Why is a matrix argument of my objective function changed when I minimize it with scipy.optimize.minimize()?

Question

I'm trying to do the Space-Time Auto-Regression ( STAR ). The code below basically defines the objective function above that I need to minimize, where Y is an N-by-K matrix and D an N-by-N matrix.

import numpy as np
from sys import exit

def obj_func(Y, D, Phi):

    # check what went wrong
    if not D.shape[0]==D.shape[1]:
        print("D =", D)
        exit()
    if not Y.shape[0]==D.shape[0]:
        print("Y =", Y)
        print("D =", D)
        exit()
    if Y.shape[1]<len(Phi):
        print("Y =", Y)
        print("T =", len(Phi)-1)
        exit()

    T = len(Phi) - 1
    N = Y.shape[0]
    K = Y.shape[1]
    c = Phi[0] * np.ones((N,1))

    loss = 0
    for j in range(T,K):
        y = Y[:,j].reshape((N,1))
        v = y - c 
        for tau in range(1,T+1):
            y = Y[:, j-tau].reshape((N,1))
            v = v - Phi[tau] * D.dot(y)
        loss += np.linalg.norm(v)

    return(loss / (K-T))

The optimization went wrong, and so the first chunk was just added to check which part went wrong exactly. I use scipy.optimize.minimize( ) to minimize the objective function.

from scipy.optimize import minimize

def STAR_pm(Y, D, T):
    phi = np.random.normal(loc=0, scale=5, size=T+1)
    result = minimize(obj_func, x0=phi, args=(Y,D,), )
    if not result.success:
        print("No convergence. Try again.")
        exit()
    return(result.x)

However, when I ran the following, the optimization failed and printed out the matrix D. Turned out that somehow, Y had been assigned to D and so D was not no more an N-by-N matrix.

Y = np.random.randint(0,10, (3,10))
D = np.random.rand(3,3)

STAR_pm(Y, D, T=2)

I find it very confusing. Why is D changed at all? Has this happened to someone else? Anybody help me out here?

Answer 1

In scipy.optimize.minimize the first argument of the objective function is always the design vector. The extra arguments are given with args, it will be called as obj_func(x, *args) . From your example I assume, that your design vector is Phi , All you need to do is to rewrite the signature of your objective as obj_func(Phi, Y, D) .