Artikel mit Tag Units:

  • Spectral Units in ADQL

    math formulae.

    In case you find the piece of Python given below too hard to read: It's just this table of conversion expressions between the different SI units we are dealing with here.

    Astronomers these days work all along the electromagnetic spectrum (and beyond, of course). Depending on where they observe, they will have very different instrumentation, and hence some see their messengers very naturally as waves, others quite as naturally as particles, others just as electrons flowing out of a CCD that is sitting behind a filter.

    In consequence, when people say where in the spectrum they are, they use very different notions. A radio astronomer will say “I'm observing at 21 cm” or “at 50 GHz“. There's an entire field named after a wavelength, “submillimeter“, and blueward of that people give their bands in micrometers. Optical astronomers can't be cured of their Ångström habit. Going still more high-energy, after an island of nanometers in the UV you end up in the realm of keV in X-ray, and then MeV, GeV, TeV and even EeV.

    However, there is just one VO (or at least that's where we want to go). Historically, the VO has had a slant towards optical astronomy, which gives us the legacy of having wavelengths in far too many places, including Obscore. Retrospectively, this was an unfortunate choice not only because it makes us look optical bigots, but in particular because in contrast to energy and, by ν = E/h, frequency, messenger wavelength depends on the medium you work in, and I shudder to think how many wavelengths in my data center actually are air wavelengths rather than vacuum wavelengths. Also, as you go beyond photons, energy really is the only thing that reasonably characterises all messengers alike (well, even that still isn't quite settled for gravitational waves as long as we're not done with a quantum theory of gravitation).

    Well – the wavelength milk is spilled. Still, the VO has been boldly expanding its reach beyond the optical and infrared windows (recently, with neutrinos and gravitational waves, not to mention EPN-TAP's in-situ measurements in the solar system, even beyond the electromagnetic spectrum). Which means we will have to accomodate the various customs regarding spectral units described above. Where there are “thick” user interfaces, these can care about that. For instance, my datalink XSLT and javascript lets people constrain spectral cutouts (along BAND) in a variety of units (Example).

    But what if the UI is as shallow as it is in ADQL, where you deal with whatever is in the underlying database tables? This has come up again at last week's EuroVO Technology Forum in virtual Strasbourg in the context of making Obscore more attractive to radio astronomers. And thus I've sat down and taught DaCHS a new user defined function to address just that.

    Up front: When you read this in 2022 or beyond and everything has panned out, the function might be called ivo_specconv already, and perhaps the arguments have changed slightly. I hope I'll remember to update this post accordingly. If not, please poke me to do so.

    The function I'm proposing is, mainly, gavo_specconv(expr, target_unit). All it does is convert the SQL expression expr to the (spectral) target_unit if it knows how to do that (i.e., if the expression's unit and the target unit are spectral units properly written in VOUnit) and raise an error otherwise.

    So, you can now post:

    SELECT TOP 5 gavo_specconv(em_min, 'GHz') AS nu
    FROM ivoa.obscore
    WHERE gavo_specconv((em_min+em_max)/2, 'GHz')
        BETWEEN 1 AND 2
      AND obs_collection='VLBA LH sources'
    

    to the TAP service at http://dc.g-vo.org/tap. You will get your result in GHz, and you write your constraint in GHz, too. Oh, and see below on the ugly constraint on obs_collection.

    Similarly, an X-ray astronomer would say, perhaps:

    SELECT TOP 5 access_url, gavo_specconv(em_min, 'keV') AS energy
    FROM ivoa.obscore
    WHERE gavo_specconv((em_min+em_max)/2, 'keV')
      BETWEEN 0.5 AND 2
      AND obs_collection='RASS'
    

    This works because the ADQL translator can figure out the unit of its first argument. But, perhaps regrettably, ADQL has no notion of literals with units, and so there is no way to meaningfully say the equivalent of gavo_specconv(656, 'Hz') to get Hα in Hz, and you will receive a (hopefully helpful) error message if you try that.

    However, this functionality is highly desirable not the least because the queries above are fairly inefficient. That's why I added the funny constraints on the collection: without them, the queries will take perhaps half a minute and thus require async operation on my box.

    The (fundamental) reason for that is that postgres is not smart enough to work out it could be using an index on em_min and em_max if it sees something like nu between 3e8/em_min and 3e7/em_max by re-writing the constraint into 3e8/nu between em_min and em_max (and think really hard about whether this is equivalent in the presence of NULLs). To be sure, I will not teach that to my translation layer either. Not using indexes, however, is a recipe for slow queries when the obscore table you query has about 85 million rows (hi there in 2050: yes, that was a sizable table in our day).

    To let users fix what's too hard for postgres (or, for that matter, the translation engine when it cannot figure out units), there is a second form of gavo_specconv that takes a third argument: gavo_specconv(expr, unit_of_expr, target_unit). With that, you can write queries like:

    SELECT TOP 5 gavo_specconv(em_min, 'Angstrom') AS nu
    FROM ivoa.obscore
    WHERE gavo_specconv(5000, 'Angstrom', 'm')
      BETWEEN em_min AND em_max
    

    and hope the planner will use indexes. Full disclosure: Right now, I don't have indexes on the spectral limits of all tables contributing to my obscore table, so this particular query only looks fast because it's easy to find five datasets covering 500 nm – but that's an oversight I'll fix soon.

    Of course, to make this functionality useful in practice, it needs to be available on all obscore services (say) – only then can people run all-VO obscore searches without the optical bias. The next step (before Bambi-eyeing the TAP implementors) therefore would be to get it into the catalogue of ADQL user defined functions.

    For this, one would need to specify a bit more carefully what units must minimally be supported. In DaCHS, I have built this on a full implementation of VOUnits, which means you can query using attoparsecs of wavelength and get your result in dekaerg (which is a microjoule: 1 daerg = 1 uJ in VOUnits – don't you just love this?):

    SELECT gavo_specconv(
      (spectral_start+spectral_end)/2, 'daerg')
      AS energy
    FROM rr.stc_spectral
    WHERE gavo_specconv(0.0002, 'apc', 'J')
      BETWEEN spectral_start AND spectral_end
    

    (stop computing: an attoparsec is about 3 cm). This, incidentally, queries the draft RegTAP extension for the VODataService 1.2 coverage in space, time, and spectrum, which is another reason I'm proposing this function: I'm not quite sure how well my rationale that using Joules of energy is equally inconvenient for all communities will be generally received. The real rationale – that Joule is the SI unit for energy – I don't dare bring forward in the first place.

    Playing with wavelengths in AU (you can do that, too; note, though, that VOUnit forbids prefixes on AU, so don't even try mAU) is perhaps entertaining in a slightly twisted way, but admittedly poses a bit of a challenge in implementation when one does not have full VOUnits available. I'm currently thinking that m, nm, Angstrom, MHz, GHz, keV and MeV (ach! No Joule! But no erg, either!) plus whatever spectral units are in use in the local tables would about cover our use cases. But I'd be curious what other people think.

    Since I found the implementation of this a bit more challenging than I had at first expected, let me say a few words on how the underlying code works; I guess you can stop reading here unless you are planning to implement something like this.

    The fundamental trouble is that spectral conversions are non-linear. That means that what I do for ADQL's IN_UNIT – just compute a conversion factor and then multiply that to whatever expression is in its first argument – will not work. Instead, one has to write a new expression. And building these expressions becomes involved because there are thousands of possible combinations of input and output units.

    What I ended up doing is adopting standard (i.e., SI) units for energy (J), wavelength (m), and frequency (Hz) as common bases, and then first convert the source and target units to the applicable standard unit. This entails trying to convert each input unit to each standard unit until a conversion actually works, which in DaCHS' Python looks like this:

    def toStdUnit(fromUnit):
        for stdUnit in ["J", "Hz", "m"]:
            try:
                 factor = base.computeConversionFactor(
                     fromUnit, stdUnit)
            except base.IncompatibleUnits:
                continue
            return stdUnit, factor
    
        raise common.UfuncError(
            f"specconv: {fromUnit} is not a spectral unit understood here")
    

    The VOUnits code is hidden away in base.computeConversionFactor, which raises an IncompatibleUnits when a conversion is impossible; hence, in the end, as a by-product this function also determines what kind of spectral value (energy, frequency, or wavelength) I am dealing with.

    That accomplished, all I need to do is look up the conversions between the basic units, which can be done in a single dictionary mapping pairs of standard units to the conversion expression templates. I have not tried to make these templates particularly pretty, but if you squint, you can still, I hope, figure out this is actually what the opening image shows:

    SPEC_CONVERSION = {
        ("J", "m"): "h*c/(({expr})*{f})",
        ("J", "Hz"): "({expr})*{f}/h",
        ("J", "J"): "({expr})*{f}",
        ("Hz", "m"): "c/({expr})/{f}",
        ("Hz", "Hz"): "{f}*({expr})",
        ("Hz", "J"): "h*{f}*({expr})",
        ("m", "m"): "{f}*({expr})",
        ("m", "Hz"): "c/({expr})/{f}",
        ("m", "J"): "h*c/({expr})/{f}",}
    

    expr is (conceptually) replaced by the first argument of the UDF, and f is the conversion factor between the input unit and the unit expr is in. Note that thankfully, not additive operators are involved and thus all this is numerically well-conditioned. Hence, I can afford not attempting to simplify any of the expressions involved.

