def inverse(self):
assert self.n == self.m, 'Only square matrices are invertible'
if self.n == 1:
return Matrix([1 / self(0, 0)])
elif self.n == 2:
inv_det = impl.expr_init(1.0 / self.determinant(self))
# Discussion: https://github.com/taichi-dev/taichi/pull/943#issuecomment-626344323
return inv_det * Matrix([[self(1, 1), -self(0, 1)],
[-self(1, 0), self(0, 0)]]).variable()
elif self.n == 3:
n = 3
import taichi as ti
inv_determinant = ti.expr_init(1.0 / ti.determinant(self))
entries = [[0] * n for _ in range(n)]
def E(x, y):
return self(x % n, y % n)
for i in range(n):
for j in range(n):
entries[j][i] = ti.expr_init(
inv_determinant * (E(i + 1, j + 1) * E(i + 2, j + 2) -
E(i + 2, j + 1) * E(i + 1, j + 2)))
return Matrix(entries)
elif self.n == 4:
n = 4
import taichi as ti
inv_determinant = ti.expr_init(1.0 / ti.determinant(self))
entries = [[0] * n for _ in range(n)]
def E(x, y):
return self(x % n, y % n)
for i in range(n):
for j in range(n):
entries[j][i] = ti.expr_init(
inv_determinant * (-1)**(i + j) *
((E(i + 1, j + 1) *
(E(i + 2, j + 2) * E(i + 3, j + 3) -
E(i + 3, j + 2) * E(i + 2, j + 3)) -
E(i + 2, j + 1) *
(E(i + 1, j + 2) * E(i + 3, j + 3) -
E(i + 3, j + 2) * E(i + 1, j + 3)) +
E(i + 3, j + 1) *
(E(i + 1, j + 2) * E(i + 2, j + 3) -
E(i + 2, j + 2) * E(i + 1, j + 3)))))
return Matrix(entries)
else:
raise Exception(
"Inversions of matrices with sizes >= 5 are not supported")
def inverse(self):
assert self.n == self.m, 'Only square matrices are invertible'
if self.n == 1:
return Matrix([1 / self(0, 0)])
elif self.n == 2:
inv_det = impl.expr_init(1.0 / self.determinant(self))
return inv_det * Matrix([[self(1, 1), -self(0, 1)],
[-self(1, 0), self(0, 0)]])
elif self.n == 3:
n = 3
import taichi as ti
inv_determinant = ti.expr_init(1.0 / ti.determinant(self))
entries = [[0] * n for _ in range(n)]
def E(x, y):
return self(x % n, y % n)
for i in range(n):
for j in range(n):
entries[j][i] = ti.expr_init(
inv_determinant * (E(i + 1, j + 1) * E(i + 2, j + 2) -
E(i + 2, j + 1) * E(i + 1, j + 2)))
return Matrix(entries)
else:
raise Exception(
"Inversions of matrices with sizes >= 4 are not supported")
def p2g(f: ti.i32):
for p in range(0, n_particles):
base = ti.cast(x[f, p] * inv_dx - 0.5, ti.i32)
fx = x[f, p] * inv_dx - ti.cast(base, ti.i32)
w = [
0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1),
0.5 * ti.sqr(fx - 0.5)
]
new_F = (ti.Matrix.diag(dim=dim, val=1) + dt * C[f, p]) @ F[f, p]
J = ti.determinant(new_F)
if particle_type[p] == 0: # fluid
sqrtJ = ti.sqrt(J)
# TODO: need pow(x, 1/3)
new_F = ti.Matrix([[sqrtJ, 0, 0], [0, sqrtJ, 0], [0, 0, 1]])
F[f + 1, p] = new_F
# r, s = ti.polar_decompose(new_F)
act_id = actuator_id[p]
act = actuation[f, ti.max(0, act_id)] * act_strength
if act_id == -1:
act = 0.0
# ti.print(act)
A = ti.Matrix([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 1.0]
]) * act
cauchy = ti.Matrix(zero_matrix())
mass = 0.0
ident = [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
if particle_type[p] == 0:
mass = 4
cauchy = ti.Matrix(ident) * (J - 1) * E
else:
mass = 1
cauchy = mu * (new_F @ ti.transposed(new_F)) + ti.Matrix(ident) * (
la * ti.log(J) - mu)
cauchy += new_F @ A @ ti.transposed(new_F)
stress = -(dt * p_vol * 4 * inv_dx * inv_dx) * cauchy
affine = stress + mass * C[f, p]
for i in ti.static(range(3)):
for j in ti.static(range(3)):
for k in ti.static(range(3)):
offset = ti.Vector([i, j, k])
dpos = (ti.cast(ti.Vector([i, j, k]), real) - fx) * dx
weight = w[i](0) * w[j](1) * w[k](2)
grid_v_in[base + offset].atomic_add(
weight * (mass * v[f, p] + affine @ dpos))
grid_m_in[base + offset].atomic_add(weight * mass)
def p2g(f: ti.i32):
for p in range(n_particles):
base = ti.cast(x[f, p] * inv_dx - 0.5, ti.i32)
fx = x[f, p] * inv_dx - ti.cast(base, ti.i32)
w = [0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1), 0.5 * ti.sqr(fx - 0.5)]
new_F = (ti.Matrix.diag(dim=2, val=1) + dt * C[f, p]) @ F[f, p]
J = ti.determinant(new_F)
if particle_type[p] == 0: # fluid
sqrtJ = ti.sqrt(J)
new_F = ti.Matrix([[sqrtJ, 0], [0, sqrtJ]])
F[f + 1, p] = new_F
r, s = ti.polar_decompose(new_F)
act_id = actuator_id[p]
act = actuation[f, ti.max(0, act_id)] * act_strength
if act_id == -1:
act = 0.0
# ti.print(act)
A = ti.Matrix([[0.0, 0.0], [0.0, 1.0]]) * act
cauchy = ti.Matrix([[0.0, 0.0], [0.0, 0.0]])
mass = 0.0
if particle_type[p] == 0:
mass = 4
cauchy = ti.Matrix([[1.0, 0.0], [0.0, 0.1]]) * (J - 1) * E
else:
mass = 1
cauchy = 2 * mu * (new_F - r) @ ti.transposed(new_F) + \
ti.Matrix.diag(2, la * (J - 1) * J)
cauchy += new_F @ A @ ti.transposed(new_F)
stress = -(dt * p_vol * 4 * inv_dx * inv_dx) * cauchy
affine = stress + mass * C[f, p]
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = ti.Vector([i, j])
dpos = (ti.cast(ti.Vector([i, j]), real) - fx) * dx
weight = w[i](0) * w[j](1)
grid_v_in[base + offset] += weight * (mass * v[f, p] + affine @ dpos)
grid_m_in[base + offset] += weight * mass
def p2g(f: ti.i32):
for p in range(0, n_particles):
base = ti.cast(x[f, p] * inv_dx - 0.5, ti.i32)
fx = x[f, p] * inv_dx - ti.cast(base, ti.i32)
w = [0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1), 0.5 * ti.sqr(fx - 0.5)]
new_F = (ti.Matrix.diag(dim=2, val=1) + dt * C[f, p]) @ F[f, p]
F[f + 1, p] = new_F
J = ti.determinant(new_F)
r, s = ti.polar_decompose(new_F)
cauchy = 2 * mu * (new_F - r) @ ti.transposed(new_F) + \
ti.Matrix.diag(2, la * (J - 1) * J)
stress = -(dt * p_vol * 4 * inv_dx * inv_dx) * cauchy
affine = stress + p_mass * C[f, p]
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = ti.Vector([i, j])
dpos = (ti.cast(ti.Vector([i, j]), real) - fx) * dx
weight = w[i](0) * w[j](1)
grid_v_in[f, base + offset] += weight * (
p_mass * v[f, p] + affine @ dpos)
grid_m_in[f, base + offset] += weight * p_mass
