Add padua points example

Author: dlfivefifty

examples/padua.jl

@@ -0,0 +1,26 @@
+#############
+# This demonstrates the Padua transform and inverse transform,
+# explaining precisely the normalization and points
+#############
+
+using FastTransforms
+
+N = 15
+pts = paduapoints(N)
+x = pts[:,1]; y = pts[:,2]
+
+f = (x,y) -> exp(x + cos(y))
+f̌ = paduatransform(f.(x , y))
+f̃ = (x,y) -> begin
+    j = 1
+    ret = 0.0
+    for n in 0:N, k in 0:n
+        ret += f̌[j]*cos((n-k)*acos(x)) * cos(k*acos(y))
+        j += 1
+    end
+    ret
+end
+
+f̃(0.1,0.2) ≈ f(0.1,0.2)
+
+ipaduatransform(f̌) ≈ f̃.(x,y)