def calc_coeffs_no_i(self, wave_base_j_qq_ZS_at_xs,
wave_dual_j_qq_ZS_at_xs, j, xs, i, balls_info, qq):
"Calculate alphas (w/ dual) and alpha-duals (w/ base)"
jj = [j + j0 for j0 in self.j0s]
jpow2 = np.array([2**j for j in jj])
zs_min, zs_max = self.wave.z_range('dual', (qq, jpow2, None),
self.minx, self.maxx)
omega_no_i = calc_omega(xs.shape[0] - 1, self.k)
resp = {}
vol_no_i = balls_no_i(balls_info, i)
for zs in itt.product(*all_zs_tensor(zs_min, zs_max)):
# below, we remove factor for i from sum << this has the biggest impact in performance
# also, we calculated alpha_zs previously and cen be further optimised w/ calc_coeffs
alpha_zs = omega_no_i * (
(wave_dual_j_qq_ZS_at_xs[zs] * vol_no_i).sum() -
wave_dual_j_qq_ZS_at_xs[zs][i] * vol_no_i[i])
resp[zs] = (alpha_zs, alpha_zs)
if self.wave.orthogonal:
# we are done
return resp
zs_min, zs_max = self.wave.z_range('base', (qq, jpow2, None),
self.minx, self.maxx)
for zs in itt.product(*all_zs_tensor(zs_min, zs_max)):
if zs not in resp:
continue
# below, we remove factor for i from sum << this has the biggest impact in performance
alpha_d_zs = omega_no_i * (
(wave_base_j_qq_ZS_at_xs[zs] * vol_no_i).sum() -
wave_base_j_qq_ZS_at_xs[zs][i] * vol_no_i[i])
resp[zs] = (resp[zs][0], alpha_d_zs)
return resp
def calc_coeffs(self, wave_base_j_qq_ZS_at_xs, wave_dual_j_qq_ZS_at_xs, j,
xs, balls_info, qq):
jj = [j + j0 for j0 in self.j0s]
jpow2 = np.array([2**j for j in jj])
zs_min, zs_max = self.wave.z_range('dual', (qq, jpow2, None),
self.minx, self.maxx)
omega = calc_omega(xs.shape[0], self.k)
resp = {}
balls = balls_info.sqrt_vol_k
for zs in itt.product(*all_zs_tensor(zs_min, zs_max)):
alpha_zs = omega * (wave_dual_j_qq_ZS_at_xs[zs] * balls).sum()
resp[zs] = (alpha_zs, alpha_zs)
if self.wave.orthogonal:
# we are done
return resp
zs_min, zs_max = self.wave.z_range('base', (qq, jpow2, None),
self.minx, self.maxx)
for zs in itt.product(*all_zs_tensor(zs_min, zs_max)):
if zs not in resp:
continue
alpha_d_zs = omega * (wave_base_j_qq_ZS_at_xs[zs] * balls).sum()
resp[zs] = (resp[zs][0], alpha_d_zs)
return resp
def test_z_range_2d(wave, what, ix):
"Test several facts with the range of z values"
# region is p1=(1/3,1/4) & p2=(3/4,2/3)
minx, maxx = np.array((1 / 3, 1 / 4)), np.array((3 / 4, 2 / 3))
qq, ss, zz = ix
zs_min, zs_max = wave.z_range(what, ix, minx, maxx)
one0 = np.array([1, 0])
one1 = np.array([0, 1])
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_min - one0)).support)
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_min - one1)).support)
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_max + one0)).support)
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_max + one1)).support)
for zz in itt.product(*all_zs_tensor(zs_min, zs_max)):
assert intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zz)).support)
def calc_funs(self, j, qq):
"""
:param j: int, resolution level
:param qq: tensor index in R^d
:return: (base funs, dual funs)
funs[zs] = base|dual wave _{j,zs}^{(qq)}
wave_base_j_qq_ZS, wave_dual_j_qq_ZS
"""
jj = [j + j0 for j0 in self.j0s]
jpow2 = np.array([2**j for j in jj])
funs = {}
for what in ['dual', 'base']:
zs_min, zs_max = self.wave.z_range(what, (qq, jpow2, None),
self.minx, self.maxx)
funs[what] = {}
for zs in itt.product(*all_zs_tensor(zs_min, zs_max)):
funs[what][zs] = self.wave.fun_ix(what, (qq, jpow2, zs))
return funs['base'], funs['dual']
def test_z1():
wave = WaveletTensorProduct(('db1', 'db1'))
what = 'dual'
ix = ((0, 0), (1, 2), (0, 0))
minx, maxx = np.array((0.2, 0.2)), np.array((0.4, 0.6))
qq, ss, zz = ix
zs_min, zs_max = wave.z_range(what, ix, minx, maxx)
print(zs_min, zs_max)
one0 = np.array([1, 0])
one1 = np.array([0, 1])
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_min - one0)).support)
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_min - one1)).support)
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_max + one0)).support)
assert not intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zs_max + one1)).support)
for zz in itt.product(*all_zs_tensor(zs_min, zs_max)):
assert intersect_2d((minx, maxx),
wave.fun_ix(what, (qq, ss, zz)).support)