publicImage/gprMax
1
0
派生 0
镜像自地址 https://gitee.com/sunhf/gprMax.git 已同步 2025-08-07 23:14:03 +08:00
代码 工单 软件包 项目 版本发布 百科 动态
文件
0cd968bc7ec64efc0734a8eebe1d79aa733c47d3
gprMax/gprMax/fields_update.pyx
Craig Warren 0e4bb43142 Updated copyright notice to add 2016.
2016-01-12 18:29:10 +00:00

452 行
22 KiB
Cython
原始文件 Blame 文件历史

# Copyright (C) 2015-2016: The University of Edinburgh
# Authors: Craig Warren and Antonis Giannopoulos
#
# This file is part of gprMax.
#
# gprMax is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# gprMax is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with gprMax. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
cimport numpy as np
from cython.parallel import prange
from gprMax.constants cimport floattype_t, complextype_t
#########################################
# Electric field updates - Ex component #
#########################################
cpdef update_ex(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsE, np.uint32_t[:, :, :, :] ID, floattype_t[:, :, :] Ex, floattype_t[:, :, :] Hy, floattype_t[:, :, :] Hz):
"""This function updates the Ex field components.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, ID, E, H (memoryviews): Access to update coeffients, ID and field component arrays
"""
cdef int i, j, k, listIndex
if ny == 1 or nz == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(1, nz):
listIndex = ID[0, i, j, k]
Ex[i, j, k] = updatecoeffsE[listIndex, 0] * Ex[i, j, k] + updatecoeffsE[listIndex, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[listIndex, 3] * (Hy[i, j, k] - Hy[i, j, k - 1])
cpdef update_ex_dispersive_multipole_A(int nx, int ny, int nz, int nthreads, int maxpoles, floattype_t[:, :] updatecoeffsE, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tx, floattype_t[:, :, :] Ex, floattype_t[:, :, :] Hy, floattype_t[:, :, :] Hz):
"""This function updates the Ex field components when dispersive materials (with multiple poles) are present.
Args:
nx, ny, nz (int): Grid size in cells
maxpoles (int): Maximum number of poles
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex, p
cdef float phi = 0.0
if ny == 1 or nz == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(1, nz):
listIndex = ID[0, i, j, k]
phi = 0.0
for p in range(0, maxpoles):
phi = phi + updatecoeffsdispersive[listIndex, p * 3].real * Tx[p, i, j, k].real
Tx[p, i, j, k] = updatecoeffsdispersive[listIndex, 1 + (p * 3)] * Tx[p, i, j, k] + updatecoeffsdispersive[listIndex, 2 + (p * 3)] * Ex[i, j, k]
Ex[i, j, k] = updatecoeffsE[listIndex, 0] * Ex[i, j, k] + updatecoeffsE[listIndex, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[listIndex, 3] * (Hy[i, j, k] - Hy[i, j, k - 1]) - updatecoeffsE[listIndex, 4] * phi
cpdef update_ex_dispersive_multipole_B(int nx, int ny, int nz, int nthreads, int maxpoles, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tx, floattype_t[:, :, :] Ex):
"""This function updates the Ex field components when dispersive materials (with multiple poles) are present.
