如何解决 python 中的表达式，例如 f1(x) = f2(x)？

Question

import math
import pylab
import sympy


def f1(x):
   """function representing a cosine variant function and returned"""
   return math.cos(2 * math.pi * x) * math.exp(-x ** 2)


def f2(x):
    """function representing a log variant function and returned"""
    return math.log(x + 2.2)


def positive_places(f, xs):
    """return a list of elements of xs that are positive when operated in by
f"""
    list1 = []
    for i in xs:
        if f(i) > 0:
            list1.append(i)
    return list1


def create_plot_data(f, xmin, xmax, n):
    """returns a tuple (xs, ys) where xs and ys are two sequences,
    each containing n numbers"""
    xs = [xmin + i * ((xmax - xmin) / (n - 1)) for i in range(n)]
    ys = [f(xs[i]) for i in range(n)]
    return (xs, ys)


def myplot():
    """plots a graph of f1() and returns the graph"""
    print(create_plot_data(f1, -2, 2, 1001))
    (a1, b1) = create_plot_data(f1, -2, 2, 1001)
    (a2, b2) = create_plot_data(f2, -2, 2, 1001)
    pylab.plot(a1, b1, label='f1(x)')
    pylab.plot(a2, b2, label='f2(x)')
    pylab.xlabel('x')
    pylab.ylabel('y')
    pylab.legend()
    pylab.grid()
    pylab.savefig('plot.pdf')
    pylab.savefig('plot.png')
    pylab.show()


def find_cross():
    return sympy.solve(math.cos(2 * math.pi * x) * math.exp(-x ** 2) - math.log(x + 2.2), x)

`

您好，我正在尝试定义一个函数，该函数将找到两个方程相等的正 x 值点：f1(x) = f2(x)

f1(x) = math.cos(2 * math.pi * x) * math.e ** (-x ** 2)
f2(x) = math.log(x + 2.2)

x = 0 和 x = 0.5 之间的点

Answer 1

使用 SymPy 时，您可以利用 mpmath's root finder 处理任意多个数字的能力：

import mpmath
import sympy as sy

sy.init_printing()
mpmath.mp.dps = 30  # accuracy of 30 digits

# declare expressions:
x = sy.Symbol('x', real=True)
f1 = sy.cos(2*sy.pi*x) * sy.exp(-x**2)
f2 = sy.log(x + sy.Rational(22, 10))

g = f2 - f1  # f1 == f2 is equivalent to g == 0:
dg = g.diff(x)  # 1. derivative needed by numeric root-finder

# generate numeric functions from SymPy expressions:
g_m, dg_m = (sy.lambdify(x, f_, modules="mpmath") for f_ in (g, dg))

# find the roots:
x_sln = mpmath.findroot(g_m, [0, 0.5], solver='secant', df=dg)
print("Intersection f1(x) == f2(x) is at x = {}".format(x_sln))
# => Intersection f1(x) == f2(x) is at x = 0.0922612383093564032487110560683

请注意，混合使用 SymPy、math（和 NumPy）函数可能会产生不必要的副作用。