def test_integrals():
for N in (10, 11, 12, 13):
g = Grid_1D.periodic(N, 0, 2 * pi)
pnts = concatenate([g.verts, [g.xmax]])
for f in (sin, cos):
reference = deci.slow_integration(g.edges[0], g.edges[1], f)
eq(deci.integrate_boole1(pnts, f), reference)
eq(integrate_spectral_coarse(pnts, f), reference)
eq(integrate_spectral(pnts, f), reference)
g = Grid_1D.chebyshev(N, -1, +1)
for f in ((lambda x: x), (lambda x: x**3), (lambda x: exp(x))):
reference = deci.slow_integration(g.edges[0], g.edges[1], f)
eq(deci.integrate_boole1(g.verts, f), reference)
eq(integrate_chebyshev(g.verts, f), reference)
g = Grid_1D.chebyshev(N, -1, +1)
for f in ((lambda x: x), (lambda x: x**3), (lambda x: exp(x))):
reference = deci.slow_integration(g.edges_dual[0], g.edges_dual[1],
f)
x = concatenate(([-1], g.verts_dual, [+1]))
eq(deci.integrate_boole1(x, f), reference)
eq(integrate_chebyshev_dual(x, f), reference)
def test_integrals():
for N in (10, 11, 12, 13):
g = Grid_1D.periodic(N, 0, 2*pi)
pnts = concatenate([g.verts, [g.xmax]])
for f in (sin,
cos):
reference = deci.slow_integration(g.edges[0], g.edges[1], f)
eq( deci.integrate_boole1(pnts, f), reference )
eq( integrate_spectral_coarse(pnts, f), reference )
eq( integrate_spectral(pnts, f), reference )
g = Grid_1D.chebyshev(N, -1, +1)
for f in ((lambda x: x),
(lambda x: x**3),
(lambda x: exp(x))):
reference = deci.slow_integration(g.edges[0], g.edges[1], f)
eq( deci.integrate_boole1(g.verts, f), reference )
eq( integrate_chebyshev(g.verts, f), reference )
g = Grid_1D.chebyshev(N, -1, +1)
for f in ((lambda x: x),
(lambda x: x**3),
(lambda x: exp(x))):
reference = deci.slow_integration(g.edges_dual[0], g.edges_dual[1], f)
x = concatenate(([-1], g.verts_dual, [+1]))
eq( deci.integrate_boole1(x, f), reference )
eq( integrate_chebyshev_dual(x, f), reference )
def projection(cells):
P={(0, True) : lambda f: f(cells[0, True]),
(0, False) : lambda f: f(cells[0, False]),
(1, True) : lambda f: slow_integration(cells[1, True][0],
cells[1, True][1], f),
(1, False) : lambda f: slow_integration(cells[1, False][0],
cells[1, False][1], f),}
return P