How do I add a new column to a Spark DataFrame (using PySpark)?

You cannot add an arbitrary column to a DataFrame in Spark. New columns can be created only by using literals (other literal types are described in How to add a constant column in a Spark DataFrame?)

from pyspark.sql.functions import lit

df = sqlContext.createDataFrame(
    [(1, "a", 23.0), (3, "B", -23.0)], ("x1", "x2", "x3"))

df_with_x4 = df.withColumn("x4", lit(0))
df_with_x4.show()

## +---+---+-----+---+
## | x1| x2|   x3| x4|
## +---+---+-----+---+
## |  1|  a| 23.0|  0|
## |  3|  B|-23.0|  0|
## +---+---+-----+---+

transforming an existing column:

from pyspark.sql.functions import exp

df_with_x5 = df_with_x4.withColumn("x5", exp("x3"))
df_with_x5.show()

## +---+---+-----+---+--------------------+
## | x1| x2|   x3| x4|                  x5|
## +---+---+-----+---+--------------------+
## |  1|  a| 23.0|  0| 9.744803446248903E9|
## |  3|  B|-23.0|  0|1.026187963170189...|
## +---+---+-----+---+--------------------+

included using join:

from pyspark.sql.functions import exp

lookup = sqlContext.createDataFrame([(1, "foo"), (2, "bar")], ("k", "v"))
df_with_x6 = (df_with_x5
    .join(lookup, col("x1") == col("k"), "leftouter")
    .drop("k")
    .withColumnRenamed("v", "x6"))

## +---+---+-----+---+--------------------+----+
## | x1| x2|   x3| x4|                  x5|  x6|
## +---+---+-----+---+--------------------+----+
## |  1|  a| 23.0|  0| 9.744803446248903E9| foo|
## |  3|  B|-23.0|  0|1.026187963170189...|null|
## +---+---+-----+---+--------------------+----+

or generated with function / udf:

from pyspark.sql.functions import rand

df_with_x7 = df_with_x6.withColumn("x7", rand())
df_with_x7.show()

## +---+---+-----+---+--------------------+----+-------------------+
## | x1| x2|   x3| x4|                  x5|  x6|                 x7|
## +---+---+-----+---+--------------------+----+-------------------+
## |  1|  a| 23.0|  0| 9.744803446248903E9| foo|0.41930610446846617|
## |  3|  B|-23.0|  0|1.026187963170189...|null|0.37801881545497873|
## +---+---+-----+---+--------------------+----+-------------------+

Performance-wise, built-in functions (pyspark.sql.functions), which map to Catalyst expression, are usually preferred over Python user defined functions.

If you want to add content of an arbitrary RDD as a column you can

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