def test_refine():
g = Grid_1D.periodic(4)
compare_comps(g, form(0, c, (sin(x), )), True)
compare_comps(g, form(0, c, (sin(x), )), False)
compare_comps(g, form(1, c, (sin(x), )), True)
compare_comps(g, form(1, c, (sin(x), )), False)
g = Grid_1D.periodic(5)
for func in (sin(x), cos(x), sin(2 * x), sin(x) + cos(x), 1 + sin(x)):
compare_comps(g, form(0, c, (func, )), True)
compare_comps(g, form(0, c, (func, )), False)
compare_comps(g, form(1, c, (func, )), True)
compare_comps(g, form(1, c, (func, )), False)
g = Grid_1D.chebyshev(4)
for func in (x, (1 - x)**2, x + 1):
compare_comps(g, form(0, c, (func, )), True)
compare_comps(g, form(0, c, (func, )), False)
compare_comps(g, form(1, c, (func, )), True)
compare_comps(g, form(1, c, (func, )), False)
g = Grid_1D.chebyshev(5)
for func in (x, (1 - x)**2, x**3, x + 1):
compare_comps(g, form(0, c, (func, )), True)
compare_comps(g, form(0, c, (func, )), False)
compare_comps(g, form(1, c, (func, )), True)
compare_comps(g, form(1, c, (func, )), False)
def test_P():
g = Grid_1D.periodic(11)
f = form(0, c, (sin(x), ))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
f = form(1, c, (cos(x), ))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
g = Grid_1D.regular(11)
f = form(0, c, (x, ))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
f = form(1, c, (x**3, ))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
g = Grid_1D.chebyshev(11)
f = form(0, c, (x, ))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
f = form(1, c, (x**3, ))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
def test_P():
g = Grid_1D.periodic(11)
f = form(0, c, (sin(x),))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
f = form(1, c, (cos(x),))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
g = Grid_1D.regular(11)
f = form(0, c, (x,))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
f = form(1, c, (x**3,))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
g = Grid_1D.chebyshev(11)
f = form(0, c, (x,))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
f = form(1, c, (x**3,))
assert f.P(g, True) == g.P(f.degree, True, f.lambdify)
assert f.P(g, False) == g.P(f.degree, False, f.lambdify)
def test_W_C():
g = Grid_1D.periodic(11)
f0 = form(0, c, (cos(x), ))
f1 = form(1, c, (sin(x), ))
f = [f0, f1]
for ((d1, p1), (d2, p2), p3) in g.dec.W.keys():
assert (f[d1] ^ f[d2]).P(g, p3) == f[d1].P(g, p1).W(f[d2].P(g, p2),
toprimal=p3)
for (p1, (d2, p2), p3) in g.dec.C.keys():
assert (f[d1] ^ f[d2]).P(g, p3) == f[d1].P(g, p1).W(f[d2].P(g, p2),
toprimal=p3)
g = Grid_1D.chebyshev(11)
f0 = form(0, c, (x, ))
f1 = form(1, c, (x**2, ))
f = [f0, f1]
for ((d1, p1), (d2, p2), p3) in g.dec.W.keys():
assert (f[d1] ^ f[d2]).P(g, p3) == f[d1].P(g, p1).W(f[d2].P(g, p2),
toprimal=p3)
for (p1, (d2, p2), p3) in g.dec.C.keys():
assert f[1].C(f[d2]).P(g, p3) == f[1].P(g, p1).C(f[d2].P(g, p2),
toprimal=p3)
def test_D():
g = Grid_1D.periodic(11)
f = form(0, c, (cos(x), ))
assert f.D.P(g, True) == f.P(g, True).D
assert f.D.P(g, False) == f.P(g, False).D
g = Grid_1D.regular(11)
f = form(0, c, (x, ))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
f = form(0, c, (x**3, ))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
g = Grid_1D.chebyshev(11)
f = form(0, c, (x, ))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
f = form(0, c, (x**3, ))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
def test_refine():
g = Grid_1D.periodic(4)
compare_comps(g, form(0, c, (sin(x),)), True)
compare_comps(g, form(0, c, (sin(x),)), False)
compare_comps(g, form(1, c, (sin(x),)), True)
compare_comps(g, form(1, c, (sin(x),)), False)
g = Grid_1D.periodic(5)
for func in (sin(x), cos(x), sin(2*x), sin(x)+cos(x), 1 + sin(x)):
compare_comps(g, form(0, c, (func,)), True)
compare_comps(g, form(0, c, (func,)), False)
