def __init__(self, array=None, sub_sketch_keys=[], impl=None):
"""__init__(array)
Construct a new Sketch from an XArray.
Parameters
----------
array : XArray
Array to sketch.
sub_sketch_keys : list
The list of sub sketch to calculate, for XArray of dictionary type.
key needs to be a string, for XArray of vector(array) type, the key
needs to be positive integer
"""
if impl:
self.__impl__ = impl
else:
self.__impl__ = SketchImpl()
if not isinstance(array, XArray):
raise TypeError("Sketch object can only be constructed from XArrays")
self.__impl__.construct_from_xarray(array.__impl__, sub_sketch_keys)
class Sketch(object):
"""
The Sketch object contains a sketch of a single XArray (a column of an
SFrame). Using a sketch representation of an XArray, many approximate and
exact statistics can be computed very quickly.
To construct a Sketch object, the following methods are equivalent:
>>> my_xarray = xpatterns.XArray([1,2,3,4,5])
>>> sketch = xpatterns.Sketch(my_xarray)
>>> sketch = my_xarray.sketch_summary()
Typically, the XArray is a column of an XFrame:
>>> my_sframe = xpatterns.XFrame({'column1': [1,2,3]})
>>> sketch = xpatterns.Sketch(my_sframe['column1'])
>>> sketch = my_sframe['column1'].sketch_summary()
The sketch computation is fast, with complexity approximately linear in the
length of the XArray. After the Sketch is computed, all queryable functions
are performed nearly instantly.
A sketch can compute the following information depending on the dtype of the
XArray:
For numeric columns, the following information is provided exactly:
- length (:func:`~xpatterns.Sketch.size`)
- number of missing Values (:func:`~xpatterns.Sketch.num_undefined`)
- minimum value (:func:`~xpatterns.Sketch.min`)
- maximum value (:func:`~xpatterns.Sketch.max`)
- mean (:func:`~xpatterns.Sketch.mean`)
- variance (:func:`~xpatterns.Sketch.var`)
- standard deviation (:func:`~xpatterns.Sketch.std`)
And the following information is provided approximately:
- number of unique values (:func:`~xpatterns.Sketch.num_unique`)
- quantiles (:func:`~xpatterns.Sketch.quantile`)
- frequent items (:func:`~xpatterns.Sketch.frequent_items`)
- frequency count for any value (:func:`~xpatterns.Sketch.frequency_count`)
For non-numeric columns(str), the following information is provided exactly:
- length (:func:`~xpatterns.Sketch.size`)
- number of missing values (:func:`~xpatterns.Sketch.num_undefined`)
And the following information is provided approximately:
- number of unique Values (:func:`~xpatterns.Sketch.num_unique`)
- frequent items (:func:`~xpatterns.Sketch.frequent_items`)
- frequency count of any value (:func:`~xpatterns.Sketch.frequency_count`)
For XArray of type list or array, there is a sub sketch for all sub elements.
The sub sketch flattens all list/array values and then computes sketch summary over flattened values.
Element sub sketch may be retrieved through:
- element_summary(:func:`~xpatterns.Sketch.element_summary`)
For XArray of type dict, there are sub sketches for both dict key and value.
The sub sketch may be retrieved through:
- dict_key_summary(:func:`~xpatterns.Sketch.dict_key_summary`)
- dict_value_summary(:func:`~xpatterns.Sketch.dict_value_summary`)
For XArray of type dict, user can also pass in a list of dictionary keys to
sketch_summary function, this would generate one sub sketch for each key.
For example:
>>> sa = xpatterns.XArray([{'a':1, 'b':2}, {'a':3}])
>>> sketch = sa.sketch_summary(sub_sketch_keys=["a", "b"])
Then the sub summary may be retrieved by:
>>> sketch.element_sub_sketch()
or to get subset keys:
>>> sketch.element_sub_sketch(["a"])
Similarly, for XArray of type vector(array), user can also pass in a list of
integers which is the index into the vector to get sub sketch
For example:
>>> sa = xpatterns.XArray([[100,200,300,400,500], [100,200,300], [400,500]])
>>> sketch = sa.sketch_summary(sub_sketch_keys=[1,3,5])
Then the sub summary may be retrieved by:
>>> sketch.element_sub_sketch()
Or:
>>> sketch.element_sub_sketch([1,3])
for subset of keys.
Please see the individual function documentation for detail about each of
these statistics.
Parameters
----------
array : XArray
Array to generate sketch summary.
References
----------
- Wikipedia. `Streaming algorithms. <http://en.wikipedia.org/wiki/Streaming_algorithm>`_
- Charikar, et al. (2002) `Finding frequent items in data streams.
<https://www.cs.rutgers.edu/~farach/pubs/FrequentStream.pdf>`_
- Cormode, G. and Muthukrishnan, S. (2004) `An Improved Data Stream Summary:
The Count-Min Sketch and its Applications.
<http://dimacs.rutgers.edu/~graham/pubs/papers/cm-latin.pdf>`_
"""
def __init__(self, array=None, sub_sketch_keys=[], impl=None):
"""__init__(array)
Construct a new Sketch from an XArray.
Parameters
----------
array : XArray
Array to sketch.
sub_sketch_keys : list
The list of sub sketch to calculate, for XArray of dictionary type.
key needs to be a string, for XArray of vector(array) type, the key
needs to be positive integer
"""
if impl:
self.__impl__ = impl
else:
self.__impl__ = SketchImpl()
if not isinstance(array, XArray):
raise TypeError("Sketch object can only be constructed from XArrays")
self.__impl__.construct_from_xarray(array.__impl__, sub_sketch_keys)
def __repr__(self):
"""
Emits a brief summary of all the statistics as a string.
"""
return "<sketch>" # TODO remove
fields = [
['size', 'Length' , 'Yes'],
['min', 'Min' , 'Yes'],
['max', 'Max' , 'Yes'],
['mean', 'Mean' , 'Yes'],
['sum', 'Sum' , 'Yes'],
['var', 'Variance' , 'Yes'],
['std', 'Standard Deviation' , 'Yes'],
['num_undefined', '# Missing Values' , 'Yes',],
['num_unique', '# unique values', 'No' ]
]
s = '\n'
result = []
for field in fields:
try:
method_to_call = getattr(self, field[0])
result.append([field[1], str(method_to_call()), field[2]])
except:
pass
sf = XArray(result).unpack(column_name_prefix = "")
sf.rename({'0': 'item', '1':'value', '2': 'is exact'})
s += sf.__str__(footer=False)
s += "\n"
s += "\nMost frequent items:\n"
frequent = self.frequent_items()
sorted_freq = sorted(frequent.iteritems(), key=operator.itemgetter(1), reverse=True)
if len(sorted_freq) == 0:
s += " -- All elements appear with less than 0.01% frequency -- \n"
else:
sorted_freq = sorted_freq[:10]
sf = XFrame()
sf.add_column(XArray(['count']), 'value')
for elem in sorted_freq:
sf.add_column(XArray([elem[1]]), str(elem[0]))
s += sf.__str__(footer=False) + "\n"
s += "\n"
try:
# print quantiles
t = self.quantile(0)
s += "Quantiles: \n"
sf = XFrame()
for q in [0.0,0.01,0.05,0.25,0.5,0.75,0.95,0.99,1.00]:
sf.add_column(XArray([self.quantile(q)]), str(int(q * 100)) + '%')
s += sf.__str__(footer=False) + "\n"
except:
pass
try:
t_k = self.dict_key_summary()
t_v = self.dict_value_summary()
s += "\n******** Dictionary Element Key Summary ********\n"
s += t_k.__repr__()
s += "\n******** Dictionary Element Value Summary ********\n"
s += t_v.__repr__() + '\n'
except:
pass
try:
t_k = self.element_summary()
s += "\n******** Element Summary ********\n"
s += t_k.__repr__() + '\n'
except:
pass
return s.expandtabs(8)
def __str__(self):
"""
Emits a brief summary of all the statistics as a string.
"""
return self.__repr__()
def size(self):
"""
Returns the size of the input XArray.
Returns
-------
out : int
The number of elements of the input XArray.
"""
return int(self.__impl__.size())
def max(self):
"""
Returns the maximum value in the XArray. Returns *nan* on an empty
array. Throws an exception if called on an XArray with non-numeric type.
Raises
------
RuntimeError
Throws an exception if the XArray is a non-numeric type.
Returns
-------
out : type of XArray
Maximum value of XArray. Returns nan if the XArray is empty.
