[SPARK-16772] Correct API doc references to PySpark classes + formatting fixes

## What's Been Changed

The PR corrects several broken or missing class references in the Python API docs. It also correct formatting problems.

For example, you can see [here](http://spark.apache.org/docs/2.0.0/api/python/pyspark.sql.html#pyspark.sql.SQLContext.registerFunction) how Sphinx is not picking up the reference to `DataType`. That's because the reference is relative to the current module, whereas `DataType` is in a different module.

You can also see [here](http://spark.apache.org/docs/2.0.0/api/python/pyspark.sql.html#pyspark.sql.SQLContext.createDataFrame) how the formatting for byte, tinyint, and so on is italic instead of monospace. That's because in ReST single backticks just make things italic, unlike in Markdown.

## Testing

I tested this PR by [building the Python docs](https://github.com/apache/spark/tree/master/docs#generating-the-documentation-html) and reviewing the results locally in my browser. I confirmed that the broken or missing class references were resolved, and that the formatting was corrected.

Author: Nicholas Chammas <nicholas.chammas@gmail.com>

Closes #14393 from nchammas/python-docstring-fixes.

8 files changed, 75 insertions, 58 deletions

diff --git a/python/pyspark/sql/catalog.py b/python/pyspark/sql/catalog.py
index 4af930a3cd..3c5030722f 100644
--- a/python/pyspark/sql/catalog.py
+++ b/python/pyspark/sql/catalog.py
@@ -193,7 +193,7 @@ class Catalog(object):
 
         :param name: name of the UDF
         :param f: python function
-        :param returnType: a :class:`DataType` object
+        :param returnType: a :class:`pyspark.sql.types.DataType` object
 
         >>> spark.catalog.registerFunction("stringLengthString", lambda x: len(x))
         >>> spark.sql("SELECT stringLengthString('test')").collect()
diff --git a/python/pyspark/sql/context.py b/python/pyspark/sql/context.py
index 0debcf1de4..f7009fe589 100644
--- a/python/pyspark/sql/context.py
+++ b/python/pyspark/sql/context.py
@@ -152,9 +152,9 @@ class SQLContext(object):
     @since(1.4)
     def range(self, start, end=None, step=1, numPartitions=None):
         """
-        Create a :class:`DataFrame` with single LongType column named `id`,
-        containing elements in a range from `start` to `end` (exclusive) with
-        step value `step`.
+        Create a :class:`DataFrame` with single :class:`pyspark.sql.types.LongType` column named
+        ``id``, containing elements in a range from ``start`` to ``end`` (exclusive) with
+        step value ``step``.
 
         :param start: the start value
         :param end: the end value (exclusive)
@@ -184,7 +184,7 @@ class SQLContext(object):
 
         :param name: name of the UDF
         :param f: python function
-        :param returnType: a :class:`DataType` object
+        :param returnType: a :class:`pyspark.sql.types.DataType` object
 
         >>> sqlContext.registerFunction("stringLengthString", lambda x: len(x))
         >>> sqlContext.sql("SELECT stringLengthString('test')").collect()
@@ -209,7 +209,7 @@ class SQLContext(object):
 
         :param rdd: an RDD of Row or tuple
         :param samplingRatio: sampling ratio, or no sampling (default)
-        :return: StructType
+        :return: :class:`pyspark.sql.types.StructType`
         """
         return self.sparkSession._inferSchema(rdd, samplingRatio)
 
@@ -226,28 +226,34 @@ class SQLContext(object):
         from ``data``, which should be an RDD of :class:`Row`,
         or :class:`namedtuple`, or :class:`dict`.
 
-        When ``schema`` is :class:`DataType` or datatype string, it must match the real data, or
-        exception will be thrown at runtime. If the given schema is not StructType, it will be
-        wrapped into a StructType as its only field, and the field name will be "value", each record
-        will also be wrapped into a tuple, which can be converted to row later.
+        When ``schema`` is :class:`pyspark.sql.types.DataType` or
+        :class:`pyspark.sql.types.StringType`, it must match the
+        real data, or an exception will be thrown at runtime. If the given schema is not
+        :class:`pyspark.sql.types.StructType`, it will be wrapped into a
+        :class:`pyspark.sql.types.StructType` as its only field, and the field name will be "value",
+        each record will also be wrapped into a tuple, which can be converted to row later.
 
         If schema inference is needed, ``samplingRatio`` is used to determined the ratio of
         rows used for schema inference. The first row will be used if ``samplingRatio`` is ``None``.
 
-        :param data: an RDD of any kind of SQL data representation(e.g. row, tuple, int, boolean,
-            etc.), or :class:`list`, or :class:`pandas.DataFrame`.
-        :param schema: a :class:`DataType` or a datatype string or a list of column names, default
-            is None.  The data type string format equals to `DataType.simpleString`, except that
-            top level struct type can omit the `struct<>` and atomic types use `typeName()` as
-            their format, e.g. use `byte` instead of `tinyint` for ByteType. We can also use `int`
-            as a short name for IntegerType.
+        :param data: an RDD of any kind of SQL data representation(e.g. :class:`Row`,
+            :class:`tuple`, ``int``, ``boolean``, etc.), or :class:`list`, or
+            :class:`pandas.DataFrame`.
+        :param schema: a :class:`pyspark.sql.types.DataType` or a
+            :class:`pyspark.sql.types.StringType` or a list of
+            column names, default is None.  The data type string format equals to
+            :class:`pyspark.sql.types.DataType.simpleString`, except that top level struct type can
+            omit the ``struct<>`` and atomic types use ``typeName()`` as their format, e.g. use
+            ``byte`` instead of ``tinyint`` for :class:`pyspark.sql.types.ByteType`.
+            We can also use ``int`` as a short name for :class:`pyspark.sql.types.IntegerType`.
         :param samplingRatio: the sample ratio of rows used for inferring
         :return: :class:`DataFrame`
 
         .. versionchanged:: 2.0
-           The schema parameter can be a DataType or a datatype string after 2.0. If it's not a
-           StructType, it will be wrapped into a StructType and each record will also be wrapped
-           into a tuple.
+           The ``schema`` parameter can be a :class:`pyspark.sql.types.DataType` or a
+           :class:`pyspark.sql.types.StringType` after 2.0.
+           If it's not a :class:`pyspark.sql.types.StructType`, it will be wrapped into a
+           :class:`pyspark.sql.types.StructType` and each record will also be wrapped into a tuple.
 
         >>> l = [('Alice', 1)]
         >>> sqlContext.createDataFrame(l).collect()
diff --git a/python/pyspark/sql/dataframe.py b/python/pyspark/sql/dataframe.py
index 0cbb3adfa8..a986092f5d 100644
--- a/python/pyspark/sql/dataframe.py
+++ b/python/pyspark/sql/dataframe.py
@@ -196,7 +196,7 @@ class DataFrame(object):
     @property
     @since(1.3)
     def schema(self):
-        """Returns the schema of this :class:`DataFrame` as a :class:`types.StructType`.
+        """Returns the schema of this :class:`DataFrame` as a :class:`pyspark.sql.types.StructType`.
 
         >>> df.schema
         StructType(List(StructField(age,IntegerType,true),StructField(name,StringType,true)))
diff --git a/python/pyspark/sql/functions.py b/python/pyspark/sql/functions.py
index 92d709ee40..e422363ec1 100644
--- a/python/pyspark/sql/functions.py
+++ b/python/pyspark/sql/functions.py
@@ -142,7 +142,7 @@ _functions_1_6 = {
 _binary_mathfunctions = {
     'atan2': 'Returns the angle theta from the conversion of rectangular coordinates (x, y) to' +
              'polar coordinates (r, theta).',
-    'hypot': 'Computes `sqrt(a^2 + b^2)` without intermediate overflow or underflow.',
+    'hypot': 'Computes ``sqrt(a^2 + b^2)`` without intermediate overflow or underflow.',
     'pow': 'Returns the value of the first argument raised to the power of the second argument.',
 }
 
@@ -958,7 +958,8 @@ def months_between(date1, date2):
 @since(1.5)
 def to_date(col):
     """
-    Converts the column of StringType or TimestampType into DateType.
+    Converts the column of :class:`pyspark.sql.types.StringType` or
+    :class:`pyspark.sql.types.TimestampType` into :class:`pyspark.sql.types.DateType`.
 
     >>> df = spark.createDataFrame([('1997-02-28 10:30:00',)], ['t'])
     >>> df.select(to_date(df.t).alias('date')).collect()
@@ -1074,18 +1075,18 @@ def window(timeColumn, windowDuration, slideDuration=None, startTime=None):
     [12:05,12:10) but not in [12:00,12:05). Windows can support microsecond precision. Windows in
     the order of months are not supported.
 
-    The time column must be of TimestampType.
+    The time column must be of :class:`pyspark.sql.types.TimestampType`.
 
     Durations are provided as strings, e.g. '1 second', '1 day 12 hours', '2 minutes'. Valid
     interval strings are 'week', 'day', 'hour', 'minute', 'second', 'millisecond', 'microsecond'.
-    If the `slideDuration` is not provided, the windows will be tumbling windows.
+    If the ``slideDuration`` is not provided, the windows will be tumbling windows.
 
     The startTime is the offset with respect to 1970-01-01 00:00:00 UTC with which to start
     window intervals. For example, in order to have hourly tumbling windows that start 15 minutes
     past the hour, e.g. 12:15-13:15, 13:15-14:15... provide `startTime` as `15 minutes`.
 
     The output column will be a struct called 'window' by default with the nested columns 'start'
-    and 'end', where 'start' and 'end' will be of `TimestampType`.
+    and 'end', where 'start' and 'end' will be of :class:`pyspark.sql.types.TimestampType`.
 
     >>> df = spark.createDataFrame([("2016-03-11 09:00:07", 1)]).toDF("date", "val")
     >>> w = df.groupBy(window("date", "5 seconds")).agg(sum("val").alias("sum"))
@@ -1367,7 +1368,7 @@ def locate(substr, str, pos=1):
     could not be found in str.
 
     :param substr: a string
-    :param str: a Column of StringType
+    :param str: a Column of :class:`pyspark.sql.types.StringType`
     :param pos: start position (zero based)
 
     >>> df = spark.createDataFrame([('abcd',)], ['s',])
@@ -1506,8 +1507,9 @@ def bin(col):
 @ignore_unicode_prefix
 @since(1.5)
 def hex(col):
-    """Computes hex value of the given column, which could be StringType,
-    BinaryType, IntegerType or LongType.
+    """Computes hex value of the given column, which could be :class:`pyspark.sql.types.StringType`,
+    :class:`pyspark.sql.types.BinaryType`, :class:`pyspark.sql.types.IntegerType` or
+    :class:`pyspark.sql.types.LongType`.
 
     >>> spark.createDataFrame([('ABC', 3)], ['a', 'b']).select(hex('a'), hex('b')).collect()
     [Row(hex(a)=u'414243', hex(b)=u'3')]
@@ -1781,6 +1783,9 @@ def udf(f, returnType=StringType()):
     duplicate invocations may be eliminated or the function may even be invoked more times than
     it is present in the query.
 
+    :param f: python function
+    :param returnType: a :class:`pyspark.sql.types.DataType` object
+
     >>> from pyspark.sql.types import IntegerType
     >>> slen = udf(lambda s: len(s), IntegerType())
     >>> df.select(slen(df.name).alias('slen')).collect()
diff --git a/python/pyspark/sql/readwriter.py b/python/pyspark/sql/readwriter.py
index f7c354f513..4020bb3fa4 100644
--- a/python/pyspark/sql/readwriter.py
+++ b/python/pyspark/sql/readwriter.py
@@ -96,7 +96,7 @@ class DataFrameReader(OptionUtils):
         By specifying the schema here, the underlying data source can skip the schema
         inference step, and thus speed up data loading.
 
-        :param schema: a StructType object
+        :param schema: a :class:`pyspark.sql.types.StructType` object
         """
         if not isinstance(schema, StructType):
             raise TypeError("schema should be StructType")
@@ -125,7 +125,7 @@ class DataFrameReader(OptionUtils):
 
         :param path: optional string or a list of string for file-system backed data sources.
         :param format: optional string for format of the data source. Default to 'parquet'.
-        :param schema: optional :class:`StructType` for the input schema.
+        :param schema: optional :class:`pyspark.sql.types.StructType` for the input schema.
         :param options: all other string options
 
         >>> df = spark.read.load('python/test_support/sql/parquet_partitioned', opt1=True,
@@ -166,7 +166,7 @@ class DataFrameReader(OptionUtils):
 
         :param path: string represents path to the JSON dataset,
                      or RDD of Strings storing JSON objects.
-        :param schema: an optional :class:`StructType` for the input schema.
+        :param schema: an optional :class:`pyspark.sql.types.StructType` for the input schema.
         :param primitivesAsString: infers all primitive values as a string type. If None is set,
                                    it uses the default value, ``false``.
         :param prefersDecimal: infers all floating-point values as a decimal type. If the values
@@ -294,7 +294,7 @@ class DataFrameReader(OptionUtils):
         ``inferSchema`` option or specify the schema explicitly using ``schema``.
 
