def test_mat_vec_mult(self):
# Given
n = 3
a = np.random.random((3, 3))
b = np.random.random((3, ))
result = [0.0] * 3
# When
mat_vec_mult(a.ravel(), b, n, result)
# Then.
expect = np.dot(a, b)
result = np.asarray(result)
np.testing.assert_allclose(result, expect)
def loop(self, d_idx, s_idx, d_sigma, s_sigma, d_au, d_av, d_aw, s_m,
DWIJ):
i = declare('int')
sigmaij = declare('matrix(9)')
res = declare('matrix(3)')
for i in range(9):
sigmaij[i] = d_sigma[d_idx * 9 + i] + s_sigma[s_idx * 9 + i]
mat_vec_mult(sigmaij, DWIJ, 3, res)
d_au[d_idx] += s_m[s_idx] * res[0]
d_av[d_idx] += s_m[s_idx] * res[1]
d_aw[d_idx] += s_m[s_idx] * res[2]
def loop(self, d_idx, s_idx, d_rho, s_rho, d_u, d_v, d_w, d_uhat, d_vhat,
d_what, s_u, s_v, s_w, s_uhat, s_vhat, s_what, d_au, d_av, d_aw,
s_m, DWIJ):
rhoi = d_rho[d_idx]
rhoj = s_rho[s_idx]
i, j = declare('int', 2)
ui, uj, uidif, ujdif, res = declare('matrix(3)', 5)
Aij = declare('matrix(9)')
for i in range(3):
res[i] = 0.0
for j in range(3):
Aij[3 * i + j] = 0.0
ui[0] = d_u[d_idx]
ui[1] = d_v[d_idx]
ui[2] = d_w[d_idx]
uj[0] = s_u[s_idx]
uj[1] = s_v[s_idx]
uj[2] = s_w[s_idx]
uidif[0] = d_uhat[d_idx] - d_u[d_idx]
uidif[1] = d_vhat[d_idx] - d_v[d_idx]
uidif[2] = d_what[d_idx] - d_w[d_idx]
ujdif[0] = s_uhat[s_idx] - s_u[s_idx]
ujdif[1] = s_vhat[s_idx] - s_v[s_idx]
ujdif[2] = s_what[s_idx] - s_w[s_idx]
for i in range(3):
for j in range(3):
Aij[3 * i + j] = (ui[i] * uidif[j] / rhoi +
uj[i] * ujdif[j] / rhoj)
mat_vec_mult(Aij, DWIJ, 3, res)
d_au[d_idx] += s_m[s_idx] * res[0]
d_av[d_idx] += s_m[s_idx] * res[1]
d_aw[d_idx] += s_m[s_idx] * res[2]
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]