"""
return self.__impl__.max()
def min(self):
"""
Returns the minimum value in the XArray. Returns *nan* on an empty
array. Throws an exception if called on an XArray with non-numeric type.
Raises
------
RuntimeError
If the xarray is a non-numeric type.
Returns
-------
out : type of XArray
Minimum value of XArray. Returns nan if the xarray is empty.
"""
return self.__impl__.min()
def sum(self):
"""
Returns the sum of all the values in the XArray. Returns 0 on an empty
array. Throws an exception if called on an xarray with non-numeric type.
Will overflow without warning.
Raises
------
RuntimeError
If the xarray is a non-numeric type.
Returns
-------
out : type of XArray
Sum of all values in XArray. Returns 0 if the XArray is empty.
"""
return self.__impl__.sum()
def mean(self):
"""
Returns the mean of the values in the XArray. Returns 0 on an empty
array. Throws an exception if called on an XArray with non-numeric type.
Raises
------
RuntimeError
If the xarray is a non-numeric type.
Returns
-------
out : float
Mean of all values in XArray. Returns 0 if the xarray is empty.
"""
return self.__impl__.mean()
def std(self):
"""
Returns the standard deviation of the values in the XArray. Returns 0 on
an empty array. Throws an exception if called on an XArray with
non-numeric type.
Returns
-------
out : float
The standard deviation of all the values. Returns 0 if the xarray is
empty.
Raises
------
RuntimeError
If the xarray is a non-numeric type.
"""
return sqrt(self.var())
def var(self):
"""
Returns the variance of the values in the xarray. Returns 0 on an empty
array. Throws an exception if called on an XArray with non-numeric type.
Raises
------
RuntimeError
If the xarray is a non-numeric type.
Returns
-------
out : float
The variance of all the values. Returns 0 if the XArray is empty.
"""
return self.__impl__.var()
def num_undefined(self):
"""
Returns the the number of undefined elements in the XArray. Return 0
on an empty XArray.
Returns
-------
out : int
The number of missing values in the XArray.
"""
return int(self.__impl__.num_undefined())
def num_unique(self):
"""
Returns a sketched estimate of the number of unique values in the
XArray based on the Hyperloglog sketch.
Returns
-------
out : float
An estimate of the number of unique values in the XArray.
"""
return int(self.__impl__.num_unique())
def frequent_items(self):
"""
Returns a sketched estimate of the most frequent elements in the XArray
based on the SpaceSaving sketch. It is only guaranteed that all
elements which appear in more than 0.01% rows of the array will
appear in the set of returned elements. However, other elements may
also appear in the result. The item counts are estimated using
the CountSketch.
Missing values are not taken into account when copmuting frequent items.
If this function returns no elements, it means that all elements appear
with less than 0.01% occurrence.
Returns
-------
out : dict
A dictionary mapping items and their estimated occurrence frequencies.
"""
return self.__impl__.frequent_items()
def quantile(self, quantile_val):
"""
Returns a sketched estimate of the value at a particular quantile
between 0.0 and 1.0. The quantile is guaranteed to be accurate within
1%: meaning that if you ask for the 0.55 quantile, the returned value is
guaranteed to be between the true 0.54 quantile and the true 0.56
quantile. The quantiles are only defined for numeric arrays and this
function will throw an exception if called on a sketch constructed for a
non-numeric column.
Parameters
----------
quantile_val : float
A value between 0.0 and 1.0 inclusive. Values below 0.0 will be
interpreted as 0.0. Values above 1.0 will be interpreted as 1.0.
Raises
------
RuntimeError
If the xarray is a non-numeric type.
Returns
-------
out : float | str
An estimate of the value at a quantile.
"""
return self.__impl__.get_quantile(quantile_val)
def frequency_count(self, element):
"""
Returns a sketched estimate of the number of occurrences of a given
element. This estimate is based on the count sketch. The element type
must be of the same type as the input XArray. Throws an exception if
element is of the incorrect type.
Parameters
----------
element : val
An element of the same type as the XArray.
Raises
------
RuntimeError
Throws an exception if element is of the incorrect type.
Returns
-------
out : int
An estimate of the number of occurrences of the element.
