vectors

class laddu.utils.vectors.Vec3(px, py, pz)

A 3-momentum vector formed from Cartesian components.

Parameters:

px (float) – The Cartesian components of the 3-vector
py (float) – The Cartesian components of the 3-vector
pz (float) – The Cartesian components of the 3-vector

static from_array(array)

Convert an array into a 3-vector.

Parameters:: array_like – An array containing the components of this Vec3
Returns:: laddu_vec – A copy of the input array as a laddu vector
Return type:: Vec3

cross(other)

Calculate the cross product of two Vec3s.

Parameters:: other (Vec3) – A vector input with which the cross product is taken
Returns:: The cross product of this vector and other
Return type:: Vec3

dot(other)

Calculate the dot product of two Vec3s.

Parameters:: other (Vec3) – A vector input with which the dot product is taken
Returns:: The dot product of this vector and other
Return type:: float

to_numpy()

Convert the 3-vector to a numpy array.

Returns:: numpy_vec – A numpy array built from the components of this Vec3
Return type:: array_like

with_energy(mass)

Convert a 3-vector momentum to a 4-momentum with the given energy.

Parameters:: energy (float) – The mass of the new 4-momentum
Returns:: A new 4-momentum with the given energy
Return type:: Vec4

with_mass(mass)

Convert a 3-vector momentum to a 4-momentum with the given mass.

The mass-energy equivalence is used to compute the energy of the 4-momentum:

\[E = \sqrt{m^2 + p^2}\]

Parameters:: mass (float) – The mass of the new 4-momentum
Returns:: A new 4-momentum with the given mass
Return type:: Vec4

costheta: The cosine of the polar angle of this vector in spherical coordinates

\[-1 \leq \cos\theta \leq +1\]

\[\cos\theta = \frac{p_z}{|\vec{p}|}\]

mag: The magnitude of the 3-vector

\[|\vec{p}| = \sqrt{p_x^2 + p_y^2 + p_z^2}\]

mag2: The squared magnitude of the 3-vector

\[|\vec{p}|^2 = p_x^2 + p_y^2 + p_z^2\]

phi: The azimuthal angle of this vector in spherical coordinates

\[0 \leq \varphi \leq 2\pi\]

\[\varphi = \text{sgn}(p_y)\arccos\left(\frac{p_x}{\sqrt{p_x^2 + p_y^2}}\right)\]

px: The x-component of this vector

See also

Vec3.x

py: The y-component of this vector

See also

Vec3.y

pz: The z-component of this vector

See also

Vec3.z

theta: The polar angle of this vector in spherical coordinates

\[0 \leq \theta \leq \pi\]

\[\theta = \arccos\left(\frac{p_z}{|\vec{p}|}\right)\]

unit: The normalized unit vector pointing in the direction of this vector

x: The x-component of this vector

See also

Vec3.px

y: The y-component of this vector

See also

Vec3.py

z: The z-component of this vector

See also

Vec3.pz

class laddu.utils.vectors.Vec4(px, py, pz, e)

A 4-momentum vector formed from energy and Cartesian 3-momentum components.

This vector is ordered with energy as the fourth component (\([p_x, p_y, p_z, E]\)) and assumes a \((---+)\) signature

Parameters:

px (float) – The Cartesian components of the 3-vector
py (float) – The Cartesian components of the 3-vector
pz (float) – The Cartesian components of the 3-vector
e (float) – The energy component

static from_array(array)

Convert an array into a 4-vector.

Parameters:: array_like – An array containing the components of this Vec4
Returns:: laddu_vec – A copy of the input array as a laddu vector
Return type:: Vec4

boost(beta)

Boost the given 4-momentum according to a boost velocity.

The resulting 4-momentum is equal to the original boosted to an inertial frame with relative velocity \(\beta\):

\[\left[\vec{p}'; E'\right] = \left[ \vec{p} + \left(\frac{(\gamma - 1) \vec{p}\cdot\vec{\beta}}{\beta^2} + \gamma E\right)\vec{\beta}; \gamma E + \vec{\beta}\cdot\vec{p} \right]\]

Parameters:: beta (Vec3) – The relative velocity needed to get to the new frame from the current one
Returns:: The boosted 4-momentum
Return type:: Vec4