How to define piecewise functions in Python

How does Python define piecewise functions? The following is a piecewise function:

At the beginning, I wrote a simple version of log_norm0, which can only be performed element by element. Needless to say, vectors with a large number of elements will definitely slow down.

Later I thought of using an indicator function to distinguish the two situations of segmentation, and I got log_norm1. However, this situation is quite special and cannot be successfully constructed every time.

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Finally, I found that there is a function piecewise(x, condlist, funclist, *args, **kw) in numpy, It is specially used to construct segmented functions, x is the input, condlist represents the condition of segmentation, and funclist represents the processing function of the corresponding segment. This gives us log_norm2.

# elementwise
def log_norm0(x):
    if x >= 0:
        return np.log(x + 1)
    else:
        return - np.log(- x + 1)
# indicator
def log_norm1(x):
    # ind = np.where(x > 0, 1, 0)
    ind = (x > 0)
    return np.log(x * ind + 1) - np.log(- x * (1.0 - ind) + 1)
# numpy.piecewise()
def log_norm2(x):
    return np.piecewise(x, [x >= 0, x < 0], [lambda x: np.log(1 + x), lambda x: - np.log(1 - x)])

Finally, observe the running time of each function.

tic = time.time()
for i in range(x.size):
    y[i] = log_norm0(x[i])
toc = time.time()
print('log0: ', toc - tic)
tic = time.time()
y = log_norm1(x)
toc = time.time()
print('log1: ', toc - tic)
tic = time.time()
z = log_norm2(x)
toc = time.time()
print('log2: ', toc - tic)

Observation results show that the method using the indicator function is still the fastest, but it is not much different from piecewise.

log0:  33.59282732009888
log1:  0.4863457679748535
log2:  0.5942573547363281

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