-numpy- | 把numpy翻译为一个中文库 | Data Manipulation library

I am looking for a tweak that I could apply to the code shown later or an alternate method that would lead to faster run time. In general, I want to find the values of two parameters that are governed by a set of multiple nonlinear equations. These equations use multiple variable arguments.

An Example of the problem at hand is presented for only a small array (4 values) as an example:

• I want to find the values of q and h that are governed by 2 non-linear equations
• I will need to apply this procedure to larger a and b arrays each of about 50k values

Equations are:

• q = k/2L * (h^2 - b^2)
• q = -2 * pi * k * (h-a) / ln((h-d)/r)

arguments/variables:

• k = 144.0
• L = 550.0
• d = 140.9
• r = 0.5
• a = [190.0, 185.0, 160.0, 150.0]
• b = [70.0, 70.0, 30.0, 10.0]

I followed suggestions in similar posts at stackoverflow, mostly This post, and modified my original code to avoid using a for loop. Though, after doing that, I tried applying the code to a big array of variables, but it took quite some time.

I should also mention that I am only interested in the solution when h is between a certain limit (when h is greater than d+r and less than 300), but I didn't know how to apply this in fsolve when I am solving for multiple parameters and using multiple non-linear functions.

The final code that I am currently using is shown in this post, but I am looking for something that is faster and more efficient.

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Two examples to clarify: given this text file:

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Array:

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This is the solution I have come up so far:

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Say I have an array: