- grmatch [options] -r <reference> -i <input> [-o <output>]
- The program `grmatch` matches lines read from two input files, namely from a reference and from an input file. All implemented algorithms are symmetric, in the manner that the result should be the same if these two files are swapped. The only case when the order of these files is important is when a geometrical transformation is also returned (see point matching below), in this case the swapping of the files results the inverse form of the original transformation. The lines (rows) can be matched using various criteria. 1. Lines can be matched by identifier, where the identifier can be any concatenation of arbitrary, space-separated columns found in the files. Generally, the identifier is represented by a single column (e.g. it is an astronomical catalog identifier). The behaviour of the program can be tuned for the cases when there are more than one rows with the same identifier. 2. Lines can be matched using a 2-dimensional point matchig algorithm. In this method, the program expects two-two columns both from the reference and input files which can be treated as X and Y coordinates. If both point lists are known, the program tries to find the appropriate geometrical transformation which transforms the points from the frame of the reference list to the frame of the input list and, simultaneously, tries to find as many pairs as possible. The parameters of the geometrical transformation and the whole algorithm can be fine-tuned. 3. Lines can be matched using arbitrary- (N-) dimensional coordinate matching algorithm. This method expects N-N columns both from the reference and input files which can be treated as X_1, ..., X_N Cartesian coordinates and the method assumes both of the point sets in the same reference frame. The point 'A' from the reference list and the point 'P' from the input list forms a pair if the closest point to 'A' from the input list is 'P' and vice versa.
- -h, --help
- Give general summary about the command line options.
- Give a detailed list of command line options.
- Give some version information about the program.
- -C, --comment
- Comment the output (both the transformation file and the match file).
Options for input/output specifications:
- -r <referencefile>, --input-reference <referencefile>
- Mandatory, name of the reference file.
- <inputfile>, -i <inputile>, --input <inputfile>
- Name of the input file. If this switch is omitted, the input isread from stdin (specifying some input is mandatory).
- -o <output>, --output <output>, --output-matched <output>
- Name of the output file, containing the matched lines. The matched lines are pasted lines, the first part is from the reference file and the second part is from the input file, these two parts are concatenated by a TAB character. This switch is optional, if it is not specified, no such output will be generated.
- --output-excluded-reference <out>, --output-excluded-input <out>
- Names of the files which contain the valid but excluded lines from the reference and from the input. These outputs are disjoint from the previous output and altogether contaions all valid lines.
- --output-id <out>
- Name of the file which contaions only the identifiers of the matched lines. If the primary matching method was not identifier matching, one should specify the column indices of the identifiers by --col-ref-id and --col-inp-id also.
- --output-transformation <output-transformation-file>
- Name of the output file containing the geometrical transformation, in human-readable format, if the matching method was point matching (in other case, this option has no effect). The commented version of this file includes some statistics about the matching (the total number of lines used and matched, the required CPU time, the final triangulation level, the fit residuals and other things like these).
- In all of the above input/output file specifications, the replacement of the file name by "-" (a single minus sign) forces the reading from stdin or writing to stdout. Note that all parts of the any line after "#" (hashmark) are treated as a comment, therefore ignored.
General options for point matching:
- This switch forces the usage of the point matching method. By default, this method is assumed to be used, therefore this switch can be omitted.
- --col-ref <x>,<y>, --col-inp <x>,<y>
- The column indices containing the X and Y coordinates, for the reference and for the input file, respectively. The index of the first column is always 1, the index of the second is 2 and so on. Lines in which these columns do not contain valid real numbers bers are omitted.
- -a <order>, --order <order>
- This switch specifies the polynomial order of the resulted geometrical transformation. It can be arbitrary positive integer. Note that if the order is A, at least (A+1)*(A+2)/2 valid points are needed both from the reference and both from the input file to fit the transformation.
