Add Mat6 and Mat7 synonyms.

Move the example FEM into its own FEM.R1.Exampl1 module.
Use the new example FEM module in the FEM.R1 doctests.

diff --git a/numerical-analysis.cabal b/numerical-analysis.cabal
index 8212344920afeacc00b3593b6043e57f8de46bea..6dfb49886d1da0970760983bfaadd9d97a3e05fb 100644 (file)
--- a/numerical-analysis.cabal
+++ b/numerical-analysis.cabal
@@ -19,6 +19,7 @@ data-files: makefile
 library
   exposed-modules:
     FEM.R1
+    FEM.R1.Example1
     Integration.Gaussian,
     Integration.Simpson,
     Integration.Trapezoid,

diff --git a/src/FEM/R1.hs b/src/FEM/R1.hs
index 4794a3c939af6ac9a31624c04300d3e63c7ca274..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
 --

diff --git a/examples/fem1.hs b/src/FEM/R1/Example1.hs
similarity index 96%
rename from examples/fem1.hs
rename to src/FEM/R1/Example1.hs
index 59d48bb7ad0b454a6699715f34149a3f9dc7e714..ffdf6395209c4850c35484c0c14ec0a5d1ea3881 100644 (file)
--- a/examples/fem1.hs
+++ b/src/FEM/R1/Example1.hs
@@ -1,4 +1,4 @@
-module Main
+module FEM.R1.Example1
 where
 
 import FEM.R1

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index f6dbec07d316b7209e5e24450647fab27719358f..3af2788ee4c0a3796cd781ae717c2553ca676bce 100644 (file)
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -67,6 +67,8 @@ type Mat2 a = Mat N2 N2 a
 type Mat3 a = Mat N3 N3 a
 type Mat4 a = Mat N4 N4 a
 type Mat5 a = Mat N5 N5 a
+type Mat6 a = Mat N6 N6 a
+type Mat7 a = Mat N7 N7 a
 
 -- * Type synonyms for 1-by-n row "vectors".