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 set_codebook(self, D):
'''Clobber the existing codebook and encoder with a new one.'''
self.components_ = D
extra_args = {}
if self.penalty == 'l1_space':
extra_args['height'] = D.shape[1]
extra_args['width'] = D.shape[2]
extra_args['pad_data'] = self.pad_data
extra_args['nonneg'] = self.nonneg
D = D.swapaxes(0, 1).swapaxes(1, 2)
D = _cdl.patches_to_vectors(D, pad_data=self.pad_data)
D = _cdl.columns_to_diags(D)
self.fft_components_ = D
encoder, D, diagnostics = _cdl.learn_dictionary([],
self.n_atoms,
reg=self.penalty,
alpha=self.alpha,
max_steps=0,
verbose=False,
D=D,
**extra_args)
self.encoder_ = encoder
return self
def set_codebook(self, D):
'''Clobber the existing codebook and encoder with a new one.'''
self.components_ = D
extra_args = {}
if self.penalty == 'l1_space':
extra_args['height'] = D.shape[1]
extra_args['width'] = D.shape[2]
extra_args['pad_data'] = self.pad_data
extra_args['nonneg'] = self.nonneg
D = D.swapaxes(0, 1).swapaxes(1, 2)
D = _cdl.patches_to_vectors(D, pad_data=self.pad_data)
D = _cdl.columns_to_diags(D)
self.fft_components_ = D
encoder, D, diagnostics = _cdl.learn_dictionary(
[],
self.n_atoms,
reg = self.penalty,
alpha = self.alpha,
max_steps = 0,
verbose = False,
D = D,
**extra_args)
self.encoder_ = encoder
return self
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
def __test(d, m):
# Generate a random 2d-by-n matrix
X = numpy.random.randn(2 * d, m)
# Cut it in half to get the real and imag components
A = X[:d, :]
B = X[d:, :]
# Convert to its diagonal-block form
Q = _cdl.columns_to_diags(X)
for k in range(m):
for j in range(d):
# Verify A
assert (EQ(A[j, k], Q[j, k * d + j]) and
EQ(A[j, k], Q[d + j, m * d + k *d + j]))
# Verify B
assert (EQ(B[j, k], - Q[j, m * d + k * d + j]) and
EQ(B[j, k], Q[d + j, k *d + j]))
pass
pass
pass
def __test(d, m):
X = numpy.random.randn(2 * d, m)
Q = _cdl.columns_to_diags(X)
X_back = _cdl.diags_to_columns(Q)
assert EQ(X, X_back)
pass