- --max-distance <maxdist>
- The maximal accepted distance between the matched points in the coordinate frame of the input coordinate list (and not in the coordinate frame of the reference coordinate list). Possible pairs (which are valid pairs due to the symmetric coordinate matching algorihms) are excluded if their Eucledian distance is larger than maxdist. Note that this option has no initial value, therefore, if omitted, all possible pairs due to the symmetric matching are resulted, which, in certain cases in practice, can result unexpected behaviour. One should always specify a reasonable maximal distance which can be estimated only by the knowledge of the physics of the input files.
- See more options concerning to point matching in the section "Fine-Tuning of Point Matching" below. That section also describes the tuning of the triangulation used by the point matching algorithm. For a more detailed description about the point matching algorithms based on pattern and triangle matching see ,  or .
General options for coordinate matching:
- --match-coord, --match-coords
- This switch forces the usage of the coordinate matching method. Note that because of the common options with the point matching method, one should specify this switch to force the usage of the coordinate matching method (the default method is point matching, see above).
- --col-ref <x>[,<y>,[<z>...]] --col-inp <x>[,<y>,[<z>...]]
- The column indices containing the spatial coordinates, for the reference and for the input file, respectively. The index of the first column is always 1, the index of the second is 2 and so on. Lines in which these columns do not contain valid real numbers are omitted. Note that the dimension of the coordinate matching space is specified indirectly, by the number of column indices listed here. Because of this, the number of column indices should be the same for the reference and input, in other case, when the dimensions are mismatched, the program exits unsuccessfully.
- --max-distance <maxdist>
- The maximal accepted distance between the matched points. Possible pairs (which are valid pairs due to the symmetric coordinate matching algorihms) are excluded if their Eucledian distance is larger than maxdist. Note that this option has no initial value, therefore, if omitted, all possible pairs due to the symmetric matching are resulted (see also point matching, above).
General options for identifier matching:
- --match-id, --match-identifiers
- This switch forces the usage of the identifier matching method.
- --col-ref-id <i>[,<j>,[<k>...]] --col-inp-id <i>[,<j>,[<k>...]]
- Column index or indices containing the identifiers, from the reference and from the input file, respectively.
- --no-ambiguity, --first-ambiguity, --any-ambiguity, --full-ambiguity
- These options tune the behaviour of the matching when there is more than one occurrence of a given identifier in the reference and/or input file. If --no-ambiguity is specified, these identifiers are discarded, this is the default method. If --first-ambiguity is specified, only the first occurence is treated as a matched line, independently from the number of occurrences. If the switch --any-ambiguity is specified, the lines are paired sequentally, until there is any left from the reference and from the input. For example, if there is 4 occurrences in the reference and 6 in the input file of a given identifier, 4 matched pairs are returned. Otherwise, if --full-ambiguity is specified, all possible combinations of the lines are treated as matched lines. For example, if there is 4 occurrences in the reference and 6 in the input file of a given identifier, all 4*6=24 combinations are returned as matched pairs.
Fine-tuning of point matching:
- --triangulation <parameters>
- This switch is followed by comma-separated directives, which specify the parameters of the triangulation-based point matching algorithm:
- delaunay, level=<level>, full, auto, unitarity=<U>
- These directives specify the triangulation level used for point matching. delaunay forces the usage only of the Delaunay-triangles. This is the fastest method, however, it is only working if the points in the reference and input lists are almost competely overlapping and describe almost the same point sets (within a ratio of common points above 60-70%). The level specifies the level of the expansion of the Delaunay-triangulation (see  for more details). In practice, the lower the ratio of common points and/or the ratio of the overlapping, the higher level should be used. Specifying level=1 or level=2 gives a robust but still fast method for general usage. The directive full forces full triangulation. This can be overwhelmingly slow and annoying and requires tons of memory if there are more than 40-50 points (the amounts of these resources are proportional to the 6th(!) and 3rd power of the number of the points, respectively). The directive auto increases the level of the triangulation expansion automatically until a proper match is found. A match is considered as a good match if the unitarity of the transformation is less than the unitarity U specified by the unitarity=U directive (see also the section Notes/Unitarity below).
