def U(a, side):
'''The unit function: 0 when x<a and 1 when x>a.
The value at x=a is determined by the 'side' argument.
side = 'left' -> 0 at x=a
side = 'right' -> 1 at x=a
'''
# Using the definition of Heaviside where it's 1 at x=0
# uncomment these if you want it when it's 0 at x=0
# H0 = Heaviside(x, 0) # heaviside, 0 at x=0
# H1 = 1-H0.subs(x,-x) # heaviside, 1 at x=0
H1 = Heaviside(x, 1)
H0 = 1 - H1.subs(x, -x)
if side == 'left':
return H0.subs(x, x - a)
elif side == 'right':
return H1.subs(x, x - a)
else:
raise ValueError("side was not left or right (%s)" % (side))
if x is S.Zero:
return S.One
elif x is S.Infinity:
return S.Zero
def _eval_is_real(self):
returnself.args[0].is_real
h(0)
h(oo)
# %%
plot(x*x, (x, 0, 6))
# %%
H = Heaviside(x - 2)
H.subs(x, 1)
plot(H)
# %%
y = Symbol('y')
f = y**2
g = log(y)
p = Piecewise((99, y < -1), (f, y <= 1), (g, True))
[p.subs(y, i) for i in range(-20, 20)]
