def make(cls, n, xmin=0, xmax=pi):
assert xmax > xmin
N = n
pnts = linspace(xmin, xmax, num=n)
lenx = abs(xmax - xmin)
delta = diff(pnts)
verts = pnts
verts_dual = verts[:-1] + 0.5*delta
edges = (pnts[:-1], pnts[1:])
tmp = concatenate(([xmin], verts_dual, [xmax]))
delta_dual = diff(tmp)
edges_dual = (tmp[:-1], tmp[1:])
N = {(0, True) : n,
(1, True) : n-1,
(0, False) : n-1,
(1, False) : n}
Delta = {True : delta,
False : delta_dual}
cells = {(0, True) : verts,
(1, True) : edges,
(0, False) : verts_dual,
(1, False) : edges_dual,}
B={(0, True) : lambda i: lambda x: sp.kappa0(n, i, x),
(1, True) : lambda i: lambda x: sp.kappa1_symm(n, i, x),
(0, False) : lambda i: lambda x: sp.kappad0(n, i, x),
(1, False) : lambda i: lambda x: sp.kappad1_symm(n, i, x),}
D={(0, True) : lambda f: diff(f),
(1, True) : lambda f: 0,
(0, False) : lambda f: diff(concatenate(([0], f, [0]))),
(1, False) : lambda f: 0,}
H={(0, True) : H0_regular,
(1, True) : H1_regular,
(0, False) : H0d_regular,
(1, False) : H1d_regular,}
refine=dec.common.wrap_refine(to_refine, from_refine)
return cls(n=n,
xmin=xmin,
xmax=xmax,
delta=Delta,
N=N,
cells=cells,
dec=bunch(P=dec.common.projection(cells),
B=B,
D=D,
H=H,
W=None,
C=None),
refine=refine)
def make(cls, n, xmin=-1, xmax=+1):
# 2n-1 points: n primal, n-1 dual
x = sin(linspace(-pi/2, pi/2, 2*n-1))
pnts = 0.5*(xmin*(1-x) + xmax*(1+x))
verts = pnts[::2]
delta = diff(verts)
edges = (verts[:-1], verts[1:])
verts_dual = pnts[1::2]
tmp = concatenate(([pnts[0]], verts_dual, [pnts[-1]]))
delta_dual = diff(tmp)
edges_dual = (tmp[:-1], tmp[1:])
N = {(0, True) : n,
(1, True) : n-1,
(0, False) : n-1,
(1, False) : n}
Delta = {True : delta,
False : delta_dual}
cells = {(0, True) : verts,
(1, True) : edges,
(0, False) : verts_dual,
(1, False) : edges_dual,}
B={(0, True) : lambda i: lambda x: sp.psi0(n, i, x),
(1, True) : lambda i: lambda x: sp.psi1(n, i, x),
(0, False) : lambda i: lambda x: sp.psid0(n, i, x),
(1, False) : lambda i: lambda x: sp.psid1(n, i, x),}
D={(0, True) : lambda f: diff(f),
(1, True) : lambda f: 0,
(0, False) : lambda f: diff(concatenate(([0], f, [0]))),
(1, False) : lambda f: 0,}
H={(0, True) : H0_cheb,
(1, True) : H1_cheb,
(0, False) : H0d_cheb,
(1, False) : H1d_cheb,}
refine=dec.common.wrap_refine(to_refine, from_refine)
return cls(n=n,
xmin=xmin,
xmax=xmax,
delta=Delta,
N=N,
cells=cells,
dec=bunch(P=dec.common.projection(cells),
B=B,
D=D,
H=H,
W=dec.common.wedge(refine),
C=dec.common.contraction(refine)),
refine=refine)
def __init__(self, *coords):
self.coords = coords
self.dimension = len(coords)
if len(coords) == 1:
x, = coords
dec = bunch(D=derivative_1d(x),
H=hodge_star_1d(),
W=wedge_1d(),
C=contraction_1d(),
)
elif len(coords) == 2:
x, y = coords
dec = bunch(D=derivative_2d(x, y),
H=hodge_star_2d(),
W=wedge_2d(),
C=contraction_2d(),
)
else:
raise NotImplementedError
self.dec = dec
def __init__(self, *coords):
self.coords = coords
self.dimension = len(coords)
if len(coords) == 1:
x, = coords
dec = bunch(
D=derivative_1d(x),
H=hodge_star_1d(),
W=wedge_1d(),
C=contraction_1d(),
)
elif len(coords) == 2:
x, y = coords
dec = bunch(
D=derivative_2d(x, y),
H=hodge_star_2d(),
W=wedge_2d(),
C=contraction_2d(),
)
else:
raise NotImplementedError
self.dec = dec
def wrap_refine(to_refine, from_refine):
T0, T1, T0d, T1d = to_refine()
U0, U1, U0d, U1d = from_refine()
T = {(0, True): T0,
(1, True): T1,
(0, False): T0d,
(1, False): T1d,}
U = {(0, True): U0,
(1, True): U1,
(0, False): U0d,
(1, False): U1d,}
return bunch(T=T, U=U)
def make(cls, n, xmin=0, xmax=2 * pi):
pnts = linspace(xmin, xmax, num=(n + 1))
lenx = abs(xmax - xmin)
delta = diff(pnts)
verts = pnts[:-1]
