def xy_theta_xy_theta(lib, x1, y1, theta1, x2, y2, theta2):
return xy_z_xy_z(
lib,
x.xy(lib, x1, y1),
y.xy(lib, x1, y1),
z.xy_theta(lib, x1, y1, theta1),
x.xy(lib, x2, y2),
y.xy(lib, x2, y2),
z.xy_theta(lib, x2, y2, theta2),
)
def xy_theta_t(lib, beta, x, y, theta, t):
gam = (1 - beta**2)**-0.5
bgam = beta * gam
exx = x
why = y
zee = z.xy_theta(lib, x, y, theta)
tee = t
return (exx, gam * why + bgam * tee, zee, bgam * why + gam * tee)
def xy_theta_t(lib, gamma, x, y, theta, t):
gam = lib.absolute(gamma)
bgam = lib.copysign(lib.sqrt(gam**2 - 1), gamma)
exx = x
why = y
zee = z.xy_theta(lib, x, y, theta)
tee = t
return (exx, gam * why + bgam * tee, zee, bgam * why + gam * tee)
def xy_theta_tau(lib, beta, x, y, theta, tau):
gam = (1 - beta**2)**-0.5
bgam = beta * gam
exx = x
why = y
zee = z.xy_theta(lib, x, y, theta)
tee = t.xy_theta_tau(lib, x, y, theta, tau)
return (gam * exx + bgam * tee, why, zee, tau)
def xy_theta_tau(lib, gamma, x, y, theta, tau):
gam = lib.absolute(gamma)
bgam = lib.copysign(lib.sqrt(gam ** 2 - 1), gamma)
exx = x
why = y
zee = z.xy_theta(lib, x, y, theta)
tee = t.xy_theta_tau(lib, x, y, theta, tau)
return (gam * exx + bgam * tee, why, zee, tau)
def rhophi_z_xy_theta(lib, rho1, phi1, z1, x2, y2, theta2):
return xy_z_xy_z(
lib,
x.rhophi(lib, rho1, phi1),
y.rhophi(lib, rho1, phi1),
z1,
x2,
y2,
z.xy_theta(lib, x2, y2, theta2),
)
def rhophi_eta_xy_theta(lib, rho1, phi1, eta1, x2, y2, theta2):
return xy_z_xy_z(
lib,
x.rhophi(lib, rho1, phi1),
y.rhophi(lib, rho1, phi1),
z.rhophi_eta(lib, rho1, phi1, eta1),
x.xy(lib, x2, y2),
y.xy(lib, x2, y2),
z.xy_theta(lib, x2, y2, theta2),
)
def xy_theta_rhophi_eta(lib, x1, y1, theta1, rho2, phi2, eta2):
return xy_z_xy_z(
lib,
x.xy(lib, x1, y1),
y.xy(lib, x1, y1),
z.xy_theta(lib, x1, y1, theta1),
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_eta(lib, rho2, phi2, eta2),
)
def xy_theta_rhophi_z(lib, x1, y1, theta1, rho2, phi2, z2):
return xy_z_xy_z(
lib,
x1,
y1,
z.xy_theta(lib, x1, y1, theta1),
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z2,
)
def xy_theta_xy_eta(lib, x1, y1, theta1, x2, y2, eta2):
return xy_z_xy_z(
lib,
x1,
y1,
z.xy_theta(lib, x1, y1, theta1),
x2,
y2,
z.xy_eta(lib, x2, y2, eta2),
)
def rhophi_z_xy_theta(lib, rtol, atol, equal_nan, rho1, phi1, z1, x2, y2, theta2):
return xy_z_xy_z(
lib,
rtol,
atol,
equal_nan,
x.rhophi(lib, rho1, phi1),
y.rhophi(lib, rho1, phi1),
z1,
x2,
y2,
z.xy_theta(lib, x2, y2, theta2),
)
def cartesian_tau_xy_theta_t(lib, x1, y1, z1, tau1, x2, y2, theta2, t2):
energy = t2
energy2 = energy**2
mass2 = energy2 - mag2.xy_theta(lib, x2, y2, theta2)
mass = lib.sqrt(mass2) # NaN for spacelike boosts propagates everywhere!
