Scipy.optimize.root doesn't converge in Python and Matlab fsolve works, why?
I am trying to find the y root of a function f using Python.
Here is my code:
def f(y):
w,p1,p2,p3,p4,p5,p6 = y[:7]
t1 = w - 0.99006633*(p1**0.5) - (-1.010067)*((1-p1))
t2 = w - 22.7235687*(p2**0.5) - (-1.010067)*((1-p2))
t3 = w - 9.71323491*(p3**0.5) - (-1.010067)*((1-p3))
t4 = w - 2.43852877*(p4**0.5) - (-1.010067)*((1-p4))
t5 = w - 3.93640207*(p5**0.5) - (-1.010067)*((1-p5))
t6 = w - 9.22688144*(p6**0.5) - (-1.010067)*((1-p6))
t7 = p1 + p2 + p3 + p4 + p5 + p6 - 1
return [t1,t2,t3,t4,t5,t6,t7]
x0 = np.array([-0.01,0.4,0.1,0.2,0.1,0.1,0.1])
sol = scipy.optimize.root(f, x0)
print sol
Python does not find root. However, there is one, I found it with the fsolve function in Matlab.
It:
[0.3901, 0.6166, 0.0038, 0.0202, 0.2295, 0.1076, 0.0223]
I really want to use Python. Can anyone explain why scipy.optimize.root in Python doesn't converge, but fsolve in Matlab does?
For reference scipy.optimize.solve does not converge.
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1 answer
Try another method. For me method="lm"
(I'm assuming Levenberg-Marquardt, but I'm not entirely sure) works very well:
import numpy as np
import scipy.optimize
def f(y):
w,p1,p2,p3,p4,p5,p6 = y[:7]
t1 = w - 0.99006633*(p1**0.5) - (-1.010067)*((1-p1))
t2 = w - 22.7235687*(p2**0.5) - (-1.010067)*((1-p2))
t3 = w - 9.71323491*(p3**0.5) - (-1.010067)*((1-p3))
t4 = w - 2.43852877*(p4**0.5) - (-1.010067)*((1-p4))
t5 = w - 3.93640207*(p5**0.5) - (-1.010067)*((1-p5))
t6 = w - 9.22688144*(p6**0.5) - (-1.010067)*((1-p6))
t7 = p1 + p2 + p3 + p4 + p5 + p6 - 1
return [t1,t2,t3,t4,t5,t6,t7]
x0 = np.array([-0.01,0.4,0.1,0.2,0.1,0.1,0.1])
sol = scipy.optimize.root(f, x0, method='lm')
assert sol['success']
print 'Solution: ', sol.x
print 'Misfit: ', f(sol.x)
This gives:
Solution: [ 0.39012036 0.61656436 0.00377616 0.02017937 0.22954825
0.10763827 0.02229359]
Misfit: [0.0, 0.0, 1.1102230246251565e-16, -1.1102230246251565e-16,
1.1102230246251565e-16, 0.0, -2.2204460492503131e-16]
I'm actually a little surprised that Levenberg-Marquardt is not a default. This is usually one of the first gradient-descent style solvers you can try.
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