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Optimizers are a set of procedures defined in SciPy that either find the minimum value of a function, or the root of an equation
Optimizers are a set of procedures defined in SciPy that either find the minimum value of a function, or the root of an equation.
Essentially, all of the algorithms in Machine Learning are nothing more than a complex equation that needs to be minimized with the help of given data.
NumPy is capable of finding roots for polynomials and linear equations, but it can not find roots for non linear equations, like this one:
x + cos(x)
For that you can use SciPy's optimze.root
function.
This function takes two required arguments:
The function returns an object with information regarding the solution.
The actual solution is given under attribute x
of the returned object:
Find root of the equation x + cos(x)
:
from scipy.optimize import root
from math import cos
def eqn(x):
return x + cos(x)
myroot = root(eqn, 0)
print(myroot.x)
Note: The returned object has much more information about the solution.
Print all information about the solution (not just x
which is the root)
print(myroot)
A function, in this context, represents a curve, curves have high points and low points.
High points are called maxima.
Low points are called minima.
The highest point in the whole curve is called global maxima, whereas the rest of them are called local maxima.
The lowest point in whole curve is called global minima, whereas the rest of them are called local minima.
We can use scipy.optimize.minimize()
function to minimize the function.
The minimize()
function takes the following arguments:
'CG'
'BFGS'
'Newton-CG'
'L-BFGS-B'
'TNC'
'COBYLA'
'SLSQP'
{
"disp": boolean - print detailed description
"gtol": number - the tolerance of the error
}
Minimize the function x^2 + x + 2
with BFGS
:
from scipy.optimize import minimize
def eqn(x):
return x**2 + x + 2
mymin = minimize(eqn, 0, method='BFGS')
print(mymin)
Insert the missing parts to print the square root of the equation:
from scipy.optimize import root from math import cos def eqn(x): return x + cos(x) myroot = (eqn, 0) print()