def __test(w, h, m, n, rho, alpha, nonneg):
# Generate several frames of data
X_space = numpy.random.randn(h, w, m, n) * alpha / rho
# Compute shrinkage point-wise
Xshrunk = (X_space > alpha / rho) * (X_space - alpha / rho)
if not nonneg:
Xshrunk = Xshrunk + (X_space < -alpha / rho) * (X_space + alpha / rho)
# Compute 2d-dfts
X_freq = numpy.fft.fft2(X_space, axes=(0, 1))
# Reshape the data into columns
X_cols = X_freq.reshape((h * w * m, n), order='F')
# Split real and complex
X = _cdl.complex_to_real2(X_cols)
# First try without pre-allocation
Xout = _cdl.reg_l1_space(X, rho, alpha, width=w, height=h, nonneg=nonneg)
# Convert back to complex
Xout_cplx = _cdl.real2_to_complex(Xout)
# reshape back into four dimensions
Xout_freq = Xout_cplx.reshape((h, w, m, n), order='F')
# Invert the fourier transform
Xout_space = numpy.fft.ifft2(Xout_freq, axes=(0, 1)).real
assert EQ(Xout_space, Xshrunk)
# Now do it again with pre-allocation
Xout_pre = numpy.empty_like(X, order='A')
_cdl.reg_l1_space(X, rho, alpha, width=w, height=h, nonneg=nonneg, Xout=Xout_pre)
# Convert back to complex
Xout_cplx_pre = _cdl.real2_to_complex(Xout_pre)
# reshape back into four dimensions
Xout_freq_pre = Xout_cplx_pre.reshape((h, w, m, n), order='F')
# Invert the fourier transform
Xout_space_pre = numpy.fft.ifft2(Xout_freq_pre, axes=(0, 1)).real
assert EQ(Xout_space_pre, Xshrunk)
pass
def __test(d, n, rho, alpha):
# Generate a random matrix, scale by alpha/rho to encourage
# non-trivial solutions
X = numpy.random.randn(2 * d, n) * alpha / rho
# Compute magnitudes of complex values
X_cplx = _cdl.real2_to_complex(X)
X_abs = numpy.abs(X_cplx)
# Compute shrinkage on X
# x -> (1 - (alpha/rho) / |x|)_+ * x
S = X_abs.copy()
# Avoid numerical instability here
S[S < alpha / rho] = (alpha / rho)
S = (1 - (alpha/rho) / S)
# Tile it to get real and complex
S = numpy.tile(S, (2, 1))
# Compute shrinkage
Xshrunk = X * S
# First, test without pre-allocation
Xout = _cdl.reg_l1_complex(X, rho, alpha)
assert EQ(Xout, Xshrunk, rtol=1e-3, atol=1e-6)
# Now test with pre-allocation
Xout_pre = numpy.zeros_like(X, order='A')
_cdl.reg_l1_complex(X, rho, alpha, Xout_pre)
assert EQ(Xout_pre, Xshrunk, rtol=1e-3, atol=1e-6)
pass
def global_transform(X_batch, pad_data, encoder_, n_atoms, nonneg):
X_batch = X_batch.swapaxes(0, 1).swapaxes(1, 2)
h, w, n = X_batch.shape
# Fourier transform
X_new = _cdl.patches_to_vectors(X_batch, pad_data=pad_data)
# Encode
X_new = encoder_(X_new)
X_new = _cdl.real2_to_complex(X_new)
X_new = X_new.reshape((-1, X_new.shape[1] * n_atoms), order='F')
X_new = _cdl.complex_to_real2(X_new)
X_new = _cdl.vectors_to_patches(X_new, w, pad_data=pad_data, real=True)
X_new = X_new.reshape((X_new.shape[0], X_new.shape[1], n_atoms, n),
order='F')
X_new = X_new.swapaxes(3, 0).swapaxes(3, 2).swapaxes(3, 1)
if nonneg:
X_new = np.maximum(X_new, 0.0)
return X_new
def global_transform(X_batch, pad_data, encoder_, n_atoms, nonneg):
X_batch = X_batch.swapaxes(0, 1).swapaxes(1, 2)
h, w, n = X_batch.shape
# Fourier transform
X_new = _cdl.patches_to_vectors(X_batch, pad_data=pad_data)
# Encode
X_new = encoder_(X_new)
X_new = _cdl.real2_to_complex(X_new)
X_new = X_new.reshape( (-1, X_new.shape[1] * n_atoms), order='F')
X_new = _cdl.complex_to_real2(X_new)
X_new = _cdl.vectors_to_patches(X_new, w,
pad_data=pad_data,
real=True)
X_new = X_new.reshape( (X_new.shape[0], X_new.shape[1],
n_atoms, n),
order='F')
X_new = X_new.swapaxes(3, 0).swapaxes(3, 2).swapaxes(3, 1)
if nonneg:
X_new = np.maximum(X_new, 0.0)
return X_new
def __test(d, n):
X_real2 = numpy.random.randn(2 * d, n)
X_cplx = _cdl.real2_to_complex(X_real2)
# Verify shape match
assert (X_cplx.shape[0] * 2 == X_real2.shape[0] and
X_cplx.shape[1] == X_real2.shape[1])
# Verify numerical match
assert (EQ(X_cplx.real, X_real2[:d, :]) and
EQ(X_cplx.imag, X_real2[d:, :]))
pass
def __test(d, m, n, rho, alpha):
# Generate a random matrix 2*d*m-by-n matrix
# scale by alpha/rho to encourage non-trivial solutions
X = numpy.random.randn(2 * d * m, n) * alpha / rho
# Compute the properly shrunk matrix
X_cplx = _cdl.real2_to_complex(X)
S = (X_cplx.conj() * X_cplx).real
X_norms = numpy.zeros((m, n))
for k in range(m):
X_norms[k, :] = numpy.sum(S[k*d:(k+1)*d, :], axis=0)**0.5
Xshrunk = numpy.zeros_like(X, order='A')
for i in range(n):
for k in range(m):
if X_norms[k, i] > alpha / rho:
scale = 1.0 - alpha / (rho * X_norms[k, i])
else:
scale = 0.0
Xshrunk[(k*d):(k+1)*d, i] = scale * X[d*k:d*(k+1), i]
Xshrunk[d*(m+k):(m+k+1)*d, i] = scale * X[d*(m+k):d*(m+k+1), i]
pass
pass
# First, test without pre-allocation
Xout = _cdl.reg_l2_group(X, rho, alpha, m)
assert EQ(Xout, Xshrunk)
# Now test with pre-allocation
Xout_pre = numpy.zeros_like(X, order='A')
_cdl.reg_l2_group(X, rho, alpha, m, Xout_pre)
assert EQ(Xout_pre, Xshrunk)
pass
