def rhophi_theta_tau(lib, beta, rho, phi, theta, tau):
gam = (1 - beta**2)**-0.5
bgam = beta * gam
exx = x.rhophi(lib, rho, phi)
why = y.rhophi(lib, rho, phi)
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t.rhophi_theta_tau(lib, rho, phi, theta, tau)
return (gam * exx + bgam * tee, why, zee, tau)
def rhophi_theta_t(lib, gamma, rho, phi, theta, t):
gam = lib.absolute(gamma)
bgam = lib.copysign(lib.sqrt(gam**2 - 1), gamma)
exx = x.rhophi(lib, rho, phi)
why = y.rhophi(lib, rho, phi)
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t
return (exx, gam * why + bgam * tee, zee, bgam * why + gam * tee)
def rhophi_theta_tau(lib, rho, phi, theta, tau):
return rhophi_z_t(
lib,
rho,
phi,
z.rhophi_theta(lib, rho, phi, theta),
t.rhophi_theta_tau(lib, rho, phi, theta, tau),
)
def rhophi_theta_t(lib, beta, rho, phi, theta, t):
gam = (1 - beta**2)**-0.5
bgam = beta * gam
exx = x.rhophi(lib, rho, phi)
why = y.rhophi(lib, rho, phi)
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t
return (exx, gam * why + bgam * tee, zee, bgam * why + gam * tee)
def rhophi_theta_tau(lib, gamma, rho, phi, theta, tau):
gam = lib.absolute(gamma)
bgam = lib.copysign(lib.sqrt(gam ** 2 - 1), gamma)
exx = x.rhophi(lib, rho, phi)
why = y.rhophi(lib, rho, phi)
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t.rhophi_theta_tau(lib, rho, phi, theta, tau)
return (gam * exx + bgam * tee, why, zee, tau)
def rhophi_theta(lib, angle, rho, phi, theta):
return xy_z(
lib,
angle,
x.rhophi(lib, rho, phi),
y.rhophi(lib, rho, phi),
z.rhophi_theta(lib, rho, phi, theta),
)
def xy_eta_rhophi_theta(lib, x1, y1, eta1, rho2, phi2, theta2):
return xy_z_xy_z(
lib,
x.xy(lib, x1, y1),
y.xy(lib, x1, y1),
z.xy_eta(lib, x1, y1, eta1),
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def rhophi_eta_rhophi_theta(lib, rho1, phi1, eta1, rho2, phi2, 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.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def rhophi_theta_xy_z(lib, rho1, phi1, theta1, x2, y2, z2):
return xy_z_xy_z(
lib,
x.rhophi(lib, rho1, phi1),
y.rhophi(lib, rho1, phi1),
z.rhophi_theta(lib, rho1, phi1, theta1),
x2,
y2,
z2,
)
def rhophi_theta_xy_eta(lib, rho1, phi1, theta1, x2, y2, eta2):
return xy_z_xy_z(
lib,
x.rhophi(lib, rho1, phi1),
y.rhophi(lib, rho1, phi1),
z.rhophi_theta(lib, rho1, phi1, theta1),
x.xy(lib, x2, y2),
y.xy(lib, x2, y2),
z.xy_eta(lib, x2, y2, eta2),
)
def xy_z_rhophi_theta(lib, x1, y1, z1, rho2, phi2, theta2):
return xy_z_xy_z(
lib,
x1,
y1,
z1,
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def cartesian_tau_rhophi_theta(lib, x1, y1, z1, tau1, rho2, phi2, theta2):
return cartesian_tau(
lib,
x1,
y1,
z1,
tau1,
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def rhophi_theta_xy_z(lib, rtol, atol, equal_nan, rho1, phi1, theta1, x2, y2, z2):
return xy_z_xy_z(
lib,
rtol,
atol,
equal_nan,
x.rhophi(lib, rho1, phi1),
y.rhophi(lib, rho1, phi1),
z.rhophi_theta(lib, rho1, phi1, theta1),
x2,
y2,
z2,
)
def xy_z_rhophi_theta(lib, rtol, atol, equal_nan, x1, y1, z1, rho2, phi2, theta2):
