Row (S n) a
-    make_local_coeffs (interval, ptr_row) =
+    make_local_coeffs (_, ptr_row) =
       construct lambda
         where
           lambda _ j = if (ptr_row !!! (0,j)) == zero
@@ -623,12 +568,11 @@ solution pde params =
     solved_column = map2 solve_piece $ mesh_with_coeffs
 
     solve_piece :: (Interval a, Row (S n) a) -> (Interval a, (a -> a))
-    solve_piece (interval, coeffs_row) = (interval, f)
+    solve_piece (interval, coeffs_row) = (interval, g)
       where
         coeffs_col = transpose coeffs_row
 
-        f x = element_sum2 $ zipwith2 combine coeffs_col global_basis_functions
+        g x = element_sum2 $ zipwith2 combine coeffs_col global_basis_functions
           where
             xi = (affine interval) x
             combine ci ni = ci*(ni xi)
-