def __test(d, m):
X = numpy.random.randn(2 * d, m)
V = _cdl.columns_to_vector(X)
X_back = _cdl.vector_to_columns(V, m)
assert EQ(X, X_back)
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