"TypeError: 'tuple' object is not callable" in Python while drawing a function and its derivative?

Question

As the title question, I just encounter this problem while doing assignments, but have no idea what it is... Please can anyone help me with this?(I'm a TOTALLY newbie to this and I'm so sorry)

My code is:

#導入數學模組
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import numpy as np
import pylab

#確定坐標軸
n=1000
x=np.linspace(-10, 10, n)

#定義函數
def y(x):
    y=pylab.sqrt(2*(pylab.sin(x)+pylab.cos(2*x)+3)/(x+1))
    return y
    
def dy_dx(y, x):
    return np.sqrt(2*(pylab.sin(x)+pylab.cos(2*x)+3)/(x+1))
    
y0=[1]
x=np.arange(-10, 10, 0.01) #(start, stop, step)
y=(dy_dx, y0, x) #求y的一階導數

#繪製函數
plt.plot(x, y(x), color='blue')
plt.plot(x, y, color='green')

#加上細節
plt.grid(True)
plt.xlabel('X')
plt.ylabel('Y')
plt.title('f(x)=sqrt(2(sin(x)+cos(2*x)+3)/(x+1)) and computed derivative')
plt.xlim(0, 20) #定坐標軸範圍
plt.ylim(-1.0, 2.0)
x_main_ticks=np.linspace(0, 20, 4) #定刻度
plt.xticks(x_main_ticks)

#輸出圖像
plt.show()

And the compiler just gave me this:

> Traceback (most recent call last):
  File "/home/cg/root/66fb4a93892af/main.py", line 23, in <module>
    plt.plot(x, y(x), color='blue')
TypeError: 'tuple' object is not callable

does anyone knows what on just happened to my code?

Answer 1

This is because you name the Function y repeatedly. So basically, if you change the code as follow, it works.

#導入數學模組
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import numpy as np
import pylab

#確定坐標軸
n=1000
x=np.linspace(-10, 10, n)

#定義函數
def y_function(x):
    return pylab.sqrt(2*(pylab.sin(x)+pylab.cos(2*x)+3)/(x+1))
    
def dy_dx(y, x):
    return np.sqrt(2*(pylab.sin(x)+pylab.cos(2*x)+3)/(x+1))
    
y0=[1]
x=np.arange(-10, 10, 0.01) #(start, stop, step)
y=(dy_dx, y0, x) #求y的一階導數

#繪製函數
plt.plot(x, y_function(x), color='blue')
plt.plot(x, y[2], color='green')

#加上細節
plt.grid(True)
plt.xlabel('X')
plt.ylabel('Y')
plt.title('f(x)=sqrt(2(sin(x)+cos(2*x)+3)/(x+1)) and computed derivative')
plt.xlim(0, 20) 
#定坐標軸範圍
plt.ylim(-1.0, 2.0)
x_main_ticks=np.linspace(0, 20, 4) #定刻度
plt.xticks(x_main_ticks)

#輸出圖像
plt.show()

Answer 2

You assign a tuple to a variable named y after you've defined a function with the same name. This shadows the original function definition.

Ironically, you don't need the y variable. In fact there are a few redundancies in your code.

import matplotlib.pyplot as plt
import pylab
import numpy as np

# 定義函數
def y(x):
    return pylab.sqrt(2 * (pylab.sin(x) + pylab.cos(2 * x) + 3) / (x + 1))

x = np.arange(-10, 10, 0.1)

# 繪製函數
plt.plot(x, y(x), color="blue")
plt.plot(x, x, color="green")

# 加上細節
plt.grid(True)
plt.xlabel("X")
plt.ylabel("Y")
plt.title("f(x)=sqrt(2(sin(x)+cos(2*x)+3)/(x+1)) and computed derivative")
plt.xlim(0, 20)  # 定坐標軸範圍
plt.ylim(-1.0, 2.0)
x_main_ticks = np.linspace(0, 20, 4)  # 定刻度
plt.xticks(x_main_ticks)

# 輸出圖像
plt.show()