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

Question

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?

Is f continuous at x=1 and x=10? If it is then put the clips on x, not the function. — lastchance
– lastchance, Commented Nov 6, 2024 at 14:12

mozway · Accepted Answer · 2024-11-06 14:10:25Z

1

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:

edited Nov 6, 2024 at 14:10

answered Nov 6, 2024 at 14:04

mozway

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2 Comments

nos Over a year ago

The lambda function can be simplified with the number directly

mozway Over a year ago

@nos that's right, I'll simplify ;)

PaulS · Accepted Answer · 2024-11-06 14:41:14Z

0

Another possible solution, which uses np.where:

np.where(x < 1, 1, np.where(x < 10, g(x), 0))

NB: In case there are values of x for which g is not defined, we can use the np.errstate:

with np.errstate(invalid='ignore'):
    y = np.where(x < 1, 1, np.where(x < 10, g(x), 0))

Output (using @mozway's data):

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.        ])

edited Nov 6, 2024 at 14:41

answered Nov 6, 2024 at 14:10

PaulS

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2 Comments

mozway Over a year ago

Actually, you shouldn't use np.where in this case as it will evaluate the function for potentially invalid values of x. For instance x = np.linspace(-10, 20) ; g = np.log ;)

PaulS Over a year ago

You are right, @mozway! I have just added a way to deal with that situation. Thanks!

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