How can I apply a user-defined row function onto all rows of a loaded in array?

Question

I have written a user defined function that loops through a row of values in order to give the number of zeros between values (distance between values). Those distances are appended into a list and then averaged for a final value of average distance between values. The function works great when I load in a CSV file with just one row of values. However, I would like to be able to apply the function to a file with multiple rows, and then report the output of each row into a dataframe.

This is all being run with python 3.7. I attempted to create a nested loop in order apply the function manually. I have tried the numpy.apply_along_axis function. I have also tried reading the file in as a pandas dataframe, and then using the .apply() function. However, I am a bit unfamiliar with pandas, and when I replaced the numpy indexing in the function with pandas indexing, I began to generate multiple errors.

When I load in a larger CSV file and try to apply it to file[0] for example, the function does not work. It seems to work only when I load in a file with one row of values.

def avg_dist():
     import statistics as st


    dist = []
    ctr=0

#distances between events

    for i in range(len(n)):
        if n[i] > 0 and i < (len(n)-1):
            if n[i+1]==0:
                i+=1
                while n[i]==0 and i < (len(n)-1):
                    ctr+=1
                    i+=1
                dist.append(ctr)
                ctr=0
            else:
                i+=1
        else:
            i+=1


#Average distance between events
    aved = st.mean(dist)
    return(aved)

Answer 1

The latest response is at the end of the answer. There have been several edits.

The very end (4th edit) of the answer has a completely new approach.

I'm not certain what you're trying to do but hopefully this can help.

import numpy as np

# Generate some events
events = np.random.rand(3,12)*10.
events *= np.random.randint(5, size=(3,12))<1
events
Out[36]:
array([[ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  5.35598205,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ],
       [ 0.        ,  6.65094145,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  6.04581361],
       [ 6.88119682,  4.31178109,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  1.16999289,  0.        ,  0.        ,
         0.        ,  0.        ]])

# generate a boolean array of events.  (as int for a compact print.)
an_event = (events != 0).astype(np.int)
n_event

Out[37]:
array([[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
       [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]])

def event_range(arr):
    from_start = arr.cumsum(axis=1)
    from_end = np.flip(arr, axis=1).cumsum(axis=1)
    from_end = np.flip(from_end, axis=1)
    return np.logical_and(from_start, from_end).astype(np.int)

event_range function step by step.
from_start is the cumsum of an_event. zero before any event, >0 after that.

from_start = an_event.cumsum(axis=1) # cumsum the event count.  zeros before the first event.
from_start
Out[40]:
array([[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1],  # zeroes before the first event.
       [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2],
       [1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3]], dtype=int32)

from_end is the cumsum of an_event but from max to min. Therefore zero after the last event.

from_end = np.flip(an_event, axis=1).cumsum(axis=1) # cumsum of reversed arrays
from_end = np.flip(from_end, axis=1) # reverse the result.
from_end
Out[41]:
array([[1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], # zero after the last event.
       [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [3, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]], dtype=int32)

logically anding these together to get, zeroes before the first event, ones after that and zeroes after the last event.

ev_range = np.logical_and(from_start, from_end).astype(np.int)
ev_range
Out[42]:
# zero before first and after last event, one between the events.
array([[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], 
       [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],  
       [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]])

n_range = ev_range.sum(axis=1)
n_range
Out[43]: array([ 1, 11,  8])

n_events = an_event.sum(axis=1)
n_events
Out[44]: array([1, 2, 3])

avg = n_range / n_events
avg
Out[45]: array([ 1.        ,  5.5       ,  2.66666667])

Should avg be n_range/ (n_events-1)? ie count the gaps, not the events.

What would you expect for only one event in a row? What for zero events in a row?

Edit following comments

To count gaps longer than zero gets a bit involved. The easiest is probably to take the differences for consecutive columns. Where these are -1 there is a 1 followed by a zero. You need to add a final zero column to your data in case the last column has an event in it.

np.random.seed(10)

test = 1*(np.random.randint(4, size=(4,12))<1)

test
Out[24]: 
array([[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0],
       [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1],
       [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]])

temp = np.diff(test, axis=-1)

temp
Out[26]: 
array([[ 0,  1, -1,  1, -1,  0,  1, -1,  0,  1, -1],
       [ 0,  1, -1,  1, -1,  1, -1,  1, -1,  1,  0],
       [ 0,  0,  1, -1,  0,  0,  0,  1,  0, -1,  0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  1, -1,  0]])

np.where(temp<0, 1,0)
Out[28]: 
array([[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1],
       [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0],
       [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]])

In [29]: np.where(temp<0, 1,0).sum(axis=-1)-1
Out[29]: array([3, 3, 1, 0]) # should be [3, 4, 1, 0]

Add a column of zeros to test.

test = np.hstack((test, np.zeros((4,1), dtype = np.int)))
test 
Out[31]: 
array([[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0],
       [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0],
       [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]])

temp=np.diff(test, axis=-1)

temp
Out[35]: 
array([[ 0,  1, -1,  1, -1,  0,  1, -1,  0,  1, -1,  0],
       [ 0,  1, -1,  1, -1,  1, -1,  1, -1,  1,  0, -1], # An extra -1 here.
       [ 0,  0,  1, -1,  0,  0,  0,  1,  0, -1,  0,  0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  1, -1,  0,  0]])

np.where(temp<0, 1,0).sum(axis=-1)-1
Out[36]: array([3, 4, 1, 0])

As I said, a bit involved. It may be easier to loop through but this should be faster if more difficult to understand.

