Calculate area under a graph.
The program uses the trapezoidal rule to calculate the area under a graph with a custom number of splits. The individual splits are shown on the graph using matplotlib.
pip install matplotlib
- The line equation is calculated for each set of points by calculating the gradient and solving for the y-intercept.
# Gets gradient and y-intercept for each line
def getEquations():
# Using equation y=mx+c
counter = 1
m = []
c = []
while counter <= len(x)-1:
yDif = y[counter] - y[counter - 1]
xDif = x[counter] - x[counter - 1]
grad = yDif / xDif
yIntercept = y[counter] - x[counter] * grad
m.append(grad)
c.append(yIntercept)
counter += 1
return m, c- The x-coordinate for every split is calculated
# Gets x-coords for each split
def getSplits():
interval = (x[-1] - x[0]) / splits
x1 = [x[0]]
for i in range(splits):
xCoord = x[0] + interval * (i+1)
x1.append(xCoord)
return x1- Calculate where each vertical split intersects the graph
# Gets y-coord of the intersection for each vertical line split
def getIntersections():
# Using equation y=mx+c
counter = 1
equation = 1
y1 = [y[0]]
while counter <= splits-1:
while x1[counter] >= x[equation]:
equation += 1
gradient = m[equation-1]
yIntercept = c[equation-1]
xCoord = x1[counter]
# print(gradient, yIntercept, xCoord)
yCoord = gradient * xCoord + yIntercept
y1.append(yCoord)
counter += 1
y1.append(y[-1])
return y1Since the graph is made of straight lines, by splitting the graph into triangles and trapeziums at each point, the real area under the graph can be calculated.
def method1():
# Using equation (y1+y2)*(x2-x1)/2
area1 = 0
for i in range(len(m)):
area1 += (y[i]+y[i+1]) * (x[i+1]-x[i]) / 2
return area1By using a trapezoidal equation devised by my friend MartinMimi, the area under the graph is approximated; the higher the number of splits, the more accurate the approximation.
def method2():
# Using equation x/2n(2ฮฃy-(y[0]+y[-1]))
area2 = ((x[-1]-x[0])/(2*splits)) * (2*sum(y1)-(y1[0]+y[-1]))
return area2
Everything is coded by Alex lo Storto
Licensed under the MIT License.
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