def T(self,x,out=None):
"""Computes the antiderivative of *x* with mean zero."""
x = x.core()
scratch = self.scratch
if out is None:
out = NumpyVector(np.ndarray(x.shape))
scratch[0] = 0
for k in range(self.N):
scratch[k+1] = scratch[k] + self.h*x[k]
y=out.core()
for k in range(self.N):
y[k] = 0.5*(scratch[k] + scratch[k+1])
ybar = sum(y)/self.N
y -= ybar
return out
parser.add_option("-a","--algorithm",type='choice',choices=['sd','nlcg','ign'],default='nlcg',
help="algorithm to use [sd,nlcg,ign]: sd=steepest descent, nlcg=nonlinear conjugate gradient (default), ign=incomplete Gauss-Newton")
parser.add_option("-t","--test_linearization",action='store_true',
help='test linearization and adjoint (and exit)')
parser.add_option("-d","--discrepancy_fraction",type='float',default=1.0,metavar="D",
help='remove the fraction D of the actual error (D<1 to overfit and D>1 to underfit)')
(options, args) = parser.parse_args()
N = options.node_count
Linf_error = options.l_infty_noise
forward_problem = CoeffForwardProblem(N)
x = forward_problem.x
beta=NumpyVector((N,))
beta.core()[:] = np.sin(x*2*pi)
if options.test_linearization:
h = siple.rand.random_vector(beta,scale=1.)
(Fp1,Fp2) = forward_problem.testT(beta,h,t=1e-6)
dF = Fp1.copy(); dF -= Fp2
print 'Relative T error: %g' % (dF.norm('linf')/Fp1.norm('linf'))
g = siple.rand.random_vector(beta,scale=1.)
(ip1,ip2) = forward_problem.testTStar(beta,h,g)
print 'Relative T* error: %g' % (abs(ip1-ip2)/abs(ip1))
else: