我是 Python 新手，看过一些文章和向量化嵌套 for 循环的示例，但我不清楚如何使用我编写的一些 FDTD 代码来解决这个问题。目标是使代码更简洁，运行更高效。有人可以帮我矢量化这段代码并向我解释这些变化背后的思考过程吗？我知道这段代码不是最干净的，所以非常感谢任何帮助。
def fdtd(prl, pim, nsteps, T, xpml, ypml, zpml, Ptime_rl, Ptime_im,
Phi_rl, Phi_im, omegaT, win_Phi, PF_TIME, xpos, ypos, MDM_time):
print('n_steps =', nsteps)
print('B_0 =', B0)
for _ in range(nsteps):
T = T + 1
for n in range(1, NN - 1):
for m in range(1, MM - 1):
for k in range(1, KK - 1):
prl[n, m, k] = (xpml[n] * ypml[m] * zpml[k] * prl[n, m, k]
+ rd * V[n, m, k] * pim[n, m, k]
- ra * (-6 * pim[n, m, k]
+ pim[n + 1, m, k] + pim[n - 1, m, k]
+ pim[n, m + 1, k] + pim[n, m - 1, k]
+ pim[n, m, k - 1] + pim[n, m, k + 1]
)
+ rd * ((B0 + Btime[T]) ** 2) * VoB[n, m] * pim[n, m, k]
+ K_dfB * (B0 + Btime[T]) * 0.5 * (-(m - MC) * (prl[n + 1, m, k] -
prl[n - 1, m, k])
+ (n - NC) * (prl[n, m + 1, k] -
prl[n, m - 1, k]))
)
for n in range(1, NN - 1):
for m in range(1, MM - 1):
for k in range(1, KK - 1):
pim[n, m, k] = (xpml[n] * ypml[m] * zpml[k] * pim[n, m, k]
- rd * V[n, m, k] * prl[n, m, k]
+ ra * (-6 * prl[n, m, k]
+ prl[n + 1, m, k] + prl[n - 1, m, k]
+ prl[n, m + 1, k] + prl[n, m - 1, k]
+ prl[n, m, k - 1] + prl[n, m, k + 1]
)
- rd * ((B0 + Btime[T]) ** 2) * VoB[n, m] * prl[n, m, k]
+ K_dfB * (B0 + Btime[T]) * 0.5 * (-(m - MC) * (pim[n + 1, m, k] -
pim[n - 1, m, k])
+ (n - NC) * (pim[n, m + 1, k] - pim[n, m - 1,k])))
Ptime_rl[T] = prl[NC + 35, MC, KC]
Ptime_im[T] = pim[NC + 35, MC, KC]
for n in range(NN):
for m in range(MM):
for k in range(KK):
xpos[T] = xpos[T] + (n - NC) * (prl[n, m, k] ** 2 + pim[n, m, k] ** 2)
ypos[T] = ypos[T] + (m - MC) * (prl[n, m, k] ** 2 + pim[n, m, k] ** 2)
# print(T,'xpos,ypos:',round(xpos[T],3),round(ypos[T],3))
# This section calculates the magnetic dipole moment
mdm = 0 + 1j * 0
for n in range(1, NN - 1):
for m in range(1, MM - 1):
for k in range(KK):
pmag = prl[n, m, k] ** 2 + pim[n, m, k] ** 2
der_y = 0.5 * (n - NC) * (prl[n, m + 1, k] - prl[n, m - 1, k]
+ 1j * (pim[n, m + 1, k] - pim[n, m - 1, k]))
der_x = 0.5 * (m - MC) * (prl[n + 1, m, k] - prl[n - 1, m, k]
+ 1j * (pim[n + 1, m, k] - pim[n - 1, m, k]))
# The 0.5 are because the spatial derivative is over two cells.
mdm = mdm + (Kmdm * (1j * prl[n, m, k] + pim[n, m, k]) * (der_y - der_x)
+ (B0 + Btime[T]) * KdelB * (del_x ** 2) * ((n - NC) ** 2 + (m - MC)
** 2) * pmag)
MDM_time[T] = 1e23 * mdm.real
# This section constructs an eigenfunction
if T < PF_TIME:
cos_term = win_Phi[T] * cos(omegaT * T)
sin_term = win_Phi[T] * sin(omegaT * T)
for n in range(NN):
for m in range(MM):
for k in range(KK):
Phi_rl[n, m, k] = (Phi_rl[n, m, k]
+ cos_term * prl[n, m, k] - sin_term * pim[n, m, k])
Phi_im[n, m, k] = (Phi_im[n, m, k]
+ sin_term * prl[n, m, k] + cos_term * pim[n, m, k])
return prl, pim, T, Ptime_rl, Ptime_im, Phi_rl, Phi_im, xpos, ypos, MDM_time