如何使用Python解1参数方程式(scipy/numpy?) [英] How to solve an 1-parameter equation using Python (scipy/numpy?)

问题描述

我希望您有一些有用的提示可以帮助我完成以下任务:

I hope you have some useful tip for me to approach the following task:

我写了一些简单的python代码段来绘制概率密度函数.在我的特殊情况下，让它们表示某些参数x的类条件概率.

I wrote some simple python snippet to plot probability density functions. In my particular case, let them represent class-conditional probabilities for some parameter x.

因此，我想知道Python中是否有一种巧妙的方法(即模块)(也许通过NumPy或SciPy函数或方法)来解决参数x的简单方程式. 例如

So, I am wondering if there is an clever approach (i.e., module) in Python (maybe via a NumPy or SciPy function or method) to solve a simple equation for parameter x. E.g.,

pdf(x, mu=10, sigma=3**0.5) / pdf(x, mu=20, sigma=2**0.5) = 1
# get x

现在，我只能使用类似 x = np.arange(0, 50, 0.000001)并将x值保留在可产生最接近值的向量中 计算比率pdf1/pdf2.

Right now, I can only thing of an brute force approach where I use something like x = np.arange(0, 50, 0.000001) and keep the x value in the vector that yields the closest value for 1 when calculating the ratio pdf1/pdf2.

下面是我编写的用于计算pdf并绘制比率的代码:

Below is the code I wrote to calculate the pdf and plot the ratio:

def pdf(x, mu=0, sigma=1):
    """Calculates the normal distribution's probability density 
        function (PDF).  

    """
    term1 = 1.0 / ( math.sqrt(2*np.pi) * sigma )
    term2 = np.exp( -0.5 * ( (x-mu)/sigma )**2 )
    return term1 * term2


x = np.arange(0, 100, 0.05)

pdf1 = pdf(x, mu=10, sigma=3**0.5)
pdf2 = pdf(x, mu=20, sigma=2**0.5)

# ...
# ratio = pdf1 / pdf2
# plt.plot(x, ratio)

谢谢！

推荐答案

通常，听起来您需要标量根查找函数: http://docs.scipy.org/doc/scipy/reference/optimize.html

In general, it sounds like you need the scalar root-finding functions: http://docs.scipy.org/doc/scipy/reference/optimize.html

但是正如其他人指出的那样，似乎有一种分析解决方案.

But as others have pointed out, it seems like there is an analytical solution.

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