def test_grid_eval():
hs = create_example_hspace(p=3, dim=2, n0=6, num_levels=3)
u = rand(hs.numdofs)
grid = 2 * (np.linspace(0, 1, 50), )
f_fine = bspline.BSplineFunc(hs.knotvectors(-1), hs.represent_fine() @ u)
hsf = HSplineFunc(hs, u)
assert hsf.dim == 1 and hsf.sdim == 2
assert hsf.support == ((0.0, 1.0), (0.0, 1.0))
#
assert np.allclose(f_fine.grid_eval(grid), hsf.grid_eval(grid))
assert np.allclose(f_fine.grid_jacobian(grid), hsf.grid_jacobian(grid))
assert np.allclose(f_fine.grid_hessian(grid), hsf.grid_hessian(grid))
#
assert np.allclose(hsf(grid[1][7], grid[0][19]),
hsf.grid_eval(grid)[19, 7])
## test THBs
f_fine = bspline.BSplineFunc(hs.knotvectors(-1),
hs.represent_fine(truncate=True) @ u)
hsf = HSplineFunc(hs, u, truncate=True)
assert np.allclose(f_fine.grid_eval(grid), hsf.grid_eval(grid))
assert np.allclose(f_fine.grid_jacobian(grid), hsf.grid_jacobian(grid))
assert np.allclose(f_fine.grid_hessian(grid), hsf.grid_hessian(grid))
#
assert np.allclose(hsf(grid[1][7], grid[0][19]),
hsf.grid_eval(grid)[19, 7])
def test_parse():
from pyiga import bspline, geometry
kvs = 2 * (bspline.make_knots(2, 0.0, 1.0, 5), )
vf = parse_vf('u * v * dx', kvs, bfuns=[('u', 1), ('v', 1)])
assert vf.hash() == mass_vf(2).hash()
f = bspline.BSplineFunc(kvs, np.ones(bspline.numdofs(kvs)))
vf = parse_vf('f * v * dx', kvs, {'f': f})
assert vf.hash() == L2functional_vf(2, physical=False).hash()
f = lambda x, y: 1.0
vf = parse_vf('f * v * dx', kvs, {'f': f})
assert vf.hash() == L2functional_vf(2, physical=True).hash()
vf = parse_vf('div(u) * div(v) * dx', kvs, bfuns=[('u', 2), ('v', 2)])
assert vf.hash() == divdiv_vf(2).hash()
# some other features
vf = parse_vf('f * v * ds', kvs[:1], {'f': geometry.circular_arc(1.4)[0]})
vf = parse_vf('inner(f, v) * ds',
kvs,
bfuns=[('v', 2)],
args={
'f': lambda x, y: (-y, x)
})
def test_animate_field():
kvs = 2 * (bspline.make_knots(2, 0.0, 1.0, 5),)
fields = [ bspline.BSplineFunc(kvs,
approx.interpolate(kvs, lambda x,y: np.sin(t+x) * np.exp(y)))
for t in range(3) ]
anim = animate_field(fields, geo=geometry.bspline_quarter_annulus(), res=10)
anim.to_jshtml()
def test_prolongators():
hs = create_example_hspace(p=3, dim=2, n0=4, disparity=1, num_levels=1)
n0 = hs.mesh(0).numbf
# create a coarse B-spline function
u_tp = rand(n0)
f0 = bspline.BSplineFunc(hs.knotvectors(0), u_tp)
# bring its coefficients into canonical order (active, then deactivated)
u_lv0 = np.concatenate((
u_tp[hs.active_indices()[0]],
u_tp[hs.deactivated_indices()[0]],
))
X = 2 * (np.linspace(0, 1, 20), )
#### prolongators for HB-splines ####
# prolongate f to the finest space (hs itself)
P_hb = hs.virtual_hierarchy_prolongators()
u = u_lv0
for P in P_hb:
u = P @ u
f_hb = HSplineFunc(hs, u)
# compare it to the original function
assert np.allclose(f0.grid_eval(X), f_hb.grid_eval(X))
#### prolongators for THB-splines ####
hs.truncate = True
# prolongate f to the finest space (hs itself)
P_thb = hs.virtual_hierarchy_prolongators()
u = u_lv0
for P in P_thb:
u = P @ u
f_thb = HSplineFunc(hs, u)
# compare it to the original function
assert np.allclose(f0.grid_eval(X), f_thb.grid_eval(X))
def test_plot_field():
def f(x, y): return np.sin(x) * np.exp(y)
geo = geometry.quarter_annulus()
plot_field(f, physical=True, geo=geo, res=10)
#
kvs = 2 * (bspline.make_knots(2, 0.0, 1.0, 5),)
u = bspline.BSplineFunc(kvs, approx.interpolate(kvs, f))
plot_field(u, res=10)
plot_field(u, geo=geo, res=10)