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1.3 Program gama-local

Program gama-local is a simple command line tool for adjustment of geodetic free networks. It is available for GNU Linux (the main platform on which project GNU Gama is being developed) or for MS Windows (tested with Borland compiler from Borland free command line tools and with Microsoft Visual C++ compiler; support for Windows platform is currently limited to maintaing compatibility with the two mentioned compilers).

Program gama-local reads input data in XML format (XML input data format for gama-local) and prints adjustment results into ASCII text file. If output file name is not given, input file name with extension.txt is used. If development files for Sqlite3 (package libsqlite3-dev) are installed during the build, gama-local also supports reading adjustment input data from an sqlite3 database. If run without arguments gama-local prints a short help

$ ./gama-local

Adjustment of local geodetic network        version: 2.00 / GNU g++

Usage: gama-local  input.xml  [options]
       gama-local  input.xml  --sqlitedb sqlite.db  --configuration name  [options]
       gama-local  --sqlitedb sqlite.db  --configuration name  [options]
       gama-local  --sqlitedb sqlite.db  --readonly-configuration name  [options]


--algorithm  svd | gso | cholesky | envelope
--language   en | ca | cz | du | es | fi | fr | hu | ru | ua | zh
--encoding   utf-8 | iso-8859-2 | iso-8859-2-flat | cp-1250 | cp-1251
--angles     400 | 360
--latitude   <latitude>
--ellipsoid  <ellipsoid name>
--text       adjustment_results.txt
--html       adjustment_results.html
--xml        adjustment_results.xml
--octave     adjustment_results.m
--svg        network_configuration.svg
--cov-band   covariance matrix of adjusted parameters in XML output
             n  = -1  for full covariance matrix (implicit value)
             n >=  0  covariances are computed only for bandwidth n
--iterations maximum number of iterations allowed in the linearized
             least squares algorithm (implicit value is 5)

Program gama-local version is followed by information on compiler used to build the program (apart from GNU g++ compiler, two other possibilities are bcc and msc for Borland and Microsoft compilers respectively, when build under Microsoft Windows).

Option --algorithm enables to select numerical method used for solution of the adjustment. Implicitly is used Singular Value Decomposition (svd), alternatively user can decide for block matrix algorithm GSO by Frantisek Charamza, based on Gram-Schmidt orthogonalization. In both these cases, project equations are solved directly without forming normal equations. Third possibility is to select Cholesky decomposition of semidefinite matrix of normal equations (cholesky).

Option --language selects language used in output protocol. For example, if run with option --language cz, gama-local prints output results in Czech languague using UTF-8 encoding. Implicit value is en for output in English.

Option --encoding enables to change inplicit UTF-8 output encoding to iso-8859-2 (latin-2), iso-8859-2-flat (latin-2 without diacritics), cp-1250 (MS-EE encoding) cp-12251 (Russian encoding).

Option --angles selects angular units to be used in output.

Options --latitude and/or --ellipsoid are used when observed vertical and/or zenith angles need to be transformed into the projection plane. If none of these two options is explicitly used, no corrections are added to horizontal and/or zenith angles. If only one of these options is used, then implicit value for --latitude is 45 degrees (50 gons) and implicit ellipsoid is WGS84. Mathematical formulas for the corrections is given in the following section.

Adjustment results (--text, --xml) and others can be redirected to standard output if instead of a file name is used "-" string. If no output is given, XML adjustment format is implicitly send to standard output.

Option --octave is used to output simplified adjustment results for GNU Octave; only points’ names (identifiers), adjusted coordinates with indexes and corresponding covariances are given in the .m file.

Option --cov-band is used to reduce the number of computed covariances (cofactors) in XML adjustment output. Implicitly full matrix is written to XML output, which could degrade time efficiency for the envelope algorithm for sparse matrix solution. Explicit option for full covariance matrix is --cov-band -1, option --cov-band 0 means that only a diagonal of covariance matrix is written to XML output, --cov-band 1 results in computing the main diagonal and first codiagonal etc. If higher rank is specified then available, it is reduced do maximum possible value dim-1.

Option --iterations enables to set maximum number of iterations allowed in the linearized least squares algorithm. After the adjustment gama-local computes differences between adjusted observations computed from residuals and from adjusted coordinates. If the positional difference is higher than 0.5mm, approximate coordinates of adjusted points are updated and the whole adjustment is repeated in a new iteration. Implicit number of iterations is 5.

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1.3.1 Reductions of horizontal and zenith angles

For evaluating of reductions of horizontal and zenith angles, gama-local computes a helper point P_1 in the center of the network. Horizontal and zenith angles observed at point P_2 are transformed to the projection plane perpendicular to the normal z_1 of the helper point P_1. Coordinates (x_2, y_2) of point P_2 are conserved, but its normal z_2 is rotated by the central angle 2\gamma_12 to be parallel with z_1.

Formulas for reductions of horizontal and zenith angles are given only in the printed version.

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