# python – Calculating the area under a curve given a set of coordinates, without knowing the function

## python – Calculating the area under a curve given a set of coordinates, without knowing the function

The numpy and scipy libraries include the composite trapezoidal (numpy.trapz) and Simpsons (scipy.integrate.simps) rules.

Heres a simple example. In both `trapz`

and `simps`

, the argument `dx=5`

indicates that the spacing of the data along the x axis is 5 units.

```
import numpy as np
from scipy.integrate import simps
from numpy import trapz
# The y values. A numpy array is used here,
# but a python list could also be used.
y = np.array([5, 20, 4, 18, 19, 18, 7, 4])
# Compute the area using the composite trapezoidal rule.
area = trapz(y, dx=5)
print(area =, area)
# Compute the area using the composite Simpsons rule.
area = simps(y, dx=5)
print(area =, area)
```

Output:

```
area = 452.5
area = 460.0
```

You can use Simpsons rule or the Trapezium rule to calculate the area under a graph given a table of y-values at a regular interval.

Python script that calculates Simpsons rule:

```
def integrate(y_vals, h):
i = 1
total = y_vals[0] + y_vals[-1]
for y in y_vals[1:-1]:
if i % 2 == 0:
total += 2 * y
else:
total += 4 * y
i += 1
return total * (h / 3.0)
```

`h`

is the offset (or gap) between y values, and `y_vals`

is an array of well, y values.

Example (In same file as above function):

```
y_values = [13, 45.3, 12, 1, 476, 0]
interval = 1.2
area = integrate(y_values, interval)
print(The area is, area)
```

#### python – Calculating the area under a curve given a set of coordinates, without knowing the function

If you have sklearn installed, a simple alternative is to use sklearn.metrics.auc

This computes the area under the curve using the trapezoidal rule given arbitrary x, and y array

```
import numpy as np
from sklearn.metrics import auc
dx = 5
xx = np.arange(1,100,dx)
yy = np.arange(1,100,dx)
print(computed AUC using sklearn.metrics.auc: {}.format(auc(xx,yy)))
print(computed AUC using np.trapz: {}.format(np.trapz(yy, dx = dx)))
```

both output the same area: 4607.5

the advantage of sklearn.metrics.auc is that it can accept arbitrarily-spaced x array, just make sure it is ascending otherwise the results will be incorrect