Normal Equation Reduction and Inversion

This procedure is used to do the normal equation formation, reduction, solution and Inversion or partial reduction. The program lists the heresi record summary, the googe numbers and the variance factor summary. If any observation equations exceed a preset limit the equations are listed. If zero or negative terms are detected in the formation of the normal equations, the process is stopped. If a singularity is detected the process continues by fixing the term to one on the diagonal and zero's the row and column.

The user can optionally choose to list the normal equations, the full observation equation list, and the coordinate corrections for each pass.

The program requires the Adjsumy, Stadata,Nuispar, and Proneqs files. It generates the Normeqn (Normal equation file) and the Norminv (Normal equation inverse) file for the standard adjustment.

For a partially reduced normal equation adjustment (or lower block adjustment) it produces either a Rednor or a Prnfmt file as well as the Norminv file.

The Rednor file conforms to the Ghost position equation format and the Prnfmt conforms to the Exchange format.

Control of the Partial reduced process is done via the control record or by using program Updads. (record 6 character 9 and character 10 legal e s )

The Proneqsfile is changed to contain the normal equation block number for the Heresi record.

For a standard adjustment without error the Stadata and Nuispar files contain the adjusted values as well as estimates of the variance for each adjusted value.

To look at the residuals execute Lisres which produces a standard print file Lisres.

To look at error analysis execute Confel which produces a standard print file Confel.lis.

To look at individual stations use Updsta.

The partially reduced adjustment is followed at higher level by combining two or more lower level Rednor files and/or Prnfmt files using Assemble. If a higher level exists in the blocking scheme, the the file Rednor required for the next level is produced. If the top level, the parent block will be a complete adjustment.

Once the results at the top level are produced, they can be used to perform the back solution by executing Baksol < at each of the lower levels in turn.

Example [ denotes optional

         adjcla         <== Completes the adjustment  
                              The user is queried for a  
                               folder with adjustment files. 
        ADJCLA.LIS          contains adjustment results  
  REC# FIRST  LAST #COLS  #COEFFS.   #ZERO #NON ZERO  %NZ !      FULL  %NZ
 --------------------------------------------------------------------------
     1     1   393   393    17994    12879     5115   28% !     77421   6%
  Number of terms            8757
  Sum contributions      764559489.650634200      96561.5201063433800    
      normal equations   764559489.650635200    
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         Minimum Googe Numbers
         =====================
         Station Number and Name    Coordinate   N.E. Order   Googe Number
         =======================================================================
      1  79A803                     1 Latitude      376      0.1602587351159    
      2  776010                     2 Longitude     248      0.1807207594423    
      3  79A803                     3 Elevation     378      0.1844529645016    
      4  23611                      2 Longitude     113      0.1856979232421    
      5  79A803                     2 Longitude     377      0.1897159064060    
      6  58A028                     2 Longitude     353      0.2049293223564    
      7  60A047                     3 Elevation     393      0.2093673995950    
      8  82A671                     2 Longitude     290      0.2119029294574    
      9  60A047                     1 Latitude      391      0.2270142662477    
     10  60A047                     2 Longitude     392      0.2333015808961 
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        List of adjusted coordinates
         ==============================
    Station      Latitude      Correction   X Prime      Longitude      Correction   Y Prime      Elevation Corection    Z Prime
    -----------------------------------------------------------------------------------------------------------------------------
    128642        53.172989771  0.000000     0.0000E+00 -110.525801709  0.000000     0.0000E+00   661.9010    0.0000     0.0000E+00
    223600        49.054028042  0.000000    -0.2817E-09 -113.275261999  0.000000     0.6702E-09  1460.9369    0.0000     0.6589E-10
    323611        49.091843283  0.000000    -0.5627E-09 -110.240659856  0.000000    -0.1672E-09   974.0791    0.0000     0.2200E-09
    427625        52.034748874  0.000000    -0.3453E-09 -113.533694380  0.000000     0.2497E-09  1008.9325    0.0000    -0.3402E-09
    528662        53.332382518  0.000000    -0.7358E-09 -114.082165353  0.000000     0.3403E-09   771.9081    0.0000    -0.3244E-09
    647605        53.243025301  0.000000     0.3504E-10 -117.471175329  0.000000    -0.5096E-09  1567.9492    0.0000    -0.3322E-09
    7655016       51.291064858  0.000000     0.4752E-09 -109.591565221  0.000000    -0.2872E-09   737.5525    0.0000    -0.4516E-09
    8656009       50.472919140  0.000000    -0.3769E-09 -110.553580763  0.000000     0.1166E-09   826.2073    0.0000    -0.5952E-09
    9656025       50.521696799  0.000000     0.1192E-09 -114.173656713  0.000000     0.1504E-09  1248.4797    0.0000     0.2060E-09
   10666004       53.334176679  0.000000     0.1905E-09 -113.395284157  0.000000    -0.2022E-09   676.8667    0.0000    -0.1667E-09
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    Variance Factor Summary
    =======================

    Number of Directions            =      0
    Number of Distances             =      0
    Number of Azimuths              =      0
    Number of Position Equations    =      0
    Number of Posn Diff Equations   =    825
    Number of Elevation Differences =      0

    Accumulated Observations        =      0
    Previously Eliminated           =      0

    Number of Normal Equations      =    393
    Degrees of Freedom              =   432.

    Sum Equation R.H.S.**2          =  65306.91606866    
    Sum NE RHS * Reduced RHS        = 0.4228931134254E-09
    Accumulated VPV                 = 0.0000000000000E+00
    Sum  VTPV                       =  65306.91606866    

    Computed Variance Factor        =   151.2    


        2 SOLUTIONS COMPLETE - Maximum corrections 
         - X Prime =               0.000 (m)  at [78A144   ]
         - Y Prime =               0.000 (m)  at [82A703   ]
         - Z Prime =               0.000 (m)  at [ 906046  ]

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Revised 6 Dec 98 by Mike Craymer