def run_benchmark():
compile_time = time.time()
func(*args) # compile the kernel first
ti.sync()
compile_time = time.time() - compile_time
ti.stat_write('compilation_time', compile_time)
codegen_stat = ti.core.stat()
for line in codegen_stat.split('\n'):
try:
a, b = line.strip().split(':')
except:
continue
a = a.strip()
b = int(float(b))
if a == 'codegen_kernel_statements':
ti.stat_write('instructions', b)
if a == 'codegen_offloaded_tasks':
ti.stat_write('offloaded_tasks', b)
elif a == 'launched_tasks':
ti.stat_write('launched_tasks', b)
# The reason why we run 3 more times is to warm up
# instruction/data caches. Discussion:
# https://github.com/taichi-dev/taichi/pull/1002#discussion_r426312136
for i in range(3):
func(*args)
ti.sync()
t = time.time()
for n in range(repeat):
func(*args)
ti.sync()
elapsed = time.time() - t
avg = elapsed / repeat
ti.stat_write('running_time', avg)
def benchmark(func, repeat=300, args=()):
import taichi as ti
import time
# The reason why we run 4 times is to warm up instruction/data caches.
# Discussion: https://github.com/taichi-dev/taichi/pull/1002#discussion_r426312136
for i in range(4):
func(*args) # compile the kernel first
ti.sync()
t = time.time()
for n in range(repeat):
func(*args)
ti.get_runtime().sync()
elapsed = time.time() - t
avg = elapsed / repeat * 1000 # miliseconds
ti.stat_write(avg)
def run_benchmark():
compile_time = time.time()
func(*args) # compile the kernel first
ti.sync()
compile_time = time.time() - compile_time
ti.stat_write('compilation_time', compile_time)
codegen_stat = ti.core.stat()
for line in codegen_stat.split('\n'):
try:
a, b = line.strip().split(':')
except:
continue
a = a.strip()
b = int(float(b))
if a == 'codegen_kernel_statements':
ti.stat_write('compiled_inst', b)
if a == 'codegen_offloaded_tasks':
ti.stat_write('compiled_tasks', b)
elif a == 'launched_tasks':
ti.stat_write('launched_tasks', b)
# Use 3 initial iterations to warm up
# instruction/data caches. Discussion:
# https://github.com/taichi-dev/taichi/pull/1002#discussion_r426312136
for i in range(3):
func(*args)
ti.sync()
ti.kernel_profiler_clear()
t = time.time()
for n in range(repeat):
func(*args)
ti.sync()
elapsed = time.time() - t
avg = elapsed / repeat
ti.stat_write('wall_clk_t', avg)
device_time = ti.kernel_profiler_total_time()
ti.stat_write('exec_t', device_time)
def benchmark_range():
quality = 1 # Use a larger value for higher-res simulations
n_particles, n_grid = 9000 * quality**2, 128 * quality
dx, inv_dx = 1 / n_grid, float(n_grid)
dt = 1e-4 / quality
p_vol, p_rho = (dx * 0.5)**2, 1
p_mass = p_vol * p_rho
E, nu = 0.1e4, 0.2 # Young's modulus and Poisson's ratio
mu_0, lambda_0 = E / (2 * (1 + nu)), E * nu / (
(1 + nu) * (1 - 2 * nu)) # Lame parameters
x = ti.Vector(2, dt=ti.f32, shape=n_particles) # position
v = ti.Vector(2, dt=ti.f32, shape=n_particles) # velocity
C = ti.Matrix(2, 2, dt=ti.f32, shape=n_particles) # affine velocity field
F = ti.Matrix(2, 2, dt=ti.f32, shape=n_particles) # deformation gradient
material = ti.var(dt=ti.i32, shape=n_particles) # material id
Jp = ti.var(dt=ti.f32, shape=n_particles) # plastic deformation
grid_v = ti.Vector(2, dt=ti.f32,
shape=(n_grid, n_grid)) # grid node momemtum/velocity
grid_m = ti.var(dt=ti.f32, shape=(n_grid, n_grid)) # grid node mass
@ti.kernel
def substep():
for i, j in ti.ndrange(n_grid, n_grid):
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
for p in range(n_particles
): # Particle state update and scatter to grid (P2G)
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
# Quadratic kernels [http://mpm.graphics Eqn. 123, with x=fx, fx-1,fx-2]
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
F[p] = (ti.Matrix.identity(ti.f32, 2) +
dt * C[p]) @ F[p] # deformation gradient update
h = ti.exp(
10 * (1.0 - Jp[p])
) # Hardening coefficient: snow gets harder when compressed
if material[p] == 1: # jelly, make it softer
h = 0.3
mu, la = mu_0 * h, lambda_0 * h
if material[p] == 0: # liquid
mu = 0.0
U, sig, V = ti.svd(F[p])
J = 1.0
for d in ti.static(range(2)):
new_sig = sig[d, d]
if material[p] == 2: # Snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # Plasticity
Jp[p] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if material[
p] == 0: # Reset deformation gradient to avoid numerical instability
F[p] = ti.Matrix.identity(ti.f32, 2) * ti.sqrt(J)
elif material[p] == 2:
F[p] = U @ sig @ V.T(
) # Reconstruct elastic deformation gradient after plasticity
stress = 2 * mu * (F[p] - U @ V.T()) @ F[p].T(
) + ti.Matrix.identity(ti.f32, 2) * la * J * (J - 1)
stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
affine = stress + p_mass * C[p]
for i, j in ti.static(ti.ndrange(
3, 3)): # Loop over 3x3 grid node neighborhood
offset = ti.Vector([i, j])
dpos = (offset.cast(float) - fx) * dx
weight = w[i][0] * w[j][1]
grid_v[base +
offset] += weight * (p_mass * v[p] + affine @ dpos)
grid_m[base + offset] += weight * p_mass
for i, j in ti.ndrange(n_grid, n_grid):
if grid_m[i, j] > 0: # No need for epsilon here
grid_v[i, j] = (
1 / grid_m[i, j]) * grid_v[i, j] # Momentum to velocity
grid_v[i, j][1] -= dt * 50 # gravity
if i < 3 and grid_v[i, j][0] < 0:
grid_v[i, j][0] = 0 # Boundary conditions
if i > n_grid - 3 and grid_v[i, j][0] > 0: grid_v[i, j][0] = 0
if j < 3 and grid_v[i, j][1] < 0: grid_v[i, j][1] = 0
if j > n_grid - 3 and grid_v[i, j][1] > 0: grid_v[i, j][1] = 0
for p in range(n_particles): # grid to particle (G2P)
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
w = [
0.5 * (1.5 - fx)**2, 0.75 - (fx - 1.0)**2, 0.5 * (fx - 0.5)**2
]
new_v = ti.Vector.zero(ti.f32, 2)
new_C = ti.Matrix.zero(ti.f32, 2, 2)
for i, j in ti.static(ti.ndrange(
3, 3)): # loop over 3x3 grid node neighborhood
dpos = ti.Vector([i, j]).cast(float) - fx
g_v = grid_v[base + ti.Vector([i, j])]
weight = w[i][0] * w[j][1]
new_v += weight * g_v
new_C += 4 * inv_dx * weight * ti.outer_product(g_v, dpos)
v[p], C[p] = new_v, new_C
x[p] += dt * v[p] # advection
import random
group_size = n_particles // 3
for i in range(n_particles):
x[i] = [
random.random() * 0.2 + 0.3 + 0.10 * (i // group_size),
random.random() * 0.2 + 0.05 + 0.32 * (i // group_size)
]
material[i] = i // group_size # 0: fluid 1: jelly 2: snow
v[i] = [0, 0]
F[i] = [[1, 0], [0, 1]]
Jp[i] = 1
gui = ti.GUI("Taichi MLS-MPM-99", res=512, background_color=0x112F41)
substep()
ti.get_runtime().sync()
t = time.time()
for frame in range(200):
for s in range(20):
substep()
# colors = np.array([0x068587, 0xED553B, 0xEEEEF0], dtype=np.uint32)
# gui.circles(x.to_numpy(), radius=1.5, color=colors[material.to_numpy()])
# gui.show() # Change to gui.show(f'{frame:06d}.png') to write images to disk
ti.get_runtime().sync()
avg = (time.time() - t) / 4000 * 1000 # miliseconds
ti.stat_write(avg)