"""
return int(self.__impl__.frequency_count(element))
def element_length_summary(self):
"""
Returns the sketch summary for the element length. This is only valid for
a sketch constructed XArray of type list/array/dict, raises Runtime
exception otherwise.
Examples
--------
>>> sa = xpatterns.XArray([[j for j in range(i)] for i in range(1,1000)])
>>> sa.sketch_summary().element_length_summary()
+--------------------+---------------+----------+
| item | value | is exact |
+--------------------+---------------+----------+
| Length | 999 | Yes |
| Min | 1.0 | Yes |
| Max | 999.0 | Yes |
| Mean | 500.0 | Yes |
| Sum | 499500.0 | Yes |
| Variance | 83166.6666667 | Yes |
| Standard Deviation | 288.386314978 | Yes |
| # Missing Values | 0 | Yes |
| # unique values | 992 | No |
+--------------------+---------------+----------+
Most frequent items:
+-------+---+---+---+---+---+---+---+---+---+----+
| value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+-------+---+---+---+---+---+---+---+---+---+----+
| count | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+-------+---+---+---+---+---+---+---+---+---+----+
Quantiles:
+-----+------+------+-------+-------+-------+-------+-------+-------+
| 0% | 1% | 5% | 25% | 50% | 75% | 95% | 99% | 100% |
+-----+------+------+-------+-------+-------+-------+-------+-------+
| 1.0 | 10.0 | 50.0 | 250.0 | 500.0 | 750.0 | 950.0 | 990.0 | 999.0 |
+-----+------+------+-------+-------+-------+-------+-------+-------+
Returns
-------
out : Sketch
An new sketch object regarding the element length of the current XArray
"""
return Sketch(impl = self.__impl__.element_length_summary())
def dict_key_summary(self):
"""
Returns the sketch summary for all dictionary keys. This is only valid
for sketch object from an XArray of dict type. Dictionary keys are
converted to strings and then do the sketch summary.
Examples
--------
>>> sa = xpatterns.XArray([{'I':1, 'love': 2}, {'nature':3, 'beauty':4}])
>>> sa.sketch_summary().dict_key_summary()
+------------------+-------+----------+
| item | value | is exact |
+------------------+-------+----------+
| Length | 4 | Yes |
| # Missing Values | 0 | Yes |
| # unique values | 4 | No |
+------------------+-------+----------+
Most frequent items:
+-------+---+------+--------+--------+
| value | I | love | beauty | nature |
+-------+---+------+--------+--------+
| count | 1 | 1 | 1 | 1 |
+-------+---+------+--------+--------+
"""
return Sketch(impl = self.__impl__.dict_key_summary())
def dict_value_summary(self):
"""
Returns the sketch summary for all dictionary values. This is only valid
for sketch object from an XArray of dict type.
Type of value summary is inferred from first set of values.
Examples
--------
>>> sa = xpatterns.XArray([{'I':1, 'love': 2}, {'nature':3, 'beauty':4}])
>>> sa.sketch_summary().dict_value_summary()
+--------------------+---------------+----------+
| item | value | is exact |
+--------------------+---------------+----------+
| Length | 4 | Yes |
| Min | 1.0 | Yes |
| Max | 4.0 | Yes |
| Mean | 2.5 | Yes |
| Sum | 10.0 | Yes |
| Variance | 1.25 | Yes |
| Standard Deviation | 1.11803398875 | Yes |
| # Missing Values | 0 | Yes |
| # unique values | 4 | No |
+--------------------+---------------+----------+
Most frequent items:
+-------+-----+-----+-----+-----+
| value | 1.0 | 2.0 | 3.0 | 4.0 |
+-------+-----+-----+-----+-----+
| count | 1 | 1 | 1 | 1 |
+-------+-----+-----+-----+-----+
Quantiles:
+-----+-----+-----+-----+-----+-----+-----+-----+------+
| 0% | 1% | 5% | 25% | 50% | 75% | 95% | 99% | 100% |
+-----+-----+-----+-----+-----+-----+-----+-----+------+
| 1.0 | 1.0 | 1.0 | 2.0 | 3.0 | 4.0 | 4.0 | 4.0 | 4.0 |
+-----+-----+-----+-----+-----+-----+-----+-----+------+
"""
return Sketch(impl = self.__impl__.dict_value_summary())
def element_summary(self):
"""
Returns the sketch summary for all element values. This is only valid for
sketch object created from XArray of list or vector(array) type.
