Numpy: Fastest way to insert value into array such that array's in order

Question

Suppose I have an array my_array and a singular value my_val. (Note that my_array is always sorted).

my_array = np.array([1, 2, 3, 4, 5])
my_val = 1.5

Because my_val is 1.5, I want to put it in between 1 and 2, giving me the array [1, 1.5, 2, 3, 4, 5].

My question is: What's the fastest way (i.e. in microseconds) of producing the ordered output array as my_array grows arbitrarily large?

The original way I though of was concatenating the value to the original array and then sorting:

arr_out = np.sort(np.concatenate((my_array, np.array([my_val]))))
[ 1.   1.5  2.   3.   4.   5. ]

I know that np.concatenate is fast but I'm unsure how np.sort would scale as my_array grows, even given that my_array will always be sorted.

Edit:

I've compiled the times for the various methods listed at the time an answer was accepted:

Input:

import timeit

timeit_setup = 'import numpy as np\n' \
               'my_array = np.array([i for i in range(1000)], dtype=np.float64)\n' \
               'my_val = 1.5'
num_trials = 1000

my_time = timeit.timeit(
    'np.sort(np.concatenate((my_array, np.array([my_val]))))',
    setup=timeit_setup, number=num_trials
)

pauls_time = timeit.timeit(
    'idx = my_array.searchsorted(my_val)\n'
    'np.concatenate((my_array[:idx], [my_val], my_array[idx:]))',
    setup=timeit_setup, number=num_trials
)

sanchit_time = timeit.timeit(
    'np.insert(my_array, my_array.searchsorted(my_val), my_val)',
    setup=timeit_setup, number=num_trials
)

print('Times for 1000 repetitions for array of length 1000:')
print("My method took {}s".format(my_time))
print("Paul Panzer's method took {}s".format(pauls_time))
print("Sanchit Anand's method took {}s".format(sanchit_time))

Output:

Times for 1000 repetitions for array of length 1000:
My method took 0.017865657746239747s
Paul Panzer's method took 0.005813951002013821s
Sanchit Anand's method took 0.014003945532323987s

And the same for 100 repetitions for an array of length 1,000,000:

Times for 100 repetitions for array of length 1000000:
My method took 3.1770704101754195s
Paul Panzer's method took 0.3931240139911161s
Sanchit Anand's method took 0.40981490723551417s

Answer 1

Use np.searchsorted to find the insertion point in logarithmic time:

>>> idx = my_array.searchsorted(my_val)
>>> np.concatenate((my_array[:idx], [my_val], my_array[idx:]))
array([1. , 1.5, 2. , 3. , 4. , 5. ])

Note 1: I recommend looking at @Willem Van Onselm's and @hpaulj's insightful comments.

Note 2: Using np.insert as suggested by @Sanchit Anand may be slightly more convenient if all datatypes are matching from the beginning. It is, however, worth mentioning that this convenience comes at the cost of significant overhead:

>>> def f_pp(my_array, my_val):
...      idx = my_array.searchsorted(my_val)
...      return np.concatenate((my_array[:idx], [my_val], my_array[idx:]))
... 
>>> def f_sa(my_array, my_val):
...      return np.insert(my_array, my_array.searchsorted(my_val), my_val)
...
>>> my_farray = my_array.astype(float)
>>> from timeit import repeat
>>> kwds = dict(globals=globals(), number=100000)
>>> repeat('f_sa(my_farray, my_val)', **kwds)
[1.2453778409981169, 1.2268288589984877, 1.2298014000116382]
>>> repeat('f_pp(my_array, my_val)', **kwds)
[0.2728819379990455, 0.2697303680033656, 0.2688361559994519]

Answer 2

try

my_array = np.insert(my_array,my_array.searchsorted(my_val),my_val)

[EDIT] make sure that the array is of type float32 or float64, or add a decimal point to any of the list elements while initializing it.