         :param path: string, or list of strings, for input path(s).
-        :param schema: an optional :class:`StructType` for the input schema.
+        :param schema: an optional :class:`pyspark.sql.types.StructType` for the input schema.
         :param sep: sets the single character as a separator for each field and value.
                     If None is set, it uses the default value, ``,``.
         :param encoding: decodes the CSV files by the given encoding type. If None is set,
diff --git a/python/pyspark/sql/session.py b/python/pyspark/sql/session.py
index 594f9375f7..10bd89b03f 100644
--- a/python/pyspark/sql/session.py
+++ b/python/pyspark/sql/session.py
@@ -47,7 +47,7 @@ def _monkey_patch_RDD(sparkSession):
 
         This is a shorthand for ``spark.createDataFrame(rdd, schema, sampleRatio)``
 
-        :param schema: a StructType or list of names of columns
+        :param schema: a :class:`pyspark.sql.types.StructType` or list of names of columns
         :param samplingRatio: the sample ratio of rows used for inferring
         :return: a DataFrame
 
@@ -274,9 +274,9 @@ class SparkSession(object):
     @since(2.0)
     def range(self, start, end=None, step=1, numPartitions=None):
         """
-        Create a :class:`DataFrame` with single LongType column named `id`,
-        containing elements in a range from `start` to `end` (exclusive) with
-        step value `step`.
+        Create a :class:`DataFrame` with single :class:`pyspark.sql.types.LongType` column named
+        ``id``, containing elements in a range from ``start`` to ``end`` (exclusive) with
+        step value ``step``.
 
         :param start: the start value
         :param end: the end value (exclusive)
@@ -307,7 +307,7 @@ class SparkSession(object):
         Infer schema from list of Row or tuple.
 
         :param data: list of Row or tuple
-        :return: StructType
+        :return: :class:`pyspark.sql.types.StructType`
         """
         if not data:
             raise ValueError("can not infer schema from empty dataset")
@@ -326,7 +326,7 @@ class SparkSession(object):
 
         :param rdd: an RDD of Row or tuple
         :param samplingRatio: sampling ratio, or no sampling (default)
-        :return: StructType
+        :return: :class:`pyspark.sql.types.StructType`
         """
         first = rdd.first()
         if not first:
@@ -414,28 +414,33 @@ class SparkSession(object):
         from ``data``, which should be an RDD of :class:`Row`,
         or :class:`namedtuple`, or :class:`dict`.
 
-        When ``schema`` is :class:`DataType` or datatype string, it must match the real data, or
-        exception will be thrown at runtime. If the given schema is not StructType, it will be
-        wrapped into a StructType as its only field, and the field name will be "value", each record
-        will also be wrapped into a tuple, which can be converted to row later.
+        When ``schema`` is :class:`pyspark.sql.types.DataType` or
+        :class:`pyspark.sql.types.StringType`, it must match the
+        real data, or an exception will be thrown at runtime. If the given schema is not
+        :class:`pyspark.sql.types.StructType`, it will be wrapped into a
+        :class:`pyspark.sql.types.StructType` as its only field, and the field name will be "value",
+        each record will also be wrapped into a tuple, which can be converted to row later.
 
         If schema inference is needed, ``samplingRatio`` is used to determined the ratio of
         rows used for schema inference. The first row will be used if ``samplingRatio`` is ``None``.
 