For XArray of list type, all list values are treated as string for
sketch summary.
For XArray of vector type, the sketch summary is on FLOAT type.
Examples
--------
>>> sa = xpatterns.XArray([[1,2,3], [4,5]])
>>> sa.sketch_summary().element_summary()
+--------------------+---------------+----------+
| item | value | is exact |
+--------------------+---------------+----------+
| Length | 5 | Yes |
| Min | 1.0 | Yes |
| Max | 5.0 | Yes |
| Mean | 3.0 | Yes |
| Sum | 15.0 | Yes |
| Variance | 2.0 | Yes |
| Standard Deviation | 1.41421356237 | Yes |
| # Missing Values | 0 | Yes |
| # unique values | 5 | No |
+--------------------+---------------+----------+
Most frequent items:
+-------+-----+-----+-----+-----+-----+
| value | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 |
+-------+-----+-----+-----+-----+-----+
| count | 1 | 1 | 1 | 1 | 1 |
+-------+-----+-----+-----+-----+-----+
Quantiles:
+-----+-----+-----+-----+-----+-----+-----+-----+------+
| 0% | 1% | 5% | 25% | 50% | 75% | 95% | 99% | 100% |
+-----+-----+-----+-----+-----+-----+-----+-----+------+
| 1.0 | 1.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 5.0 | 5.0 |
+-----+-----+-----+-----+-----+-----+-----+-----+------+
"""
return Sketch(impl = self.__impl__.element_summary())
def element_sub_sketch(self, keys = None):
"""
Returns the sketch summary for the given set of keys. This is only
applicable for sketch summary created from XArray of xarray or dict type.
For dict XArray, the keys are the keys in dict value.
For array Xarray, the keys are indexes into the array value.
The keys must be passed into original sketch_summary() call in order to
be able to be retrieved later
Parameters
-----------
keys : list of str | str | list of int | int
The list of dictionary keys or array index to get sub sketch from.
if not given, then retrieve all sub sketches that are available
Returns
-------
A dictionary that maps from the key(index) to the actual sketch summary
for that key(index)
Examples
--------
>>> sa = xpatterns.XArray([{'a':1, 'b':2}, {'a':4, 'd':1}])
>>> s = sa.sketch_summary(sub_sketch_keys=['a','b'])
>>> s.element_sub_sketch(['a'])
{'a':
+--------------------+-------+----------+
| item | value | is exact |
+--------------------+-------+----------+
| Length | 2 | Yes |
| Min | 1.0 | Yes |
| Max | 4.0 | Yes |
| Mean | 2.5 | Yes |
| Sum | 5.0 | Yes |
| Variance | 2.25 | Yes |
| Standard Deviation | 1.5 | Yes |
| # Missing Values | 0 | Yes |
| # unique values | 2 | No |
+--------------------+-------+----------+
Most frequent items:
+-------+-----+-----+
| value | 1.0 | 4.0 |
+-------+-----+-----+
| count | 1 | 1 |
+-------+-----+-----+
Quantiles:
+-----+-----+-----+-----+-----+-----+-----+-----+------+
| 0% | 1% | 5% | 25% | 50% | 75% | 95% | 99% | 100% |
+-----+-----+-----+-----+-----+-----+-----+-----+------+
| 1.0 | 1.0 | 1.0 | 1.0 | 4.0 | 4.0 | 4.0 | 4.0 | 4.0 |
+-----+-----+-----+-----+-----+-----+-----+-----+------+}
"""
single_val = False
if keys is None:
keys = []
else:
if not hasattr(keys, "__iter__"):
single_val = True
keys = [keys]
value_types = set([type(i) for i in keys])
if len(value_types) > 1:
raise ValueError("All keys should have the same type.")
ret_sketches = self.__impl__.element_sub_sketch(keys)
ret = {}
# check return key matches input key
for key in keys:
if key not in ret_sketches:
raise KeyError("Cannot retrieve element sub sketch for key '" +
str(key) +
"'. Element sub sketch can only be retrieved when the sketch_summary " +
"object was created using the 'sub_sketch_keys' option.")
for key in ret_sketches:
ret[key] = Sketch(impl = ret_sketches[key])
if single_val:
return ret[keys[0]]
else:
return ret