    The rest is essentially book-keeping, where I'm using the ADQL parser to turn the expression into a tree fragment and then fiddling in the tree fragment for expr into that. The result then replaces the UDF function call in the syntax tree. You can review all this in context in DaCHS' ufunctions.py, starting at the definition of toStdUnit.

    Sure: this is no Turing award material. But perhaps these notes are useful when people want to put this kind of thing into their ADQL engines. Which I'd consider a Really Good Thing™.

  • Speak out on ADQL 2.1

    If you've always wanted to be part of a standardisation process within the IVOA (and who would not?), the time has rarely been as good as now. Because: We're updating ADQL! Yes! The ADQL you are writing your queries in will receive a few more language elements, and we're carefully trying to heal a few things that turned out to be warts. And while some of the changes are as dull and boring as you may expect standards work to be, on some of them you may wish to have a saying.

    Also, you can try things out – the GAVO data center TAP endpoint at http://dc.g-vo.org/tap already has most of the proposed features, and the new DaCHS beta 1.1.2 (out since last Friday) does, too. So, if you're running DaCHS yourself, you can start playing after switching to the beta repository.

    What's new?

    • You're now supposed to write the standard crossmatch as DISTANCE(ra1, dec1, ra2, dec2)<dist. This replaces the old dance with 1=CONTAINS(POINT(), CIRCLE()) that you've probably learned to hate. Finally: Crossmatching without having to resort to TOPCAT's example menu...

    • ADQL geometries used to require a first argument that would give the reference frame, as in POINT('ICRS', ra, dec). The hope was that services could then automagically make a statement like CONTAINS(point_in_icrs, circle_in_galactic) work as presumably intended. Few services ever did (DaCHS still tries reasonably hard), and when they did, there were all kinds of opaque oddities. One of the most common sources of confusion is the question what a service is supposed to do with POINT('GALACTIC', ra, dec), assuming it knows that ra and dec are in, say, B1950 FK4. Also, is there any expectation that services attempt to do anything beyond a simple rotation (FK4, for instance, rotates noticably against the ICRS, so proper motions would need to get fixed, too)? In all, the frame as a first argument was ill thought-out, and it's been deprecated. Simply don't put in the string-typed first argument any more. POINT(long, lat) does it. True: This, more than ever, calls for an ADQL astrometry library so you can easily convert, at least, between Galactic and ICRS (probably a few more would be useful, too). More on this in some future post.

    • Services should have CAST now. Sometimes you want to turn a number into a string or a string into a timestamp. In such cases, you can write CAST('1991-02-01', TIMESTAMP) now. The details are not quite, excuse me, cast in stone yet, so if you have a use case for this kind of thing, speak up now. The current draft also calls for a TIMESTAMP(tx) function – but since that's really not different from CAST(tx, TIMESTAMP), I'm trying to dissuade people from adding it.

    • Services should have an IN_UNIT function now. That's a nifty thing in particular when you're re-using queries on different services. Just write, say, IN_UNIT(pmra, 'deg/yr') and never worry again if it's arcsec/yr, mas/yr, rad/cy, or whatever. The second argument, by the way, is written according to the Units in the Virtual Observatory standard. It's an optional feature according to the current standard, so perhaps it's too early to party, but I've found this extremely useful, and so I hope we'll see widespread adoption.

    • Services should now have set operations. These are UNION, EXCEPT, and INTERSECT and are useful when you have two queries that result in the same table schema (because they won't work otherwise). Say you have two complex ways to filter rows from the table source, but you want to process both sorts of results further on – you can say then say something like:

           SELECT <whatever complex> FROM
               (SELECT a,b,c FROM source
                 WHERE <crazy stuff>
                 GROUP BY a, b, c) as left
             UNION
               (SELECT a,b,c FROM source
                 WHERE <other crazy stuff>
                 GROUP BY a, b, c) as right
           WHERE <more complex stuff over a, b, and c>
      
      – and similarly, EXCEPT lets you “punch a hole” in a result table.
      Another interesting use case would be to query many tables on a
      service like VizieR in one go; that still works if you make sure the
      tables defined by the sub-queries have the same columns. Given that a
      lot of cross-table operations actually boil down to JOINs and WHERE
      clauses, the set operations are used less that one would expect. But
      if you need them, there's no real alternative (short of downloading
      far too much and performing the operation locally, which of course
      defeats the purpose of TAP).
      
