Processing Cartesian Products with PyODPS DataFrame

By Ji Sheng

PyODPS provides DataFrame APIs to analyze and preprocess large-scale data with interfaces like Pandas. This article mainly introduces how to use PyODPS to perform Cartesian product operations.

The most common scenario of Cartesian products is the comparison or operation of two collections. Taking the computation of geographic distance as an example, assume that the big table Coordinates1 stores the longitude and latitude coordinates of destination points, with a total of M rows of data, while the small table Coordinates2 stores the longitude and latitude coordinates of departure points, with a total of N rows of data. Now, the coordinates of all the departure points closest to each of the destination points need to be computed. For a destination point, we need to compute the distance from all the departure points to the destination point and find the minimum distance. Therefore, the entire intermediate process requires M * N data records, which results in a Cartesian product.

Haversine Formula

def  haversine(lat1,  lon1,  lat2,  lon2):
# lat1, lon1 为位置 1 的经纬度坐标
# lat2, lon2 为位置 2 的经纬度坐标
import numpy as np
a = np.sin( dlat /2 ) **2 + np.cos(np.radians(lat1)) * np.cos(np.radians(lat2)) * np.sin( dlon /2 ) **2
c = 2 * np.arcsin(np.sqrt(a))
r = 6371 # 地球平均半径，单位为公里
return c * r

MapJoin

In  :  df1  =  o.get_table('coordinates1').to_df()                                                                                                                                                                                        In  :  df2  =  o.get_table('coordinates2').to_df()                                                                                                                                                                                        In  :  df3  =  df1.join(df2,  mapjoin=True)                                                                                                                                                                                                        In  :  df1.schema
Out:
odps.Schema {
latitude float64
longitude float64
id string
}
In : df2.schema
Out:
odps.Schema {
latitude float64
longitude float64
id string
}
In : df3.schema
Out:
odps.Schema {
latitude_x float64
longitude_x float64
id_x string
latitude_y float64
longitude_y float64
id_y string
}

We can see that the _x and _y suffixes are added to the duplicate columns by default during Join operations. The suffixes can be customized by passing a binary tuple in the suffixes parameter. After the joined table is obtained, the distance can be computed by using the user-defined function DataFrame in PyODPS, which is very simple, clear and efficient.

In  :  r  =  6371
...: dis1 = (df3.latitude_y - df3.latitude_x).radians()
...: dis2 = (df3.longitude_y - df3.longitude_x).radians()
...: a = (dis1 / 2).sin() ** 2 + df3.latitude_x.radians().cos() * df3.latitude_y.radians().cos() * (dis2 / 2).sin() ** 2
...: df3['dis'] = 2 * a.sqrt().arcsin() * r

Out:
latitude_x longitude_x id_x latitude_y longitude_y id_y dis
0 76.252432 59.628253 0 84.045210 6.517522 0 1246.864981
1 76.252432 59.628253 0 59.061796 0.794939 1 2925.953147
2 76.252432 59.628253 0 42.368304 30.119837 2 4020.604942
3 76.252432 59.628253 0 81.290936 51.682749 3 584.779748
4 76.252432 59.628253 0 34.665222 147.167070 4 6213.944942
5 76.252432 59.628253 0 58.058854 165.471565 5 4205.219179
6 76.252432 59.628253 0 79.150677 58.661890 6 323.070785
7 76.252432 59.628253 0 72.622352 123.195778 7 1839.380760
8 76.252432 59.628253 0 80.063614 138.845193 8 1703.782421
9 76.252432 59.628253 0 36.231584 90.774527 9 4717.284949
In : df1.count()
Out: 2000
In : df2.count()
Out: 100
In : df3.count()
Out: 200000

df3 already has M * N data records. Next, if we need to know the minimum distance, we can directly call groupby to df3, followed by the min aggregate function, to get the minimum distance of each target point.

Out:
dis_min
0 323.070785
1 64.755493
2 1249.283169
3 309.818288
4 1790.484748
5 385.107739
6 498.816157
7 615.987467
8 437.765432
9 272.589621

Table Resources

## use dataframe udfdf1 = o.get_table('coordinates1').to_df()
df2 = o.get_table('coordinates2').to_df()
def func(collections):
import pandas as pd

collection = collections

ids = []
latitudes = []
longitudes = []
for r in collection:
ids.append(r.id)
latitudes.append(r.latitude)
longitudes.append(r.longitude)
df = pd.DataFrame({'id': ids, 'latitude':latitudes, 'longitude':longitudes})
def h(x):
df['dis'] = haversine(x.latitude, x.longitude, df.latitude, df.longitude)
return df.iloc[df['dis'].idxmin()]['id']
return h
df1[df1.id, df1.apply(func, resources=[df2], axis=1, reduce=True, types='string').rename('min_id')].execute(
libraries=['pandas.zip', 'python-dateutil.zip', 'pytz.zip', 'six.tar.gz'])

In a UDF, the table resource is looped to be read into the Pandas DataFrame, and the row corresponding to the minimum value can be easily found by using the Pandas loc, thus obtaining the ID of the closest departure point.

Global Variable

df1 = o.get_table('coordinates1').to_df()
df2 = o.get_table('coordinates2').to_df()
df = df2.to_pandas()
def func(x):
df['dis'] = haversine(x.latitude, x.longitude, df.latitude, df.longitude)
return df.iloc[df['dis'].idxmin()]['id']
df1[df1.id, df1.apply(func, axis=1, reduce=True, types='string').rename('min_id')].execute(
libraries=['pandas.zip', 'python-dateutil.zip', 'pytz.zip', 'six.tar.gz'])

When the function is uploaded, the global variables (df in the above code) used in the function will be pickled into the UDF. However, note that applicable use cases for this method are very limited, because the size of files to be uploaded in ODPS is limited. Therefore, if there is too much data, the resources generated by the UDF will be too large to be uploaded. In addition, for this method, it is better to ensure that the client version of the third-party package is consistent with that of the server. Otherwise, serialization problems are very likely to occur, so we recommend that you only use this method when dealing with small data volumes.

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