Applying a Window function to calculate difference

I am using pySpark, and have set up my dataframe with two columns representing a daily asset price as follows:

ind = sc.parallelize(range(1,5))
prices = sc.parallelize([33.3,31.1,51.2,21.3])
data = ind.zip(prices)
df = sqlCtx.createDataFrame(data,["day","price"])

I get upon applying df.show():

+---+-----+
|day|price|
+---+-----+
|  1| 33.3|
|  2| 31.1|
|  3| 51.2|
|  4| 21.3|
+---+-----+

Which is fine and all. I would like to have another column that contains the day-to-day returns of the price column, i.e., something like

(price(day2)-price(day1))/(price(day1))

After much research, I am told that this is most efficiently accomplished through applying the pyspark.sql.window functions, but I am unable to see how.

You can bring the previous day column by using lag function, and add additional column that does actual day-to-day return from the two columns, but you may have to tell spark how to partition your data and/or order it to do lag, something like this:

from pyspark.sql.window import Window
import pyspark.sql.functions as func
from pyspark.sql.functions import lit

dfu = df.withColumn('user', lit('tmoore'))

df_lag = dfu.withColumn('prev_day_price',
                        func.lag(dfu['price'])
                                 .over(Window.partitionBy("user")))

result = df_lag.withColumn('daily_return', 
          (df_lag['price'] - df_lag['prev_day_price']) / df_lag['price'] )

>>> result.show()
+---+-----+-------+--------------+--------------------+
|day|price|   user|prev_day_price|        daily_return|
+---+-----+-------+--------------+--------------------+
|  1| 33.3| tmoore|          null|                null|
|  2| 31.1| tmoore|          33.3|-0.07073954983922816|
|  3| 51.2| tmoore|          31.1|         0.392578125|
|  4| 21.3| tmoore|          51.2|  -1.403755868544601|
+---+-----+-------+--------------+--------------------+

Here is longer introduction into Window functions in Spark.