ymir

Quick start

open Ymir

let () =
  (* Ages of a Planck 2018 universe at four redshifts, in gigayears. *)
  let planck = Cosmology.planck2018 ~codata:Codata.v2022 Nx.float64 in
  let z = Nx.create Nx.float64 [| 4 |] [| 0.; 1.; 3.; 1100. |] in
  let gyr = Unit.giga Units.julian_year in
  Nx.print (Quantity.value gyr (Cosmology.age planck z));

  (* The angle between two directions, in arcseconds. *)
  let deg x = Quantity.v Unit.degree (Nx.scalar Nx.float64 x) in
  let a = Direction.lonlat Frame.icrs ~lon:(deg 10.) ~lat:(deg 20.) in
  let b = Direction.lonlat Frame.icrs ~lon:(deg 10.001) ~lat:(deg 20.) in
  Nx.print (Quantity.value Unit.arcsecond (Direction.separation a b))

The examples teach each part on small synthetic data.

Libraries

• ymir is the astronomy; open Ymir brings every module below except Fits into scope.
• ymir.units holds the units alone, for code that needs no astronomy.
• ymir.fits reads and writes FITS files; open Ymir_fits brings Fits. Neither ymir nor ymir.fits depends on the other, and a program that reads files links both.
• ymir.spk reads SPK ephemeris files, such as JPL's DE440, as Ymir_spk.

What's inside

• Units: Unit is a unit as an exact value, a product of primes, π and named symbols with rational exponents, with one canonical text. A conversion rounds the exact factor once, or raises when the units don't convert. Quantity is a tensor in a unit. The SI's units, prefixes and exact constants are built in, Codata.v2018 and Codata.v2022 hold the measured constants, and Vocabulary spells units with symbols such as MJy sr^-1.
• Time scales: Time holds batches of instants on UTC, TAI, TT and TDB, the scale in the type, and converts between them: leap seconds and UTC before 1972 from the IERS's tables, TDB at the geocentre from the Fairhead & Bretagnon series.
• The Earth: Earth holds the Earth's orientation at instants, its rotation angle and sidereal times under the IAU 2006/2000A precession-nutation, and its position and velocity from SOFA's analytic ephemeris.
• Frames and directions: Frame names ICRS, FK5 J2000, Galactic, the J2000 ecliptic and supergalactic, and the geocentric GCRS, CIRS, true equator and equinox of date and TIRS; a frame mismatch is a type error. Direction holds batches of directions with their separations, position angles and rotations between frames, and converts them between the barycentre and the geocentre through light deflection and aberration.
• HEALPix: Healpix divides a frame's sphere into equal-area pixels at nside up to 2^29, numbered RING or NESTED: the pixel of each direction, pixel centres, corners and neighbours, and spherical harmonic analysis and synthesis of maps, with Jacobi iterations.
• Transforms: Transform maps pixels to the sky as a list of stages that compose with >>, invert, and print back what they read: axis order, shift, linear maps, SIP and TPV distortions, thirteen zenithal and cylindrical projections, and rotations between frames.
• Grids, regions and observations: Grid is an image's cells seen through a transform, with each cell's exact area or solid angle; Grid.agree says whether two grids are the same cells. Region places circles, annuli, ellipses and polygons on a grid and weighs each cell by its exact covered fraction. Observation holds data with variance and validity; add, sub and scale combine observations on agreeing grids with their variances, and integrate sums one over a region: aperture photometry, differentiable in the aperture's centre and size.
• FITS: ymir.fits's Fits reads and writes headers, images (tile compression included), binary and ASCII tables, and BUNIT and TUNIT units. Wcs reads a header's world coordinates as a Transform and writes one back as keyword edits; a program composes an image's data, error and world coordinates into an Observation.
• Cosmology: Cosmology.t is one record of tensors for flat and curved ΛCDM, wCDM and w0waCDM with radiation and massive neutrinos. Expansion rate, density parameters, distances, volumes and times are fixed Gauss–Legendre sums with a stated error bound (2⁻⁴⁶ relative in float64), batched over models and redshifts. The Planck and WMAP fits are built in.

Validation

Two results on public data reproduce published ones. They download their data, so they run outside runtest; runtest checks the same paths on bundled cutouts and simulated data.

• test/nircam: aperture photometry on a JWST NIRCam mosaic agrees with photutils within 10⁻⁶ of the sums, with gradients in the aperture's centre and radius checked against finite differences.
• test/pantheon: fitting Ω_m and Ω_Λ to the Pantheon+ and SH0ES supernovae with their full covariance reproduces Brout et al. (2022), Table 3.

Examples

• 01-units ↗A unit is an exact value with one canonical text, and a quantity is a tensor in a unit.
• 02-constants-and-names ↗The SI's defining constants are exact units.
• 03-frames-and-directions ↗A direction is a batch of unit vectors in a celestial frame, and the frame is part of its type.
• 04-transforms ↗A transform maps points through a list of stages: pixel coordinates to a plane, a plane to the sky.
• 05-fits-images ↗A FITS file is a list of HDUs, each a header and a data unit.
• 06-fits-tables ↗A binary table holds rows of typed columns.
• 07-fits-wcs ↗Wcs.read turns a header's celestial keywords into a transform from pixels to the sky, asking for each keyword's value as ymir.fits decodes it.
• 08-grids-and-regions ↗A grid is an image's cells seen through a transform; a region is a shape placed on the grid's world.
• 09-observations ↗An observation is data on a grid with a variance and a mask of valid samples.
• 10-cosmology ↗A cosmology is a record of tensors, and distances, volumes and times are functions of it and of redshifts.
• 11-derivatives ↗Every ymir function is a formula of nx operations, so rune differentiates and compiles it.

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