Is there a Python function for finding each section of "Area Under curve"?

Question

I am trying to calculate Area under curve("A1", "A2", "A3", which is sliced by red line, first row graph) using Python packages (simps, trapz).

The problem is that the result of "A2"(second row graph, "Area2") is partially drawn unlike what I expected. How can I cut out "A2"(not "Area2") to calculate the area of the section?

Lastly, does anyone know how to calculate absolute area ignoring negative y-axis values(A3)?


a1y = [-731.11059984, -728.47093717, -713.86716911, -680.2975881 ,
       -618.76047483, -524.25410195, -396.7767379 , -240.32665095,
        -63.9021133 ,  122.49859465,  306.87718006,  478.23533331,
        630.57472375,  757.89699553,  849.20376345,  912.49660913,
        966.77707721, 1008.04667182, 1037.30685332, 1055.55903521,
       1065.80458132]
a1x = np.arange(len(a1y))

a2y=[1069.04480327, 1068.2809582 , 1064.51424672, 1057.74581119,
       1048.97673424, 1038.20803754, 1023.44068087, 1004.67556141,
        983.91351339,  959.15530785,  928.40165277,  890.65319339,
        844.9105128 ,  791.17413276,  730.4445147 ,  664.72206101,
        596.00711644,  526.29996976,  465.60085552,  409.90995604,
        354.22740345,  302.5532819 ,  256.88762985]
a2x= np.arange(len(a2y))

a3y=[ 216.23044249,  181.58167415,  149.94124091,  121.30902312,
         94.68486807,   69.06859264,   42.45998605,   14.85881254,
        -10.73518588,  -35.32228663,  -63.90278387,  -94.47698566,
       -127.0452113 , -160.60778851, -194.16505079, -227.71733472,
       -261.26497733, -294.8083135 , -327.34767345, -358.88338026,
       -385.41574752, -407.94507695, -433.47165627, -459.99575703,
       -486.51763258, -513.03751622, -537.55561935, -561.07212984,
       -582.58721047, -603.10099754, -622.61359958, -640.12509628,
       -657.63553747, -670.14494237, -681.6532989 , -696.16056319,
       -711.66665933, -727.17147916, -742.67488235, -758.17669657,
       -773.67671795, -789.17471161, -804.67041247, -821.16352618,
       -837.65373036, -849.1406759 , -855.62398858]
a3x=np.arange(len(a3y))

wave = [-731.11059984, -728.47093717, -713.86716911, -680.2975881 ,
       -618.76047483, -524.25410195, -396.7767379 , -240.32665095,
        -63.9021133 ,  122.49859465,  306.87718006,  478.23533331,
        630.57472375,  757.89699553,  849.20376345,  912.49660913,
        966.77707721, 1008.04667182, 1037.30685332, 1055.55903521,
       1065.80458132, 1069.04480327, 1068.2809582 , 1064.51424672,
       1057.74581119, 1048.97673424, 1038.20803754, 1023.44068087,
       1004.67556141,  983.91351339,  959.15530785,  928.40165277,
        890.65319339,  844.9105128 ,  791.17413276,  730.4445147 ,
        664.72206101,  596.00711644,  526.29996976,  465.60085552,
        409.90995604,  354.22740345,  302.5532819 ,  256.88762985,
        216.23044249,  181.58167415,  149.94124091,  121.30902312,
         94.68486807,   69.06859264,   42.45998605,   14.85881254,
        -10.73518588,  -35.32228663,  -63.90278387,  -94.47698566,
       -127.0452113 , -160.60778851, -194.16505079, -227.71733472,
       -261.26497733, -294.8083135 , -327.34767345, -358.88338026,
       -385.41574752, -407.94507695, -433.47165627, -459.99575703,
       -486.51763258, -513.03751622, -537.55561935, -561.07212984,
       -582.58721047, -603.10099754, -622.61359958, -640.12509628,
       -657.63553747, -670.14494237, -681.6532989 , -696.16056319,
       -711.66665933, -727.17147916, -742.67488235, -758.17669657,
       -773.67671795, -789.17471161, -804.67041247, -821.16352618,
       -837.65373036, -849.1406759 , -855.62398858]

%matplotlib notebook
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import trapz, simps       


fig=plt.figure()
plt.subplot(2, 1, 1)
plt.plot(wave)
plt.title('Area under curve')

plt.subplot(2, 3, 4)
plt.plot(a1x,a1y)
plt.title('Area 1')

plt.subplot(2, 3, 5)
plt.plot(a2x,a2y)
plt.title('Area 2')

plt.subplot(2, 3, 6)
plt.plot(a3x,a3y)
plt.title('Area 3')

print ("Area under curve", simps(wave, np.arange(len(wave)))
print("area under graph A1", simps(a1y, a1x))
print("area under graph A2", simps(a2y, a2x))
print("area under graph A3", simps(a3y, a3x))

Does anyone know how to how to calculate "A2" (not "Area2")??

mozway · Answer

IIUC, you want to calculate the area of the curve between the horizontal line defined by the min value of wave and the curve for each chunk?

Just subtract the min value:

M = min(wave)
print("Area under curve", simps(np.array(wave)-M, np.arange(len(wave))))
print("area under graph A1", simps(np.array(a1y)-M, a1x))
print("area under graph A2", simps(np.array(a2y)-M, a2x))
print("area under graph A3", simps(np.array(a3y)-M, a3x))

output:

Area under curve 81497.49533938
area under graph A1 21437.511782499998
area under graph A2 36243.834408466675
area under graph A3 20800.25109029666

NB. the total is of the three areas is slightly less than the total area because you're skipping two fine bands between the three chunks. To avoid that, ensure the last point of one chunk is the first one of the next chunk.

With consecutive intervals:

Area under curve 81497.49533938
area under graph A1 23361.64246073833
area under graph A2 36243.834408466675
area under graph A3 21891.767255634997

Is there a Python function for finding each section of "Area Under curve"?

1 Answers