dm-dt maps

A dm-dt map is a 2D histogram of magnitude differences (dm) versus log-time differences (lg dt) for all pairs of observations in a light curve. It was introduced as an input representation for ML classifiers by Mahabal et al. 2011 and Soraisam et al. 2020.

Unlike scalar feature extractors, DmDt produces a 2D array — a fixed-size image that can be fed directly into a CNN.

Basic usage

import light_curve as lc
import numpy as np

dmdt = lc.DmDt.from_borders(
    min_lgdt=0,       # log10(dt_min) in days
    max_lgdt=2,       # log10(dt_max) in days
    max_abs_dm=1,     # maximum |dm| in magnitudes
    lgdt_size=32,     # number of dt bins
    dm_size=32,       # number of dm bins
    norm=["dt"],      # normalise each dt row
)

rng = np.random.default_rng(0)
t = np.sort(rng.uniform(0, 100, 200))
m = 15.0 + rng.normal(0, 0.1, 200)

map_ = dmdt.points(t, m)   # shape (32, 32)

The output array has shape (lgdt_size, dm_size). Each cell counts the number of observation pairs \((i, j)\) with \(i < j\) that fall into the corresponding \((\lg\Delta t,\, \Delta m)\) bin.

Normalisation

The norm parameter accepts a list of zero, one, or both of the following strings:

norm value	Effect
[] (empty)	Raw pair counts
["dt"]	Divide each Δt row by its total count (row sums to ≤1)
["max"]	Divide the entire map by its maximum value (max = 1)
["dt", "max"]	Apply both normalisations in sequence

Batch processing

light_curves = [(t1, m1), (t2, m2), ...]
maps = dmdt.points_many(light_curves)   # shape (N, 32, 32)

Error-weighted maps (Gaussian kernel)

When photometric errors are available, use gausses() to spread each pair into a Gaussian kernel in Δm space. The err2 argument is the variance (σ²), not the standard deviation:

err = np.full(200, 0.05)          # 1-σ photometric error
map_g = dmdt.gausses(t, m, err**2)   # shape (32, 32)

See the API reference for the full DmDt signature.