return xy_z_xy_z(
lib,
rtol,
atol,
equal_nan,
x1,
y1,
z1,
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def rhophi_z_rhophi_theta(
lib, rtol, atol, equal_nan, rho1, phi1, z1, rho2, phi2, theta2
):
return rhophi_z_rhophi_z(
lib,
rtol,
atol,
equal_nan,
rho1,
phi1,
z1,
rho2,
phi2,
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def rhophi_theta_rhophi_z(
lib, rtol, atol, equal_nan, rho1, phi1, theta1, rho2, phi2, z2
):
return rhophi_z_rhophi_z(
lib,
rtol,
atol,
equal_nan,
rho1,
phi1,
z.rhophi_theta(lib, rho1, phi1, theta1),
rho2,
phi2,
z2,
)
def rhophi_theta(lib, xx, xy, xz, yx, yy, yz, zx, zy, zz, rho, phi, theta):
return cartesian(
lib,
xx,
xy,
xz,
yx,
yy,
yz,
zx,
zy,
zz,
x.rhophi(lib, rho, phi),
y.rhophi(lib, rho, phi),
z.rhophi_theta(lib, rho, phi, theta),
)
def cartesian_t_rhophi_theta_t(lib, x1, y1, z1, t1, rho2, phi2, theta2, t2):
energy = t2
energy2 = energy**2
mass2 = energy2 - mag2.rhophi_theta(lib, rho2, phi2, theta2)
mass = lib.sqrt(mass2) # NaN for spacelike boosts propagates everywhere!
return cartesian_t(
lib,
x1,
y1,
z1,
t1,
energy,
mass,
mass2,
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def cartesian_tau_rhophi_theta_tau(lib, x1, y1, z1, tau1, rho2, phi2, theta2,
tau2):
mass = tau2
mass2 = mass**2
energy2 = mass2 + mag2.rhophi_theta(lib, rho2, phi2, theta2)
energy = lib.sqrt(
energy2) # NaN for spacelike boosts propagates everywhere!
return cartesian_tau(
lib,
x1,
y1,
z1,
tau1,
energy,
mass,
mass2,
x.rhophi(lib, rho2, phi2),
y.rhophi(lib, rho2, phi2),
z.rhophi_theta(lib, rho2, phi2, theta2),
)
def rhophi_theta_rhophi_theta(lib, rho1, phi1, theta1, rho2, phi2, theta2):
rho, phi = subtract.rhophi_rhophi(lib, rho1, phi1, rho2, phi2)
z1 = z.rhophi_theta(lib, rho1, phi1, theta1)
z2 = z.rhophi_theta(lib, rho2, phi2, theta2)
return (rho, phi, theta.rhophi_z(lib, rho, phi, z1 - z2))
def rhophi_theta_t(lib, beta, rho, phi, theta, t):
gam = (1 - beta ** 2) ** -0.5
bgam = beta * gam
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t
return (rho, phi, gam * zee + bgam * tee, bgam * zee + gam * tee)
def rhophi_theta_t(lib, rho, phi, theta, t):
return rhophi_z_t(lib, rho, phi, z.rhophi_theta(lib, rho, phi, theta), t)
def rhophi_theta_tau(lib, beta, rho, phi, theta, tau):
gam = (1 - beta ** 2) ** -0.5
bgam = beta * gam
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t.rhophi_theta_tau(lib, rho, phi, theta, tau)
return (rho, phi, gam * zee + bgam * tee, tau)
def rhophi_theta_tau(lib, gamma, rho, phi, theta, tau):
gam = lib.absolute(gamma)
bgam = lib.copysign(lib.sqrt(gam ** 2 - 1), gamma)
zee = z.rhophi_theta(lib, rho, phi, theta)
tee = t.rhophi_theta_tau(lib, rho, phi, theta, tau)
return (rho, phi, gam * zee + bgam * tee, tau)
def rhophi_theta_rhophi_z(lib, rho1, phi1, theta1, rho2, phi2, z2):
return rhophi_z_rhophi_z(lib, rho1, phi1,
z.rhophi_theta(lib, rho1, phi1, theta1), rho2,
phi2, z2)
def rhophi_z_rhophi_theta(lib, rho1, phi1, z1, rho2, phi2, theta2):
return rhophi_z_rhophi_z(lib, rho1, phi1, z1, rho2, phi2,
z.rhophi_theta(lib, rho2, phi2, theta2))