return cartesian_tau(
lib,
x1,
y1,
z1,
tau1,
energy,
mass,
mass2,
x2,
y2,
z.xy_theta(lib, x2, y2, theta2),
)
def cartesian_tau_xy_theta_tau(lib, x1, y1, z1, tau1, x2, y2, theta2, tau2):
mass = tau2
mass2 = mass**2
energy2 = mass2 + mag2.xy_theta(lib, x2, y2, theta2)
energy = lib.sqrt(
energy2) # NaN for spacelike boosts propagates everywhere!
return cartesian_tau(
lib,
x1,
y1,
z1,
tau1,
energy,
mass,
mass2,
x2,
y2,
z.xy_theta(lib, x2, y2, theta2),
)
def xy_theta_t(lib, beta, x, y, theta, t):
gam = (1 - beta ** 2) ** -0.5
bgam = beta * gam
zee = z.xy_theta(lib, x, y, theta)
tee = t
return (x, y, gam * zee + bgam * tee, bgam * zee + gam * tee)
def xy_theta_tau(lib, x, y, theta, tau):
return xy_z_t(
lib, x, y, z.xy_theta(lib, x, y, theta), t.xy_theta_tau(lib, x, y, theta, tau)
)
def xy_theta_xy_theta(lib, x1, y1, theta1, x2, y2, theta2):
x = x1 - x2
y = y1 - y2
z1 = z.xy_theta(lib, x1, y1, theta1)
z2 = z.xy_theta(lib, x2, y2, theta2)
return (x, y, theta.xy_z(lib, x, y, z1 - z2))
def cartesian_t_xy_theta(lib, x1, y1, z1, t1, x2, y2, theta2):
return cartesian_t(lib, x1, y1, z1, t1, x2, y2,
z.xy_theta(lib, x2, y2, theta2))
def cartesian_tau_xy_theta(lib, x1, y1, z1, tau1, x2, y2, theta2):
return cartesian_tau(lib, x1, y1, z1, tau1, x2, y2,
z.xy_theta(lib, x2, y2, theta2))
def xy_z_xy_theta(lib, x1, y1, z1, x2, y2, theta2):
return xy_z_xy_z(lib, x1, y1, z1, x2, y2, z.xy_theta(lib, x2, y2, theta2))
def xy_theta(lib, xx, xy, xz, yx, yy, yz, zx, zy, zz, x, y, theta):
return cartesian(
lib, xx, xy, xz, yx, yy, yz, zx, zy, zz, x, y, z.xy_theta(lib, x, y, theta)
)
def xy_theta_t(lib, x, y, theta, t):
return xy_z_t(lib, x, y, z.xy_theta(lib, x, y, theta), t)
def xy_theta(lib, angle, x, y, theta):
return xy_z(lib, angle, x, y, z.xy_theta(lib, x, y, theta))
def xy_theta_xy_z(lib, rtol, atol, equal_nan, x1, y1, theta1, x2, y2, z2):
return xy_z_xy_z(
lib, rtol, atol, equal_nan, x1, y1, z.xy_theta(lib, x1, y1, theta1), x2, y2, z2
)
def xy_theta_tau(lib, gamma, x, y, theta, tau):
gam = lib.absolute(gamma)
bgam = lib.copysign(lib.sqrt(gam ** 2 - 1), gamma)
zee = z.xy_theta(lib, x, y, theta)
tee = t.xy_theta_tau(lib, x, y, theta, tau)
return (x, y, gam * zee + bgam * tee, tau)
def xy_theta_tau(lib, beta, x, y, theta, tau):
gam = (1 - beta ** 2) ** -0.5
bgam = beta * gam
zee = z.xy_theta(lib, x, y, theta)
tee = t.xy_theta_tau(lib, x, y, theta, tau)
return (x, y, gam * zee + bgam * tee, tau)
