What is the most efficient way to produce an array of 100 numbers that form the shape of the triangle wave below, with a max/min amplitude of 0.5?
Triangle waveform in mind:
7 Answers
The simplest way to generate a triangle wave is by using signal.sawtooth. Notice that signal.sawtooth(phi, width) accepts two arguments. The first argument is the phase, the next argument specifies the symmetry. width = 1 gives a right-sided sawtooth, width = 0 gives a left-sided sawtooth and width = 0.5 gives a symmetric triangle. Enjoy!
from scipy import signal
import numpy as np
import matplotlib.pyplot as plt
t = np.linspace(0, 1, 500)
triangle = signal.sawtooth(2 * np.pi * 5 * t, 0.5)
plt.plot(t, triangle)
1 Comment
Matt Popovich
Documentation: docs.scipy.org/doc/scipy/reference/generated/…
Use a generator:
def triangle(length, amplitude):
section = length // 4
for direction in (1, -1):
for i in range(section):
yield i * (amplitude / section) * direction
for i in range(section):
yield (amplitude - (i * (amplitude / section))) * direction
This'll work fine for a length divisible by 4, you may miss up to 3 values for other lengths.
>>> list(triangle(100, 0.5))
[0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.22, 0.24, 0.26, 0.28, 0.3, 0.32, 0.34, 0.36, 0.38, 0.4, 0.42, 0.44, 0.46, 0.48, 0.5, 0.48, 0.46, 0.44, 0.42, 0.4, 0.38, 0.36, 0.33999999999999997, 0.32, 0.3, 0.28, 0.26, 0.24, 0.21999999999999997, 0.2, 0.18, 0.15999999999999998, 0.14, 0.12, 0.09999999999999998, 0.08000000000000002, 0.06, 0.03999999999999998, 0.020000000000000018, -0.0, -0.02, -0.04, -0.06, -0.08, -0.1, -0.12, -0.14, -0.16, -0.18, -0.2, -0.22, -0.24, -0.26, -0.28, -0.3, -0.32, -0.34, -0.36, -0.38, -0.4, -0.42, -0.44, -0.46, -0.48, -0.5, -0.48, -0.46, -0.44, -0.42, -0.4, -0.38, -0.36, -0.33999999999999997, -0.32, -0.3, -0.28, -0.26, -0.24, -0.21999999999999997, -0.2, -0.18, -0.15999999999999998, -0.14, -0.12, -0.09999999999999998, -0.08000000000000002, -0.06, -0.03999999999999998, -0.020000000000000018]
answered Sep 8, 2012 at 16:33
Martijn Pieters
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Triangle is absolute value of sawtooth.
from scipy import signal
time=np.arange(0,1,0.001)
freq=3
tri=np.abs(signal.sawtooth(2 * np.pi * freq * time))
Comments
To use numpy:
def triangle2(length, amplitude):
section = length // 4
x = np.linspace(0, amplitude, section+1)
mx = -x
return np.r_[x, x[-2::-1], mx[1:], mx[-2:0:-1]]
Comments
You can use an iterator generator along with the numpy fromiter method.
import numpy
def trigen(n, amp):
y = 0
x = 0
s = amp / (n/4)
while x < n:
yield y
y += s
if abs(y) > amp:
s *= -1
x += 1
a = numpy.fromiter(trigen(100, 0.5), "d")
Now you have an array with the square wave.
Comments
Here is a home-made python function for triangular signals
import matplotlib.pyplot as plt
import numpy as np
phase=-10
length=30 # should be positive
amplitude=10
x=np.arange(0,100,0.1)
def triang(x,phase,length,amplitude):
alpha=(amplitude)/(length/2)
return -amplitude/2+amplitude*((x-phase)%length==length/2) \
+alpha*((x-phase)%(length/2))*((x-phase)%length<=length/2) \
+(amplitude-alpha*((x-phase)%(length/2)))*((x-phase)%length>length/2)
tr=triang(x,phase,length,amplitude)
plt.plot(tr)
Comments
You can simply use traditional trig functions (arcsin and sin) from the math library to create a triangle-wave as a function of x and call it inside a list comprehension that loops over 100 slices of the function's period (2π).
import math
triangle_function = lambda x: 0.5 * math.asin(math.sin(2*math.pi*x))
L = [triangle_function(i/2*math.pi) for i in range(100)]
pylab.arange(0,0.5,25)np.arangeas you said, create an empty array and then fill it withnp.arangeelements for example (instead of iterations below).