Position and Trajectory

Position and Trajectory#

Classes for representing particle positions and trajectories during integration.

Position Tracking#

class lagrangian.core.Position#

Base class for tracking particle positions during integration.

__init__()

Default constructor

Note

This constructor may lead to an error in diagnostic because start time is set to zero: if stencil has not been advected then delta_t is equal to minus advection starting time (-start_time) which is not correct.

__init__(self: lagrangian.core.Position, start_time: lagrangian::DateTime, spherical_equatorial: bool = True) → None#

Constructor with start_time setting

Parameters:

  • start_time – Advection starting time particles

  • spherical_equatorial – True if the coordinates system is Lon/lat otherwise false

Key Methods

Properties

  • is_completed: Whether integration is complete

  • time: Current time of integration

compute(self: lagrangian.core.Position, rk4: lagrangian.core.RungeKutta, it: Iterator, cell: lagrangian.core.CellProperties) → bool#

To move a particle with a velocity field.

Parameters:

  • rk (lagrangian.RungeKutta) – Runge-Kutta handler

  • it (lagrangian.Iterator) – Iterator

  • cell (lagrangian.CellProperties) – Cell properties of the grid used for the interpolation.

Returns:

True if the particle could be moved otherwise false

Return type:

bool

strain_tensor(self: lagrangian.core.Position) → tuple#
max_distance(self: lagrangian.core.Position) → float#

Compute the distance max

xi(self: lagrangian.core.Position) → numpy.typing.NDArray[numpy.float64]#

Returns the x-axis of the point

yi(self: lagrangian.core.Position) → numpy.typing.NDArray[numpy.float64]#

Returns the y-axis of the point

property is_completed#

Test if the integration is over

property time#

Returns the time at the end of the integration

Stencil Configurations#

class lagrangian.core.Stencil#

Enumeration of stencil types for finite difference calculations:

  • TRIPLET: 3-point stencil

  • QUINTUPLET: 5-point stencil

Triplet Position#

class lagrangian.core.Triplet#

Bases: lagrangian.Position

3-point stencil for computing Lyapunov exponents using three particles.

The triplet method uses three particles arranged in a specific pattern to compute the finite-time Lyapunov exponents. This is computationally efficient but may be less accurate than the quintuplet method.

Examples

Creating a triplet configuration:

import lagrangian
from datetime import datetime

triplet = lagrangian.Triplet(
    x=10.0,      # Initial longitude
    y=45.0,      # Initial latitude
    delta=0.01,  # Initial separation
    start_time=datetime(2010, 1, 1),
    spherical_equatorial=True
)

Quintuplet Position#

class lagrangian.core.Quintuplet#

5-point stencil for computing Lyapunov exponents using five particles.

The quintuplet method uses five particles (one central particle plus four surrounding particles) to compute finite-time Lyapunov exponents. This provides higher accuracy than the triplet method at the cost of additional computation.

Examples

Creating a quintuplet configuration:

import lagrangian
from datetime import datetime

quintuplet = lagrangian.Quintuplet(
    x=10.0,      # Initial longitude
    y=45.0,      # Initial latitude
    delta=0.01,  # Initial separation
    start_time=datetime(2010, 1, 1),
    spherical_equatorial=True
)
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