我需要在 Python 中计算并绘制下面的积分:
函数 e^(-t^2) 从 x=0 到 x=3 的积分
到目前为止,我已经成功地使用辛普森法则计算积分。我正在努力解决的下一个问题是绘制 e^(-t^2) 与 x 从 x=0 到 x=3 的积分(参见上图)。
这是我编写的用于计算积分的代码 -
from math import exp
def f(t):
return exp(-(t**2))
a = 0
b = 3
h = 0.1
N = int((b-a)/h)
s_even = 0
s_odd = 0
for k in range(1,N,2):
s_odd += f(a+k*h)
for k in range(2,N,2):
s_even += f(a+k*h)
s = f(a) + f(b) + 4*s_odd + 2*s_even
Integral = h*s/3
print(Integral)
然后我如何创建这个积分的图表?
这是我编写的一个脚本,用于执行计算并使用 PyQtGraph 绘制它。 :
from pyqtgraph.Qt import QtGui, QtCore
import pyqtgraph as pg
from math import exp
class I:
def f(self,t):
return exp(-(t**2))
def __init__(self, a = 0, b = 3, h = 0.1):
N = int((b-a)/h)
s_even = s_odd = 0
for k in range(1,N,2):
s_odd += self.f(a+k*h)
for k in range(2,N,2):
s_even += self.f(a+k*h)
s = self.f(a) + self.f(b) + 4*s_odd + 2*s_even
self.I = h*s/3
def __str__(self):
return "I: %s" % self.I
def plot(array):
app = QtGui.QApplication([])
win = pg.GraphicsWindow(title="Basic plotting examples")
win.resize(1000,600)
win.setWindowTitle('pyqtgraph example: Plotting')
# Enable antialiasing for prettier plots
pg.setConfigOptions(antialias=True)
p1 = win.addPlot(title="Basic array plotting", y=array)
QtGui.QApplication.instance().exec_()
def main():
a=0
b=a+0.001
points=[]
while(a<3):
points.append(I(a,b).I)
a=b
b=a+0.001
plot(points)
## Start Qt event loop unless running in interactive mode or using pyside.
if __name__ == '__main__':
main()
这是它绘制的图表:
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