Vectors

This guide covers the creation and use of vector objects in coordinax, including positions, velocities, accelerations, arithmetic, dimensionality, spaces, and vector functions.

Creating Vector Objects

You can create vectors for positions, velocities, and accelerations in many supported dimension:

>>> import coordinax.vecs as cxv
>>> q1 = cxv.CartesianPos1D.from_(1, "kpc")
>>> q2 = cxv.CartesianPos2D.from_([1, 2], "kpc")
>>> q3 = cxv.CartesianPos3D.from_([1, 2, 3], "kpc")
>>> v3 = cxv.CartesianVel3D.from_([4, 5, 6], "kpc/Myr")
>>> a3 = cxv.CartesianAcc3D.from_([0.1, 0.2, 0.3], "kpc/Myr^2")

You can also create N-D vectors:

>>> qn = cxv.CartesianPosND.from_([1, 2, 3, 4], "kpc")

All vector types support flexible input: scalars, lists, arrays, or Quantity.

The component values can be multidimensional arrays, allowing for batch operations:

>>> arr = cxv.CartesianPos3D.from_([[1, 2, 3], [4, 5, 6]], "kpc")

Arithmetic and Mathematical Operations

Vector objects support arithmetic and mathematical operations:

>>> q3 + q3
CartesianPos3D(
    x=Quantity(2, unit='kpc'), y=Quantity(4, unit='kpc'), z=Quantity(6, unit='kpc')
)

>>> 2 * q3
CartesianPos3D(
    x=Quantity(2, unit='kpc'), y=Quantity(4, unit='kpc'), z=Quantity(6, unit='kpc')
)

>>> v3 - v3
CartesianVel3D(
    x=Quantity(0, unit='kpc / Myr'),
    y=Quantity(0, unit='kpc / Myr'),
    z=Quantity(0, unit='kpc / Myr')
)

Dimensionality: 1,N-D

coordinax provides vector classes for many dimensions:

• CartesianPos1D, CartesianPos2D, CartesianPos3D, CartesianPosND

• Similar classes for velocities (CartesianVel*), accelerations (CartesianAcc*), etc.

• Spacetime vectors FourVector

Conversion Between Representations

Vectors can be converted between coordinate systems:

>>> sph = q3.vconvert(cxv.SphericalPos)
>>> print(sph)
<SphericalPos: (r[kpc], theta[rad], phi[rad])
    [3.742 0.641 1.107]>

Batch and Broadcast Operations

All vector types support batch operations and broadcasting:

>>> arr = cxv.CartesianPos3D.from_([[1,2,3],[4,5,6]], "kpc")
>>> arr * 2
CartesianPos3D(
    x=Quantity([2, 8], unit='kpc'),
    y=Quantity([ 4, 10], unit='kpc'),
    z=Quantity([ 6, 12], unit='kpc')
)

Space Objects: Grouping Related Vectors

A KinematicSpace object collects related vectors (e.g., position, velocity, acceleration):

>>> space = cxv.KinematicSpace(length=q3, speed=v3, acceleration=a3)
>>> print(space)
KinematicSpace({
    'length':
    <CartesianPos3D: (x, y, z) [kpc]
         [1 2 3]>,
    'speed':
    <CartesianVel3D: (x, y, z) [kpc / Myr]
        [4 5 6]>,
    'acceleration':
    <CartesianAcc3D: (x, y, z) [kpc / Myr2]
        [0.1 0.2 0.3]>
})

You can convert all vectors in a KinematicSpace at once:

>>> space_sph = space.vconvert(cxv.SphericalPos)
>>> print(space_sph)
KinematicSpace({
       'length':
       <SphericalPos: (r[kpc], theta[rad], phi[rad])
           [3.742 0.641 1.107]>,
       'speed':
       <SphericalVel: (r[kpc / Myr], theta[rad / Myr], phi[rad / Myr])
           [ 8.552  0.383 -0.6  ]>,
       'acceleration':
       <SphericalAcc: (r[kpc / Myr2], theta[rad / Myr2], phi[rad / Myr2])
           [ 3.742e-01 -9.355e-09  1.639e-09]>
    })

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See also

API Documentation for Vectors