Optimizing function using optimize function

Question

I want to define a function :

And I want to find minimum with respect to (a,b) for points :

x = np.array([.2, .5, .8, .9, 1.3, 1.7, 2.1, 2.7])
y = f(x) + np.random.randn(len(x))

Using function : optimize.fmin_cg (you can find documentation here : https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_cg.html)

My work so far

I managed to define a compute_error() function :

def compute_error(a,b):
    k=[0]*len(x)
    for i in range(0,len(x)):
        k[i]=(y[i]-(a*x[i]+b))**2
    return sum(k)

And I tried to minimize it using this optimize function, however I met some problems.

x_0=np.array((0,0))     #start optimization from point (0,0)
 
minimum = optimize.fmin_cg(compute_error,x_0)

TypeError: compute_error() missing 1 required positional argument: 'b'

piterbarg · Accepted Answer · 2020-10-31 18:11:26Z

3

I think compute_error should take a two-element array not two separate arguments

def compute_error(params_to_optimize):
    a = params_to_optimize[0]
    b = params_to_optimize[1]
    k=[0]*len(x)
    for i in range(0,len(x)):
        k[i]=(y[i]-(a*x[i]+b))**2
    return sum(k)

also, possibly related, x0 initialization looks a bit weird I would use a list not a tuple in the np.array constructor

x_0=np.array([0,0])

answered Oct 31, 2020 at 18:11

piterbarg

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1 Comment

igrinis Over a year ago

Two style remarks: 1) you can write a, b = params_to_optimize to unpack the tuple, instead of the two first lines 2) instead of the for loop you can use vector form (for numpy it is generally faster) k = (y - (a*x + b))**2. This way your code will be more readable, concise and error prone.

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