scipy minimize TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple'

Question

I'm playing a bit with some SIR models, and trying to minimize a function with scipy.

def SIR_Model(parametros, valores_iniciais, valores_reais):

    Dias = len(valores_reais)-1
    Dia=[0]

    N=valores_iniciais[0]

    S=[]
    E=[]
    A=[]
    I=[]
    H=[]
    R=[]

    S.append(valores_iniciais[1])
    E.append(valores_iniciais[2])
    A.append(valores_iniciais[3])
    I.append(valores_iniciais[4])
    H.append(valores_iniciais[5])
    R.append(valores_iniciais[6])


    sigma=valores_iniciais[7]
    lambda_model=valores_iniciais[8]
    k1=valores_iniciais[9]
    k2=valores_iniciais[10]
    delta=valores_iniciais[11]

    beta1=parametros[0]
    beta2=parametros[1]
    beta3=parametros[2]
    gamma=parametros[3]

    for i in range(0,Dias):
        Dia.append(i+1)
        S.append(S[i]*(1-beta1*A[i]/N-beta2*I[i]/N-beta3*H[i]/N))
        E.append(E[i]*(1-sigma)+S[i]/N*(beta1*A[i]+beta2*I[i]+beta3*H[i]))
        A.append(A[i]*(1-k1)+(1-gamma)*sigma*E[i])
        I.append(sigma*gamma*E[i]-lambda_model*I[i])
        H.append(H[i]*(1-k2-delta)+lambda_model*I[i])
        R.append(R[i]+k1*A[i]+(k2+delta)*H[i])

    df_model=pd.DataFrame(np.column_stack([S, E, A, I, H, R, Dia, valores_reais]), columns=['Susceptible','Exposed','Asymptomatic','Infected','Hospitalized','Removed','Dia', 'Infected Portugal'])

    RMSE = ((df_model["Infected"] - df_model["Infected Portugal"]) ** 2).mean() ** .5
    R_0 = ((1-gamma)*beta1*S[0])/(k1*N) + (gamma*beta2*S[0])/(lambda_model*N) + (gamma*beta3*S[0])/((k2+delta)*N)

    return RMSE, df_model, R_0

Calling the function with some values, it works fine eg RMSE_Model, df_Model, R_0_Model = SIR_Model(parametros_x0, valores_inicio, infected_portugal)

When I try to minimize I get the error: TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple'

from scipy.optimize import minimize
res = minimize(SIR_Model,x0=parametros, args=(valores_inicio, infected_portugal))

May you help pls? Thanks

Answer 1

The function SIR_model returns a tuple but scipy.optimize.minimize expects the function to return a scalar.

The description in the docs says:

Minimization of scalar function of one or more variables.

A function that return a tuple could probably work on the condition that the tuples can be ordered with comparison. In your case, the tuple contains objects that can't be ordered.

You may want to wrap the SIR_Model function so that it returns a scalar and apply the minimize function to the wrapper.

def wrapper(parametros, valores_iniciais, valores_reais):
    res = SIR_Model(parametros, valores_iniciais, valores_reais)
    return res[0]