def test_jac_simpl():
model = Model("dxxU", "U")
model_simp = Model("dxxU", "U", simplify=True)
x = np.linspace(0, 2 * np.pi, 50, endpoint=False)
U = np.cos(x)
assert np.isclose(
model.J(model.fields_template(x=x, U=U), dict(periodic=True)).todense(),
model.J(model_simp.fields_template(x=x, U=U), dict(periodic=True)).todense(),
).all()
def test_jac_simpl():
model = Model("dxxU", "U")
model_simp = Model("dxxU", "U", simplify=True)
x = np.linspace(0, 2 * np.pi, 50, endpoint=False)
U = np.cos(x)
assert np.isclose(
model.J(model.fields_template(x=x, U=U),
dict(periodic=True)).todense(),
model.J(model_simp.fields_template(x=x, U=U),
dict(periodic=True)).todense(),
).all()
def test_routines_api():
x = np.linspace(0, 10, 100)
U = np.cos(x * 2 * np.pi / 10)
model = Model(differential_equations="dxxU",
dependent_variables="U")
fields = model.fields_template(x=x, U=U)
F = model.F
print(F)
F(fields, dict(periodic=True))
F.diff_approx(fields, dict(periodic=True))
J = model.J
print(J)
J(fields, dict(periodic=True))
def test_upwind(compiler, uporder, vel, periodic):
model = Model(
differential_equations=["upwind(%s, U, %i)" % (vel, uporder)],
dependent_variables="U",
parameters="k",
help_functions="s",
compiler=compiler,
)
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
s = np.zeros_like(x)
fields = model.fields_template(x=x, U=U, s=s)
parameters = dict(periodic=periodic, k=1)
model.F(fields, parameters)
model.J(fields, parameters)
def test_upwind(compiler, uporder, vel, periodic):
model = Model(
differential_equations=["upwind(%s, U, %i)" % (vel, uporder)],
dependent_variables="U",
parameters="k",
help_functions="s",
compiler=compiler,
)
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
s = np.zeros_like(x)
fields = model.fields_template(x=x, U=U, s=s)
parameters = dict(periodic=periodic, k=1)
model.F(fields, parameters)
model.J(fields, parameters)
def test_fields_api():
model = Model(differential_equations=["dxxU1", "dxxU2"],
dependent_variables=["U1", "U2"],
help_functions='s')
x = np.linspace(0, 1, 100)
U1 = np.cos(x)
U2 = np.sin(x)
s = np.sin(x)
fields = model.fields_template(x=x, U1=U1, U2=U2, s=s)
print(fields)
assert np.isclose(fields.uflat, np.vstack([U1, U2]).flatten('F')).all()
assert np.isclose(fields.uarray.to_array(), np.vstack([U1, U2])).all()
assert np.isclose(fields["x"], x).all()
assert np.isclose(fields["U1"], U1).all()
assert np.isclose(fields["U2"], U2).all()
assert np.isclose(fields["s"], s).all()
assert fields.size == x.size
def test_fields_api():
model = Model(differential_equations=["dxxU1", "dxxU2"],
dependent_variables=["U1", "U2"], help_functions='s')
x = np.linspace(0, 1, 100)
U1 = np.cos(x)
U2 = np.sin(x)
s = np.sin(x)
fields = model.fields_template(x=x, U1=U1, U2=U2, s=s)
print(fields)
assert np.isclose(fields.uflat,
np.vstack([U1, U2]).flatten('F')).all()
assert np.isclose(fields.uarray.to_array(),
np.vstack([U1, U2])).all()
assert np.isclose(fields["x"], x).all()
assert np.isclose(fields["U1"], U1).all()
assert np.isclose(fields["U2"], U2).all()
assert np.isclose(fields["s"], s).all()
assert fields.size == x.size
def test_model_monovariate(func, var, par, k, compiler):
model = Model(func, var, par, compiler=compiler)
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
fields = model.fields_template(x=x, U=U)
parameters = dict(periodic=True, k=k)
F = model.F(fields, parameters)
J_sparse = model.J(fields, parameters)
J_dense = model.J(fields, parameters, sparse=False)
J_approx = model.F.diff_approx(fields, parameters)
dxU = np.gradient(np.pad(U, 2, mode="wrap")) / dx
dxxU = np.gradient(dxU) / dx
dxU = dxU[2:-2]
dxxU = dxxU[2:-2]
assert np.isclose(F, k * dxxU, rtol=1E-2).all()
assert np.isclose(J_approx, J_sparse.todense(), rtol=1E-2).all()
assert np.isclose(J_approx, J_dense, rtol=1E-2).all()
def test_model_monovariate(func, var, par, k, compiler):
model = Model(func, var, par, compiler=compiler)
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
fields = model.fields_template(x=x, U=U)
parameters = dict(periodic=True, k=k)
F = model.F(fields, parameters)
J_sparse = model.J(fields, parameters)
J_dense = model.J(fields, parameters, sparse=False)
J_approx = model.F.diff_approx(fields, parameters)
dxU = np.gradient(np.pad(U, 2, mode="wrap")) / dx
dxxU = np.gradient(dxU) / dx
dxU = dxU[2:-2]
dxxU = dxxU[2:-2]
assert np.isclose(F, k * dxxU, rtol=1E-2).all()
assert np.isclose(J_approx, J_sparse.todense(), rtol=1E-2).all()
assert np.isclose(J_approx, J_dense, rtol=1E-2).all()
def test_model_api(compiler, periodic):
model = Model(
differential_equations=["k * dxxU + s"],
dependent_variables="U",
parameters="k",
help_functions="s",
compiler=compiler,
)
assert set(model._args) == set(
["x", "U_m1", "U", "U_p1", "s_m1", "s", "s_p1", "k", "dx"])
with pytest.raises(NotImplementedError):
Model("dxxxxxU", "U")
with pytest.raises(ValueError):
Model("dxxx(dx)", "U")
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
s = np.zeros_like(x)
fields = model.fields_template(x=x, U=U, s=s)
parameters = dict(periodic=periodic, k=1)
model.F(fields, parameters)
model.J(fields, parameters)
def test_model_api(compiler, periodic):
model = Model(
differential_equations=["k * dxxU + s"],
dependent_variables="U",
parameters="k",
help_functions="s",
compiler=compiler,
)
assert set(model._args) == set(
["x", "U_m1", "U", "U_p1", "s_m1", "s", "s_p1", "k", "dx"]
)
with pytest.raises(NotImplementedError):
Model("dxxxxxU", "U")
with pytest.raises(ValueError):
Model("dxxx(dx)", "U")
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
s = np.zeros_like(x)
fields = model.fields_template(x=x, U=U, s=s)
parameters = dict(periodic=periodic, k=1)
model.F(fields, parameters)
model.J(fields, parameters)
def test_model_bivariate():
model = Model(["k1 * dxx(v)", "k2 * dxx(u)"], ["u", "v"], ["k1", "k2"])
x, dx = np.linspace(0, 10, 50, retstep=True, endpoint=False)
u = np.cos(x * 2 * np.pi / 10)
v = np.sin(x * 2 * np.pi / 10)
fields = model.fields_template(x=x, u=u, v=v)
parameters = dict(periodic=True, k1=1, k2=1)
F = model.F(fields, parameters)
J_sparse = model.J(fields, parameters)
J_dense = model.J(fields, parameters, sparse=False)
J_approx = model.F.diff_approx(fields, parameters, eps=1E-3)
dxu = np.gradient(np.pad(u, 2, mode="wrap")) / dx
dxxu = np.gradient(dxu) / dx
dxu = dxu[2:-2]
dxxu = dxxu[2:-2]
dxv = np.gradient(np.pad(v, 2, mode="wrap")) / dx
dxxv = np.gradient(dxv) / dx
dxv = dxv[2:-2]
dxxv = dxxv[2:-2]
assert np.isclose(F, np.vstack([dxxv, dxxu]).flatten("F"), rtol=1E-2).all()
assert np.isclose(J_approx, J_sparse.todense(), rtol=1E-4).all()
assert np.isclose(J_approx, J_dense, rtol=1E-4).all()
def test_model_bivariate():
model = Model(["k1 * dxx(v)", "k2 * dxx(u)"], ["u", "v"], ["k1", "k2"])
x, dx = np.linspace(0, 10, 50, retstep=True, endpoint=False)
u = np.cos(x * 2 * np.pi / 10)
v = np.sin(x * 2 * np.pi / 10)
fields = model.fields_template(x=x, u=u, v=v)
parameters = dict(periodic=True, k1=1, k2=1)
F = model.F(fields, parameters)
J_sparse = model.J(fields, parameters)
J_dense = model.J(fields, parameters, sparse=False)
J_approx = model.F.diff_approx(fields, parameters, eps=1E-3)
dxu = np.gradient(np.pad(u, 2, mode="wrap")) / dx
dxxu = np.gradient(dxu) / dx
dxu = dxu[2:-2]
dxxu = dxxu[2:-2]
dxv = np.gradient(np.pad(v, 2, mode="wrap")) / dx
dxxv = np.gradient(dxv) / dx
dxv = dxv[2:-2]
dxxv = dxxv[2:-2]
assert np.isclose(F, np.vstack([dxxv, dxxu]).flatten("F"), rtol=1E-2).all()
assert np.isclose(J_approx, J_sparse.todense(), rtol=1E-4).all()
assert np.isclose(J_approx, J_dense, rtol=1E-4).all()
import numpy as np
import pylab as pl
from triflow import Model, Simulation
model = Model("k * dxxU - c * dxU", "U", ["k", "c"])
x, dx = np.linspace(0, 1, 200, retstep=True)
U = np.cos(2 * np.pi * x * 5)
fields = model.fields_template(x=x, U=U)
parameters = dict(c=.03, k=.001, dx=dx, periodic=False)
t = 0
dt = 5E-1
tmax = 2.5
pl.plot(fields.x, fields.U, label='t: %g' % t)
def dirichlet_condition(t, fields, pars):
fields.U[0] = 1
fields.U[-1] = 0
return fields, pars
simul = Simulation(model,
fields,
parameters,
dt,
hook=dirichlet_condition,
import numpy as np
import pylab as pl
from triflow import Model, schemes
model = Model("k * dxxU - c * dxU",
"U", ["k", "c"])
x, dx = np.linspace(0, 1, 200, retstep=True)
U = np.cos(2 * np.pi * x * 5)
fields = model.fields_template(x=x, U=U)
pl.plot(fields.x, fields.U)
parameters = dict(c=.03, k=.001, dx=dx, periodic=True)
t = 0
dt = 1E-1
scheme = schemes.Theta(model, theta=.5) # Crank-Nicolson scheme
new_t, new_fields = scheme(t, fields, dt, parameters)
pl.plot(new_fields.x, new_fields.U)
pl.xlim(0, 1)
pl.show()