- mixed, conformable, reverse
- These directives define the chirality of the triangle spaces to be used. Practically, it means the following. If we don't know whether the input and reference lists are inverted respecting to each other, one should use mixed triangle space. If we are sure about that the input and reference lists are not inverted, we can use conformable triangle space. If we know that the input and reference lists are inverted, we can use reverse space. Note that although mixed triangle space can always result a good match, it is a wise idea to fix the chirality by specifying conformable or reverse if we really know that the point sets are not inverted or inverted respecting to each other. If the chirality is fixed, the program yields more matched pairs, the appropriate triangulation level can be smaller and in auto mode, the program returns the match definitely faster.
- maxnumber=<max>, maxref=<mr>, maxinp=<mi>
- These directives specify the maximal number of points which are used for triangulation (for any type of triangulation). If maxnumber is specified, it is equivalent to define maxref and maxinp with the same values. Then, the first <mr> points from the reference and the first <mi> points from the input list are used to generate the triangle sets. The first points are selected using the optional information found in one of the columns, see the following switches.
- (Note that there should be only one --triangulation switch, all desired directives should be written in the same argument, separated by commas.)
- --col-ref-ordering [-]<w>, --col-inp-ordering [-]<w>.
- These switches specify one-one column index from the reference and from the input files which are used to order these lists and select the first maxref and maxinp points (see above) for the generation of the two triangle meshes. Both columns should contain valid real numbers, otherwise the whole(!) line is excluded (not only from sorting but from the whole matching procedure). If there is no negative sign before the column index, the data are sorted in descending(!) order, therefore the lines with the lines with the highest(!) values are selected for triangulation. If there is a negative sign before the index, the data are sorted in ascending order by these values, therefore the lines with the smallest(!) values are selected for triangulation. For example, if we want to match star lists, we might want to use only the brightest ones to generate the triangle sets. If the brightnesses of the stars are specified by their fluxes, we should not use the negative sign (the list should be sorted in descending order to select the first few lines as the brightest stars), and if the brightness is known by the magnitude, we have to use the negative sign.
- --fit iterations=<N>,firstrejection=<F>,sigma=<S>
- Like --triangulation, this switch is followed by some directives. These directives specify the number <N> of iterations (iterations=<N>) for point matching. The firstrejection directive speciy the serial number <F> of the first iteration where points farer than <S;gt; sigma level are excluded in the next iteration. Note that in practice these type of iteration is really not important (due to, for instance, the limitations of the outliers by the --max-distance switch), however, some suspicious users can be convinced by such arguments.
- --weight reference|input,column=<wi>,[magnitude],[power=<p>]
- These directives specify the weights which are used during the fit of the geometrical transformation. For example, in practice it is useful in the following situation. We try to match star lists, then the fainter stars are believed to have higher astrometrical errors, therefore they should have smaller influence in the fit. We can take the weights from the reference (specify reference) and from the input (specify input), from the column specified by the weight-index. The weights can be derived from stellar magnitudes, if so, specify magnitude to convert the read values in magnitude to flux. The real weights then is the powerth power of the flux. The default value of the power is 1, however, for the maximum-likelihood estimation of an assumed Gaussian distribution, the weights should be the second power of the fluxes.
- Some notes on unitarity. The unitarity of a geometrical transformation measures how it differs from the closest transformation which is affine and a combination of dilation, rotation and shift. For such a transformation the unitarity is 0 and if the second-order terms in a transformation distort a such unitary transformation, the unitarity will have the same magnitude like the magnitude of this second-order effect. For example, to map a part of a sphere with the size of d degrees will have an unitarity of 1-cos(d). Therefore, for astrometrical purposes, a reasonable value of the critical unitarity in "auto" triangulation mode can be estimated as 2 or 3 times 1-cos(d/2) where d is the size of the field in which astrometry should be performed.