# Solutions to exercises

#
# 1. Pure Random Search
#
def PRS_2d(f, x_range=(0,1), y_range=(0,1), n_iter=100): 
    # f a 2D function to minimize
    # x_range: [x_min, x_max] interval
    # y_range: [y_min, y_max] interval
    
    xy = []  # successive temporary solutions
    fs = []  # values of f as improved over iterations
    min_f = np.Inf

    for i in range(n_iter):
        x = np.random.uniform(-2, 2)
        y = np.random.uniform(-2, 2)

        val_f = f(x, y)
        
        if val_f < min_f:
            min_f = val_f
            xy.append((x, y))
            fs.append(val_f)

    return xy, fs


#
# 2. Simulated annealing
#
def SA_2d(f, n_iter):
    # Simple simulated annealing procedure for continuous 2d functions
    x = np.random.normal(0, 1, 2)  # 2 values, normally distributed
    fx = f(x[0], x[1])
    fbest = fx
    xbest = np.copy(x)

    fs = []
    
    for i in range(n_iter):
        xp = x + np.random.normal(0, 1, 2)
        T = (n_iter - i) / n_iter
        fxp = f(xp[0], xp[1])
        if (fxp < fx) or (np.exp(-(fxp-fx)/T) > np.random.rand()):
            x = np.copy(xp)
            if fxp < fbest:
                fbest = fxp
                xbest = np.copy(xp)
        fs.append(fbest)

    return xbest, fs