Table Operations#
In this section we describe high-level operations that can be used to generate a new table from one or more input tables. This includes:
Documentation |
Description |
Function |
|---|---|---|
Group tables and columns by keys |
||
Binning tables |
||
Concatenate input tables along rows |
||
Concatenate input tables along columns |
||
Database-style join of two tables |
||
Unique table rows by keys |
||
Set difference of two tables |
||
Generic difference of two simple tables |
Grouped Operations#
Sometimes in a table or table column there are natural groups within the dataset for which it makes sense to compute some derived values. A minimal example is a list of objects with photometry from various observing runs:
>>> from astropy.table import Table
>>> obs = Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 17.5
... M31 2012-01-02 17.1 17.4
... M101 2012-01-02 15.1 13.5
... M82 2012-02-14 16.2 14.5
... M31 2012-02-14 16.9 17.3
... M82 2012-02-14 15.2 15.5
... M101 2012-02-14 15.0 13.6
... M82 2012-03-26 15.7 16.5
... M101 2012-03-26 15.1 13.5
... M101 2012-03-26 14.8 14.3
... """, format='ascii')
>>> # Make sure magnitudes are printed with one digit after the decimal point
>>> obs['mag_b'].info.format = '{:.1f}'
>>> obs['mag_v'].info.format = '{:.1f}'
Table Groups#
Now suppose we want the mean magnitudes for each object. We first group the data
by the name column with the group_by() method.
This returns a new table sorted by name which has a groups property
specifying the unique values of name and the corresponding table rows:
>>> obs_by_name = obs.group_by('name')
>>> print(obs_by_name)
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-01-02 15.1 13.5 << First group (index=0, key='M101')
M101 2012-02-14 15.0 13.6
M101 2012-03-26 15.1 13.5
M101 2012-03-26 14.8 14.3
M31 2012-01-02 17.0 17.5 << Second group (index=4, key='M31')
M31 2012-01-02 17.1 17.4
M31 2012-02-14 16.9 17.3
M82 2012-02-14 16.2 14.5 << Third group (index=7, key='M83')
M82 2012-02-14 15.2 15.5
M82 2012-03-26 15.7 16.5
<< End of groups (index=10)
>>> print(obs_by_name.groups.keys)
name
----
M101
M31
M82
>>> print(obs_by_name.groups.indices)
[ 0 4 7 10]
The groups property is the portal to all grouped operations with tables and
columns. It defines how the table is grouped via an array of the unique row key
values and the indices of the group boundaries for those key values. The groups
here correspond to the row slices 0:4, 4:7, and 7:10 in the
obs_by_name table.
The output grouped table has two important properties:
The groups in the order of the lexically sorted key values (
M101,M31,M82in our example).The rows within each group are in the same order as they appear in the original table.
The initial argument (keys) for the group_by()
function can take a number of input data types:
Single string value with a table column name (as shown above)
List of string values with table column names
numpystructured array with same length as tablenumpyhomogeneous array with same length as table
In all cases the corresponding row elements are considered as a tuple
of values which form a key value that is used to sort the original table and
generate the required groups.
As an example, to get the average magnitudes for each object on each observing
night, we would first group the table on both name and obs_date as
follows:
>>> print(obs.group_by(['name', 'obs_date']).groups.keys)
name obs_date
---- ----------
M101 2012-01-02
M101 2012-02-14
M101 2012-03-26
M31 2012-01-02
M31 2012-02-14
M82 2012-02-14
M82 2012-03-26
Manipulating Groups#
Once you have applied grouping to a table then you can access the individual groups or subsets of groups. In all cases this returns a new grouped table. For instance, to get the subtable which corresponds to the second group (index=1) do:
>>> print(obs_by_name.groups[1])
name obs_date mag_b mag_v
---- ---------- ----- -----
M31 2012-01-02 17.0 17.5
M31 2012-01-02 17.1 17.4
M31 2012-02-14 16.9 17.3
To get the first and second groups together use a slice:
>>> groups01 = obs_by_name.groups[0:2]
>>> print(groups01)
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-01-02 15.1 13.5
M101 2012-02-14 15.0 13.6
M101 2012-03-26 15.1 13.5
M101 2012-03-26 14.8 14.3
M31 2012-01-02 17.0 17.5
M31 2012-01-02 17.1 17.4
M31 2012-02-14 16.9 17.3
>>> print(groups01.groups.keys)
name
----
M101
M31
You can also supply a numpy array of indices or a boolean mask to select
particular groups, for example:
>>> mask = obs_by_name.groups.keys['name'] == 'M101'
>>> print(obs_by_name.groups[mask])
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-01-02 15.1 13.5
M101 2012-02-14 15.0 13.6
M101 2012-03-26 15.1 13.5
M101 2012-03-26 14.8 14.3
You can iterate over the group subtables and corresponding keys with:
>>> for key, group in zip(obs_by_name.groups.keys, obs_by_name.groups):
... print(f'****** {key["name"]} *******')
... print(group)
... print('')
...
