Step 1 SVI Quasi Explicit -- Python

step1.py

def f_gradient(params,y,market_vols,tte,q):
    c,d,abar = params
    y = y[market_vols>0]
    vols = market_vols[market_vols>0]
    n = len(y)
    Y1 = np.sum(y)
    Y2 = np.sum(y**2)
    Y3 = np.sum(np.sqrt(y**2+1))
    Y4 = np.sum(y*np.sqrt(y**2+1))
    var_t = vols**2*tte
    v = np.sum(var_t)
    vY = np.sum(var_t*y)
    vY2 = np.sum(var_t*np.sqrt(y**2+1))
    A = np.array([(n+Y2),Y4,Y3,Y4,Y2,Y1,Y3,Y1,n]).reshape((3,3))
    b = np.array([vY2,vY,v])
    return np.ascontiguousarray(np.linalg.solve(A,b))