    • Common table expressions (“WITH”). DaCHS doesn't do these yet, and it will only pick them up if someone else implements them first. In the way ADQL 2.1 has them (“nonrecursive”), CTEs are little more than syntactic sugar, and I'm not quite sure if the additional implementation complexity is worth it. If you're curious, check CTEs in the postgres manual. If that makes you drool for WITH in ADQL, let me know. It'll not be too hard to sway me to put them in.

    • Bitwise Operations. That's when integers are treated as bit patterns. If this sounds like nerd stuff to you, well, it happens quite a bit in actual catalogs. See, for instance, Note 3 for the PPMXL. You'd need the flags column described there if you wanted to exclude PPMXL objects that replaced multiple USNO-B1.0 objects (bit 3), you will right now have to write something like MOD(flags,16)>7. That's a bit of magic that everyone will have to think about for a while. With bitwise operations, you'll just write BITWISE_AND(flags,8)=8, which will look familiar to everyone who has used the pattern before (in particular, it's clear we're talking about bit 3). There still is discussion whether bitwise operations are common enough to warrant special syntax – the draft currently says the above should be written as flags&8=8 – or whether the functions DaCHS has at the moment (they're called BITWISE_AND, BITWISE_OR, BITWISE_XOR, and BITWISE_NOT) are good enough.

    • Offset. If you've ever done anything with ADQL, you'll know that SELECT TOP 10 * FROM hipparcos.main ORDER BY parallax DESC will give you the 10 objects with the larges parallaxes. But what if you want the next but 10 closest stars? Well, OFFSET to the rescue:

      SELECT TOP 10 *
      FROM hipparcos.main
      ORDER BY parallax DESC
      OFFSET 10
      

      There is another, more sinister, application for OFFSET, which happens to be the actual reason I've put it into DaCHS' ADQL ages ago: Written as OFFSET 0 several databases use it to denote a barries for the query planner. This is explained to some degree in the class DaCHS TAP example Crossmatch for a Guide Star – which still mentions the first hack I had built into DaCHS to let query authors rein in overzealous query planners.

    • LOWER and ILIKE. ADQL has been extremely weak on the side of text processing, so weak indeed that it wasn't nearly enough to cover the use cases for the registry when it moved to RegTAP. ADQL 2.1 adds two basic features – LOWER, a function that lets people query in a case-insensitive fashion, and ILIKE, an operator that is like LIKE, but again ignores case. While both features are obviously great as soon as people dump any kind of text (think object names) into their databases, I'm not terribly happy with ILIKE, as it does the same as RegTAP's ivoa_nocasematch user defined function, and it's always bad when a two standards forsee two different mechanisms for the same thing.

    • Geometry-typed arguments. CIRCLE and POLYGON now accept POINTs in alternative constructor functions. That is, you can now say CIRCLE(POINT(ra, dec), radius) in addition to the traditional CIRCLE(ra, dec, radius). In itself, that's probably not terribly exciting, but when you have actual POINTs in your database, it's much more compact to write, say:

      SELECT *
      FROM zcosmos.data
      WHERE 0=CONTAINS(
        ssa_targetpos,
        CIRCLE(ssa_location, ssa_aperture))
      

      (which would return rows for those spectra for which the declared aperture does not contain the declared target). Before, you'd had to write some fairly ugly expression involving COORD1 and whatnot in order to achieve the same effect.

    • Boolean expressions. That's another one that's still a bit up in the air. First, the rough goal is to allow boolean values in ADQL-accessible tables, which so far have been a hack at best. In the future, you should be able to say WHERE is_broken=True. However, people coming from other languages will find that odd, and indeed, in python I'd cringe on if is_broken==True:. What I'd expect is if is_broken:. Do we want this in ADQL? Currently, it's in the grammar (more or less like this), but this kind of thing makes it still harder to produce useful syntax error messages. Is it worth it, either way? I'm not sure.

    That about concludes my quick review of the new features of ADQL 2.1. If you'd like to know more, the current draft is on the IVOA document repository, and if you can deal with version control (you should!), you can follow the bleeding edge in the ADQL document in Volute. Discussion happens on the DAL mailing list.

    Update (2018-04-13): Well, as to the CTEs, I couldn't resist after all, and they're in with DaCHS 1.1.3. And I have to say a love them -- they weren't hard to put in, and once they're there they make so many queries a good deal more readable than before. I've even put it a server-defined example for CTEs on the Heidelberg TAP service showcasing a particularly compelling use case.

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