1EXAMPLE  1

 TEST SIMPLE ODR PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODR.
 DATA SET REFERENCE:  DRAPER AND SMITH, 1981, EXERCISE I, PAGE 521-522                               



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF ODR
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                                8
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS           8
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     2
 NUMBER OF FUNCTION PARAMETERS                         2
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 2



 INDEPENDENT VARIABLE AND DELTA WEIGHT SUMMARY:
 ----------------------------------------------

                               COLUMN   1                COLUMN   2     
                           OBS 1        OBS N        OBS 1        OBS N
               X -   0.10900E+03  0.68000E+02  0.60000E+03  0.64000E+03
           FIXED -            NO           NO           NO           NO
   INITIAL DELTA -   0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
     DELTA SCALE -   0.91743E-02  0.14706E-01  0.15625E-02  0.15625E-02
   DELTA WEIGHTS -   0.10000E+01  0.10000E+01  0.10000E+01  0.10000E+01



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.91200E+00  0.37600E+00
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2
 INITIAL BETA -   0.11550000E-01  0.50000000E+04
        FIXED -               NO              NO
   BETA SCALE -   0.86580086E+02  0.19999999E-03



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00010         6  0.10E+01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE INITIALIZED TO ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE SUPPLIED BY USER.
      USER-SUPPLIED DERIVATIVES WERE CHECKED.
      THE DERIVATIVES APPEAR TO BE CORRECT.
  E.  FIT IS BY METHOD OF ORTHOGONAL DISTANCE REGRESSION.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.67661995E+00
 SUM OF SQUARED WEIGHTED DELTAS                  0.00000000E+00
 SUM OF SQUARED WEIGHTED EPSILONS                0.67661995E+00





 ITERATION REPORTS FOR FIT BY METHOD OF ODR
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1      12  0.19694E+00   0.7089E+00   0.4162E+00  0.151E+01   YES
    2      13  0.18529E+00   0.5916E-01   0.4945E-01  0.177E-01   YES
    3      14  0.18445E+00   0.4544E-02   0.3701E-02  0.523E-02   YES
    4      15  0.18440E+00   0.2841E-03   0.2289E-03  0.134E-02   YES







 FINAL SUMMARY FOR FIT BY METHOD OF ODR
 ======================================



 STOPPING CONDITION (INFO =     11):
 -----------------------------------

 THE RELATIVE CHANGE IN THE SUM OF THE SQUARED
 WEIGHTED OBSERVATIONAL ERRORS IS LESS THAN SSTOL

 NOTE:

 THE RESULTS FROM ODRPACK ARE QUESTIONABLE BECAUSE

 THE JACOBIAN OF THE MODEL FUNCTION WITH RESPECT TO  
 THE FUNCTION PARAMETERS (BETA) IS NOT FULL RANK AT  
 THE SOLUTION. 

                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
               4         16          5 0.1000E+01           1



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.18439893E+00
 SUM OF SQUARED WEIGHTED DELTAS                  0.47393845E-04
 SUM OF SQUARED WEIGHTED EPSILONS                0.18435153E+00



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

 N.B. STANDARD ERRORS OF THE ESTIMATED BETAS WERE NOT
      COMPUTED BECAUSE EITHER THE JACOBIAN IS NOT FULL
      RANK AT THE SOLUTION, OR THE MOST RECENTLY TRIED
      VALUES OF BETA AND/OR X+DELTA WERE UNACCEPTABLE.

         INDEX            VALUE -------------->
     1 TO    2   0.39548320E-02  0.18767850E+05



 ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
 ---------------------------------------------------

     I      EPSILON(I)      DELTA(I,1)      DELTA(I,2)
     1 -0.57429135E-01 -0.70321454E-04 -0.39960103E-03
     2  0.13377562E+00  0.70100470E-03  0.20878091E-02
     3 -0.21450824E+00 -0.56725923E-04 -0.34896410E-02
     4  0.13454801E+00  0.69795956E-03  0.21107197E-02
     5 -0.18172356E+00 -0.42248586E-04 -0.27972544E-02
     6  0.13718215E+00  0.69036236E-03  0.21826401E-02
     7 -0.17820957E+00 -0.43872311E-04 -0.28132722E-02
     8  0.12425584E+00  0.63165824E-03  0.19680990E-02


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.276273320312499981454834596661E+05 0.753263942897319793701171875000E-03     1

  NEW TEST RESULT      = 
 0.187678496093750002415845301584E+05 0.184398934245109558105468750000E+00    11

  DIFFERENCE           = 
 0.885948242187500056843418860808E+04 0.183645665645599365234375000000E+00    10



 *** WARNING ***

 NEW RESULTS AND EXPECTED RESULTS DO NOT AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULT.
1EXAMPLE  2

 TEST SIMPLE OLS PROBLEM
 WITH FINITE DIFFERENCE DERIVATIVES USING SODR.
 DATA SET REFERENCE:  DRAPER AND SMITH, 1981, EXERCISE I, PAGE 521-522                               



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF OLS
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                                8
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS           8
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     2
 NUMBER OF FUNCTION PARAMETERS                         2
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 2



 INDEPENDENT VARIABLE SUMMARY:
 -----------------------------

                 COLUMN   1                COLUMN   2     
             OBS 1        OBS N        OBS 1        OBS N
 X -   0.10900E+03  0.68000E+02  0.60000E+03  0.64000E+03



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.91200E+00  0.37600E+00
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2
 INITIAL BETA -   0.11550000E-01  0.50000000E+04
        FIXED -               NO              NO
   BETA SCALE -   0.86580086E+02  0.19999999E-03



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00001         6  0.10E+01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE FIXED AT ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE COMPUTED BY FINITE DIFFERENCES.
  E.  FIT IS BY METHOD OF ORDINARY LEAST SQUARES.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.67661995E+00





 ITERATION REPORTS FOR FIT BY METHOD OF OLS
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1      10  0.19708E+00   0.7087E+00   0.4162E+00  0.151E+01   YES
    2      14  0.18532E+00   0.5967E-01   0.5006E-01  0.178E-01   YES
    3      18  0.18449E+00   0.4518E-02   0.3747E-02  0.527E-02   YES
    4      22  0.18444E+00   0.2633E-03   0.2304E-03  0.135E-02   YES







 FINAL SUMMARY FOR FIT BY METHOD OF OLS
 ======================================



 STOPPING CONDITION (INFO =     11):
 -----------------------------------

 THE RELATIVE CHANGE IN THE SUM OF THE SQUARED
 WEIGHTED OBSERVATIONAL ERRORS IS LESS THAN SSTOL

 NOTE:

 THE RESULTS FROM ODRPACK ARE QUESTIONABLE BECAUSE

 THE JACOBIAN OF THE MODEL FUNCTION WITH RESPECT TO  
 THE FUNCTION PARAMETERS (BETA) IS NOT FULL RANK AT  
 THE SOLUTION. 

