How to write a function for numpy array input whose action depends on the input's numerical value

The function has this mathematical form

f(x) = 1, if x<1
     = g(x), for 1<=x<10
     = 0, for x >=10

where g(x) is a simple function.

It is straightforward to write such a function if the input is a float using if/else. If the input is a numpy array, is there a neat/efficient implementation without explicit loop?

You can use numpy.piecewise:

x = np.linspace(0, 20, 30)
g = lambda x: -x

y = np.piecewise(x, [x<1, (1<=x)&(x<10), x>=10],
                    [1, g, 0])

NB. In contrast to numpy.where, it will only evaluate the function for each valid chunk of x.

Output:

array([ 1.        ,  1.        , -1.37931034, -2.06896552, -2.75862069,
       -3.44827586, -4.13793103, -4.82758621, -5.51724138, -6.20689655,
       -6.89655172, -7.5862069 , -8.27586207, -8.96551724, -9.65517241,
        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
        0.        ,  0.        ,  0.        ,  0.        ,  0.        ])

As a function:

def f(x):
    return np.piecewise(x,
                        [x<1, (1<=x)&(x<10), x>=10],
                        [1, np.log, 0])

x = np.linspace(-10, 20, num=200)

plt.plot(x, f(x))

Output: