def __test(d, m):
# Generate a random dictionary
X = numpy.random.randn(2 * d, m)
# Convert to diagonals
Xdiags = _cdl.columns_to_diags(X)
# Normalize
N_Xdiag = _cdl.normalize_dictionary(Xdiags)
# Convert back
N_X = _cdl.diags_to_columns(N_Xdiag)
# 1. verify unit norms
norms = numpy.sum(N_X**2, axis=0)**0.5
assert EQ(norms, numpy.ones_like(norms))
# 2. verify that directions are correct:
# projection onto the normalized basis should equal norm
# of the original basis
norms_orig = numpy.sum(X**2, axis=0)**0.5
projection = numpy.sum(X * N_X, axis=0)
assert EQ(norms_orig, projection)
pass
def __test(d, m):
# Build a random dictionary in diagonal form
X = numpy.random.randn(2 * d, m)
# Normalize the dictionary and convert back to columns
X_norm = _cdl.diags_to_columns(_cdl.normalize_dictionary(_cdl.columns_to_diags(X)))
# Rescale the normalized dictionary to have some inside, some outside
R = 2.0**numpy.linspace(-4, 4, m)
X_scale = X_norm * R
# Vectorize
V_scale = _cdl.columns_to_vector(X_scale)
# Project
V_proj = _cdl.proj_l2_ball(V_scale, m)
# Rearrange the projected matrix into columns
X_proj = _cdl.vector_to_columns(V_proj, m)
# Compute norms
X_scale_norms = numpy.sum(X_scale**2, axis=0)**0.5
X_proj_norms = numpy.sum(X_proj**2, axis=0)**0.5
Xdot = numpy.sum(X_scale * X_proj, axis=0)
for k in range(m):
# 1. verify norm is at most 1
# allow some fudge factor here for numerical instability
assert X_proj_norms[k] <= 1.0 + 1e-10
# 2. verify that points with R < 1 were untouched
assert R[k] > 1.0 or EQ(X_proj[:, k], X_scale[:, k])
# 3. verify that points with R >= 1.0 preserve direction
assert R[k] < 1.0 or EQ(Xdot[k], X_scale_norms[k])
pass
