def gauscurv_gen(N,m,n):
rarr = test_spectrum.sin_cos_arr(N,m,n)
gc = curvature.gaus_curv(rarr)
X,Y = np.ogrid[0:N, 0:N]
X -= N/2; Y -= N/2
Fxx = -(1.0*m)**2 * np.sin(2*m*np.pi*X/N)
Fyy = (1.0*n)**2 * np.cos(2*n*np.pi*Y/N)
Fx = (1.0*m) * np.cos(2*m*np.pi*X/N)
Fy = (1.0*n) * np.sin(2*n*np.pi*Y/N)
denom = (Fx**2 + Fy**2 + 1)**2
calc_gc = Fxx*Fyy / denom
ok_(np.allclose(calc_gc, gc))
def meancurv_gen(N,m,n):
rarr = test_spectrum.sin_cos_arr(N,m,n)
mc = curvature.mean_curv(rarr)
X,Y = np.ogrid[0:N, 0:N]
X -= N/2; Y -= N/2
Fx = (1.0*m) * np.cos(2*m*np.pi*X/N)
Fy = (1.0*n) * np.sin(2*n*np.pi*Y/N)
Fxx = -(1.0*m)**2 * np.sin(2*m*np.pi*X/N)
Fyy = (1.0*n)**2 * np.cos(2*n*np.pi*Y/N)
denom = np.power(Fx**2 + Fy**2 + 1, 1.5)
calc_mc = 0.5 * ((1+Fx**2)*Fyy + (1+Fy**2)*Fxx) / denom
ok_(np.allclose(calc_mc, mc))
