# 
# Fast discrete cosine transform algorithms (Python)
# 
# Copyright (c) 2020 Project Nayuki. (MIT License)
# https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
# 
# Permission is hereby granted, free of charge, to any person obtaining a copy of
# this software and associated documentation files (the "Software"), to deal in
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import math


# DCT type II, unscaled.
# See: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II
def transform(vector):
	result = []
	factor = math.pi / len(vector)
	for i in range(len(vector)):
		sum = 0.0
		for (j, val) in enumerate(vector):
			sum += val * math.cos((j + 0.5) * i * factor)
		result.append(sum)
	return result


# DCT type III, unscaled.
# See: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-III
def inverse_transform(vector):
	result = []
	factor = math.pi / len(vector)
	for i in range(len(vector)):
		sum = vector[0] / 2
		for j in range(1, len(vector)):
			sum += vector[j] * math.cos(j * (i + 0.5) * factor)
		result.append(sum)
	return result