****** M101 *******
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-01-02 15.1 13.5
M101 2012-02-14 15.0 13.6
M101 2012-03-26 15.1 13.5
M101 2012-03-26 14.8 14.3
****** M31 *******
name obs_date mag_b mag_v
---- ---------- ----- -----
M31 2012-01-02 17.0 17.5
M31 2012-01-02 17.1 17.4
M31 2012-02-14 16.9 17.3
****** M82 *******
name obs_date mag_b mag_v
---- ---------- ----- -----
M82 2012-02-14 16.2 14.5
M82 2012-02-14 15.2 15.5
M82 2012-03-26 15.7 16.5
Column Groups#
Like Table objects, Column objects can also be grouped for subsequent
manipulation with grouped operations. This can apply both to columns within a
Table or bare Column objects.
As for Table, the grouping is generated with the
group_by() method. The difference here is that
there is no option of providing one or more column names since that
does not make sense for a Column.
Examples#
To generate grouping in columns:
>>> from astropy.table import Column
>>> import numpy as np
>>> c = Column([1, 2, 3, 4, 5, 6], name='a')
>>> key_vals = np.array(['foo', 'bar', 'foo', 'foo', 'qux', 'qux'])
>>> cg = c.group_by(key_vals)
>>> for key, group in zip(cg.groups.keys, cg.groups):
... print(f'****** {key} *******')
... print(group)
... print('')
...
****** bar *******
a
---
2
****** foo *******
a
---
1
3
4
****** qux *******
a
---
5
6
Aggregation#
Aggregation is the process of applying a specified reduction function to the
values within each group for each non-key column. This function must accept a
numpy.ndarray as the first argument and return a single scalar value. Common
function examples are numpy.sum(), numpy.mean(), and
numpy.std().
For the example grouped table obs_by_name from above, we compute the group
means with the aggregate() method:
>>> obs_mean = obs_by_name.groups.aggregate(np.mean)
AstropyUserWarning: Cannot aggregate column 'obs_date' with type '<U10': ...
>>> print(obs_mean)
name mag_b mag_v
---- ----- -----
M101 15.0 13.7
M31 17.0 17.4
M82 15.7 15.5
It seems the magnitude values were successfully averaged, but what about the
AstropyUserWarning? Since the obs_date
column is a string-type array, the numpy.mean() function failed and
raised an exception cannot perform reduceat with flexible type. Any time this happens
aggregate() will issue a warning and
then drop that column from the output result. Note that the name column is
one of the keys used to determine the grouping so it is automatically
ignored from aggregation.
From a grouped table it is possible to select one or more columns on which to perform the aggregation:
>>> print(obs_by_name['mag_b'].groups.aggregate(np.mean))
mag_b
-----
15.0
17.0
15.7
The order of the columns can be specified too:
>>> print(obs_by_name['name', 'mag_v', 'mag_b'].groups.aggregate(np.mean))
name mag_v mag_b
---- ----- -----
M101 13.7 15.0
M31 17.4 17.0
M82 15.5 15.7
A single column of data can be aggregated as well:
>>> c = Column([1, 2, 3, 4, 5, 6], name='a')
>>> key_vals = np.array(['foo', 'bar', 'foo', 'foo', 'qux', 'qux'])
>>> cg = c.group_by(key_vals)
>>> cg_sums = cg.groups.aggregate(np.sum)
>>> for key, cg_sum in zip(cg.groups.keys, cg_sums):
... print(f'Sum for {key} = {cg_sum}')
...
Sum for bar = 2
Sum for foo = 8
Sum for qux = 11
If the specified function has a numpy.ufunc.reduceat() method, this will
be called instead. This can improve the performance by a factor of 10 to 100
(or more) for large unmasked tables or columns with many relatively small
groups. It also allows for the use of certain numpy functions which
normally take more than one input array but also work as reduction functions,
like numpy.add. The numpy functions which should take advantage of using
numpy.ufunc.reduceat() include:
In special cases, numpy.sum() and numpy.mean() are substituted with
their respective reduceat methods.
Filtering#
Table groups can be filtered by means of the
filter() method. This is done by
supplying a function which is called for each group. The function
which is passed to this method must accept two arguments:
table:Tableobjectkey_colnames: list of columns intableused as keys for grouping
It must then return either True or False.
Example#
The following will select all table groups with only positive values in the non- key columns:
>>> def all_positive(table, key_colnames):
... colnames = [name for name in table.colnames if name not in key_colnames]
... for colname in colnames:
... if np.any(table[colname] <= 0):
... return False
... return True
An example of using this function is:
>>> t = Table.read(""" a b c
... -2 7.0 2
... -2 5.0 1
... 1 3.0 -5
... 1 -2.0 -6
... 1 1.0 7
... 0 4.0 4
... 3 3.0 5
... 3 -2.0 6
... 3 1.0 7""", format='ascii')
>>> tg = t.group_by('a')
>>> t_positive = tg.groups.filter(all_positive)
>>> for group in t_positive.groups:
... print(group)
... print('')
...
a b c
--- --- ---
-2 7.0 2
-2 5.0 1
a b c
--- --- ---
0 4.0 4
As can be seen only the groups with a == -2 and a == 0 have all
positive values in the non-key columns, so those are the ones that are selected.
Likewise a grouped column can be filtered with the
filter(), method but in this case the
filtering function takes only a single argument which is the column group. It
still must return either True or False. For example:
def all_positive(column):
return np.all(column > 0)
Binning#
A common tool in analysis is to bin a table based on some reference value. Examples:
Photometry of a binary star in several bands taken over a span of time which should be binned by orbital phase.
Reducing the sampling density for a table by combining 100 rows at a time.
Unevenly sampled historical data which should binned to four points per year.
All of these examples of binning a table can be accomplished using grouped operations. The examples in that section are focused on the case of discrete key values such as the name of a source. In this section we show a concise yet powerful way of applying grouped operations to accomplish binning on key values such as time, phase, or row number.
The common theme in all of these cases is to convert the key value array into a new float- or int-valued array whose values are identical for rows in the same output bin.
Example#
As an example, we generate a fake light curve:
>>> year = np.linspace(2000.0, 2010.0, 200) # 200 observations over 10 years
>>> period = 1.811
>>> y0 = 2005.2
>>> mag = 14.0 + 1.2 * np.sin(2 * np.pi * (year - y0) / period)
>>> phase = ((year - y0) / period) % 1.0
>>> dat = Table([year, phase, mag], names=['year', 'phase', 'mag'])
Now we make an array that will be used for binning the data by 0.25 year intervals:
>>> year_bin = np.trunc(year / 0.25)
This has the property that all samples in each 0.25 year bin have the same
value of year_bin. Think of year_bin as the bin number for year.
Then do the binning by grouping and immediately aggregating with
numpy.mean().
>>> dat_grouped = dat.group_by(year_bin)
>>> dat_binned = dat_grouped.groups.aggregate(np.mean)
We can plot the results with plt.plot(dat_binned['year'], dat_binned['mag'],
'.'). Alternately, we could bin into 10 phase bins:
>>> phase_bin = np.trunc(phase / 0.1)
>>> dat_grouped = dat.group_by(phase_bin)
>>> dat_binned = dat_grouped.groups.aggregate(np.mean)
This time, try plotting with plt.plot(dat_binned['phase'],
dat_binned['mag']).
Stack Vertically#
The Table class supports stacking tables vertically with the
vstack() function. This process is also commonly known as
concatenating or appending tables in the row direction. It corresponds roughly
to the numpy.vstack() function.
Examples#
Suppose we have two tables of observations with several column names in common:
>>> from astropy.table import Table, vstack
>>> obs1 = Table.read("""name obs_date mag_b logLx
... M31 2012-01-02 17.0 42.5
... M82 2012-10-29 16.2 43.5
... M101 2012-10-31 15.1 44.5""", format='ascii')
>>> obs2 = Table.read("""name obs_date logLx
... NGC3516 2011-11-11 42.1
... M31 1999-01-05 43.1
... M82 2012-10-30 45.0""", format='ascii')
Now we can stack these two tables:
>>> print(vstack([obs1, obs2]))
name obs_date mag_b logLx
------- ---------- ----- -----
M31 2012-01-02 17.0 42.5
M82 2012-10-29 16.2 43.5
M101 2012-10-31 15.1 44.5
NGC3516 2011-11-11 -- 42.1
M31 1999-01-05 -- 43.1
M82 2012-10-30 -- 45.0
Notice that the obs2 table is missing the mag_b column, so in the
stacked output table those values are marked as missing. This is the default
behavior and corresponds to join_type='outer'. There are two other allowed
values for the join_type argument, 'inner' and 'exact':
>>> print(vstack([obs1, obs2], join_type='inner'))
name obs_date logLx
------- ---------- -----
M31 2012-01-02 42.5
M82 2012-10-29 43.5
M101 2012-10-31 44.5
NGC3516 2011-11-11 42.1
M31 1999-01-05 43.1
M82 2012-10-30 45.0
>>> print(vstack([obs1, obs2], join_type='exact'))
Traceback (most recent call last):
...
TableMergeError: Inconsistent columns in input arrays (use 'inner'
or 'outer' join_type to allow non-matching columns)
In the case of join_type='inner', only the common columns (the intersection)
are present in the output table. When join_type='exact' is specified, then
vstack() requires that all of the input tables have
exactly the same column names.
More than two tables can be stacked by supplying a longer list of tables:
>>> obs3 = Table.read("""name obs_date mag_b logLx
... M45 2012-02-03 15.0 40.5""", format='ascii')
>>> print(vstack([obs1, obs2, obs3]))
name obs_date mag_b logLx
------- ---------- ----- -----
M31 2012-01-02 17.0 42.5
M82 2012-10-29 16.2 43.5
M101 2012-10-31 15.1 44.5
NGC3516 2011-11-11 -- 42.1
M31 1999-01-05 -- 43.1
M82 2012-10-30 -- 45.0
M45 2012-02-03 15.0 40.5
See also the sections on Merging metadata and Merging column attributes
for details on how these characteristics of the input tables are merged in the
single output table. Note also that you can use a single table Row instead of
a full table as one of the inputs.
Stack Horizontally#
The Table class supports stacking tables horizontally (in the column-wise
direction) with the hstack() function. It corresponds
roughly to the numpy.hstack() function.
Examples#
Suppose we have the following two tables:
>>> from astropy.table import Table, hstack
>>> t1 = Table.read("""a b c
... 1 foo 1.4
... 2 bar 2.1
... 3 baz 2.8""", format='ascii')
>>> t2 = Table.read("""d e
... ham eggs
... spam toast""", format='ascii')
Now we can stack these two tables horizontally:
>>> print(hstack([t1, t2]))
a b c d e
--- --- --- ---- -----
1 foo 1.4 ham eggs
2 bar 2.1 spam toast
3 baz 2.8 -- --
As with vstack(), there is an optional join_type
argument that can take values 'inner', 'exact', and 'outer'. The
default is 'outer', which effectively takes the union of available rows and
masks out any missing values. This is illustrated in the example above. The
other options give the intersection of rows, where 'exact' requires that
all tables have exactly the same number of rows:
>>> print(hstack([t1, t2], join_type='inner'))
a b c d e
--- --- --- ---- -----
1 foo 1.4 ham eggs
2 bar 2.1 spam toast
>>> print(hstack([t1, t2], join_type='exact'))
Traceback (most recent call last):
...
TableMergeError: Inconsistent number of rows in input arrays (use 'inner' or
'outer' join_type to allow non-matching rows)
More than two tables can be stacked by supplying a longer list of tables. The example below also illustrates the behavior when there is a conflict in the input column names (see the section on Column renaming for details):
>>> t3 = Table.read("""a b
... M45 2012-02-03""", format='ascii')
>>> print(hstack([t1, t2, t3]))
a_1 b_1 c d e a_3 b_3
--- --- --- ---- ----- --- ----------
1 foo 1.4 ham eggs M45 2012-02-03
2 bar 2.1 spam toast -- --
3 baz 2.8 -- -- -- --
The metadata from the input tables is merged by the process described in the
Merging metadata section. Note also that you can use a single table Row
instead of a full table as one of the inputs.
Stack Depth-Wise#
The Table class supports stacking columns within tables depth-wise using the
dstack() function. It corresponds roughly to running the
numpy.dstack() function on the individual columns matched by name.
Examples#
Suppose we have tables of data for sources giving information on the enclosed source counts for different PSF fractions:
>>> from astropy.table import Table, dstack
>>> src1 = Table.read("""psf_frac counts
... 0.10 45.
... 0.50 90.
... 0.90 120.
... """, format='ascii')
>>> src2 = Table.read("""psf_frac counts
... 0.10 200.
... 0.50 300.
... 0.90 350.
... """, format='ascii')
Now we can stack these two tables depth-wise to get a single table with the characteristics of both sources:
>>> srcs = dstack([src1, src2])
>>> print(srcs)
psf_frac counts
---------- --------------
0.1 .. 0.1 45.0 .. 200.0
0.5 .. 0.5 90.0 .. 300.0
0.9 .. 0.9 120.0 .. 350.0
In this case the counts for the first source are accessible as
srcs['counts'][:, 0], and likewise the second source counts are
srcs['counts'][:, 1].
For this function the length of all input tables must be the same. This
function can accept join_type and metadata_conflicts just like the
vstack() function. The join_type argument controls how
to handle mismatches in the columns of the input table.
See also the sections on Merging metadata and Merging column attributes
for details on how these characteristics of the input tables are merged in the
single output table. Note also that you can use a single table Row instead of
a full table as one of the inputs.
Join#
The Table class supports the database join operation. This provides a flexible
and powerful way to combine tables based on the values in one or more key
columns.
Examples#
Suppose we have two tables of observations, the first with B and V magnitudes and the second with X-ray luminosities of an overlapping (but not identical) sample:
>>> from astropy.table import Table, join
>>> optical = Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 16.0
... M82 2012-10-29 16.2 15.2
... M101 2012-10-31 15.1 15.5""", format='ascii')
>>> xray = Table.read(""" name obs_date logLx
... NGC3516 2011-11-11 42.1
... M31 1999-01-05 43.1
... M82 2012-10-29 45.0""", format='ascii')
The join() method allows you to merge these two tables into a single table based
on matching values in the “key columns”. By default, the key columns are the set
of columns that are common to both tables. In this case the key columns are
name and obs_date. We can find all of the observations of the same
object on the same date as follows:
>>> opt_xray = join(optical, xray)
>>> print(opt_xray)
name obs_date mag_b mag_v logLx
---- ---------- ----- ----- -----
M82 2012-10-29 16.2 15.2 45.0
We can perform the match by name only by providing the keys argument,
which can be either a single column name or a list of column names:
>>> print(join(optical, xray, keys='name'))
name obs_date_1 mag_b mag_v obs_date_2 logLx
---- ---------- ----- ----- ---------- -----
M31 2012-01-02 17.0 16.0 1999-01-05 43.1
M82 2012-10-29 16.2 15.2 2012-10-29 45.0
This output table has all of the observations that have both optical and X-ray
data for an object (M31 and M82). Notice that since the obs_date column
occurs in both tables, it has been split into two columns, obs_date_1 and
obs_date_2. The values are taken from the “left” (optical) and “right”
(xray) tables, respectively.
Different Join Options#
The table joins so far are known as “inner” joins and represent the strict intersection of the two tables on the key columns.
If you want to make a new table which has every row from the left table and includes matching values from the right table when available, this is known as a left join:
>>> print(join(optical, xray, join_type='left'))
name obs_date mag_b mag_v logLx
---- ---------- ----- ----- -----
M101 2012-10-31 15.1 15.5 --
M31 2012-01-02 17.0 16.0 --
M82 2012-10-29 16.2 15.2 45.0
Two of the observations do not have X-ray data, as indicated by the -- in
the table. You might be surprised that there is no X-ray data for M31 in the
output. Remember that the default matching key includes both name and
obs_date. Specifying the key as only the name column gives:
>>> print(join(optical, xray, join_type='left', keys='name'))
name obs_date_1 mag_b mag_v obs_date_2 logLx
---- ---------- ----- ----- ---------- -----
M101 2012-10-31 15.1 15.5 -- --
M31 2012-01-02 17.0 16.0 1999-01-05 43.1
M82 2012-10-29 16.2 15.2 2012-10-29 45.0
Likewise you can construct a new table with every row of the right table and
matching left values (when available) using join_type='right'.
To make a table with the union of rows from both tables do an “outer” join:
>>> print(join(optical, xray, join_type='outer'))
name obs_date mag_b mag_v logLx
------- ---------- ----- ----- -----
M101 2012-10-31 15.1 15.5 --
M31 1999-01-05 -- -- 43.1
M31 2012-01-02 17.0 16.0 --
M82 2012-10-29 16.2 15.2 45.0
NGC3516 2011-11-11 -- -- 42.1
In all the above cases the output join table will be sorted by the key column(s) and in general will not preserve the row order of the input tables.
Finally, you can do a “Cartesian” join, which is the Cartesian product of all
available rows. In this case there are no key columns (and supplying the
keys argument is an error):
>>> print(join(optical, xray, join_type='cartesian'))
name_1 obs_date_1 mag_b mag_v name_2 obs_date_2 logLx
------ ---------- ----- ----- ------- ---------- -----
M31 2012-01-02 17.0 16.0 NGC3516 2011-11-11 42.1
M31 2012-01-02 17.0 16.0 M31 1999-01-05 43.1
M31 2012-01-02 17.0 16.0 M82 2012-10-29 45.0
M82 2012-10-29 16.2 15.2 NGC3516 2011-11-11 42.1
M82 2012-10-29 16.2 15.2 M31 1999-01-05 43.1
M82 2012-10-29 16.2 15.2 M82 2012-10-29 45.0
M101 2012-10-31 15.1 15.5 NGC3516 2011-11-11 42.1
M101 2012-10-31 15.1 15.5 M31 1999-01-05 43.1
M101 2012-10-31 15.1 15.5 M82 2012-10-29 45.0
Non-Identical Key Column Names#
To use the join() function with non-identical key column names, use the
keys_left and keys_right arguments. In the following example one table
has a 'name' column while the other has an 'obj_id' column:
>>> optical = Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 16.0
... M82 2012-10-29 16.2 15.2
... M101 2012-10-31 15.1 15.5""", format='ascii')
>>> xray_1 = Table.read("""obj_id obs_date logLx
... NGC3516 2011-11-11 42.1
... M31 1999-01-05 43.1
... M82 2012-10-29 45.0""", format='ascii')
In order to perform a match based on the names of the objects, do the following:
>>> print(join(optical, xray_1, keys_left='name', keys_right='obj_id'))
name obs_date_1 mag_b mag_v obj_id obs_date_2 logLx
---- ---------- ----- ----- ------ ---------- -----
M31 2012-01-02 17.0 16.0 M31 1999-01-05 43.1
M82 2012-10-29 16.2 15.2 M82 2012-10-29 45.0
The keys_left and keys_right arguments can also take a list of column
names or even a list of column-like objects. The latter case allows specifying
the matching key column values independent of the tables being joined.
Identical Key Values#
The Table join operation works even if there are multiple rows with identical
key values. For example, the following tables have multiple rows for the column
'key':
>>> from astropy.table import Table, join
>>> left = Table([[0, 1, 1, 2], ['L1', 'L2', 'L3', 'L4']], names=('key', 'L'))
>>> right = Table([[1, 1, 2, 4], ['R1', 'R2', 'R3', 'R4']], names=('key', 'R'))
>>> print(left)
key L
--- ---
0 L1
1 L2
1 L3
2 L4
>>> print(right)
key R
--- ---
1 R1
1 R2
2 R3
4 R4
Doing an outer join on these tables shows that what is really happening is a Cartesian product. For each matching key, every combination of the left and right tables is represented. When there is no match in either the left or right table, the corresponding column values are designated as missing:
>>> print(join(left, right, join_type='outer'))
key L R
--- --- ---
0 L1 --
1 L2 R1
1 L2 R2
1 L3 R1
1 L3 R2
2 L4 R3
4 -- R4
An inner join is the same but only returns rows where there is a key match in both the left and right tables:
>>> print(join(left, right, join_type='inner'))
key L R
--- --- ---
1 L2 R1
1 L2 R2
1 L3 R1
1 L3 R2
2 L4 R3
Conflicts in the input table names are handled by the process described in the section on Column renaming. See also the sections on Merging metadata and Merging column attributes for details on how these characteristics of the input tables are merged in the single output table.
Merging Details#
When combining two or more tables there is the need to merge certain characteristics in the inputs and potentially resolve conflicts. This section describes the process.
Column Renaming#
In cases where the input tables have conflicting column names, there is a mechanism to generate unique output column names. There are two keyword arguments that control the renaming behavior:
table_namesList of strings that provide names for the tables being joined. By default this is
['1', '2', ...], where the numbers correspond to the input tables.uniq_col_nameString format specifier with a default value of
'{col_name}_{table_name}'.
This is best understood by example using the optical and xray tables
in the join() example defined previously:
>>> print(join(optical, xray, keys='name',
... table_names=['OPTICAL', 'XRAY'],
... uniq_col_name='{table_name}_{col_name}'))
name OPTICAL_obs_date mag_b mag_v XRAY_obs_date logLx
---- ---------------- ----- ----- ------------- -----
M31 2012-01-02 17.0 16.0 1999-01-05 43.1
M82 2012-10-29 16.2 15.2 2012-10-29 45.0
Merging Metadata#
Table objects can have associated metadata:
Table.meta: table-level metadata as an ordered dictionaryColumn.meta: per-column metadata as an ordered dictionary
The table operations described here handle the task of merging the metadata in the input tables into a single output structure. Because the metadata can be arbitrarily complex there is no unique way to do the merge. The current implementation uses a recursive algorithm with four rules:
dictelements are merged by keys.Conflicting
dictelements are merged by recursively calling the merge function.Conflicting elements that are not
list,tuple, ordictwill follow the following rules:
By default, a warning is emitted in the last case (both metadata values are not
None). The warning can be silenced or made into an exception using the
metadata_conflicts argument to hstack(),
vstack(), or
join(). The metadata_conflicts option can be set to:
'silent'– no warning is emitted, the value for the last table is silently picked.'warn'– a warning is emitted, the value for the last table is picked.'error'– an exception is raised.
The default strategies for merging metadata can be augmented or customized by
defining subclasses of the MergeStrategy base class.
In most cases you will also use
enable_merge_strategies() for enabling the custom
strategies. The linked documentation strings provide details.
Merging Column Attributes#
In addition to the table and column meta attributes, the column attributes
unit, format, and description are merged by going through the input
tables in order and taking the last value which is defined (i.e., is not
None).
Example#
To merge column attributes unit, format, or description:
>>> from astropy.table import Column, Table, vstack
>>> col1 = Column([1], name='a')
>>> col2 = Column([2], name='a', unit='cm')
>>> col3 = Column([3], name='a', unit='m')
>>> t1 = Table([col1])
>>> t2 = Table([col2])
>>> t3 = Table([col3])
>>> out = vstack([t1, t2, t3])
MergeConflictWarning: In merged column 'a' the 'unit' attribute does
not match (cm != m). Using m for merged output
>>> out['a'].unit
Unit("m")
The rules for merging are the same as for Merging metadata, and the
metadata_conflicts option also controls the merging of column attributes.
Joining Coordinates and Custom Join Functions#
Source catalogs that have SkyCoord coordinate columns can be joined using
cross-matching of the coordinates with a specified distance threshold. This is
a special case of a more general problem of “fuzzy” matching of key column
values, where instead of an exact match we require only an approximate match.
This is supported using the join_funcs argument.
Warning
The coordinate and distance table joins discussed in this section are most applicable in the case where the relevant entries in at least one of the tables are all separated from one another by more than twice the join distance. If this is not satisfied then the join results may be unexpected.
This is a consequence of the algorithm which effectively finds clusters of
nearby points (an “equivalence class”) and assigns a unique cluster
identifier to each entry in both tables. This assumes the join matching
function is a transitive relation where join_func(A, B) and
join_func(B, C) implies join_func(A, C). With multiple matches on
both left and right sides it is possible for the cluster of points having a
single cluster identifier to expand in size beyond the distance threshold.
Users should be especially aware of this issue if additional join keys
are provided beyond the join_funcs. The code does not do a “pre-join”
on the other keys, so the possibility of having overlaps within the distance
in both tables is higher.
Example#
To join two tables on a SkyCoord key column we use the join_funcs keyword
to supply a dict of functions that specify how to match a particular
key column by name. In the example below we are joining on the sc column,
so we provide the following argument:
join_funcs={'sc': join_skycoord(0.2 * u.deg)}
This tells join() to match the sc key column using the join function
join_skycoord() with a matching distance threshold of 0.2
deg. Under the hood this calls
search_around_sky() or
search_around_3d() to do the
cross-matching. The default is to use
search_around_sky() (angle) matching, but
search_around_3d() (length or
dimensionless) is also available. This is specified using the distance_func
argument of join_skycoord(), which can also be a function
that matches the input and output API of
search_around_sky().
Now we show the whole process:
>>> from astropy.coordinates import SkyCoord
>>> import astropy.units as u
>>> from astropy.table import Table, join, join_skycoord
>>> sc1 = SkyCoord([0, 1, 1.1, 2], [0, 0, 0, 0], unit='deg')
>>> sc2 = SkyCoord([1.05, 0.5, 2.1], [0, 0, 0], unit='deg')
>>> t1 = Table([sc1, [0, 1, 2, 3]], names=['sc', 'idx'])
>>> t2 = Table([sc2, [0, 1, 2]], names=['sc', 'idx'])
>>> t12 = join(t1, t2, keys='sc', join_funcs={'sc': join_skycoord(0.2 * u.deg)})
>>> print(t12)
sc_id sc_1 idx_1 sc_2 idx_2
deg,deg deg,deg
----- ------- ----- -------- -----
1 1.0,0.0 1 1.05,0.0 0
1 1.1,0.0 2 1.05,0.0 0
2 2.0,0.0 3 2.1,0.0 2
The joined table has matched the sources within 0.2 deg and created a new
column sc_id with a unique identifier for each source.
You might be wondering what is happening in the join function defined above, especially if you are interested in defining your own such function. This could be done in order to allow fuzzy word matching of tables, for example joining tables of people by name where the names do not always match exactly.
The first thing to note here is that the join_skycoord()
function actually returns a function itself. This allows specifying a variable
match distance via a function enclosure. The requirement of the join function
is that it accepts two arguments corresponding to the two key columns, and
returns a tuple of (ids1, ids2). These identifiers correspond to the
identification of each column entry with a unique matched source.
>>> join_func = join_skycoord(0.2 * u.deg)
>>> join_func(sc1, sc2) # Associate each coordinate with unique source ID
(array([3, 1, 1, 2]), array([1, 4, 2]))
If you would like to write your own fuzzy matching function, we suggest starting
from the source code for join_skycoord() or
join_distance().
