def post_loop(self, d_idx, d_gradv, d_invtt, d_divv):
tt, invtt, idmat, gradv = declare('matrix(9)', 4)
augtt = declare('matrix(18)')
start_indx, row, col, rowcol, drowcol, dim = declare('int', 6)
dim = self.dim
start_indx = 9 * d_idx
identity(idmat, 3)
identity(tt, 3)
for row in range(3):
for col in range(3):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
gradv[rowcol] = d_gradv[drowcol]
for row in range(dim):
for col in range(dim):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
tt[rowcol] = d_invtt[drowcol]
augmented_matrix(tt, idmat, 3, 3, 3, augtt)
gj_solve(augtt, 3, 3, invtt)
gradvls = declare('matrix(9)')
mat_mult(gradv, invtt, 3, gradvls)
for row in range(dim):
d_divv[d_idx] += gradvls[row * 3 + row]
for col in range(dim):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
d_gradv[drowcol] = gradvls[rowcol]
def loop_all(self, d_idx, d_rho, d_x, d_y, d_z, s_x, s_y, s_z, d_h, s_h,
s_m, s_rhotmp, SPH_KERNEL, NBRS, N_NBRS):
n, i, j, k, s_idx = declare('int', 5)
n = 4
amls = declare('matrix(16)')
aug_mls = declare('matrix(20)')
x = d_x[d_idx]
y = d_y[d_idx]
z = d_z[d_idx]
xij = declare('matrix(4)')
for i in range(n):
for j in range(n):
amls[n * i + j] = 0.0
for k in range(N_NBRS):
s_idx = NBRS[k]
xij[0] = x - s_x[s_idx]
xij[1] = y - s_y[s_idx]
xij[2] = z - s_z[s_idx]
rij = sqrt(xij[0] * xij[0] + xij[1] * xij[1] + xij[2] * xij[2])
hij = (d_h[d_idx] + s_h[s_idx]) * 0.5
wij = SPH_KERNEL.kernel(xij, rij, hij)
for i in range(n):
if i == 0:
fac1 = 1.0
else:
fac1 = xij[i - 1]
for j in range(n):
if j == 0:
fac2 = 1.0
else:
fac2 = xij[j - 1]
amls[n * i + j] += fac1 * fac2 * \
s_m[s_idx] * wij / s_rhotmp[s_idx]
res = declare('matrix(4)')
res[0] = 1.0
res[1] = 0.0
res[2] = 0.0
res[3] = 0.0
augmented_matrix(amls, res, n, 1, aug_mls)
gj_solve(aug_mls, n, 1, res)
b0 = res[0]
b1 = res[1]
b2 = res[2]
b3 = res[3]
d_rho[d_idx] = 0.0
for k in range(N_NBRS):
s_idx = NBRS[k]
xij[0] = x - s_x[s_idx]
xij[1] = y - s_y[s_idx]
xij[2] = z - s_z[s_idx]
rij = sqrt(xij[0] * xij[0] + xij[1] * xij[1] + xij[2] * xij[2])
hij = (d_h[d_idx] + s_h[s_idx]) * 0.5
wij = SPH_KERNEL.kernel(xij, rij, hij)
wmls = (b0 + b1 * xij[0] + b2 * xij[1] + b3 * xij[2]) * wij
d_rho[d_idx] += s_m[s_idx] * wmls
def test_augmented_matrix_with_gjsolve_with_lower_dimension(self):
# Given
nmax = 3
mat = np.array([[7., 4., 2.], [8., 9., 4.], [1., 4., 10.]])
b = np.array([5., 4., 2.])
expect = np.linalg.solve(mat[:2, :2], b[:2])
augmat = np.zeros((3, 4)).ravel().tolist()
res = np.zeros(2).ravel().tolist()
# When
augmented_matrix(mat.ravel(), b.ravel(), 2, 1, nmax, augmat)
gj_solve(augmat, 2, 1, res)
# Then
np.testing.assert_array_almost_equal(res, expect)
def test_augmented_matrix(self):
# Given
a = np.random.random((3, 3))
b = np.random.random((3, 2))
res = np.zeros((3, 5)).ravel().tolist()
expect = np.zeros((3, 5))
expect[:, :3] = a
expect[:, 3:] = b
# When
augmented_matrix(a.ravel(), b.ravel(), 3, 2, 3, res)
res = self._to_array(res, (3, 5))
# Then
np.testing.assert_array_almost_equal(res, expect)
def test_augmented_matrix_with_lower_dimension(self):
# Given
a = np.random.random((3, 3))
b = np.random.random((3, 2))
res = np.zeros((3, 5)).ravel().tolist()
expect = np.zeros((2, 4))
expect[:, :2] = a[:2, :2]
expect[:, 2:] = b[:2, :]
expect.resize((3, 5), refcheck=False)
# When
augmented_matrix(a.ravel(), b.ravel(), 2, 2, 3, res)
res = self._to_array(res, (3, 5))
# Then
np.testing.assert_array_almost_equal(res, expect)
def test_inverse(self):
# Given
n = 3
mat = [[1.0, 2.0, 2.5], [2.5, 1.0, 0.0], [0.0, 0.0, 1.0]]
b = np.identity(3).ravel().tolist()
A = np.zeros((3, 6)).ravel().tolist()
augmented_matrix(np.ravel(mat), b, 3, 3, 3, A)
result = np.zeros((3, 3)).ravel().tolist()
# When
sing = gj_solve(A, n, n, result)
# Then
mat = np.asarray(mat)
res = np.asarray(result)
res.shape = 3, 3
np.testing.assert_allclose(res, np.linalg.inv(mat))
self.assertAlmostEqual(sing, 0.0)
def post_loop(self, d_idx, d_A, d_po, d_Bp):
a_mat = declare('matrix(16)')
aug_mat = declare('matrix(20)')
b_p = declare('matrix(4)')
res_p = declare('matrix(4)')
i, n, i16, i4 = declare('int', 4)
i16 = 16 * d_idx
i4 = 4 * d_idx
for i in range(16):
a_mat[i] = d_A[i16 + i]
for i in range(20):
aug_mat[i] = 0.0
for i in range(4):
b_p[i] = d_Bp[i4 + i]
res_p[i] = 0.0
n = self.dim + 1
augmented_matrix(a_mat, b_p, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_p)
for i in range(4):
d_po[i4 + i] = res_p[i]
def post_loop(self, d_idx, d_moment, d_prop, d_p_sph):
a_mat = declare('matrix(16)')
aug_mat = declare('matrix(20)')
b = declare('matrix(4)')
res = declare('matrix(4)')
i, n, i16, i4 = declare('int', 4)
i16 = 16 * d_idx
i4 = 4 * d_idx
for i in range(16):
a_mat[i] = d_moment[i16 + i]
for i in range(20):
aug_mat[i] = 0.0
for i in range(4):
b[i] = d_p_sph[4 * d_idx + i]
res[i] = 0.0
n = self.dim + 1
augmented_matrix(a_mat, b, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res)
for i in range(4):
d_prop[i4 + i] = res[i]
def post_loop(self, d_idx, d_A, d_uho, d_Buh, d_vho, d_Bvh, d_who, d_Bwh):
a_mat = declare('matrix(16)')
aug_mat = declare('matrix(20)')
b_uh = declare('matrix(4)')
res_uh = declare('matrix(4)')
b_vh = declare('matrix(4)')
res_vh = declare('matrix(4)')
b_wh = declare('matrix(4)')
res_wh = declare('matrix(4)')
i, n, i16, i4 = declare('int', 4)
i16 = 16 * d_idx
i4 = 4 * d_idx
for i in range(16):
a_mat[i] = d_A[i16 + i]
for i in range(20):
aug_mat[i] = 0.0
for i in range(4):
b_uh[i] = d_Buh[i4 + i]
res_uh[i] = 0.0
b_vh[i] = d_Bvh[i4 + i]
res_vh[i] = 0.0
b_wh[i] = d_Bwh[i4 + i]
res_wh[i] = 0.0
n = self.dim + 1
augmented_matrix(a_mat, b_uh, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_uh)
for i in range(4):
d_uho[i4 + i] = res_uh[i]
augmented_matrix(a_mat, b_vh, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_vh)
for i in range(4):
d_vho[i4 + i] = res_vh[i]
augmented_matrix(a_mat, b_wh, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_wh)
for i in range(4):
d_who[i4 + i] = res_wh[i]
def post_loop(self, d_idx, d_A, d_uo, d_Bu, d_vo, d_Bv, d_wo, d_Bw):
a_mat = declare('matrix(16)')
aug_mat = declare('matrix(20)')
b_u = declare('matrix(4)')
res_u = declare('matrix(4)')
b_v = declare('matrix(4)')
res_v = declare('matrix(4)')
b_w = declare('matrix(4)')
res_w = declare('matrix(4)')
i, n, i16, i4 = declare('int', 4)
i16 = 16 * d_idx
i4 = 4 * d_idx
for i in range(16):
a_mat[i] = d_A[i16 + i]
for i in range(20):
aug_mat[i] = 0.0
for i in range(4):
b_u[i] = d_Bu[i4 + i]
res_u[i] = 0.0
b_v[i] = d_Bv[i4 + i]
res_v[i] = 0.0
b_w[i] = d_Bw[i4 + i]
res_w[i] = 0.0
n = self.dim + 1
augmented_matrix(a_mat, b_u, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_u)
for i in range(4):
d_uo[i4 + i] = res_u[i]
augmented_matrix(a_mat, b_v, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_v)
for i in range(4):
d_vo[i4 + i] = res_v[i]
augmented_matrix(a_mat, b_w, n, 1, 4, aug_mat)
gj_solve(aug_mat, n, 1, res_w)
for i in range(4):
d_wo[i4 + i] = res_w[i]
def gj_solve_helper(a, b, n):
m = np.zeros((n, n + 1)).ravel().tolist()
augmented_matrix(a, b, n, 1, n, m)
result = [0.0] * n
is_singular = gj_solve(m, n, 1, result)
return is_singular, result
def loop_all(self, d_idx, d_x, d_y, d_z, d_h, s_x, s_y, s_z, s_h, s_m,
s_rho, SPH_KERNEL, NBRS, N_NBRS, d_ai, d_gradai, d_bi, s_V,
d_gradbi):
x = d_x[d_idx]
y = d_y[d_idx]
z = d_z[d_idx]
h = d_h[d_idx]
i, j, k, s_idx, d, d2 = declare('int', 6)
alp, bet, gam, phi, psi = declare('int', 5)
xij = declare('matrix(3)')
dwij = declare('matrix(3)')
d = self.dim
d2 = d * d
m0 = 0.0
m1 = declare('matrix(3)')
m2 = declare('matrix(9)')
temp_vec = declare('matrix(3)')
temp_aug_m2 = declare('matrix(18)')
m2inv = declare('matrix(9)')
grad_m0 = declare('matrix(3)')
grad_m1 = declare('matrix(9)')
grad_m2 = declare('matrix(27)')
ai = 0.0
bi = declare('matrix(3)')
grad_ai = declare('matrix(3)')
grad_bi = declare('matrix(9)')
for i in range(3):
m1[i] = 0.0
grad_m0[i] = 0.0
bi[i] = 0.0
grad_ai[i] = 0.0
for j in range(3):
m2[3 * i + j] = 0.0
grad_m1[3 * i + j] = 0.0
grad_bi[3 * i + j] = 0.0
for k in range(3):
grad_m2[9 * i + 3 * j + k] = 0.0
for i in range(N_NBRS):
s_idx = NBRS[i]
xij[0] = x - s_x[s_idx]
xij[1] = y - s_y[s_idx]
xij[2] = z - s_z[s_idx]
hij = (h + s_h[s_idx]) * 0.5
rij = sqrt(xij[0] * xij[0] + xij[1] * xij[1] + xij[2] * xij[2])
wij = SPH_KERNEL.kernel(xij, rij, hij)
SPH_KERNEL.gradient(xij, rij, hij, dwij)
V = 1.0 / s_V[s_idx]
m0 += V * wij
for alp in range(d):
m1[alp] += V * wij * xij[alp]
for bet in range(d):
m2[d * alp + bet] += V * wij * xij[alp] * xij[bet]
for gam in range(d):
grad_m0[gam] += V * dwij[gam]
for alp in range(d):
fac = 1.0 if alp == gam else 0.0
temp = (xij[alp] * dwij[gam] + fac * wij)
grad_m1[d * gam + alp] += V * temp
for bet in range(d):
fac2 = 1.0 if bet == gam else 0.0
temp = xij[alp] * fac2 + xij[bet] * fac
temp2 = (xij[alp] * xij[bet] * dwij[gam] + temp * wij)
grad_m2[d2 * gam + d * alp + bet] += V * temp2
identity(m2inv, d)
augmented_matrix(m2, m2inv, d, d, d, temp_aug_m2)
# If is_singular > 0 then matrix was singular
is_singular = gj_solve(temp_aug_m2, d, d, m2inv)
if is_singular > 0.0:
# Cannot do much if the matrix is singular. Perhaps later
# we can tag such particles to see if the user can do something.
pass
else:
mat_vec_mult(m2inv, m1, d, temp_vec)
# Eq. 12.
ai = 1.0 / (m0 - dot(temp_vec, m1, d))
# Eq. 13.
mat_vec_mult(m2inv, m1, d, bi)
for gam in range(d):
bi[gam] = -bi[gam]
# Eq. 14. and 15.
for gam in range(d):
temp1 = grad_m0[gam]
for alp in range(d):
temp2 = 0.0
for bet in range(d):
temp1 -= m2inv[d * alp + bet] * (
m1[bet] * grad_m1[d * gam + alp] +
m1[alp] * grad_m1[d * gam + bet])
temp2 -= (m2inv[d * alp + bet] *
grad_m1[d * gam + bet])
for phi in range(d):
for psi in range(d):
temp1 += (m2inv[d * alp + phi] *
m2inv[d * psi + bet] *
grad_m2[d2 * gam + d * phi + psi] *
m1[bet] * m1[alp])
temp2 += (m2inv[d * alp + phi] *
m2inv[d * psi + bet] *
grad_m2[d2 * gam + d * phi + psi] *
m1[bet])
grad_bi[d * gam + alp] = temp2
grad_ai[gam] = -ai * ai * temp1
if N_NBRS < 2 or is_singular > 0.0:
d_ai[d_idx] = 1.0
for i in range(d):
d_gradai[d * d_idx + i] = 0.0
d_bi[d * d_idx + i] = 0.0
for j in range(d):
d_gradbi[d2 * d_idx + d * i + j] = 0.0
else:
d_ai[d_idx] = ai
for i in range(d):
d_gradai[d * d_idx + i] = grad_ai[i]
d_bi[d * d_idx + i] = bi[i]
for j in range(d):
d_gradbi[d2 * d_idx + d * i + j] = grad_bi[d * i + j]
def post_loop(self, d_idx, d_gradv, d_invtt, d_divv, d_grada, d_adivv,
d_ss, d_trssdsst):
tt = declare('matrix(9)')
invtt = declare('matrix(9)')
augtt = declare('matrix(18)')
idmat = declare('matrix(9)')
gradv = declare('matrix(9)')
grada = declare('matrix(9)')
start_indx, row, col, rowcol, drowcol, dim, colrow = declare('int', 7)
ltstart_indx, dltrowcol = declare('int', 2)
dim = self.dim
start_indx = 9 * d_idx
identity(idmat, 3)
identity(tt, 3)
for row in range(3):
for col in range(3):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
gradv[rowcol] = d_gradv[drowcol]
grada[rowcol] = d_grada[drowcol]
for row in range(dim):
for col in range(dim):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
tt[rowcol] = d_invtt[drowcol]
augmented_matrix(tt, idmat, 3, 3, 3, augtt)
gj_solve(augtt, 3, 3, invtt)
gradvls = declare('matrix(9)')
gradals = declare('matrix(9)')
mat_mult(gradv, invtt, 3, gradvls)
mat_mult(grada, invtt, 3, gradals)
for row in range(dim):
d_divv[d_idx] += gradvls[row * 3 + row]
d_adivv[d_idx] += gradals[row * 3 + row]
for col in range(dim):
rowcol = row * 3 + col
colrow = row + col * 3
drowcol = start_indx + rowcol
d_gradv[drowcol] = gradvls[rowcol]
d_grada[drowcol] = gradals[rowcol]
d_adivv[d_idx] -= gradals[rowcol] * gradals[colrow]
# Traceless Symmetric Strain Rate
divvbydim = d_divv[d_idx] / dim
start_indx = d_idx * 9
ltstart_indx = d_idx * 6
for row in range(dim):
col = row
rowcol = start_indx + row * 3 + col
dltrowcol = ltstart_indx + (row * (row + 1)) / 2 + col
d_ss[dltrowcol] = d_gradv[rowcol] - divvbydim
for row in range(1, dim):
for col in range(row):
rowcol = row * 3 + col
colrow = row + col * 3
dltrowcol = ltstart_indx + (row * (row + 1)) / 2 + col
d_ss[dltrowcol] = 0.5 * (gradvls[rowcol] + gradvls[colrow])
# Trace ( S dot transpose(S) )
for row in range(dim):
for col in range(dim):
dltrowcol = ltstart_indx + (row * (row + 1)) / 2 + col
d_trssdsst[d_idx] += d_ss[dltrowcol] * d_ss[dltrowcol]
