how to specify a range in numpy.piecewise (2 conditions per range)

Question

I am trying to construct a piecewise function for some digital signal processing, but I cannot get numpy.piecewise to allow me to specify a range.

Here is what I want to input:

t = np.arange(-10,10,1)
x = lambda x: x**3
fx = np.piecewise(t, [t < -1 and t>-2, t <= 0 and t>-1, t>=0 and t<1,t>1 and t<2], [x(t + 2), x(-t),x(t),-x(2-t)])
plot(t,fx)

However, I get the error: "ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"

After dissecting the function, it seems the issue is that this function won't allow 2 conditions in one such as: t < -1 and t>-2

But it seems to me that allowing a range to be specified would be essential to many piecewise functions. Is there a way to accomplish this?

Thanks!

Answer 1

This is because you cannot use and on numpy arrays. You need to replace the and with * and the or with + for numpy boolean arrays. (and do not forget to add parentheses).

Answer 2

Another problem, to add to Nicolas's answer, is that each element of funclist must be callable if you want to use piecewise. Your corrected code would look like

t = np.arange(-2,2,.01)
f1 = lambda t: (t+2)**3
f2 = lambda t: (-t)**3
f3 = lambda t: (t)**3
f4 = lambda t: -(2-t)**3
fx = np.piecewise(t, [(t< -1)*(t>=-2), (t <= 0) * (t>=-1), (t>0) * (t<1),(t>=1) * (t<=2)], [f1,f2,f3,f4])
plot(t,fx)

Instead, you could use select

t = np.arange(-2,2,.01)
f = lambda x: x**3
fx = np.select([(t< -1)*(t>=-2), (t <= 0) * (t>=-1), (t>0) * (t<1),(t>=1) * (t<=2)], [f(t+2),f(-t),f(t),-f(2-t)])
plot(t,fx)

Moreover, select allows you to set a default value outside the defined intervals, by passing it into the parameter default. You may need that if you want to stick to a range (-10,10) with your intervals.