def test_inner_products():
kvs = [bspline.make_knots(p, 0.0, 1.0, 8+p) for p in range(3,6)]
def f(x,y,z): return np.cos(x) * np.exp(y) * np.sin(z)
inp = inner_products(kvs, f)
assert inp.shape == tuple(kv.numdofs for kv in kvs)
inp2 = inner_products(kvs, f, geo=geometry.unit_cube())
assert np.allclose(inp, inp2)
def test_stiffness_3d():
kvs = (bspline.make_knots(3, 0.0, 1.0, 4),
bspline.make_knots(3, 0.0, 1.0, 5),
bspline.make_knots(3, 0.0, 1.0, 6))
assert(np.allclose(
bsp_stiffness_3d(kvs, geo=None).A,
bsp_stiffness_3d(kvs, geo=geometry.unit_cube()).A,
rtol=0, atol=1e-14)
)
def test_integrate():
def one(*X): return 1.0
geo = geometry.unit_square()
assert abs(1.0 - integrate(geo.kvs, one)) < 1e-8
assert abs(1.0 - integrate(geo.kvs, one, f_physical=True, geo=geo)) < 1e-8
geo = geometry.unit_cube()
assert abs(1.0 - integrate(geo.kvs, one)) < 1e-8
assert abs(1.0 - integrate(geo.kvs, one, f_physical=True, geo=geo)) < 1e-8
kvs = 2 * (bspline.make_knots(3, 0.0, 1.0, 10),)
geo = geometry.quarter_annulus()
assert abs(3*np.pi/4 - integrate(kvs, one, geo=geo)) < 1e-8
def test_wave_st_2d():
T_end = 2.0
geo = geometry.unit_cube(dim=1).extrude(0.0, T_end, support=(0.0,T_end))
kv_t = bspline.make_knots(2, 0.0, T_end, 6) # time axis
kv = bspline.make_knots(3, 0.0, 1.0, 8) # space axis
kvs = (kv_t, kv)
M = mass(kv)
DxDx = stiffness(kv)
D0Dt = bsp_mixed_deriv_biform_1d(kv_t, 0, 1)
DttDt = bsp_mixed_deriv_biform_1d(kv_t, 2, 1)
A_ref = (spkron(DttDt, M) + spkron(D0Dt, DxDx)).tocsr()
A = assemble(assemblers.WaveAssembler_ST2D(kvs, geo))
assert abs(A_ref - A).max() < 1e-14
def test_heat_st_2d():
T_end = 2.0
geo = geometry.unit_cube(dim=1).cylinderize(0.0, T_end, support=(0.0,T_end))
kv_t = bspline.make_knots(2, 0.0, T_end, 6) # time axis
kv = bspline.make_knots(3, 0.0, 1.0, 8) # space axis
kvs = (kv_t, kv)
M = mass(kv)
M_t = mass(kv_t)
DxDx = stiffness(kv)
DtD0 = bsp_mixed_deriv_biform_1d(kv_t, 1, 0)
A_ref = (spkron(DtD0, M) + spkron(M_t, DxDx)).tocsr()
A = assemble_entries(assemblers.HeatAssembler_ST2D(kvs, geo))
assert abs(A_ref - A).max() < 1e-14
def test_assemble_string():
kvs = 2 * (bspline.make_knots(2, 0.0, 1.0, 10),)
geo = geometry.quarter_annulus()
A1 = assemble('inner(grad(u), grad(v)) * dx', kvs, geo=geo)
A2 = stiffness(kvs, geo)
assert np.allclose(A1.A, A2.A)
# use Assembler class
asm = Assembler('inner(grad(u), grad(v)) * dx', kvs, geo=geo, symmetric=True, updatable=['geo'])
A3 = asm.assemble()
assert np.allclose(A2.A, A3.A)
with unittest.TestCase().assertRaises(RuntimeError):
asm.assemble(f=geo) # not an updatable field
with unittest.TestCase().assertRaises(ValueError):
asm = Assembler('inner(grad(u), grad(v)) * dx', kvs, geo=geo, updatable=['f']) # f is not an input
f = lambda x, y: x * y**2
f1 = assemble('f * v * dx', kvs, geo=geo, f=f)
f2 = inner_products(kvs, f, geo=geo, f_physical=True)
assert np.allclose(f1, f2)
# vector-valued problems
f1 = assemble('f * div(v) * dx', kvs, bfuns=[('v',2)], geo=geo, f=f, layout='packed')
f2 = assemble('f * div(v) * dx', kvs, bfuns=[('v',2)], geo=geo, f=f, layout='blocked')
assert np.allclose(f1.transpose(2, 0, 1), f2)
# 1D problem - matrix
geo = geometry.unit_cube(dim=1)
A1 = assemble('inner(grad(u), grad(v)) * dx', kvs[:1], geo=geo)
A2 = stiffness(kvs[0])
assert np.allclose(A1.A, A2.A)
# 1D problem - rhs
f = lambda x: 1 + x**2
f1 = assemble('f * v * dx', kvs[:1], geo=geo, f=f)
f2 = inner_products(kvs[0], f=f, f_physical=True, geo=geo)
assert np.allclose(f1, f2)
# test error handling
with unittest.TestCase().assertRaises(ValueError) as cm:
assemble('inner(grad(u), grad(v)) * dx', kvs)
assert str(cm.exception) == "required input parameter 'geo' missing"
def test_inner_products():
kvs = [bspline.make_knots(p, 0.0, 1.0, 8+p) for p in range(3,6)]
def f(x,y,z): return np.cos(x) * np.exp(y) * np.sin(z)
inp = inner_products(kvs, f)
assert inp.shape == tuple(kv.numdofs for kv in kvs)
inp2 = inner_products(kvs, f, geo=geometry.unit_cube())
assert np.allclose(inp, inp2)
# compare to autogenerated assemblers when using geometry
geo = geometry.twisted_box()
import pyiga.assemblers
# physical=False
asm = pyiga.assemblers.L2FunctionalAssembler3D(kvs, geo, f=f)
inp = asm.assemble_vector()
inp2 = inner_products(kvs, f, geo=geo)
assert np.allclose(inp, inp2)
# physical=True
asm = pyiga.assemblers.L2FunctionalAssemblerPhys3D(kvs, geo, f=f)
inp = asm.assemble_vector()
inp2 = inner_products(kvs, f, f_physical=True, geo=geo)
assert np.allclose(inp, inp2)
def test_interpolate_physical():
f = lambda x,y,z: np.cos(x)*np.sin(y)*np.exp(z)
kvs = 3 * (bspline.make_knots(3, 0.0, 1.0, 10),)
x1 = interpolate(kvs, f)
x2 = interpolate(kvs, f, geo=geometry.unit_cube())
assert np.allclose(x1, x2)
def test_project_L2_geo():
f = lambda x,y,z: np.cos(x)*np.sin(y)*np.exp(z)
kvs = 3 * (bspline.make_knots(3, 0.0, 1.0, 10),)
x1 = project_L2(kvs, f)
x2 = project_L2(kvs, f, geo=geometry.unit_cube())
assert np.allclose(x1, x2)