Join on Distance#
The example above focused on joining on a SkyCoord, but you can also join on
a generic distance between column values using the
join_distance() join function. This can apply to 1D or 2D
(vector) columns. This will look very similar to the coordinates example, but
here there is a bit more flexibility. The matching is done using
scipy.spatial.cKDTree and
scipy.spatial.cKDTree.query_ball_tree(), and the behavior of these can be
controlled via the kdtree_args and query_args arguments, respectively.
Unique Rows#
Sometimes it makes sense to use only rows with unique key columns or even
fully unique rows from a table. This can be done using the above described
group_by() method and groups attribute, or with
the unique() convenience function. The
unique() function returns a sorted table containing the
first row for each unique keys column value. If no keys is provided, it
returns a sorted table containing all of the fully unique rows.
Example#
An example of a situation where you might want to use rows with unique key
columns is a list of objects with photometry from various observing
runs. Using 'name' as the only keys, it returns with the first
occurrence of each of the three targets:
>>> from astropy import table
>>> obs = table.Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 17.5
... M82 2012-02-14 16.2 14.5
... M101 2012-01-02 15.1 13.5
... M31 2012-01-02 17.1 17.4
... M101 2012-01-02 15.1 13.5
... M82 2012-02-14 16.2 14.5
... M31 2012-02-14 16.9 17.3
... M82 2012-02-14 15.2 15.5
... M101 2012-02-14 15.0 13.6
... M82 2012-03-26 15.7 16.5
... M101 2012-03-26 15.1 13.5
... M101 2012-03-26 14.8 14.3
... """, format='ascii')
>>> unique_by_name = table.unique(obs, keys='name')
>>> print(unique_by_name)
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-01-02 15.1 13.5
M31 2012-01-02 17.0 17.5
M82 2012-02-14 16.2 14.5
Using multiple columns as keys:
>>> unique_by_name_date = table.unique(obs, keys=['name', 'obs_date'])
>>> print(unique_by_name_date)
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-01-02 15.1 13.5
M101 2012-02-14 15.0 13.6
M101 2012-03-26 15.1 13.5
M31 2012-01-02 17.0 17.5
M31 2012-02-14 16.9 17.3
M82 2012-02-14 16.2 14.5
M82 2012-03-26 15.7 16.5
Set Difference#
A set difference will tell you the elements that are contained in the first set
but not in the other. This concept can be applied to rows of a table by using
the setdiff() function. You provide the function with two
input tables and it will return all rows in the first table which do not occur
in the second table.
The optional keys parameter specifies the names of columns that are used to
match table rows. This can be a subset of the full list of columns, but both
the first and second tables must contain all columns specified by keys.
If not provided, then keys defaults to all column names in the first table.
If no different rows are found, the setdiff() function
will return an empty table.
Example#
The example below illustrates finding the set difference of two observation lists using a common subset of the columns in two tables.:
>>> from astropy.table import Table, setdiff
>>> cat_1 = Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 16.0
... M82 2012-10-29 16.2 15.2
... M101 2012-10-31 15.1 15.5""", format='ascii')
>>> cat_2 = Table.read(""" name obs_date logLx
... NGC3516 2011-11-11 42.1
... M31 2012-01-02 43.1
... M82 2012-10-29 45.0""", format='ascii')
>>> sdiff = setdiff(cat_1, cat_2, keys=['name', 'obs_date'])
>>> print(sdiff)
name obs_date mag_b mag_v
---- ---------- ----- -----
M101 2012-10-31 15.1 15.5
In this example there is a column in the first table that is not
present in the second table, so the keys parameter must be used to specify
the desired column names.
Table Diff#
To compare two tables, you can use
report_diff_values(), which would produce a report
identical to FITS diff.
Example#
The example below illustrates finding the difference between two tables:
>>> from astropy.table import Table
>>> from astropy.utils.diff import report_diff_values
>>> import sys
>>> cat_1 = Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 16.0
... M82 2012-10-29 16.2 15.2
... M101 2012-10-31 15.1 15.5""", format='ascii')
>>> cat_2 = Table.read("""name obs_date mag_b mag_v
... M31 2012-01-02 17.0 16.5
... M82 2012-10-29 16.2 15.2
... M101 2012-10-30 15.1 15.5
... NEW 2018-05-08 nan 9.0""", format='ascii')
>>> identical = report_diff_values(cat_1, cat_2, fileobj=sys.stdout)
name obs_date mag_b mag_v
---- ---------- ----- -----
a> M31 2012-01-02 17.0 16.0
? ^
b> M31 2012-01-02 17.0 16.5
? ^
M82 2012-10-29 16.2 15.2
a> M101 2012-10-31 15.1 15.5
? ^
b> M101 2012-10-30 15.1 15.5
? ^
b> NEW 2018-05-08 nan 9.0
>>> identical
False