                             CONDITION            
       NUMBER OF  NUMBER OF     NUMBER        RANK
      ITERATIONS   FN EVALS  (INVERSE)  DEFICIENCY
               4         23 0.1000E+01           1



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.18443863E+00



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

 N.B. STANDARD ERRORS OF THE ESTIMATED BETAS WERE NOT
      COMPUTED BECAUSE EITHER THE JACOBIAN IS NOT FULL
      RANK AT THE SOLUTION, OR THE MOST RECENTLY TRIED
      VALUES OF BETA AND/OR X+DELTA WERE UNACCEPTABLE.

         INDEX            VALUE -------------->
     1 TO    2   0.39568404E-02  0.18768018E+05



 ESTIMATED EPSILON(I), I = 1, ..., N:
 ------------------------------------

         INDEX            VALUE -------------->
     1 TO    4  -0.57499111E-01  0.13363585E+00 -0.21471928E+00  0.13440818E+00
     5 TO    8  -0.18191282E+00  0.13704097E+00 -0.17840375E+00  0.12411129E+00


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.276273261718749996163069226895E+05 0.753846776206046342849731445312E-03     1

  NEW TEST RESULT      = 
 0.187680175781250007105427357601E+05 0.184438630938529968261718750000E+00    11

  DIFFERENCE           = 
 0.885930859375000068212102632969E+04 0.183684781193733215332031250000E+00    10



 *** WARNING ***

 NEW RESULTS AND EXPECTED RESULTS DO NOT AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULT.
1EXAMPLE  3

 TEST PARAMETER FIXING CAPABILITIES FOR POORLY SCALED OLS PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODRC.
 DATA SET REFERENCE:  BOGGS, BYRD AND SCHNABEL, 1985, EXAMPLE 3                                      



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF OLS
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                               44
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS          44
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     1
 NUMBER OF FUNCTION PARAMETERS                         9
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 4



 INDEPENDENT VARIABLE SUMMARY:
 -----------------------------

                 COLUMN   1     
             OBS 1        OBS N
 X -   0.25000E-08  0.10000E+01



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.98823E+00  0.94728E+00
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2               3               4
 INITIAL BETA -   0.28188751E-05 -0.23129054E-02  0.58303556E+01  0.00000000E+00
        FIXED -               NO              NO              NO             YES
   BETA SCALE -   0.35475144E+06  0.43235663E+03  0.17151612E+00  0.35475143E+07

        INDEX -                5               6               7               8
 INITIAL BETA -   0.40691076E+08  0.13800111E-02  0.59603851E-01  0.67058210E+01
        FIXED -               NO             YES             YES             YES
   BETA SCALE -   0.24575414E-07  0.72463184E+03  0.16777439E+02  0.14912418E+00

        INDEX -                9
 INITIAL BETA -   0.10699441E+10
        FIXED -              YES
   BETA SCALE -   0.93462826E-09



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00031         6  0.10E+01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE FIXED AT ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE SUPPLIED BY USER.
      USER-SUPPLIED DERIVATIVES WERE NOT CHECKED.
  E.  FIT IS BY METHOD OF ORDINARY LEAST SQUARES.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.72853649E+17





 ITERATION REPORTS FOR FIT BY METHOD OF OLS
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1       7  0.18750E+04   0.1000E+01   0.1000E+01  0.200E+01   YES
    2       8  0.12128E-04   0.1000E+01   0.1000E+01  0.855E+04   YES
    3       9  0.12128E-04   0.3409E-04   0.8913E-05  0.110E-02   YES
    4      10  0.12128E-04   0.1347E-04   0.6620E-09  0.918E-05   YES







 FINAL SUMMARY FOR FIT BY METHOD OF OLS
 ======================================



 STOPPING CONDITION (INFO =      2):
 -----------------------------------

 THE RELATIVE CHANGE IN THE NORM OF BETA AND DELTA
 IS LESS THAN PARTOL

                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
               4         11          5 0.4567E-05           0



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.12127827E-04

 ESTIMATED RESIDUAL VARIANCE                     0.30319569E-06
 (   40 DEGREES OF FREEDOM)



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

             J          BETA(J)     STD. DEV. BETA(J)
             1   0.23864218E-05        0.44959907E-06
             2  -0.22044973E-02        0.40155868E-04
             3   0.38227286E+01        0.38315620E-01
             4   0.00000000E+00                 FIXED
             5   0.45336449E+00        0.52740788E-02
             6   0.13800111E-02                 FIXED
             7   0.59603851E-01                 FIXED
             8   0.67058210E+01                 FIXED
             9   0.10699441E+10                 FIXED



 ESTIMATED EPSILON(I), I = 1, ..., N:
 ------------------------------------

         INDEX            VALUE -------------->
     1 TO    4  -0.58531761E-04 -0.98884106E-04 -0.17184019E-03 -0.21141768E-03
     5 TO    8  -0.10657310E-03 -0.16033649E-03 -0.14322996E-03 -0.13500452E-03
     9 TO   12  -0.16081333E-03 -0.15139580E-03 -0.11914968E-03 -0.29265881E-04
    13 TO   16   0.11324883E-05  0.79393387E-04  0.11879206E-03  0.32174587E-03
    17 TO   20   0.40936470E-03  0.49537420E-03  0.64468384E-03  0.71024895E-03
    21 TO   24   0.69665909E-03  0.65493584E-03  0.48458576E-03  0.21833181E-03
    25 TO   28   0.18537045E-04 -0.57220459E-05 -0.69797039E-04 -0.52750111E-04
    29 TO   32  -0.30934811E-03 -0.68235397E-03 -0.10501742E-02 -0.12425184E-02
    33 TO   36  -0.11814237E-02 -0.96982718E-03 -0.30291080E-03  0.52142143E-03
    37 TO   40   0.90557337E-03  0.11147261E-02  0.79053640E-03  0.32657385E-03
    41 TO   44  -0.32705069E-03 -0.27650595E-03 -0.58716536E-03  0.92387199E-04


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.106994412799999993879396242846E+10 0.121280854727956466376781463623E-04     1

  NEW TEST RESULT      = 
 0.106994412799999993879396242846E+10 0.121278271763003431260585784912E-04     2

  DIFFERENCE           = 
 0.000000000000000000000000000000E+00 0.258296495303511619567871093750E-09     1



 NEW RESULTS AND EXPECTED RESULTS AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULTS.
1EXAMPLE  4

 TEST WEIGHTING CAPABILITIES FOR ODR PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODRC. 
 ALSO SHOWS SOLUTION OF POORLY SCALED ODR PROBLEM.
 (DERIVATIVE CHECKING TURNED OFF.)
 DATA SET REFERENCE:  BOGGS, BYRD AND SCHNABEL, 1985, EXAMPLE 3                                      



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF ODR
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                               44
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS          43
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     1
 NUMBER OF FUNCTION PARAMETERS                         9
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 6



 INDEPENDENT VARIABLE AND DELTA WEIGHT SUMMARY:
 ----------------------------------------------

                               COLUMN   1     
                           OBS 1        OBS N
               X -   0.25000E-08  0.10000E+01
           FIXED -            NO           NO
   INITIAL DELTA -   0.00000E+00  0.00000E+00
     DELTA SCALE -   0.40000E+09  0.10000E+01
   DELTA WEIGHTS -   0.40000E+07  0.10000E-01



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.98823E+00  0.94728E+00
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2               3               4
 INITIAL BETA -   0.23864218E-05 -0.22044973E-02  0.38227286E+01  0.00000000E+00
        FIXED -               NO              NO              NO             YES
   BETA SCALE -   0.41903741E+06  0.45361813E+03  0.26159325E+00  0.41903740E+07

        INDEX -                5               6               7               8
 INITIAL BETA -   0.45336449E+00  0.13800111E-02  0.59603851E-01  0.67058210E+01
        FIXED -               NO              NO              NO             YES
   BETA SCALE -   0.22057307E+01  0.72463184E+03  0.16777439E+02  0.14912418E+00

        INDEX -                9
 INITIAL BETA -   0.10699441E+10
        FIXED -              YES
   BETA SCALE -   0.93462826E-09



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00020         6  0.10E+01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE INITIALIZED TO ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE SUPPLIED BY USER.
      USER-SUPPLIED DERIVATIVES WERE NOT CHECKED.
  E.  FIT IS BY METHOD OF ORTHOGONAL DISTANCE REGRESSION.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.12125044E-04
 SUM OF SQUARED WEIGHTED DELTAS                  0.00000000E+00
 SUM OF SQUARED WEIGHTED EPSILONS                0.12125044E-04





 ITERATION REPORTS FOR FIT BY METHOD OF ODR
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N      BETA -------------->
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP     INDEX           VALUE
 ----  ------  -----------  -----------  -----------  ---------  ----     -----           -----

    1       9  0.56149E-05   0.5369E+00   0.6022E+00  0.125E+00    NO   1 TO  3  0.26165972E-05 -0.18485609E-02  0.38174613E+01
                                                                        4 TO  6  0.00000000E+00  0.45277756E+00  0.11730099E-02
                                                                        7 TO  9  0.51484443E-01  0.67058210E+01  0.10699441E+10
    4      15  0.12075E-05   0.3885E+00   0.4366E+00  0.172E+00    NO   1 TO  3  0.44206258E-05 -0.12757953E-02  0.35238521E+01
                                                                        4 TO  6  0.00000000E+00  0.49268886E+00  0.11917221E-02
                                                                        7 TO  9  0.37987329E-01  0.67058210E+01  0.10699441E+10
    7      21  0.78737E-06   0.9943E-01   0.1135E+00  0.110E+00    NO   1 TO  3  0.74505861E-05 -0.11967927E-02  0.34890401E+01
                                                                        4 TO  6  0.00000000E+00  0.49737310E+00  0.16501858E-02
                                                                        7 TO  9  0.35349328E-01  0.67058210E+01  0.10699441E+10
   10      26  0.62892E-06   0.8130E-01   0.1132E+00  0.129E+00    NO   1 TO  3  0.11543758E-04 -0.11336262E-02  0.34598379E+01
                                                                        4 TO  6  0.00000000E+00  0.50130433E+00  0.21526238E-02
                                                                        7 TO  9  0.33040479E-01  0.67058210E+01  0.10699441E+10
   13      29  0.55848E-06   0.2304E-01   0.3533E-01  0.944E-01    NO   1 TO  3  0.16416994E-04 -0.10886485E-02  0.34377537E+01
                                                                        4 TO  6  0.00000000E+00  0.50427830E+00  0.26265059E-02
                                                                        7 TO  9  0.31212864E-01  0.67058210E+01  0.10699441E+10
   16      32  0.54524E-06   0.4935E-02   0.5066E-02  0.488E-02   YES   1 TO  3  0.19589772E-04 -0.10685262E-02  0.34273231E+01
                                                                        4 TO  6  0.00000000E+00  0.50568295E+00  0.28879053E-02
                                                                        7 TO  9  0.30315554E-01  0.67058210E+01  0.10699441E+10







 FINAL SUMMARY FOR FIT BY METHOD OF ODR
 ======================================



 STOPPING CONDITION (INFO =      1):
 -----------------------------------

 THE RELATIVE CHANGE IN THE SUM OF THE SQUARED
 WEIGHTED OBSERVATIONAL ERRORS IS LESS THAN SSTOL

                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
              17         34         18 0.2257E-05           0



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.54524378E-06
 SUM OF SQUARED WEIGHTED DELTAS                  0.34236064E-06
 SUM OF SQUARED WEIGHTED EPSILONS                0.20288314E-06

 ESTIMATED RESIDUAL VARIANCE                     0.14736320E-07
 (   37 DEGREES OF FREEDOM)



