为什么我的optimize.leastsq无法正常工作？

Question

I am trying to fit function to my data. I have two different axis, x-axis: height, y-axis: weight. By visual inspection, I can see, that it gives more or less the shape of square root function saturating around weight = 10. Here is what I am doing:

from scipy import optimize

fitfunc = lambda p, x: np.sqrt(p[0]* x + p[1]) +p[2] # Target function
errfunc = lambda p, x, y: fitfunc(p, x) - y

sort_idx = np.argsort(height)
height = height[sort_idx]
weight = weight[sort_idx]

p0 = [0.1, 0.2, 0.3] # initial values
p1, success = optimize.leastsq(errfunc, p0, args=(height, weight), maxfev=10000)

No matter what values I set as p0, the output is always p1 = p0

What am I doing wrong?

Do you think it would be better to use different function if it is saturating?

Thanks in advance!

Answer 1

You may have weight and height reversed, if they are the weight and height of a human population. Other than that your code runs beautifully well:

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

fitfunc = lambda p, x: np.sqrt(p[0]* x + p[1]) +p[2] # Target function
errfunc = lambda p, x, y: fitfunc(p, x) - y

height = np.random.normal(loc=1.70, scale=.15, size=(100))
bmi = np.random.normal(loc=20, scale=2, size=(100))
weight = bmi * height**2

sort_idx = np.argsort(weight)
height = height[sort_idx]
weight = weight[sort_idx]

p0 = [0.1, 0.2, 0.3] # initial values
p1, success = optimize.leastsq(errfunc, p0, args=(weight, height), maxfev=10000)

plt.plot(weight, height, 'o')
plt.plot(weight, fitfunc(p1, weight), '-')
plt.xlabel('weight')
plt.ylabel('height')
plt.show()

>>> p1
array([ 0.01625167, -0.32844465,  0.9256349 ])

The code does sometime give warnings like:

RuntimeWarning: invalid value encountered in sqrt
  fitfunc = lambda p, x: np.sqrt(p[0]* x + p[1]) +p[2] # Target function

You may want to redefine your fitfunc and errfunc as

fitfunc2 = lambda p, y: ((y - p[2])**2 - p[1]) / p[0] # Target function
errfunc2 = lambda p, x, y: fitfunc2(p, y) - x

and then do :

p2, success2 = optimize.leastsq(errfunc2, p0, args=(weight, height), maxfev=10000)

Plotting this and the previous gives slightly different but comparable results:

Answer 2

Not directly an answer to your problem, but with your data given, I have no problem fitting this:

import sys
from scipy import optimize
import numpy as np
from matplotlib import pyplot as plt


height=np.array([34.75625407,126.90646855,369.02594015,321.33822843,100.89398254,119.73654933,421.4400502,98.09051003,72.61433571,626.54970675,45.97802204,741.65476066,39.13568217,67.21666378,58.44445182,31.9950751,32.74788721,168.3256637,149.57003524,1058.41323859])
weight=np.array([4.375,3.95833333,9.16666667,8.125,3.75,8.4375,7.91666667,7.5,5.,10.,6.25,7.625,5.,6.25,10.,3.75,4.375,6.66666667,6.25,8.28125])

fitfunc = lambda p, x: np.sqrt(p[0]* x + p[1]) +p[2] # Target function
errfunc = lambda p, x, y: fitfunc(p, x) - y

pp = [0.2, 0.3, 0.4]
sort_idx = np.argsort(height)
height = height[sort_idx]
weight = weight[sort_idx]

p0 = [0.2, 0.2, 0.3] # initial values
result = optimize.leastsq(errfunc, p0, args=(height, weight), maxfev=10000, full_output=1)
p1 = result[0]
print result[3]

plt.plot(height, weight, 'o')
plt.plot(height, fitfunc(p1, height), '-')
plt.show()

One thing you could do, as I've done in my code above, is set full_output=1 and print the message you get. Note that my success value is actually 2, not 4. So there is some odd difference. Since we should be using the same data, something in your scipy setup may be incorrect. That, or you're not showing the whole problem and something's up elsewhere.

Looking at the figure, I do see that the values are scattered pretty much around anywhere, so it'll be hard to fit anyway (in fact, I wouldn't!).

Answer 3

Thanks for your help. I think I know what was the problem. Somehow the sqrt was becoming negative, and was giving the errors. When I took out the variables so that it cannot be negative it started to work, ie:

p[0]* np.sqrt(x + np.abs(p[1]))

It's not exactly the same, but it works for me. I should have thought about that before. Thanks again