def unit_variance_mlpg_matrix(windows, T):
"""Compute MLPG matrix assuming input is normalized to have unit-variances.
Let :math:`\mu` is the input mean sequence (``num_windows*T x static_dim``),
:math:`W` is a window matrix ``(T x num_windows*T)``, assuming input is
normalized to have unit-variances, MLPG can be written as follows:
.. math::
y = R \mu
where
.. math::
R = (W^{T} W)^{-1} W^{T}
Here we call :math:`R` as the MLPG matrix.
Args:
windows: (list): List of windows.
T (int): Number of frames.
Returns:
numpy.ndarray: MLPG matrix (``T x nun_windows*T``).
See also:
:func:`nnmnkwii.autograd.UnitVarianceMLPG`,
:func:`nnmnkwii.paramgen.mlpg`.
Examples:
>>> from nnmnkwii import paramgen as G
>>> import numpy as np
>>> windows = [
... (0, 0, np.array([1.0])),
... (1, 1, np.array([-0.5, 0.0, 0.5])),
... (1, 1, np.array([1.0, -2.0, 1.0])),
... ]
>>> G.unit_variance_mlpg_matrix(windows, 3)
array([[ 2.73835927e-01, 1.95121944e-01, 9.20177400e-02,
9.75609720e-02, -9.09090936e-02, -9.75609720e-02,
-3.52549881e-01, -2.43902430e-02, 1.10864742e-02],
[ 1.95121944e-01, 3.41463417e-01, 1.95121944e-01,
1.70731708e-01, -5.55111512e-17, -1.70731708e-01,
-4.87804860e-02, -2.92682916e-01, -4.87804860e-02],
[ 9.20177400e-02, 1.95121944e-01, 2.73835927e-01,
9.75609720e-02, 9.09090936e-02, -9.75609720e-02,
1.10864742e-02, -2.43902430e-02, -3.52549881e-01]], dtype=float32)
"""
win_mats = build_win_mats(windows, T)
sdw = np.max([win_mat.l + win_mat.u for win_mat in win_mats])
P = bm.zeros(sdw, sdw, T)
for win_index, win_mat in enumerate(win_mats):
bm.dot_mm_plus_equals(win_mat.T, win_mat, target_bm=P)
chol_bm = bla.cholesky(P, lower=True)
Pinv = cholesky_inv_banded(chol_bm.full(), width=chol_bm.l + chol_bm.u + 1)
cocatenated_window = full_window_mat(win_mats, T)
return Pinv.dot(cocatenated_window.T).astype(np.float32)
def gen_chol_factor_BandMat(size, depth=None, contrib_rank=2, transposed=None):
"""Generates a random Cholesky factor BandMat.
This works by generating a random positive definite matrix and then
computing its Cholesky factor, since using a random matrix as a Cholesky
factor seems to often lead to ill-conditioned matrices.
"""
if transposed is None:
transposed = rand_bool()
mat_bm = gen_pos_def_BandMat(size, depth=depth, contrib_rank=contrib_rank)
chol_bm = bla.cholesky(mat_bm, lower=rand_bool())
if transposed:
chol_bm = chol_bm.T
assert chol_bm.l == 0 or chol_bm.u == 0
assert chol_bm.l + chol_bm.u == mat_bm.l
randomize_extra_entries_bm(chol_bm)
return chol_bm
def gen_chol_factor_BandMat(size, depth=None, contrib_rank=2, transposed=None):
"""Generates a random Cholesky factor BandMat.
This works by generating a random positive definite matrix and then
computing its Cholesky factor, since using a random matrix as a Cholesky
factor seems to often lead to ill-conditioned matrices.
"""
if transposed is None:
transposed = rand_bool()
mat_bm = gen_pos_def_BandMat(size, depth=depth, contrib_rank=contrib_rank)
chol_bm = bla.cholesky(mat_bm, lower=rand_bool())
if transposed:
chol_bm = chol_bm.T
assert chol_bm.l == 0 or chol_bm.u == 0
assert chol_bm.l + chol_bm.u == mat_bm.l
randomize_extra_entries_bm(chol_bm)
return chol_bm
def test_cholesky(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mat_bm = gen_pos_def_BandMat(size)
depth = mat_bm.l
lower = rand_bool()
alternative = rand_bool()
chol_bm = bla.cholesky(mat_bm, lower=lower,
alternative=alternative)
assert chol_bm.l == (depth if lower else 0)
assert chol_bm.u == (0 if lower else depth)
assert not np.may_share_memory(chol_bm.data, mat_bm.data)
if lower != alternative:
mat_bm_again = bm.dot_mm(chol_bm, chol_bm.T)
else:
mat_bm_again = bm.dot_mm(chol_bm.T, chol_bm)
assert_allclose(mat_bm_again.full(), mat_bm.full())
def test_cholesky(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mat_bm = gen_pos_def_BandMat(size)
depth = mat_bm.l
lower = rand_bool()
alternative = rand_bool()
chol_bm = bla.cholesky(mat_bm, lower=lower,
alternative=alternative)
assert chol_bm.l == (depth if lower else 0)
assert chol_bm.u == (0 if lower else depth)
assert not np.may_share_memory(chol_bm.data, mat_bm.data)
if lower != alternative:
mat_bm_again = bm.dot_mm(chol_bm, chol_bm.T)
else:
mat_bm_again = bm.dot_mm(chol_bm.T, chol_bm)
assert_allclose(mat_bm_again.full(), mat_bm.full())
