def test_fmm_force_ewald_2():
R = 3
eps = 10.**-6
free_space = True
N = 2
E = 4.
rc = E / 8
A = state.State()
A.domain = domain.BaseDomainHalo(extent=(E, E, E))
A.domain.boundary_condition = domain.BoundaryTypePeriodic()
ASYNC = False
DIRECT = True if MPISIZE == 1 else False
DIRECT = True
EWALD = True
fmm = PyFMM(domain=A.domain, r=R, eps=eps, free_space=free_space)
A.npart = N
rng = np.random.RandomState(seed=1234)
A.P = data.PositionDat(ncomp=3)
A.F = data.ParticleDat(ncomp=3)
A.FE = data.ParticleDat(ncomp=3)
A.Q = data.ParticleDat(ncomp=1)
A.crr = data.ScalarArray(ncomp=1)
A.cri = data.ScalarArray(ncomp=1)
A.crs = data.ScalarArray(ncomp=1)
if N == 4:
ra = 0.25 * E
nra = -0.25 * E
A.P[0, :] = (0.21, 0.21, 0.00)
A.P[1, :] = (-0.21, 0.21, 0.00)
A.P[2, :] = (-0.21, -0.21, 0.00)
A.P[3, :] = (0.21, -0.21, 0.00)
#A.P[0,:] = ( 0.00, 0.21, 0.21)
#A.P[1,:] = ( 0.00, 0.21,-0.21)
#A.P[2,:] = ( 0.00, -0.21,-0.21)
#A.P[3,:] = ( 0.00, -0.21, 0.21)
#A.P[0,:] = ( 1.01, 1.01, 0.00)
#A.P[1,:] = (-1.01, 1.01, 0.00)
#A.P[2,:] = (-1.01, -1.01, 0.00)
#A.P[3,:] = ( 1.01, -1.01, 0.00)
A.Q[0, 0] = -1.
A.Q[1, 0] = 1.
A.Q[2, 0] = -1.
A.Q[3, 0] = 1.
elif N == 1:
A.P[0, :] = (0.25 * E, 0.25 * E, 0.25 * E)
A.P[0, :] = (10.**-6, 10.**-6, 10.**-6)
#A.P[0,:] = (0, -0.25*E, 0)
#A.P[1,:] = (0, 0.25*E, 0)
#A.P[0,:] = (0, 0, -0.25*E)
#A.P[1,:] = (0, 0, 0.25*E)
#A.Q[:,0] = 1.
A.Q[0, 0] = 1.
elif N == 2:
#A.P[0,:] = ( 0.25*E, 0.25*E, 0.25*E)
#A.P[1,:] = ( -0.25*E, -0.25*E, 0)
#A.P[0,:] = (0, -0.25*E, 0)
#A.P[1,:] = (0, 0.25*E, 0)
#A.P[0,:] = (0, 0, -0.25*E)
#A.P[1,:] = (0, 0, 0.25*E)
#A.Q[:,0] = 1.
ra = 0.25 * E
nra = -0.25 * E
eps = 0.00
epsx = 0
epsy = 0
epsz = 0
A.P[0, :] = (1.999999, 0., 0.)
A.P[1, :] = (0., 0., 0.)
#A.P[:2:,:] = rng.uniform(low=-0.4999*E, high=0.4999*E, size=(N,3))
A.Q[0, 0] = -1.
A.Q[1, 0] = 1.
elif N == 8:
for px in range(8):
phi = (float(px) / 8) * 2. * math.pi
pxr = 0.25 * E
pxx = pxr * math.cos(phi)
pxy = pxr * math.sin(phi)
A.P[px, :] = (pxx, pxy, 0)
A.Q[px, 0] = 1. - 2. * (px % 2)
#A.Q[px, 0] = -1.
#A.P[0,:] += eps
eps = 0.00001
#A.P[0:N:2,0] += eps
#A.P[0,0] -= eps
A.P[4, 0] -= eps
A.P[:, 2] -= 0.200
A.P[:, 1] -= 0.200
#A.Q[0,0] = 0.
A.Q[1, 0] = 0.
A.Q[4, 0] = 0.
A.Q[3, 0] = 0.
A.Q[5, 0] = 0.
A.Q[6, 0] = 0.
A.Q[7, 0] = 0.
else:
assert N % 2 == 0
for px in range(N // 2):
pos = rng.uniform(low=-0.4999 * E, high=0.4999 * E, size=(1, 3))
cha = rng.uniform(low=-1., high=1.)
A.P[px, :] = pos
A.Q[px, 0] = cha
A.P[-1 * (px + 1), :] = -1.0 * pos
A.Q[-1 * (px + 1), 0] = cha
bias = np.sum(A.Q[:])
A.Q[:, 0] -= bias / N
dipole = np.zeros(3)
for px in range(N):
dipole[:] += A.P[px, :] * A.Q[px, 0]
bias = np.sum(A.Q[:])
print("DIPOLE:\t", dipole, "TOTAL CHARGE:\t", bias)
A.scatter_data_from(0)
print("boundary", A.domain.boundary)
t0 = time.time()
phi_py = fmm(A.P, A.Q, forces=A.F, execute_async=ASYNC)
t1 = time.time()
if MPIRANK == 0 and DEBUG:
print("\n")
#print(60*"-")
#opt.print_profile()
#print(60*"-")
print("TIME FMM:\t", t1 - t0)
print("ENERGY FMM:\t", phi_py)
A.gather_data_on(0)
if MPIRANK == 0:
for px in range(N):
print("PX:", px)
print("\t\tFORCE FMM:", A.F[px, :])
fmm.free()
def test_fmm_force_direct_3():
R = 3
L = 12
free_space = True
N = 2
E = 4.
rc = E / 4
A = state.State()
A.domain = domain.BaseDomainHalo(extent=(E, E, E))
A.domain.boundary_condition = domain.BoundaryTypePeriodic()
ASYNC = False
DIRECT = True if MPISIZE == 1 else False
DIRECT = True
EWALD = True
fmm = PyFMM(domain=A.domain, r=R, eps=None, l=L, free_space=free_space)
A.npart = N
rng = np.random.RandomState(seed=1234)
A.P = data.PositionDat(ncomp=3)
A.F = data.ParticleDat(ncomp=3)
A.FE = data.ParticleDat(ncomp=3)
A.Q = data.ParticleDat(ncomp=1)
A.crr = data.ScalarArray(ncomp=1)
A.cri = data.ScalarArray(ncomp=1)
A.crs = data.ScalarArray(ncomp=1)
if N == 2:
eps = 0.00
epsx = 0
epsy = 0
epsz = 0
A.P[0, :] = (-0.0001, 0.0001, 1.0001)
A.P[1, :] = (-0.0001, 0.0001, -0.0001)
A.Q[0, 0] = 1.
A.Q[1, 0] = 1.
A.scatter_data_from(0)
t0 = time.time()
#phi_py = fmm._test_call(A.P, A.Q, execute_async=ASYNC)
phi_py = fmm(A.P, A.Q, forces=A.F, execute_async=ASYNC)
t1 = time.time()
direct_forces = np.zeros((N, 3))
if DIRECT:
#print("WARNING 0-th PARTICLE ONLY")
phi_direct = 0.0
# compute phi from image and surrounding 26 cells
for ix in range(N):
phi_part = 0.0
for jx in range(ix + 1, N):
rij = np.linalg.norm(A.P[jx, :] - A.P[ix, :])
phi_direct += A.Q[ix, 0] * A.Q[jx, 0] / rij
phi_part += A.Q[ix, 0] * A.Q[jx, 0] / rij
direct_forces[ix,:] -= A.Q[ix, 0] * A.Q[jx, 0] * \
(A.P[jx,:] - A.P[ix,:]) / (rij**3.)
direct_forces[jx,:] += A.Q[ix, 0] * A.Q[jx, 0] * \
(A.P[jx,:] - A.P[ix,:]) / (rij**3.)
if free_space == '27':
for ofx in cube_offsets:
cube_mid = np.array(ofx) * E
for jx in range(N):
rij = np.linalg.norm(A.P[jx, :] + cube_mid -
A.P[ix, :])
phi_direct += 0.5 * A.Q[ix, 0] * A.Q[jx, 0] / rij
phi_part += 0.5 * A.Q[ix, 0] * A.Q[jx, 0] / rij
direct_forces[ix,:] -= A.Q[ix, 0] * A.Q[jx, 0] * \
(A.P[jx,:] - A.P[ix,:] + cube_mid) \
/ (rij**3.)
local_err = abs(phi_py - phi_direct)
if local_err > eps: serr = red(local_err)
else: serr = green(local_err)
if MPIRANK == 0 and DEBUG:
print("\n")
#print(60*"-")
#opt.print_profile()
#print(60*"-")
print("TIME FMM:\t", t1 - t0)
print("ENERGY DIRECT:\t{:.20f}".format(phi_direct))
print("ENERGY FMM:\t", phi_py)
print("ERR:\t\t", serr)
for px in range(N):
cell = A._fmm_cell[px, 0]
stride = fmm.tree_plain[0].shape[-1]
ss = fmm.tree_plain[R - 1].shape[0:3:]
cx = cell % ss[2]
cy = ((cell - cx) // ss[2]) % ss[1]
cz = (((cell - cx) // ss[2]) - cy) // ss[1]
mom = fmm.tree_plain[fmm.R - 1][cz, cy, cx, :]
mid = (0.5 * E / 2.**
(R - 1)) * np.ones(3) + (E / 2.**(R - 1)) * np.array(
(cx, cy, cz)) - 0.5 * E * np.ones(3)
disp_cart = A.P[px, :] - mid
disp = spherical(disp_cart)
print(cell, "|", cx, cy, cz, "|", mid)
fpy = force_from_multipole(mom, fmm, disp.reshape(1, 3), A.Q[px, 0])
err_re_c = red_tol(
np.linalg.norm(direct_forces[px, :] - A.F[px, :], ord=np.inf),
10.**-6)
err_re_p = red_tol(
np.linalg.norm(direct_forces[px, :] - fpy, ord=np.inf), 10.**-6)
print("PX:", px)
print("\t\tFORCE DIR :", direct_forces[px, :])
print("\t\tFORCE FMMC:", A.F[px, :], err_re_c)
print("\t\tFORCE py :", fpy, err_re_p)
fmm.free()
def test_fmm_force_ewald_1():
R = 3
eps = 10.**-8
free_space = False
N = 32
E = 4.
#N = 10000
#E = 100.
rc = E / 8
A = state.State()
A.domain = domain.BaseDomainHalo(extent=(E, E, E))
A.domain.boundary_condition = domain.BoundaryTypePeriodic()
ASYNC = False
CUDA = False
fmm = PyFMM(domain=A.domain, r=R, l=22, free_space=free_space, cuda=CUDA)
A.npart = N
rng = np.random.RandomState(seed=1234)
rng = np.random.RandomState(seed=95235)
A.P = data.PositionDat(ncomp=3)
A.F = data.ParticleDat(ncomp=3)
A.FE = data.ParticleDat(ncomp=3)
A.Q = data.ParticleDat(ncomp=1)
A.crr = data.ScalarArray(ncomp=1)
A.cri = data.ScalarArray(ncomp=1)
A.crs = data.ScalarArray(ncomp=1)
if N == 4:
ra = 0.25 * E
nra = -0.25 * E
A.P[0, :] = (0.21, 0.21, 0.00)
A.P[1, :] = (-0.21, 0.21, 0.00)
A.P[2, :] = (-0.21, -0.21, 0.00)
A.P[3, :] = (0.21, -0.21, 0.00)
#A.P[0,:] = ( 0.00, 0.21, 0.21)
#A.P[1,:] = ( 0.00, 0.21,-0.21)
#A.P[2,:] = ( 0.00, -0.21,-0.21)
#A.P[3,:] = ( 0.00, -0.21, 0.21)
#A.P[0,:] = ( 1.01, 1.01, 0.00)
#A.P[1,:] = (-1.01, 1.01, 0.00)
#A.P[2,:] = (-1.01, -1.01, 0.00)
#A.P[3,:] = ( 1.01, -1.01, 0.00)
A.Q[0, 0] = -1.
A.Q[1, 0] = 1.
A.Q[2, 0] = -1.
A.Q[3, 0] = 1.
elif N == 1:
A.P[0, :] = (0.25 * E, 0.25 * E, 0.25 * E)
A.P[0, :] = (10.**-6, 10.**-6, 10.**-6)
#A.P[0,:] = (0, -0.25*E, 0)
#A.P[1,:] = (0, 0.25*E, 0)
#A.P[0,:] = (0, 0, -0.25*E)
#A.P[1,:] = (0, 0, 0.25*E)
#A.Q[:,0] = 1.
A.Q[0, 0] = 1.
elif N == 2:
#A.P[0,:] = ( 0.25*E, 0.25*E, 0.25*E)
#A.P[1,:] = ( -0.25*E, -0.25*E, 0)
#A.P[0,:] = (0, -0.25*E, 0)
#A.P[1,:] = (0, 0.25*E, 0)
#A.P[0,:] = (0, 0, -0.25*E)
#A.P[1,:] = (0, 0, 0.25*E)
#A.Q[:,0] = 1.
ra = 0.25 * E
nra = -0.25 * E
epsx = 0
epsy = 0
epsz = 0
A.P[0, :] = (0.001, 0.001, 1.001)
A.P[1, :] = (0.001, 0.001, -1.001)
#A.P[:2:,:] = rng.uniform(low=-0.4999*E, high=0.4999*E, size=(N,3))
A.Q[0, 0] = -1.
A.Q[1, 0] = 1.
elif N == 8:
for px in range(8):
phi = (float(px) / 8) * 2. * math.pi
pxr = 0.25 * E
pxx = pxr * math.cos(phi)
pxy = pxr * math.sin(phi)
A.P[px, :] = (pxx, pxy, 0)
A.Q[px, 0] = 1. - 2. * (px % 2)
#A.Q[px, 0] = -1.
#A.P[0,:] += eps
#A.P[0:N:2,0] += eps
#A.P[0,0] -= eps
A.P[4, 0] -= eps
A.P[:, 2] -= 0.200
A.P[:, 1] -= 0.200
#A.Q[0,0] = 0.
A.Q[1, 0] = 0.
A.Q[4, 0] = 0.
A.Q[3, 0] = 0.
A.Q[5, 0] = 0.
A.Q[6, 0] = 0.
A.Q[7, 0] = 0.
else:
assert N % 2 == 0
for px in range(N // 2):
pos = rng.uniform(low=-0.4999 * E, high=0.4999 * E, size=(1, 3))
cha = rng.uniform(low=-1., high=1.)
A.P[px, :] = pos
A.Q[px, 0] = cha
A.P[-1 * (px + 1), :] = -1.0 * pos
A.Q[-1 * (px + 1), 0] = cha
bias = np.sum(A.Q[:])
A.Q[:, 0] -= bias / N
dipole = np.zeros(3)
for px in range(N):
dipole[:] += A.P[px, :] * A.Q[px, 0]
bias = np.sum(A.Q[:])
Q = np.sum(np.abs(A.Q[:N:, 0]))
A.scatter_data_from(0)
t0 = time.time()
phi_py = fmm(A.P, A.Q, forces=A.F, execute_async=ASYNC)
t1 = time.time()
ewald = EwaldOrthoganalHalf(domain=A.domain,
real_cutoff=rc,
eps=eps,
shared_memory=SHARED_MEMORY)
t2 = time.time()
ewald.evaluate_contributions(positions=A.P, charges=A.Q)
A.cri[0] = 0.0
ewald.extract_forces_energy_reciprocal(A.P, A.Q, A.FE, A.cri)
A.crr[0] = 0.0
ewald.extract_forces_energy_real(A.P, A.Q, A.FE, A.crr)
A.crs[0] = 0.0
ewald.evaluate_self_interactions(A.Q, A.crs)
t3 = time.time()
phi_ewald = A.cri[0] + A.crr[0] + A.crs[0]
local_err = abs(phi_py - phi_ewald) / Q
if local_err > eps: serr = red(local_err)
else: serr = green(local_err)
for px in range(A.npart_local):
assert np.linalg.norm(A.FE[px, :] - A.F[px, :], ord=np.inf) < 10.**-6
if MPIRANK == 0 and DEBUG:
print("\n")
#print(60*"-")
#opt.print_profile()
#print(60*"-")
print("TIME EWALD:\t", t3 - t2)
print("TIME FMM:\t", t1 - t0)
print("ENERGY EWALD:\t{:.20f}".format(phi_ewald))
print("ENERGY FMM:\t", phi_py)
print("ERR:\t\t", serr)
# run the same again
A.F[:] = 0.0
t0 = time.time()
phi_py = fmm(A.P, A.Q, forces=A.F, execute_async=ASYNC)
t1 = time.time()
local_err = abs(phi_py - phi_ewald) / Q
if local_err > eps: serr = red(local_err)
else: serr = green(local_err)
A.gather_data_on(0)
if MPIRANK == 0:
for px in range(N):
err_re_c = red_tol(
np.linalg.norm(A.FE[px, :] - A.F[px, :], ord=np.inf), 10.**-6)
assert np.linalg.norm(A.FE[px, :] - A.F[px, :],
ord=np.inf) < 10.**-6
if MPIRANK == 0 and DEBUG:
print("TIME FMM:\t", t1 - t0)
print("ENERGY FMM:\t", phi_py)
print("ERR:\t\t", serr)
fmm.free()
def test_fmm_force_direct_1():
R = 3
eps = 10.**-6
free_space = '27'
N = 4
E = 4.
rc = E / 4
A = state.State()
A.domain = domain.BaseDomainHalo(extent=(E, E, E))
A.domain.boundary_condition = domain.BoundaryTypePeriodic()
ASYNC = False
DIRECT = True if MPISIZE == 1 else False
DIRECT = True
EWALD = True
fmm = PyFMM(domain=A.domain, r=R, eps=eps, free_space=free_space)
A.npart = N
rng = np.random.RandomState(seed=1234)
A.P = data.PositionDat(ncomp=3)
A.F = data.ParticleDat(ncomp=3)
A.FE = data.ParticleDat(ncomp=3)
A.Q = data.ParticleDat(ncomp=1)
A.crr = data.ScalarArray(ncomp=1)
A.cri = data.ScalarArray(ncomp=1)
A.crs = data.ScalarArray(ncomp=1)
if N == 4:
ra = 0.25 * E
nra = -0.25 * E
A.P[0, :] = (1.01, 1.01, 0.0)
A.P[1, :] = (-1.01, 1.01, 0.0)
A.P[2, :] = (-1.01, -1.01, 0.0)
A.P[3, :] = (1.01, -1.01, 0.0)
A.Q[0, 0] = -1.
A.Q[1, 0] = 1.
A.Q[2, 0] = -1.
A.Q[3, 0] = 1.
elif N == 1:
A.P[0, :] = (0.25 * E, 0.25 * E, 0.25 * E)
A.P[0, :] = (10.**-6, 10.**-6, 10.**-6)
#A.P[0,:] = (0, -0.25*E, 0)
#A.P[1,:] = (0, 0.25*E, 0)
#A.P[0,:] = (0, 0, -0.25*E)
#A.P[1,:] = (0, 0, 0.25*E)
#A.Q[:,0] = 1.
A.Q[0, 0] = 1.
elif N == 2:
#A.P[0,:] = ( 0.25*E, 0.25*E, 0.25*E)
#A.P[1,:] = ( -0.25*E, -0.25*E, 0)
#A.P[0,:] = (0, -0.25*E, 0)
#A.P[1,:] = (0, 0.25*E, 0)
#A.P[0,:] = (0, 0, -0.25*E)
#A.P[1,:] = (0, 0, 0.25*E)
#A.Q[:,0] = 1.
ra = 0.25 * E
nra = -0.25 * E
eps = 0.00
epsx = 0
epsy = 0
epsz = 0
A.P[0, :] = (1.000, 0.001, 0.001)
A.P[1, :] = (-1.001, 0.001, 0.001)
#A.P[:2:,:] = rng.uniform(low=-0.4999*E, high=0.4999*E, size=(N,3))
A.Q[0, 0] = -1.
A.Q[1, 0] = 1.
elif N == 8:
for px in range(8):
phi = (float(px) / 8) * 2. * math.pi
pxr = 0.25 * E
pxx = pxr * math.cos(phi)
pxy = pxr * math.sin(phi)
A.P[px, :] = (pxx, pxy, 0)
A.Q[px, 0] = 1. - 2. * (px % 2)
#A.Q[px, 0] = -1.
#A.P[0,:] += eps
eps = 0.00001
#A.P[0:N:2,0] += eps
#A.P[0,0] -= eps
A.P[4, 0] -= eps
A.P[:, 2] -= 0.200
A.P[:, 1] -= 0.200
#A.Q[0,0] = 0.
A.Q[1, 0] = 0.
A.Q[4, 0] = 0.
A.Q[3, 0] = 0.
A.Q[5, 0] = 0.
A.Q[6, 0] = 0.
A.Q[7, 0] = 0.
else:
assert N % 2 == 0
for px in range(N // 2):
pos = rng.uniform(low=-0.4999 * E, high=0.4999 * E, size=(1, 3))
cha = rng.uniform(low=-1., high=1.)
A.P[px, :] = pos
A.Q[px, 0] = cha
A.P[-1 * (px + 1), :] = -1.0 * pos
A.Q[-1 * (px + 1), 0] = cha
bias = np.sum(A.Q[:])
A.Q[:, 0] -= bias / N
dipole = np.zeros(3)
for px in range(N):
dipole[:] += A.P[px, :] * A.Q[px, 0]
bias = np.sum(A.Q[:])
print("DIPOLE:\t", dipole, "TOTAL CHARGE:\t", bias)
A.scatter_data_from(0)
t0 = time.time()
#phi_py = fmm._test_call(A.P, A.Q, execute_async=ASYNC)
phi_py = fmm(A.P, A.Q, forces=A.F, execute_async=ASYNC)
t1 = time.time()
direct_forces = np.zeros((N, 3))
if DIRECT:
#print("WARNING 0-th PARTICLE ONLY")
phi_direct = 0.0
# compute phi from image and surrounding 26 cells
for ix in range(N):
phi_part = 0.0
for jx in range(ix + 1, N):
rij = np.linalg.norm(A.P[jx, :] - A.P[ix, :])
phi_direct += A.Q[ix, 0] * A.Q[jx, 0] / rij
phi_part += A.Q[ix, 0] * A.Q[jx, 0] / rij
direct_forces[ix,:] -= A.Q[ix, 0] * A.Q[jx, 0] * \
(A.P[jx,:] - A.P[ix,:]) / (rij**3.)
direct_forces[jx,:] += A.Q[ix, 0] * A.Q[jx, 0] * \
(A.P[jx,:] - A.P[ix,:]) / (rij**3.)
if free_space == '27':
for ofx in cube_offsets:
cube_mid = np.array(ofx) * E
for jx in range(N):
rij = np.linalg.norm(A.P[jx, :] + cube_mid -
A.P[ix, :])
phi_direct += 0.5 * A.Q[ix, 0] * A.Q[jx, 0] / rij
phi_part += 0.5 * A.Q[ix, 0] * A.Q[jx, 0] / rij
direct_forces[ix,:] -= A.Q[ix, 0] * A.Q[jx, 0] * \
(A.P[jx,:] - A.P[ix,:] + cube_mid) \
/ (rij**3.)
local_err = abs(phi_py - phi_direct)
if local_err > eps: serr = red(local_err)
else: serr = green(local_err)
if MPIRANK == 0 and DEBUG:
print("\n")
#print(60*"-")
#opt.print_profile()
#print(60*"-")
print("TIME FMM:\t", t1 - t0)
print("ENERGY DIRECT:\t{:.20f}".format(phi_direct))
print("ENERGY FMM:\t", phi_py)
print("ERR:\t\t", serr)
for px in range(N):
err_re_c = red_tol(
np.linalg.norm(direct_forces[px, :] - A.F[px, :], ord=np.inf),
10.**-6)
print("PX:", px)
print("\t\tFORCE DIR :", direct_forces[px, :])
print("\t\tFORCE FMMC:", A.F[px, :], err_re_c)
fmm.free()
def test_fmm_sim_1():
input_data = np.load(get_res_file_path('coulomb/CO2cuboid.npy'))
N = input_data.shape[0]
E = 50.
A = state.State()
A.npart = N
A.domain = domain.BaseDomainHalo(extent=(E, E, E))
A.domain.boundary_condition = domain.BoundaryTypePeriodic()
eps = 10.**-6
fmm = PyFMM(domain=A.domain, r=3, N=N, eps=eps, free_space=True)
A.P = data.PositionDat(ncomp=3)
A.Q = data.ParticleDat(ncomp=1)
if MPIRANK == 0:
A.P[:] = input_data[:, 0:3:]
A.Q[:, 0] = input_data[:, 3]
A.scatter_data_from(0)
if MPISIZE == 1:
# compute potential energy to point across all charges directly
P2 = data.PositionDat(npart=N, ncomp=3)
Q2 = data.ParticleDat(npart=N, ncomp=1)
P2[:, :] = A.P[:N:, :]
Q2[:, :] = A.Q[:N:, :]
phi_ga = data.ScalarArray(ncomp=1, dtype=ctypes.c_double)
src = """
const double d0 = P.j[0] - P.i[0];
const double d1 = P.j[1] - P.i[1];
const double d2 = P.j[2] - P.i[2];
phi[0] += 0.5 * Q.i[0] * Q.j[0] / sqrt(d0*d0 + d1*d1 + d2*d2);
"""
phi_kernel = kernel.Kernel('all_to_all_phi',
src,
headers=(kernel.Header('math.h'), ))
phi_loop = pairloop.AllToAllNS(kernel=phi_kernel,
dat_dict={
'P': P2(access.READ),
'Q': Q2(access.READ),
'phi': phi_ga(access.INC_ZERO)
})
phi_loop.execute()
phi_direct = phi_ga[0]
else:
phi_direct = None
t0 = time.time()
phi_fmm = fmm(A.P, A.Q)
t1 = time.time()
if DEBUG and MPIRANK == 0:
print("Time:", t1 - t0)
print("MPISIZE", MPISIZE)
print("phi_fmm", phi_fmm)
if MPISIZE == 1:
print("phi_direct: {:.30f}".format(phi_direct))
print("phi_fmm", phi_fmm)
print("ERROR:", abs(phi_direct - phi_fmm))
fmm.free()
def test_fmm_init_2_1():
E = 20.
A = state.State()
A.domain = domain.BaseDomainHalo(extent=(E, E, E))
A.domain.boundary_condition = domain.BoundaryTypePeriodic()
eps = 10.**-3
fmm = PyFMM(domain=A.domain, r=3, eps=eps, free_space=True)
ncubeside = 2**(fmm.R - 1)
N = ncubeside**3
N = 100
A.npart = N
rng = np.random.RandomState(seed=1234)
#rng = np.random
A.P = data.PositionDat(ncomp=3)
A.Q = data.ParticleDat(ncomp=1)
A.U = data.ParticleDat(ncomp=1)
A.F = data.ParticleDat(ncomp=3)
A.P[:] = rng.uniform(low=-0.5 * E, high=0.5 * E, size=(N, 3))
A.Q[:] = rng.uniform(low=-0.5 * E, high=0.5 * E, size=(N, 1))
bias = np.sum(A.Q[:]) / N
A.Q[:] -= bias
#A.Q[:] = 1.0
#A.Q[0:-2] = 0.0
#A.P[2,:] = (-7.5, -7.5, 2.5)
#A.Q[2, 0] = -1.
#A.P[0,:] = (-6., 2., -1.)
#A.P[1,:] = (5.000000001, 5.000000001, -4.5)
#A.Q[0, 0] = 1.0
#A.Q[1, 0] = -1.0
A.scatter_data_from(0)
maxt = 5
for tx in itertools.product(range(-1 * maxt, maxt + 1),
range(-1 * maxt, maxt + 1),
range(-1 * maxt, maxt + 1)):
dispt = (tx[0] * E, tx[1] * E, tx[2] * E)
dispt_sph = spherical(dispt)
dispt_fmm = fmm._image_to_sph(tx)
assert abs(dispt_sph[0] - dispt_fmm[0]) < 10.**-16, "bad radius"
assert abs(dispt_sph[2] - dispt_fmm[1]) < 10.**-16, "bad phi"
assert abs(dispt_sph[1] - dispt_fmm[2]) < 10.**-16, "bad theta"
fmm._check_aux_dat(A.P)
fmm._compute_cube_contrib(A.P, A.Q, A._fmm_cell)
# compute potential energy to point across all charges directly
P2 = data.PositionDat(npart=N, ncomp=3)
Q2 = data.ParticleDat(npart=N, ncomp=1)
U2 = data.ParticleDat(npart=N, ncomp=1)
P2[:, :] = A.P[:N:, :]
Q2[:, :] = A.Q[:N:, :]
phi_ga = data.ScalarArray(ncomp=1, dtype=ctypes.c_double)
src = """
const double d0 = P.j[0] - P.i[0];
const double d1 = P.j[1] - P.i[1];
const double d2 = P.j[2] - P.i[2];
const double contrib = Q.i[0] * Q.j[0] / sqrt(d0*d0 + d1*d1 + d2*d2);
phi[0] += 0.5 * contrib;
U.i[0] += contrib;
"""
phi_kernel = kernel.Kernel('all_to_all_phi',
src,
headers=(kernel.Header('math.h'), ))
phi_loop = pairloop.AllToAllNS(kernel=phi_kernel,
dat_dict={
'P': P2(access.READ),
'Q': Q2(access.READ),
'phi': phi_ga(access.INC_ZERO),
'U': U2(access.INC_ZERO)
})
phi_loop.execute()
if DEBUG:
phi_py = 0.0
for ix in range(N):
for jx in range(ix + 1, N):
r2 = np.linalg.norm(A.P[jx, :] - A.P[ix, :])
phi_py += A.Q[ix, 0] * A.Q[jx, 0] / r2
print("Direct", phi_ga[0], phi_py)
extent = A.domain.extent
cube_ilen = 2**(fmm.R - 1) / extent[:]
cube_half_len = 0.5 * extent[:] / (2**(fmm.R - 1))
shift_pos = A.P[:] + 0.5 * extent[:]
shift_pos[:, 0] = shift_pos[:, 0] * cube_ilen[0]
shift_pos[:, 1] = shift_pos[:, 1] * cube_ilen[1]
shift_pos[:, 2] = shift_pos[:, 2] * cube_ilen[2]
shift_pos = np.array(shift_pos, dtype='int')
phi_local = fmm._compute_local_interaction(A.P, A.Q)
#print("phi_local:", phi_local)
#print("------------------------------------------------")
phi_local_pair = fmm._compute_local_interaction_pairloop(A.P, A.Q)
#print("correct :", phi_local)
assert abs(phi_local - phi_local_pair) < 10.**-12
level = fmm.R - 1
phi_sph_re = 0.0
phi_sph_im = 0.0
lsize = fmm.tree_plain[level][:, :, :, 0].shape
sep = A.domain.extent[0] / float(2.**level)
start_point = -0.5 * E + 0.5 * sep
for px in range(N):
point = A.P[px, :]
charge = A.Q[px, 0]
if DEBUG:
print(px, point, charge, shift_pos[px, :])
cubex = shift_pos[px, :]
for momx in itertools.product(range(lsize[0]), range(lsize[1]),
range(lsize[2])):
dist = ((momx[2] - cubex[0])**2 + (momx[1] - cubex[1])**2 +
(momx[0] - cubex[2])**2)
if dist > 3:
center = np.array((start_point + (momx[2]) * sep,
start_point + (momx[1]) * sep,
start_point + (momx[0]) * sep))
disp = point - center
moments = fmm.tree_halo[level][momx[0] + 2, momx[1] + 2,
momx[2] + 2, :]
disp_sph = spherical(np.reshape(disp, (1, 3)))
phi_sph_re1, phi_sph_im1 = compute_phi(fmm.L, moments,
disp_sph)
phi_sph_re += phi_sph_re1 * charge * 0.5
phi_sph_im += phi_sph_im1 * charge * 0.5
if DEBUG:
print("direct:", phi_ga[0])
print("multipole:", phi_sph_re + phi_local, "local:", phi_local,
"expansions:", phi_sph_re)
assert abs(phi_ga[0] - phi_sph_re - phi_local) < eps, "bad real part"
phi_py2 = fmm(A.P, A.Q, forces=A.F, potential=A.U)
for px in range(A.npart_local):
assert abs(U2[px, 0] - A.U[px, 0]) < eps
fmm.free()
def _direct():
_phi_direct = fmm(positions=B.P, charges=B.Q)
return _phi_direct