Args:
nx, ny, nz (int): Grid size in cells
maxpoles (int): Maximum number of poles
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex, p
if ny == 1 or nz == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(1, nz):
listIndex = ID[0, i, j, k]
for p in range(0, maxpoles):
Tx[p, i, j, k] = Tx[p, i, j, k] - updatecoeffsdispersive[listIndex, 2 + (p * 3)] * Ex[i, j, k]
cpdef update_ex_dispersive_1pole_A(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsE, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tx, floattype_t[:, :, :] Ex, floattype_t[:, :, :] Hy, floattype_t[:, :, :] Hz):
"""This function updates the Ex field components when dispersive materials (with 1 pole) are present.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex
cdef float phi = 0.0
if ny == 1 or nz == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(1, nz):
listIndex = ID[0, i, j, k]
phi = updatecoeffsdispersive[listIndex, 0].real * Tx[0, i, j, k].real
Tx[0, i, j, k] = updatecoeffsdispersive[listIndex, 1] * Tx[0, i, j, k] + updatecoeffsdispersive[listIndex, 2] * Ex[i, j, k]
Ex[i, j, k] = updatecoeffsE[listIndex, 0] * Ex[i, j, k] + updatecoeffsE[listIndex, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[listIndex, 3] * (Hy[i, j, k] - Hy[i, j, k - 1]) - updatecoeffsE[listIndex, 4] * phi
cpdef update_ex_dispersive_1pole_B(int nx, int ny, int nz, int nthreads, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tx, floattype_t[:, :, :] Ex):
"""This function updates the Ex field components when dispersive materials (with 1 pole) are present.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex
if ny == 1 or nz == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(1, nz):
listIndex = ID[0, i, j, k]
Tx[0, i, j, k] = Tx[0, i, j, k] - updatecoeffsdispersive[listIndex, 2] * Ex[i, j, k]
#########################################
# Electric field updates - Ey component #
#########################################
cpdef update_ey(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsE, np.uint32_t[:, :, :, :] ID, floattype_t[:, :, :] Ey, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Hz):
"""This function updates the Ey field components.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, ID, E, H (memoryviews): Access to update coeffients, ID and field component arrays
"""
cdef int i, j, k, listIndex
if nx == 1 or nz == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(1, nz):
listIndex = ID[1, i, j, k]
Ey[i, j, k] = updatecoeffsE[listIndex, 0] * Ey[i, j, k] + updatecoeffsE[listIndex, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[listIndex, 1] * (Hz[i, j, k] - Hz[i - 1, j, k])
cpdef update_ey_dispersive_multipole_A(int nx, int ny, int nz, int nthreads, int maxpoles, floattype_t[:, :] updatecoeffsE, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Ty, floattype_t[:, :, :] Ey, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Hz):
"""This function updates the Ey field components when dispersive materials (with multiple poles) are present.
Args:
nx, ny, nz (int): Grid size in cells
maxpoles (int): Maximum number of poles
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex, p
cdef float phi = 0.0
if nx == 1 or nz == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(1, nz):
listIndex = ID[1, i, j, k]
phi = 0.0
for p in range(0, maxpoles):
phi = phi + updatecoeffsdispersive[listIndex, p * 3].real * Ty[p, i, j, k].real
Ty[p, i, j, k] = updatecoeffsdispersive[listIndex, 1 + (p * 3)] * Ty[p, i, j, k] + updatecoeffsdispersive[listIndex, 2 + (p * 3)] * Ey[i, j, k]
Ey[i, j, k] = updatecoeffsE[listIndex, 0] * Ey[i, j, k] + updatecoeffsE[listIndex, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[listIndex, 1] * (Hz[i, j, k] - Hz[i - 1, j, k]) - updatecoeffsE[listIndex, 4] * phi
cpdef update_ey_dispersive_multipole_B(int nx, int ny, int nz, int nthreads, int maxpoles, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Ty, floattype_t[:, :, :] Ey):
"""This function updates the Ey field components when dispersive materials (with multiple poles) are present.
