def adjointness_error(op, its=100):
"""Check adjointness of op.A and op.As for 'its' instances of random data.
For random unit-normed x and y, this finds the error in the adjoint
identity <Ax, y> == <x, A*y>:
err = abs( vdot(A(x), y) - vdot(x, Astar(y)) ).
The type and shape of the input to A are specified by inshape and indtype.
Returns a vector of the error magnitudes.
"""
inshape = op.inshape
indtype = op.indtype
outshape = op.outshape
outdtype = op.outdtype
x = get_random_normal(inshape, indtype)
errs = np.zeros(its, dtype=indtype)
for k in xrange(its):
x = get_random_normal(inshape, indtype)
x = x/np.linalg.norm(x)
y = get_random_normal(outshape, outdtype)
y = y/np.linalg.norm(y)
ip_A = np.vdot(op.A(x), y)
ip_Astar = np.vdot(x, op.As(y))
errs[k] = np.abs(ip_A - ip_Astar)
return errs
def opnorm(op, reltol=1e-8, abstol=1e-6, maxits=100, printrate=None):
"""Estimate the l2-induced operator norm: sup_v ||A(v)||/||v|| for v != 0.
Uses the power iteration method to estimate the operator norm of
op.A and op.As.
The type and shape of the input to A are specified by inshape and indtype.
Returns a tuple: (norm of A, norm of As, vector inducing maximum scaling).
"""
inshape = op.inshape
indtype = op.indtype
v0 = get_random_normal(inshape, indtype)
v = v0/np.linalg.norm(v0)
norm_f0 = 1
norm_a0 = 1
for k in xrange(maxits):
Av = op.A(v)
norm_f = np.linalg.norm(Av)
w = Av/norm_f
Asw = op.As(w)
norm_a = np.linalg.norm(Asw)
v = Asw/norm_a
delta_f = abs(norm_f - norm_f0)
delta_a = abs(norm_a - norm_a0)
if printrate is not None and (k % printrate) == 0:
s = 'Iteration {0}, forward norm: {1}, adjoint norm: {2}'
s = s.format(k, norm_f, norm_a)
print(s)
if (delta_f < abstol + reltol*max(norm_f, norm_f0)
and delta_a < abstol + reltol*max(norm_a, norm_a0)):
break
norm_f0 = norm_f
norm_a0 = norm_a
return norm_f, norm_a, v