2nd Edit following another idea.

import numpy as np

np.random.seed(10)
test = 1*(np.random.randint(4, size=(4,12))<1)
test

Out[2]: 
array([[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0],
       [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1],
       [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]])

temp = np.diff(test, axis=-1)

np.where(temp<0, 1, 0).sum(axis=-1)+test[:,-1]-1
# +test[:,-1] adds the last column to include any 1's from there.
Out[4]: array([3, 4, 1, 0])

3rd Edit

Thinking this through I created 2 functions, I also show a do_divide which copes with divide by zero.

import numpy as np

def zero_after_last_event(arr):
    """
    Returns an array set to zero in all cells after the last event
    """
    from_end = np.flip(arr, axis=-1).cumsum(axis=-1) # cumsum of reversed arrays
    from_end = np.flip(from_end, axis=-1) # reverse the result.
    from_end[from_end>0] = 1  # gt zero set to 1
    return from_end

def event_range(arr):
    """ event_range is zero before the first event, 
        zero after the last event and 1 elsewhere. """
    return np.logical_and(arr.cumsum(axis=-1), zero_after_last_event(arr)).astype(np.int)

def do_divide(a, b):
    """ Does a protected divide.  Returns zero for divide by zero """
    with np.errstate(invalid='ignore'): # Catch divide by zero
        result = a / b
        result[~np.isfinite(result)] = 0.
    return result

Set up a test array

np.random.seed(10)
events = 1*(np.random.randint(4, size=(4,12))<1)
events
Out[15]: 
array([[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0],
       [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1],
       [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]])

With the functions and data above above this follows.

# Count gap lengths  
gaps = 1 - events # invert the values in events (1->0, 0->1) 
gaps = np.logical_and(gaps, event_range(events)).astype(np.int)
gaps
Out[19]: 
array([[0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0],
       [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0],
       [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

sumgaps = gaps.sum(axis = -1)
sumgaps
Out[22]: array([5, 4, 4, 0])

# Count how many gaps
temp = np.diff(events, axis=-1) # temp is -1 when an event isn't immediately followed by another event.
n_gaps = np.where(temp<0, 1, 0).sum(axis=-1)+events[:,-1]-1
# +test[:,-1] adds the last column to include any 1's from there.
n_gaps
Out[23]: array([3, 4, 1, 0])

do_divide(sum_gaps, n_gaps)
Out[21]: array([1.66666667, 1.        , 4.        , 0.        ])

4th Edit - using np.bincount

import numpy as np

def do_divide(a, b):
""" Does a protected divide.  Returns zero for divide by zero """
    with np.errstate(invalid='ignore'): # Catch divide by zero
        result = a / b
        result[~np.isfinite(result)] = 0.
        return result

np.random.seed(10)
events = 1*(np.random.randint(4, size=(4,12))<1)

cumulative = events.cumsum(axis=1)
cumulative
Out[2]: 
array([[0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4],
       [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6],
       [0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 3, 3],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]])

bin_count_len = 1+cumulative.max()  # Biggest bins length required.

result = np.zeros((cumulative.shape[0], bin_count_len), dtype=np.int)
for ix, row in enumerate(cumulative):
    result[ix] = np.bincount( row, minlength = bin_count_len )

result
Out[4]: 
array([[2, 2, 3, 3, 2, 0, 0],
       [2, 2, 2, 2, 2, 1, 1],
       [3, 5, 1, 3, 0, 0, 0],
       [9, 3, 0, 0, 0, 0, 0]])

Lose column 0. Its before any events. Lose the last column, always after the last event. The gaps include the opening event, -1 removes it from the gap size.

temp = result[:, 1:-1]-1   # 
temp
Out[6]: 
array([[ 1,  2,  2,  1, -1],
       [ 1,  1,  1,  1,  0],
       [ 4,  0,  2, -1, -1],
       [ 2, -1, -1, -1, -1]])

Set any cell temp[r, n] = 0 if temp[r, n+1]==0

temp_lag = (result[:, 2:]>0)*1
temp_lag
Out[8]: 
array([[1, 1, 1, 0, 0],
       [1, 1, 1, 1, 1],
       [1, 1, 0, 0, 0],
       [0, 0, 0, 0, 0]])

temp *= temp_lag
temp
Out[10]: 
array([[1, 2, 2, 0, 0],
       [1, 1, 1, 1, 0],
       [4, 0, 0, 0, 0],
       [0, 0, 0, 0, 0]])

tot_gaps = temp.sum(axis=1)
n_gaps = np.count_nonzero(temp, axis=1)

tot_gaps, n_gaps
Out[13]: (array([5, 4, 4, 0]), array([3, 4, 1, 0]))

do_divide(tot_gaps, n_gaps)
Out[14]: array([1.66666667, 1.        , 4.        , 0.        ])

HTH