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#### A.8.1.1 Match Criteria

Match Criteria panel. The details will differ depending on what match type is chosen.

The match criteria box allows you to specify what counts as a match between two rows. It has two parts. First, you must select one of the options in the Algorithm selector. This effectively selects the coordinate space in which rows will be compared with each other. Depending on the chosen value, a number of fields will be displayed below, which you must fill in with values that determine how close two rows have to be in terms of a metric on that space to count as a match.

The following match types (algorithm values) are offered:

Sky
  Comparison of positions on the celestial sphere. In this case you will need to specify columns giving Right Ascension and Declination for each table participating in the match. The Max Error value you must fill in is the maximum separation of matched points around a great circle.
Sky with Errors
  The matching is like that for the Sky option above, but an error radius (positional uncertainty) is given for each row in the input tables, rather than just a single value for the whole match. Along with the Right Ascension and Declination columns, you also specify an Error column which gives the error radius corresponding to that position. Two rows are considered to match when the separation between the two RA,Dec positions is no larger than the sum of the two Error values for the corresponding rows. The Scale value should be set to a rough average of the per-row errors. It is used only to set a sensible default for the Healpix-k tuning parameter, and its value does not affect the result. If Healpix-k is set directly (see Appendix A.8.1.3), Scale is ignored. Note: the semantics of this matcher have changed slightly since version 3.8 of TOPCAT and earlier. In earlier versions the single parameter was named Max Error and provided an additional constraint on the maximum accepted separation between matched objects. For most uses, the old and new behaviours are expected to give the same results, but in cases of difference, the new behaviour is more likely what you want.
Sky Ellipses
  Compares elliptical regions on the sky for overlap. You will need to specify columns giving the central position, major and minor radii, and position angle of the ellipse. Two rows are considered to match if there is any overlap between the ellipses. The goodness of match is a normalised generalisation of the symmetrical case used by the Sky with Errors option above. The position angle is measured from north to the semi-major axis, in the direction towards the positive RA axis. The Scale value should be set to a rough average of the major radii; It is used only to set a sensible default for the Healpix-k tuning parameter, and its value does not affect the result. If Healpix-k is set directly (see Appendix A.8.1.3), Scale is ignored. The calculations are approximate since in some cases they rely on projecting the ellipses onto a Cartesian tangent plane before evaluating the match, so for larger ellipses the criterion will be less exact. For objects the size of most observed stars or galaxies, this approximation is not expected to be problematic.
Sky 3D
  Comparison of positions in the sky taking account of distance from the observer. In this case you will need to specify columns giving Right Ascension and Declination in angular units, as well as distance from the origin in arbitrary units for each table participating in the match. The Error value is a maximum separation in Cartesian space of matched points in the same units as the radial distance.
Exact Value
  Requires exact matching of values. In this case you will need to specify the column containing the match key for each table participating in the match; this might typically be an object name or index number. Two rows count as matching if they have exactly the same entry in the specified field, except rows with a null value in that column, which don't match any other row. Note that the values must also be of the same type, so for instance a Long (64-bit) integer value will not match an Integer (32-bit) value.
N-dimensional Cartesian
  Comparison of positions in an isotropic N-dimensional Cartesian space. In this case you will need to specify N columns giving coordinates for each table participating in the match. The Error value is the maximum spatial separation of matched points. Currently the highest dimensionality you can select is 3-d - does anyone want a higher number?
N-dimensional Cartesian, Anisotropic
  Comparison of positions in an N-dimensional Cartesian space with an anisotropic metric. In this case you will need to specify N columns giving coordinates for each table participating in the match, and an error distance for each of these dimensions. Points P1 and P2 are considered to match if P2 falls within the ellipsoid with radii given by the error distances, centered on P1. This kind of match will typically be used for non-'spatial' spaces, for instance (magnitude,redshift) space, in which the metrics in different dimensions are not related to each other. Currently the highest dimensionality you can select is 4-d - does anyone want a higher number?
N-dimensional Cuboids
  This matching is like that for N-dimensional Cartesian above, but points are considered to match if they fall within the same cuboid rather than ellipsoid. The error values are the half-axis lengths of the cuboid, like rectangular "radii". This kind of match is suitable for grouping items into regularly-spaced pixels, though it's not a very efficient way of doing that.
N-dimensional Cartesian with Errors
  The matching is like that for the N-dimensional Cartesian option above, but an error radius (positional uncertainty) is given for each row in the input tables, rather than just a single value for the whole match. Along with the Cartesian coordinate columns, you also specify an Error column which gives the error radius corresponding to that position. Two rows are considered to match when the separation between the two positions is no larger than the sum of the two Error values for the corresponding rows. The Scale parameter should be approximately the characteristic size of the per-object error values. Its value, in conjunction with the Bin Factor tuning parameter, affects the performance of the match but not the result.
2-d Cartesian Ellipses
  Compares elliptical regions in the plane for overlap. You will need to specify columns giving the central position, major and minor radii, and orientation angle of the ellipse. Two rows are considered to overlap if there is any overlap between the ellipses. The goodness of match is a generalisation of the symmetrical case used by the 2-d Cartesian with Errors option above. The orientation angle is measured anticlockwise from the X-axis to the ellipse major axis. The Scale parameter should be set to a rough average of the major radii. Its value, in conjunction with the Bin Factor tuning parameter, affects the performance of the match but not the result.
Sky + X
  Comparison of positions on the celestial sphere with an additional numeric constraint. This is a combination of the Sky and 1-d Cartesian matches above, so the columns you need to supply are RA, Dec and one extra, and the errors are angular separation on the sky and the error in the extra column. A match is registered if it matches in both of the constituent tests. You could use this for instance to match objects which are both close on the sky and have similar luminosities. The "distance" measure for Best* matches scales the Sky distance and X distance by their maximum values and adds them in quadrature, so they have equal weight (d=sqrt([r/rmax]2 +[dX/dXmax]2)).

