Question

早在我的微积分课程中，我有一个想法是创建一个图表来更新自己，以显示牛顿方法找到函数根的进展。所以我的问题是，使用Python和Sympy处理问题背后的所有混乱的微积分，我如何以信息的方式绘制图形。

乍一看，Sympy最新的图书馆似乎没有提供任何方法来简单地将多个图表添加到现有图表上，这是一个问题。

希望有人找到以下使用答案：）

Answer 1

经过大约2天的工作，我设法提出了这个解决方案。我仍然使用Sympy作为派生计算和函数输入的后端，但是我将这些表达式转换为lambda函数以生成我可以提供给Matplotlib坐标的值。我还清理了代码并在最重要的部分添加了注释。

要使用此程序（仅在Windows上测试），我安装了最新的Anaconda软件包。

'''
Created on Aug 10, 2016

@author: Clement Hathaway

Example: enter in:

6*x**3 -73*x**2 -86*x +273
-20
-10
20
-2200
2000

GO!

'''
from numpy import linspace
from sympy.parsing.sympy_parser import parse_expr
from sympy import *
from sympy.solvers.solveset import solveset, solveset_real

import matplotlib.pyplot as plt
#from numpy.doc.constants import lines

def distanceFromRoot(x, values):  ## Return the lowest distance between the supplied roots
    currentDistance = abs(x-values[0])

    if len(values) > 1:  ## Only run if there is more than one root

        for value in values:
            newDist = abs(x-value)
            if newDist < currentDistance:
                currentDistance = newDist

    return currentDistance


def generateTangents(x0, real_roots, accuracy):
    if distanceFromRoot(x0, real_roots) > accuracy: ## Continue if the value we have calculated is still too far from a real root
        tangent = simplify(dy.subs(x, x0)*(x-x0)+(y.subs(x,x0))) ## Find equation of tangent at our x0
        tangent_intercept = solve(tangent, x)[0]                 ## Find tangent's x intercept

        lam_tan = lambdify(x, tangent, modules=['numpy'])        ## Function to generate y values of the tangent line
        tan_y_vals = lam_tan(x_values)                           ## Y values of the tangent line to plot

        text.set_text("Current x-estimate:  " + str(N(tangent_intercept))) ## Display estimate

        plt.plot(x_values, tan_y_vals, 'b-')                     ## Plot our new y values with a colour of blue and a ocnsistent line
        plt.draw()                                               ## Draw the plot
        plt.pause(0.5)                                             ## Pause for 1 second before drawing the next line

        generateTangents(N(tangent_intercept), real_roots, accuracy)     ## Call itself again recursively
    else: ## Do nothing
        ## Display some ending text
        print("Found value to be: " + str(x0))
        print("With real roots: " + str(real_roots))
        pass

if __name__ == '__main__':
    ## Equation
    x = symbols('x')
    y = parse_expr(str(raw_input("Enter Equation: ")))
    dy = diff(y, x) ## Differentiate y in terms of x

    x0 = float(input("Enter starting value for x: "))
    roots = solveset_real(y, x) ## Find roots of y in terms of x
    roots_array = [] ## Get in terms of array
    for root in roots:
        roots_array.append(N(root))


    ## Setup Values
    x_min = int(input("Enter x-axis min: "))
    x_max = int(input("Enter x-axis max: "))

    y_min = int(input("Enter y-axis min: "))
    y_max = int(input("Enter y-axis max: "))

    res = 200

    ## Convert to use with other library
    lam_y = lambdify(x, y, modules=['numpy'])   ## Functions of our main func
    lam_dy = lambdify(x, dy, modules=['numpy']) ## Differential of our eq

    ## Calculate starting values
    x_values = linspace(x_min, x_max, res)      ## Array of x values between xmin and max seperated by res
    y_values = lam_y(x_values)                  ## Calculated y values

    ## Graph Setup
    plt.axis([x_min, x_max, y_min, y_max])      ## Setup graph axis
    plt.grid()                                  ## Enable the graph grid
    plt.ion()                                   ## Make graph interactive to add future lines

    ## Plot main Function
    y0_values = linspace(0,0, res)
    plt.plot(x_values, y_values, 'g-', linewidth=2)
    plt.plot(x_values, y0_values,'k-', linewidth=2) ## Create more noticable x axis
    text = plt.text(0,5,"Current x-estimate:  " + str(x0), fontsize = 30)
    plt.draw()
    plt.pause(0.1)

    ## Start generating tangent lines! weo
    generateTangents(x0, roots_array, 0.0000001)

    ## Keep the graph from disappearing
    plt.ioff()
    plt.show()

制作牛顿方法的动画，用于查找函数的根

1 个答案: