Graham McIntire
4c1013cdbd
Cover the pure-math invariants of the ITU-R P.526-16 diffraction helpers, the haversine metric on Geo, and the Magnus / dry-adiabat helpers in the skew-T renderer. 29 properties, one invariant each.
97 lines
3.3 KiB
Elixir
97 lines
3.3 KiB
Elixir
defmodule Microwaveprop.GeoPropertyTest do
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@moduledoc """
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StreamData property tests for `Microwaveprop.Geo`.
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The haversine formula defines a metric on the surface of the Earth,
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so it must satisfy the three metric axioms: non-negativity with
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identity-of-indiscernibles, symmetry, and the triangle inequality.
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These properties encode those axioms directly, plus the global
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bound of half the Earth's circumference.
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"""
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use ExUnit.Case, async: true
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use ExUnitProperties
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alias Microwaveprop.Geo
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@half_circumference_km 20_015.1
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describe "haversine_km/4 metric axioms" do
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property "distance from a point to itself is exactly 0" do
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check all(
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lat <- float(min: -89.9, max: 89.9),
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lon <- float(min: -179.9, max: 179.9)
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) do
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assert Geo.haversine_km(lat, lon, lat, lon) == 0.0
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end
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end
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property "is non-negative for every pair of points" do
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check all(
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lat1 <- float(min: -89.9, max: 89.9),
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lon1 <- float(min: -179.9, max: 179.9),
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lat2 <- float(min: -89.9, max: 89.9),
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lon2 <- float(min: -179.9, max: 179.9)
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) do
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assert Geo.haversine_km(lat1, lon1, lat2, lon2) >= 0
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end
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end
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property "is symmetric in its endpoints" do
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check all(
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lat1 <- float(min: -89.9, max: 89.9),
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lon1 <- float(min: -179.9, max: 179.9),
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lat2 <- float(min: -89.9, max: 89.9),
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lon2 <- float(min: -179.9, max: 179.9)
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) do
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forward = Geo.haversine_km(lat1, lon1, lat2, lon2)
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reverse = Geo.haversine_km(lat2, lon2, lat1, lon1)
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assert_in_delta forward, reverse, 1.0e-9
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end
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end
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property "satisfies the triangle inequality for any three points" do
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check all(
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lat1 <- float(min: -89.9, max: 89.9),
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lon1 <- float(min: -179.9, max: 179.9),
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lat2 <- float(min: -89.9, max: 89.9),
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lon2 <- float(min: -179.9, max: 179.9),
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lat3 <- float(min: -89.9, max: 89.9),
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lon3 <- float(min: -179.9, max: 179.9)
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) do
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d_ab = Geo.haversine_km(lat1, lon1, lat2, lon2)
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d_bc = Geo.haversine_km(lat2, lon2, lat3, lon3)
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d_ac = Geo.haversine_km(lat1, lon1, lat3, lon3)
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# Small epsilon for accumulated floating-point error.
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assert d_ac <= d_ab + d_bc + 1.0e-6
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end
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end
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property "is bounded above by half the Earth's circumference" do
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check all(
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lat1 <- float(min: -89.9, max: 89.9),
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lon1 <- float(min: -179.9, max: 179.9),
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lat2 <- float(min: -89.9, max: 89.9),
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lon2 <- float(min: -179.9, max: 179.9)
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) do
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assert Geo.haversine_km(lat1, lon1, lat2, lon2) <= @half_circumference_km
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end
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end
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end
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describe "bearing_deg/4" do
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property "result is always in [0, 360) for distinct points" do
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check all(
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lat1 <- float(min: -80.0, max: 80.0),
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lon1 <- float(min: -179.0, max: 179.0),
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# Ensure a nonzero displacement.
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dlat <- float(min: 0.1, max: 5.0),
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dlon <- float(min: 0.1, max: 5.0)
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) do
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b = Geo.bearing_deg(lat1, lon1, lat1 + dlat, lon1 + dlon)
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assert b >= 0.0
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assert b < 360.0
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end
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end
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end
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end
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