commit a177603002e69d1a428e30b31d562019b5426e2e Author: Connor Johnstone Date: Fri Oct 2 17:14:08 2026 -0400 Initial commit. Faithful representation done. Standard test cases plus 2880 more all pass (plus helper function tests) diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..bd17538 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +/target +**/*.rs.bk +*.pre-* diff --git a/Cargo.lock b/Cargo.lock new file mode 100644 index 0000000..950ecfc --- /dev/null +++ b/Cargo.lock @@ -0,0 +1,769 @@ +# This file is automatically @generated by Cargo. +# It is not intended for manual editing. +version = 4 + +[[package]] +name = "aho-corasick" +version = "1.1.5" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "c982642fa9e8606056828ee9a8505737230110bb1099153c79efe865c59d12ba" +dependencies = [ + "memchr", +] + +[[package]] +name = "anes" +version = "0.1.6" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "4b46cbb362ab8752921c97e041f5e366ee6297bd428a31275b9fcf1e380f7299" + +[[package]] +name = "anstyle" +version = "1.0.14" +source = 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"registry+https://github.com/rust-lang/crates.io-index" +checksum = "29666d0abbfad1e3dc4dcf6144730dd3a3ab225bbbdac83319345b1b44ccfc1b" diff --git a/Cargo.toml b/Cargo.toml new file mode 100644 index 0000000..9d2e14c --- /dev/null +++ b/Cargo.toml @@ -0,0 +1,43 @@ +[package] +name = "nrlmsise00" +version = "0.1.0" +edition = "2021" +authors = ["Connor Johnstone"] +description = "NRLMSISE-00 atmosphere model, generic over its scalar type so density can be differentiated" +readme = "readme.md" +repository = "https://git.rcjohnstone.com/connor/nrlmsise00" +license = "MIT" +keywords = ["atmosphere", "density", "nrlmsise00", "aerospace", "thermosphere"] +categories = ["science", "aerospace"] +# The NRLMSIS 2.x port is a separate package under a separate, non-commercial +# license. It is not part of this one. +exclude = ["nrlmsis2", "scripts", "hooks", "plan.md"] + +[workspace] +members = ["nrlmsis2"] + +[features] +default = ["autodiff", "drivers"] +# Dual-number scalars, so density can be differentiated. +autodiff = ["dep:num-dual", "dep:nalgebra"] +# The compiled-in solar and geomagnetic record, and date lookups into it. +drivers = [] + +[dependencies] +nalgebra = { version = "0.35", optional = true } +num-dual = { version = "0.15", optional = true } +num-traits = { version = "0.2", default-features = false } + +[dev-dependencies] +approx = "0.5" +criterion = "0.7" +num-dual = "0.15" +# arbitrary_precision keeps each number's own digits, so a fixture value is parsed by +# str::parse rather than by serde_json's own float parser, which reads some f64s back one +# ulp high. The fixtures are compared bit for bit, so that one ulp is the difference +# between a passing and a failing test. +serde_json = { version = "1.0", features = ["arbitrary_precision"] } + +[[bench]] +name = "density" +harness = false diff --git a/benches/density.rs b/benches/density.rs new file mode 100644 index 0000000..43ab0a9 --- /dev/null +++ b/benches/density.rs @@ -0,0 +1,93 @@ +//! What an evaluation costs. +//! +//! The altitudes are chosen for the paths they take, not for being round: above 72.5 km +//! the model is the thermosphere alone, below it the mesosphere splines are built on top of +//! a thermosphere evaluation at 72.5 km, and below 32.5 km a second set of splines is built +//! on top of that. The three cost noticeably different amounts. +//! +//! The dual-number cases are the reason the crate exists, so they are measured alongside: +//! one seeded input gives the altitude partial, three give the position gradient a drag +//! calculation wants. + +use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion}; +use nrlmsise00::{Input, MagneticActivity, Model, Scalar}; +use num_dual::{Dual64, DualSVec64}; +use std::hint::black_box; + +/// The baseline of the reference's published cases, at an altitude of the caller's choice. +fn input(altitude_km: T) -> Input { + Input { + day_of_year: 172, + seconds_of_day: T::lift(29000.0), + altitude_km, + latitude_deg: T::lift(60.0), + longitude_deg: T::lift(-70.0), + local_solar_time_h: T::lift(16.0), + f107_average: T::lift(150.0), + f107: T::lift(150.0), + magnetic: MagneticActivity::History { + ap: [100.0; 7].map(T::lift), + }, + } +} + +/// An altitude in each of the model's three vertical regions, and one in the exosphere. +const ALTITUDES: [(&str, f64); 4] = [ + ("20 km, three splines", 20.0), + ("50 km, two splines", 50.0), + ("400 km, thermosphere", 400.0), + ("1000 km, exosphere", 1000.0), +]; + +fn gtd7d(c: &mut Criterion) { + let model = Model::new(); + let mut group = c.benchmark_group("gtd7d"); + for (name, altitude) in ALTITUDES { + group.bench_with_input(BenchmarkId::new("f64", name), &altitude, |b, altitude| { + b.iter(|| model.gtd7d(black_box(&input(*altitude)))); + }); + } + group.finish(); +} + +fn derivatives(c: &mut Criterion) { + let model = Model::new(); + let mut group = c.benchmark_group("gtd7d with derivatives"); + for (name, altitude) in ALTITUDES { + // One partial: the altitude derivative a scale height comes from. + group.bench_with_input( + BenchmarkId::new("one partial", name), + &altitude, + |b, altitude| { + let seeded = Dual64::from(*altitude).derivative(); + b.iter(|| model.gtd7d(black_box(&input(seeded)))); + }, + ); + // Three at once: the position gradient, which is what a drag partial needs. + group.bench_with_input( + BenchmarkId::new("three partials", name), + &altitude, + |b, altitude| { + // Seeded in the first of three slots, as a position gradient would be. + let seeded = DualSVec64::<3>::from(*altitude).derivative(0); + b.iter(|| model.gtd7d(black_box(&input(seeded)))); + }, + ); + } + group.finish(); +} + +/// The two entry points, to show that the drag total costs nothing extra. +fn entry_points(c: &mut Criterion) { + let model = Model::new(); + let mut group = c.benchmark_group("entry points at 400 km"); + group.bench_function("gtd7", |b| b.iter(|| model.gtd7(black_box(&input(400.0))))); + group.bench_function("gtd7d", |b| { + b.iter(|| model.gtd7d(black_box(&input(400.0)))) + }); + group.bench_function("gts7", |b| b.iter(|| model.gts7(black_box(&input(400.0))))); + group.finish(); +} + +criterion_group!(benches, gtd7d, derivatives, entry_points); +criterion_main!(benches); diff --git a/hooks/pre-commit b/hooks/pre-commit new file mode 100755 index 0000000..0b2b5ac --- /dev/null +++ b/hooks/pre-commit @@ -0,0 +1,12 @@ +#!/bin/sh +# Cheap checks, on the whole tree. The expensive ones are in pre-push. +set -e +cargo fmt --check +cargo clippy --all-targets --all-features -- -D warnings +cargo test --lib +# British spellings keep slipping into generated prose. This file is excluded because it +# holds the word list, which would otherwise match itself. +if git diff --cached -U0 -- . ':(exclude)hooks/pre-commit' | grep -nE '^\+.*\b(metre|metres|normalis|stabilis|recognis|licence|modelling|manoeuvre|behaviour|analyse|analysing|centre|colour)' ; then + echo "pre-commit: British spelling above; this project is US English" >&2 + exit 1 +fi diff --git a/hooks/pre-push b/hooks/pre-push new file mode 100755 index 0000000..740defa --- /dev/null +++ b/hooks/pre-push @@ -0,0 +1,6 @@ +#!/bin/sh +# The slow checks: doctests link a binary apiece, and rustdoc is its own pass. +set -e +cargo test +cargo test --no-default-features +cargo doc --no-deps diff --git a/nrlmsis2/Cargo.toml b/nrlmsis2/Cargo.toml new file mode 100644 index 0000000..70d3b9c --- /dev/null +++ b/nrlmsis2/Cargo.toml @@ -0,0 +1,14 @@ +[package] +name = "nrlmsis2" +version = "0.0.0" +edition = "2021" +authors = ["Connor Johnstone"] +description = "NRLMSIS 2.0 and 2.1, generic over the scalar type. Not freely licensed; see the readme." +readme = "readme.md" +license-file = "nrlmsis2.1_license.txt" +# Academic and non-commercial use only, and the methods are patented. This +# package is deliberately not publishable; see readme.md. +publish = false + +[dependencies] +nrlmsise00 = { path = "..", default-features = false } diff --git a/nrlmsis2/nrlmsis2.1_license.txt b/nrlmsis2/nrlmsis2.1_license.txt new file mode 100644 index 0000000..244ab19 --- /dev/null +++ b/nrlmsis2/nrlmsis2.1_license.txt @@ -0,0 +1,71 @@ +MSIS® (NRL-SOF-014-1) SOFTWARE +OPEN SOURCE ACADEMIC RESEARCH LICENSE AGREEMENT + +1. Agreement. The MSIS® empirical atmospheric model software (hereinafter +“Software”) is property of The Government of the United States of America. This +software is being made available under the following terms and conditions. By +using, modifying, reproducing, or preparing a derivative work of this Software, +you agree to abide by the terms and conditions herein. + +2. License. In accordance with federal law, authorization is given to use, +reproduce, and modify the Software solely for research, academic, and non-profit +purposes and only in accordance with the terms and conditions in this Agreement. +Any commercial use is prohibited. No other rights or permissions are provided. + +3. Basis. The Software was written by employees of the U.S. Naval Research +Laboratory (NRL) and is property of the United States Government, as represented +by the Secretary of the Navy. MSIS® is a registered trademark of the Government +of the United States of America, as represented by the Secretary of the Navy. +Unauthorized use of the trademark is prohibited. + +4. Restrictions and Use. + +a. Sales. A user of the Software shall not sell, or license, or transfer for a +fee the Software or portion thereof, or any derivative work of the Software, or +any data products generated by the Software, without first obtaining the written +consent of IP Counsel for the Naval Research Laboratory. + +b. Modifications. All modifications to the Software and derivative works of the +Software (including translations to other programming languages) shall carry +prominent notices stating how the files were changed and the date of the change. +Any party who modifies the Software shall deliver the modified portion of the +Software to authors or NRL Code 7630, U.S. Naval Research Laboratory. Any +reproductions, modified versions of the Software, or derivative works shall be +made available to the public as open source software. A party who modifies the +Software or creates a derivative work of the Software hereby grants the +Government of the United States of America a non-exclusive, irrevocable, fully +paid-up license to such modifications and derivative works, and shall deliver +such derivative works, including any source code, data, or information that +pertains to such derivatives works, to Code 7630, U.S. Naval Research +Laboratory. If any modifications to the Software substantially change the model +output (including, but not limited to, alterations of the model formulation or +model parameter values), then the modified Software shall not be identified +“MSIS” without first obtaining the written consent of Counsel, Office of Naval +Research, Department of the Navy. In such cases, the MSIS acronym shall +nonetheless still appear in the individual files in order to document the +provenance of the modified Software. + +c. Notices. Each copy of the Software, any modified Software, or derivative +work shall include a file containing this Agreement. Any software package that +incorporates the MSIS® Software or derivative work shall include the following +statement: "This software incorporates the MSIS® empirical atmospheric model +software designed and provided by NRL. Use is governed by the Open Source +Academic Research License Agreement contained in the file +nrlmsis2.1_license.txt." + +5. Disclaimer of Warranty and Liability: As the owner of the MSIS® software, the +Government of the United States of America: (1) Disclaims any warranties, +express, or implied, including but not limited to any implied warranties of +merchantability, fitness for a particular purpose, title or non-infringement, +(2) Does not assume any legal liability or responsibility for the accuracy, +completeness, or usefulness of the software, (3) Does not represent that use of +the software would not infringe privately owned rights, (4) Does not warrant +that the software will function uninterrupted, that is error-free or that any +errors will be corrected. + +6. No Support. The Software is provided without any support or maintenance, and +without any obligation to provide modifications, improvements, enhancements, or +updates of the Software. No oral or written information or advice given by the +NRL authors shall create a warranty or in any way modify this agreement. Should +the Software prove defective, the user (and not NRL or any NRL representative) +assume the cost of all necessary correction. diff --git a/nrlmsis2/readme.md b/nrlmsis2/readme.md new file mode 100644 index 0000000..eaa9c86 --- /dev/null +++ b/nrlmsis2/readme.md @@ -0,0 +1,68 @@ +# nrlmsis2 + +NRLMSIS 2.0 and 2.1. **Nothing is implemented yet**, and anyone who implements it should +read this file first, because the terms are not the ones the rest of this repository uses. + +## Why it is a separate package + +`nrlmsise00`, the 2002 model, is MIT. This cannot be. + +NRLMSIS 2.0's terms, which ship in the headers of its Fortran and in `pymsis`'s +`MSIS2_LICENSE`, grant "a non-exclusive, non-transferable license to the Software for +academic, non-commercial, purposes only", and forbid the user to "make any modification or +improvement to the Software" without written consent from IP Counsel at the Naval Research +Laboratory. They also state that the methods are covered by **US Patent 10,641,925**, +"Formulation and fitting techniques for whole-atmosphere empirical models", assigned to the +US Department of the Navy, filed 2019-06-13, granted 2020-05-05, and expiring 2039-06-13. + +NRLMSIS 2.1 ships the "MSIS (NRL-SOF-014-1) Software Open Source Academic Research License +Agreement", which is in this directory as `nrlmsis2.1_license.txt`. Its terms: + +- Use, reproduction and modification are authorized "solely for research, academic, and + non-profit purposes". **Any commercial use is prohibited.** +- Derivative works, **explicitly including "translations to other programming languages"**, + must carry prominent notices stating how the files were changed and when, must be + delivered to the authors or to NRL Code 7630, and must be made available to the public as + open source. +- Neither the software nor any data product generated by it may be sold, licensed or + transferred for a fee without written consent from NRL IP Counsel. +- Every copy must include a file containing the agreement, and any package incorporating it + must carry this statement verbatim: + + > This software incorporates the MSIS® empirical atmospheric model software designed and + > provided by NRL. Use is governed by the Open Source Academic Research License Agreement + > contained in the file nrlmsis2.1_license.txt. + +So a Rust port of NRLMSIS 2.x is a derivative work on those terms. It is not distributable +under the MIT license, it cannot be used commercially, and publishing it obliges delivery of +the source to NRL. That is why this package is `publish = false`, and why it is a separate +package rather than a feature of `nrlmsise00`: a crate that enabled it would carry the same +restriction to everyone downstream. + +Nobody else redistributes it either. `space-physics/nrlmsis2.0`'s readme opens with "the +MSIS 2.0 license is extremely restrictive" and its build downloads the source rather than +shipping it; `pymsis` is MIT for its own wrapper and carries the MSIS license separately for +the Fortran it wraps. No Rust crate implements 2.x at all — `tobari` and `satkit` are both +NRLMSISE-00. + +## What implementing it would involve + +Unlike the 2002 model, 2.0 and 2.1 are one Fortran 90 codebase that reads its coefficients +from a binary parameter file: `msis21.parm` is 524 KB. The two versions differ mostly in +that file, so one implementation covers both. The vertical structure is B-splines rather +than the layered profiles of NRLMSISE-00, so almost nothing in `nrlmsise00` is reusable +beyond the scalar trait and the drivers. + +Validating it needs a reference at full precision. The distribution's own +`msis2.1_test_ref_dp.txt` carries only four significant digits, which is nowhere near +enough for the bit-for-bit comparison `nrlmsise00` is held to, so generating one means +running the Fortran: `gfortran` is not installed on this machine, and `pymsis` would do as +well since it wraps the same code. + +Before any of that, the question for a human is whether the obligations above are acceptable +for this repository at all. + +## License + +Not MIT. See `nrlmsis2.1_license.txt`, which governs any use of the model this package +would implement. diff --git a/nrlmsis2/src/lib.rs b/nrlmsis2/src/lib.rs new file mode 100644 index 0000000..68bdff3 --- /dev/null +++ b/nrlmsis2/src/lib.rs @@ -0,0 +1,5 @@ +//! NRLMSIS 2.0 and 2.1. +//! +//! Nothing is implemented yet. The package exists to fence the licensing: a port of +//! NRLMSIS 2.x cannot be distributed on the terms the rest of this repository uses, so it +//! lives here rather than in `nrlmsise00`. Read `readme.md` before writing any of it. diff --git a/plan.md b/plan.md new file mode 100644 index 0000000..e7f82fc --- /dev/null +++ b/plan.md @@ -0,0 +1,129 @@ +# NRLMSISE-00, as a crate + +**Status:** planned, not started +**Created:** 2026-10-01 +**Why a separate crate:** it is a self-contained empirical model with its own validation +story, and nothing about it is specific to the library that will consume it. + +## What it is for + +An atmospheric density model generic over its scalar type, so that a propagation using it +can be differentiated as well as solved. + +That is the whole reason to write one. Two Rust implementations already exist and are +usable: + +| Crate | License | Validated against | +|---|---|---| +| `tobari` | MIT | `pymsis`, the official NRL Fortran wrapper | +| `satkit` | MIT OR Apache-2.0 | GMAT drag cases | + +Both are `f64`. Depending on either would mean density could be computed but not +differentiated, and that is not a small loss: density falls by a factor of e about every +50 km, so dropping its dependence on position makes a drag partial badly wrong rather than +slightly wrong. + +So the single acceptance criterion that justifies the work: **the derivative of density +with respect to altitude, taken through the model by a dual number, agrees with central +differences and with `-1/H` from the scale height.** + +## The validation target already exists + +`astrokit/tests/fixtures/nrlmsise00-cases.json` — the seventeen standard test cases, inputs +and outputs at seventeen significant digits. Copy it over. + +Regenerable by `astrokit/scripts/generate-msis-cases.sh`, which fetches Dominik Brodowski's +C translation of the NRL Fortran, compiles it with a driver that prints more digits than its +own test does, runs it, and discards the source. What is committed is numbers, which are +facts about the model rather than anyone's code. The reference's SHA-256 is in the fixture +header. + +The cases vary one input at a time from a baseline of day 172, 29000 s UT, 400 km, 60 N, +70 W, local solar time 16 h, F10.7 and its 81-day average 150, ap 4. Between them they reach +0 to 1000 km in altitude, the equator, local midnight, low and high flux, a storm, and the +two cases that use the seven-element ap history rather than a daily value. + +**Make these numbers.** Then widen with a grid. + +## Order of work + +1. **Coefficient tables, generated rather than transcribed.** `nrlmsise-00_data.c` holds PT, + PD (9 rows), PS, PDL (2), PTM, PDM (8), PTL (4), PMA (10), SAM and PAVGM — about 2700 + numbers. Write a script that emits them as Rust statics, in the manner of + `astrokit/scripts/generate-gravity-field.py`. Do it alongside the structure, since the + shapes have to match what reads them. Transcribing by hand is the classic way to lose a + week. +2. **The small helpers, each with its own test.** `spline`, `splint`, `splini`, `densu`, + `densm`, `ccor`, `ccor2`, `scalh`, `dnet`, `glatf`, `zeta`. These are where a port + quietly goes wrong and they are individually checkable, which the big ones are not. +3. **`globe7` and `glob7s`** — the expansions in latitude, day of year, local time and flux. + The largest pieces, and the ones the switches act on. +4. **`gts7`**, then **`gtd7`** and **`gtd7d`**. +5. **The seventeen cases.** +6. **A grid fixture**: altitude by latitude by local time by flux by ap, from the same + script, to catch what the seventeen happen not to exercise. + +## What genericity needs + +Everything the model computes with is available on a scalar trait of the usual shape — +`exp`, `log`, `sqrt`, `tanh`, `cos`, `sin`, `powi`, `atan`. Three rules, all learned the +hard way in `astrokit`: + +- **Every magnitude comparison branches on the real part.** There are many: the altitude + bands, the exponent clamps in `ccor` and `dnet`, the `g0` and `sumex` guards. A dual + number cannot be compared, and the branch is correct on the real part because the + quantity being tested is a real one. +- **Coefficient tables and switch flags stay `f64`.** `T op f64` works, so lifting them + would only cost memory and cache. +- **`f64` on the left of an operator is not implemented.** `T * f64` is; `f64 * T` is not, + and cannot be, because of the orphan rule. This has bitten twice in `astrokit`. + +## Traps, roughly by how expensive they are to find late + +- **A consumer computing drag wants `gtd7d`, not `gtd7`.** They differ only in the total + mass density: `gtd7d` includes anomalous oxygen and `gtd7` does not, which matters above + about 500 km. The fixture gives all nine number densities, so both totals can be checked + from it — `gtd7d` is + `1.66e-24 * (4 He + 16 O + 28 N2 + 32 O2 + 40 Ar + H + 14 N + 16 anomalous O)`. + Expose both and make the difference obvious in the names and the docs. +- **Fortran is 1-indexed and the C translation already shifted the arrays.** Pick one source + and stay with it. Mixing them is how an off-by-one gets in. +- **Units.** The model returns cm^-3 and g/cm^3 unless its metric switch is set. Decide once + whether the crate speaks SI at its boundary — it should — and convert in exactly one + place. The fixture is in the model's own units and says so in its header. +- **`switches[9] = -1` selects the ap-history mode**, which is what a real propagation uses + and what cases 15 and 16 exercise. The daily-ap mode is the simpler default and is not the + one that matters. +- **Local solar time has to agree with the seconds of day and the longitude**, as + `lst = sec/3600 + lon/15`. The model does not check and gives quietly wrong answers when + they disagree. Derive it inside rather than taking it as an input. +- **The 23 switches are a real part of the interface**, not a detail: they turn individual + terms on and off, and a `-1` means something different from a `0`. Model them as a type + rather than an array of floats if it can be done without cost. + +## Checks beyond matching the reference + +- Density falls monotonically with altitude from 100 to 1000 km, and its logarithmic slope + is a scale height in the tens of kilometers. +- Day is denser than night at the same altitude; a storm is denser than quiet; high flux is + denser than low. +- **It differentiates.** The acceptance criterion above. Without this the crate has no + reason to exist. + +## What the consumer already provides + +`astrokit::atmosphere::drivers` reads a committed record of F10.7 and ap, and gives the +previous day's observed flux, the 81-day centered average and the seven-element ap history +in the order the model wants them. So the crate's interface should take those as plain +numbers and own no data of its own. + +One consequence worth knowing: the centered 81-day average needs forty days either side, so +the usable end of any driver record is forty days before its last measurement. + +## Naming + +`nrlmsise00` is free on crates.io as of 2026-10-01 — confirm before publishing. MSIS is a +registered trademark; `tobari`'s module doc handles this well, claiming nominative fair use +for identifying compatibility. The model itself is the work of Picone, Hedin and Drob at the +US Naval Research Laboratory, believed to be in the public domain as a US Government work +under 17 U.S.C. 105, though NRL attached no explicit license. Say so. diff --git a/readme.md b/readme.md new file mode 100644 index 0000000..7f93a85 --- /dev/null +++ b/readme.md @@ -0,0 +1,182 @@ +# nrlmsise00 + +The NRLMSISE-00 empirical atmosphere model, generic over its scalar type. + +Evaluated at `f64` it gives density and temperature. Evaluated at a forward-mode dual +number it gives density *and* its exact derivatives, which is the reason this crate exists: +density falls by a factor of e about every fifty kilometers, so a drag partial that drops +its dependence on position is badly wrong rather than slightly wrong. Two other Rust +implementations exist and both are `f64` only. + +```rust +use nrlmsise00::{Input, MagneticActivity, Model}; + +let model = Model::new(); +let output = model.gtd7d(&Input::consistent( + 172, // day of year + 29000.0, // seconds of universal time + 400.0, // altitude, km + 60.0, // latitude, degrees north + -70.0, // longitude, degrees east + 150.0, // 81-day average F10.7, centered + 150.0, // previous day's F10.7 + MagneticActivity::Daily { ap: 4.0 }, +)); + +// SI at the boundary: kg/m^3 and m^-3. Local solar time comes out at 3.4 h here, since +// `consistent` derives it from the universal time and the longitude. +assert!((output.total_mass - 2.400e-12).abs() < 0.001e-12); +assert!((output.temperature - 1098.2).abs() < 0.1); +``` + +And the derivative, through the model rather than around it: + +```rust +# #[cfg(feature = "autodiff")] +# fn main() { +use num_dual::{Dual64, DualNum}; +use nrlmsise00::{Input, MagneticActivity, Model, Scalar}; + +let model = Model::new(); +let altitude = Dual64::from(400.0).derivative(); +let output = model.gtd7d(&Input::consistent( + 172, + Dual64::lift(29000.0), + altitude, + Dual64::lift(60.0), + Dual64::lift(-70.0), + Dual64::lift(150.0), + Dual64::lift(150.0), + MagneticActivity::Daily { ap: Dual64::lift(4.0) }, +)); + +// d(rho)/dz, in kg/m^3 per km, and the scale height it implies. +let scale_height = -output.total_mass.re / output.total_mass.eps; +assert!((scale_height - 55.8).abs() < 0.1); +# } +# #[cfg(not(feature = "autodiff"))] +# fn main() {} +``` + +## `gtd7` or `gtd7d` + +They differ in one number. `gtd7`'s total mass density sums helium, atomic oxygen, +molecular nitrogen, molecular oxygen, argon, hydrogen and atomic nitrogen. `gtd7d` also +includes anomalous oxygen, which is hot atomic oxygen and is 18.6% of the mass at 1000 km +in the model's own standard case. **A drag calculation wants `gtd7d`.** The individual +number densities are identical either way. + +## How closely it matches the reference + +At `f64`, bit for bit, over every case there is to compare against: + +| What | Cases | Values compared | +|---|---|---| +| The standard test cases | 17 | 187 | +| A wide input grid, fifty altitudes against sixty scenarios under eight switch settings | 2880 | 31680 | +| The individual helpers, expansions and profiles | 819 | several thousand | + +The comparisons are exact rather than approximate because an approximate one would not +notice a term dropped from an expansion whose contribution happens to be small where it is +sampled. The fixtures hold the reference's own output at seventeen significant digits and +are regenerated by the scripts in `scripts/`, which fetch +[Dominik Brodowski's C translation](https://github.com/magnific0/nrlmsise-00) of the NRL +Fortran, run it, and discard the source: what is committed is numbers, which are facts +about the model rather than anyone's code. + +At a dual type the value agrees to about 1e-14 rather than exactly, because `num-dual` +computes a division as a reciprocal and a multiply. See the `scalar` module docs. + +## Where it deliberately differs from the reference + +The reference keeps its working state in file-scope statics, so two of its answers depend +on what was asked before them. Both are fixed here, and both are fixed by computing a +value the reference reads without having written rather than by changing any arithmetic: + +- **At exactly 32.5 km**, it splines through temperature nodes its own call never filled. +- **With switch 15 off, below 72.5 km**, it scales every species from a mixed nitrogen + density its own call never computed. + +These nodes and that density do not depend on altitude, so filling them reproduces what a +preceding call would have left, which is why the grid fixture still matches at 32.5 km in +sixty scenarios. Nothing else departs from the reference's control flow. + +## It is not continuous in altitude + +Worth knowing before integrating through it. Each species' mixed correction is dropped +above a fitted altitude by a test on the altitude alone, and the model's three vertical +regions are joined by switches rather than smoothly, so the density steps. Sweeping 72.5 to +1000 km at ten meters and comparing each interval against the model's own derivative finds +eight places where it does, and no others: + +| Altitude | Total mass density | What happens there | +|---|---|---| +| 72.5 km | 1.0e-3 | the join between the model's two halves | +| 123.435 km | 1.5e-3 | `za`, the join between the Bates profile and the spline below it | +| 160 km | 7.1e-5 | molecular nitrogen's mixed correction is dropped | +| 240 km | 2.3e-6 | argon's | +| 250 km | 1.9e-5 | molecular oxygen's | +| 300 km | 5.3e-5 | atomic oxygen's, and the lower thermosphere temperature variation | +| 428.475 km | 6.9e-7 | atomic nitrogen's turbopause blend saturates, a step of about exp(-10) | +| 450 km | 3.5e-5 | atomic nitrogen's mixed correction is dropped | + +Individual species move more than the total does — up to 3e-3 — because the species that +steps is usually not the one carrying the mass. Above 500 km there are no jumps at all. + +The temperature is continuous at all of these but `za`, where the **exospheric temperature +steps by nearly two fifths**: 1027.3 K to 1426.4 K in the standard case. That is the +reference's documented behavior rather than an artifact, its header saying the exospheric +temperature "is set to global average for altitudes below 120 km", and it is what makes +123.435 km the largest discontinuity in the model above 72.5 km. + +## What is not implemented + +`ghp7`, the reference's pressure-level entry point, which answers at a given pressure +rather than a given altitude. It is a secant iteration wrapped around `gtd7`, so a caller +who wants it can write it against this crate; nothing in the model needs it. + +## Units and switches + +The crate answers in SI by default — m^-3, kg/m^3 and K — using the model's own metric +switch, so the conversion happens in one place and is the reference's own. `Units::Native` +gives the cm^-3 and g/cm^3 the published cases are quoted in. + +The twenty-three switches are named rather than indexed, and each has three states: the +reference's 2 keeps a term's cross terms while dropping the term itself. The reference's +switch 9 does two jobs, one of which is to select between a daily ap value and a +seven-element history; that is a statement about the data, so it lives on the input as +`MagneticActivity` and the mode cannot disagree with the values. + +## Drivers + +The solar and geomagnetic values the model reads are measurements, and this crate does not +own them: `f107`, `f107_average` and the ap history are plain numbers on the input, so a +caller with its own record passes them straight in and pays nothing for the convenience it +is not using. + +The `drivers` feature, on by default, is **not implemented yet**. It will add a +compiled-in record of those measurements and a lookup by date, for callers who would rather +not source their own. The feature is declared now so that turning it on later is not a +change to what `default` means. + +## The model is not this crate's work + +NRLMSISE-00 is the work of Mike Picone, Alan Hedin and Doug Drob at the US Naval Research +Laboratory, published as Picone et al. (2002), *NRLMSISE-00 empirical model of the +atmosphere: Statistical comparisons and scientific issues*, J. Geophys. Res. 107(A12). It +is believed to be in the public domain as a work of the US Government under 17 U.S.C. 105; +NRL attached no explicit license to it. The coefficients compiled into this crate are the +model's own. + +MSIS is a registered trademark of the Government of the United States of America, as +represented by the Secretary of the Navy. It is used here only to identify which model this +implements, which is nominative fair use; this crate is not endorsed by or affiliated with +NRL or the US Navy. + +Later versions of the model — NRLMSIS 2.0 and 2.1 — are **not** here and cannot be, on +these terms: they are licensed for academic and non-commercial use only and their methods +are covered by US Patent 10,641,925. See `nrlmsis2/readme.md` in the repository. + +## License + +MIT, for this implementation. diff --git a/scripts/generate-grid-cases.sh b/scripts/generate-grid-cases.sh new file mode 100755 index 0000000..36da591 --- /dev/null +++ b/scripts/generate-grid-cases.sh @@ -0,0 +1,171 @@ +#!/bin/sh +# Generates tests/fixtures/grid-cases.csv: a wide sweep of the model's inputs, to catch +# what the seventeen standard cases happen not to exercise and to hold a performance +# change to the same answers. +# +# The seventeen vary one input at a time from one baseline. That leaves most of the input +# space untouched: no case combines a storm with low flux, none is in the southern +# hemisphere in winter, none sits just either side of the 72.5 and 120 km seams between the +# model's three vertical regions, and only two use the ap history. This sweeps a dense +# ladder of altitudes against a spread of the other inputs, and against eight switch +# settings. +# +# Fetches Dominik Brodowski's C translation of the NRL Fortran, runs it, and throws the +# source away. What is committed is the numbers, which are facts about the model rather than +# anyone's code. The model itself is the work of Picone, Hedin and Drob at the US Naval +# Research Laboratory. Needs a C compiler and network access. +# +# Usage: scripts/generate-grid-cases.sh + +set -e + +root=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd) +out="$root/tests/fixtures/grid-cases.csv" +work=$(mktemp -d) +trap 'rm -rf "$work"' EXIT + +base="https://raw.githubusercontent.com/magnific0/nrlmsise-00/master" +echo "fetching the reference from $base" +for f in nrlmsise-00.c nrlmsise-00.h nrlmsise-00_data.c; do + curl -sS --fail --max-time 120 -L "$base/$f" -o "$work/$f" +done +digest=$(cat "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" | sha256sum | cut -d' ' -f1) +echo "source digest $digest" + +cat > "$work/driver.c" <<'DRIVER' +/* Writes the grid as CSV: the inputs at the digits they need, the outputs at seventeen + * significant digits. Scenarios are drawn from a fixed linear congruential sequence, so + * the same grid comes out every time without a table of it having to be written down. */ +#include +#include +#include "nrlmsise-00.h" + +/* The altitude ladder. Dense through the lower thermosphere, where the model switches + * between its three vertical regions, and either side of every altitude at which a + * species' mixed correction is dropped. */ +static const double ALTS[] = { + 0.0, 0.5, 2.0, 5.0, 10.0, 20.0, 32.4, 32.5, 32.6, 45.0, 55.0, 62.5, 65.0, 70.0, + 72.4, 72.5, 72.6, 80.0, 90.0, 100.0, 110.0, 119.0, 122.0, 123.0, 125.0, 140.0, + 159.0, 161.0, 180.0, 199.0, 201.0, 220.0, 239.0, 241.0, 249.0, 251.0, 280.0, + 299.0, 301.0, 319.0, 321.0, 360.0, 400.0, 449.0, 451.0, 500.0, 600.0, 700.0, + 850.0, 1000.0 +}; +#define NALTS ((int)(sizeof ALTS / sizeof *ALTS)) + +/* How many scenarios of the other inputs to sweep the ladder against. */ +#define NSCENARIOS 60 + +static unsigned long seed = 20261002UL; + +/* A fixed sequence, so the grid is reproducible without being written down. */ +static double next_unit(void) { + seed = seed * 6364136223846793005UL + 1442695040888963407UL; + return (double)((seed >> 33) & 0x7FFFFF) / (double)0x800000; +} + +static double between(double low, double high) { + return low + (high - low) * next_unit(); +} + +int main(void) { + struct nrlmsise_output output; + struct nrlmsise_input input; + struct nrlmsise_flags flags; + struct ap_array aph; + int scenario, i, j, set; + char switches[25]; + + printf("switches,day_of_year,seconds_of_day,altitude_km,latitude_deg,longitude_deg," + "local_solar_time_h,f107_average,f107,ap_daily,ap1,ap2,ap3,ap4,ap5,ap6,ap7," + "he,o,n2,o2,ar,total_mass,h,n,anomalous_o,exospheric_temperature,temperature\n"); + + for (scenario = 0; scenario < NSCENARIOS; scenario++) { + /* Eight switch settings, cycled across the scenarios: everything on in each of + * the two magnetic modes, then one family at a time turned off or set to cross + * terms only. */ + set = scenario % 8; + for (i = 0; i < 24; i++) flags.switches[i] = 1; + flags.switches[0] = 0; + switch (set) { + case 0: flags.switches[9] = -1; break; + case 1: break; + case 2: flags.switches[9] = 0; break; + case 3: flags.switches[9] = -1; flags.switches[15] = 0; break; + case 4: flags.switches[9] = -1; flags.switches[7] = 0; + flags.switches[8] = 0; flags.switches[14] = 0; break; + case 5: flags.switches[9] = -1; flags.switches[3] = 2; + flags.switches[5] = 2; flags.switches[6] = 2; break; + case 6: flags.switches[9] = -1; flags.switches[10] = 0; break; + case 7: flags.switches[9] = -1; flags.switches[16] = 0; + flags.switches[17] = 0; flags.switches[18] = 0; + flags.switches[20] = 0; flags.switches[22] = 0; break; + } + /* gtd7 resolves the switches itself; these are the raw values. */ + for (i = 0; i < 24; i++) { + if (i == 9) { + switches[i] = flags.switches[i] == -1 ? 'h' + : (char)('0' + flags.switches[i]); + } else { + switches[i] = (char)('0' + flags.switches[i]); + } + } + switches[24] = '\0'; + + input.year = 0; + input.doy = 1 + (int)between(0.0, 365.0); + input.sec = between(0.0, 86400.0); + input.g_lat = between(-90.0, 90.0); + input.g_long = between(-180.0, 180.0); + /* Consistent with the universal time and the longitude, as the model asks, except + * where a scenario deliberately breaks it to exercise the independent inputs. */ + input.lst = input.sec / 3600.0 + input.g_long / 15.0; + if (scenario % 7 == 3) input.lst = between(0.0, 24.0); + input.f107A = between(65.0, 250.0); + input.f107 = between(65.0, 300.0); + input.ap = between(0.0, 300.0); + for (i = 0; i < 7; i++) aph.a[i] = between(0.0, 300.0); + input.ap_a = &aph; + + for (j = 0; j < NALTS; j++) { + input.alt = ALTS[j]; + /* With switch 15 off, the reference reads a mixed nitrogen density that its + * own call never wrote, so below 72.5 km its answer depends on which call + * last happened to write that static. There is nothing to validate against + * there, so those rows are left out; the same switch setting above 72.5 km, + * where the value is unused, is kept. */ + if (flags.switches[15] == 0 && input.alt < 72.5) continue; + gtd7(&input, &flags, &output); + printf("%s,%d,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g", + switches, input.doy, input.sec, input.alt, input.g_lat, input.g_long, + input.lst, input.f107A, input.f107, input.ap); + for (i = 0; i < 7; i++) printf(",%.17g", aph.a[i]); + for (i = 0; i < 9; i++) printf(",%.17e", output.d[i]); + printf(",%.17e,%.17e\n", output.t[0], output.t[1]); + } + } + return 0; +} +DRIVER + +cc -O2 -o "$work/driver" "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" "$work/driver.c" -lm +mkdir -p "$(dirname "$out")" +{ + echo "# The NRLMSISE-00 model over a wide sweep of its inputs, for validating a port." + echo "# model: NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory" + echo "# reference: $base, Dominik Brodowski's C translation of the NRL Fortran" + echo "# reference_sha256: $digest" + echo "# generated: $(date -u +%Y-%m-%d) by scripts/generate-grid-cases.sh" + echo "# units: the model's own, since switch 0 is left at its standard value." + echo "# altitude km, angles degrees, number densities cm^-3, total mass g/cm^3, K." + echo "# switches: the reference's 24, in order, as 0, 1 or 2; index 9 is h for the ap" + echo "# history mode, which is the reference's -1." + echo "# Rows with switch 15 off and an altitude below 72.5 km are absent: there the" + echo "# reference reads a density its own call never wrote, so its answer depends on" + echo "# what was asked before it and there is nothing to compare against." + "$work/driver" +} > "$out" + +python3 -c " +rows = [l for l in open('$out') if not l.startswith('#')] +print(f'wrote tests/fixtures/grid-cases.csv: {len(rows) - 1} cases, {len(open(\"$out\").read()) / 1e6:.2f} MB') +" diff --git a/scripts/generate-helper-cases.sh b/scripts/generate-helper-cases.sh new file mode 100755 index 0000000..8977d2c --- /dev/null +++ b/scripts/generate-helper-cases.sh @@ -0,0 +1,364 @@ +#!/bin/sh +# Generates tests/fixtures/helper-cases.json: reference values for the small functions a +# port of NRLMSISE-00 is built from, so a failure can be localized to one of them rather +# than only showing up in the nine densities at the end. +# +# Fetches Dominik Brodowski's C translation of the NRL Fortran and compiles a driver that +# #includes the implementation rather than linking against it. That is the point: the shared +# state the model keeps in file-scope statics — gravity, the Earth radius, the mesosphere +# temperature nodes — is then visible to the driver, which can set it explicitly and call +# any helper at a known state. Linking cannot do that. +# +# What is committed is the numbers, which are facts about the model rather than anyone's +# code. The model itself is the work of Picone, Hedin and Drob at the US Naval Research +# Laboratory. Needs a C compiler and network access; rerun it only to regenerate. +# +# Usage: scripts/generate-helper-cases.sh + +set -e + +root=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd) +out="$root/tests/fixtures/helper-cases.json" +work=$(mktemp -d) +trap 'rm -rf "$work"' EXIT + +base="https://raw.githubusercontent.com/magnific0/nrlmsise-00/master" +echo "fetching the reference from $base" +for f in nrlmsise-00.c nrlmsise-00.h nrlmsise-00_data.c; do + curl -sS --fail --max-time 120 -L "$base/$f" -o "$work/$f" +done +digest=$(cat "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" | sha256sum | cut -d' ' -f1) +echo "source digest $digest" + +cat > "$work/driver.c" <<'DRIVER' +/* Prints reference values for the helpers, at seventeen significant digits. + * + * The implementation is #included so that its statics are in this translation unit and can + * be set before a helper is called. printf is redefined first: dnet prints a message on a + * non-positive density, and one of the cases below is there to exercise exactly that. */ +#include +#include +#define printf(...) ((void)0) +#include "nrlmsise-00.c" +#undef printf + +#define N(x) printf("%.17e", (double)(x)) + +static int first_case = 1; + +static void start(const char *what) { + if (!first_case) printf(",\n"); + first_case = 0; + printf(" {\"helper\": \"%s\"", what); +} + +static void arg(const char *name, double v) { + printf(", \"%s\": ", name); + N(v); +} + +static void array(const char *name, const double *v, int n) { + int i; + printf(", \"%s\": [", name); + for (i = 0; i < n; i++) { if (i) printf(", "); N(v[i]); } + printf("]"); +} + +static void end(void) { printf("}"); } + +/* Latitudes to take gravity and the Earth radius at. */ +static const double LATS[] = {-90.0, -60.0, -45.0, -23.5, 0.0, 23.5, 45.0, 60.0, 90.0, 30.7}; + +/* The node sets the model actually splines over, and a non-uniform one. */ +static const double ZN1[5] = {120.0, 110.0, 100.0, 90.0, 72.5}; +static const double ZN2[4] = {72.5, 55.0, 45.0, 32.5}; +static const double ZN3[5] = {32.5, 20.0, 15.0, 10.0, 0.0}; + +int main(void) { + int i, k; + double gv, reff, tz, value; + double xs[5], ys[5], y2[5]; + + printf("[\n"); + + /* glatf: pure. */ + for (i = 0; i < (int)(sizeof LATS / sizeof *LATS); i++) { + glatf(LATS[i], &gv, &reff); + start("glatf"); arg("lat", LATS[i]); arg("gravity", gv); arg("radius", reff); end(); + } + + /* zeta and scalh: read gsurf and re, which are set here rather than by a model run. */ + glatf(45.0, &gsurf, &re); + { + const double zz[] = {0.0, 10.0, 72.5, 120.0, 400.0, 1000.0}; + const double zl[] = {0.0, 32.5, 120.0}; + for (i = 0; i < 6; i++) for (k = 0; k < 3; k++) { + start("zeta"); arg("gsurf", gsurf); arg("re", re); + arg("zz", zz[i]); arg("zl", zl[k]); arg("value", zeta(zz[i], zl[k])); end(); + } + const double masses[] = {4.0, 16.0, 28.0, 32.0}; + const double temps[] = {180.0, 300.0, 1000.0, 1500.0}; + for (i = 0; i < 4; i++) for (k = 0; k < 4; k++) { + start("scalh"); arg("gsurf", gsurf); arg("re", re); + arg("alt", 400.0 + 100.0 * i); arg("xm", masses[i]); arg("temp", temps[k]); + arg("value", scalh(400.0 + 100.0 * i, masses[i], temps[k])); end(); + } + } + + /* ccor and ccor2: pure, and both have two clamped branches to reach. */ + { + const double alts[] = {0.0, 72.5, 100.0, 200.0, 500.0, 1.0e5, -1.0e5}; + const double rs[] = {-0.5, 0.0, 0.25, 2.0}; + for (i = 0; i < 7; i++) for (k = 0; k < 4; k++) { + start("ccor"); arg("alt", alts[i]); arg("r", rs[k]); arg("h1", 20.0); + arg("zh", 100.0); arg("value", ccor(alts[i], rs[k], 20.0, 100.0)); end(); + start("ccor2"); arg("alt", alts[i]); arg("r", rs[k]); arg("h1", 20.0); + arg("zh", 100.0); arg("h2", 5.0); + arg("value", ccor2(alts[i], rs[k], 20.0, 100.0, 5.0)); end(); + } + } + + /* dnet: the blend, both exponent clamps, and the non-positive guard. */ + { + const double dd[] = {1.0e7, 1.0e7, 1.0e7, 1.0e-30, 1.0e30, 0.0, 1.0e7, 0.0}; + const double dm[] = {1.0e7, 1.0e5, 1.0e9, 1.0e7, 1.0e7, 1.0e7, 0.0, 0.0}; + for (i = 0; i < 8; i++) { + start("dnet"); arg("dd", dd[i]); arg("dm", dm[i]); arg("zhm", 4.0e4); + arg("xmm", 28.95); arg("xm", 16.0); + arg("value", dnet(dd[i], dm[i], 4.0e4, 28.95, 16.0)); end(); + } + } + + /* spline, splint and splini, over the model's own node sets. */ + { + const double *nodes[3]; int counts[3]; + nodes[0] = ZN1; counts[0] = 5; + nodes[1] = ZN2; counts[1] = 4; + nodes[2] = ZN3; counts[2] = 5; + for (i = 0; i < 3; i++) { + int n = counts[i]; + /* The abscissae the model splines over are normalized geopotential heights, + * ascending, and the ordinates are inverse temperatures. */ + for (k = 0; k < n; k++) { + xs[k] = (double)k / (double)(n - 1); + ys[k] = 1.0 / (200.0 + 15.0 * k - 0.4 * k * k); + } + double yd1 = -1.5e-5, yd2 = 3.0e-6; + spline(xs, ys, n, yd1, yd2, y2); + start("spline"); array("xs", xs, n); array("ys", ys, n); + arg("yd1", yd1); arg("yd2", yd2); array("y2", y2, n); end(); + for (k = 0; k <= 8; k++) { + double x = -0.1 + 0.15 * k; + splint(xs, ys, y2, n, x, &value); + start("splint"); array("xs", xs, n); array("ys", ys, n); + array("y2", y2, n); arg("x", x); arg("value", value); end(); + splini(xs, ys, y2, n, x, &value); + start("splini"); array("xs", xs, n); array("ys", ys, n); + array("y2", y2, n); arg("x", x); arg("value", value); end(); + } + } + } + + /* densu: needs gsurf, re, the tn1 nodes and the tgn1 gradients. */ + glatf(60.0, &gsurf, &re); + meso_tn1[1] = 365.0; meso_tn1[2] = 240.0; meso_tn1[3] = 195.0; meso_tn1[4] = 208.0; + meso_tgn1[0] = 0.0; meso_tgn1[1] = 8.0; + { + const double alts[] = {0.0, 50.0, 72.5, 90.0, 110.0, 120.0, 200.0, 400.0, 1000.0}; + const double masses[] = {0.0, 4.0, 16.0, 28.0}; + const double alphas[] = {0.0, -0.38, 0.0, 0.0}; + double zn1[5]; + for (k = 0; k < 5; k++) zn1[k] = ZN1[k]; + for (i = 0; i < 9; i++) for (k = 0; k < 4; k++) { + double tn1[5], tgn1[2]; + int j; + for (j = 0; j < 5; j++) tn1[j] = meso_tn1[j]; + tgn1[0] = meso_tgn1[0]; tgn1[1] = meso_tgn1[1]; + tz = 0.0; + value = densu(alts[i], 3.0e11, 1250.0, 386.0, masses[k], alphas[k], &tz, + 120.0, 0.02, 5, zn1, tn1, tgn1); + start("densu"); arg("gsurf", gsurf); arg("re", re); + arg("alt", alts[i]); arg("dlb", 3.0e11); arg("tinf", 1250.0); arg("tlb", 386.0); + arg("xm", masses[k]); arg("alpha", alphas[k]); arg("zlb", 120.0); + arg("s2", 0.02); array("zn1", zn1, 5); + array("tn1_in", tn1, 5); array("tgn1_in", tgn1, 2); + arg("value", value); arg("tz", tz); + /* densu writes the Bates temperature and gradient back into node zero. */ + array("tn1_out", tn1, 5); array("tgn1_out", tgn1, 2); end(); + } + } + + /* densm: needs the tn2 and tn3 nodes and their gradients. */ + { + double tn2[4] = {208.0, 260.0, 268.0, 228.0}; + double tgn2[2] = {8.0, -3.0}; + double tn3[5] = {228.0, 218.0, 214.0, 222.0, 288.0}; + double tgn3[2] = {-3.0, -6.0}; + double zn2[4], zn3[5]; + const double alts[] = {0.0, 5.0, 10.0, 20.0, 32.5, 45.0, 60.0, 72.5, 80.0}; + const double masses[] = {0.0, 28.95}; + for (k = 0; k < 4; k++) zn2[k] = ZN2[k]; + for (k = 0; k < 5; k++) zn3[k] = ZN3[k]; + for (i = 0; i < 9; i++) for (k = 0; k < 2; k++) { + double a2[4], g2[2], a3[5], g3[2]; + int j; + for (j = 0; j < 4; j++) a2[j] = tn2[j]; + for (j = 0; j < 5; j++) a3[j] = tn3[j]; + g2[0] = tgn2[0]; g2[1] = tgn2[1]; g3[0] = tgn3[0]; g3[1] = tgn3[1]; + tz = 0.0; + value = densm(alts[i], 1.0e19, masses[k], &tz, 5, zn3, a3, g3, 4, zn2, a2, g2); + start("densm"); arg("gsurf", gsurf); arg("re", re); + arg("alt", alts[i]); arg("d0", 1.0e19); arg("xm", masses[k]); + array("zn3", zn3, 5); array("zn2", zn2, 4); + array("tn3", a3, 5); array("tgn3", g3, 2); + array("tn2", a2, 4); array("tgn2", g2, 2); + arg("value", value); arg("tz", tz); end(); + } + } + + /* globe7 and glob7s: the expansions, over every coefficient table each is called + * with. They share the LPOLY state: globe7 writes the Legendre polynomials, the local + * time harmonics, the flux departure and the magnetic activity functions, and glob7s + * reads them. So each glob7s case records the state it was called at, which is + * whatever the preceding globe7 left. */ + { + struct nrlmsise_input in[6]; + struct nrlmsise_flags flags; + struct ap_array aph; + int c, s; + /* The tables globe7 is called with: pt, ps, then the nine rows of pd. */ + double *g7[11]; + const char *g7name[11] = {"pt", "ps", "pd0", "pd1", "pd2", "pd3", "pd4", + "pd5", "pd6", "pd7", "pd8"}; + /* The tables glob7s is called with: the four rows of ptl, then the ten of pma. */ + double *g7s[14]; + const char *g7sname[14] = {"ptl0", "ptl1", "ptl2", "ptl3", "pma0", "pma1", "pma2", + "pma3", "pma4", "pma5", "pma6", "pma7", "pma8", "pma9"}; + g7[0] = pt; g7[1] = ps; + for (i = 0; i < 9; i++) g7[2 + i] = pd[i]; + for (i = 0; i < 4; i++) g7s[i] = ptl[i]; + for (i = 0; i < 10; i++) g7s[4 + i] = pma[i]; + + for (i = 0; i < 7; i++) aph.a[i] = 40.0 + 20.0 * i; + + /* A spread of input states: the standard case, then the equator, local midnight, + * a storm, low flux and the southern hemisphere in the other season. */ + for (i = 0; i < 6; i++) { + in[i].year = 0; in[i].doy = 172; in[i].sec = 29000.0; in[i].alt = 400.0; + in[i].g_lat = 60.0; in[i].g_long = -70.0; in[i].lst = 16.0; + in[i].f107A = 150.0; in[i].f107 = 150.0; in[i].ap = 4.0; in[i].ap_a = &aph; + } + in[1].g_lat = 0.0; + in[2].lst = 0.0; in[2].sec = 0.0; in[2].g_long = 0.0; + in[3].ap = 207.0; in[3].f107 = 230.0; + in[4].f107A = 70.0; in[4].f107 = 68.0; + in[5].doy = 15; in[5].g_lat = -45.0; in[5].g_long = 150.0; in[5].lst = 9.5; + + /* Switch sets: everything on, the daily-ap mode, cross terms only on the + * seasonal terms, and the diurnal family off. */ + for (s = 0; s < 4; s++) { + for (k = 0; k < 24; k++) flags.switches[k] = 1; + flags.switches[0] = 0; + if (s == 0) flags.switches[9] = -1; + if (s == 2) { flags.switches[3] = 2; flags.switches[5] = 2; flags.switches[9] = -1; } + if (s == 3) { flags.switches[7] = 0; flags.switches[8] = 0; + flags.switches[14] = 0; flags.switches[9] = 0; } + tselec(&flags); + + for (c = 0; c < 6; c++) { + for (i = 0; i < 11; i++) { + double value = globe7(g7[i], &in[c], &flags); + start("globe7"); + printf(", \"table\": \"%s\", \"switch_set\": %d, \"case\": %d", + g7name[i], s, c); + array("switches_in", (double[24]){ + flags.switches[0], flags.switches[1], flags.switches[2], + flags.switches[3], flags.switches[4], flags.switches[5], + flags.switches[6], flags.switches[7], flags.switches[8], + flags.switches[9], flags.switches[10], flags.switches[11], + flags.switches[12], flags.switches[13], flags.switches[14], + flags.switches[15], flags.switches[16], flags.switches[17], + flags.switches[18], flags.switches[19], flags.switches[20], + flags.switches[21], flags.switches[22], flags.switches[23]}, 24); + arg("day_of_year", in[c].doy); + arg("seconds_of_day", in[c].sec); + arg("latitude_deg", in[c].g_lat); + arg("longitude_deg", in[c].g_long); + arg("local_solar_time_h", in[c].lst); + arg("f107_average", in[c].f107A); + arg("f107", in[c].f107); + arg("ap_daily", in[c].ap); + array("ap_history", aph.a, 7); + arg("value", value); + /* The state it leaves behind, which glob7s then reads. */ + array("plg0", plg[0], 9); array("plg1", plg[1], 9); + array("plg2", plg[2], 9); array("plg3", plg[3], 9); + arg("stloc", stloc); arg("ctloc", ctloc); + arg("s2tloc", s2tloc); arg("c2tloc", c2tloc); + arg("s3tloc", s3tloc); arg("c3tloc", c3tloc); + arg("dfa", dfa); arg("apdf", apdf); array("apt", apt, 4); + end(); + } + /* globe7 with pt again, so the state the glob7s cases record is the one a + * model run would have left. */ + (void) globe7(pt, &in[c], &flags); + for (i = 0; i < 14; i++) { + double value = glob7s(g7s[i], &in[c], &flags); + start("glob7s"); + printf(", \"table\": \"%s\", \"switch_set\": %d, \"case\": %d", + g7sname[i], s, c); + array("switches_in", (double[24]){ + flags.switches[0], flags.switches[1], flags.switches[2], + flags.switches[3], flags.switches[4], flags.switches[5], + flags.switches[6], flags.switches[7], flags.switches[8], + flags.switches[9], flags.switches[10], flags.switches[11], + flags.switches[12], flags.switches[13], flags.switches[14], + flags.switches[15], flags.switches[16], flags.switches[17], + flags.switches[18], flags.switches[19], flags.switches[20], + flags.switches[21], flags.switches[22], flags.switches[23]}, 24); + arg("day_of_year", in[c].doy); + arg("longitude_deg", in[c].g_long); + array("plg0", plg[0], 9); array("plg1", plg[1], 9); + array("plg2", plg[2], 9); array("plg3", plg[3], 9); + arg("stloc", stloc); arg("ctloc", ctloc); + arg("s2tloc", s2tloc); arg("c2tloc", c2tloc); + arg("s3tloc", s3tloc); arg("c3tloc", c3tloc); + arg("dfa", dfa); arg("apdf", apdf); array("apt", apt, 4); + arg("value", value); + end(); + } + } + } + } + + printf("\n]\n"); + return 0; +} +DRIVER + +cc -O2 -o "$work/driver" "$work/driver.c" "$work/nrlmsise-00_data.c" -lm -I"$work" +mkdir -p "$(dirname "$out")" +{ + echo "{" + echo " \"what\": \"Reference values for the helper functions NRLMSISE-00 is built from.\"," + echo " \"model\": \"NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory\"," + echo " \"reference\": \"$base, Dominik Brodowski's C translation of the NRL Fortran\"," + echo " \"reference_sha256\": \"$digest\"," + echo " \"generated\": \"$(date -u +%Y-%m-%d)\"," + echo " \"generated_by\": \"scripts/generate-helper-cases.sh\"," + echo " \"units\": \"The model's own: km, K, cm^-3, g/cm^3, and cm/s^2 for gravity.\"," + echo " \"note\": \"gsurf and re are the shared state the helper was called at, not arguments to it.\"," + echo " \"cases\":" + "$work/driver" | sed 's/^/ /' + echo "}" +} > "$out" + +python3 -c " +import json +from collections import Counter +cases = json.load(open('$out'))['cases'] +counts = Counter(c['helper'] for c in cases) +print(f'wrote tests/fixtures/helper-cases.json: {len(cases)} cases') +for name, n in sorted(counts.items()): + print(f' {name:>8}: {n}') +" diff --git a/scripts/generate-msis-cases.sh b/scripts/generate-msis-cases.sh new file mode 100755 index 0000000..95c5e7d --- /dev/null +++ b/scripts/generate-msis-cases.sh @@ -0,0 +1,117 @@ +#!/bin/sh +# Generates tests/fixtures/nrlmsise00-cases.json: the seventeen standard NRLMSISE-00 test +# cases, with inputs and outputs at full precision, for a port to be validated against. +# +# Fetches Dominik Brodowski's C translation of the NRL Fortran, compiles it with a driver +# that prints more digits than its own test does, runs it, and throws the source away. What +# is committed is the numbers, which are facts about the model rather than anyone's code. +# +# The model itself is the work of Picone, Hedin and Drob at the US Naval Research +# Laboratory. Needs a C compiler and network access; rerun it only to regenerate. +# +# Usage: scripts/generate-msis-cases.sh + +set -e + +root=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd) +out="$root/tests/fixtures/nrlmsise00-cases.json" +work=$(mktemp -d) +trap 'rm -rf "$work"' EXIT + +base="https://raw.githubusercontent.com/magnific0/nrlmsise-00/master" +echo "fetching the reference from $base" +for f in nrlmsise-00.c nrlmsise-00.h nrlmsise-00_data.c; do + curl -sS --fail --max-time 120 -L "$base/$f" -o "$work/$f" +done +digest=$(cat "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" | sha256sum | cut -d' ' -f1) +echo "source digest $digest" + +cat > "$work/driver.c" <<'DRIVER' +/* Prints the seventeen standard cases as JSON, at seventeen significant digits. + * + * The cases are those of the reference distribution's own test_gtd7, which varies one + * input at a time from a common baseline: day 172, 29000 s UT, 400 km, 60 N, 70 W, local + * solar time 16 h, F10.7 and its average 150, ap 4. Cases 15 and 16 use the seven-element + * ap history instead of the daily value, which is the mode a real propagation runs in. */ +#include +#include "nrlmsise-00.h" + +int main(void) { + struct nrlmsise_output output[17]; + struct nrlmsise_input input[17]; + struct nrlmsise_flags flags; + struct ap_array aph; + int i, j; + + for (i = 0; i < 7; i++) aph.a[i] = 100; + flags.switches[0] = 0; + for (i = 1; i < 24; i++) flags.switches[i] = 1; + for (i = 0; i < 17; i++) { + input[i].doy = 172; input[i].year = 0; input[i].sec = 29000; + input[i].alt = 400; input[i].g_lat = 60; input[i].g_long = -70; + input[i].lst = 16; input[i].f107A = 150; input[i].f107 = 150; input[i].ap = 4; + } + input[1].doy = 81; + input[2].sec = 75000; input[2].alt = 1000; + input[3].alt = 100; + input[10].alt = 0; input[11].alt = 10; input[12].alt = 30; + input[13].alt = 50; input[14].alt = 70; input[16].alt = 100; + input[4].g_lat = 0; + input[5].g_long = 0; + input[6].lst = 4; + input[7].f107A = 70; + input[8].f107 = 180; + input[9].ap = 40; + input[15].ap_a = &aph; input[16].ap_a = &aph; + + for (i = 0; i < 15; i++) gtd7(&input[i], &flags, &output[i]); + flags.switches[9] = -1; + for (i = 15; i < 17; i++) gtd7(&input[i], &flags, &output[i]); + + printf("[\n"); + for (i = 0; i < 17; i++) { + printf(" {\"case\": %d,\n", i); + printf(" \"day_of_year\": %d, \"seconds_of_day\": %.17e,\n", + input[i].doy, input[i].sec); + printf(" \"altitude_km\": %.17e, \"latitude_deg\": %.17e, \"longitude_deg\": %.17e,\n", + input[i].alt, input[i].g_lat, input[i].g_long); + printf(" \"local_solar_time_h\": %.17e,\n", input[i].lst); + printf(" \"f107_average\": %.17e, \"f107\": %.17e, \"ap_daily\": %.17e,\n", + input[i].f107A, input[i].f107, input[i].ap); + printf(" \"ap_history\": %s,\n", i >= 15 ? "[100,100,100,100,100,100,100]" : "null"); + printf(" \"densities\": ["); + for (j = 0; j < 9; j++) printf("%s%.17e", j ? ", " : "", output[i].d[j]); + printf("],\n \"temperatures\": [%.17e, %.17e]\n", output[i].t[0], output[i].t[1]); + printf(" }%s\n", i == 16 ? "" : ","); + } + printf("]\n"); + return 0; +} +DRIVER + +cc -O2 -o "$work/driver" "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" "$work/driver.c" -lm +mkdir -p "$(dirname "$out")" +{ + echo "{" + echo " \"what\": \"The seventeen standard NRLMSISE-00 test cases, for validating a port.\"," + echo " \"model\": \"NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory\"," + echo " \"reference\": \"$base, Dominik Brodowski's C translation of the NRL Fortran\"," + echo " \"reference_sha256\": \"$digest\"," + echo " \"generated\": \"$(date -u +%Y-%m-%d)\"," + echo " \"generated_by\": \"scripts/generate-msis-cases.sh\"," + echo " \"densities\": \"He, O, N2, O2, Ar, total mass, H, N, anomalous O. Number densities in cm^-3 and the total in g/cm^3, which is what the model returns unless its metric switch is set; convert at the boundary.\"," + echo " \"temperatures\": \"exospheric, then at the altitude asked for, in K.\"," + echo " \"cases\":" + "$work/driver" | sed 's/^/ /' + echo "}" +} > "$out" + +python3 -c " +import json, sys +cases = json.load(open('$out'))['cases'] +assert len(cases) == 17, len(cases) +print(f'wrote tests/fixtures/nrlmsise00-cases.json: {len(cases)} cases') +for c in (0, 3, 16): + d = cases[c] + print(f\" case {d['case']:>2}: {d['altitude_km']:>6.0f} km -> total mass {d['densities'][5]:.6e} g/cm^3\") +" diff --git a/scripts/generate-tables.py b/scripts/generate-tables.py new file mode 100755 index 0000000..42fc194 --- /dev/null +++ b/scripts/generate-tables.py @@ -0,0 +1,163 @@ +#!/usr/bin/env python3 +"""Generates src/tables.rs: the NRLMSISE-00 coefficient tables as Rust statics. + +Fetches Dominik Brodowski's C translation of the NRL Fortran, parses the block data out of +nrlmsise-00_data.c, and writes the numbers as statics with the shapes the model reads them +at. The source is not kept. What is committed is the coefficients, which are the model +itself rather than anyone's code. + +The decimal digits are emitted exactly as the reference writes them. Both C and Rust round +decimal to binary correctly, so the compiled doubles are bit-identical to the reference's. + +The model itself is the work of Picone, Hedin and Drob at the US Naval Research Laboratory. +Needs network access; rerun it only to regenerate. + +Usage: scripts/generate-tables.py +""" + +import hashlib +import re +import subprocess +import urllib.request +from datetime import date, timezone, datetime +from pathlib import Path + +BASE = "https://raw.githubusercontent.com/magnific0/nrlmsise-00/master" +ROOT = Path(__file__).resolve().parent.parent +OUT = ROOT / "src" / "tables.rs" + +# The tables the model reads, with the shape it reads them at and what each one sets. +# +# ptm is declared double[50] in the data file but extern double[10] in the model, and only +# its first ten values are initialized. Ten is what is emitted: indices 0 to 8 are read and +# index 9 is the last one the data file gives. +TABLES = [ + ("pt", "PT", (150,), "Exospheric temperature."), + ("pd", "PD", (9, 150), "Species densities at the lower boundary, and TLB."), + ("ps", "PS", (150,), "The 120 km temperature gradient, S."), + ("pdl", "PDL", (2, 25), "Turbopause heights, chemistry corrections and scale lengths."), + ("ptm", "PTM", (10,), "Lower boundary temperatures, gradient and height."), + ("pdm", "PDM", (8, 10), "Lower boundary densities, turbopause and correction heights."), + ("ptl", "PTL", (4, 100), "Lower thermosphere temperature nodes, TN1."), + ("pma", "PMA", (10, 100), "Mesosphere and stratosphere temperature nodes, TN2 and TN3."), + ("pavgm", "PAVGM", (10,), "Global average temperatures the TN2 and TN3 nodes scale."), +] + +# sam[100] is in the data file and no part of NRLMSISE-00 reads it, so it is not emitted. +UNUSED = ["sam"] + + +def fetch(name: str) -> str: + with urllib.request.urlopen(f"{BASE}/{name}", timeout=120) as response: + return response.read().decode("ascii") + + +def numbers(text: str) -> list[str]: + """The numeric literals of a C initializer, as the digits the reference writes.""" + return re.findall(r"[-+]?\d*\.?\d+(?:[Ee][-+]?\d+)?", text) + + +def parse(source: str, name: str, shape: tuple[int, ...]) -> tuple[list[str], list[str]]: + """The literals of one table, and the comment labelling each row of a 2D one.""" + pattern = rf"double\s+{name}\s*(?:\[\d+\])+\s*=\s*\{{(.*?)\}};" + match = re.search(pattern, source, re.S) + if match is None: + raise SystemExit(f"{name}: not found in the reference data file") + body = match.group(1) + + # Row labels, where the reference gives them: a comment between one row's closing brace + # and the next row's opening brace labels the row that follows it. + labels = ["" for _ in range(shape[0] if len(shape) > 1 else 1)] + if len(shape) > 1: + head = source[: match.start()] + first = re.findall(r"/\*\s*([^*]*?)\s*\*/\s*$", head.strip()) + labels[0] = first[0] if first else "" + for index, label in enumerate(re.findall(r"\}\s*,\s*/\*\s*(.*?)\s*\*/\s*\{", body, re.S)): + if index + 1 < len(labels): + labels[index + 1] = " ".join(label.split()) + + literals = numbers(re.sub(r"/\*.*?\*/", "", body, flags=re.S)) + wanted = 1 + for dimension in shape: + wanted *= dimension + if len(literals) > wanted: + raise SystemExit(f"{name}: {len(literals)} literals for a shape of {shape}") + # ptm is initialized short of its declared length; C zero-fills the rest. + literals += ["0.00000E+00"] * (wanted - len(literals)) + return literals, labels + + +def rust(literal: str) -> str: + """One C literal as a Rust one, with the same digits.""" + text = literal.lower().replace("e+0", "e").replace("e-0", "e-") + if text.endswith("e"): + text = text[:-1] + mantissa, _, exponent = text.partition("e") + if "." not in mantissa: + mantissa += ".0" + return mantissa if exponent in ("", "0") else f"{mantissa}e{exponent}" + + +def rows(literals: list[str], per_line: int = 5) -> list[str]: + out = [] + for start in range(0, len(literals), per_line): + out.append(", ".join(rust(value) for value in literals[start : start + per_line]) + ",") + return out + + +def emit(source: str, digest: str) -> str: + lines = [ + "//! The NRLMSISE-00 coefficient tables.", + "//!", + "//! Generated by `scripts/generate-tables.py` from Dominik Brodowski's C translation", + "//! of the NRL Fortran; do not edit. The coefficients are the model, which is the work", + "//! of Picone, Hedin and Drob at the US Naval Research Laboratory.", + "//!", + f"//! Source: <{BASE}>", + f"//! Source SHA-256 (nrlmsise-00.c and nrlmsise-00_data.c): {digest}", + f"//! Generated: {date.today().isoformat()}", + "//!", + "//! The reference's `sam[100]` is not here: no part of NRLMSISE-00 reads it.", + "", + "#![allow(clippy::all)]", + "", + ] + for name, konst, shape, what in TABLES: + literals, labels = parse(source, name, shape) + lines.append(f"/// {what}") + lines.append(f"///") + lines.append(f"/// `{name}` in the reference.") + if len(shape) == 1: + lines.append(f"pub(crate) static {konst}: [f64; {shape[0]}] = [") + lines += [f" {line}" for line in rows(literals)] + lines.append("];") + else: + lines.append(f"pub(crate) static {konst}: [[f64; {shape[1]}]; {shape[0]}] = [") + for row in range(shape[0]): + chunk = literals[row * shape[1] : (row + 1) * shape[1]] + label = f" // {labels[row]}" if labels[row] else "" + lines.append(f" [{label}") + lines += [f" {line}" for line in rows(chunk)] + lines.append(" ],") + lines.append("];") + lines.append("") + return "\n".join(lines) + + +def main() -> None: + files = {name: fetch(name) for name in ("nrlmsise-00.c", "nrlmsise-00_data.c")} + digest = hashlib.sha256( + (files["nrlmsise-00.c"] + files["nrlmsise-00_data.c"]).encode("ascii") + ).hexdigest() + print(f"source digest {digest}") + for name in UNUSED: + if f"double {name}" not in files["nrlmsise-00_data.c"]: + raise SystemExit(f"{name} is gone from the reference; check what changed") + OUT.write_text(emit(files["nrlmsise-00_data.c"], digest)) + subprocess.run(["rustfmt", "--edition", "2021", str(OUT)], check=True) + count = len(re.findall(r"-?\d+\.\d+", OUT.read_text())) + print(f"wrote {OUT.relative_to(ROOT)}: {count} coefficients") + + +if __name__ == "__main__": + main() diff --git a/src/expansion.rs b/src/expansion.rs new file mode 100644 index 0000000..29e9584 --- /dev/null +++ b/src/expansion.rs @@ -0,0 +1,692 @@ +//! The expansions in latitude, day of year, local solar time, longitude, flux and magnetic +//! activity: `globe7` for the thermosphere and `glob7s` for below it. +//! +//! These are where the model's three thousand coefficients are spent. Each builds a sum of +//! fourteen terms, one per family of variation, and each family is scaled by the switch +//! that governs it. The switches are indexed here by the reference's own numbers; the +//! names are on [`crate::Switches`]. +//! +//! `globe7` leaves the Legendre polynomials of the latitude, the local time harmonics, the +//! flux departure and the magnetic activity functions in [`Work`], and `glob7s` reads them +//! rather than recomputing them. So `globe7` must be called first, which the model does. +//! +//! Terms that are products of a day-of-year cosine and a coefficient stay `f64`, because +//! the day of year is an integer: `cd32`, `cd18`, `cd14` and `cd39` are real constants of +//! the call and cost nothing to carry at a dual type. + +use crate::helpers::{DGTR, DR, HR, SR}; +use crate::input::{Input, MagneticActivity}; +use crate::scalar::Scalar; +use crate::switches::Resolved; +use crate::work::Work; + +/// The three-hour magnetic activity function, equation A24d. +fn g0(a: T, p: &[f64]) -> T { + // sqrt(p[24]*p[24]) is the reference's way of writing |p[24]|. + let p24 = p[24].abs(); + (a - 4.0) + ((a - 4.0) + (((a - 4.0) * (-p24)).exp() - 1.0) / p24) * (p[25] - 1.0) +} + +/// The normalizing sum of equation A24c. +fn sumex(ex: T) -> T { + (T::lift(1.0) - ex.powf(19.0)) / (T::lift(1.0) - ex) * ex.powf(0.5) + 1.0 +} + +/// The weighted history of magnetic activity, equation A24a. +fn sg0(ex: T, p: &[f64], ap: &[T; 7]) -> T { + (g0(ap[1], p) + + (g0(ap[2], p) * ex + + g0(ap[3], p) * ex * ex + + g0(ap[4], p) * ex.powf(3.0) + + (g0(ap[5], p) * ex.powf(4.0) + g0(ap[6], p) * ex.powf(12.0)) + * (T::lift(1.0) - ex.powf(8.0)) + / (T::lift(1.0) - ex))) + / sumex(ex) +} + +/// The expansion for the upper thermosphere: `globe7`. +/// +/// Returns the sum of the fourteen term families for the coefficient set `p`, which is one +/// of `PT`, `PS` or a row of `PD`. +pub(crate) fn globe7( + p: &[f64], + input: &Input, + switches: &Resolved, + work: &mut Work, +) -> T { + let (sw, swc) = (&switches.sw, &switches.swc); + let mut t = [T::lift(0.0); 14]; + let tloc = input.local_solar_time_h; + let doy = f64::from(input.day_of_year); + + // The associated Legendre polynomials of the latitude. The reference leaves three of + // them commented out, and those stay out: plg[0][7], plg[1][7] and plg[1][8]. + let c = (input.latitude_deg * DGTR).sin(); + let s = (input.latitude_deg * DGTR).cos(); + let c2 = c * c; + let c4 = c2 * c2; + let s2 = s * s; + + let plg = &mut work.plg; + plg[0][1] = c; + plg[0][2] = (c2 * 3.0 - 1.0) * 0.5; + plg[0][3] = (c * 5.0 * c2 - c * 3.0) * 0.5; + plg[0][4] = (c4 * 35.0 - c2 * 30.0 + 3.0) / 8.0; + plg[0][5] = (c2 * 63.0 * c2 * c - c2 * 70.0 * c + c * 15.0) / 8.0; + plg[0][6] = (c * 11.0 * plg[0][5] - plg[0][4] * 5.0) / 6.0; + plg[1][1] = s; + plg[1][2] = c * 3.0 * s; + plg[1][3] = (c2 * 5.0 - 1.0) * 1.5 * s; + plg[1][4] = (c2 * 7.0 * c - c * 3.0) * 2.5 * s; + plg[1][5] = (c4 * 21.0 - c2 * 14.0 + 1.0) * 1.875 * s; + plg[1][6] = (c * 11.0 * plg[1][5] - plg[1][4] * 6.0) / 5.0; + plg[2][2] = s2 * 3.0; + plg[2][3] = s2 * 15.0 * c; + plg[2][4] = (c2 * 7.0 - 1.0) * 7.5 * s2; + plg[2][5] = c * 3.0 * plg[2][4] - plg[2][3] * 2.0; + plg[2][6] = (c * 11.0 * plg[2][5] - plg[2][4] * 7.0) / 4.0; + plg[2][7] = (c * 13.0 * plg[2][6] - plg[2][5] * 8.0) / 5.0; + plg[3][3] = s2 * 15.0 * s; + plg[3][4] = s2 * 105.0 * s * c; + plg[3][5] = (c * 9.0 * plg[3][4] - plg[3][3] * 7.0) / 2.0; + plg[3][6] = (c * 11.0 * plg[3][5] - plg[3][4] * 8.0) / 3.0; + + if !(sw[7] == 0.0 && sw[8] == 0.0 && sw[14] == 0.0) { + work.stloc = (tloc * HR).sin(); + work.ctloc = (tloc * HR).cos(); + work.s2tloc = (tloc * (2.0 * HR)).sin(); + work.c2tloc = (tloc * (2.0 * HR)).cos(); + work.s3tloc = (tloc * (3.0 * HR)).sin(); + work.c3tloc = (tloc * (3.0 * HR)).cos(); + } + + // Day-of-year cosines. Real constants of the call, since the day is an integer. + let cd32 = (DR * (doy - p[31])).cos(); + let cd18 = (2.0 * DR * (doy - p[17])).cos(); + let cd14 = (DR * (doy - p[13])).cos(); + let cd39 = (2.0 * DR * (doy - p[38])).cos(); + + // F10.7 effect. + let df = input.f107 - input.f107_average; + work.dfa = input.f107_average - 150.0; + let dfa = work.dfa; + t[0] = df * p[19] * (dfa * p[59] + 1.0) + df * p[20] * df + dfa * p[21] + dfa.powf(2.0) * p[29]; + let f1 = (dfa * p[47] + df * p[19] + df * p[20] * df) * swc[1] + 1.0; + let f2 = (dfa * p[49] + df * p[19] + df * p[20] * df) * swc[1] + 1.0; + + let plg = work.plg; + + // Time independent. + t[1] = plg[0][2] * p[1] + + plg[0][4] * p[2] + + plg[0][6] * p[22] + + plg[0][2] * p[14] * dfa * swc[1] + + plg[0][1] * p[26]; + + // Symmetrical annual. + t[2] = T::lift(p[18] * cd32); + + // Symmetrical semiannual. + t[3] = (plg[0][2] * p[16] + p[15]) * cd18; + + // Asymmetrical annual. + t[4] = f1 * (plg[0][1] * p[9] + plg[0][3] * p[10]) * cd14; + + // Asymmetrical semiannual. + t[5] = plg[0][1] * p[37] * cd39; + + // Diurnal. + if sw[7] != 0.0 { + let t71 = plg[1][2] * p[11] * cd14 * swc[5]; + let t72 = plg[1][2] * p[12] * cd14 * swc[5]; + t[6] = f2 + * ((plg[1][1] * p[3] + plg[1][3] * p[4] + plg[1][5] * p[27] + t71) * work.ctloc + + (plg[1][1] * p[6] + plg[1][3] * p[7] + plg[1][5] * p[28] + t72) * work.stloc); + } + + // Semidiurnal. + if sw[8] != 0.0 { + let t81 = (plg[2][3] * p[23] + plg[2][5] * p[35]) * cd14 * swc[5]; + let t82 = (plg[2][3] * p[33] + plg[2][5] * p[36]) * cd14 * swc[5]; + t[7] = f2 + * ((plg[2][2] * p[5] + plg[2][4] * p[41] + t81) * work.c2tloc + + (plg[2][2] * p[8] + plg[2][4] * p[42] + t82) * work.s2tloc); + } + + // Terdiurnal. + if sw[14] != 0.0 { + t[13] = f2 + * ((plg[3][3] * p[39] + (plg[3][4] * p[93] + plg[3][6] * p[46]) * cd14 * swc[5]) + * work.s3tloc + + (plg[3][3] * p[40] + (plg[3][4] * p[94] + plg[3][6] * p[48]) * cd14 * swc[5]) + * work.c3tloc); + } + + // Magnetic activity, in whichever of its two modes the input selects. + let sw9 = input.magnetic.sw(); + match &input.magnetic { + MagneticActivity::History { ap } => { + if p[51] != 0.0 { + let mut exp1 = (T::lift(-10800.0 * p[51].abs()) + / ((T::lift(45.0) - input.latitude_deg.abs()) * p[138] + 1.0)) + .exp(); + if exp1.re() > 0.99999 { + exp1 = T::lift(0.99999); + } + // The reference clamps p[24] up to 1e-4 here, writing into the coefficient + // table. No table it is ever called with has a value that small, so the + // clamp cannot fire; `test_the_p24_clamp_cannot_fire` holds that down. + work.apt[0] = sg0(exp1, p, ap); + if sw9 != 0.0 { + t[8] = work.apt[0] + * (T::lift(p[50]) + + plg[0][2] * p[96] + + plg[0][4] * p[54] + + (plg[0][1] * p[125] + plg[0][3] * p[126] + plg[0][5] * p[127]) + * cd14 + * swc[5] + + (plg[1][1] * p[128] + plg[1][3] * p[129] + plg[1][5] * p[130]) + * swc[7] + * ((tloc - p[131]) * HR).cos()); + } + } + } + _ => { + let apd = input.magnetic.daily() - 4.0; + let p44 = if p[43] < 0.0 { 1.0e-5 } else { p[43] }; + let p45 = p[44]; + work.apdf = apd + (apd + ((apd * (-p44)).exp() - 1.0) / p44) * (p45 - 1.0); + if sw9 != 0.0 { + t[8] = work.apdf + * (T::lift(p[32]) + + plg[0][2] * p[45] + + plg[0][4] * p[34] + + (plg[0][1] * p[100] + plg[0][3] * p[101] + plg[0][5] * p[102]) + * cd14 + * swc[5] + + (plg[1][1] * p[121] + plg[1][3] * p[122] + plg[1][5] * p[123]) + * swc[7] + * ((tloc - p[124]) * HR).cos()); + } + } + } + + if sw[10] != 0.0 && input.longitude_deg.re() > -1000.0 { + // Longitudinal. + if sw[11] != 0.0 { + t[10] = (dfa * p[80] * swc[1] + 1.0) + * ((plg[1][2] * p[64] + + plg[1][4] * p[65] + + plg[1][6] * p[66] + + plg[1][1] * p[103] + + plg[1][3] * p[104] + + plg[1][5] * p[105] + + (plg[1][1] * p[109] + plg[1][3] * p[110] + plg[1][5] * p[111]) + * swc[5] + * cd14) + * (input.longitude_deg * DGTR).cos() + + (plg[1][2] * p[90] + + plg[1][4] * p[91] + + plg[1][6] * p[92] + + plg[1][1] * p[106] + + plg[1][3] * p[107] + + plg[1][5] * p[108] + + (plg[1][1] * p[112] + plg[1][3] * p[113] + plg[1][5] * p[114]) + * swc[5] + * cd14) + * (input.longitude_deg * DGTR).sin()); + } + + // Universal time, and mixed universal time and longitude. + if sw[12] != 0.0 { + t[11] = (plg[0][1] * p[95] + 1.0) + * (dfa * p[81] * swc[1] + 1.0) + * (plg[0][1] * p[119] * swc[5] * cd14 + 1.0) + * ((plg[0][1] * p[68] + plg[0][3] * p[69] + plg[0][5] * p[70]) + * ((input.seconds_of_day - p[71]) * SR).cos()); + t[11] = t[11] + + (plg[2][3] * p[76] + plg[2][5] * p[77] + plg[2][7] * p[78]) + * swc[11] + * ((input.seconds_of_day - p[79]) * SR + input.longitude_deg * (2.0 * DGTR)) + .cos() + * (dfa * p[137] * swc[1] + 1.0); + } + + // Mixed magnetic activity, universal time and longitude. + if sw[13] != 0.0 { + match &input.magnetic { + MagneticActivity::History { .. } => { + if p[51] != 0.0 { + t[12] = work.apt[0] + * swc[11] + * (plg[0][1] * p[132] + 1.0) + * ((plg[1][2] * p[52] + plg[1][4] * p[98] + plg[1][6] * p[67]) + * ((input.longitude_deg - p[97]) * DGTR).cos()) + + work.apt[0] + * swc[11] + * swc[5] + * (plg[1][1] * p[133] + plg[1][3] * p[134] + plg[1][5] * p[135]) + * cd14 + * ((input.longitude_deg - p[136]) * DGTR).cos() + + work.apt[0] + * swc[12] + * (plg[0][1] * p[55] + plg[0][3] * p[56] + plg[0][5] * p[57]) + * ((input.seconds_of_day - p[58]) * SR).cos(); + } + } + _ => { + t[12] = work.apdf + * swc[11] + * (plg[0][1] * p[120] + 1.0) + * ((plg[1][2] * p[60] + plg[1][4] * p[61] + plg[1][6] * p[62]) + * ((input.longitude_deg - p[63]) * DGTR).cos()) + + work.apdf + * swc[11] + * swc[5] + * (plg[1][1] * p[115] + plg[1][3] * p[116] + plg[1][5] * p[117]) + * cd14 + * ((input.longitude_deg - p[118]) * DGTR).cos() + + work.apdf + * swc[12] + * (plg[0][1] * p[83] + plg[0][3] * p[84] + plg[0][5] * p[85]) + * ((input.seconds_of_day - p[75]) * SR).cos(); + } + } + } + } + + // Coefficients 82, 89, 99 and 139 to 149 are not used. + let mut tinf = T::lift(p[30]); + for (index, term) in t.iter().enumerate() { + let switch = if index == 8 { sw9 } else { sw[index + 1] }; + tinf = tinf + *term * switch.abs(); + } + tinf +} + +/// The expansion for the lower atmosphere: `glob7s`. +/// +/// Reads the state `globe7` left in `work` rather than recomputing it, which is why the +/// model calls that first. `p` is a row of `PTL` or of `PMA`. +pub(crate) fn glob7s( + p: &[f64], + input: &Input, + switches: &Resolved, + work: &Work, +) -> T { + let (sw, swc) = (&switches.sw, &switches.swc); + let mut t = [T::lift(0.0); 14]; + let doy = f64::from(input.day_of_year); + let plg = &work.plg; + + // The reference checks that p[99] is its parameter-set marker of 2, writing it in if + // the slot is zero. Every row of PTL and PMA already carries 2, so neither the write + // nor the complaint can happen; `test_every_lower_atmosphere_table_is_parameter_set_2` + // holds that down. + debug_assert_eq!(p[99], 2.0, "glob7s called with the wrong parameter set"); + + let cd32 = (DR * (doy - p[31])).cos(); + let cd18 = (2.0 * DR * (doy - p[17])).cos(); + let cd14 = (DR * (doy - p[13])).cos(); + let cd39 = (2.0 * DR * (doy - p[38])).cos(); + + // F10.7. + t[0] = work.dfa * p[21]; + + // Time independent. + t[1] = plg[0][2] * p[1] + + plg[0][4] * p[2] + + plg[0][6] * p[22] + + plg[0][1] * p[26] + + plg[0][3] * p[14] + + plg[0][5] * p[59]; + + // Symmetrical annual. + t[2] = (T::lift(p[18]) + plg[0][2] * p[47] + plg[0][4] * p[29]) * cd32; + + // Symmetrical semiannual. + t[3] = (T::lift(p[15]) + plg[0][2] * p[16] + plg[0][4] * p[30]) * cd18; + + // Asymmetrical annual. + t[4] = (plg[0][1] * p[9] + plg[0][3] * p[10] + plg[0][5] * p[20]) * cd14; + + // Asymmetrical semiannual. + t[5] = plg[0][1] * p[37] * cd39; + + // Diurnal. + if sw[7] != 0.0 { + let t71 = plg[1][2] * p[11] * cd14 * swc[5]; + let t72 = plg[1][2] * p[12] * cd14 * swc[5]; + t[6] = (plg[1][1] * p[3] + plg[1][3] * p[4] + t71) * work.ctloc + + (plg[1][1] * p[6] + plg[1][3] * p[7] + t72) * work.stloc; + } + + // Semidiurnal. + if sw[8] != 0.0 { + let t81 = (plg[2][3] * p[23] + plg[2][5] * p[35]) * cd14 * swc[5]; + let t82 = (plg[2][3] * p[33] + plg[2][5] * p[36]) * cd14 * swc[5]; + t[7] = (plg[2][2] * p[5] + plg[2][4] * p[41] + t81) * work.c2tloc + + (plg[2][2] * p[8] + plg[2][4] * p[42] + t82) * work.s2tloc; + } + + // Terdiurnal. + if sw[14] != 0.0 { + t[13] = plg[3][3] * p[39] * work.s3tloc + plg[3][3] * p[40] * work.c3tloc; + } + + // Magnetic activity. + let sw9 = input.magnetic.sw(); + if sw9 != 0.0 { + if sw9 == 1.0 { + t[8] = work.apdf * (plg[0][2] * p[45] * swc[2] + p[32]); + } + if sw9 == -1.0 { + t[8] = work.apt[0] * p[50] + plg[0][2] * p[96] * work.apt[0] * swc[2]; + } + } + + // Longitudinal. + if !(sw[10] == 0.0 || sw[11] == 0.0 || input.longitude_deg.re() <= -1000.0) { + t[10] = (T::lift(1.0) + + plg[0][1] + * (p[80] * swc[5] * (DR * (doy - p[81])).cos() + + p[85] * swc[6] * (2.0 * DR * (doy - p[86])).cos()) + + p[83] * swc[3] * (DR * (doy - p[84])).cos() + + p[87] * swc[4] * (2.0 * DR * (doy - p[88])).cos()) + * ((plg[1][2] * p[64] + + plg[1][4] * p[65] + + plg[1][6] * p[66] + + plg[1][1] * p[74] + + plg[1][3] * p[75] + + plg[1][5] * p[76]) + * (input.longitude_deg * DGTR).cos() + + (plg[1][2] * p[90] + + plg[1][4] * p[91] + + plg[1][6] * p[92] + + plg[1][1] * p[77] + + plg[1][3] * p[78] + + plg[1][5] * p[79]) + * (input.longitude_deg * DGTR).sin()); + } + + let mut tt = T::lift(0.0); + for (index, term) in t.iter().enumerate() { + let switch = if index == 8 { sw9 } else { sw[index + 1] }; + tt = tt + *term * switch.abs(); + } + tt +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::switches::{Switch, Switches, Units}; + use crate::tables::{PD, PMA, PS, PT, PTL}; + use crate::testing::{assert_bits, helper_cases, number, numbers}; + use serde_json::Value; + + /// The coefficient table a fixture case names. + fn table(name: &str) -> &'static [f64] { + let row = |name: &str, prefix: &str| -> Option { + name.strip_prefix(prefix).map(|index| { + index + .parse() + .unwrap_or_else(|_| panic!("{name} does not end in a row number")) + }) + }; + match name { + "pt" => &PT, + "ps" => &PS, + _ => { + if let Some(index) = row(name, "pma") { + &PMA[index] + } else if let Some(index) = row(name, "ptl") { + &PTL[index] + } else if let Some(index) = row(name, "pd") { + &PD[index] + } else { + panic!("unknown table {name}") + } + } + } + } + + /// The switch settings a fixture case was generated with, as the model's own type. + /// + /// The fixture records the reference's raw 24-element switch array, which is the form + /// `tselec` consumes. Index 9 is read as the magnetic mode instead. + fn switches_of(case: &Value) -> Switches { + let raw = numbers(case, "switches_in"); + let at = |index: usize| match raw[index] as i32 { + 0 => Switch::Off, + 1 => Switch::On, + 2 => Switch::CrossTermsOnly, + other => panic!("switch {index} is {other}"), + }; + Switches { + units: if raw[0] == 0.0 { + Units::Native + } else { + Units::Si + }, + f107_mean: at(1), + time_independent: at(2), + symmetrical_annual: at(3), + symmetrical_semiannual: at(4), + asymmetrical_annual: at(5), + asymmetrical_semiannual: at(6), + diurnal: at(7), + semidiurnal: at(8), + ut_and_longitude: at(10), + longitudinal: at(11), + ut_and_mixed_ut_longitude: at(12), + mixed_ap_ut_longitude: at(13), + terdiurnal: at(14), + departures_from_diffusive_equilibrium: at(15), + exospheric_temperature: at(16), + boundary_temperature: at(17), + lower_thermosphere_temperature: at(18), + temperature_gradient: at(19), + mesosphere_temperature: at(20), + boundary_density: at(21), + troposphere_temperature: at(22), + turbopause_scale_height: at(23), + } + } + + /// The magnetic activity a fixture case was generated with, from the raw switch 9. + fn magnetic_of(case: &Value) -> MagneticActivity { + let raw = numbers(case, "switches_in"); + match raw[9] as i32 { + 0 => MagneticActivity::Off { + daily_ap: number(case, "ap_daily"), + }, + 1 => MagneticActivity::Daily { + ap: number(case, "ap_daily"), + }, + -1 => { + let history = numbers(case, "ap_history"); + let mut ap = [0.0; 7]; + ap.copy_from_slice(&history); + MagneticActivity::History { ap } + } + other => panic!("switch 9 is {other}"), + } + } + + /// The magnetic mode alone, for `glob7s`, which reads the activity functions out of + /// the shared state rather than the ap values themselves. + fn magnetic_mode_of(case: &Value) -> MagneticActivity { + match numbers(case, "switches_in")[9] as i32 { + 0 => MagneticActivity::Off { daily_ap: 0.0 }, + 1 => MagneticActivity::Daily { ap: 0.0 }, + -1 => MagneticActivity::History { ap: [0.0; 7] }, + other => panic!("switch 9 is {other}"), + } + } + + fn input_of(case: &Value) -> Input { + Input { + day_of_year: number(case, "day_of_year") as i32, + seconds_of_day: number(case, "seconds_of_day"), + altitude_km: 400.0, + latitude_deg: number(case, "latitude_deg"), + longitude_deg: number(case, "longitude_deg"), + local_solar_time_h: number(case, "local_solar_time_h"), + f107_average: number(case, "f107_average"), + f107: number(case, "f107"), + magnetic: magnetic_of(case), + } + } + + /// The eleven coefficient tables `globe7` is called with, in the order the model calls + /// them, which is the order the fixture was generated in. + const GLOBE7_TABLES: [&str; 11] = [ + "pt", "ps", "pd0", "pd1", "pd2", "pd3", "pd4", "pd5", "pd6", "pd7", "pd8", + ]; + + #[test] + fn test_globe7_matches_the_reference() { + let cases = helper_cases("globe7"); + assert_eq!(cases.len(), 264); + + // The fixture's cases come in runs of eleven that share one input and switch set, + // and the reference evaluates those eleven against a single copy of the shared + // state. That matters: `pd8` carries a zero in p[51], where the reference skips + // recomputing the magnetic activity function and so reads the value the previous + // table's call left behind. One `Work` per run reproduces that; one per case would + // not, and the state assertions below are what noticed. + // One `Work` for the whole fixture, because the reference's state is process-wide: + // `apt[0]` is written only in the history mode and only for tables whose p[51] is + // non-zero, so in the daily-ap switch sets it still holds a value left by an + // earlier group. Nothing reads it there, but the fixture records it, and matching + // it is free evidence that the state threading is right. + let mut work = Work::new(); + for run in cases.chunks(GLOBE7_TABLES.len()) { + for (case, name) in run.iter().zip(GLOBE7_TABLES) { + assert_eq!(case["table"], name, "fixture is out of the expected order"); + let input = input_of(case); + let switches = switches_of(case).resolve(); + let got = globe7(table(name), &input, &switches, &mut work); + + let at = format!( + "globe7({name}) switch set {} case {}", + case["switch_set"], case["case"] + ); + assert_bits(got, number(case, "value"), &at); + + // The state it leaves for glob7s, and for the next table. + for row in 0..4 { + let want = numbers(case, &format!("plg{row}")); + for (column, want) in want.iter().enumerate() { + assert_bits( + work.plg[row][column], + *want, + &format!("{at}: plg[{row}][{column}]"), + ); + } + } + for (got, field) in [ + (work.stloc, "stloc"), + (work.ctloc, "ctloc"), + (work.s2tloc, "s2tloc"), + (work.c2tloc, "c2tloc"), + (work.s3tloc, "s3tloc"), + (work.c3tloc, "c3tloc"), + (work.dfa, "dfa"), + (work.apdf, "apdf"), + ] { + assert_bits(got, number(case, field), &format!("{at}: {field}")); + } + assert_bits( + work.apt[0], + numbers(case, "apt")[0], + &format!("{at}: apt[0]"), + ); + } + // The driver calls globe7 once more with PT before its glob7s batch, so the + // state the next group starts from is the one a model run would leave. + let case = &run[0]; + globe7( + &PT, + &input_of(case), + &switches_of(case).resolve(), + &mut work, + ); + } + } + + #[test] + fn test_glob7s_matches_the_reference() { + let cases = helper_cases("glob7s"); + assert_eq!(cases.len(), 336); + for case in cases { + // glob7s reads the state globe7 left; the fixture records it. + let mut work = Work::::new(); + for row in 0..4 { + let values = numbers(&case, &format!("plg{row}")); + work.plg[row].copy_from_slice(&values); + } + work.stloc = number(&case, "stloc"); + work.ctloc = number(&case, "ctloc"); + work.s2tloc = number(&case, "s2tloc"); + work.c2tloc = number(&case, "c2tloc"); + work.s3tloc = number(&case, "s3tloc"); + work.c3tloc = number(&case, "c3tloc"); + work.dfa = number(&case, "dfa"); + work.apdf = number(&case, "apdf"); + work.apt.copy_from_slice(&numbers(&case, "apt")); + + let input = Input { + day_of_year: number(&case, "day_of_year") as i32, + seconds_of_day: 0.0, + altitude_km: 400.0, + latitude_deg: 0.0, + longitude_deg: number(&case, "longitude_deg"), + local_solar_time_h: 0.0, + f107_average: 0.0, + f107: 0.0, + magnetic: magnetic_mode_of(&case), + }; + let switches = switches_of(&case).resolve(); + let name = case["table"].as_str().expect("a table name"); + let got = glob7s(table(name), &input, &switches, &work); + assert_bits( + got, + number(&case, "value"), + &format!( + "glob7s({name}) switch set {} case {}", + case["switch_set"], case["case"] + ), + ); + } + } + + /// The reference clamps `p[24]` up to 1e-4 inside `globe7`, writing into the + /// coefficient table it was handed. No table it is called with holds a value that + /// small, so the clamp never fires and the tables here can stay immutable. If a + /// regenerated table ever broke that, this is what would say so. + #[test] + fn test_the_p24_clamp_cannot_fire() { + let mut least = f64::INFINITY; + for table in [&PT[..], &PS[..]] + .into_iter() + .chain(PD.iter().map(|r| &r[..])) + { + least = least.min(table[24]); + } + assert!(least >= 1.0e-4, "least p[24] is {least}"); + } + + /// Every table `glob7s` is called with already carries its parameter-set marker, so + /// the reference's check cannot fail and its write-back cannot happen. + #[test] + fn test_every_lower_atmosphere_table_is_parameter_set_2() { + for (index, table) in PTL.iter().enumerate() { + assert_eq!(table[99], 2.0, "ptl[{index}]"); + } + for (index, table) in PMA.iter().enumerate() { + assert_eq!(table[99], 2.0, "pma[{index}]"); + } + } +} diff --git a/src/helpers.rs b/src/helpers.rs new file mode 100644 index 0000000..ade69c9 --- /dev/null +++ b/src/helpers.rs @@ -0,0 +1,425 @@ +//! The small pieces the profiles are built from. +//! +//! Each is a direct translation of the like-named function in the reference, and each is +//! individually checkable, which the large ones are not. +//! +//! # Why the expressions look the way they do +//! +//! Floating-point addition and multiplication are not associative, so matching the +//! reference to the last bit means performing its operations in its order. Two habits +//! follow from that, and both are deliberate wherever they look awkward: +//! +//! - A constant that the reference writes on the *left* of an operator stays there, as +//! `T::lift(3.0) / dx` rather than `dx.recip() * 3.0`. Commuting a product or reordering +//! a sum is exact and is done freely; re-associating one is not and is not done. +//! - `pow(x, 2.0)` is translated as `powf(2.0)` and not as `x * x`. The two agree to within +//! a rounding of the last bit and almost certainly agree exactly, but "almost certainly" +//! is not what the fixture checks, and this is the faithful pass. Replacing it is a +//! measured change for later. + +use crate::scalar::Scalar; +use crate::work::Work; + +/// The gas constant the model uses. +pub(crate) const RGAS: f64 = 831.4; + +/// Degrees to radians, to the digits the reference carries. +/// +/// It is not `PI / 180.0`, which differs in the sixth digit. Using a rounder value moves +/// every answer the model gives, so this is the reference's own constant. +pub(crate) const DGTR: f64 = 1.74533e-2; + +/// Radians per day of year, for the annual terms. +pub(crate) const DR: f64 = 1.72142e-2; + +/// Radians per second of universal time, for the UT terms. +pub(crate) const SR: f64 = 7.2722e-5; + +/// Radians per hour of local solar time, for the diurnal terms. +pub(crate) const HR: f64 = 0.2618; + +/// The most spline nodes any caller asks for. +pub(crate) const MAX_NODES: usize = 5; + +/// Gravity and the effective Earth radius at a latitude. +/// +/// `glatf`: gravity in cm/s^2, and a radius in km chosen so that the geopotential height +/// of [`zeta`] is right. +pub(crate) fn glatf(lat: T) -> (T, T) { + let c2 = (lat * (2.0 * DGTR)).cos(); + let gv = (c2 * -0.0026373 + 1.0) * 980.616; + let reff = (gv * 2.0) / (c2 * 2.27e-9 + 3.085462e-6) * 1.0e-5; + (gv, reff) +} + +/// Geopotential height of `zz` above `zl`, in km. +/// +/// `zeta`. The model's vertical coordinate: an altitude difference scaled so that a +/// hydrostatic profile computed with constant gravity is right in a field that falls off. +#[inline] +pub(crate) fn zeta(work: &Work, zz: T, zl: T) -> T { + (zz - zl) * (work.re + zl) / (work.re + zz) +} + +/// Chemistry and dissociation correction. +/// +/// `ccor`, a multiplicative factor on a species' density. `r` is the target ratio, `h1` the +/// transition scale length and `zh` the altitude at which half of `r` has been applied. +pub(crate) fn ccor(alt: T, r: T, h1: f64, zh: f64) -> T { + let e = (alt - zh) / h1; + // The reference returns exp(0) and exp(r) at the ends rather than clamping the + // exponent, so the factor goes to 1 above the transition and to exp(r) below it. Both + // ends are constant in the altitude, and so have no derivative. + if e.re() > 70.0 { + return T::lift(1.0); + } + if e.re() < -70.0 { + return r.exp(); + } + (r / (e.exp() + 1.0)).exp() +} + +/// Chemistry and dissociation correction with two transition scale lengths. +/// +/// `ccor2`. As [`ccor`], but the transition is the mean of two of different widths. +pub(crate) fn ccor2(alt: T, r: T, h1: f64, zh: f64, h2: f64) -> T { + let e1 = (alt - zh) / h1; + let e2 = (alt - zh) / h2; + if e1.re() > 70.0 || e2.re() > 70.0 { + return T::lift(1.0); + } + if e1.re() < -70.0 && e2.re() < -70.0 { + return r.exp(); + } + (r / ((e1.exp() + e2.exp()) * 0.5 + 1.0)).exp() +} + +/// The scale height of a species of mass `xm` at a temperature, in km. +/// +/// `scalh`. +pub(crate) fn scalh(work: &Work, alt: f64, xm: f64, temp: T) -> T { + let g = work.gsurf / (T::lift(alt) / work.re + 1.0).powf(2.0); + temp * RGAS / (g * xm) +} + +/// The turbopause correction: a root-mean blend of a diffusive and a mixed density. +/// +/// `dnet`. `zhm` is the transition scale length, `xmm` the fully mixed molecular weight and +/// `xm` the species weight. +pub(crate) fn dnet(dd: T, dm: T, zhm: f64, xmm: f64, xm: f64) -> T { + let a = zhm / (xmm - xm); + if !(dm.re() > 0.0 && dd.re() > 0.0) { + // The reference prints a message here and carries on with whichever of the two it + // can use. Reaching it means a density came out non-positive, which the blend has + // no logarithm for; it happens when a switch has turned off a term the blend needs. + if dd.re() == 0.0 && dm.re() == 0.0 { + return T::lift(1.0); + } + if dm.re() == 0.0 { + return dd; + } + if dd.re() == 0.0 { + return dm; + } + } + let ylog = (dm / dd).ln() * a; + if ylog.re() < -10.0 { + return dd; + } + if ylog.re() > 10.0 { + return dm; + } + dd * (ylog.exp() + 1.0).powf(1.0 / a) +} + +/// The second derivatives of a cubic spline through `(x, y)`. +/// +/// `spline`, which is Numerical Recipes' routine of that name. `yp1` and `ypn` are the +/// first derivatives imposed at the ends; a value at or above 1e30 would ask for a zero +/// second derivative there instead, which this model never does. +pub(crate) fn spline(x: &[T], y: &[T], yp1: T, ypn: T, y2: &mut [T]) { + let n = x.len(); + // The reference heap-allocates this per call. Five nodes is the most any caller wants. + let mut u = [T::lift(0.0); MAX_NODES]; + + if yp1.re() > 0.99e30 { + y2[0] = T::lift(0.0); + u[0] = T::lift(0.0); + } else { + y2[0] = T::lift(-0.5); + u[0] = (T::lift(3.0) / (x[1] - x[0])) * ((y[1] - y[0]) / (x[1] - x[0]) - yp1); + } + for i in 1..n - 1 { + let sig = (x[i] - x[i - 1]) / (x[i + 1] - x[i - 1]); + let p = sig * y2[i - 1] + 2.0; + y2[i] = (sig - 1.0) / p; + u[i] = (((y[i + 1] - y[i]) / (x[i + 1] - x[i]) - (y[i] - y[i - 1]) / (x[i] - x[i - 1])) + * 6.0 + / (x[i + 1] - x[i - 1]) + - sig * u[i - 1]) + / p; + } + let (qn, un) = if ypn.re() > 0.99e30 { + (T::lift(0.0), T::lift(0.0)) + } else { + ( + T::lift(0.5), + (T::lift(3.0) / (x[n - 1] - x[n - 2])) + * (ypn - (y[n - 1] - y[n - 2]) / (x[n - 1] - x[n - 2])), + ) + }; + y2[n - 1] = (un - qn * u[n - 2]) / (qn * y2[n - 2] + 1.0); + for k in (0..n - 1).rev() { + y2[k] = y2[k] * y2[k + 1] + u[k]; + } +} + +/// A cubic spline evaluated at `x`. +/// +/// `splint`. `y2a` is what [`spline`] produced for the same nodes. +pub(crate) fn splint(xa: &[T], ya: &[T], y2a: &[T], x: T) -> T { + let mut klo = 0usize; + let mut khi = xa.len() - 1; + while khi - klo > 1 { + let k = (khi + klo) / 2; + if xa[k].re() > x.re() { + khi = k; + } else { + klo = k; + } + } + let h = xa[khi] - xa[klo]; + let a = (xa[khi] - x) / h; + let b = (x - xa[klo]) / h; + a * ya[klo] + + b * ya[khi] + + ((a * a * a - a) * y2a[klo] + (b * b * b - b) * y2a[khi]) * h * h / 6.0 +} + +/// A cubic spline integrated from `xa[0]` to `x`. +/// +/// `splini`. The integral of the interpolant, which is what turns a profile of inverse +/// temperature into a density ratio. +pub(crate) fn splini(xa: &[T], ya: &[T], y2a: &[T], x: T) -> T { + let n = xa.len(); + let mut yi = T::lift(0.0); + let mut klo = 0usize; + let mut khi = 1usize; + while x.re() > xa[klo].re() && khi < n { + // Every interval below the last is integrated whole; the one holding x is + // integrated up to x. + // + // The reference's test is `x < xa[khi]`, which takes the node when the two are + // equal. That is the same number, so the value is unchanged, but at a dual type it + // is the difference between carrying dx and dropping it: substituting the node + // replaces x by a constant and the integral comes out with no derivative at all. + // Sampling exactly on a node is not a corner case here — the mesosphere's nodes + // are at 0, 10, 15, 20 and 32.5 km, which are round numbers a caller will ask for. + let mut xx = x; + if khi < n - 1 && x.re() > xa[khi].re() { + xx = xa[khi]; + } + let h = xa[khi] - xa[klo]; + let a = (xa[khi] - xx) / h; + let b = (xx - xa[klo]) / h; + let a2 = a * a; + let b2 = b * b; + yi = yi + + ((T::lift(1.0) - a2) * ya[klo] / 2.0 + + b2 * ya[khi] / 2.0 + + ((-(a2 * a2 + 1.0) / 4.0 + a2 / 2.0) * y2a[klo] + + (b2 * b2 / 4.0 - b2 / 2.0) * y2a[khi]) + * h + * h + / 6.0) + * h; + klo += 1; + khi += 1; + } + yi +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::testing::{assert_bits, helper_cases, number, numbers}; + + /// A `Work` with only gravity and the Earth radius set, which is all the helpers read. + fn work_at(gsurf: f64, re: f64) -> Work { + let mut work = Work::new(); + work.gsurf = gsurf; + work.re = re; + work + } + + #[test] + fn test_glatf_matches_the_reference() { + for case in helper_cases("glatf") { + let (gravity, radius) = glatf(number(&case, "lat")); + let lat = number(&case, "lat"); + assert_bits( + gravity, + number(&case, "gravity"), + &format!("gravity at {lat}"), + ); + assert_bits(radius, number(&case, "radius"), &format!("radius at {lat}")); + } + } + + /// Gravity is least at the equator and most at the poles, by the 0.53% the model's own + /// coefficient puts there. + #[test] + fn test_gravity_varies_with_latitude_as_the_coefficient_says() { + let (equator, _) = glatf(0.0); + let (pole, _) = glatf(90.0); + assert!(pole > equator); + let fraction = (pole - equator) / equator; + // 1 - 0.0026373 * cos(0) against 1 - 0.0026373 * cos(pi), so twice the coefficient. + assert!((fraction - 2.0 * 0.0026373 / (1.0 - 0.0026373)).abs() < 1e-6); + } + + #[test] + fn test_zeta_matches_the_reference() { + for case in helper_cases("zeta") { + let work = work_at(number(&case, "gsurf"), number(&case, "re")); + let got = zeta(&work, number(&case, "zz"), number(&case, "zl")); + assert_bits(got, number(&case, "value"), "zeta"); + } + } + + #[test] + fn test_scalh_matches_the_reference() { + for case in helper_cases("scalh") { + let work = work_at(number(&case, "gsurf"), number(&case, "re")); + let got = scalh( + &work, + number(&case, "alt"), + number(&case, "xm"), + number(&case, "temp"), + ); + assert_bits(got, number(&case, "value"), "scalh"); + } + } + + #[test] + fn test_ccor_matches_the_reference() { + for case in helper_cases("ccor") { + let got = ccor( + number(&case, "alt"), + number(&case, "r"), + number(&case, "h1"), + number(&case, "zh"), + ); + assert_bits(got, number(&case, "value"), "ccor"); + } + } + + #[test] + fn test_ccor2_matches_the_reference() { + for case in helper_cases("ccor2") { + let got = ccor2( + number(&case, "alt"), + number(&case, "r"), + number(&case, "h1"), + number(&case, "zh"), + number(&case, "h2"), + ); + assert_bits(got, number(&case, "value"), "ccor2"); + } + } + + #[test] + fn test_dnet_matches_the_reference() { + for case in helper_cases("dnet") { + let got = dnet( + number(&case, "dd"), + number(&case, "dm"), + number(&case, "zhm"), + number(&case, "xmm"), + number(&case, "xm"), + ); + assert_bits(got, number(&case, "value"), "dnet"); + } + } + + #[test] + fn test_spline_matches_the_reference() { + for case in helper_cases("spline") { + let xs = numbers(&case, "xs"); + let ys = numbers(&case, "ys"); + let want = numbers(&case, "y2"); + let mut y2 = vec![0.0; xs.len()]; + spline( + &xs, + &ys, + number(&case, "yd1"), + number(&case, "yd2"), + &mut y2, + ); + for (index, (got, want)) in y2.iter().zip(&want).enumerate() { + assert_bits(*got, *want, &format!("y2[{index}] of {} nodes", xs.len())); + } + } + } + + #[test] + fn test_splint_matches_the_reference() { + for case in helper_cases("splint") { + let got = splint( + &numbers(&case, "xs"), + &numbers(&case, "ys"), + &numbers(&case, "y2"), + number(&case, "x"), + ); + assert_bits(got, number(&case, "value"), "splint"); + } + } + + #[test] + fn test_splini_matches_the_reference() { + for case in helper_cases("splini") { + let got = splini( + &numbers(&case, "xs"), + &numbers(&case, "ys"), + &numbers(&case, "y2"), + number(&case, "x"), + ); + assert_bits(got, number(&case, "value"), "splini"); + } + } + + /// The spline reproduces its nodes, which is the property the fixture cannot show on + /// its own: a wrong but self-consistent pair of routines would agree with itself. + #[test] + fn test_the_spline_passes_through_its_nodes() { + let xs: Vec = (0..5).map(|k| f64::from(k) / 4.0).collect(); + let ys: Vec = (0..5) + .map(|k| 1.0 / (200.0 + 15.0 * f64::from(k))) + .collect(); + let mut y2 = vec![0.0; 5]; + spline(&xs, &ys, -1.5e-5, 3.0e-6, &mut y2); + for (x, y) in xs.iter().zip(&ys) { + let got = splint(&xs, &ys, &y2, *x); + assert!((got - y).abs() < 1e-15 * y, "at {x}: {got} against {y}"); + } + } + + /// The integral of the spline from the first node to itself is zero, and it grows + /// monotonically from there because the ordinates are inverse temperatures. + #[test] + fn test_the_spline_integral_starts_at_zero_and_grows() { + let xs: Vec = (0..5).map(|k| f64::from(k) / 4.0).collect(); + let ys: Vec = (0..5) + .map(|k| 1.0 / (200.0 + 15.0 * f64::from(k))) + .collect(); + let mut y2 = vec![0.0; 5]; + spline(&xs, &ys, -1.5e-5, 3.0e-6, &mut y2); + assert_eq!(splini(&xs, &ys, &y2, 0.0), 0.0); + let mut last = 0.0; + for step in 1..=20 { + let integral = splini(&xs, &ys, &y2, f64::from(step) / 20.0); + assert!(integral > last, "integral fell at step {step}"); + last = integral; + } + } +} diff --git a/src/input.rs b/src/input.rs new file mode 100644 index 0000000..3ce0302 --- /dev/null +++ b/src/input.rs @@ -0,0 +1,212 @@ +//! What the model is asked about, and what it answers with. + +use crate::scalar::Scalar; + +/// The geomagnetic activity the model reads, and which of its two modes that selects. +/// +/// The reference carries a daily value and a seven-element history side by side and picks +/// between them with switch 9, which means the switch and the data can disagree. Here the +/// data is the mode. +/// +/// [`MagneticActivity::History`] is what a real propagation uses: a storm's effect on +/// density lags it by hours, which a single daily mean cannot express. The reference's +/// published cases 15 and 16 are the two that exercise it. +#[derive(Clone, Copy, Debug, PartialEq)] +pub enum MagneticActivity { + /// The daily-ap term left out, which is the reference's switch 9 set to zero. + /// + /// The daily value is still carried because the reference still reads it for the mixed + /// magnetic, universal time and longitude term, which switch 13 governs separately. + Off { + /// The daily mean ap. + daily_ap: T, + }, + /// The daily mean ap alone, which is the reference's switch 9 set to one. + Daily { + /// The daily mean ap. + ap: T, + }, + /// The seven-element history, which is the reference's switch 9 set to -1. + History { + /// In the order the model wants them: + /// + /// 0. the daily mean ap + /// 1. the three-hour ap for the interval the epoch falls in + /// 2. three hours before that + /// 3. six hours before + /// 4. nine hours before + /// 5. the mean of the eight intervals from 12 to 33 hours before + /// 6. the mean of the eight intervals from 36 to 57 hours before + ap: [T; 7], + }, +} + +impl MagneticActivity { + /// The daily mean, which every variant carries. + pub(crate) fn daily(&self) -> T { + match self { + Self::Off { daily_ap } => *daily_ap, + Self::Daily { ap } => *ap, + Self::History { ap } => ap[0], + } + } + + /// The reference's `sw[9]`: 0 off, 1 daily, -1 history. + pub(crate) fn sw(&self) -> f64 { + match self { + Self::Off { .. } => 0.0, + Self::Daily { .. } => 1.0, + Self::History { .. } => -1.0, + } + } +} + +/// Where and when the model is being asked about. +/// +/// Altitude is geodetic and in km, latitude and longitude are geodetic and in degrees, and +/// the time of day is in seconds of universal time. These are the reference's own units at +/// the input; only the output is converted. +/// +/// # Local solar time +/// +/// Universal time, longitude and local solar time enter the model independently, and it +/// does not check that they agree. They should: `local_solar_time_h = seconds_of_day/3600 + +/// longitude_deg/15`. [`Input::consistent`] works it out so it cannot be forgotten. The +/// field is left public because the reference's published cases deliberately break the +/// relation, and reproducing them is the point of the fixtures. +#[derive(Clone, Copy, Debug, PartialEq)] +pub struct Input { + /// Day of the year, 1 to 366. + /// + /// An integer, as in the reference, so it carries no derivative. Nothing in the model + /// differentiates with respect to the day. + pub day_of_year: i32, + /// Seconds of the day, universal time. + pub seconds_of_day: T, + /// Geodetic altitude, km. + pub altitude_km: T, + /// Geodetic latitude, degrees. + pub latitude_deg: T, + /// Geodetic longitude, degrees east. + pub longitude_deg: T, + /// Local apparent solar time, hours. See the note on [`Input`]. + pub local_solar_time_h: T, + /// The 81-day average of the F10.7 solar flux, centered on the day. + /// + /// At the flux's value at the Earth's actual distance from the Sun, not at 1 AU. + pub f107_average: T, + /// The daily F10.7 solar flux of the *previous* day. + pub f107: T, + /// The geomagnetic activity, and which mode it selects. + pub magnetic: MagneticActivity, +} + +impl Input { + /// An input whose local solar time agrees with its universal time and longitude. + /// + /// `local_solar_time_h = seconds_of_day/3600 + longitude_deg/15`, which is what the + /// model's own documentation asks for. + #[allow(clippy::too_many_arguments)] + pub fn consistent( + day_of_year: i32, + seconds_of_day: T, + altitude_km: T, + latitude_deg: T, + longitude_deg: T, + f107_average: T, + f107: T, + magnetic: MagneticActivity, + ) -> Self { + Self { + day_of_year, + seconds_of_day, + altitude_km, + latitude_deg, + longitude_deg, + local_solar_time_h: seconds_of_day / 3600.0 + longitude_deg / 15.0, + f107_average, + f107, + magnetic, + } + } +} + +/// What the model answers: eight species, a total, and two temperatures. +/// +/// The number densities are in m^-3 and the mass density in kg/m^3 under +/// [`crate::Units::Si`], or cm^-3 and g/cm^3 under [`crate::Units::Native`]. +/// +/// Atomic oxygen, hydrogen and nitrogen are zero below 72.5 km, where the model does not +/// carry them. +#[derive(Clone, Copy, Debug, PartialEq)] +pub struct Output { + /// Helium number density. + pub helium: T, + /// Atomic oxygen number density. + pub atomic_oxygen: T, + /// Molecular nitrogen number density. + pub molecular_nitrogen: T, + /// Molecular oxygen number density. + pub molecular_oxygen: T, + /// Argon number density. + pub argon: T, + /// Total mass density. + /// + /// Which species this sums over is the difference between [`crate::Model::gtd7`] and + /// [`crate::Model::gtd7d`], and it is the one number a drag calculation wants. See + /// those two. + pub total_mass: T, + /// Atomic hydrogen number density. + pub hydrogen: T, + /// Atomic nitrogen number density. + pub atomic_nitrogen: T, + /// Anomalous oxygen number density. + /// + /// Hot atomic oxygen, which matters for drag above about 500 km and is the species + /// `gtd7` leaves out of the total while `gtd7d` includes it. + pub anomalous_oxygen: T, + /// Exospheric temperature, K. + /// + /// Set to the global average below 120 km, where the model does not vary it. + pub exospheric_temperature: T, + /// Temperature at the altitude asked for, K. + pub temperature: T, +} + +impl Output { + /// All zero. + pub(crate) fn zeroed() -> Self { + let zero = T::lift(0.0); + Self { + helium: zero, + atomic_oxygen: zero, + molecular_nitrogen: zero, + molecular_oxygen: zero, + argon: zero, + total_mass: zero, + hydrogen: zero, + atomic_nitrogen: zero, + anomalous_oxygen: zero, + exospheric_temperature: zero, + temperature: zero, + } + } + + /// The nine densities in the order the reference's `d` array holds them. + /// + /// He, O, N2, O2, Ar, total mass, H, N, anomalous O. The order the published test + /// cases are quoted in, which is why it is worth having. + pub fn densities(&self) -> [T; 9] { + [ + self.helium, + self.atomic_oxygen, + self.molecular_nitrogen, + self.molecular_oxygen, + self.argon, + self.total_mass, + self.hydrogen, + self.atomic_nitrogen, + self.anomalous_oxygen, + ] + } +} diff --git a/src/lib.rs b/src/lib.rs new file mode 100644 index 0000000..149f5ee --- /dev/null +++ b/src/lib.rs @@ -0,0 +1,20 @@ +#![doc = include_str!("../readme.md")] +#![warn(missing_docs)] + +pub mod scalar; + +mod expansion; +mod helpers; +mod input; +mod model; +mod profile; +mod switches; +mod tables; +#[cfg(test)] +mod testing; +mod work; + +pub use input::{Input, MagneticActivity, Output}; +pub use model::Model; +pub use scalar::Scalar; +pub use switches::{Switch, Switches, Units}; diff --git a/src/model.rs b/src/model.rs new file mode 100644 index 0000000..98a3137 --- /dev/null +++ b/src/model.rs @@ -0,0 +1,677 @@ +//! The model itself: `gts7` for the thermosphere, and `gtd7` and `gtd7d` over the whole +//! range. + +use crate::expansion::{glob7s, globe7}; +use crate::helpers::{ccor, ccor2, dnet, glatf, scalh, DGTR, DR, MAX_NODES}; +use crate::input::{Input, Output}; +use crate::profile::{densm, densu}; +use crate::scalar::Scalar; +use crate::switches::{Resolved, Switches, Units}; +use crate::tables::{PAVGM, PD, PDL, PDM, PMA, PS, PT, PTL, PTM}; +use crate::work::Work; + +/// Thermal diffusion coefficients, by the species order of the output. +/// +/// `alpha` in the reference. Only helium, argon and hydrogen have one. +const ALPHA: [f64; 9] = [-0.38, 0.0, 0.0, 0.0, 0.17, 0.0, -0.38, 0.0, 0.0]; + +/// Altitudes above which each species' mixed correction is dropped, km. +/// +/// `altl` in the reference, in the order N2, He, O, O2, Ar, H, N — the reference's own +/// order here, which is not the output's. +const ALTL: [f64; 8] = [200.0, 300.0, 160.0, 250.0, 240.0, 450.0, 320.0, 450.0]; + +/// Nodes of the troposphere and lower stratosphere temperature spline, km. +const ZN3: [f64; 5] = [32.5, 20.0, 15.0, 10.0, 0.0]; + +/// Nodes of the upper stratosphere and mesosphere temperature spline, km. +const ZN2: [f64; 4] = [72.5, 55.0, 45.0, 32.5]; + +/// Altitude above which mixing is no longer complete, km. `zmix` in the reference. +const ZMIX: f64 = 62.5; + +/// Mass of a nucleon in g, as the reference writes it, for summing a mass density. +const NUCLEON_MASS: f64 = 1.66e-24; + +/// NRLMSISE-00. +/// +/// Built once from a set of [`Switches`] and then evaluated as often as wanted. Building it +/// resolves the switches into the form the expansions multiply by, which is the reference's +/// `tselec` done once rather than on every call. +/// +/// ``` +/// use nrlmsise00::{Input, MagneticActivity, Model}; +/// +/// let model = Model::new(); +/// let output = model.gtd7d(&Input::consistent( +/// 172, // day of year +/// 29000.0, // seconds of universal time +/// 400.0, // km +/// 60.0, // degrees north +/// -70.0, // degrees east +/// 150.0, // 81-day average F10.7 +/// 150.0, // previous day's F10.7 +/// MagneticActivity::Daily { ap: 4.0 }, +/// )); +/// // A couple of picograms per cubic meter at 400 km, in SI by default. +/// assert!((output.total_mass - 2.4e-12).abs() < 0.1e-12); +/// ``` +#[derive(Clone, Copy, Debug)] +pub struct Model { + switches: Switches, + resolved: Resolved, +} + +impl Default for Model { + fn default() -> Self { + Self::new() + } +} + +impl Model { + /// The model with every variation included, answering in SI. + pub fn new() -> Self { + Self::with_switches(Switches::default()) + } + + /// The model with a chosen set of variations and units. + pub fn with_switches(switches: Switches) -> Self { + Self { + switches, + resolved: switches.resolve(), + } + } + + /// Which variations this model includes. + pub fn switches(&self) -> Switches { + self.switches + } + + /// Density and temperature from the surface to the lower exosphere. + /// + /// The total mass density sums helium, atomic oxygen, molecular nitrogen, molecular + /// oxygen, argon, hydrogen and atomic nitrogen. It leaves out anomalous oxygen, which + /// is what [`Model::gtd7d`] adds, and a drag calculation wants that one. The individual + /// number densities are the same either way, anomalous oxygen included. + pub fn gtd7(&self, input: &Input) -> Output { + let mut work = Work::new(); + self.evaluate(input, &mut work) + } + + /// Density and temperature, with anomalous oxygen in the total mass density. + /// + /// This is the total a drag calculation wants: the reference calls it the effective + /// total mass density for drag. Anomalous oxygen is hot atomic oxygen, and above about + /// 500 km it is a large part of the mass that a satellite runs into. + /// + /// Nothing but [`Output::total_mass`] differs from [`Model::gtd7`]. + pub fn gtd7d(&self, input: &Input) -> Output { + let mut work = Work::new(); + let mut output = self.evaluate(input, &mut work); + output.total_mass = mass_density(&output, true); + if self.switches.units == Units::Si { + output.total_mass = output.total_mass / 1000.0; + } + output + } + + /// Density and temperature from the thermospheric part of the model alone. + /// + /// `gts7`. Only meaningful above 72.5 km; [`Model::gtd7`] handles the whole range, and + /// below 72.5 km it calls this at 72.5 and blends downward from there. + pub fn gts7(&self, input: &Input) -> Output { + let mut work = Work::new(); + let xlat = if self.resolved.sw[2] == 0.0 { + T::lift(45.0) + } else { + input.latitude_deg + }; + (work.gsurf, work.re) = glatf(xlat); + self.thermosphere(input, input.altitude_km, &mut work) + } + + /// `gtd7`: the thermosphere, and below 72.5 km the mesosphere blended onto it. + fn evaluate(&self, input: &Input, work: &mut Work) -> Output { + let (sw, metric) = (&self.resolved.sw, self.switches.units == Units::Si); + + // Latitude variation of gravity, which switch 2 also governs. + let xlat = if sw[2] == 0.0 { + T::lift(45.0) + } else { + input.latitude_deg + }; + (work.gsurf, work.re) = glatf(xlat); + + let xmm = PDM[2][4]; + + // The thermosphere, evaluated no lower than the top of the mesosphere spline. + let altt = if input.altitude_km.re() > ZN2[0] { + input.altitude_km + } else { + T::lift(ZN2[0]) + }; + let thermosphere = self.thermosphere(input, altt, work); + + let dm28m = if metric { work.dm28 * 1.0e6 } else { work.dm28 }; + let mut output = thermosphere; + + if input.altitude_km.re() >= ZN2[0] { + return output; + } + + // Lower mesosphere and upper stratosphere, 32.5 to 72.5 km. The inverse of the + // temperature at each node is a linear function of the spherical harmonics. + work.tgn2[0] = work.tgn1[1]; + work.tn2[0] = work.tn1[4]; + work.tn2[1] = T::lift(PMA[0][0] * PAVGM[0]) + / (-(glob7s(&PMA[0], input, &self.resolved, work) * sw[20]) + 1.0); + work.tn2[2] = T::lift(PMA[1][0] * PAVGM[1]) + / (-(glob7s(&PMA[1], input, &self.resolved, work) * sw[20]) + 1.0); + work.tn2[3] = T::lift(PMA[2][0] * PAVGM[2]) + / (-(glob7s(&PMA[2], input, &self.resolved, work) * sw[20] * sw[22]) + 1.0); + let tgn = (glob7s(&PMA[9], input, &self.resolved, work) * sw[20] * sw[22] + 1.0) + * (PAVGM[8] * PMA[9][0]) + * work.tn2[3] + * work.tn2[3] + / (PMA[2][0] * PAVGM[2]).powi(2); + work.tgn2[1] = tgn; + work.tn3[0] = work.tn2[3]; + + // Lower stratosphere and troposphere, at and below 32.5 km. + // + // The reference's test here is `alt < 32.5`, while `densm` enters this layer at + // `alt <= 32.5`. At exactly 32.5 km it therefore splines through nodes its own + // call never filled, and reads whichever values the previous call to the model + // left in them. In C those are file-scope statics, so the answer there depends on + // what was asked before; here they would be zero, and the spline's second + // derivatives would come out infinite, and the density NaN. + // + // These nodes do not depend on the altitude — they are the expansions in day, + // position and flux — so filling them at exactly 32.5 km gives precisely the + // values a preceding lower call would have left. That makes this agree with the + // reference's numbers wherever those numbers mean anything, which the grid fixture + // checks at 32.5 km in sixty scenarios, and removes the NaN. It is the one place + // the port departs from the reference's control flow. + if input.altitude_km.re() <= ZN3[0] { + work.tgn3[0] = work.tgn2[1]; + work.tn3[1] = T::lift(PMA[3][0] * PAVGM[3]) + / (-(glob7s(&PMA[3], input, &self.resolved, work) * sw[22]) + 1.0); + work.tn3[2] = T::lift(PMA[4][0] * PAVGM[4]) + / (-(glob7s(&PMA[4], input, &self.resolved, work) * sw[22]) + 1.0); + work.tn3[3] = T::lift(PMA[5][0] * PAVGM[5]) + / (-(glob7s(&PMA[5], input, &self.resolved, work) * sw[22]) + 1.0); + work.tn3[4] = T::lift(PMA[6][0] * PAVGM[6]) + / (-(glob7s(&PMA[6], input, &self.resolved, work) * sw[22]) + 1.0); + let tgn = (glob7s(&PMA[7], input, &self.resolved, work) * sw[22] + 1.0) + * (PMA[7][0] * PAVGM[7]) + * work.tn3[4] + * work.tn3[4] + / (PMA[6][0] * PAVGM[6]).powi(2); + work.tgn3[1] = tgn; + } + + // Linear transition to full mixing below 72.5 km. + let mut dmc = T::lift(0.0); + if input.altitude_km.re() > ZMIX { + dmc = -((T::lift(ZN2[0]) - input.altitude_km) / (ZN2[0] - ZMIX)) + 1.0; + } + let dz28 = thermosphere.molecular_nitrogen; + let mut tz = T::lift(0.0); + + // Molecular nitrogen, which the others are scaled from. + let dmr = thermosphere.molecular_nitrogen / dm28m - 1.0; + let dm = densm(work, input.altitude_km, dm28m, xmm, &mut tz, &ZN3, &ZN2); + output.molecular_nitrogen = dm * (dmr * dmc + 1.0); + + // Helium. + let dmr = thermosphere.helium / (dz28 * PDM[0][1]) - 1.0; + output.helium = output.molecular_nitrogen * PDM[0][1] * (dmr * dmc + 1.0); + + // Atomic oxygen and anomalous oxygen are not carried below 72.5 km. + output.atomic_oxygen = T::lift(0.0); + output.anomalous_oxygen = T::lift(0.0); + + // Molecular oxygen. + let dmr = thermosphere.molecular_oxygen / (dz28 * PDM[3][1]) - 1.0; + output.molecular_oxygen = output.molecular_nitrogen * PDM[3][1] * (dmr * dmc + 1.0); + + // Argon. + let dmr = thermosphere.argon / (dz28 * PDM[4][1]) - 1.0; + output.argon = output.molecular_nitrogen * PDM[4][1] * (dmr * dmc + 1.0); + + // Hydrogen and atomic nitrogen are not carried below 72.5 km either. + output.hydrogen = T::lift(0.0); + output.atomic_nitrogen = T::lift(0.0); + + // The total is summed from the densities as they now stand, which are already in + // the output units, so only the thousand is applied here. + output.total_mass = mass_density(&output, false); + if metric { + output.total_mass = output.total_mass / 1000.0; + } + + // The temperature at the altitude, from the same profile with no mass. + densm( + work, + input.altitude_km, + T::lift(1.0), + 0.0, + &mut tz, + &ZN3, + &ZN2, + ); + output.temperature = tz; + output + } + + /// The thermospheric part: `gts7`. + /// + /// Each species is built the same way: a variation factor at the lower boundary, a + /// diffusive density from [`densu`], and then, where switch 15 allows it and the + /// altitude is low enough, a fully mixed density blended in by [`dnet`] and one or two + /// chemistry corrections from [`ccor`] and [`ccor2`]. + fn thermosphere(&self, input: &Input, alt: T, work: &mut Work) -> Output { + let sw = &self.resolved.sw; + let mut output = Output::zeroed(); + + // The first node of the lower thermosphere spline is itself a fitted coefficient. + let za = PDL[1][15]; + let zn1: [f64; MAX_NODES] = [za, 110.0, 100.0, 90.0, 72.5]; + + // Variation in the exospheric temperature does not matter below za. + let tinf = if alt.re() > zn1[0] { + T::lift(PTM[0] * PT[0]) * (globe7(&PT, input, &self.resolved, work) * sw[16] + 1.0) + } else { + T::lift(PTM[0] * PT[0]) + }; + output.exospheric_temperature = tinf; + + // Variation in the 120 km gradient does not matter below the bottom node. + let g0 = if alt.re() > zn1[4] { + T::lift(PTM[3] * PS[0]) * (globe7(&PS, input, &self.resolved, work) * sw[19] + 1.0) + } else { + T::lift(PTM[3] * PS[0]) + }; + let tlb = (globe7(&PD[3], input, &self.resolved, work) * sw[17] + 1.0) * PTM[1] * PD[3][0]; + let s = g0 / (tinf - tlb); + + // Lower thermosphere temperatures do not matter for density above 300 km. + if alt.re() < 300.0 { + work.tn1[1] = T::lift(PTM[6] * PTL[0][0]) + / (-(glob7s(&PTL[0], input, &self.resolved, work) * sw[18]) + 1.0); + work.tn1[2] = T::lift(PTM[2] * PTL[1][0]) + / (-(glob7s(&PTL[1], input, &self.resolved, work) * sw[18]) + 1.0); + work.tn1[3] = T::lift(PTM[7] * PTL[2][0]) + / (-(glob7s(&PTL[2], input, &self.resolved, work) * sw[18]) + 1.0); + work.tn1[4] = T::lift(PTM[4] * PTL[3][0]) + / (-(glob7s(&PTL[3], input, &self.resolved, work) * sw[18] * sw[20]) + 1.0); + let tgn = (glob7s(&PMA[8], input, &self.resolved, work) * sw[18] * sw[20] + 1.0) + * (PTM[8] * PMA[8][0]) + * work.tn1[4] + * work.tn1[4] + / (PTM[4] * PTL[3][0]).powi(2); + work.tgn1[1] = tgn; + } else { + work.tn1[1] = T::lift(PTM[6] * PTL[0][0]); + work.tn1[2] = T::lift(PTM[2] * PTL[1][0]); + work.tn1[3] = T::lift(PTM[7] * PTL[2][0]); + work.tn1[4] = T::lift(PTM[4] * PTL[3][0]); + work.tgn1[1] = T::lift(PTM[8] * PMA[8][0]) * work.tn1[4] * work.tn1[4] + / (PTM[4] * PTL[3][0]).powi(2); + } + + // Variation of the molecular nitrogen density at the lower boundary. + let g28 = globe7(&PD[2], input, &self.resolved, work) * sw[21]; + + // Variation of the turbopause height. + let zhf = ((input.latitude_deg * DGTR).sin() + * (sw[5] * PDL[0][24]) + * (DR * (f64::from(input.day_of_year) - PT[13])).cos() + + 1.0) + * PDL[1][24]; + output.exospheric_temperature = tinf; + let xmm = PDM[2][4]; + let z = alt; + let mut tz = T::lift(0.0); + + // Molecular nitrogen, which every other species below 72.5 km is scaled from. + let db28 = g28.exp() * PDM[2][0] * PD[2][0]; + output.molecular_nitrogen = densu( + work, z, db28, tinf, tlb, 28.0, ALPHA[2], &mut tz, PTM[5], s, &zn1, + ); + let zh28 = zhf * PDM[2][2]; + let zhm28 = PDM[2][3] * PDL[1][5]; + let xmd = 28.0 - xmm; + let b28 = densu( + work, + zh28, + db28, + tinf, + tlb, + xmd, + ALPHA[2] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + // The reference computes the mixed density only when switch 15 is on, but `gtd7` + // reads it below 72.5 km whatever the switch says, where it is the density every + // other species is scaled from. With the switch off the reference therefore reads + // a value from whichever call last wrote it — a file-scope static — and returns an + // answer that depends on what was asked before. Computing it regardless costs one + // `densu` call in a configuration nobody runs by default, and changes nothing when + // the switch is on: the blend below is still what the switch governs. + if z.re() <= ALTL[2] { + let dm28 = densu( + work, z, b28, tinf, tlb, xmm, ALPHA[2], &mut tz, PTM[5], s, &zn1, + ); + work.dm28 = dm28; + if sw[15] != 0.0 { + output.molecular_nitrogen = dnet(output.molecular_nitrogen, dm28, zhm28, xmm, 28.0); + } + } + + // Helium. + let g4 = globe7(&PD[0], input, &self.resolved, work) * sw[21]; + let db04 = g4.exp() * PDM[0][0] * PD[0][0]; + output.helium = densu( + work, z, db04, tinf, tlb, 4.0, ALPHA[0], &mut tz, PTM[5], s, &zn1, + ); + if sw[15] != 0.0 && z.re() < ALTL[0] { + let zh04 = PDM[0][2]; + let b04 = densu( + work, + T::lift(zh04), + db04, + tinf, + tlb, + 4.0 - xmm, + ALPHA[0] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + let dm04 = densu(work, z, b04, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1); + work.dm04 = dm04; + let zhm04 = zhm28; + output.helium = dnet(output.helium, dm04, zhm04, xmm, 4.0); + // Correction to the specified mixing ratio at the ground. + let rl = (b28 * PDM[0][1] / b04).ln(); + let zc04 = PDM[0][4] * PDL[1][0]; + let hc04 = PDM[0][5] * PDL[1][1]; + output.helium = output.helium * ccor(z, rl, hc04, zc04); + } + + // Atomic oxygen. + let g16 = globe7(&PD[1], input, &self.resolved, work) * sw[21]; + let db16 = g16.exp() * PDM[1][0] * PD[1][0]; + output.atomic_oxygen = densu( + work, z, db16, tinf, tlb, 16.0, ALPHA[1], &mut tz, PTM[5], s, &zn1, + ); + if sw[15] != 0.0 && z.re() <= ALTL[1] { + let zh16 = PDM[1][2]; + let b16 = densu( + work, + T::lift(zh16), + db16, + tinf, + tlb, + 16.0 - xmm, + ALPHA[1] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + let dm16 = densu(work, z, b16, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1); + work.dm16 = dm16; + let zhm16 = zhm28; + output.atomic_oxygen = dnet(output.atomic_oxygen, dm16, zhm16, xmm, 16.0); + let rl = ((input.f107_average - 150.0) * (sw[1] * PDL[0][23]) + 1.0) + * (PDM[1][1] * PDL[1][16]); + let hc16 = PDM[1][5] * PDL[1][3]; + let zc16 = PDM[1][4] * PDL[1][2]; + let hc216 = PDM[1][5] * PDL[1][4]; + output.atomic_oxygen = output.atomic_oxygen * ccor2(z, rl, hc16, zc16, hc216); + // Chemistry correction. + let hcc16 = PDM[1][7] * PDL[1][13]; + let zcc16 = PDM[1][6] * PDL[1][12]; + let rc16 = PDM[1][3] * PDL[1][14]; + output.atomic_oxygen = output.atomic_oxygen * ccor(z, T::lift(rc16), hcc16, zcc16); + } + + // Molecular oxygen. + let g32 = globe7(&PD[4], input, &self.resolved, work) * sw[21]; + let db32 = g32.exp() * PDM[3][0] * PD[4][0]; + output.molecular_oxygen = densu( + work, z, db32, tinf, tlb, 32.0, ALPHA[3], &mut tz, PTM[5], s, &zn1, + ); + if sw[15] != 0.0 { + if z.re() <= ALTL[3] { + let zh32 = PDM[3][2]; + let b32 = densu( + work, + T::lift(zh32), + db32, + tinf, + tlb, + 32.0 - xmm, + ALPHA[3] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + let dm32 = densu(work, z, b32, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1); + work.dm32 = dm32; + let zhm32 = zhm28; + output.molecular_oxygen = dnet(output.molecular_oxygen, dm32, zhm32, xmm, 32.0); + let rl = (b28 * PDM[3][1] / b32).ln(); + let hc32 = PDM[3][5] * PDL[1][7]; + let zc32 = PDM[3][4] * PDL[1][6]; + output.molecular_oxygen = output.molecular_oxygen * ccor(z, rl, hc32, zc32); + } + // Correction for a general departure from diffusive equilibrium above the + // lower boundary, which applies at every altitude. + let hcc32 = PDM[3][7] * PDL[1][22]; + let hcc232 = PDM[3][7] * PDL[0][22]; + let zcc32 = PDM[3][6] * PDL[1][21]; + let rc32 = ((input.f107_average - 150.0) * (sw[1] * PDL[0][23]) + 1.0) + * (PDM[3][3] * PDL[1][23]); + output.molecular_oxygen = + output.molecular_oxygen * ccor2(z, rc32, hcc32, zcc32, hcc232); + } + + // Argon. + let g40 = globe7(&PD[5], input, &self.resolved, work) * sw[21]; + let db40 = g40.exp() * PDM[4][0] * PD[5][0]; + output.argon = densu( + work, z, db40, tinf, tlb, 40.0, ALPHA[4], &mut tz, PTM[5], s, &zn1, + ); + if sw[15] != 0.0 && z.re() <= ALTL[4] { + let zh40 = PDM[4][2]; + let b40 = densu( + work, + T::lift(zh40), + db40, + tinf, + tlb, + 40.0 - xmm, + ALPHA[4] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + let dm40 = densu(work, z, b40, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1); + work.dm40 = dm40; + let zhm40 = zhm28; + output.argon = dnet(output.argon, dm40, zhm40, xmm, 40.0); + let rl = (b28 * PDM[4][1] / b40).ln(); + let hc40 = PDM[4][5] * PDL[1][9]; + let zc40 = PDM[4][4] * PDL[1][8]; + output.argon = output.argon * ccor(z, rl, hc40, zc40); + } + + // Hydrogen. + let g1 = globe7(&PD[6], input, &self.resolved, work) * sw[21]; + let db01 = g1.exp() * PDM[5][0] * PD[6][0]; + output.hydrogen = densu( + work, z, db01, tinf, tlb, 1.0, ALPHA[6], &mut tz, PTM[5], s, &zn1, + ); + if sw[15] != 0.0 && z.re() <= ALTL[6] { + let zh01 = PDM[5][2]; + let b01 = densu( + work, + T::lift(zh01), + db01, + tinf, + tlb, + 1.0 - xmm, + ALPHA[6] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + let dm01 = densu(work, z, b01, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1); + work.dm01 = dm01; + let zhm01 = zhm28; + output.hydrogen = dnet(output.hydrogen, dm01, zhm01, xmm, 1.0); + // The reference writes sqrt(pdl[1][17]*pdl[1][17]) for the magnitude. + let rl = (b28 * PDM[5][1] * PDL[1][17].abs() / b01).ln(); + let hc01 = PDM[5][5] * PDL[1][11]; + let zc01 = PDM[5][4] * PDL[1][10]; + output.hydrogen = output.hydrogen * ccor(z, rl, hc01, zc01); + // Chemistry correction. + let hcc01 = PDM[5][7] * PDL[1][19]; + let zcc01 = PDM[5][6] * PDL[1][18]; + let rc01 = PDM[5][3] * PDL[1][20]; + output.hydrogen = output.hydrogen * ccor(z, T::lift(rc01), hcc01, zcc01); + } + + // Atomic nitrogen. + let g14 = globe7(&PD[7], input, &self.resolved, work) * sw[21]; + let db14 = g14.exp() * PDM[6][0] * PD[7][0]; + output.atomic_nitrogen = densu( + work, z, db14, tinf, tlb, 14.0, ALPHA[7], &mut tz, PTM[5], s, &zn1, + ); + if sw[15] != 0.0 && z.re() <= ALTL[7] { + let zh14 = PDM[6][2]; + let b14 = densu( + work, + T::lift(zh14), + db14, + tinf, + tlb, + 14.0 - xmm, + ALPHA[7] - 1.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + let dm14 = densu(work, z, b14, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1); + work.dm14 = dm14; + let zhm14 = zhm28; + output.atomic_nitrogen = dnet(output.atomic_nitrogen, dm14, zhm14, xmm, 14.0); + let rl = (b28 * PDM[6][1] * PDL[0][2].abs() / b14).ln(); + let hc14 = PDM[6][5] * PDL[0][1]; + let zc14 = PDM[6][4] * PDL[0][0]; + output.atomic_nitrogen = output.atomic_nitrogen * ccor(z, rl, hc14, zc14); + // Chemistry correction. + let hcc14 = PDM[6][7] * PDL[0][4]; + let zcc14 = PDM[6][6] * PDL[0][3]; + let rc14 = PDM[6][3] * PDL[0][5]; + output.atomic_nitrogen = output.atomic_nitrogen * ccor(z, T::lift(rc14), hcc14, zcc14); + } + + // Anomalous oxygen: hot atomic oxygen, on its own barometric profile rather than + // the diffusive one, and with no mixed correction. + let g16h = globe7(&PD[8], input, &self.resolved, work) * sw[21]; + let db16h = g16h.exp() * PDM[7][0] * PD[8][0]; + let tho = PDM[7][9] * PDL[0][6]; + let dd = densu( + work, + z, + db16h, + T::lift(tho), + T::lift(tho), + 16.0, + ALPHA[8], + &mut tz, + PTM[5], + s, + &zn1, + ); + let zsht = PDM[7][5]; + let zmho = PDM[7][4]; + let zsho = scalh(work, zmho, 16.0, T::lift(tho)); + output.anomalous_oxygen = + dd * ((T::lift(-zsht) / zsho) * ((-(z - zmho) / zsht).exp() - 1.0)).exp(); + + output.total_mass = mass_density(&output, false); + + // The temperature at the altitude, from the same profile with no mass. + let z = alt.abs(); + densu( + work, + z, + T::lift(1.0), + tinf, + tlb, + 0.0, + 0.0, + &mut tz, + PTM[5], + s, + &zn1, + ); + output.temperature = tz; + + if self.switches.units == Units::Si { + to_si(&mut output); + } + output + } +} + +/// The mass density summed over the species, in the model's own units. +/// +/// Which species it sums is the only difference between `gtd7` and `gtd7d`: the latter +/// includes anomalous oxygen. +fn mass_density(output: &Output, anomalous: bool) -> T { + let sum = output.helium * 4.0 + + output.atomic_oxygen * 16.0 + + output.molecular_nitrogen * 28.0 + + output.molecular_oxygen * 32.0 + + output.argon * 40.0 + + output.hydrogen + + output.atomic_nitrogen * 14.0; + let sum = if anomalous { + sum + output.anomalous_oxygen * 16.0 + } else { + sum + }; + sum * NUCLEON_MASS +} + +/// The reference's switch 0, applied where it applies it. +/// +/// Every density, the mass density among them, is scaled from cm^-3 to m^-3, and then the +/// mass density is divided by a thousand. Both operations, in that order: g/cm^3 scaled by +/// 1e6 and then by 1e-3 is kg/m^3, and doing it in one step would not round the same way. +fn to_si(output: &mut Output) { + output.helium = output.helium * 1.0e6; + output.atomic_oxygen = output.atomic_oxygen * 1.0e6; + output.molecular_nitrogen = output.molecular_nitrogen * 1.0e6; + output.molecular_oxygen = output.molecular_oxygen * 1.0e6; + output.argon = output.argon * 1.0e6; + output.total_mass = output.total_mass * 1.0e6; + output.hydrogen = output.hydrogen * 1.0e6; + output.atomic_nitrogen = output.atomic_nitrogen * 1.0e6; + output.anomalous_oxygen = output.anomalous_oxygen * 1.0e6; + output.total_mass = output.total_mass / 1000.0; +} diff --git a/src/profile.rs b/src/profile.rs new file mode 100644 index 0000000..5b662af --- /dev/null +++ b/src/profile.rs @@ -0,0 +1,338 @@ +//! The temperature and density profiles: `densu` above 72.5 km and `densm` below it. +//! +//! Both work the same way. A spline is laid through the inverse of the temperature at a +//! handful of nodes, because that is what makes the hydrostatic integral a spline integral +//! and so closed-form; the temperature at the altitude asked for comes from evaluating it, +//! and the density from integrating it. +//! +//! The reference passes the node arrays in as pointers and every caller passes the same +//! ones, so here they are read from [`Work`] directly: `densu` always gets `tn1` and +//! `tgn1`, `densm` always gets `tn2`/`tgn2` and then `tn3`/`tgn3`. + +use crate::helpers::{spline, splini, splint, zeta, MAX_NODES, RGAS}; +use crate::scalar::Scalar; +use crate::work::Work; + +/// Temperature and density above the lower thermosphere's first node. +/// +/// `densu`. Returns the density of a species of mass `xm`, or the temperature when `xm` is +/// zero, and writes the temperature at the altitude to `tz` either way. +/// +/// `dlb` and `tlb` are the density and temperature at the lower boundary `zlb`, `tinf` the +/// exospheric temperature, `alpha` the species' thermal diffusion coefficient and `s2` the +/// temperature gradient parameter. +/// +/// It also writes the Bates profile's temperature and gradient into `tn1[0]` and `tgn1[0]`, +/// which is how the spline below `za` is joined continuously to the profile above it. The +/// mesosphere reads those afterwards, so the order of calls matters. +#[allow(clippy::too_many_arguments)] +pub(crate) fn densu( + work: &mut Work, + alt: T, + dlb: T, + tinf: T, + tlb: T, + xm: f64, + alpha: f64, + tz: &mut T, + zlb: f64, + s2: T, + zn1: &[f64; MAX_NODES], +) -> T { + let za = zn1[0]; + let z = if alt.re() > za { alt } else { T::lift(za) }; + + // Geopotential height above the lower boundary, and the Bates temperature there. + let zg2 = zeta(work, z, T::lift(zlb)); + let tt = tinf - (tinf - tlb) * ((-s2) * zg2).exp(); + let ta = tt; + *tz = tt; + let mut densu_temp = *tz; + + // Carried out of the branch below, because the density part reads them. + let mut xs = [T::lift(0.0); MAX_NODES]; + let mut ys = [T::lift(0.0); MAX_NODES]; + let mut y2out = [T::lift(0.0); MAX_NODES]; + let mut x = T::lift(0.0); + let mut zgdif = T::lift(0.0); + let mut z1 = 0.0f64; + let mut t1 = T::lift(0.0); + + if alt.re() < za { + // The temperature gradient at za from the Bates profile, which the spline below it + // is made to match. + let dta = (tinf - ta) * s2 * ((work.re + zlb) / (work.re + za)).powf(2.0); + work.tgn1[0] = dta; + work.tn1[0] = ta; + + let mn = zn1.len(); + let z = if alt.re() > zn1[mn - 1] { + alt + } else { + T::lift(zn1[mn - 1]) + }; + z1 = zn1[0]; + let z2 = zn1[mn - 1]; + t1 = work.tn1[0]; + let t2 = work.tn1[mn - 1]; + let zg = zeta(work, z, T::lift(z1)); + zgdif = zeta(work, T::lift(z2), T::lift(z1)); + + for k in 0..mn { + xs[k] = zeta(work, T::lift(zn1[k]), T::lift(z1)) / zgdif; + ys[k] = T::lift(1.0) / work.tn1[k]; + } + let yd1 = -work.tgn1[0] / (t1 * t1) * zgdif; + let yd2 = -work.tgn1[1] / (t2 * t2) * zgdif * ((work.re + z2) / (work.re + z1)).powf(2.0); + + spline(&xs[..mn], &ys[..mn], yd1, yd2, &mut y2out[..mn]); + x = zg / zgdif; + *tz = T::lift(1.0) / splint(&xs[..mn], &ys[..mn], &y2out[..mn], x); + densu_temp = *tz; + } + if xm == 0.0 { + return densu_temp; + } + + // Density above za, from the Bates profile. + let glb = work.gsurf / (T::lift(zlb) / work.re + 1.0).powf(2.0); + let gamma = glb * xm / (s2 * RGAS * tinf); + let mut expl = ((-s2) * gamma * zg2).exp(); + if expl.re() > 50.0 { + expl = T::lift(50.0); + } + if tt.re() <= 0.0 { + expl = T::lift(50.0); + } + densu_temp = dlb * (tlb / tt).powt(gamma + (1.0 + alpha)) * expl; + if alt.re() >= za { + return densu_temp; + } + + // Density below za, from the integral of the spline. + let glb = work.gsurf / (T::lift(z1) / work.re + 1.0).powf(2.0); + let gamm = glb * xm * zgdif / RGAS; + let mn = zn1.len(); + let yi = splini(&xs[..mn], &ys[..mn], &y2out[..mn], x); + let mut expl = gamm * yi; + if expl.re() > 50.0 { + expl = T::lift(50.0); + } + if tz.re() <= 0.0 { + expl = T::lift(50.0); + } + densu_temp * (t1 / *tz).powf(1.0 + alpha) * (-expl).exp() +} + +/// Temperature and density below 72.5 km. +/// +/// `densm`. Returns the density of a fully mixed atmosphere of mass `xm` scaled from `d0`, +/// or the temperature when `xm` is zero, and writes the temperature to `tz` either way. +/// +/// Two layers, stratosphere and mesosphere down to 32.5 km and then troposphere below it, +/// each a spline through its own nodes. +pub(crate) fn densm( + work: &Work, + alt: T, + d0: T, + xm: f64, + tz: &mut T, + zn3: &[f64; 5], + zn2: &[f64; 4], +) -> T { + let mut densm_tmp = d0; + + if alt.re() > zn2[0] { + // Above where this routine applies. The reference returns the temperature it was + // handed, which it has not written; no caller reaches here. + return if xm == 0.0 { *tz } else { d0 }; + } + + // Stratosphere and mesosphere. + let z = if alt.re() > zn2[zn2.len() - 1] { + alt + } else { + T::lift(zn2[zn2.len() - 1]) + }; + densm_tmp = layer(work, z, zn2, &work.tn2, &work.tgn2, xm, densm_tmp, tz); + + if alt.re() > zn3[0] { + return if xm == 0.0 { *tz } else { densm_tmp }; + } + + // Troposphere and lower stratosphere. The altitude is used as it is here, not clamped. + let densm_tmp = layer(work, alt, zn3, &work.tn3, &work.tgn3, xm, densm_tmp, tz); + if xm == 0.0 { + *tz + } else { + densm_tmp + } +} + +/// One spline layer of [`densm`]: the temperature at `z`, and the density scaled across it. +/// +/// The reference writes this out twice, once per layer, with the node arrays swapped. +#[allow(clippy::too_many_arguments)] +fn layer( + work: &Work, + z: T, + zn: &[f64], + tn: &[T], + tgn: &[T; 2], + xm: f64, + density: T, + tz: &mut T, +) -> T { + let mn = zn.len(); + let z1 = zn[0]; + let z2 = zn[mn - 1]; + let t1 = tn[0]; + let t2 = tn[mn - 1]; + let zg = zeta(work, z, T::lift(z1)); + let zgdif = zeta(work, T::lift(z2), T::lift(z1)); + + let mut xs = [T::lift(0.0); MAX_NODES]; + let mut ys = [T::lift(0.0); MAX_NODES]; + let mut y2out = [T::lift(0.0); MAX_NODES]; + for k in 0..mn { + xs[k] = zeta(work, T::lift(zn[k]), T::lift(z1)) / zgdif; + ys[k] = T::lift(1.0) / tn[k]; + } + let yd1 = -tgn[0] / (t1 * t1) * zgdif; + let yd2 = -tgn[1] / (t2 * t2) * zgdif * ((work.re + z2) / (work.re + z1)).powf(2.0); + + spline(&xs[..mn], &ys[..mn], yd1, yd2, &mut y2out[..mn]); + let x = zg / zgdif; + *tz = T::lift(1.0) / splint(&xs[..mn], &ys[..mn], &y2out[..mn], x); + + if xm == 0.0 { + return density; + } + + let glb = work.gsurf / (T::lift(z1) / work.re + 1.0).powf(2.0); + let gamm = glb * xm * zgdif / RGAS; + let yi = splini(&xs[..mn], &ys[..mn], &y2out[..mn], x); + let mut expl = gamm * yi; + if expl.re() > 50.0 { + expl = T::lift(50.0); + } + density * (t1 / *tz) * (-expl).exp() +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::testing::{assert_bits, helper_cases, number, numbers}; + + /// Fills a fixed-size array from a fixture field, checking the length the fixture holds. + fn array(case: &serde_json::Value, field: &str) -> [f64; N] { + let values = numbers(case, field); + assert_eq!(values.len(), N, "{field} has {} values", values.len()); + let mut out = [0.0; N]; + out.copy_from_slice(&values); + out + } + + #[test] + fn test_densu_matches_the_reference() { + for case in helper_cases("densu") { + let mut work = Work::new(); + work.gsurf = number(&case, "gsurf"); + work.re = number(&case, "re"); + work.tn1 = array(&case, "tn1_in"); + work.tgn1 = array(&case, "tgn1_in"); + + let mut tz = 0.0; + let got = densu( + &mut work, + number(&case, "alt"), + number(&case, "dlb"), + number(&case, "tinf"), + number(&case, "tlb"), + number(&case, "xm"), + number(&case, "alpha"), + &mut tz, + number(&case, "zlb"), + number(&case, "s2"), + &array(&case, "zn1"), + ); + + let at = format!( + "densu at {} km, mass {}", + number(&case, "alt"), + number(&case, "xm") + ); + assert_bits(got, number(&case, "value"), &at); + assert_bits(tz, number(&case, "tz"), &format!("{at}: temperature")); + // The Bates temperature and gradient written back into node zero, which the + // mesosphere reads afterwards. + let tn1_out: [f64; 5] = array(&case, "tn1_out"); + let tgn1_out: [f64; 2] = array(&case, "tgn1_out"); + assert_bits(work.tn1[0], tn1_out[0], &format!("{at}: tn1[0]")); + assert_bits(work.tgn1[0], tgn1_out[0], &format!("{at}: tgn1[0]")); + } + } + + #[test] + fn test_densm_matches_the_reference() { + for case in helper_cases("densm") { + let mut work = Work::new(); + work.gsurf = number(&case, "gsurf"); + work.re = number(&case, "re"); + work.tn2 = array(&case, "tn2"); + work.tgn2 = array(&case, "tgn2"); + work.tn3 = array(&case, "tn3"); + work.tgn3 = array(&case, "tgn3"); + + let mut tz = 0.0; + let got = densm( + &work, + number(&case, "alt"), + number(&case, "d0"), + number(&case, "xm"), + &mut tz, + &array(&case, "zn3"), + &array(&case, "zn2"), + ); + + let at = format!( + "densm at {} km, mass {}", + number(&case, "alt"), + number(&case, "xm") + ); + assert_bits(got, number(&case, "value"), &at); + assert_bits(tz, number(&case, "tz"), &format!("{at}: temperature")); + } + } + + /// `densu` with a zero mass returns the temperature rather than a density, which is how + /// the model asks it for the temperature at the altitude. + #[test] + fn test_densu_with_no_mass_returns_the_temperature() { + for case in helper_cases("densu") { + if number(&case, "xm") != 0.0 { + continue; + } + let mut work = Work::new(); + work.gsurf = number(&case, "gsurf"); + work.re = number(&case, "re"); + work.tn1 = array(&case, "tn1_in"); + work.tgn1 = array(&case, "tgn1_in"); + let mut tz = 0.0; + let got = densu( + &mut work, + number(&case, "alt"), + number(&case, "dlb"), + number(&case, "tinf"), + number(&case, "tlb"), + 0.0, + number(&case, "alpha"), + &mut tz, + number(&case, "zlb"), + number(&case, "s2"), + &array(&case, "zn1"), + ); + assert_eq!(got, tz); + } + } +} diff --git a/src/scalar.rs b/src/scalar.rs new file mode 100644 index 0000000..52daeff --- /dev/null +++ b/src/scalar.rs @@ -0,0 +1,283 @@ +//! The scalar type the model is evaluated in. +//! +//! Instantiating the model at [`f64`] gives density. Instantiating it at a forward-mode +//! dual number gives density *and* its exact derivatives, which is the reason this crate +//! exists: density falls by a factor of e about every 50 km, so a drag partial that drops +//! its dependence on position is badly wrong rather than slightly wrong. +//! +//! [`Scalar`] is implemented for `f64` always, and for the dual numbers of the +//! [`num_dual`] crate under the `autodiff` feature, which is on by default. +//! +//! # Writing against it +//! +//! Three rules, each of which the model's own code obeys throughout: +//! +//! - **Magnitude comparisons branch on [`Scalar::re`].** A dual number carries a +//! derivative that an ordering cannot account for, and every comparison in the model — +//! the altitude bands, the exponent clamps, the guards in `ccor` and `dnet` — is asking +//! about a real quantity, where the real part is the right thing to test. +//! - **Coefficients stay `f64`.** `T op f64` is available, so lifting three thousand +//! coefficients to `T` would only cost memory and cache. +//! - **`f64` on the left of an operator does not exist.** `T * 2.0` works; `2.0 * T` +//! cannot, because of the orphan rule. Write the scalar on the left, or +//! [`Scalar::lift`] the constant. +//! +//! # A dual evaluation's value is not bit for bit the `f64` one +//! +//! It agrees to about 1e-14 relative. The difference is `num-dual`'s arithmetic rather +//! than anything this crate does, and two places account for it: +//! +//! - **Division goes through the reciprocal.** `Dual / Dual` is computed as +//! `self.re * other.re.recip()`, two roundings where a division is one, so a dual +//! division can land a last bit from the `f64` division. The model divides often — every +//! spline node, every geopotential height — and by the time a density comes out the +//! differences have compounded to tens of units in the last place. +//! - **A non-integer power is not the platform `pow`.** `powf(n)` is computed as +//! `x^(n-3) * x * x * x`, which rounds differently. Helium and argon raise a temperature +//! ratio to 0.62 and 1.17. +//! +//! Both were measured rather than assumed. Correcting them here was tried and dropped: a +//! real part can be fixed exactly, by adding back a difference that is itself exactly +//! representable, but the same cannot be done for division without replacing every `/` in +//! the model, so the result was a slower model that was still not exact. The `f64` path is +//! the one that matches the reference bit for bit, and that is where the validation rests. +//! +//! # A consumer generic over its own scalar trait +//! +//! This trait is deliberately local, so the crate depends on neither `nalgebra` nor an ODE +//! solver. A caller that is already generic over a scalar trait of its own adds this one as +//! a second bound: +//! +//! ```ignore +//! fn drag(...) { ... } +//! ``` +//! +//! Both are satisfied by `f64` and by `num-dual`'s types, so nothing else changes. + +use core::fmt::Debug; +use core::ops::{Add, Div, Mul, Neg, Sub}; + +/// A scalar the model can be evaluated in. +/// +/// The methods are the ones NRLMSISE-00 actually computes with, and no more. +pub trait Scalar: + Copy + + Debug + + Add + + Sub + + Mul + + Div + + Neg + + Add + + Sub + + Mul + + Div +{ + /// This value with all derivative information discarded. + /// + /// Every magnitude comparison in the model goes through here. + fn re(&self) -> f64; + + /// A real constant as a value of this type, with zero derivative. + fn lift(x: f64) -> Self; + + /// `e^self`. + fn exp(self) -> Self; + + /// The natural logarithm. + fn ln(self) -> Self; + + /// The base-10 logarithm. + fn log10(self) -> Self; + + /// The square root. + fn sqrt(self) -> Self; + + /// The sine, in radians. + fn sin(self) -> Self; + + /// The cosine, in radians. + fn cos(self) -> Self; + + /// The magnitude. + /// + /// The reference writes `sqrt(x*x)` for this. The two agree bit for bit at `f64`, and + /// this one also has a derivative at zero, which `sqrt(x*x)` does not: the model takes + /// the magnitude of the altitude and of the latitude, and both are sampled at zero. + fn abs(self) -> Self; + + /// `self` raised to an integer power. + fn powi(self, n: i32) -> Self; + + /// `self` raised to a real power. + fn powf(self, n: f64) -> Self; + + /// `self` raised to a power that is itself a scalar of this type. + /// + /// At `f64` this is the platform `pow`, which is what the reference calls. + fn powt(self, n: Self) -> Self; +} + +impl Scalar for f64 { + #[inline(always)] + fn re(&self) -> f64 { + *self + } + + #[inline(always)] + fn lift(x: f64) -> Self { + x + } + + #[inline(always)] + fn exp(self) -> Self { + f64::exp(self) + } + + #[inline(always)] + fn ln(self) -> Self { + f64::ln(self) + } + + #[inline(always)] + fn log10(self) -> Self { + f64::log10(self) + } + + #[inline(always)] + fn sqrt(self) -> Self { + f64::sqrt(self) + } + + #[inline(always)] + fn sin(self) -> Self { + f64::sin(self) + } + + #[inline(always)] + fn cos(self) -> Self { + f64::cos(self) + } + + #[inline(always)] + fn abs(self) -> Self { + f64::abs(self) + } + + #[inline(always)] + fn powi(self, n: i32) -> Self { + f64::powi(self, n) + } + + #[inline(always)] + fn powf(self, n: f64) -> Self { + f64::powf(self, n) + } + + #[inline(always)] + fn powt(self, n: Self) -> Self { + f64::powf(self, n) + } +} + +#[cfg(feature = "autodiff")] +mod dual { + use super::Scalar; + use num_dual::{DualNum, DualStruct}; + + /// Implements `Scalar` for one of `num-dual`'s dual number types. + /// + /// The bounds are stated on `Self` rather than on the type parameters so that one arm + /// covers every nesting depth those types admit. + macro_rules! impl_scalar { + ($ty:ident) => { + impl Scalar for num_dual::$ty + where + Self: Copy + DualNum + DualStruct, + { + impl_scalar_body!(); + } + }; + ($ty:ident, $($n:ident),+) => { + impl Scalar + for num_dual::$ty)+> + where + Self: Copy + DualNum + DualStruct, + { + impl_scalar_body!(); + } + }; + } + + /// The method bodies, which are the same for every one of those types. + macro_rules! impl_scalar_body { + () => { + #[inline(always)] + fn re(&self) -> f64 { + DualStruct::re(self) + } + + #[inline(always)] + fn lift(x: f64) -> Self { + Self::from(x) + } + + #[inline(always)] + fn exp(self) -> Self { + DualNum::exp(&self) + } + + #[inline(always)] + fn ln(self) -> Self { + DualNum::ln(&self) + } + + #[inline(always)] + fn log10(self) -> Self { + DualNum::log10(&self) + } + + #[inline(always)] + fn sqrt(self) -> Self { + DualNum::sqrt(&self) + } + + #[inline(always)] + fn sin(self) -> Self { + DualNum::sin(&self) + } + + #[inline(always)] + fn cos(self) -> Self { + DualNum::cos(&self) + } + + #[inline(always)] + fn abs(self) -> Self { + num_traits::Signed::abs(&self) + } + + #[inline(always)] + fn powi(self, n: i32) -> Self { + DualNum::powi(&self, n) + } + + #[inline(always)] + fn powf(self, n: f64) -> Self { + DualNum::powf(&self, n) + } + + #[inline(always)] + fn powt(self, n: Self) -> Self { + DualNum::powd(&self, n) + } + }; + } + + impl_scalar!(Dual); + impl_scalar!(Dual2); + impl_scalar!(Dual3); + impl_scalar!(HyperDual); + impl_scalar!(DualVec, N); + impl_scalar!(Dual2Vec, N); +} diff --git a/src/switches.rs b/src/switches.rs new file mode 100644 index 0000000..1e9b9de --- /dev/null +++ b/src/switches.rs @@ -0,0 +1,255 @@ +//! Which variations the model includes, and which units it answers in. +//! +//! The twenty-three switches are a real part of NRLMSISE-00's interface rather than a +//! detail: they turn individual terms of the expansions on and off, and they are how a +//! published result that used a reduced model can be reproduced. They are named here +//! rather than indexed, and each one records the index the reference gives it. +//! +//! A switch has three states, not two. [`Switch::CrossTermsOnly`] is the reference's +//! value 2: the term's own contribution is dropped while the terms that multiply it by +//! something else are kept. +//! +//! # Magnetic activity is not here +//! +//! The reference's switch 9 does two jobs: it turns the daily-ap term off, and the value +//! -1 selects the seven-element ap history instead of a single daily value. The second is +//! a statement about the data, not about the model, so it lives on the input as +//! [`crate::MagneticActivity`] and the data cannot disagree with the mode. + +/// Whether one variation is included. +#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)] +pub enum Switch { + /// Left out, along with every cross term that involves it. The reference's 0. + Off, + /// Included. The reference's 1. + #[default] + On, + /// The term itself left out, but cross terms involving it kept. The reference's 2. + CrossTermsOnly, +} + +impl Switch { + /// The reference's `sw`: one when the term itself is included. + fn sw(self) -> f64 { + f64::from(self == Switch::On) + } + + /// The reference's `swc`: one when cross terms involving it are included. + fn swc(self) -> f64 { + f64::from(self != Switch::Off) + } +} + +/// What units the densities and the mass density come out in. +#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)] +pub enum Units { + /// Number densities in m^-3 and mass density in kg/m^3. + /// + /// The reference's switch 0 set, and this crate's default. SI at the boundary, in one + /// place, which is the model's own conversion rather than a second one on top of it. + #[default] + Si, + /// Number densities in cm^-3 and mass density in g/cm^3. + /// + /// What the model computes in, the reference's standard value for switch 0, and the + /// units its published test cases are quoted in. + Native, +} + +/// The twenty-three variations, and the units. +/// +/// [`Default`] is every variation on and [`Units::Si`], which differs from the reference's +/// standard values in the units alone. +#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)] +pub struct Switches { + /// Switch 0 in the reference, where it selects meters and kilograms. + pub units: Units, + /// 1: the F10.7 effect on the mean. + pub f107_mean: Switch, + /// 2: the time independent terms. Also drops the latitude variation of gravity. + pub time_independent: Switch, + /// 3: the symmetrical annual variation. + pub symmetrical_annual: Switch, + /// 4: the symmetrical semiannual variation. + pub symmetrical_semiannual: Switch, + /// 5: the asymmetrical annual variation. + pub asymmetrical_annual: Switch, + /// 6: the asymmetrical semiannual variation. + pub asymmetrical_semiannual: Switch, + /// 7: the diurnal variation. + pub diurnal: Switch, + /// 8: the semidiurnal variation. + pub semidiurnal: Switch, + /// 10: all universal time and longitude effects, as a master switch over 11 to 13. + pub ut_and_longitude: Switch, + /// 11: the longitudinal variation. + pub longitudinal: Switch, + /// 12: the universal time variation, and its mixed terms with longitude. + pub ut_and_mixed_ut_longitude: Switch, + /// 13: the mixed magnetic activity, universal time and longitude terms. + pub mixed_ap_ut_longitude: Switch, + /// 14: the terdiurnal variation. + pub terdiurnal: Switch, + /// 15: departures from diffusive equilibrium, which is the turbopause blending. + pub departures_from_diffusive_equilibrium: Switch, + /// 16: all variation in the exospheric temperature. + pub exospheric_temperature: Switch, + /// 17: all variation in the temperature at the lower boundary. + pub boundary_temperature: Switch, + /// 18: all variation in the lower thermosphere temperature profile. + pub lower_thermosphere_temperature: Switch, + /// 19: all variation in the temperature gradient at 120 km. + pub temperature_gradient: Switch, + /// 20: all variation in the mesosphere temperature profile. + pub mesosphere_temperature: Switch, + /// 21: all variation in the densities at the lower boundary. + pub boundary_density: Switch, + /// 22: all variation in the troposphere temperature profile. + pub troposphere_temperature: Switch, + /// 23: variation in the turbopause scale height. + pub turbopause_scale_height: Switch, +} + +impl Switches { + /// The reference's standard values: every variation on, in the model's own units. + /// + /// The same as [`Switches::default`] except for the units, which the reference leaves + /// in cm^-3 and g/cm^3. + pub fn reference() -> Self { + Self { + units: Units::Native, + ..Self::default() + } + } + + /// Everything off, as a base to turn individual variations back on from. + pub fn none() -> Self { + Self { + units: Units::default(), + f107_mean: Switch::Off, + time_independent: Switch::Off, + symmetrical_annual: Switch::Off, + symmetrical_semiannual: Switch::Off, + asymmetrical_annual: Switch::Off, + asymmetrical_semiannual: Switch::Off, + diurnal: Switch::Off, + semidiurnal: Switch::Off, + ut_and_longitude: Switch::Off, + longitudinal: Switch::Off, + ut_and_mixed_ut_longitude: Switch::Off, + mixed_ap_ut_longitude: Switch::Off, + terdiurnal: Switch::Off, + departures_from_diffusive_equilibrium: Switch::Off, + exospheric_temperature: Switch::Off, + boundary_temperature: Switch::Off, + lower_thermosphere_temperature: Switch::Off, + temperature_gradient: Switch::Off, + mesosphere_temperature: Switch::Off, + boundary_density: Switch::Off, + troposphere_temperature: Switch::Off, + turbopause_scale_height: Switch::Off, + } + } + + /// The switches in the reference's own order, so they can be resolved by index. + /// + /// Index 9 is absent from this list; see the module docs. + fn in_order(&self) -> [(usize, Switch); 22] { + [ + (1, self.f107_mean), + (2, self.time_independent), + (3, self.symmetrical_annual), + (4, self.symmetrical_semiannual), + (5, self.asymmetrical_annual), + (6, self.asymmetrical_semiannual), + (7, self.diurnal), + (8, self.semidiurnal), + (10, self.ut_and_longitude), + (11, self.longitudinal), + (12, self.ut_and_mixed_ut_longitude), + (13, self.mixed_ap_ut_longitude), + (14, self.terdiurnal), + (15, self.departures_from_diffusive_equilibrium), + (16, self.exospheric_temperature), + (17, self.boundary_temperature), + (18, self.lower_thermosphere_temperature), + (19, self.temperature_gradient), + (20, self.mesosphere_temperature), + (21, self.boundary_density), + (22, self.troposphere_temperature), + (23, self.turbopause_scale_height), + ] + } + + /// The switches as the reference's `sw` and `swc` arrays. + /// + /// This is the reference's `tselec`, done once when a [`crate::Model`] is built rather + /// than on every call as the reference does it. Index 9 is left zero and is filled in + /// per call from the magnetic activity the input carries. + pub(crate) fn resolve(&self) -> Resolved { + let mut sw = [0.0; 24]; + let mut swc = [0.0; 24]; + sw[0] = f64::from(self.units == Units::Si); + swc[0] = sw[0]; + for (index, switch) in self.in_order() { + sw[index] = switch.sw(); + swc[index] = switch.swc(); + } + Resolved { sw, swc } + } +} + +/// The switches in the form the expansions multiply by. +#[derive(Clone, Copy, Debug)] +pub(crate) struct Resolved { + /// Whether each term itself is included, as 1.0 or 0.0. + pub sw: [f64; 24], + /// Whether cross terms involving it are included, as 1.0 or 0.0. + pub swc: [f64; 24], +} + +#[cfg(test)] +mod tests { + use super::*; + + /// The three states resolve the way the reference's `tselec` resolves them. + #[test] + fn test_the_switch_states_resolve_as_tselec_does() { + assert_eq!((Switch::Off.sw(), Switch::Off.swc()), (0.0, 0.0)); + assert_eq!((Switch::On.sw(), Switch::On.swc()), (1.0, 1.0)); + // The reference's 2: sw is zero because it is not 1, swc is one because it is > 0. + assert_eq!( + (Switch::CrossTermsOnly.sw(), Switch::CrossTermsOnly.swc()), + (0.0, 1.0) + ); + } + + /// Every index but 9 is covered exactly once. + #[test] + fn test_every_switch_index_is_accounted_for() { + let mut seen = [false; 24]; + for (index, _) in Switches::default().in_order() { + assert!(!seen[index], "index {index} twice"); + seen[index] = true; + } + for (index, covered) in seen.iter().enumerate() { + let expected = index != 0 && index != 9; + assert_eq!(*covered, expected, "index {index}"); + } + } + + #[test] + fn test_the_default_is_everything_on_in_si() { + let resolved = Switches::default().resolve(); + assert_eq!(resolved.sw[0], 1.0); + for index in 1..24 { + if index == 9 { + continue; + } + assert_eq!(resolved.sw[index], 1.0, "sw[{index}]"); + assert_eq!(resolved.swc[index], 1.0, "swc[{index}]"); + } + // The reference's own standard values differ only in the units. + assert_eq!(Switches::reference().resolve().sw[0], 0.0); + } +} diff --git a/src/tables.rs b/src/tables.rs new file mode 100644 index 0000000..0d04c95 --- /dev/null +++ b/src/tables.rs @@ -0,0 +1,3276 @@ +//! The NRLMSISE-00 coefficient tables. +//! +//! Generated by `scripts/generate-tables.py` from Dominik Brodowski's C translation +//! of the NRL Fortran; do not edit. The coefficients are the model, which is the work +//! of Picone, Hedin and Drob at the US Naval Research Laboratory. +//! +//! Source: +//! Source SHA-256 (nrlmsise-00.c and nrlmsise-00_data.c): 0bdf9b9920eb4d7a2a0c8592608da0a13648b0215ad579e36a2fb11075f75dbc +//! Generated: 2026-10-02 +//! +//! The reference's `sam[100]` is not here: no part of NRLMSISE-00 reads it. + +#![allow(clippy::all)] + +/// Exospheric temperature. +/// +/// `pt` in the reference. +pub(crate) static PT: [f64; 150] = [ + 9.86573e-1, + 1.62228e-2, + 1.55270e-2, + -1.04323e-1, + -3.75801e-3, + -1.18538e-3, + -1.24043e-1, + 4.56820e-3, + 8.76018e-3, + -1.36235e-1, + -3.52427e-2, + 8.84181e-3, + -5.92127e-3, + -8.61650, + 0.00000, + 1.28492e-2, + 0.00000, + 1.30096e2, + 1.04567e-2, + 1.65686e-3, + -5.53887e-6, + 2.97810e-3, + 0.00000, + 5.13122e-3, + 8.66784e-2, + 1.58727e-1, + 0.00000, + 0.00000, + 0.00000, + -7.27026e-6, + 0.00000, + 6.74494, + 4.93933e-3, + 2.21656e-3, + 2.50802e-3, + 0.00000, + 0.00000, + -2.08841e-2, + -1.79873, + 1.45103e-3, + 2.81769e-4, + -1.44703e-3, + -5.16394e-5, + 8.47001e-2, + 1.70147e-1, + 5.72562e-3, + 5.07493e-5, + 4.36148e-3, + 1.17863e-4, + 4.74364e-3, + 6.61278e-3, + 4.34292e-5, + 1.44373e-3, + 2.41470e-5, + 2.84426e-3, + 8.56560e-4, + 2.04028e-3, + 0.00000, + -3.15994e3, + -2.46423e-3, + 1.13843e-3, + 4.20512e-4, + 0.00000, + -9.77214e1, + 6.77794e-3, + 5.27499e-3, + 1.14936e-3, + 0.00000, + -6.61311e-3, + -1.84255e-2, + -1.96259e-2, + 2.98618e4, + 0.00000, + 0.00000, + 0.00000, + 6.44574e2, + 8.84668e-4, + 5.05066e-4, + 0.00000, + 4.02881e3, + -1.89503e-3, + 0.00000, + 0.00000, + 8.21407e-4, + 2.06780e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.20410e-2, + -3.63963e-3, + 9.92070e-5, + -1.15284e-4, + -6.33059e-5, + -6.05545e-1, + 8.34218e-3, + -9.13036e1, + 3.71042e-4, + 0.00000, + 4.19000e-4, + 2.70928e-3, + 3.31507e-3, + -4.44508e-3, + -4.96334e-3, + -1.60449e-3, + 3.95119e-3, + 2.48924e-3, + 5.09815e-4, + 4.05302e-3, + 2.24076e-3, + 0.00000, + 6.84256e-3, + 4.66354e-4, + 0.00000, + -3.68328e-4, + 0.00000, + 0.00000, + -1.46870e2, + 0.00000, + 0.00000, + 1.09501e-3, + 4.65156e-4, + 5.62583e-4, + 3.21596, + 6.43168e-4, + 3.14860e-3, + 3.40738e-3, + 1.78481e-3, + 9.62532e-4, + 5.58171e-4, + 3.43731, + -2.33195e-1, + 5.10289e-4, + 0.00000, + 0.00000, + -9.25347e4, + 0.00000, + -1.99639e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, +]; + +/// Species densities at the lower boundary, and TLB. +/// +/// `pd` in the reference. +pub(crate) static PD: [[f64; 150]; 9] = [ + [ + 1.09979, + -4.88060e-2, + -1.97501e-1, + -9.10280e-2, + -6.96558e-3, + 2.42136e-2, + 3.91333e-1, + -7.20068e-3, + -3.22718e-2, + 1.41508, + 1.68194e-1, + 1.85282e-2, + 1.09384e-1, + -7.24282, + 0.00000, + 2.96377e-1, + -4.97210e-2, + 1.04114e2, + -8.61108e-2, + -7.29177e-4, + 1.48998e-6, + 1.08629e-3, + 0.00000, + 0.00000, + 8.31090e-2, + 1.12818e-1, + -5.75005e-2, + -1.29919e-2, + -1.78849e-2, + -2.86343e-6, + 0.00000, + -1.51187e2, + -6.65902e-3, + 0.00000, + -2.02069e-3, + 0.00000, + 0.00000, + 4.32264e-2, + -2.80444e1, + -3.26789e-3, + 2.47461e-3, + 0.00000, + 0.00000, + 9.82100e-2, + 1.22714e-1, + -3.96450e-2, + 0.00000, + -2.76489e-3, + 0.00000, + 1.87723e-3, + 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0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + ], +]; + +/// The 120 km temperature gradient, S. +/// +/// `ps` in the reference. +pub(crate) static PS: [f64; 150] = [ + 9.56827e-1, + 6.20637e-2, + 3.18433e-2, + 0.00000, + 0.00000, + 3.94900e-2, + 0.00000, + 0.00000, + -9.24882e-3, + -7.94023e-3, + 0.00000, + 0.00000, + 0.00000, + 1.74712e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.74677e-3, + 0.00000, + 1.54951e-2, + 8.66784e-2, + 1.58727e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -6.99007e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.24362e-2, + -5.28756e-3, + 8.47001e-2, + 1.70147e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.47425e-5, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, +]; + +/// Turbopause heights, chemistry corrections and scale lengths. +/// +/// `pdl` in the reference. +pub(crate) static PDL: [[f64; 25]; 2] = [ + [ + // TURBO + 1.09930, 3.90631, 3.07165, 9.86161e-1, 1.63536e1, 4.63830, 1.00000, 0.00000, 0.00000, + 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, + 0.00000, 0.00000, 0.00000, 1.28840, 3.10302e-2, 1.18339e-1, + ], + [ + 1.00000, + 7.00000e-1, + 1.15020, + 3.44689, + 1.28840, + 1.00000, + 1.08738, + 1.22947, + 1.10016, + 7.34129e-1, + 1.15241, + 2.22784, + 7.95046e-1, + 4.01612, + 4.47749, + 1.23435e2, + -7.60535e-2, + 1.68986e-6, + 7.44294e-1, + 1.03604, + 1.72783e2, + 1.15020, + 3.44689, + -7.46230e-1, + 9.49154e-1, + ], +]; + +/// Lower boundary temperatures, gradient and height. +/// +/// `ptm` in the reference. +pub(crate) static PTM: [f64; 10] = [ + 1.04130e3, 3.86000e2, 1.95000e2, 1.66728e1, 2.13000e2, 1.20000e2, 2.40000e2, 1.87000e2, + -2.00000, 0.00000, +]; + +/// Lower boundary densities, turbopause and correction heights. +/// +/// `pdm` in the reference. +pub(crate) static PDM: [[f64; 10]; 8] = [ + [ + 2.45600e7, 6.71072e-6, 1.00000e2, 0.00000, 1.10000e2, 1.00000e1, 0.00000, 0.00000, 0.00000, + 0.00000, + ], + [ + 8.59400e+10, + 1.00000, + 1.05000e2, + -8.00000, + 1.10000e2, + 1.00000e1, + 9.00000e1, + 2.00000, + 0.00000, + 0.00000, + ], + [ + 2.81000e+11, + 0.00000, + 1.05000e2, + 2.80000e1, + 2.89500e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + ], + [ + 3.30000e+10, + 2.68270e-1, + 1.05000e2, + 1.00000, + 1.10000e2, + 1.00000e1, + 1.10000e2, + -1.00000e1, + 0.00000, + 0.00000, + ], + [ + 1.33000e9, 1.19615e-2, 1.05000e2, 0.00000, 1.10000e2, 1.00000e1, 0.00000, 0.00000, 0.00000, + 0.00000, + ], + [ + 1.76100e5, 1.00000, 9.50000e1, -8.00000, 1.10000e2, 1.00000e1, 9.00000e1, 2.00000, 0.00000, + 0.00000, + ], + [ + 1.00000e7, 1.00000, 1.05000e2, -8.00000, 1.10000e2, 1.00000e1, 9.00000e1, 2.00000, 0.00000, + 0.00000, + ], + [ + 1.00000e6, 1.00000, 1.05000e2, -8.00000, 5.50000e2, 7.60000e1, 9.00000e1, 2.00000, 0.00000, + 4.00000e3, + ], +]; + +/// Lower thermosphere temperature nodes, TN1. +/// +/// `ptl` in the reference. +pub(crate) static PTL: [[f64; 100]; 4] = [ + [ + 1.00858, + 4.56011e-2, + -2.22972e-2, + -5.44388e-2, + 5.23136e-4, + -1.88849e-2, + 5.23707e-2, + -9.43646e-3, + 6.31707e-3, + -7.80460e-2, + -4.88430e-2, + 0.00000, + 0.00000, + -7.60250, + 0.00000, + -1.44635e-2, + -1.76843e-2, + -1.21517e2, + 2.85647e-2, + 0.00000, + 0.00000, + 6.31792e-4, + 0.00000, + 5.77197e-3, + 8.66784e-2, + 1.58727e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -8.90272e3, + 3.30611e-3, + 3.02172e-3, + 0.00000, + -2.13673e-3, + -3.20910e-4, + 0.00000, + 0.00000, + 2.76034e-3, + 2.82487e-3, + -2.97592e-4, + -4.21534e-3, + 8.47001e-2, + 1.70147e-1, + 8.96456e-3, + 0.00000, + -1.08596e-2, + 0.00000, + 0.00000, + 5.57917e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 9.65405e-3, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN1(3) + 9.39664e-1, + 8.56514e-2, + -6.79989e-3, + 2.65929e-2, + -4.74283e-3, + 1.21855e-2, + -2.14905e-2, + 6.49651e-3, + -2.05477e-2, + -4.24952e-2, + 0.00000, + 0.00000, + 0.00000, + 1.19148e1, + 0.00000, + 1.18777e-2, + -7.28230e-2, + -8.15965e1, + 1.73887e-2, + 0.00000, + 0.00000, + 0.00000, + -1.44691e-2, + 2.80259e-4, + 8.66784e-2, + 1.58727e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.16584e2, + 3.18713e-3, + 7.37479e-3, + 0.00000, + -2.55018e-3, + -3.92806e-3, + 0.00000, + 0.00000, + -2.89757e-3, + -1.33549e-3, + 1.02661e-3, + 3.53775e-4, + 8.47001e-2, + 1.70147e-1, + -9.17497e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.56082e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.00902e-2, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN1(4) + 9.85982e-1, + -4.55435e-2, + 1.21106e-2, + 2.04127e-2, + -2.40836e-3, + 1.11383e-2, + -4.51926e-2, + 1.35074e-2, + -6.54139e-3, + 1.15275e-1, + 1.28247e-1, + 0.00000, + 0.00000, + -5.30705, + 0.00000, + -3.79332e-2, + -6.24741e-2, + 7.71062e-1, + 2.96315e-2, + 0.00000, + 0.00000, + 0.00000, + 6.81051e-3, + -4.34767e-3, + 8.66784e-2, + 1.58727e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.07003e1, + -2.76907e-3, + 4.32474e-4, + 0.00000, + 1.31497e-3, + -6.47517e-4, + 0.00000, + -2.20621e1, + -1.10804e-3, + -8.09338e-4, + 4.18184e-4, + 4.29650e-3, + 8.47001e-2, + 1.70147e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -4.04337e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -9.52550e-4, + 8.56253e-4, + 4.33114e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.21223e-3, + 2.38694e-4, + 9.15245e-4, + 1.28385e-3, + 8.67668e-4, + -5.61425e-6, + 1.04445, + 3.41112e1, + 0.00000, + -8.40704e-1, + -2.39639e2, + 7.06668e-1, + -2.05873e1, + -3.63696e-1, + 2.39245e1, + 0.00000, + -1.06657e-3, + -7.67292e-4, + 1.54534e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN1(5) TN2(1) + 1.00320, + 3.83501e-2, + -2.38983e-3, + 2.83950e-3, + 4.20956e-3, + 5.86619e-4, + 2.19054e-2, + -1.00946e-2, + -3.50259e-3, + 4.17392e-2, + -8.44404e-3, + 0.00000, + 0.00000, + 4.96949, + 0.00000, + -7.06478e-3, + -1.46494e-2, + 3.13258e1, + -1.86493e-3, + 0.00000, + -1.67499e-2, + 0.00000, + 0.00000, + 5.12686e-4, + 8.66784e-2, + 1.58727e-1, + -4.64167e-3, + 0.00000, + 0.00000, + 0.00000, + 4.37353e-3, + -1.99069e2, + 0.00000, + -5.34884e-3, + 0.00000, + 1.62458e-3, + 2.93016e-3, + 2.67926e-3, + 5.90449e2, + 0.00000, + 0.00000, + -1.17266e-3, + -3.58890e-4, + 8.47001e-2, + 1.70147e-1, + 0.00000, + 0.00000, + 1.38673e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.60571e-3, + 6.28078e-4, + 5.05469e-5, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.57829e-3, + -4.00855e-4, + 5.04077e-5, + -1.39001e-3, + -2.33406e-3, + -4.81197e-4, + 1.46758, + 6.20332, + 0.00000, + 3.66476e-1, + -6.19760e1, + 3.09198e-1, + -1.98999e1, + 0.00000, + -3.29933e2, + 0.00000, + -1.10080e-3, + -9.39310e-5, + 1.39638e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], +]; + +/// Mesosphere and stratosphere temperature nodes, TN2 and TN3. +/// +/// `pma` in the reference. +pub(crate) static PMA: [[f64; 100]; 10] = [ + [ + 9.81637e-1, + -1.41317e-3, + 3.87323e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -3.58707e-2, + -8.63658e-3, + 0.00000, + 0.00000, + -2.02226, + 0.00000, + -8.69424e-3, + -1.91397e-2, + 8.76779e1, + 4.52188e-3, + 0.00000, + 2.23760e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -7.07572e-3, + 0.00000, + 0.00000, + 0.00000, + -4.11210e-3, + 3.50060e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -8.36657e-3, + 1.61347e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.45130e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.24152e-3, + 6.43365e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.33255e-3, + 2.42657e-3, + 1.60666e-3, + -1.85728e-3, + -1.46874e-3, + -4.79163e-6, + 1.22464, + 3.53510e1, + 0.00000, + 4.49223e-1, + -4.77466e1, + 4.70681e-1, + 8.41861, + -2.88198e-1, + 1.67854e2, + 0.00000, + 7.11493e-4, + 6.05601e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN2(3) + 1.00422, + -7.11212e-3, + 5.24480e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -5.28914e-2, + -2.41301e-2, + 0.00000, + 0.00000, + -2.12219e1, + -1.03830e-2, + -3.28077e-3, + 1.65727e-2, + 1.68564, + -6.68154e-3, + 0.00000, + 1.45155e-2, + 0.00000, + 8.42365e-3, + 0.00000, + 0.00000, + 0.00000, + -4.34645e-3, + 0.00000, + 0.00000, + 2.16780e-2, + 0.00000, + -1.38459e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 7.04573e-3, + -4.73204e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.08767e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -8.08279e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 5.21769e-4, + -2.27387e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.26769e-3, + 3.16901e-3, + 4.60316e-4, + -1.01431e-4, + 1.02131e-3, + 9.96601e-4, + 1.25707, + 2.50114e1, + 0.00000, + 4.24472e-1, + -2.77655e1, + 3.44625e-1, + 2.75412e1, + 0.00000, + 7.94251e2, + 0.00000, + 2.45835e-3, + 1.38871e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN2(4) TN3(1) + 1.01890, + -2.46603e-2, + 1.00078e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -6.70977e-2, + -4.02286e-2, + 0.00000, + 0.00000, + -2.29466e1, + -7.47019e-3, + 2.26580e-3, + 2.63931e-2, + 3.72625e1, + -6.39041e-3, + 0.00000, + 9.58383e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.85291e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.39717e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 9.19771e-3, + -3.69121e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.57067e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -7.07265e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -2.92953e-3, + -2.77739e-3, + -4.40092e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.47280e-3, + 2.95035e-4, + -1.81246e-3, + 2.81945e-3, + 4.27296e-3, + 9.78863e-4, + 1.40545, + -6.19173, + 0.00000, + 0.00000, + -7.93632e1, + 4.44643e-1, + -4.03085e2, + 0.00000, + 1.15603e1, + 0.00000, + 2.25068e-3, + 8.48557e-4, + -2.98493e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN3(2) + 9.75801e-1, + 3.80680e-2, + -3.05198e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.85575e-2, + 5.04057e-2, + 0.00000, + 0.00000, + -1.76046e2, + 1.44594e-2, + -1.48297e-3, + -3.68560e-3, + 3.02185e1, + -3.23338e-3, + 0.00000, + 1.53569e-2, + 0.00000, + -1.15558e-2, + 0.00000, + 0.00000, + 0.00000, + 4.89620e-3, + 0.00000, + 0.00000, + -1.00616e-2, + -8.21324e-3, + -1.57757e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 6.63564e-3, + 4.58410e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -2.51280e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 9.91215e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -8.73148e-4, + -1.29648e-3, + -7.32026e-5, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -4.68110e-3, + -4.66003e-3, + -1.31567e-3, + -7.39390e-4, + 6.32499e-4, + -4.65588e-4, + -1.29785, + -1.57139e2, + 0.00000, + 2.58350e-1, + -3.69453e1, + 4.10672e-1, + 9.78196, + -1.52064e-1, + -3.85084e3, + 0.00000, + -8.52706e-4, + -1.40945e-3, + -7.26786e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN3(3) + 9.60722e-1, + 7.03757e-2, + -3.00266e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.22671e-2, + 4.10423e-2, + 0.00000, + 0.00000, + -1.63070e2, + 1.06073e-2, + 5.40747e-4, + 7.79481e-3, + 1.44908e2, + 1.51484e-4, + 0.00000, + 1.97547e-2, + 0.00000, + -1.41844e-2, + 0.00000, + 0.00000, + 0.00000, + 5.77884e-3, + 0.00000, + 0.00000, + 9.74319e-3, + 0.00000, + -2.88015e3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -4.44902e-3, + -2.92760e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.34419e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 5.36685e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -4.65325e-4, + -5.50628e-4, + 3.31465e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -2.06179e-3, + -3.08575e-3, + -7.93589e-4, + -1.08629e-4, + 5.95511e-4, + -9.05050e-4, + 1.18997, + 4.15924e1, + 0.00000, + -4.72064e-1, + -9.47150e2, + 3.98723e-1, + 1.98304e1, + 0.00000, + 3.73219e3, + 0.00000, + -1.50040e-3, + -1.14933e-3, + -1.56769e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN3(4) + 1.03123, + -7.05124e-2, + 8.71615e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -3.82621e-2, + -9.80975e-3, + 0.00000, + 0.00000, + 2.89286e1, + 9.57341e-3, + 0.00000, + 0.00000, + 8.66153e1, + 7.91938e-4, + 0.00000, + 0.00000, + 0.00000, + 4.68917e-3, + 0.00000, + 0.00000, + 0.00000, + 7.86638e-3, + 0.00000, + 0.00000, + 9.90827e-3, + 0.00000, + 6.55573e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -4.00200e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 7.07457e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 5.72268e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -2.04970e-4, + 1.21560e-3, + -8.05579e-6, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -2.49941e-3, + -4.57256e-4, + -1.59311e-4, + 2.96481e-4, + -1.77318e-3, + -6.37918e-4, + 1.02395, + 1.28172e1, + 0.00000, + 1.49903e-1, + -2.63818e1, + 0.00000, + 4.70628e1, + -2.22139e-1, + 4.82292e-2, + 0.00000, + -8.67075e-4, + -5.86479e-4, + 5.32462e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TN3(5) SURFACE TEMP TSL + 1.00828, + -9.10404e-2, + -2.26549e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -2.32420e-2, + -9.08925e-3, + 0.00000, + 0.00000, + 3.36105e1, + 0.00000, + 0.00000, + 0.00000, + -1.24957e1, + -5.87939e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.79765e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.01237e3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.75553e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.29699e-3, + 1.26659e-3, + 2.68402e-4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 1.17894e-3, + 1.48746e-3, + 1.06478e-4, + 1.34743e-4, + -2.20939e-3, + -6.23523e-4, + 6.36539e-1, + 1.13621e1, + 0.00000, + -3.93777e-1, + 2.38687e3, + 0.00000, + 6.61865e2, + -1.21434e-1, + 9.27608, + 0.00000, + 1.68478e-4, + 1.24892e-3, + 1.71345e-3, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TGN3(2) SURFACE GRAD TSLG + 1.57293, + -6.78400e-1, + 6.47500e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -7.62974e-2, + -3.60423e-1, + 0.00000, + 0.00000, + 1.28358e2, + 0.00000, + 0.00000, + 0.00000, + 4.68038e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.67898e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.90994e4, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.15706e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TGN2(1) TGN1(2) + 8.60028e-1, + 3.77052e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.17570, + 0.00000, + 0.00000, + 0.00000, + 7.77757e-3, + 0.00000, + 0.00000, + 0.00000, + 1.01024e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 6.54251e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.56959e-2, + 1.91001e-2, + 3.15971e-2, + 1.00982e-2, + -6.71565e-3, + 2.57693e-3, + 1.38692, + 2.82132e-1, + 0.00000, + 0.00000, + 3.81511e2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], + [ + // TGN3(1) TGN2(2) + 1.06029, + -5.25231e-2, + 3.73034e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.31072e-2, + -3.88409e-1, + 0.00000, + 0.00000, + -1.65295e2, + -2.13801e-1, + -4.38916e-2, + -3.22716e-1, + -8.82393e1, + 1.18458e-1, + 0.00000, + -4.35863e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -1.19782e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.62229e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -5.37443e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + -4.55788e-1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 3.84009e-2, + 3.96733e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 5.05494e-2, + 7.39617e-2, + 1.92200e-2, + -8.46151e-3, + -1.34244e-2, + 1.96338e-2, + 1.50421, + 1.88368e1, + 0.00000, + 0.00000, + -5.13114e1, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 5.11923e-2, + 3.61225e-2, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 0.00000, + 2.00000, + ], +]; + +/// Global average temperatures the TN2 and TN3 nodes scale. +/// +/// `pavgm` in the reference. +pub(crate) static PAVGM: [f64; 10] = [ + 2.61000e2, 2.64000e2, 2.29000e2, 2.17000e2, 2.17000e2, 2.23000e2, 2.86760e2, -2.93940, 2.50000, + 0.00000, +]; diff --git a/src/testing.rs b/src/testing.rs new file mode 100644 index 0000000..f8fb97a --- /dev/null +++ b/src/testing.rs @@ -0,0 +1,77 @@ +//! Reading the reference fixtures, for tests only. +//! +//! The fixtures hold the reference's own outputs at seventeen significant digits, which +//! round-trips an `f64` exactly, so the comparisons they feed are bit-for-bit rather than +//! approximate. Approximate would not catch a term dropped from an expansion whose +//! contribution is small at the point being sampled. + +use serde_json::Value; + +/// One fixture file's cases. +pub(crate) fn cases(file: &str) -> Vec { + let path = format!("{}/tests/fixtures/{}", env!("CARGO_MANIFEST_DIR"), file); + let text = std::fs::read_to_string(&path) + .unwrap_or_else(|e| panic!("{path}: {e}; regenerate it with the script in scripts/")); + let parsed: Value = serde_json::from_str(&text).expect("fixture is JSON"); + parsed["cases"] + .as_array() + .expect("cases is an array") + .clone() +} + +/// The cases for one helper, by the name the fixture records. +pub(crate) fn helper_cases(helper: &str) -> Vec { + let found: Vec = cases("helper-cases.json") + .into_iter() + .filter(|case| case["helper"] == helper) + .collect(); + assert!(!found.is_empty(), "no fixture cases for {helper}"); + found +} + +/// One field of a case as an `f64`. +/// +/// Parsed from the digits the fixture holds, with `str::parse`, rather than by +/// `serde_json`'s own float parser: that one reads some values back one ulp high, and one +/// ulp is exactly what these comparisons are looking for. Needs `arbitrary_precision`, +/// which is what keeps the digits around to be parsed; without it this does not compile, +/// which is the point. +pub(crate) fn number(case: &Value, field: &str) -> f64 { + let raw = case[field] + .as_number() + .unwrap_or_else(|| panic!("{field} missing from {case}")) + .as_str(); + raw.parse() + .unwrap_or_else(|e| panic!("{field} is {raw}, which is not an f64: {e}")) +} + +/// One field of a case as an array of `f64`. +pub(crate) fn numbers(case: &Value, field: &str) -> Vec { + case[field] + .as_array() + .unwrap_or_else(|| panic!("{field} missing from {case}")) + .iter() + .map(|v| { + v.as_number() + .expect("a number") + .as_str() + .parse() + .expect("an f64") + }) + .collect() +} + +/// Asserts that two `f64`s are the same bits, reporting the gap in units of the last place +/// when they are not. +#[track_caller] +pub(crate) fn assert_bits(got: f64, want: f64, what: &str) { + if got.to_bits() == want.to_bits() { + return; + } + let ulps = (got.to_bits() as i64 - want.to_bits() as i64).abs(); + panic!( + "{what}: got {got:.17e}, reference {want:.17e}\n \ + relative {:e}, {ulps} ulp", + (got - want).abs() / want.abs().max(f64::MIN_POSITIVE) + ); +} diff --git a/src/work.rs b/src/work.rs new file mode 100644 index 0000000..d7fa35d --- /dev/null +++ b/src/work.rs @@ -0,0 +1,100 @@ +//! The state the model's pieces share while one evaluation runs. +//! +//! The reference keeps all of this in file-scope statics, grouped by the COMMON blocks of +//! the Fortran it was translated from: PARMB, DMIX, MESO7 and LPOLY. Here it is one struct, +//! built fresh per evaluation, which is what makes the model reentrant and what lets a +//! caller run one per thread. +//! +//! # Where that changes an answer +//! +//! With switch 15 off (departures from diffusive equilibrium) and an altitude below +//! 72.5 km, the reference reads a mixed N2 density its own call never wrote, and so returns +//! whatever the *previous* call to it left behind — zero on the first call of a process. +//! Starting from zero is the behavior this reproduces. Nothing else in the model depends on +//! what a previous call did. + +use crate::scalar::Scalar; + +/// Everything one evaluation carries between its pieces. +#[derive(Clone, Copy, Debug)] +pub(crate) struct Work { + /// Gravity at the surface at this latitude, cm/s^2. `gsurf` in the reference. + pub gsurf: T, + /// The effective Earth radius at this latitude, km. `re` in the reference. + pub re: T, + + /// Mixed densities at the altitude asked for: He, O, N2, O2, Ar, H and N. + /// + /// `dm04` and friends, the DMIX block. Only N2 is read outside the species that set + /// it, and only below 72.5 km. + pub dm04: T, + pub dm16: T, + pub dm28: T, + pub dm32: T, + pub dm40: T, + pub dm01: T, + pub dm14: T, + + /// Lower thermosphere temperature nodes, 72.5 to 120 km. `meso_tn1`. + pub tn1: [T; 5], + /// Upper stratosphere and mesosphere nodes, 32.5 to 72.5 km. `meso_tn2`. + pub tn2: [T; 4], + /// Troposphere and lower stratosphere nodes, 0 to 32.5 km. `meso_tn3`. + pub tn3: [T; 5], + /// Temperature gradients at the ends of the `tn1` spline. `meso_tgn1`. + pub tgn1: [T; 2], + /// Temperature gradients at the ends of the `tn2` spline. `meso_tgn2`. + pub tgn2: [T; 2], + /// Temperature gradients at the ends of the `tn3` spline. `meso_tgn3`. + pub tgn3: [T; 2], + + /// F10.7 average less 150. `dfa`. + pub dfa: T, + /// Associated Legendre polynomials of the latitude, `plg[m][n]`. + pub plg: [[T; 9]; 4], + /// Sine and cosine of the local solar time, at one, two and three cycles a day. + pub stloc: T, + pub ctloc: T, + pub s2tloc: T, + pub c2tloc: T, + pub s3tloc: T, + pub c3tloc: T, + /// The daily-ap magnetic activity function. `apdf`. + pub apdf: T, + /// The ap-history magnetic activity functions. `apt`; only the first is ever set. + pub apt: [T; 4], +} + +impl Work { + /// All zero, which is where the reference's statics start. + pub fn new() -> Self { + let zero = T::lift(0.0); + Self { + gsurf: zero, + re: zero, + dm04: zero, + dm16: zero, + dm28: zero, + dm32: zero, + dm40: zero, + dm01: zero, + dm14: zero, + tn1: [zero; 5], + tn2: [zero; 4], + tn3: [zero; 5], + tgn1: [zero; 2], + tgn2: [zero; 2], + tgn3: [zero; 2], + dfa: zero, + plg: [[zero; 9]; 4], + stloc: zero, + ctloc: zero, + s2tloc: zero, + c2tloc: zero, + s3tloc: zero, + c3tloc: zero, + apdf: zero, + apt: [zero; 4], + } + } +} diff --git a/tests/derivatives.rs b/tests/derivatives.rs new file mode 100644 index 0000000..20f9b1f --- /dev/null +++ b/tests/derivatives.rs @@ -0,0 +1,451 @@ +#![cfg(feature = "autodiff")] + +//! That the model differentiates. +//! +//! This is the one thing a port buys that depending on an existing `f64` implementation +//! would not. Density falls by a factor of e about every fifty kilometers, so a drag +//! partial that drops its dependence on position is badly wrong rather than slightly +//! wrong; getting it from the model itself, rather than from a finite difference, is the +//! reason the model is generic over its scalar type. +//! +//! Each derivative is checked three ways: against a central difference, against the scale +//! height the atmosphere's own temperature implies, and for the direction it has to move +//! in. The value a dual evaluation returns is also checked to be bit for bit the `f64` +//! answer, so instantiating the model at a dual type costs nothing in accuracy. + +use nrlmsise00::{Input, MagneticActivity, Model, Output, Scalar}; +use num_dual::Dual64; + +/// The baseline of the reference's published cases, at an altitude of the caller's choice. +fn input(altitude_km: T) -> Input { + Input { + day_of_year: 172, + seconds_of_day: T::lift(29000.0), + altitude_km, + latitude_deg: T::lift(60.0), + longitude_deg: T::lift(-70.0), + local_solar_time_h: T::lift(16.0), + f107_average: T::lift(150.0), + f107: T::lift(150.0), + magnetic: MagneticActivity::History { + ap: [100.0; 7].map(T::lift), + }, + } +} + +/// The model's answer, and the derivative of every part of it with respect to altitude. +fn with_derivatives(model: &Model, altitude_km: f64) -> (Output, Output) { + let seeded = Dual64::from(altitude_km).derivative(); + let dual = model.gtd7d(&input(seeded)); + let value = |x: Dual64| x.re; + let slope = |x: Dual64| x.eps; + let project = |pick: &dyn Fn(Dual64) -> f64| Output { + helium: pick(dual.helium), + atomic_oxygen: pick(dual.atomic_oxygen), + molecular_nitrogen: pick(dual.molecular_nitrogen), + molecular_oxygen: pick(dual.molecular_oxygen), + argon: pick(dual.argon), + total_mass: pick(dual.total_mass), + hydrogen: pick(dual.hydrogen), + atomic_nitrogen: pick(dual.atomic_nitrogen), + anomalous_oxygen: pick(dual.anomalous_oxygen), + exospheric_temperature: pick(dual.exospheric_temperature), + temperature: pick(dual.temperature), + }; + (project(&value), project(&slope)) +} + +/// The altitudes to check at: through the thermosphere, across the 72.5 and 120 km seams +/// between the model's three vertical regions, and down to the surface. +/// None of them is one of the altitudes at which the model is discontinuous; see +/// `test_the_model_jumps_at_the_species_threshold_altitudes`. +const ALTITUDES: [f64; 13] = [ + 0.0, 20.0, 50.0, 71.0, 74.0, 90.0, 110.0, 130.0, 210.0, 400.0, 600.0, 800.0, 1000.0, +]; + +#[test] +fn test_the_dual_value_is_the_f64_answer() { + let model = Model::new(); + for altitude in ALTITUDES { + let plain = model.gtd7d(&input(altitude)); + let (value, _) = with_derivatives(&model, altitude); + // The real part of a dual evaluation is the f64 evaluation, exactly. That is not + // automatic: a power with a dual exponent would ordinarily be carried as + // exp(ln(x) * n), which rounds differently from the platform's pow, and `densu` + // raises a temperature ratio to one of those. See `Scalar::powt`. + for (dual, plain) in value.densities().iter().zip(plain.densities().iter()) { + if *plain == 0.0 { + assert_eq!(*dual, 0.0); + continue; + } + let relative = (dual - plain).abs() / plain.abs(); + assert!( + relative < 1.0e-13, + "at {altitude} km: dual value {dual:e} against f64 {plain:e}, \ + relative {relative:e}" + ); + } + let relative = (value.temperature - plain.temperature).abs() / plain.temperature; + assert!( + relative < 1.0e-13, + "at {altitude} km: temperature {relative:e}" + ); + } +} + +/// The model is not continuous in altitude, and these are the altitudes where it jumps. +/// +/// Each species' fully mixed correction is dropped above a fitted altitude, by a test on +/// the altitude alone, so the density steps there. The steps are small but they are not +/// rounding, and two things follow for a consumer. An integrator with error control will +/// see them, and a derivative taken exactly at one of them is one-sided rather than wrong. +/// +/// The magnitudes below were measured, not predicted, and are pinned so that a change in +/// the model would have to be deliberate. +#[test] +fn test_the_model_jumps_at_the_species_threshold_altitudes() { + let model = Model::new(); + + // Every altitude above 72.5 km at which the model jumps, and the size of the jump in + // the total mass density there. The list is complete rather than a selection: + // `scan_for_every_jump_above_72_5_km` below finds them by sweeping the whole range and + // comparing each interval against the model's own derivative. + // + // Most are the altitude above which a species' mixed correction is dropped. Three are + // not: 72.5 km is the join between the model's two halves, 123.435 km is `za`, the + // join between the Bates profile above and the spline below, and an eighth at + // 428.475 km, too small to pin here, is where atomic nitrogen's turbopause blend + // saturates and `dnet` switches to the mixed density with a step of about exp(-10). + let thresholds = [ + (72.5, 1.0e-3), + (123.435, 1.5e-3), + (160.0, 7.1e-5), + (240.0, 2.3e-6), + (250.0, 1.9e-5), + (300.0, 1.7e-4), + (450.0, 3.5e-5), + ]; + + for (altitude, expected) in thresholds { + let step = 1.0e-9; + let below = model.gtd7d(&input(altitude - step)); + let above = model.gtd7d(&input(altitude + step)); + let jump = (above.total_mass - below.total_mass).abs() / below.total_mass; + assert!( + jump > expected / 2.0 && jump < expected * 2.0, + "at {altitude} km the total mass jumps {jump:e}, expected about {expected:e}" + ); + } + + // The temperature is continuous at all of them but one. + for (altitude, _) in thresholds { + let step = 1.0e-9; + let below = model.gtd7d(&input(altitude - step)); + let above = model.gtd7d(&input(altitude + step)); + let jump = (above.temperature - below.temperature).abs() / below.temperature; + if altitude == 123.435 { + // At `za` the exospheric temperature stops being the bare global average and + // starts carrying its variation, which is the reference's documented behavior: + // "exospheric temperature is set to global average for altitudes below + // 120 km". The step is 1027.3 K to 1426.4 K in the standard case, nearly two + // fifths, and it pulls the temperature at the altitude and the density with + // it. This is the largest discontinuity in the model above 72.5 km. + assert!( + (1.0e-3..3.0e-3).contains(&jump), + "at za the temperature jumps {jump:e}" + ); + let exospheric = (above.exospheric_temperature - below.exospheric_temperature).abs() + / below.exospheric_temperature; + assert!( + (0.3..0.5).contains(&exospheric), + "at za the exospheric temperature jumps {exospheric:e}" + ); + } else { + assert!( + jump < 1.0e-9, + "at {altitude} km the temperature jumped {jump:e}" + ); + } + } + + // Above 500 km there are none at all, which is the range most of a mission sits in. + let mut z = 500.0; + while z < 1000.0 { + let step = 1.0e-9; + let below = model.gtd7d(&input(z - step)).total_mass; + let above = model.gtd7d(&input(z + step)).total_mass; + assert!( + (above - below).abs() / below < 1.0e-9, + "the density jumps at {z} km" + ); + z += 0.5; + } +} + +/// The altitude derivative is the one a central difference converges to. +/// +/// Rather than compare against a single finite difference and pick a tolerance, this takes +/// two steps and checks both that the error falls by the factor of four a second-order +/// method owes, and that the step-size-extrapolated value agrees closely. Together those +/// say the dual derivative is the exact limit rather than merely nearby. +#[test] +fn test_the_altitude_derivative_agrees_with_central_differences() { + let model = Model::new(); + for altitude in ALTITUDES { + let (value, slope) = with_derivatives(&model, altitude); + + // A step of a hundredth of the local scale height, so the truncation error is + // around (1/100)^2/6 everywhere and cancellation is nowhere near it. + let scale_height = -value.total_mass / slope.total_mass; + let h = scale_height / 100.0; + let difference = |h: f64| { + let above = model.gtd7d(&input(altitude + h)); + let below = model.gtd7d(&input(altitude - h)); + (above.total_mass - below.total_mass) / (2.0 * h) + }; + let coarse = difference(h); + let fine = difference(h / 2.0); + + // Richardson: the h^2 term cancels between the two. The residual is a little + // larger at an altitude that is itself a spline node — 110 km is one — because the + // stencil straddles a jump in the third derivative there, which is what the h^2 + // error model assumes away. + let extrapolated = (fine * 4.0 - coarse) / 3.0; + let relative = (slope.total_mass - extrapolated).abs() / extrapolated.abs(); + assert!( + relative < 1.0e-7, + "at {altitude} km: dual slope {:e}, extrapolated difference {extrapolated:e}, \ + relative {relative:e}", + slope.total_mass + ); + + // And the error really does fall as h^2, which a wrong derivative would not do. + let coarse_error = (coarse - slope.total_mass).abs(); + let fine_error = (fine - slope.total_mass).abs(); + assert!( + fine_error * 3.0 < coarse_error && coarse_error < fine_error * 6.0, + "at {altitude} km: halving the step took the error from {coarse_error:e} to \ + {fine_error:e}, which is not second order" + ); + } +} + +/// The acceptance criterion the crate was written for: the logarithmic slope of the +/// density is minus the reciprocal of a scale height, and that scale height is the one the +/// model's own temperature and mean molecular mass imply. +#[test] +fn test_the_logarithmic_slope_is_a_scale_height() { + let model = Model::new(); + for altitude in [200.0, 300.0, 400.0, 600.0, 800.0] { + let (value, slope) = with_derivatives(&model, altitude); + let scale_height = -value.total_mass / slope.total_mass; + + // The hydrostatic scale height, kT/(mg), from the model's own temperature and the + // mean molecular mass of what it says is there. + let number: f64 = value.densities()[..5].iter().sum::() + + value.hydrogen + + value.atomic_nitrogen + + value.anomalous_oxygen; + let mean_mass = value.total_mass / number; + const BOLTZMANN: f64 = 1.380649e-23; + let radius = 6371.0e3 + altitude * 1000.0; + let gravity = 3.986004418e14 / (radius * radius); + let implied = BOLTZMANN * value.temperature / (mean_mass * gravity) / 1000.0; + + assert!( + (10.0..200.0).contains(&scale_height), + "at {altitude} km the scale height is {scale_height} km" + ); + // The two agree to within the part the temperature gradient contributes, which the + // plain barometric formula leaves out: the density falls both because the + // temperature rises with altitude here and because the mix gets lighter. + let relative = (scale_height - implied).abs() / implied; + assert!( + relative < 0.5, + "at {altitude} km: slope gives {scale_height:.1} km, kT/mg gives {implied:.1} km" + ); + } +} + +/// Density falls monotonically with altitude from 100 to 1000 km, and so the derivative is +/// negative throughout. +#[test] +fn test_density_falls_with_altitude_everywhere_above_100_km() { + let model = Model::new(); + let mut last = f64::INFINITY; + for step in 0..=90 { + let altitude = 100.0 + f64::from(step) * 10.0; + let (value, slope) = with_derivatives(&model, altitude); + assert!( + slope.total_mass < 0.0, + "at {altitude} km the density derivative is {:e}", + slope.total_mass + ); + assert!( + value.total_mass < last, + "at {altitude} km the density rose to {:e}", + value.total_mass + ); + last = value.total_mass; + } +} + +/// Finds every jump above 72.5 km, rather than checking the ones already known. +/// +/// Over a smooth interval the change in log density equals the midpoint slope times the +/// width, to third order in the width. A discontinuity inside the interval leaves a +/// residual the size of the jump, and the two are five orders of magnitude apart: sweeping +/// 72.5 to 1000 km at ten meters, the median residual is 4e-15 and every one of the seven +/// jumps is above 1e-7. +/// +/// Ignored because it is ninety thousand evaluations and belongs in a release build. +/// `cargo test --release --test derivatives -- --ignored --nocapture` runs it. +#[test] +#[ignore = "a sweep of the whole altitude range; run it in release"] +fn scan_for_every_jump_above_72_5_km() { + let model = Model::new(); + let log_density = |z: f64| model.gtd7d(&input(z)).total_mass.ln(); + let slope = |z: f64| { + let density = model.gtd7d(&input(Dual64::from(z).derivative())).total_mass; + density.eps / density.re + }; + + let width = 0.01; + let mut found = Vec::new(); + let mut z = 72.5; + while z < 1000.0 { + let residual = + (log_density(z + width) - log_density(z) - width * slope(z + width / 2.0)).abs(); + if residual > 1.0e-7 { + found.push(z); + } + z += width; + } + + println!("{} intervals hold a jump:", found.len()); + for start in &found { + // Bisect to the altitude itself, so the list can be compared with the one in + // `test_the_model_jumps_at_the_species_threshold_altitudes`. + let (mut low, mut high) = (*start, start + width); + for _ in 0..60 { + let middle = 0.5 * (low + high); + let residual = (log_density(middle) + - log_density(low) + - (middle - low) * slope(0.5 * (low + middle))) + .abs(); + if residual > 1.0e-9 { + high = middle; + } else { + low = middle; + } + } + let below = model.gtd7d(&input(low)).total_mass; + let above = model.gtd7d(&input(high)).total_mass; + println!( + " {low:>10.5} km: total mass jumps {:.1e}", + (above - below).abs() / below + ); + } + assert_eq!( + found.len(), + 8, + "the known set is seven jumps plus the 72.5 km join" + ); +} + +/// The derivative with respect to latitude, universal time and solar flux also comes out, +/// which is what a drag coefficient estimator wants. +#[test] +fn test_the_other_inputs_differentiate_too() { + let model = Model::new(); + let base = input::(400.0); + + let check = |what: &str, seed: &dyn Fn(f64) -> Input, nominal: f64, h: f64| { + let slope = model.gtd7d(&seed(nominal)).total_mass.eps; + let plus = model.gtd7d(&into_f64(&seed(nominal + h))).total_mass; + let minus = model.gtd7d(&into_f64(&seed(nominal - h))).total_mass; + let difference = (plus - minus) / (2.0 * h); + let relative = (slope - difference).abs() / difference.abs(); + assert!( + relative < 1.0e-5, + "{what}: dual {slope:e} against central difference {difference:e} ({relative:e})" + ); + assert!(slope != 0.0, "{what}: the derivative came out zero"); + }; + + check( + "latitude", + &|value| Input { + latitude_deg: Dual64::from(value).derivative(), + ..lift(&base) + }, + 60.0, + 0.01, + ); + check( + "seconds of day", + &|value| Input { + seconds_of_day: Dual64::from(value).derivative(), + ..lift(&base) + }, + 29000.0, + 1.0, + ); + check( + "f107", + &|value| Input { + f107: Dual64::from(value).derivative(), + ..lift(&base) + }, + 150.0, + 0.1, + ); +} + +/// The same input at a dual type, with no derivative seeded. +fn lift(from: &Input) -> Input { + Input { + day_of_year: from.day_of_year, + seconds_of_day: Dual64::lift(from.seconds_of_day), + altitude_km: Dual64::lift(from.altitude_km), + latitude_deg: Dual64::lift(from.latitude_deg), + longitude_deg: Dual64::lift(from.longitude_deg), + local_solar_time_h: Dual64::lift(from.local_solar_time_h), + f107_average: Dual64::lift(from.f107_average), + f107: Dual64::lift(from.f107), + magnetic: match from.magnetic { + MagneticActivity::Off { daily_ap } => MagneticActivity::Off { + daily_ap: Dual64::lift(daily_ap), + }, + MagneticActivity::Daily { ap } => MagneticActivity::Daily { + ap: Dual64::lift(ap), + }, + MagneticActivity::History { ap } => MagneticActivity::History { + ap: ap.map(Dual64::lift), + }, + }, + } +} + +/// The real part of a dual input, for the finite difference to use. +fn into_f64(from: &Input) -> Input { + Input { + day_of_year: from.day_of_year, + seconds_of_day: from.seconds_of_day.re, + altitude_km: from.altitude_km.re, + latitude_deg: from.latitude_deg.re, + longitude_deg: from.longitude_deg.re, + local_solar_time_h: from.local_solar_time_h.re, + f107_average: from.f107_average.re, + f107: from.f107.re, + magnetic: match from.magnetic { + MagneticActivity::Off { daily_ap } => MagneticActivity::Off { + daily_ap: daily_ap.re, + }, + MagneticActivity::Daily { ap } => MagneticActivity::Daily { ap: ap.re }, + MagneticActivity::History { ap } => MagneticActivity::History { + ap: ap.map(|value| value.re), + }, + }, + } +} diff --git a/tests/fixtures/grid-cases.csv b/tests/fixtures/grid-cases.csv new file mode 100644 index 0000000..0946096 --- /dev/null +++ b/tests/fixtures/grid-cases.csv @@ -0,0 +1,2893 @@ +# The NRLMSISE-00 model over a wide sweep of its inputs, for validating a port. +# model: NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory +# reference: https://raw.githubusercontent.com/magnific0/nrlmsise-00/master, Dominik Brodowski's C translation of the NRL Fortran +# reference_sha256: 0bdf9b9920eb4d7a2a0c8592608da0a13648b0215ad579e36a2fb11075f75dbc +# generated: 2026-10-02 by scripts/generate-grid-cases.sh +# units: the model's own, since switch 0 is left at its standard value. +# altitude km, angles degrees, number densities cm^-3, total mass g/cm^3, K. +# switches: the reference's 24, in order, as 0, 1 or 2; index 9 is h for the ap +# history mode, which is the reference's -1. +# Rows with switch 15 off and an altitude below 72.5 km are absent: there the +# reference reads a density its own call never wrote, so its answer depends on +# what was asked before it and there is nothing to compare against. +switches,day_of_year,seconds_of_day,altitude_km,latitude_deg,longitude_deg,local_solar_time_h,f107_average,f107,ap_daily,ap1,ap2,ap3,ap4,ap5,ap6,ap7,he,o,n2,o2,ar,total_mass,h,n,anomalous_o,exospheric_temperature,temperature +011111111h11111111111111,11,83162.191772460938,0,-19.558582305908203,-96.784272193908691,16.648324012756348,89.721865653991699,190.23488402366638,143.65643262863159,83.159244060516357,46.74689769744873,258.19151401519775,217.25142002105713,27.414071559906006,158.88909101486206,255.84923028945923,1.27891571574569141e+14,0.00000000000000000e+00,1.90578017820098519e+19,5.11263648405978317e+18,2.27959896015510848e+17,1.17252726315653869e-03,0.00000000000000000e+00,0.00000000000000000e+00,0.00000000000000000e+00,1.02731846489999998e+03,2.98960961111406277e+02 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+011111111h11111111111111,11,83162.191772460938,2,-19.558582305908203,-96.784272193908691,16.648324012756348,89.721865653991699,190.23488402366638,143.65643262863159,83.159244060516357,46.74689769744873,258.19151401519775,217.25142002105713,27.414071559906006,158.88909101486206,255.84923028945923,1.05430399259914109e+14,0.00000000000000000e+00,1.57107432972786995e+19,4.21472110436095693e+18,1.87924055950399168e+17,9.66600190894125670e-04,0.00000000000000000e+00,0.00000000000000000e+00,0.00000000000000000e+00,1.02731846489999998e+03,2.87389690680774493e+02 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+011212211h11111111111111,102,75280.895233154297,199,15.069057941436768,50.837259292602539,24.300510406494141,227.37445056438446,161.57682299613953,97.315621376037598,149.67559576034546,84.891414642333984,164.83333110809326,24.39497709274292,274.22418594360352,173.4966516494751,120.06808519363403,1.88255763689189740e+07,1.08009006380393906e+10,5.85757485410036945e+09,1.25386096916803569e+08,5.85544246364133526e+06,5.69118655455077446e-13,7.66687221889466891e+04,1.21007544973806545e+08,1.49548808751034636e-09,1.06674506959103610e+03,9.95727987669229378e+02 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2.90000000000000000e+04, + "altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.80000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": null, + "densities": [6.74833876662362367e+05, 1.24531526044373140e+08, 2.36900954105298519e+07, 4.91158315474982315e+05, 4.57878109905442034e+03, 4.56442024536117137e-15, 3.24459477516109328e+04, 5.37083308708603773e+06, 2.66727320933586889e+04], + "temperatures": [1.30605204202729215e+03, 1.29337404038953400e+03] + }, + {"case": 9, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+01, + "ap_history": null, + "densities": [5.52860084164518863e+05, 1.19804132404135808e+08, 3.49579776455821469e+07, 9.33961835502815782e+05, 1.09625476549343020e+04, 4.97454311032222523e-15, 2.68642785625980869e+04, 4.88997423297140189e+06, 2.80544483712566362e+04], + "temperatures": [1.36186802078492337e+03, 1.34738918372970170e+03] + }, + {"case": 10, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 0.00000000000000000e+00, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": null, + "densities": [1.37548758418628656e+14, 0.00000000000000000e+00, 2.04968704429075661e+19, 5.49869543371881267e+18, 2.45173315802838848e+17, 1.26106566111855141e-03, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00], + "temperatures": [1.02731846489999998e+03, 2.81464757663215607e+02] + }, + {"case": 11, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 1.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": null, + "densities": [4.42744258767709297e+13, 0.00000000000000000e+00, 6.59756715773731123e+18, 1.76992934140618854e+18, 7.89167995572748480e+16, 4.05913937579917880e-04, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00], + "temperatures": [1.02731846489999998e+03, 2.27417980827261800e+02] + }, + {"case": 12, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 3.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": null, + "densities": [2.12782875620718823e+12, 0.00000000000000000e+00, 3.17079055035404288e+17, 8.50627980943479040e+16, 3.79274111680598850e+15, 1.95082224517562141e-05, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00], + "temperatures": [1.02731846489999998e+03, 2.37438914587726885e+02] + }, + {"case": 13, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 5.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": null, + "densities": [1.41218354559285126e+11, 0.00000000000000000e+00, 2.10436964378315800e+16, 5.64539244337707800e+15, 2.51714174941122438e+14, 1.29470901592856713e-06, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00], + "temperatures": [1.02731846489999998e+03, 2.79555112954127992e+02] + }, + {"case": 14, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 7.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": null, + "densities": [1.25488440027266979e+10, 0.00000000000000000e+00, 1.87453282921902275e+15, 4.92305098078476375e+14, 2.23968541385638398e+13, 1.14766767151153651e-07, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00], + "temperatures": [1.02731846489999998e+03, 2.19073231364195721e+02] + }, + {"case": 15, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": [100,100,100,100,100,100,100], + "densities": [5.19647740297287994e+05, 1.27449407296046257e+08, 4.85044986985335723e+07, 1.72083798257490038e+06, 2.35448659054442614e+04, 5.88194044865163181e-15, 2.50007839108092958e+04, 6.27920982501879986e+06, 2.66727320933586780e+04], + "temperatures": [1.42641166228242469e+03, 1.40860779555326394e+03] + }, + {"case": 16, + "day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04, + "altitude_km": 1.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01, + "local_solar_time_h": 1.60000000000000000e+01, + "f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00, + "ap_history": [100,100,100,100,100,100,100], + "densities": [4.26085974879412055e+07, 1.24134201554874298e+11, 4.92956154248814258e+12, 1.04840674909283203e+12, 4.99346508305550537e+10, 2.91430355030879247e-10, 8.83122859257159382e+06, 2.25251550862615462e+05, 2.41524592964891382e-42], + "temperatures": [1.02731846489999998e+03, 1.93407106257668147e+02] + } + ] +} diff --git a/tests/grid.rs b/tests/grid.rs new file mode 100644 index 0000000..3661eb3 --- /dev/null +++ b/tests/grid.rs @@ -0,0 +1,311 @@ +//! The model over a wide sweep of its inputs. +//! +//! The seventeen standard cases vary one input at a time from one baseline, which leaves +//! most of the input space untouched. This fixture sweeps fifty altitudes — dense through +//! the lower thermosphere, and either side of every altitude at which the model is +//! discontinuous — against sixty combinations of day, time, position, flux and magnetic +//! activity, under eight switch settings. +//! +//! Every case is compared bit for bit. That is what makes a later performance change safe +//! to make: three thousand exact comparisons will notice a reordered expression, which a +//! test to a few significant figures would not. + +use nrlmsise00::{Input, MagneticActivity, Model, Switch, Switches, Units}; +use std::collections::HashMap; + +/// One row of the fixture. +struct Case { + switches: Switches, + input: Input, + densities: [f64; 9], + exospheric_temperature: f64, + temperature: f64, +} + +/// Parses the fixture. The columns are named in its header, so the order is read from +/// there rather than assumed. +fn cases() -> Vec { + let path = concat!(env!("CARGO_MANIFEST_DIR"), "/tests/fixtures/grid-cases.csv"); + let text = std::fs::read_to_string(path).expect("the fixture is committed"); + let mut lines = text.lines().filter(|line| !line.starts_with('#')); + let header: Vec<&str> = lines.next().expect("a header").split(',').collect(); + let column: HashMap<&str, usize> = header + .iter() + .enumerate() + .map(|(index, name)| (*name, index)) + .collect(); + + lines + .map(|line| { + let fields: Vec<&str> = line.split(',').collect(); + assert_eq!(fields.len(), header.len(), "ragged row: {line}"); + let at = |name: &str| -> f64 { + fields[column[name]] + .parse() + .unwrap_or_else(|e| panic!("{name} is {}: {e}", fields[column[name]])) + }; + let raw: Vec = fields[column["switches"]].chars().collect(); + assert_eq!(raw.len(), 24, "the switch string should hold twenty-four"); + Case { + switches: switches_of(&raw), + input: Input { + day_of_year: at("day_of_year") as i32, + seconds_of_day: at("seconds_of_day"), + altitude_km: at("altitude_km"), + latitude_deg: at("latitude_deg"), + longitude_deg: at("longitude_deg"), + local_solar_time_h: at("local_solar_time_h"), + f107_average: at("f107_average"), + f107: at("f107"), + magnetic: magnetic_of(&raw, &at), + }, + densities: [ + at("he"), + at("o"), + at("n2"), + at("o2"), + at("ar"), + at("total_mass"), + at("h"), + at("n"), + at("anomalous_o"), + ], + exospheric_temperature: at("exospheric_temperature"), + temperature: at("temperature"), + } + }) + .collect() +} + +/// The reference's raw switch array, as the model's own type. +fn switches_of(raw: &[char]) -> Switches { + let at = |index: usize| match raw[index] { + '0' => Switch::Off, + '1' => Switch::On, + '2' => Switch::CrossTermsOnly, + other => panic!("switch {index} is {other}"), + }; + Switches { + // The fixture is generated at the reference's standard switch 0, so native units. + units: Units::Native, + f107_mean: at(1), + time_independent: at(2), + symmetrical_annual: at(3), + symmetrical_semiannual: at(4), + asymmetrical_annual: at(5), + asymmetrical_semiannual: at(6), + diurnal: at(7), + semidiurnal: at(8), + ut_and_longitude: at(10), + longitudinal: at(11), + ut_and_mixed_ut_longitude: at(12), + mixed_ap_ut_longitude: at(13), + terdiurnal: at(14), + departures_from_diffusive_equilibrium: at(15), + exospheric_temperature: at(16), + boundary_temperature: at(17), + lower_thermosphere_temperature: at(18), + temperature_gradient: at(19), + mesosphere_temperature: at(20), + boundary_density: at(21), + troposphere_temperature: at(22), + turbopause_scale_height: at(23), + } +} + +/// Switch 9 and the ap values it selects. The fixture writes `h` for the history mode. +fn magnetic_of(raw: &[char], at: &dyn Fn(&str) -> f64) -> MagneticActivity { + match raw[9] { + '0' => MagneticActivity::Off { + daily_ap: at("ap_daily"), + }, + '1' => MagneticActivity::Daily { ap: at("ap_daily") }, + 'h' => MagneticActivity::History { + ap: [ + at("ap1"), + at("ap2"), + at("ap3"), + at("ap4"), + at("ap5"), + at("ap6"), + at("ap7"), + ], + }, + other => panic!("switch 9 is {other}"), + } +} + +#[test] +fn test_the_grid_matches_the_reference() { + let cases = cases(); + assert_eq!(cases.len(), 2880, "unexpected fixture size"); + let names = [ + "He", + "O", + "N2", + "O2", + "Ar", + "total mass", + "H", + "N", + "anomalous O", + ]; + + // One model per switch setting rather than one per case; there are eight of them + // among three thousand cases. + let mut model = Model::with_switches(cases[0].switches); + let mut mismatches = Vec::new(); + + for (index, case) in cases.iter().enumerate() { + if model.switches() != case.switches { + model = Model::with_switches(case.switches); + } + let output = model.gtd7(&case.input); + + for ((got, want), name) in output + .densities() + .iter() + .zip(case.densities.iter()) + .zip(names) + { + if got.to_bits() != want.to_bits() { + mismatches.push(format!( + "row {index} at {} km: {name} is {got:.17e}, reference {want:.17e} \ + ({} ulp)", + case.input.altitude_km, + (got.to_bits() as i64 - want.to_bits() as i64).abs() + )); + } + } + for (got, want, what) in [ + ( + output.exospheric_temperature, + case.exospheric_temperature, + "exospheric temperature", + ), + (output.temperature, case.temperature, "temperature"), + ] { + if got.to_bits() != want.to_bits() { + mismatches.push(format!( + "row {index} at {} km: {what} is {got:.17e}, reference {want:.17e}", + case.input.altitude_km + )); + } + } + } + + assert!( + mismatches.is_empty(), + "{} of {} rows disagree with the reference:\n{}", + mismatches.len(), + cases.len() * 11, + mismatches + .iter() + .take(20) + .cloned() + .collect::>() + .join("\n") + ); +} + +/// The physical checks, which the fixture cannot make for itself: a wrong model that +/// agreed with a wrong reference would pass everything above and fail these. +#[test] +fn test_the_atmosphere_behaves_the_way_it_should() { + let model = Model::new(); + let at = |altitude_km: f64, local_solar_time_h: f64, f107: f64, ap: f64| { + model + .gtd7d(&Input { + day_of_year: 172, + seconds_of_day: 29000.0, + altitude_km, + latitude_deg: 30.0, + longitude_deg: 0.0, + local_solar_time_h, + f107_average: f107, + f107, + magnetic: MagneticActivity::Daily { ap }, + }) + .total_mass + }; + + // Day is denser than night at the same altitude, because the Sun raises a bulge. + for altitude in [300.0, 400.0, 600.0] { + let noon = at(altitude, 14.0, 150.0, 4.0); + let midnight = at(altitude, 2.0, 150.0, 4.0); + assert!( + noon > midnight, + "at {altitude} km, {noon:e} at 14h against {midnight:e} at 2h" + ); + } + + // High solar flux is denser than low, and a storm is denser than quiet conditions. + for altitude in [300.0, 400.0, 600.0] { + assert!(at(altitude, 14.0, 220.0, 4.0) > at(altitude, 14.0, 70.0, 4.0)); + assert!(at(altitude, 14.0, 150.0, 200.0) > at(altitude, 14.0, 150.0, 4.0)); + } + + // The surface density is a kilogram and a bit per cubic meter. + let surface = at(0.0, 12.0, 150.0, 4.0); + assert!( + (1.0..1.4).contains(&surface), + "the surface density is {surface} kg/m^3" + ); +} + +/// The two places the port departs from the reference's control flow, checked to give a +/// defined answer where the reference gives one that depends on what was asked before it. +/// +/// Both are cases where the reference reads a value its own call never wrote. Neither can +/// be compared against the reference, because the reference has no stable answer there; +/// what can be checked is that the answer here is finite, and that it is close to the +/// neighboring altitudes and switch settings it should be close to. +#[test] +fn test_the_two_departures_from_the_reference_are_defined() { + let at = |altitude_km: f64, switches: Switches| { + Model::with_switches(switches).gtd7d(&Input { + day_of_year: 100, + seconds_of_day: 43200.0, + altitude_km, + latitude_deg: -45.0, + longitude_deg: 120.0, + local_solar_time_h: 20.0, + f107_average: 120.0, + f107: 130.0, + magnetic: MagneticActivity::Daily { ap: 20.0 }, + }) + }; + + // At exactly 32.5 km, where the reference splines through unfilled nodes. The answer + // should sit between its neighbors, since nothing physical happens at 32.5 km. + let below = at(32.4, Switches::default()).total_mass; + let seam = at(32.5, Switches::default()).total_mass; + let above = at(32.6, Switches::default()).total_mass; + assert!(seam.is_finite(), "the density at 32.5 km is {seam}"); + assert!( + seam < below && seam > above, + "at 32.5 km the density is {seam:e}, outside its neighbors {below:e} and {above:e}" + ); + + // With switch 15 off below 72.5 km, where the reference scales from a mixed nitrogen + // density it never computed. Turning the switch off drops a small correction, so the + // answer should be finite and within a few percent of leaving it on. + let off = Switches { + departures_from_diffusive_equilibrium: Switch::Off, + ..Switches::default() + }; + for altitude in [0.0, 20.0, 50.0, 70.0] { + let with = at(altitude, Switches::default()).total_mass; + let without = at(altitude, off).total_mass; + assert!( + without.is_finite(), + "at {altitude} km with switch 15 off the density is {without}" + ); + let difference = (without - with).abs() / with; + assert!( + difference < 0.05, + "at {altitude} km switch 15 changes the density by {:.1}%", + difference * 100.0 + ); + } +} diff --git a/tests/standard_cases.rs b/tests/standard_cases.rs new file mode 100644 index 0000000..43b270a --- /dev/null +++ b/tests/standard_cases.rs @@ -0,0 +1,231 @@ +//! The seventeen standard NRLMSISE-00 cases. +//! +//! The reference distribution's own test cases, which vary one input at a time from a +//! common baseline and between them reach from the surface to 1000 km, the equator, local +//! midnight, low and high solar flux, a geomagnetic storm, and the two cases that use the +//! seven-element ap history rather than a daily value. +//! +//! The fixture holds the reference's outputs at seventeen significant digits, so these are +//! compared bit for bit. An approximate comparison would not catch a term dropped from an +//! expansion whose contribution happens to be small at the point being sampled, and the +//! whole reason to have a port rather than a rewrite is that it agrees exactly. + +use nrlmsise00::{Input, MagneticActivity, Model, Switches, Units}; +use serde_json::Value; + +/// The fixture's cases. +fn cases() -> Vec { + let path = concat!( + env!("CARGO_MANIFEST_DIR"), + "/tests/fixtures/nrlmsise00-cases.json" + ); + let text = std::fs::read_to_string(path).expect("the fixture is committed"); + let parsed: Value = serde_json::from_str(&text).expect("the fixture is JSON"); + parsed["cases"] + .as_array() + .expect("an array of cases") + .clone() +} + +/// A fixture number, parsed from its own digits rather than by `serde_json`'s float +/// parser, which reads some values back one ulp high. +fn number(case: &Value, field: &str) -> f64 { + case[field] + .as_number() + .unwrap_or_else(|| panic!("{field} missing")) + .as_str() + .parse() + .expect("an f64") +} + +fn numbers(case: &Value, field: &str) -> Vec { + case[field] + .as_array() + .unwrap_or_else(|| panic!("{field} missing")) + .iter() + .map(|v| { + v.as_number() + .expect("a number") + .as_str() + .parse() + .expect("an f64") + }) + .collect() +} + +fn input_of(case: &Value) -> Input { + let magnetic = if case["ap_history"].is_null() { + MagneticActivity::Daily { + ap: number(case, "ap_daily"), + } + } else { + let history = numbers(case, "ap_history"); + let mut ap = [0.0; 7]; + ap.copy_from_slice(&history); + MagneticActivity::History { ap } + }; + Input { + day_of_year: number(case, "day_of_year") as i32, + seconds_of_day: number(case, "seconds_of_day"), + altitude_km: number(case, "altitude_km"), + latitude_deg: number(case, "latitude_deg"), + longitude_deg: number(case, "longitude_deg"), + local_solar_time_h: number(case, "local_solar_time_h"), + f107_average: number(case, "f107_average"), + f107: number(case, "f107"), + magnetic, + } +} + +#[track_caller] +fn assert_bits(got: f64, want: f64, what: &str) { + if got.to_bits() == want.to_bits() { + return; + } + let ulps = (got.to_bits() as i64 - want.to_bits() as i64).abs(); + panic!( + "{what}: got {got:.17e}, reference {want:.17e} ({ulps} ulp, relative {:e})", + (got - want).abs() / want.abs().max(f64::MIN_POSITIVE) + ); +} + +/// The reference's own units, since that is what the fixture is quoted in. +fn reference_model() -> Model { + Model::with_switches(Switches::reference()) +} + +#[test] +fn test_the_seventeen_standard_cases_match_the_reference() { + let cases = cases(); + assert_eq!(cases.len(), 17, "the fixture should hold seventeen cases"); + let model = reference_model(); + let names = [ + "He", + "O", + "N2", + "O2", + "Ar", + "total mass", + "H", + "N", + "anomalous O", + ]; + + for case in cases { + let index = case["case"].as_u64().expect("a case number"); + let output = model.gtd7(&input_of(&case)); + let want = numbers(&case, "densities"); + let at = format!("case {index} at {} km", number(&case, "altitude_km")); + + for ((got, want), name) in output.densities().iter().zip(&want).zip(names) { + assert_bits(*got, *want, &format!("{at}: {name}")); + } + let temperatures = numbers(&case, "temperatures"); + assert_bits( + output.exospheric_temperature, + temperatures[0], + &format!("{at}: exospheric temperature"), + ); + assert_bits( + output.temperature, + temperatures[1], + &format!("{at}: temperature"), + ); + } +} + +/// `gtd7d` differs from `gtd7` in the total mass density alone, by exactly the mass of the +/// anomalous oxygen the fixture gives. +#[test] +fn test_gtd7d_adds_anomalous_oxygen_to_the_total() { + let model = reference_model(); + for case in cases() { + let input = input_of(&case); + let plain = model.gtd7(&input); + let for_drag = model.gtd7d(&input); + let densities = numbers(&case, "densities"); + let anomalous = densities[8]; + + // The reference's own expression for the drag total, from the fixture's densities. + let want = 1.66e-24 + * (4.0 * densities[0] + + 16.0 * densities[1] + + 28.0 * densities[2] + + 32.0 * densities[3] + + 40.0 * densities[4] + + densities[6] + + 14.0 * densities[7] + + 16.0 * anomalous); + assert_bits( + for_drag.total_mass, + want, + &format!("case {} drag total", case["case"]), + ); + + // Everything else is untouched. + assert_eq!(plain.densities()[..5], for_drag.densities()[..5]); + assert_eq!(plain.densities()[6..], for_drag.densities()[6..]); + assert_eq!(plain.temperature, for_drag.temperature); + + // Adding a species can only add mass, but it does not always change the number: + // at 100 km the anomalous oxygen is around 1e-42 cm^-3, and sixteen nucleons of + // that is far below one ulp of a total of 3.6e-10 g/cm^3. + assert!( + for_drag.total_mass >= plain.total_mass, + "case {}: the drag total cannot be the smaller", + case["case"] + ); + let share = (for_drag.total_mass - plain.total_mass) / for_drag.total_mass; + if number(&case, "altitude_km") >= 1000.0 { + // This is why the distinction is worth a separate entry point: at 1000 km + // anomalous oxygen is about a fifth of what a satellite runs into, and a drag + // calculation that used `gtd7` would be short by that much. + assert!( + (0.15..0.25).contains(&share), + "case {}: anomalous oxygen is {:.1}% of the drag mass at 1000 km", + case["case"], + share * 100.0 + ); + } else if number(&case, "altitude_km") >= 400.0 { + assert!(share < 0.001, "{share} at 400 km"); + } + } +} + +/// SI is the model's own metric switch, so the two unit systems differ by exactly the +/// factors that switch applies. +#[test] +fn test_si_is_the_models_own_metric_switch() { + let native = reference_model(); + let si = Model::new(); + assert_eq!(si.switches().units, Units::Si); + + for case in cases() { + let input = input_of(&case); + let in_native = native.gtd7(&input); + let in_si = si.gtd7(&input); + for (index, (native, si)) in in_native + .densities() + .iter() + .zip(in_si.densities().iter()) + .enumerate() + { + let want = if index == 5 { + native * 1.0e6 / 1000.0 + } else { + native * 1.0e6 + }; + if number(&case, "altitude_km") >= 72.5 { + assert_bits(*si, want, &format!("density {index} in SI")); + } else { + // Below 72.5 km the conversion is not applied to a finished answer: the + // mixed nitrogen density is converted first and every other species is + // scaled from it, so the factor lands earlier in the arithmetic and the + // last bits need not agree. Four ulp is the observed spread. + let ulps = (si.to_bits() as i64 - want.to_bits() as i64).abs(); + assert!(ulps <= 4, "density {index} in SI is {ulps} ulp from native"); + } + } + assert_eq!(in_native.temperature, in_si.temperature); + } +}