The required size of the matrix (which determines the number of ELEM records in the "Matrix elements records" section) is determined by the number N of records in the "Set of measurement value records" as follows:

For example, if we have the following three (N = 3) sets of coordinate difference observations:

Station 1 to station 2: d1 = X2 - X1; d2 = Y2 - Y1; d3 = Z2 - Z1;
Station 2 to station 3: d4 = X3 - X2; d5 = Y3 - Y2; d6 = Z3 - Z2;
Station 3 to station 1: d7 = X3 - X1; d8 = Y3 - Y1; d9 = Z3 - Z1;

for a total of nine observations (3 sets of dX, dY, and dZ), we would input them in three DXYZ records as follows:

 3DD
 DXYZ12 d1 d2 d3
 DXYZ23 d4 d5 d6
 DXYZ31 d7 d8 d9

If we denote a covariance matrix element as sij (where s11 is the variance of d1, and s12 is the covariance between d1 and d2, etc) the upper-triangular portion of the covariance matrix for these observations is as follows (note that the order of the covariance elements depends only on the order in which the observations are given as DXYZ records):

The COV and ELEM records for this observation would therefore be:

 COV  CT UPPR
 ELEM s11 s12 s13
 ELEM s14 s15 s16
 ELEM s17 s18 s19
 ELEM s22 s23 s24
 ELEM s25 s26 s27
 ELEM s28 s29
 ELEM s33 s34 s35
 ELEM s36 s37 s38
 ELEM s39
 ELEM s44 s45 s46
 ELEM s47 s48 s49
 ELEM s55 s56 s57
 ELEM s58 s59
 ELEM s66 s67 s68
 ELEM s69
 ELEM s77 s78 s79
 ELEM s88 s89
 ELEM s99

As you can see, the general approach is to start the entry of each row of the upper-triangular portion of the matrix with a new ELEM record, and you use as many ELEM records as required for the elements of each row (an ELEM record can hold up to three elements). For the UPPR matrix form, each row is entered starting with the diagonal element. For the DIAG matrix form, you simply enter the diagonal elements (three at a time) in ELEM records from the upper-left element to the lower-right element.

The structure of the ELEM records is similar when you use the WGT matrix header (except, of course, weight matrix elements are entered instead of covariance matrix elements).

The structure of the ELEM records is slightly different when you use the CORR matrix header record. In this case the diagonal elements must always be 1.0, and the off-diagonal elements are the correlation coefficients. Immediately following these elements, you must also provide ELEM records that specify the standard deviations of the coordinate or coordinate difference measurements. If the matrix size is N, then N standard deviations must be entered in as many ELEM records as required (an ELEM record can only contain up to three elements).

The "Set of 2D coordinate records" must contain only PL, NE, or XY coordinate records. It may also contain HI, HT, 4PAR, and 7PAR records.
 

The "Set of 2D coordinate records" must contain only PL, NE, or XY coordinate records (it may also contain HI, HT, 4PAR, and 7PAR records). GeoLab will automatically subtract the first of these records from the others to arrive at the actual coordinate difference measurement values. Note that the covariance matrix elements entered must correspond to these computed coordinate differences.
 

The "Set of 3D coordinate records" must contain only PLH, PLO, NEH, NEO, or XYZ coordinate records (it may also contain HI, HT, 4PAR, and 7PAR records).
 

The "Set of 3D coordinate records or DXYZ records" must contain only PLH, PLO, NEH, NEO, XYZ coordinate records, or DXYZ coordinate difference records (it may also contain HI, HT, 4PAR, and 7PAR records). If DXYZ records are not used, GeoLab will automatically subtract the first of these records from the others to arrive at the actual coordinate difference measurement values (in which case the covariance matrix elements entered must correspond to these computed coordinate differences).
 

Note that if centering errors are used in the sigma-record, the covariance matrix coordinate system must be LG (local geodetic).
 
The covariance matrix header record can be one of the following record types:

The "matrix revision" fields of the matrix header record (COV, CORR, GENC, and WGT) are as follows:

For the GENC matrix header, all elements of the covariance matrix are initially set to zero before the following revisions are made. For all other matrix header types, the elements of the covariance matrix are initially given (either directly or indirectly) by the ELEM records.
 
The "Addition constant (entire matrix)" and the "Addition constant (diagonal)" are first added directly to the covariance matrix. The "PPM (diagonal)" value is used to calculate a standard deviation (using either a geocentric radius for 2DC and 3DC groups, or the vector lengths for 2DD and 3DD groups) and that value is squared and added to the diagonal of the covariance matrix.

Next, for 3DC and 3DD groups, the "Addition constant (height/Z)" and "Factor (height/Z)" values are used to revise the covariance matrix. If the matrix coordinate system is CT then the Z or Z-difference diagonal elements are revised. If the matrix coordinate system is LG then the height or height-difference diagonal elements are revised. The revision is performed as follows (E denotes the current matrix element, A the  "Addition constant (entire matrix)" value, and F the "Factor (height/Z)" value:

   E = (E + A) * F.

Finally, the "Factor (entire matrix)" and the "Factor (diagonal)" are applied to the covariance matrix.
 

Each DIR record in a DSET must have the same from-station specified.

If a sigma-record is used for a DSET, the standard deviation, the from-centering, and to-centering values are used to modify or define the standard deviations of the direction measurements in the DSET group.