  Note that in TOPCAT versions 4.3-5 and earlier a linear unscaled distance combination was used here, which did not give very meaningful Best match results.

Sky + X with Errors
  Comparisons of positions on the celestial sphere with an additional numeric constraint that can itself vary per row. This is a combination of the Sky and 1-dimensional Cartesian with Errors matches above, so the columns you will need to supply for each table are RA, Dec, X (the additional coordinate), and Error (the error on X). The values in the Match Criteria box are Max Error giving the sky position tolerance and Scale which should be approximately the characteristic size of the X error values. You could use this for instance to match tables by sky position and redshift, where the redshift uncertainty varies per source.
Sky + XY
  Comparison of positions on the celestial sphere with two additional numeric constraints. This is a combination of the Sky and 2-d Anisotropic Cartesian matches above, so the columns you need to supply are RA, Dec and two extra, and the errors are angular separation on the sky and the error radii corresponding to the extra columns. A match is registered if it matches in all of the constituent tests. You could use this for instance to match objects which are both close on the sky and have similar luminosities and redshifts. The "distance" measure for Best* matches scales the Sky, X and Y distances by their maximum values and adds them in quadrature, so they have equal weight (d=sqrt([r/rmax]2 +[dX/dXmax]2 +[dY/dYmax]2)).

  Note that in TOPCAT versions 4.3-5 and earlier a linear unscaled distance combination was used here, which did not give very meaningful Best match results.

HTM
  Performs sky matching in just the same way as the Sky option above, but using a different algorithm (pixelisation of the celestial sphere is performed using the Hierarchical Triangular Mesh rather than the HEALPix scheme). The results in both cases should be identical, but HTM is much slower. Hence, this option is only useful for debugging. It may be withdrawn in future releases.

Depending on the match type, the units of the error value(s) you enter may be significant. In this case, there will be a unit selector displayed alongside the entry box. You must choose units which are correct for the number you enter.

More information is available in the GUI as a tooltip by hovering with the mouse pointer over the field in question.

See Appendix A.8.1.3 for information on optional tuning parameters which are sometimes displayed in this panel.

The matching framework is capable of performing even more complicated types of match, for instance Sky + 6-dimensional anisotropic Cartesian. These are not offered purely to avoid complicating the GUI. More flexible matching requirements in this in and other respects can be achieved by using the matching commands in STILTS instead.

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TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk