make tests more exhaustive

Author: dlfivefifty

test/test_disk.jl

@@ -1,15 +1,48 @@
 using Revise, ApproxFun, MultivariateOrthogonalPolynomials
 import MultivariateOrthogonalPolynomials: checkerboard, icheckerboard, CDisk2CxfPlan
 import ApproxFunBase: totensor
-import ApproxFunOrthogonalPolynomials: jacobip
+import ApproxFunOrthogonalPolynomials: jacobip, chebyshevt
+
+
+
+
 
 f = (x,y) -> x*y+cos(y-0.1)+sin(x)+1; 
 ff = Fun(f, ChebyshevDisk(), 1000)
-
 @test ff(0.1,0.2) ≈ f(0.1,0.2)
+
 ff = Fun(f, ChebyshevDisk())
 @test ff(0.1,0.2) ≈ f(0.1,0.2)
 
+function chebydiskeval(c::AbstractMatrix{T}, r, θ) where T
+    ret = zero(T)
+    for j = 1:2:size(c,2), k=1:size(c,1)
+        m,ℓ = j ÷ 2, k-1
+        ret += c[k,j] * cos(m*θ) * cos((2ℓ+isodd(m))*acos(r))
+    end
+    for j = 2:2:size(c,2), k=1:size(c,1)
+        m = j ÷ 2; ℓ = k-1
+        ret += c[k,j] * sin(m*θ) * cos((2ℓ+isodd(m))*acos(r))
+    end
+    ret
+end
+
+
+for (m,ℓ) in ((0,1),(0,2),(0,3), (1,0), (1,1), (1,2), (2,0), (2,1),(3,0),(3,4))
+    p1 = (r,θ) -> cos(m*θ) * cos((2ℓ+isodd(m))*acos(r))
+    f = Fun((x,y) -> p1(sqrt(x^2+y^2), atan(y,x)), ChebyshevDisk())
+    c = totensor(f.space, chop(f.coefficients,1E-12))    
+    @test c[ℓ+1, 2m+1] ≈ 1
+    @test f(0.1cos(0.2),0.1sin(0.2)) ≈ chebydiskeval(c, 0.1, 0.2)
+
+    if m > 0
+        p2 = (r,θ) -> sin(m*θ) * cos((2ℓ+isodd(m))*acos(r))
+        f = Fun((x,y) -> p2(sqrt(x^2+y^2), atan(y,x)), ChebyshevDisk())
+        c = totensor(f.space, chop(f.coefficients,1E-12))    
+        @test c[ℓ+1, 2m] ≈ 1
+        @test f(0.1cos(0.2),0.1sin(0.2)) ≈ chebydiskeval(c, 0.1, 0.2)
+    end
+end
 
 f = Fun((x,y) -> 1, ChebyshevDisk()); n = 1;
     c = totensor(f.space, f.coefficients)
@@ -31,14 +64,19 @@ f = Fun((x,y) -> x, ChebyshevDisk()); n = 2;
     @test d ≈  [0.0  0.0  0.5  0.0  0.0; 0.0  0.0  0.0  0.0  0.0]
 
 
-m,ℓ = (0,2);
-m,ℓ = (1,1);
-m,ℓ = (2,2);
-m,ℓ = (2,4);
+# m,ℓ = (0,2);
+# m,ℓ = (1,1);
+# m,ℓ = (2,2);
+
 
+m,ℓ = (2,4);
 p1 = (r,θ) -> sqrt(2ℓ+2)*r^m*jacobip((ℓ-m)÷2, m, 0, 2r^2-1)*cos(m*θ)/sqrt(2π)
 f = Fun((x,y) -> p1(sqrt(x^2+y^2), atan(y,x)), ChebyshevDisk());
+    @test f(0.1*cos(0.2),0.1*sin(0.2)) ≈ p1(0.1,0.2)
     c = totensor(f.space, chop(f.coefficients,1E-12))
+    @test chebydiskeval(c, 0.1, 0.2) ≈ p1(0.1,0.2)
+    
+
     n = size(c,1); c = sqrt(2π)*pad(c,n,4n-3)
     P = CDisk2CxfPlan(n)
     d = P \ c