def spline_matrix(x, xi, yi, bc_type="not-a-knot"):
"""calculate spline interpolation"""
xi_m = spline_xi_matrix(xi) # (N_range, 4, N_yi)
x_m = spline_x_matrix(x, xi) # (..., N_range, 4)
x_m = tf.expand_dims(x_m, axis=-1)
m = tf.reduce_sum(xi_m * x_m, axis=[-3, -2])
return tf.reduce_sum(tf.cast(m, yi.dtype) * yi, axis=-1)
def interp(self, m):
# q = data_extra[self.outs[0]]["|q|"]
# a = self.a()
p = self.point_value()
zeros = tf.zeros_like(m)
ones = tf.ones_like(m)
def poly_i(i, xi):
tmp = zeros
for j in range(i - 1, i + 1):
if j < 0 or j > self.interp_N - 1:
continue
r = ones
for k in range(j, j + 2):
if k == i:
continue
r = r * (m - xi[k]) / (xi[i] - xi[k])
r = tf.where((m >= xi[j]) & (m < xi[j + 1]), r, zeros)
tmp = tmp + r
return tmp
h = tf.stack(
[poly_i(i, self.points) for i in range(1, self.interp_N - 1)],
axis=-1,
)
h = tf.stop_gradient(h)
p_r = tf.math.real(p)
p_i = tf.math.imag(p)
ret_r = tf.reduce_sum(h * p_r, axis=-1)
ret_i = tf.reduce_sum(h * p_i, axis=-1)
return tf.complex(ret_r, ret_i)
def interp(self, m):
zeros = tf.zeros_like(m)
p = self.point_value()
p_r = tf.math.real(p)
p_i = tf.math.imag(p)
xi_m = self.h_matrix
x_m = spline_x_matrix(m, self.points)
x_m = tf.expand_dims(x_m, axis=-1)
m_xi = tf.reduce_sum(xi_m * x_m, axis=[-3, -2])
m_xi = tf.stop_gradient(m_xi)
ret_r = tf.reduce_sum(tf.cast(m_xi, p_r.dtype) * p_r, axis=-1)
ret_i = tf.reduce_sum(tf.cast(m_xi, p_i.dtype) * p_i, axis=-1)
return tf.complex(ret_r, ret_i)
def get_amp(self, data, data_c=None, **kwargs):
m = data["m"]
mass1 = self.mass1()
mass2 = self.mass2()
width1 = self.width1()
width2 = self.width2()
q = data_c["|q|"]
mdaughter1 = kwargs["all_data"]["particle"][self.decay[0].outs[0]]["m"]
mdaughter2 = kwargs["all_data"]["particle"][self.decay[0].outs[1]]["m"]
q1 = get_relative_p(mass1, mdaughter1, mdaughter2)
q2 = get_relative_p(mass2, mdaughter1, mdaughter2)
mlist = tf.stack([mass1, mass2])
wlist = tf.stack([width1, width2])
qlist = tf.stack([q1, q2])
Klist = []
for mi, wi, qi in zip(mlist, wlist, qlist):
rw = Gamma(m, wi, q, qi, self.bw_l, mi, self.d)
Klist.append(mi * rw / (mi**2 - m**2))
KK = tf.reduce_sum(Klist, axis=0)
KK += self.alpha()
beta_term = self.get_beta(
m=m,
mlist=mlist,
wlist=wlist,
q=q,
qlist=qlist,
Klist=Klist,
**kwargs,
)
MM = tf.complex(np.float64(1), -KK)
MM = beta_term / MM
return MM + self.KNR()
def do_spline_hmatrix(h_matrix, y, m, idx):
ai, bi, ci, di = tf.unstack(tf.reduce_sum(h_matrix * y, axis=-1), axis=0)
a, b, c, d = (
tf.gather(ai, idx),
tf.gather(bi, idx),
tf.gather(ci, idx),
tf.gather(di, idx),
)
ret = a + m * (b + m * (c + d * m))
return ret
def interp(self, m):
p = self.point_value()
ones = tf.ones_like(m)
zeros = tf.zeros_like(m)
def add_f(x, bl, br):
return tf.where((x > bl) & (x <= br), ones, zeros)
x_bin = tf.stack(
[
add_f(
m,
(self.points[i] + self.points[i + 1]) / 2,
(self.points[i + 1] + self.points[i + 2]) / 2,
) for i in range(self.interp_N - 2)
],
axis=-1,
)
p_r = tf.math.real(p)
p_i = tf.math.imag(p)
x_bin = tf.stop_gradient(x_bin)
ret_r = tf.reduce_sum(x_bin * p_r, axis=-1)
ret_i = tf.reduce_sum(x_bin * p_i, axis=-1)
return tf.complex(ret_r, ret_i)
def interp(self, m):
# q = data_extra[self.outs[0]]["|q|"]
# a = self.a()
zeros = tf.zeros_like(m)
p = tf.abs(self.point_value())
def add_f(x, bl, br, pl, pr):
return tf.where(
(x > bl) & (x <= br),
(x - bl) / (br - bl) * (pr - pl) + pl,
zeros,
)
ret = [
add_f(m, self.points[i], self.points[i + 1], p[i], p[i + 1])
for i in range(self.interp_N - 1)
]
return tf.complex(tf.reduce_sum(ret, axis=0), zeros)
def interp(self, m):
zeros = tf.zeros_like(m)
p = self.point_value()
xs = []
def poly_i(i):
x = 1.0
for j in range(self.interp_N):
if i == j:
continue
x = (x * (m - self.points[j]) /
(self.points[i] - self.points[j]))
return x
xs = tf.stack([poly_i(i) for i in range(self.interp_N)], axis=-1)
zeros = tf.zeros_like(xs)
xs = tf.complex(xs, zeros)
ret = tf.reduce_sum(xs[:, 1:-1] * p, axis=-1)
return ret