def setup(self, L, U, N, discontinuities=None, **kwargs):
super(GaussQuad, self).setup(L, U, N, **kwargs)
k = self.k
L = self.L
U = self.U
N = self.N
if k:
# compute quad weights and points
if self.qtype == 'GaussLegendre':
from scipy.special.orthogonal import p_roots
xi, w = p_roots(k)
elif self.qtype == 'ClenshawCurtis':
import nodes
xi = np.asarray(map(float, nodes.clenshaw_curtis_nodes(k-1)))
w = np.asarray(map(float, nodes.clenshaw_curtis_weights(k-1)))
# compute cell edges and adjust if necessary
edges = np.linspace(L, U, N+1)
jumps = getattr(self, 'discontinuities', discontinuities)
if self.adjust and jumps:
edges = adjust(edges, jumps)
# compute quad weights and points
x = np.zeros(k*N)
P = np.zeros(k*N)
for i in range(N):
dx2 = 0.5 * (edges[i+1] - edges[i])
for l in range(k):
x[i*k+l] = edges[i] + dx2 * (xi[l] + 1.0)
P[i*k+l] = dx2 * w[l]
self.P = P
self.x = x
else:
# compute quad weights and points
if self.qtype == 'GaussLegendre':
from scipy.special.orthogonal import p_roots
xi, w = p_roots(N)
elif self.qtype == 'ClenshawCurtis':
import nodes
xi = np.asarray(map(float, nodes.clenshaw_curtis_nodes(N-1)))
w = np.asarray(map(float, nodes.clenshaw_curtis_weights(N-1)))
self.P = w * (U - L)/2.0
self.x = (U + L)/2 + (U - L)/2 * xi
def __init__(self, k=None, qtype='GaussLegendre'):
if k:
if qtype == 'GaussLegendre':
name = 'GENClarkGL(' + str(k) + ')'
from scipy.special.orthogonal import p_roots
self.xi, self.w = p_roots(k)
elif qtype == 'ClenshawCurtis':
name = 'GENClarkCC(' + str(k) + ')'
import nodes
self.xi = np.asarray(map(float, nodes.clenshaw_curtis_nodes(k-1)))
self.w = np.asarray(map(float, nodes.clenshaw_curtis_weights(k-1)))
else:
name = 'GENClarkQP'
self.k = k
self.name = name