         :param data: an RDD of any kind of SQL data representation(e.g. row, tuple, int, boolean,
             etc.), or :class:`list`, or :class:`pandas.DataFrame`.
-        :param schema: a :class:`DataType` or a datatype string or a list of column names, default
-            is None.  The data type string format equals to `DataType.simpleString`, except that
-            top level struct type can omit the `struct<>` and atomic types use `typeName()` as
-            their format, e.g. use `byte` instead of `tinyint` for ByteType. We can also use `int`
-            as a short name for IntegerType.
+        :param schema: a :class:`pyspark.sql.types.DataType` or a
+            :class:`pyspark.sql.types.StringType` or a list of
+            column names, default is ``None``.  The data type string format equals to
+            :class:`pyspark.sql.types.DataType.simpleString`, except that top level struct type can
+            omit the ``struct<>`` and atomic types use ``typeName()`` as their format, e.g. use
+            ``byte`` instead of ``tinyint`` for :class:`pyspark.sql.types.ByteType`. We can also use
+            ``int`` as a short name for ``IntegerType``.
         :param samplingRatio: the sample ratio of rows used for inferring
         :return: :class:`DataFrame`
 
         .. versionchanged:: 2.0
-           The schema parameter can be a DataType or a datatype string after 2.0. If it's not a
-           StructType, it will be wrapped into a StructType and each record will also be wrapped
-           into a tuple.
+           The ``schema`` parameter can be a :class:`pyspark.sql.types.DataType` or a
+           :class:`pyspark.sql.types.StringType` after 2.0. If it's not a
+           :class:`pyspark.sql.types.StructType`, it will be wrapped into a
+           :class:`pyspark.sql.types.StructType` and each record will also be wrapped into a tuple.
 
         >>> l = [('Alice', 1)]
         >>> spark.createDataFrame(l).collect()
diff --git a/python/pyspark/sql/streaming.py b/python/pyspark/sql/streaming.py
index 8bac347e13..a364555003 100644
--- a/python/pyspark/sql/streaming.py
+++ b/python/pyspark/sql/streaming.py
@@ -269,7 +269,7 @@ class DataStreamReader(OptionUtils):
 
         .. note:: Experimental.
 
-        :param schema: a StructType object
+        :param schema: a :class:`pyspark.sql.types.StructType` object
 
         >>> s = spark.readStream.schema(sdf_schema)
         """
@@ -310,7 +310,7 @@ class DataStreamReader(OptionUtils):
 
         :param path: optional string for file-system backed data sources.
         :param format: optional string for format of the data source. Default to 'parquet'.
-        :param schema: optional :class:`StructType` for the input schema.
+        :param schema: optional :class:`pyspark.sql.types.StructType` for the input schema.
         :param options: all other string options
 
         >>> json_sdf = spark.readStream.format("json")\
@@ -349,7 +349,7 @@ class DataStreamReader(OptionUtils):
 
         :param path: string represents path to the JSON dataset,
                      or RDD of Strings storing JSON objects.
-        :param schema: an optional :class:`StructType` for the input schema.
+        :param schema: an optional :class:`pyspark.sql.types.StructType` for the input schema.
         :param primitivesAsString: infers all primitive values as a string type. If None is set,
                                    it uses the default value, ``false``.
         :param prefersDecimal: infers all floating-point values as a decimal type. If the values
@@ -461,7 +461,7 @@ class DataStreamReader(OptionUtils):
         .. note:: Experimental.
 
         :param path: string, or list of strings, for input path(s).
-        :param schema: an optional :class:`StructType` for the input schema.
+        :param schema: an optional :class:`pyspark.sql.types.StructType` for the input schema.
         :param sep: sets the single character as a separator for each field and value.
                     If None is set, it uses the default value, ``,``.
         :param encoding: decodes the CSV files by the given encoding type. If None is set,
diff --git a/python/pyspark/sql/types.py b/python/pyspark/sql/types.py
index eea80684e2..1ca4bbc379 100644
--- a/python/pyspark/sql/types.py
+++ b/python/pyspark/sql/types.py
@@ -786,9 +786,10 @@ def _parse_struct_fields_string(s):
 def _parse_datatype_string(s):
     """
     Parses the given data type string to a :class:`DataType`. The data type string format equals
-    to `DataType.simpleString`, except that top level struct type can omit the `struct<>` and
-    atomic types use `typeName()` as their format, e.g. use `byte` instead of `tinyint` for
-    ByteType. We can also use `int` as a short name for IntegerType.
+    to :class:`DataType.simpleString`, except that top level struct type can omit
+    the ``struct<>`` and atomic types use ``typeName()`` as their format, e.g. use ``byte`` instead
+    of ``tinyint`` for :class:`ByteType`. We can also use ``int`` as a short name
+    for :class:`IntegerType`.
 
     >>> _parse_datatype_string("int ")
     IntegerType