Adding DFT to python and fixing code examples for FFT. (#382)

* Adding dft to python

* updating cooley_tukey.md

* adding code examples for cooley tukey

Author: Gathros

contents/cooley_tukey/code/python/fft.py

@@ -2,6 +2,14 @@
 from cmath import exp, pi
 from math import log2
 
+def dft(X):
+    N = len(X)
+    temp = [0]*N
+    for i in range(N):
+        for k in range(N):
+            temp[i] += X[k] * exp(-2.0j*pi*i*k/N)
+    return temp
+
 def cooley_tukey(X):
 	N = len(X)
 	if N <= 1:
@@ -47,5 +55,7 @@ def iterative_cooley_tukey(X):
 
 Y = cooley_tukey(X)
 Z = iterative_cooley_tukey(X)
+T = dft(X)
 
 print(all(abs([Y[i] - Z[i] for i in range(64)][j]) < 1 for j in range(64)))
+print(all(abs([Y[i] - T[i] for i in range(64)][j]) < 1 for j in range(64)))

contents/cooley_tukey/cooley_tukey.md

@@ -74,11 +74,11 @@ For some reason, though, putting code to this transformation really helped me fi
 {% sample lang="c" %}
 [import:8-19, lang:"c_cpp"](code/c/fft.c)
 {% sample lang="cpp" %}
-[import:2-11, lang:"julia"](code/julia/fft.jl)
+[import:23-33, lang:"c_cpp"](code/c++/fft.cpp)
 {% sample lang="hs" %}
 [import:2-11, lang:"julia"](code/julia/fft.jl)
 {% sample lang="py" %}
-[import:2-11, lang:"julia"](code/julia/fft.jl)
+[import:5-11, lang:"python"](code/python/fft.py)
 {% sample lang="scratch" %}
 [import:2-11, lang:"julia"](code/julia/fft.jl)
 {% endmethod %}
@@ -119,11 +119,11 @@ In the end, the code looks like:
 {% sample lang="c" %}
 [import:20-39, lang:"c_cpp"](code/c/fft.c)
 {% sample lang="cpp" %}
-[import:35-66, lang:"c_cpp"](code/c++/fft.cpp)
+[import:36-66, lang:"c_cpp"](code/c++/fft.cpp)
 {% sample lang="hs" %}
 [import:6-19, lang:"haskell"](code/haskell/fft.hs)
 {% sample lang="py" %}
-[import:5-16, lang:"python"](code/python/fft.py)
+[import:13-24, lang:"python"](code/python/fft.py)
 {% sample lang="scratch" %}
 [import:14-31, lang:"julia"](code/julia/fft.jl)
 {% endmethod %}