edges = (pnts[:-1], pnts[1:])
verts_dual = verts + 0.5 * delta
edges_dual = (roll(verts_dual, shift=1), verts_dual)
edges_dual[0][0] -= lenx
delta_dual = delta
N = {(0, True): n, (1, True): n, (0, False): n, (1, False): n}
Delta = {True: delta, False: delta_dual}
cells = {
(0, True): verts,
(1, True): edges,
(0, False): verts_dual,
(1, False): edges_dual,
}
B = {
(0, True): lambda i: lambda x: sp.phi0(n, i, x),
(1, True): lambda i: lambda x: sp.phi1(n, i, x),
(0, False): lambda i: lambda x: sp.phid0(n, i, x),
(1, False): lambda i: lambda x: sp.phid1(n, i, x),
}
D = {
(0, True): lambda f: roll(f, shift=-1) - f,
(1, True): lambda f: 0,
(0, False): lambda f: roll(D[0, True](f), shift=+1),
(1, False): lambda f: 0,
}
H = {
(0, True): lambda x: real(sp.H(x)),
(1, True): lambda x: real(sp.Hinv(x)),
(0, False): lambda x: H[0, True](x),
(1, False): lambda x: H[1, True](x),
}
refine = dec.common.wrap_refine(to_refine, from_refine)
return cls(n=n,
xmin=xmin,
xmax=xmax,
delta=Delta,
N=N,
cells=cells,
dec=bunch(P=dec.common.projection(cells),
B=B,
D=D,
H=H,
W=dec.common.wedge(refine),
C=dec.common.contraction(refine)),
refine=refine)
def make(cls, n, xmin=-1, xmax=+1):
# 2n-1 points: n primal, n-1 dual
x = sin(linspace(-pi / 2, pi / 2, 2 * n - 1))
pnts = 0.5 * (xmin * (1 - x) + xmax * (1 + x))
verts = pnts[::2]
delta = diff(verts)
edges = (verts[:-1], verts[1:])
verts_dual = pnts[1::2]
tmp = concatenate(([pnts[0]], verts_dual, [pnts[-1]]))
delta_dual = diff(tmp)
edges_dual = (tmp[:-1], tmp[1:])
N = {(0, True): n, (1, True): n - 1, (0, False): n - 1, (1, False): n}
Delta = {True: delta, False: delta_dual}
cells = {
(0, True): verts,
(1, True): edges,
(0, False): verts_dual,
(1, False): edges_dual,
}
B = {
(0, True): lambda i: lambda x: sp.psi0(n, i, x),
(1, True): lambda i: lambda x: sp.psi1(n, i, x),
(0, False): lambda i: lambda x: sp.psid0(n, i, x),
(1, False): lambda i: lambda x: sp.psid1(n, i, x),
}
D = {
(0, True): lambda f: diff(f),
(1, True): lambda f: 0,
(0, False): lambda f: diff(concatenate(([0], f, [0]))),
(1, False): lambda f: 0,
}
H = {
(0, True): H0_cheb,
(1, True): H1_cheb,
(0, False): H0d_cheb,
(1, False): H1d_cheb,
}
refine = dec.common.wrap_refine(to_refine, from_refine)
return cls(n=n,
xmin=xmin,
xmax=xmax,
delta=Delta,
N=N,
cells=cells,
dec=bunch(P=dec.common.projection(cells),
B=B,
D=D,
H=H,
W=dec.common.wedge(refine),
C=dec.common.contraction(refine)),
refine=refine)
def make(cls, n, xmin=0, xmax=pi):
assert xmax > xmin
N = n
pnts = linspace(xmin, xmax, num=n)
lenx = abs(xmax - xmin)
delta = diff(pnts)
verts = pnts
verts_dual = verts[:-1] + 0.5 * delta
edges = (pnts[:-1], pnts[1:])
tmp = concatenate(([xmin], verts_dual, [xmax]))
delta_dual = diff(tmp)
edges_dual = (tmp[:-1], tmp[1:])
N = {(0, True): n, (1, True): n - 1, (0, False): n - 1, (1, False): n}
Delta = {True: delta, False: delta_dual}
cells = {
(0, True): verts,
(1, True): edges,
(0, False): verts_dual,
(1, False): edges_dual,
}
B = {
(0, True): lambda i: lambda x: sp.kappa0(n, i, x),
(1, True): lambda i: lambda x: sp.kappa1_symm(n, i, x),
(0, False): lambda i: lambda x: sp.kappad0(n, i, x),
(1, False): lambda i: lambda x: sp.kappad1_symm(n, i, x),
}
D = {
(0, True): lambda f: diff(f),
(1, True): lambda f: 0,
(0, False): lambda f: diff(concatenate(([0], f, [0]))),
(1, False): lambda f: 0,
}
H = {
(0, True): H0_regular,
(1, True): H1_regular,
(0, False): H0d_regular,
(1, False): H1d_regular,
}
refine = dec.common.wrap_refine(to_refine, from_refine)
return cls(n=n,
xmin=xmin,
xmax=xmax,
delta=Delta,
N=N,
cells=cells,
dec=bunch(P=dec.common.projection(cells),
B=B,
D=D,
H=H,
W=None,
C=None),
refine=refine)