Args:
nx, ny, nz (int): Grid size in cells
maxpoles (int): Maximum number of poles
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex, p
if nx == 1 or nz == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(1, nz):
listIndex = ID[1, i, j, k]
for p in range(0, maxpoles):
Ty[p, i, j, k] = Ty[p, i, j, k] - updatecoeffsdispersive[listIndex, 2 + (p * 3)] * Ey[i, j, k]
cpdef update_ey_dispersive_1pole_A(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsE, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Ty, floattype_t[:, :, :] Ey, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Hz):
"""This function updates the Ey field components when dispersive materials (with 1 pole) are present.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex
cdef float phi = 0.0
if nx == 1 or nz == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(1, nz):
listIndex = ID[1, i, j, k]
phi = updatecoeffsdispersive[listIndex, 0].real * Ty[0, i, j, k].real
Ty[0, i, j, k] = updatecoeffsdispersive[listIndex, 1] * Ty[0, i, j, k] + updatecoeffsdispersive[listIndex, 2] * Ey[i, j, k]
Ey[i, j, k] = updatecoeffsE[listIndex, 0] * Ey[i, j, k] + updatecoeffsE[listIndex, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[listIndex, 1] * (Hz[i, j, k] - Hz[i - 1, j, k]) - updatecoeffsE[listIndex, 4] * phi
cpdef update_ey_dispersive_1pole_B(int nx, int ny, int nz, int nthreads, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Ty, floattype_t[:, :, :] Ey):
"""This function updates the Ey field components when dispersive materials (with 1 pole) are present.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex
if nx == 1 or nz == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(1, nz):
listIndex = ID[1, i, j, k]
Ty[0, i, j, k] = Ty[0, i, j, k] - updatecoeffsdispersive[listIndex, 2] * Ey[i, j, k]
#########################################
# Electric field updates - Ez component #
#########################################
cpdef update_ez(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsE, np.uint32_t[:, :, :, :] ID, floattype_t[:, :, :] Ez, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Hy):
"""This function updates the Ez field components.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, ID, E, H (memoryviews): Access to update coeffients, ID and field component arrays
"""
cdef int i, j, k, listIndex
if nx == 1 or ny == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(0, nz):
listIndex = ID[2, i, j, k]
Ez[i, j, k] = updatecoeffsE[listIndex, 0] * Ez[i, j, k] + updatecoeffsE[listIndex, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[listIndex, 2] * (Hx[i, j, k] - Hx[i, j - 1, k])
cpdef update_ez_dispersive_multipole_A(int nx, int ny, int nz, int nthreads, int maxpoles, floattype_t[:, :] updatecoeffsE, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tz, floattype_t[:, :, :] Ez, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Hy):
"""This function updates the Ez field components when dispersive materials (with multiple poles) are present.
Args:
nx, ny, nz (int): Grid size in cells
maxpoles (int): Maximum number of poles
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex, p
cdef float phi = 0.0
if nx == 1 or ny == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(0, nz):
listIndex = ID[2, i, j, k]
phi = 0.0
for p in range(0, maxpoles):
phi = phi + updatecoeffsdispersive[listIndex, p * 3].real * Tz[p, i, j, k].real
Tz[p, i, j, k] = updatecoeffsdispersive[listIndex, 1 + (p * 3)] * Tz[p, i, j, k] + updatecoeffsdispersive[listIndex, 2 + (p * 3)] * Ez[i, j, k]
Ez[i, j, k] = updatecoeffsE[listIndex, 0] * Ez[i, j, k] + updatecoeffsE[listIndex, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[listIndex, 2] * (Hx[i, j, k] - Hx[i, j - 1, k]) - updatecoeffsE[listIndex, 4] * phi
cpdef update_ez_dispersive_multipole_B(int nx, int ny, int nz, int nthreads, int maxpoles, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tz, floattype_t[:, :, :] Ez):
"""This function updates the Ez field components when dispersive materials (with multiple poles) are present.
