apply udf to multiple columns and use numpy operations

The error message is misleading, but is trying to tell you that your function doesn't return a float. Your function returns value of type numpy.float64 which you can fetch with the VectorUDT type (Function: newFunctionVector in the example below). Another way to make use of numpy is by casting the numpy type numpy.float64 to the python type float (Function: newFunctionWithArray in the example below).

Last but not least, it is not necessary to call array as udfs can use more than one parameter (Function: newFunction in the example below).

import numpy as np
from pyspark.sql.functions import udf, array
from pyspark.sql.types import FloatType
from pyspark.mllib.linalg import Vectors, VectorUDT

result = sqlContext.createDataFrame([(138,5,10), (128,4,10), (112,3,10), (120,3,10), (189,1,10)], ["count","df","docs"])

def newFunctionVector(arr):
    return (1 + np.log(arr[0])) * np.log(arr[2]/arr[1])

@udf("float")
def newFunctionWithArray(arr):
    returnValue = (1 + np.log(arr[0])) * np.log(arr[2]/arr[1])
    return returnValue.item()

@udf("float")
def newFunction(count, df, docs):
    returnValue = (1 + np.log(count)) * np.log(docs/df)
    return returnValue.item()


vector_udf = udf(newFunctionVector, VectorUDT())

result=result.withColumn("new_function_result", newFunction("count","df","docs"))

result=result.withColumn("new_function_result_WithArray", newFunctionWithArray(array("count","df","docs")))

result=result.withColumn("new_function_result_Vector", newFunctionWithArray(array("count","df","docs")))

result.printSchema()

result.show()

Output:

root 
|-- count: long (nullable = true) 
|-- df: long (nullable = true) 
|-- docs: long (nullable = true) 
|-- new_function_result: float (nullable = true) 
|-- new_function_result_WithArray: float (nullable = true) 
|-- new_function_result_Vector: float (nullable = true)

+-----+---+----+-------------------+-----------------------------+--------------------------+ 
|count| df|docs|new_function_result|new_function_result_WithArray|new_function_result_Vector|
+-----+---+----+-------------------+-----------------------------+--------------------------+ 
|  138|  5|  10|           4.108459|                     4.108459|                  4.108459| 
|  128|  4|  10|           5.362161|                     5.362161|                  5.362161|
|  112|  3|  10|          6.8849173|                    6.8849173|                 6.8849173|
|  120|  3|  10|           6.967983|                     6.967983|                  6.967983|
|  189|  1|  10|          14.372153|                    14.372153|                 14.372153|  
+-----+---+----+-------------------+-----------------------------+--------------------------+