#### Exponential Moving Average

R
```"""
Calculate the exponential moving average (EMA) on the series of stock prices.
Wikipedia Reference: https://en.wikipedia.org/wiki/Exponential_smoothing
https://www.investopedia.com/terms/e/ema.asp#toc-what-is-an-exponential
-moving-average-ema

Exponential moving average is used in finance to analyze changes stock prices.
EMA is used in conjunction with Simple moving average (SMA), EMA reacts to the
changes in the value quicker than SMA, which is one of the advantages of using EMA.
"""

from collections.abc import Iterator

def exponential_moving_average(
stock_prices: Iterator[float], window_size: int
) -> Iterator[float]:
"""
Yields exponential moving averages of the given stock prices.
>>> tuple(exponential_moving_average(iter([2, 5, 3, 8.2, 6, 9, 10]), 3))
(2, 3.5, 3.25, 5.725, 5.8625, 7.43125, 8.715625)

:param stock_prices: A stream of stock prices
:param window_size: The number of stock prices that will trigger a new calculation
of the exponential average (window_size > 0)
:return: Yields a sequence of exponential moving averages

Formula:

st = alpha * xt + (1 - alpha) * st_prev

Where,
st : Exponential moving average at timestamp t
xt : stock price in from the stock prices at timestamp t
st_prev : Exponential moving average at timestamp t-1
alpha : 2/(1 + window_size) - smoothing factor

Exponential moving average (EMA) is a rule of thumb technique for
smoothing time series data using an exponential window function.
"""

if window_size <= 0:
raise ValueError("window_size must be > 0")

# Calculating smoothing factor
alpha = 2 / (1 + window_size)

# Exponential average at timestamp t
moving_average = 0.0

for i, stock_price in enumerate(stock_prices):
if i <= window_size:
# Assigning simple moving average till the window_size for the first time
# is reached
moving_average = (moving_average + stock_price) * 0.5 if i else stock_price
else:
# Calculating exponential moving average based on current timestamp data
# point and previous exponential average value
moving_average = (alpha * stock_price) + ((1 - alpha) * moving_average)
yield moving_average

if __name__ == "__main__":
import doctest

doctest.testmod()

stock_prices = [2.0, 5, 3, 8.2, 6, 9, 10]
window_size = 3
result = tuple(exponential_moving_average(iter(stock_prices), window_size))
print(f"{stock_prices = }")
print(f"{window_size = }")
print(f"{result = }")
```