I've been looking through the minimize function declaration files, and I am really confused as to how the function works. So for example, if I have something like this:
import numpy as np
from scipy.integrate import quad
from scipy.optimize import minimize
encoderdistance = 2.53141952655
Dx = lambda t: -3.05 * np.sin(t)
Dy = lambda t: 2.23 * np.cos(t)
def func(x): return np.sqrt(Dx(x)**2 + Dy(x)**2)
print minimize(lambda x: abs(quad(func, 0, x)[0] - encoderdistance), 1).x
print minimize(lambda x: abs(4.24561823393 - encoderdistance), 1).x
the second print statement at the bottom will yield a different result than the one on the top even though I subbed out the quad function for the value it produced. If this is due to the lambda x part, can you explain how that affects that line of code exactly? Also, how would you type the second to last line into a calculator such as wolfram alpha? Thanks!
The optimizer needs a function to minimize -- that's what the lambda x: is about.
In the second-to-last line, you're asking the optimizer to find a value of x such that the integral from 0 to x of func(x) is close to encoderdistance.
In the last line, the function to be minimized in your last line is just a scalar value, with no dependency on x, and the optimizer is bailing out because it can't change that.