def toroidal_shell_integral(n, minval, maxval, eps, benchmark=False):
coordvals = np.linspace(minval, maxval, n, dtype=np.float32)
delta = (maxval - minval) / (n - 1) # grid spacing
X_data = coordvals.reshape(n, 1, 1)
Y_data = coordvals.reshape(1, n, 1)
Z_data = coordvals.reshape(1, 1, n)
X = edsl.Tensor(edsl.LogicalShape(plaidml.DType.FLOAT32, X_data.shape))
Y = edsl.Tensor(edsl.LogicalShape(plaidml.DType.FLOAT32, Y_data.shape))
Z = edsl.Tensor(edsl.LogicalShape(plaidml.DType.FLOAT32, Z_data.shape))
# f-rep of torodial shell f(x, y, z) = (sqrt(x^2 + y^2) - 1)^2 + z^2 + (0.1)^2
F = sq(edsl.sqrt(sq(X) + sq(Y)) - 1.0) + sq(Z) - sq(0.1)
# moment of inertia about z axis at each point g(x, y, z) = x^2 + y^2
G = sq(X) + sq(Y)
DFDX = partial(F, 'x', delta)
DFDY = partial(F, 'y', delta)
DFDZ = partial(F, 'z', delta)
# chi: occupancy function: 1 inside the region (f<0), 0 outside the region (f>0)
DCHIDX = partial_chi(F, 'x', delta)
DCHIDY = partial_chi(F, 'y', delta)
DCHIDZ = partial_chi(F, 'z', delta)
NUMER = DFDX * DCHIDX + DFDY * DCHIDY + DFDZ * DCHIDZ
DENOM = edsl.sqrt(sq(DFDX) + sq(DFDY) + sq(DFDZ))
H = edsl.select(DENOM < eps, 0, NUMER / DENOM)
O = sum(-G * H)
program = edsl.Program('toroidal_shell_integral', [O])
binder = plaidml_exec.Binder(program)
executable = binder.compile()
def run():
binder.input(X).copy_from_ndarray(X_data)
binder.input(Y).copy_from_ndarray(Y_data)
binder.input(Z).copy_from_ndarray(Z_data)
executable.run()
return binder.output(O).as_ndarray()
if benchmark:
# the first run will compile and run
print('compiling...')
result = run()
# subsequent runs should not include compile time
print('running...')
ITERATIONS = 100
elapsed = timeit.timeit(run, number=ITERATIONS)
print('runtime:', elapsed / ITERATIONS)
else:
result = run()
return result * (delta**3)
def sqrt(x):
logger.debug('sqrt(x: {})'.format(x))
return _KerasNode('sqrt', tensor=edsl.sqrt(x.tensor))
def sqrt(x):
return _KerasNode('sqrt', tensor=edsl.sqrt(x.tensor))