"""
fvals = f(self.nodes)
self.fvals = fvals
if self.factor:
self.ivals = self.factor * self.fvals
else:
self.ivals = self.fvals
result = 0.
for rule, start in zip(self.rules, self.starts):
result += rule.quad(self.ivals[start:start+rule.npts])
return result
if __name__ == '__main__':
from ccf import ClenshawCurtis, Fejer1
cc = ClenshawCurtis(6, 3, 5)
f1 = Fejer1(5, 5, 8)
# 4-part composite rule over [0, 10] with CC and Fejer1 pieces:
cq = CompositeQuad(ClenshawCurtis(4, 0, 3),
(cc.nodes, cc.wts),
(f1.l, f1.u, f1.nodes, f1.wts),
Fejer1(7, 8., 10) )
def f(x):
"""
Integrates to 10 over [0,10].
"""
try:
return ones(len(x), float)
except TypeError:
return 1.
Rolling power law.
"""
pl1 = -beta + .5
return (x/mid)**pl1 / (1. + x/mid)
def roll_map(y, beta=beta, range=range, mid=mid):
"""
Rolling exponential, transformed.
"""
x = x_y(y)
return roll(x) * x**beta
l, u = 1., range
y_l, y_u = y_x(l), y_x(u)
for n in [5, 10, 15, 25, 50, 100, 200, 500]:
ccx = ClenshawCurtis(n, l, u)
ccy = ClenshawCurtis(n, y_l, y_u)
xq = ccx.quad(roll)
yq = ccy.quad(roll_map)
print n, xq, yq
loglog(ccx.nodes, roll(ccx.nodes), 'b.')
cc = ClenshawCurtis(25, l, u)
loglog(cc.nodes, roll(cc.nodes), 'r.')
xlabel('$x$')
ylabel('$f(x)$')
figure()
loglog(-ccy.nodes, roll_map(ccy.nodes), 'g.')
cc = ClenshawCurtis(25, y_l, y_u)
loglog(-cc.nodes, roll_map(cc.nodes), 'r.')
xlabel('$-y$')
"""
Rolling exponential, -.6 at 1, -.4 at 10
"""
return exp((alpha + .2*(x-.5*range)/range)*x)
def rexp_map(y, alpha=alpha, range=range):
"""
Rolling exponential, transformed.
"""
x = x_y(y)
return exp((alpha + .2*(x-.5*range)/range)*x) / exp(alpha*x)
l, u = 1., range
y_l, y_u = y_x(l), y_x(u)
for n in [5, 10, 15, 25, 50, 100, 200, 500]:
ccx = ClenshawCurtis(n, l, u)
ccy = ClenshawCurtis(n, y_l, y_u)
xq = ccx.quad(rexp)
yq = ccy.quad(rexp_map)
print n, xq, yq
semilogy(ccx.nodes, rexp(ccx.nodes), 'b.')
xlabel('$x$')
ylabel('$f(x)$')
figure()
semilogy(ccy.nodes, rexp_map(ccy.nodes), 'g.')
cc = ClenshawCurtis(25, y_l, y_u)
semilogy(cc.nodes, rexp_map(cc.nodes), 'r.')
xlabel('$y$')
ylabel(r'$f(x)/\exp(\alpha x)$')
show()
"""
fvals = f(self.nodes)
self.fvals = fvals
if self.factor:
self.ivals = self.factor * self.fvals
else:
self.ivals = self.fvals
result = 0.
for rule, start in zip(self.rules, self.starts):
result += rule.quad(self.ivals[start:start + rule.npts])
return result
if __name__ == '__main__':
from ccf import ClenshawCurtis, Fejer1
cc = ClenshawCurtis(6, 3, 5)
f1 = Fejer1(5, 5, 8)
# 4-part composite rule over [0, 10] with CC and Fejer1 pieces:
cq = CompositeQuad(ClenshawCurtis(4, 0, 3), (cc.nodes, cc.wts),
(f1.l, f1.u, f1.nodes, f1.wts), Fejer1(7, 8., 10))
def f(x):
"""
Integrates to 10 over [0,10].
"""
try:
return ones(len(x), float)
except TypeError:
return 1.
def g(x):