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

             J          BETA(J)     STD. DEV. BETA(J)
             1   0.19589772E-04        0.52653781E-05
             2  -0.10685262E-02        0.40957897E-04
             3   0.34273231E+01        0.33461187E-01
             4   0.00000000E+00                 FIXED
             5   0.50568295E+00        0.46738111E-02
             6   0.28879053E-02        0.42487506E-03
             7   0.30315554E-01        0.15303779E-02
             8   0.67058210E+01                 FIXED
             9   0.10699441E+10                 FIXED



 ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
 ---------------------------------------------------

     I      EPSILON(I)      DELTA(I,1)
     1  0.88512897E-04  0.69538535E-17
     2  0.48160553E-04  0.24792062E-16
     3 -0.24795532E-04 -0.31197530E-16
     4 -0.64373016E-04 -0.65629582E-14
     5  0.39935112E-04  0.50193026E-12
     6 -0.15437603E-04 -0.30741863E-11
     7 -0.11324883E-05 -0.10857734E-11
     8  0.33378601E-05  0.10780253E-10
     9 -0.33438206E-04 -0.52062593E-09
    10 -0.39577484E-04 -0.18795692E-08
    11 -0.27477741E-04 -0.30498837E-08
    12  0.37789345E-04  0.82184677E-08
    13  0.22828579E-04  0.10967525E-07
    14  0.57220459E-05  0.70269186E-08
    15 -0.68247318E-04 -0.14481884E-06
    16  0.13709068E-04  0.37873974E-07
    17 -0.15914440E-04 -0.37617106E-07
    18 -0.33259392E-04  0.20522912E-08
    19  0.33736229E-04 -0.18751678E-06
    20  0.42200089E-04 -0.64051505E-06
    21 -0.37550926E-05  0.18539616E-06
    22  0.20086765E-04 -0.22377897E-05
    23 -0.55432320E-05  0.11036406E-05
    24 -0.68843365E-04  0.21943364E-04
    25 -0.50544739E-04  0.23404340E-04
    26  0.20980835E-04 -0.11482354E-04
    27  0.57339668E-04 -0.36242633E-04
    28  0.30237436E-03  0.00000000E+00
    29  0.17416477E-03 -0.17715925E-03
    30  0.19729137E-04 -0.23990526E-04
    31 -0.79154968E-04  0.12471073E-03
    32 -0.14775991E-03  0.27653735E-03
    33 -0.11229515E-03  0.23145282E-03
    34 -0.48041344E-04  0.99174431E-04
    35  0.14054775E-03 -0.14259368E-03
    36  0.16260147E-03  0.71720022E-03
    37  0.10865927E-03  0.12324597E-02
    38 -0.11622906E-04 -0.41706034E-03
    39 -0.63896179E-04 -0.44254786E-02
    40 -0.10323524E-03 -0.94536031E-02
    41 -0.93400478E-04 -0.13989517E-01
    42 -0.12338161E-04 -0.30919479E-02
    43  0.16987324E-04  0.65795151E-02
    44  0.65803528E-04  0.37051391E-01


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.106994412799999993879396242846E+10 0.545208479252323741093277931213E-06     1

  NEW TEST RESULT      = 
 0.106994412799999993879396242846E+10 0.545243779015436302870512008666E-06     1

  DIFFERENCE           = 
 0.000000000000000000000000000000E+00 0.352997631125617772340774536132E-10     0



 NEW RESULTS AND EXPECTED RESULTS AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULTS.
1EXAMPLE  5

 TEST DELTA INITIALIZATION CAPABILITIES
 AND USE OF ISTOPF TO RESTRICT PARAMETER VALUES FOR ODR PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODRC.
 DATA SET REFERENCE:  BOGGS, BYRD AND SCHNABEL, 1985, EXAMPLE 1                                      



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF ODR
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                               40
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS          40
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     1
 NUMBER OF FUNCTION PARAMETERS                         2
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 2



 INDEPENDENT VARIABLE AND DELTA WEIGHT SUMMARY:
 ----------------------------------------------

                               COLUMN   1     
                           OBS 1        OBS N
               X -  -0.21370E-01  0.19933E+01
           FIXED -            NO           NO
   INITIAL DELTA -   0.00000E+00  0.00000E+00
     DELTA SCALE -   0.20000E+01  0.20000E+01
   DELTA WEIGHTS -   0.10000E+01  0.10000E+01



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -  -0.11957E+01  0.12617E+01
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2
 INITIAL BETA -   0.10000000E+01  0.10000000E+01
        FIXED -               NO              NO
   BETA SCALE -   0.20000000E+00  0.10000000E+01



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  01010         6  0.10E+01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE INITIALIZED BY USER.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE SUPPLIED BY USER.
      USER-SUPPLIED DERIVATIVES WERE CHECKED.
      THE DERIVATIVES APPEAR TO BE CORRECT.
  E.  FIT IS BY METHOD OF ORTHOGONAL DISTANCE REGRESSION.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.21300319E+03
 SUM OF SQUARED WEIGHTED DELTAS                  0.22299876E-02
 SUM OF SQUARED WEIGHTED EPSILONS                0.21300096E+03





 ITERATION REPORTS FOR FIT BY METHOD OF ODR
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1      13  0.26186E+02   0.8771E+00   0.9918E+00  0.718E-01    NO
    2      19  0.26949E+01   0.8971E+00   0.9518E+00  0.537E-01    NO
    3      24  0.11496E+01   0.5734E+00   0.5813E+00  0.208E-01    NO
    4      28  0.10967E+01   0.4596E-01   0.4601E-01  0.404E-02    NO
    5      32  0.10891E+01   0.6979E-02   0.6979E-02  0.858E-03    NO
    6      37  0.10862E+01   0.2622E-02   0.2622E-02  0.336E-03    NO
    7      38  0.10862E+01  -0.1000E+01   0.2529E-02  0.336E-04    NO







 FINAL SUMMARY FOR FIT BY METHOD OF ODR
 ======================================



 STOPPING CONDITION (INFO =    102):
 -----------------------------------

 THE RELATIVE CHANGE IN THE NORM OF BETA AND DELTA
 IS LESS THAN PARTOL

 NOTE:

 THE RESULTS FROM ODRPACK ARE QUESTIONABLE BECAUSE

 THE MOST RECENTLY TRIED STEP WAS REJECTED BY THE    
 USER AS INDICATED BY THE VALUE OF VARIABLE ISTOPF   
 RETURNED FROM USER-SUPPLIED SUBROUTINE FUN.    


