# Integral of a triangle function in python

I have just defined a function which is the integral of a given step function, and now I would like to integrate the triangle function obtained. jerk:1,-1,1-1 The step function correspond of a given list of successive jerk. For getting the triangle function,

I have used the formula: `a(t)=kt+ac`

with k the Jerk and ac a constant which ensures the continuity and change for each step. But know, if I use the formula `v(t)=(1/2)kt^2+ac*t+vc`

, I get negative value for velocity which is incorrect.

I have found some scipy function which return a number for an integral but I need a curve, do you have any idea of how I could integrate this? tks you

Asked by:

**Grace182**| Posted: 06-12-2021

# Answer 1

You can use `scipy.integrate.quad`

function...

```
from scipy.integrate import quad
def g(x): # your triangle function
return abs((x+1)%2-1)
for x in (0.1*i for i in xrange(40)):
I = quad(g, 0, x)[0]
print "x = %f -> g(x) = %f -> I(g, 0, x) = %f" % (x, g(x), I)
```

Is it the thing you are looking for?

@edit:

When the g function is discrete then you can sum the integrates of non-discrete intervals:

```
from math import floor
from scipy.integrate import quad
I = 0.0
for x in (1.0*i for i in xrange(4)):
print "x = %f -> g(x) = %f -> I(g, 0, x) = %f" % (x, g(x), I)
if floor(x) % 2 == 0:
g = lambda x: 1
else:
g = lambda x: -1
I += quad(g, x, x+1.0)[0]
```

Answered by: **Lucas739**| Posted: 07-01-2022

# Answer 2

This may be what your are looking for :

```
import numpy as np
import matplotlib.pyplot as plt
from scipy import integrate
# step Function
def jerkstep(xprime,k):
return (1 - 2*( int(xprime)%2 == 1 ) )*k
# Triangle function ( step integration)
def jerkint(x,k,ac):
return integrate.quad( jerkstep ,0, x, args =(k) )[0] + ac*x
# Integrate of triangle
def jerkintint(x,k,ac,vc):
return integrate.quad( jerkint, 0 , x , args = (1,0) )[0] + vc*x
# linearly spaced time samples (~ x axis)
t = np.linspace(2.0, 10.0, num = 100)
#optional arguments
k = 1
ac = 0
vc = 0
#output functions
jerk = np.array(t);
triangle = np.array(t);
curve = np.array(t);
# Warning : it can be long ( integration not optimized )
for indice,time in zip(range(len(t)),t): # Double indexation on t indices and t values
print "Time, in seconds : ", time
jerk[indice] = jerkstep(time,k)
print "Step function : " , jerk[indice]
triangle[indice] =jerkint(time,k,ac)
print "Step function integrate ( = triangle ) : " , triangle[indice]
curve[indice] = jerkintint(time,k,ac,vc)
print "Step function double integrate ( = triangle integrate ) : " , curve[indice]
print "\n"
# plot figure in mathplotlib
fig, axs = plt.subplots(3, 1, sharex=True, sharey=False)
axs[0].plot(t, jerk, 'o-', label=str("Step Function"))
axs[1].plot(t, triangle, 'o-' , label=str("Triangle Function"))
axs[2].plot(t, curve, 'o-' , label=str("Curve Function"))
fig.show()
plt.show()
```

Answered by: **Emily549**| Posted: 07-01-2022

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