将数学方程式作为参数传递（numpy）

Question

I am looking to write a program that calculates the left+right riemann sum of a function. My only problem is, I want the function to take np.sin(x^2) or np.cos(3*x +2) or perhaps ax^2 + 3*x + 2 (polynomial function) as the y parameter and np.linspace() as the x parameter and 'left' or 'right' as a string. So far, my code does take sin(x) / cos(x) to calculate the left/right riemann sum of those 2 function. But I am struggling to let's say pass a function like sin(x^2)+3 and take it's approximation. I have the logic of the equation right but perhaps, I'm not understanding the data structures of numpy/python really well. Here is my code:

import numpy as np
def r_sums(y,x,method='left'):
    #f = y(x)
    l = []
    delta_x = abs(x[0]-x[-1])/len(x)
    while method != 'right':
        #Calculating Left Riemann Sum (below the list comprehension is a normal for loop of the list comprehension func)
        return sum([ y(x[0]+ i*delta_x) for i in range(0,len(x))])*delta_x
        #for i in range(0,len(x)):
            #f_a = x[0] + i*(delta_x) #Calculating left endpoint
            #l.append(y(f_a))         #Appends all the left endpoint into a list l
        #return sum(l)*delta_x

    #Calculating Right Riemann Sum (below the list comprehension is a normal for loop of the list comprehension func)
    return sum([y(x[0]+ i*delta_x) for i in range(1,len(x)+1)])*delta_x
    #for i in range(1,len(x)+1):
        #f_a = x[0] + i*(delta_x)
        #l.append(y(f_a))
    #return sum(l)*delta_x

r_sums(np.sin,np.linspace(1,4,200),'left') should work but I am looking to have the y parameter to take something like

r_sums(np.sin(x**2+3),np.linspace(1,4,200),'left') <-- doesn't work

Really appreciate some help/feedback! Thank you.

Answer 1

You probably want to pass in a "real" function (and not a value!). Notice that you have to define a function or use a lambda expression here.

r_sums(lambda x: np.sin(x**2+3),np.linspace(1,4,200),'left')

will work.

The lambda expression is just a function taking one argument x and returning np.sin(x**2+3)

it would be the same as:

def function_sin_xsqaured_plus_3(x):
    return np.sin(x**2+3)

r_sums(function_sin_xsqaured_plus_3,np.linspace(1,4,200),'left')

(which also works)