compare_comps(g, form(1, c, (func,)), True)
compare_comps(g, form(1, c, (func,)), False)
g = Grid_1D.chebyshev(4)
for func in (x, (1-x)**2, x+1):
compare_comps(g, form(0, c, (func,)), True)
compare_comps(g, form(0, c, (func,)), False)
compare_comps(g, form(1, c, (func,)), True)
compare_comps(g, form(1, c, (func,)), False)
g = Grid_1D.chebyshev(5)
for func in (x, (1-x)**2, x**3, x+1):
compare_comps(g, form(0, c, (func,)), True)
compare_comps(g, form(0, c, (func,)), False)
compare_comps(g, form(1, c, (func,)), True)
compare_comps(g, form(1, c, (func,)), False)
def test_W_C():
g = Grid_1D.periodic(11)
f0 = form(0, c, (cos(x),))
f1 = form(1, c, (sin(x),))
f = [f0, f1]
for ((d1, p1), (d2, p2), p3) in g.dec.W.keys():
assert (f[d1]^f[d2]).P(g, p3) == f[d1].P(g, p1).W(f[d2].P(g, p2), toprimal=p3)
for (p1, (d2, p2), p3) in g.dec.C.keys():
assert (f[d1]^f[d2]).P(g, p3) == f[d1].P(g, p1).W(f[d2].P(g, p2), toprimal=p3)
g = Grid_1D.chebyshev(11)
f0 = form(0, c, (x,))
f1 = form(1, c, (x**2,))
f = [f0, f1]
for ((d1, p1), (d2, p2), p3) in g.dec.W.keys():
assert (f[d1]^f[d2]).P(g, p3) == f[d1].P(g, p1).W(f[d2].P(g, p2), toprimal=p3)
for (p1, (d2, p2), p3) in g.dec.C.keys():
assert f[1].C(f[d2]).P(g, p3) == f[1].P(g, p1).C(f[d2].P(g, p2), toprimal=p3)
def test_D():
g = Grid_1D.periodic(11)
f = form(0, c, (cos(x),))
assert f.D.P(g, True) == f.P(g, True).D
assert f.D.P(g, False) == f.P(g, False).D
g = Grid_1D.regular(11)
f = form(0, c, (x,))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
f = form(0, c, (x**3,))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
g = Grid_1D.chebyshev(11)
f = form(0, c, (x,))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
f = form(0, c, (x**3,))
assert f.D.P(g, True) == f.P(g, True).D
bc = g.boundary_condition(f.lambdify)
assert f.D.P(g, False) == f.P(g, False).D + bc
def test_H():
g = Grid_1D.periodic(11)
f = form(0, c, (cos(3 * x), ))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
f = form(1, c, (sin(x) + cos(x), ))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
g = Grid_1D.chebyshev(11)
f = form(0, c, (x**4, ))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
f = form(1, c, (x**2 + 1, ))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
def test_H():
g = Grid_1D.periodic(11)
f = form(0, c, (cos(3*x),))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
f = form(1, c, (sin(x)+cos(x),))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
g = Grid_1D.chebyshev(11)
f = form(0, c, (x**4,))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
f = form(1, c, (x**2 + 1,))
assert f.H.P(g, False) == f.P(g, True).H
assert f.H.P(g, True) == f.P(g, False).H
def test_R():
g = Grid_1D.periodic(11)
pnts = np.linspace(g.xmin, g.xmax, 50)
f = form(0, c, (sin(x), ))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
f = form(1, c, (sin(x), ))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
g = Grid_1D.chebyshev(11)
# do not include boundaries, because we get nan there
pnts = np.linspace(g.xmin, g.xmax, 50)[1:-1]
f = form(0, c, (x**2, ))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
f = form(1, c, (x**2, ))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
def test_R():
g = Grid_1D.periodic(11)
pnts = np.linspace(g.xmin, g.xmax, 50)
f = form(0, c, (sin(x),))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
f = form(1, c, (sin(x),))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
g = Grid_1D.chebyshev(11)
# do not include boundaries, because we get nan there
pnts = np.linspace(g.xmin, g.xmax, 50)[1:-1]
f = form(0, c, (x**2,))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
f = form(1, c, (x**2,))
assert np.allclose(f.lambdify(pnts), f.P(g, True).R(pnts))
assert np.allclose(f.lambdify(pnts), f.P(g, False).R(pnts))