                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
               7         39          9 0.6203E+00           0



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.10862116E+01
 SUM OF SQUARED WEIGHTED DELTAS                  0.83914362E-02
 SUM OF SQUARED WEIGHTED EPSILONS                0.10778202E+01

 ESTIMATED RESIDUAL VARIANCE                     0.28584508E-01
 (   38 DEGREES OF FREEDOM)



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

             J          BETA(J)     STD. DEV. BETA(J)
             1   0.10098528E+01        0.54642033E-01
             2   0.10080690E+01        0.28702263E-01



 ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
 ---------------------------------------------------

     I      EPSILON(I)      DELTA(I,1)
     1  0.21398973E+00  0.77019649E-03
     2  0.22572160E+00  0.93826948E-03
     3  0.10467207E+00  0.54385507E-03
     4 -0.15070486E+00 -0.66666561E-03
     5 -0.25287175E+00 -0.14750827E-02
     6  0.10103035E+00  0.75924967E-03
     7 -0.20794547E+00 -0.14733394E-02
     8 -0.20448446E-01 -0.64978092E-04
     9  0.83243966E-01  0.89894724E-03
    10  0.83509088E-01  0.13093477E-02
    11 -0.27150869E-01 -0.15885562E-03
    12 -0.22844553E-01 -0.96486758E-04
    13  0.28114152E+00  0.63913204E-02
    14 -0.23312688E+00 -0.81564207E-02
    15  0.29162264E+00  0.10717180E-01
    16  0.12397766E-02  0.23084108E-02
    17 -0.77581406E-02  0.28769793E-02
    18 -0.31136990E-01 -0.26895691E-01
    19 -0.24995804E-01 -0.43563493E-01
    20 -0.11520386E-02  0.53291705E-01
    21  0.58746338E-03  0.20395383E-01
    22  0.17700195E-02 -0.32760776E-02
    23  0.20849228E-01  0.40327583E-01
    24  0.37886143E-01  0.28744594E-02
    25  0.11559868E+00  0.15356561E-01
    26 -0.16006970E+00 -0.10929030E-01
    27 -0.40909457E+00 -0.14815369E-01
    28  0.13185191E+00  0.32352598E-02
    29  0.10531020E+00  0.20688716E-02
    30  0.91539621E-01  0.11403832E-02
    31 -0.57343364E-01 -0.10346775E-02
    32  0.35790145E+00  0.45340513E-02
    33  0.19568396E+00  0.20215872E-02
    34 -0.19317806E+00 -0.17592876E-02
    35 -0.17364621E-01 -0.28432105E-03
    36 -0.13734615E+00 -0.99461491E-03
    37 -0.20678294E+00 -0.12554711E-02
    38  0.32231927E-01  0.10125670E-03
    39  0.15409482E+00  0.57699374E-03
    40 -0.23574305E+00 -0.92025293E-03


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.142698812484741210937500000000E+01 0.108472871780395507812500000000E+01   101

  NEW TEST RESULT      = 
 0.142688667774200439453125000000E+01 0.108621156215667724609375000000E+01   102

  DIFFERENCE           = 
 0.101447105407714843750000000000E-03 0.148284435272216796875000000000E-02     1



 *** WARNING ***

 NEW RESULTS AND EXPECTED RESULTS DO NOT AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULT.
1EXAMPLE  6

 TEST STIFF STOPPING CONDITIONS FOR UNSCALED ODR PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODRC.
 DATA SET REFERENCE:  HIMMELBLAU, 1970, EXAMPLE 6.2-4, PAGE 188                                      



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF ODR
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                               13
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS          13
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     2
 NUMBER OF FUNCTION PARAMETERS                         3
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 3



 INDEPENDENT VARIABLE AND DELTA WEIGHT SUMMARY:
 ----------------------------------------------

                               COLUMN   1                COLUMN   2     
                           OBS 1        OBS N        OBS 1        OBS N
               X -   0.00000E+00  0.29000E+01  0.00000E+00  0.18000E+01
           FIXED -            NO           NO           NO           NO
   INITIAL DELTA -   0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
     DELTA SCALE -   0.10000E+02  0.34483E+00  0.10000E+02  0.33333E+00
   DELTA WEIGHTS -   0.10000E+01  0.10000E+01  0.10000E+01  0.10000E+01



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.29300E+01  0.98100E+01
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2               3
 INITIAL BETA -   0.30000000E+01  0.30000000E+01 -0.50000000E+00
        FIXED -               NO              NO              NO
   BETA SCALE -   0.33333334E+00  0.33333334E+00  0.33333334E+00



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00010         6  0.10E+01  0.24E-04  0.24E-06      2

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE INITIALIZED TO ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE SUPPLIED BY USER.
      USER-SUPPLIED DERIVATIVES WERE CHECKED.
      THE DERIVATIVES APPEAR TO BE CORRECT.
  E.  FIT IS BY METHOD OF ORTHOGONAL DISTANCE REGRESSION.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.17930526E+00
 SUM OF SQUARED WEIGHTED DELTAS                  0.00000000E+00
 SUM OF SQUARED WEIGHTED EPSILONS                0.17930526E+00





 ITERATION REPORTS FOR FIT BY METHOD OF ODR
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1      13  0.14822E-01   0.9173E+00   0.9167E+00  0.105E+01   YES
    2      14  0.14780E-01   0.2873E-02   0.2897E-02  0.269E-01   YES







 FINAL SUMMARY FOR FIT BY METHOD OF ODR
 ======================================



 STOPPING CONDITION (INFO =      4):
 -----------------------------------

 MAXIMUM NUMBER OF ITERATIONS REACHED

                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
               2         15          4 0.2281E+00           0



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.14779681E-01
 SUM OF SQUARED WEIGHTED DELTAS                  0.13389154E-01
 SUM OF SQUARED WEIGHTED EPSILONS                0.13905272E-02

 ESTIMATED RESIDUAL VARIANCE                     0.14779683E-02
 (   10 DEGREES OF FREEDOM)



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

             J          BETA(J)     STD. DEV. BETA(J)
             1   0.30212727E+01        0.36887582E-01
             2   0.29588337E+01        0.83318897E-01
             3  -0.52543277E+00        0.30452514E-01



 ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
 ---------------------------------------------------

     I      EPSILON(I)      DELTA(I,1)      DELTA(I,2)
     1  0.23071766E-02 -0.69501558E-02  0.35591233E-02
     2 -0.18256426E-01  0.55132102E-01 -0.16914347E-01
     3  0.21586478E-01 -0.65074377E-01  0.11658608E-01
     4  0.31240582E-02 -0.93540289E-02  0.99921343E-03
     5  0.64043999E-02 -0.19329511E-01  0.98682838E-02
     6  0.28228760E-02 -0.84860474E-02  0.25775696E-02
     7 -0.11911392E-01  0.35997316E-01 -0.65131458E-02
     8  0.57125092E-03 -0.16711173E-02  0.30126362E-03
     9 -0.22907257E-02  0.68901046E-02 -0.35429753E-02
    10 -0.52747726E-02  0.15936887E-01 -0.48603634E-02
    11 -0.13712406E-01  0.41421719E-01 -0.74992767E-02
    12  0.84342957E-02 -0.25412327E-01  0.45714322E-02
    13  0.96302032E-02 -0.29030550E-01  0.57946113E-02


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.426132202148437500000000000000E+01 0.147796720266342163085937500000E-01     4

  NEW TEST RESULT      = 
 0.426132202148437500000000000000E+01 0.147796813398599624633789062500E-01     4

  DIFFERENCE           = 
 0.000000000000000000000000000000E+00 0.931322574615478515625000000000E-08     0



 NEW STOPPING CONDITION AND EXPECTED STOPPING CONDITION AGREE,
 BUT INDICATE CONVERGENCE WAS NOT ATTAINED.
 NO FURTHER COMPARISONS WILL BE MADE BETWEEN NEW AND EXPECTED RESULTS.
1EXAMPLE  7

 TEST RESTART FOR UNSCALED ODR PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODRC.
 DATA SET REFERENCE:  HIMMELBLAU, 1970, EXAMPLE 6.2-4, PAGE 188                                      



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 RESTART OF FIT BY METHOD OF ODR
 ===============================





 ITERATION REPORTS FOR FIT BY METHOD OF ODR
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    3      16  0.14780E-01   0.2265E-05   0.7467E-06  0.842E-03   YES
    4      17  0.14780E-01  -0.1669E-05   0.6063E-09  0.123E-04   YES







 FINAL SUMMARY FOR FIT BY METHOD OF ODR
 ======================================



 STOPPING CONDITION (INFO =      1):
 -----------------------------------

 THE RELATIVE CHANGE IN THE SUM OF THE SQUARED
 WEIGHTED OBSERVATIONAL ERRORS IS LESS THAN SSTOL

                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
               4         18          7 0.2280E+00           0



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.14779649E-01
 SUM OF SQUARED WEIGHTED DELTAS                  0.13392352E-01
 SUM OF SQUARED WEIGHTED EPSILONS                0.13872965E-02

 ESTIMATED RESIDUAL VARIANCE                     0.14779649E-02
 (   10 DEGREES OF FREEDOM)



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

             J          BETA(J)     STD. DEV. BETA(J)
             1   0.30212231E+01        0.36886208E-01
             2   0.29588203E+01        0.83316468E-01
             3  -0.52538115E+00        0.30448763E-01



 ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
 ---------------------------------------------------

     I      EPSILON(I)      DELTA(I,1)      DELTA(I,2)
     1  0.22985935E-02 -0.69448114E-02  0.35669419E-02
     2 -0.18240571E-01  0.55110127E-01 -0.16917894E-01
     3  0.21554589E-01 -0.65122269E-01  0.11644794E-01
     4  0.31079650E-02 -0.93900282E-02  0.99841016E-03
     5  0.63900948E-02 -0.19306511E-01  0.98832482E-02
     6  0.28133392E-02 -0.84988642E-02  0.25824266E-02
     7 -0.11909962E-01  0.35983976E-01 -0.64961808E-02
     8  0.56028366E-03 -0.16917245E-02  0.30431515E-03
     9 -0.22888184E-02  0.69164815E-02 -0.35656723E-02
    10 -0.52762032E-02  0.15941484E-01 -0.48628747E-02
    11 -0.13710499E-01  0.41424938E-01 -0.74823126E-02
    12  0.84114075E-02 -0.25414694E-01  0.45614657E-02
    13  0.96082687E-02 -0.29026814E-01  0.57833334E-02


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.426127243041992187500000000000E+01 0.147796608507633209228515625000E-01     1

  NEW TEST RESULT      = 
 0.426127099990844726562500000000E+01 0.147796487435698509216308593750E-01     1

  DIFFERENCE           = 
 0.143051147460937500000000000000E-05 0.121071934700012207031250000000E-07     0



 NEW RESULTS AND EXPECTED RESULTS AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULTS.
1EXAMPLE  8

 TEST USE OF TAUFAC TO RESTRICT FIRST STEP FOR ODR PROBLEM
 WITH FINITE DIFFERENCE DERIVATIVES USING SODRC.
 DATA SET REFERENCE:  POWELL AND MACDONALD, 1972, TABLES 7 & 8, PAGES 153-154                        



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF ODR
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                               14
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS          14
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     1
 NUMBER OF FUNCTION PARAMETERS                         3
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 3



 INDEPENDENT VARIABLE AND DELTA WEIGHT SUMMARY:
 ----------------------------------------------

                               COLUMN   1     
                           OBS 1        OBS N
               X -   0.10000E+01  0.14000E+02
           FIXED -            NO           NO
   INITIAL DELTA -   0.00000E+00  0.00000E+00
     DELTA SCALE -   0.10000E+01  0.71429E-01
   DELTA WEIGHTS -   0.10000E+01  0.10000E+01



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.26380E+02  0.22220E+02
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2               3
 INITIAL BETA -   0.25000000E+02  0.30000000E+02  0.60000000E+01
        FIXED -               NO              NO              NO
   BETA SCALE -   0.33333335E-01  0.33333335E-01  0.33333335E-01



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00200         6  0.10E-01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE INITIALIZED TO ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL NOT BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE COMPUTED BY FINITE DIFFERENCES.
  E.  FIT IS BY METHOD OF ORTHOGONAL DISTANCE REGRESSION.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.66518379E+02
 SUM OF SQUARED WEIGHTED DELTAS                  0.00000000E+00
 SUM OF SQUARED WEIGHTED EPSILONS                0.66518379E+02





 ITERATION REPORTS FOR FIT BY METHOD OF ODR
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1      19  0.15740E-02   0.1000E+01   0.1000E+01  0.191E+00   YES
    2      25  0.11444E-02   0.2729E+00   0.2732E+00  0.617E-02   YES
    3      31  0.11444E-02  -0.1061E-03   0.2469E-04  0.310E-03   YES







 FINAL SUMMARY FOR FIT BY METHOD OF ODR
 ======================================



 STOPPING CONDITION (INFO =      1):
 -----------------------------------

 THE RELATIVE CHANGE IN THE SUM OF THE SQUARED
 WEIGHTED OBSERVATIONAL ERRORS IS LESS THAN SSTOL

                             CONDITION            
       NUMBER OF  NUMBER OF     NUMBER        RANK
      ITERATIONS   FN EVALS  (INVERSE)  DEFICIENCY
               3         32 0.5373E-02           0



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.11443984E-02
 SUM OF SQUARED WEIGHTED DELTAS                  0.12468603E-03
 SUM OF SQUARED WEIGHTED EPSILONS                0.10197123E-02



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

         INDEX            VALUE -------------->
     1 TO    3   0.27116505E+02  0.33649715E+02  0.66199570E+01



 ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
 ---------------------------------------------------

     I      EPSILON(I)      DELTA(I,1)
     1  0.75111389E-02  0.49383966E-02
     2  0.70571899E-03  0.39525478E-03
     3 -0.69427490E-02 -0.32811370E-02
     4 -0.17114639E-01 -0.70787980E-02
     5 -0.78239441E-02 -0.28610425E-02
     6  0.39176941E-02  0.12926311E-02
     7  0.10875702E-01  0.32408186E-02
     8  0.72460175E-02  0.19693228E-02
     9  0.72288513E-02  0.18037166E-02
    10  0.76141357E-02  0.17569412E-02
    11  0.57239532E-02  0.12277813E-02
    12 -0.66757202E-03 -0.12995179E-03
    13 -0.37670135E-02 -0.69947552E-03
    14 -0.14720917E-01 -0.25836765E-02


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.437148742675781232236431605997E+02 0.114441942423582077026367187500E-02     1

  NEW TEST RESULT      = 
 0.437199287414550763486431605997E+02 0.114439835306257009506225585937E-02     1

  DIFFERENCE           = 
 0.505447387695312500000000000000E-02 0.210711732506752014160156250000E-07     0



 NEW RESULTS AND EXPECTED RESULTS AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULTS.
1EXAMPLE  9

 TEST DETECTION OF QUESTIONABLE ANALYTIC DERIVATIVES FOR OLS PROBLEM
 USING SODRC.
 DATA SET REFERENCE:  POWELL AND MACDONALD, 1972, TABLES 7 & 8, PAGES 153-154                        



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 



 DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF OLS
 ===================================================

                                    *
                          DERIVATIVE 
       DERIVATIVE WRT     ASSESSMENT 

            BETA(  1)    QUESTIONABLE (3)
            BETA(  2)    QUESTIONABLE (3)
            BETA(  3)    QUESTIONABLE (3)

 *
  NUMBERS IN PARENTHESES REFER TO THE FOLLOWING NOTES.

  (3) USER-SUPPLIED AND FINITE DIFFERENCE DERIVATIVES
      DISAGREE, BUT RESULTS ARE QUESTIONABLE BECAUSE
      USER-SUPPLIED DERIVATIVE IS IDENTICALLY ZERO.

 NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS           6

 NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN      
 USER-SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR  
 USER-SUPPLIED DERIVATIVE TO BE CONSIDERED CORRECT       2

 ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED            1

   -VALUES OF THE INDEPENDENT VARIABLES AT THIS ROW

      X( 1, 1)   0.10000000E+01



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 





 INITIAL SUMMARY FOR FIT BY METHOD OF OLS
 ========================================



 PROBLEM SIZE:
 -------------

 NUMBER OF OBSERVATIONS                               14
 NUMBER OF OBSERVATIONS WITH NONZERO WEIGHTS          14
 NUMBER OF COLUMNS OF DATA IN INDEPENDENT VARIABLE     1
 NUMBER OF FUNCTION PARAMETERS                         3
 NUMBER OF UNFIXED FUNCTION PARAMETERS                 3



 INDEPENDENT VARIABLE SUMMARY:
 -----------------------------

                 COLUMN   1     
             OBS 1        OBS N
 X -   0.10000E+01  0.14000E+02



 DEPENDENT VARIABLE AND OBSERVATIONAL ERROR WEIGHT SUMMARY:
 ----------------------------------------------------------

                           OBS 1        OBS N
               Y -   0.26380E+02  0.22220E+02
 OBS. ERROR WTS. -   0.10000E+01  0.10000E+01



 FUNCTION PARAMETER SUMMARY:
 ---------------------------

        INDEX -                1               2               3
 INITIAL BETA -   0.25000000E+02  0.30000000E+02  0.60000000E+01
        FIXED -               NO              NO              NO
   BETA SCALE -   0.33333335E-01  0.33333335E-01  0.33333335E-01



 CONTROL VALUES AND STOPPING CRITERIA:
 --------------------------------------

       *                                     
    JOB    NDIGIT    TAUFAC     SSTOL    PARTOL  MAXIT
  00011         6  0.10E+01  0.49E-03  0.38E-04     50

 *
  A.  FIT IS NOT A RESTART.
  B.  DELTAS ARE FIXED AT ZERO.
  C.  THE COVARIANCE MATRIX OF THE PARAMETER ESTIMATORS
      WILL BE COMPUTED AT THE SOLUTION.
  D.  DERIVATIVES ARE SUPPLIED BY USER.
      USER-SUPPLIED DERIVATIVES WERE CHECKED.
      THE CORRECTNESS OF SOME OF THE DERIVATIVES IS
      QUESTIONABLE.  SEE ERROR MESSAGES FOR DETAILS.
  E.  FIT IS BY METHOD OF ORDINARY LEAST SQUARES.



