Can you tell me when to use these vectorization methods with basic examples?

I see that map is a Series method whereas the rest are DataFrame methods. I got confused about apply and applymap methods though. Why do we have two methods for applying a function to a DataFrame? Again, simple examples which illustrate the usage would be great!

Straight from Wes McKinney’s Python for Data Analysis book, pg. 132 (I highly recommended this book):

Another frequent operation is applying a function on 1D arrays to each column or row. DataFrame’s apply method does exactly this:

In [116]: frame = DataFrame(np.random.randn(4, 3), columns=list('bde'), index=['Utah', 'Ohio', 'Texas', 'Oregon'])

In [117]: frame
Out[117]: 
               b         d         e
Utah   -0.029638  1.081563  1.280300
Ohio    0.647747  0.831136 -1.549481
Texas   0.513416 -0.884417  0.195343
Oregon -0.485454 -0.477388 -0.309548

In [118]: f = lambda x: x.max() - x.min()

In [119]: frame.apply(f)
Out[119]: 
b    1.133201
d    1.965980
e    2.829781
dtype: float64

Many of the most common array statistics (like sum and mean) are DataFrame methods, so using apply is not necessary.

Element-wise Python functions can be used, too. Suppose you wanted to compute a formatted string from each floating point value in frame. You can do this with applymap:

In [120]: format = lambda x: '%.2f' % x

In [121]: frame.applymap(format)
Out[121]: 
            b      d      e
Utah    -0.03   1.08   1.28
Ohio     0.65   0.83  -1.55
Texas    0.51  -0.88   0.20
Oregon  -0.49  -0.48  -0.31

The reason for the name applymap is that Series has a map method for applying an element-wise function:

In [122]: frame['e'].map(format)
Out[122]: 
Utah       1.28
Ohio      -1.55
Texas      0.20
Oregon    -0.31
Name: e, dtype: object

Summing up, apply works on a row / column basis of a DataFrame, applymap works element-wise on a DataFrame, and map works element-wise on a Series.

Comparing map, applymap and apply: Context Matters

First major difference: DEFINITION

• map is defined on Series ONLY
• applymap is defined on DataFrames ONLY
• apply is defined on BOTH

Second major difference: INPUT ARGUMENT

• map accepts dicts, Series, or callable
• applymap and apply accept callables only

Third major difference: BEHAVIOR

• map is elementwise for Series
• applymap is elementwise for DataFrames
• apply also works elementwise but is suited to more complex operations and aggregation. The behaviour and return value depends on the function.

Fourth major difference (the most important one): USE CASE

• map is meant for mapping values from one domain to another, so is optimised for performance (e.g., df['A'].map({1:'a', 2:'b', 3:'c'}))
• applymap is good for elementwise transformations across multiple rows/columns (e.g., df[['A', 'B', 'C']].applymap(str.strip))
• apply is for applying any function that cannot be vectorised (e.g., df['sentences'].apply(nltk.sent_tokenize))

Summarising

Footnotes

1. map when passed a dictionary/Series will map elements based on the keys in that dictionary/Series. Missing values will be recorded as NaN in the output.

2. applymap in more recent versions has been optimised for some operations. You will find applymap slightly faster than apply in some cases. My suggestion is to test them both and use whatever works better.

3. map is optimised for elementwise mappings and transformation. Operations that involve dictionaries or Series will enable pandas to use faster code paths for better performance.

4. Series.apply returns a scalar for aggregating operations, Series otherwise. Similarly for DataFrame.apply. Note that apply also has fastpaths when called with certain NumPy functions such as mean, sum, etc.

There’s great information in these answers, but I’m adding my own to clearly summarize which methods work array-wise versus element-wise. jeremiahbuddha mostly did this but did not mention Series.apply. I don’t have the rep to comment.

• DataFrame.apply operates on entire rows or columns at a time.

• DataFrame.applymap, Series.apply, and Series.map operate on one element at time.

There is a lot of overlap between the capabilities of Series.apply and Series.map, meaning that either one will work in most cases. They do have some slight differences though, some of which were discussed in osa’s answer.

Adding to the other answers, in a Series there are also map and apply.

Apply can make a DataFrame out of a series; however, map will just put a series in every cell of another series, which is probably not what you want.

In [40]: p=pd.Series([1,2,3])
In [41]: p
Out[31]:
0    1
1    2
2    3
dtype: int64

In [42]: p.apply(lambda x: pd.Series([x, x]))
Out[42]: 
   0  1
0  1  1
1  2  2
2  3  3

In [43]: p.map(lambda x: pd.Series([x, x]))
Out[43]: 
0    0    1
1    1
dtype: int64
1    0    2
1    2
dtype: int64
2    0    3
1    3
dtype: int64
dtype: object

Also if I had a function with side effects, such as “connect to a web server”, I’d probably use apply just for the sake of clarity.

series.apply(download_file_for_every_element) 

Map can use not only a function, but also a dictionary or another series. Let’s say you want to manipulate permutations.

Take

1 2 3 4 5
2 1 4 5 3

The square of this permutation is

1 2 3 4 5
1 2 5 3 4

You can compute it using map. Not sure if self-application is documented, but it works in 0.15.1.

