angle

This module implements three classes Vector3, LorentzVector, EulerAngle .

class AlignmentAngle(alpha=0.0, beta=0.0, gamma=0.0)

Bases: EulerAngle

static angle_px_px(p1, x1, p2, x2)

class EulerAngle(alpha=0.0, beta=0.0, gamma=0.0)

Bases: dict

This class provides methods for Eular angle \((\alpha,\beta,\gamma)\)

static angle_zx_z_getx(z1, x1, z2)

The Eular angle from coordinate 1 to coordinate 2. Only the z-axis is provided for coordinate 2, so \(\gamma\) is set to be 0.

Parameters:

• z1 – Vector3 z-axis of the initial coordinate

• x1 – Vector3 x-axis of the initial coordinate

• z2 – Vector3 z-axis of the final coordinate

Return eular_angle:

EularAngle object with \(\gamma=0\).

Return x2:

Vector3 object, which is the x-axis of the final coordinate when \(\gamma=0\).

static angle_zx_zx(z1, x1, z2, x2)

The Euler angle from coordinate 1 to coordinate 2 (right-hand coordinates).

Parameters:

• z1 – Vector3 z-axis of the initial coordinate

• x1 – Vector3 x-axis of the initial coordinate

• z2 – Vector3 z-axis of the final coordinate

• x2 – Vector3 x-axis of the final coordinate

Returns:

Euler Angle object

static angle_zx_zzz_getx(z, x, zi)

The Eular angle from coordinate 1 to coordinate 2. Z-axis of coordinate 2 is the normal vector of a plane.

Parameters:

• z1 – Vector3 z-axis of the initial coordinate

• x1 – Vector3 x-axis of the initial coordinate

• z – list of Vector3 of the plane point.

Return eular_angle:

EularAngle object.

Return x2:

list of Vector3 object, which is the x-axis of the final coordinate in zi.

class LorentzVector

Bases: Tensor

This class provides methods for Lorentz vectors (T,X,Y,Z). or -T???

Dot(other)

M()

The invariant mass

M2()

The invariant mass squared

beta()

boost(p)

Boost this Lorentz vector into the frame indicated by the 3-d vector p.

boost_matrix()

boost_vector()

\(\beta=(X,Y,Z)/T\) :return: 3-d vector \(\beta\)

static from_p4(p_0, p_1, p_2, p_3)

Given p_0 is a real number, it will make it transform into the same shape with p_1.

gamma()

get_T()

get_X()

get_Y()

get_Z()

get_e()

rm???

get_metric()

The metric is (1,-1,-1,-1) by default

neg()

The negative vector

omega()

rest_vector(other)

Boost another Lorentz vector into the rest frame of \(\beta\).

vect()

It returns the 3-d vector (X,Y,Z).

class SU2M(x)

Bases: dict

static Boost_z(omega)

static Boost_z_from_p(p)

static Rotation_y(beta)

static Rotation_z(alpha)

get_euler_angle()

inv()

class Vector3

Bases: Tensor

This class provides methods for 3-d vectors (X,Y,Z)

angle_from(x, y)

The angle from x-axis providing the x,y axis to define a 3-d coordinate.

x  ->  self
|      /
| ang /
|    /
|   /
|  /
| /
|/
-------- y

Parameters:

• x – A Vector3 instance as x-axis

• y – A Vector3 instance as y-axis. It should be perpendicular to the x-axis.

cos_theta(other)

cos theta of included angle

cross(other)

Cross product with another Vector3 instance

cross_unit(other)

The unit vector of the cross product with another Vector3 object. It has interface to tf.linalg.normalize().

dot(other)

Dot product with another Vector3 object

get_X()

get_Y()

get_Z()

norm()

norm2()

The norm square

unit()

The unit vector of itself. It has interface to tf.linalg.normalize().

kine_max(s12, m0, m1, m2, m3)

max s23 for s12 in p0 -> p1 p2 p3

kine_min(s12, m0, m1, m2, m3)

min s23 for s12 in p0 -> p1 p2 p3

kine_min_max(s12, m0, m1, m2, m3)

min max s23 for s12 in p0 -> p1 p2 p3