Args:
nx, ny, nz (int): Grid size in cells
maxpoles (int): Maximum number of poles
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex, p
if nx == 1 or ny == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(0, nz):
listIndex = ID[2, i, j, k]
for p in range(0, maxpoles):
Tz[p, i, j, k] = Tz[p, i, j, k] - updatecoeffsdispersive[listIndex, 2 + (p * 3)] * Ez[i, j, k]
cpdef update_ez_dispersive_1pole_A(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsE, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tz, floattype_t[:, :, :] Ez, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Hy):
"""This function updates the Ez field components when dispersive materials (with 1 pole) are present.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex
cdef float phi = 0.0
if nx == 1 or ny == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(0, nz):
listIndex = ID[2, i, j, k]
phi = updatecoeffsdispersive[listIndex, 0].real * Tz[0, i, j, k].real
Tz[0, i, j, k] = updatecoeffsdispersive[listIndex, 1] * Tz[0, i, j, k] + updatecoeffsdispersive[listIndex, 2] * Ez[i, j, k]
Ez[i, j, k] = updatecoeffsE[listIndex, 0] * Ez[i, j, k] + updatecoeffsE[listIndex, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[listIndex, 2] * (Hx[i, j, k] - Hx[i, j - 1, k]) - updatecoeffsE[listIndex, 4] * phi
cpdef update_ez_dispersive_1pole_B(int nx, int ny, int nz, int nthreads, complextype_t[:, :] updatecoeffsdispersive, np.uint32_t[:, :, :, :] ID, complextype_t[:, :, :, :] Tz, floattype_t[:, :, :] Ez):
"""This function updates the Ez field components when dispersive materials (with 1 pole) are present.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
"""
cdef int i, j, k, listIndex
if nx == 1 or ny == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(0, nz):
listIndex = ID[2, i, j, k]
Tz[0, i, j, k] = Tz[0, i, j, k] - updatecoeffsdispersive[listIndex, 2] * Ez[i, j, k]
#########################################
# Magnetic field updates - Hx component #
#########################################
cpdef update_hx(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsH, np.uint32_t[:, :, :, :] ID, floattype_t[:, :, :] Hx, floattype_t[:, :, :] Ey, floattype_t[:, :, :] Ez):
"""This function updates the Hx field components.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, ID, E, H (memoryviews): Access to update coeffients, ID and field component arrays
"""
cdef int i, j, k, listIndex
if nx == 1:
pass
else:
for i in prange(1, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(0, nz):
listIndex = ID[3, i, j, k]
Hx[i, j, k] = updatecoeffsH[listIndex, 0] * Hx[i, j, k] - updatecoeffsH[listIndex, 2] * (Ez[i, j + 1, k] - Ez[i, j, k]) + updatecoeffsH[listIndex, 3] * (Ey[i, j, k + 1] - Ey[i, j, k])
#########################################
# Magnetic field updates - Hy component #
#########################################
cpdef update_hy(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsH, np.uint32_t[:, :, :, :] ID, floattype_t[:, :, :] Hy, floattype_t[:, :, :] Ex, floattype_t[:, :, :] Ez):
"""This function updates the Hy field components.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, ID, E, H (memoryviews): Access to update coeffients, ID and field component arrays
"""
cdef int i, j, k, listIndex
if ny == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(1, ny):
for k in range(0, nz):
listIndex = ID[4, i, j, k]
Hy[i, j, k] = updatecoeffsH[listIndex, 0] * Hy[i, j, k] - updatecoeffsH[listIndex, 3] * (Ex[i, j, k + 1] - Ex[i, j, k]) + updatecoeffsH[listIndex, 1] * (Ez[i + 1, j, k] - Ez[i, j, k])
#########################################
# Magnetic field updates - Hz component #
#########################################
cpdef update_hz(int nx, int ny, int nz, int nthreads, floattype_t[:, :] updatecoeffsH, np.uint32_t[:, :, :, :] ID, floattype_t[:, :, :] Hz, floattype_t[:, :, :] Ex, floattype_t[:, :, :] Ey):
"""This function updates the Hz field components.
Args:
nx, ny, nz (int): Grid size in cells
nthreads (int): Number of threads to use
updatecoeffs, ID, E, H (memoryviews): Access to update coeffients, ID and field component arrays
"""
cdef int i, j, k, listIndex
if nz == 1:
pass
else:
for i in prange(0, nx, nogil=True, schedule='static', chunksize=1, num_threads=nthreads):
for j in range(0, ny):
for k in range(1, nz):
listIndex = ID[5, i, j, k]
Hz[i, j, k] = updatecoeffsH[listIndex, 0] * Hz[i, j, k] - updatecoeffsH[listIndex, 1] * (Ey[i + 1, j, k] - Ey[i, j, k]) + updatecoeffsH[listIndex, 2] * (Ex[i, j + 1, k] - Ex[i, j, k])
在新工单中引用 查看 Git Blame 复制永久链接