In [39]: p=pd.Series([1,0,3,4,2])

In [40]: p.map(p)
Out[40]: 
0    0
1    1
2    4
3    2
4    3
dtype: int64

@jeremiahbuddha mentioned that apply works on row/columns, while applymap works element-wise. But it seems you can still use apply for element-wise computation….

    frame.apply(np.sqrt)
    Out[102]: 
                   b         d         e
    Utah         NaN  1.435159       NaN
    Ohio    1.098164  0.510594  0.729748
    Texas        NaN  0.456436  0.697337
    Oregon  0.359079       NaN       NaN

    frame.applymap(np.sqrt)
    Out[103]: 
                   b         d         e
    Utah         NaN  1.435159       NaN
    Ohio    1.098164  0.510594  0.729748
    Texas        NaN  0.456436  0.697337
    Oregon  0.359079       NaN       NaN

Just wanted to point out, as I struggled with this for a bit

def f(x):
    if x < 0:
        x = 0
    elif x > 100000:
        x = 100000
    return x

df.applymap(f)
df.describe()

this does not modify the dataframe itself, has to be reassigned

df = df.applymap(f)
df.describe()

Probably simplest explanation the difference between apply and applymap:

apply takes the whole column as a parameter and then assign the result to this column

applymap takes the separate cell value as a parameter and assign the result back to this cell.

NB If apply returns the single value you will have this value instead of the column after assigning and eventually will have just a row instead of matrix.

My understanding:

From the function point of view:

If the function has variables that need to compare within a column/ row, use apply.

e.g.: lambda x: x.max()-x.mean().

If the function is to be applied to each element:

1> If a column/row is located, use apply

2> If apply to entire dataframe, use applymap

majority = lambda x : x > 17
df2['legal_drinker'] = df2['age'].apply(majority)

def times10(x):
  if type(x) is int:
    x *= 10 
  return x
df2.applymap(times10)

Based on the answer of cs95

• map is defined on Series ONLY
• applymap is defined on DataFrames ONLY
• apply is defined on BOTH

give some examples

In [3]: frame = pd.DataFrame(np.random.randn(4, 3), columns=list('bde'), index=['Utah', 'Ohio', 'Texas', 'Oregon'])

In [4]: frame
Out[4]:
            b         d         e
Utah    0.129885 -0.475957 -0.207679
Ohio   -2.978331 -1.015918  0.784675
Texas  -0.256689 -0.226366  2.262588
Oregon  2.605526  1.139105 -0.927518

In [5]: myformat=lambda x: f'{x:.2f}'

In [6]: frame.d.map(myformat)
Out[6]:
Utah      -0.48
Ohio      -1.02
Texas     -0.23
Oregon     1.14
Name: d, dtype: object

In [7]: frame.d.apply(myformat)
Out[7]:
Utah      -0.48
Ohio      -1.02
Texas     -0.23
Oregon     1.14
Name: d, dtype: object

In [8]: frame.applymap(myformat)
Out[8]:
            b      d      e
Utah     0.13  -0.48  -0.21
Ohio    -2.98  -1.02   0.78
Texas   -0.26  -0.23   2.26
Oregon   2.61   1.14  -0.93

In [9]: frame.apply(lambda x: x.apply(myformat))
Out[9]:
            b      d      e
Utah     0.13  -0.48  -0.21
Ohio    -2.98  -1.02   0.78
Texas   -0.26  -0.23   2.26
Oregon   2.61   1.14  -0.93


In [10]: myfunc=lambda x: x**2

In [11]: frame.applymap(myfunc)
Out[11]:
            b         d         e
Utah    0.016870  0.226535  0.043131
Ohio    8.870453  1.032089  0.615714
Texas   0.065889  0.051242  5.119305
Oregon  6.788766  1.297560  0.860289

In [12]: frame.apply(myfunc)
Out[12]:
            b         d         e
Utah    0.016870  0.226535  0.043131
Ohio    8.870453  1.032089  0.615714
Texas   0.065889  0.051242  5.119305
Oregon  6.788766  1.297560  0.860289

FOMO:

The following example shows apply and applymap applied to a DataFrame.

map function is something you do apply on Series only. You cannot apply map on DataFrame.

The thing to remember is that apply can do anything applymap can, but apply has eXtra options.

The X factor options are: axis and result_type where result_type only works when axis=1 (for columns).

df = DataFrame(1, columns=list('abc'),
                  index=list('1234'))
print(df)

f = lambda x: np.log(x)
print(df.applymap(f)) # apply to the whole dataframe
print(np.log(df)) # applied to the whole dataframe
print(df.applymap(np.sum)) # reducing can be applied for rows only

# apply can take different options (vs. applymap cannot)
print(df.apply(f)) # same as applymap
print(df.apply(sum, axis=1))  # reducing example
print(df.apply(np.log, axis=1)) # cannot reduce
print(df.apply(lambda x: [1, 2, 3], axis=1, result_type='expand')) # expand result

As a sidenote, Series map function, should not be confused with the Python map function.

The first one is applied on Series, to map the values, and the second one to every item of an iterable.

Lastly don’t confuse the dataframe apply method with groupby apply method.