 INITIAL SUMS OF SQUARES:
 ------------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.66518379E+02





 ITERATION REPORTS FOR FIT BY METHOD OF OLS
 ==========================================


         CUM.                 ACT. REL.   PRED. REL.
  IT.  NO. FN     WEIGHTED   SUM-OF-SQS   SUM-OF-SQS              G-N
 NUM.   EVALS   SUM-OF-SQS    REDUCTION    REDUCTION  TAU/PNORM  STEP
 ----  ------  -----------  -----------  -----------  ---------  ----

    1      14  0.66518E+02   0.0000E+00   0.0000E+00  0.000E+00   YES







 FINAL SUMMARY FOR FIT BY METHOD OF OLS
 ======================================



 STOPPING CONDITION (INFO =   1023):
 -----------------------------------

 THE RELATIVE CHANGE IN THE SUM OF THE SQUARED
 WEIGHTED OBSERVATIONAL ERRORS IS LESS THAN SSTOL
 AND
 THE RELATIVE CHANGE IN THE NORM OF BETA AND DELTA
 IS LESS THAN PARTOL

 NOTE:

 THE RESULTS FROM ODRPACK ARE QUESTIONABLE BECAUSE

 THE ODRPACK JACOBIAN MATRIX CHECKING PROCEDURE HAS  
 DETERMINED THAT THE CORRECTNESS OF THE USER-SUPPLIED
 JACOBIAN MATRICES IS QUESTIONABLE, AND

 THE RESULTS OF THE MODEL FUNCTION AND/OR ITS        
 DERIVATIVES ARE UNAFFECTED BY CHANGES IN THE UNFIXED
 FUNCTION PARAMETERS (BETA), INDICATING A PROBABLE   
 ERROR IN USER-SUPPLIED SUBROUTINES FUN AND/OR JAC.


                                       CONDITION            
       NUMBER OF  NUMBER OF  NUMBER OF    NUMBER        RANK
      ITERATIONS   FN EVALS  JAC EVALS (INVERSE)  DEFICIENCY
               1         15          2 0.0000E+00           3



 FINAL SUMS OF SQUARES:
 ----------------------

 SUM OF SQUARED WEIGHTED OBSERVATIONAL ERRORS    0.66518379E+02



 ESTIMATED BETA(J), J = 1, ..., NP:
 ----------------------------------

 N.B. STANDARD ERRORS OF THE ESTIMATED BETAS WERE NOT
      COMPUTED BECAUSE EITHER THE JACOBIAN IS NOT FULL
      RANK AT THE SOLUTION, OR THE MOST RECENTLY TRIED
      VALUES OF BETA AND/OR X+DELTA WERE UNACCEPTABLE.

         INDEX            VALUE -------------->
     1 TO    3   0.25000000E+02  0.30000000E+02  0.60000000E+01



 ESTIMATED EPSILON(I), I = 1, ..., N:
 ------------------------------------

         INDEX            VALUE -------------->
     1 TO    4  -0.21282463E+01 -0.21533833E+01 -0.21736107E+01 -0.21929722E+01
     5 TO    8  -0.21875305E+01 -0.21785355E+01 -0.21741447E+01 -0.21804619E+01
     9 TO   12  -0.21821671E+01 -0.21829205E+01 -0.21856384E+01 -0.21926785E+01
    13 TO   14  -0.21959724E+01 -0.22071266E+01


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.395094909667968750000000000000E+02 0.665183868408203160527136788005E+02  1023

  NEW TEST RESULT      = 
 0.395094909667968750000000000000E+02 0.665183792114257776972863211994E+02  1023

  DIFFERENCE           = 
 0.000000000000000000000000000000E+00 0.762939453125000000000000000000E-05     0



 NEW RESULTS AND EXPECTED RESULTS AGREE TO WITHIN STOPPING TOLERANCE
 OF NEW RESULTS.
1EXAMPLE 10

 TEST DETECTION OF INCORRECT ANALYTIC DERIVATIVES FOR ODR PROBLEM
 WITH ANALYTIC DERIVATIVES USING SODRC.
 DATA SET REFERENCE:  POWELL AND MACDONALD, 1972, TABLES 7 & 8, PAGES 153-154                        



 ******************************************************* 
 * ODRPACK VERSION 1.71 OF 07-27-89 (SINGLE PRECISION) * 
 ******************************************************* 



 DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF ODR
 ===================================================

                                    *
                          DERIVATIVE 
       DERIVATIVE WRT     ASSESSMENT 

            BETA(  1)    QUESTIONABLE (3)
            BETA(  2)    QUESTIONABLE (3)
            BETA(  3)    QUESTIONABLE (3)
             X( 1, 1)      INCORRECT  

 *
  NUMBERS IN PARENTHESES REFER TO THE FOLLOWING NOTES.

  (3) USER-SUPPLIED AND FINITE DIFFERENCE DERIVATIVES
      DISAGREE, BUT RESULTS ARE QUESTIONABLE BECAUSE
      USER-SUPPLIED DERIVATIVE IS IDENTICALLY ZERO.

 NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS           6

 NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN      
 USER-SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR  
 USER-SUPPLIED DERIVATIVE TO BE CONSIDERED CORRECT       2

 ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED            1

   -VALUES OF THE INDEPENDENT VARIABLES AT THIS ROW

      X( 1, 1)   0.10000000E+01


 *** COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CDC CYBER 205 RESULT ***

                         NORM OF BETA        SUM OF SQUARED WTD OBS ERRORS  INFO

  CDC CYBER 205 RESULT = 
 0.395094909667968750000000000000E+02 0.665183868408203160527136788005E+02 40100

  NEW TEST RESULT      = 
 0.395094909667968750000000000000E+02 0.665183792114257776972863211994E+02 40100

  DIFFERENCE           = 
 0.000000000000000000000000000000E+00 0.762939453125000000000000000000E-05     0



 NEW STOPPING CONDITION AND EXPECTED STOPPING CONDITION AGREE,
 BUT INDICATE CONVERGENCE WAS NOT ATTAINED.
 NO FURTHER COMPARISONS WILL BE MADE BETWEEN NEW AND EXPECTED RESULTS.
