International Virtual Observatory Alliance

Difference: ADQLVectorMath (2 vs. 3)

Revision 32022-07-06 - MarkusDemleitner

META TOPICPARENT	name="ADQL"

A proposal for vector math in ADQL

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< With tables containing massive amounts of vectors (e.g., the collections of low-resolution spectra within Gaia DR3 or the Digitised Byurakan Surveys), giving TAP users a toolset to do server-side work with arrays becomes highly desirable and will significantly enhance the power of ADQL to do server-side analyses. This is an attempt to provide a baseline feature set for that.

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> With tables containing massive amounts of vectors becoming common (e.g., the collections of low-resolution spectra within Gaia DR3 or the Digitised Byurakan Surveys), giving TAP users a toolset to do server-side work with arrays becomes highly desirable and will significantly enhance the power of ADQL to do server-side analyses. This is an attempt to provide a baseline feature set for that.

TAP servers supporting this should declare that by defining a language feature. While no IVOA specification exists for array operations, use the VECTORMATH key from GAVO's ADQL extensions standards record, like this:

<languageFeatures type="ivo://org.gavo.dc/std/exts#extra-adql-keywords">
  <feature>
    <form>VECTORMATH</form>
      <description>You can compute with vectors here. See
        https://wiki.ivoa.net/twiki/bin/view/IVOA/ADQLVectorMath
        for an overview of the functions and operators available.
      </description>
   </feature>
</languageFeatures>

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Element Access

To access an element of a vector, write [element-index], where element-index is an integer-valued expression. In keeping with common SQL practices (and regrettably working against most programming languages), indexes in ADQL are 1-based (rather than 0-based). That is, the first element of an array with N elements has the index 1 and the last element has the index N.

Again in keeping with common SQL practices, accessing elements outside of that range gives NULL.

Basic Math

vec1+vec2 is the component-wise sum of two vectors. Where vec1 and vec2 have unequal length, the result is padded with NaNs to the length of the longer vector.
vec1-vec2 is the component-wise difference of two vectors. Where vec1 and vec2 have unequal length, the result is padded with NaNs to the length of the longer vector.

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vec1*vec2 is the scalar product of two vectors. Where vec1 and vec2 have unequal length, the shorter vector is padded with NaNs to the length of the longer vector. That is, the scalar product of vectors of unequal length is NaN.

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vec1*vec2 is the scalar product of two vectors. Where vec1 and vec2 have unequal length, the shorter vector is padded with NaNs to the length of the longer vector. That is, the scalar product of vectors of unequal length is NaN.

scal*vec and vec*scal is the scalar multiplication of a vector.

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vec/scal is the equivalent of (1/scal)*vec for a scalar. This is always floating point division, never integer division.

Array Aggregation

These are functions that work like SQL aggregate functions, just on the elements of arrays. These ought to return the types of the elements of the argument (real, double precision, integers).

arr_avg(arr) returns the arithmetic mean of arr's elements
arr_max(arr) returns the largest element of arr
arr_min(arr) returns the smallest element of arr
arr_stddev(arr) returns the standard deviation of arr's elements
arr_sum(arr) returns the sum of arr's elements

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