1*******************************************************************************************************************    PROBLEM   1
0(3) J. M. CAMERON DATA, UNEQUAL WEIGHTS, TWO COLUMNS LINEARLY DEPENDENT.        
0   M    N   M1    L     ITYPE     IWGHT      MODE       TOL
    7    6    0    2         2         2         2  0.0000000    
0FORMAT (2F3.0,F3.1,F3.0,F4.2,F3.0,F5.1,F4.0,F2.0)                                      
0MATRIX A, MATRIX B AND VECTOR OF WEIGHTS

   1.0000000      1.0000000     0.50000000      2.0000000     0.25000000      2.0000000      13.000000      130.00000    
   2.0000000    
   1.0000000      2.0000000     0.50000000      2.0000000     0.25000000      3.0000000      17.000000      170.00000    
   2.0000000    
   0.0000000      3.0000000      0.0000000      3.0000000      0.0000000      3.0000000      18.200001      182.00000    
   1.0000000    
   0.0000000      2.0000000      0.0000000      1.0000000      0.0000000      1.0000000      8.8000002      88.000000    
   1.0000000    
   0.0000000      1.0000000      0.0000000     -3.0000000      0.0000000      0.0000000     -3.0000000     -30.000000    
   1.0000000    
   0.0000000      1.0000000      0.0000000      0.0000000      0.0000000      0.0000000      2.8000000      28.000000    
   1.0000000    
   0.0000000      0.0000000      0.0000000      1.0000000      0.0000000      0.0000000      2.0999999      21.000000    
   1.0000000    
0COMPUTED RESULTS
0MODE =   2     IFAULT =   0
0N1 = COMPUTED RANK OF SYSTEM OF EQUATIONS =   4
0COLUMNS OF H = (SQRT(W))*A WERE SELECTED BY THE PIVOTING SCHEME IN THE FOLLOWING ORDER

   4   2   6   1
0THE FOLLOWING COLUMNS OF H ARE LINEARLY DEPENDENT.  IF MODE 1, THEY DID NOT ENTER THE REGRESSION.
 IF MODE 2, THEY ENTERED LAST.

   5   3
0NUMBER OF ZERO WEIGHTS =  0     DEG. OF FREEDOM =  3
0               REPORT ON            NUMBER OF    ESTIMATED NUMBER OF CORRECT
 B-VECTOR NO.   CONVERGENCE          ITERATIONS   DIGITS IN INITIAL SOLUTION

      1         CONVERGED                2.            6.5852823    
      2         CONVERGED                2.            6.8344755    
0SOLUTION FOR B-VECTOR NO.  1
0    J    COEFFICIENT(J)

     1    2.7952375    
     2    2.8125000    
     3    1.3976188    
     4    1.9625000    
     5   0.69880939    
     6    1.2750002    
0    I    OBSERVED(I)         PREDICTED(I)          RESIDUAL(I)

     1    13.000000            12.956250           0.43750111E-01
     2    17.000000            17.043751          -0.43750111E-01
     3    18.200001            18.150002           0.50000075E-01
     4    8.8000002            8.8625002          -0.62500015E-01
     5   -3.0000000           -3.0750000           0.75000040E-01
     6    2.8000000            2.8125000          -0.12500024E-01
     7    2.0999999            1.9625000           0.13749990    
0SUM OF SQUARED RESIDUALS    = 0.38750026E-01
 NORM OF RESIDUALS           = 0.19685027    
0SOLUTION FOR B-VECTOR NO.  2
0    J    COEFFICIENT(J)

     1    27.952381    
     2    28.125000    
     3    13.976191    
     4    19.625000    
     5    6.9880953    
     6    12.750000    
0    I    OBSERVED(I)         PREDICTED(I)          RESIDUAL(I)

     1    130.00000            129.56250           0.43750003    
     2    170.00000            170.43750          -0.43750000    
     3    182.00000            181.50000           0.50000000    
     4    88.000000            88.625000          -0.62500000    
     5   -30.000000           -30.750000           0.75000000    
     6    28.000000            28.125000          -0.12499999    
     7    21.000000            19.625000            1.3750000    
0SUM OF SQUARED RESIDUALS    =  3.8750000    
 NORM OF RESIDUALS           =  1.9685019    
1*******************************************************************************************************************    PROBLEM   2
0(9) ALBERT, REGRESSION AND THE MOORE-PENROSE INVERSE, 1972, P. 63.              
0   M    N   M1    L     ITYPE     IWGHT      MODE       TOL
    3    4    0    3         2         1         2  0.0000000    
0FORMAT (7F4.0)                                                                         
0MATRIX A, MATRIX B AND VECTOR OF WEIGHTS

   1.0000000      0.0000000      1.0000000      1.0000000      1.0000000      0.0000000      0.0000000      1.0000000    
   0.0000000      1.0000000     -1.0000000      0.0000000      0.0000000      1.0000000      0.0000000      1.0000000    
   1.0000000      1.0000000      0.0000000      1.0000000      0.0000000      0.0000000      1.0000000      1.0000000    
0COMPUTED RESULTS
0MODE =   2     IFAULT =   0
0N1 = COMPUTED RANK OF SYSTEM OF EQUATIONS =   2
0COLUMNS OF H = (SQRT(W))*A WERE SELECTED BY THE PIVOTING SCHEME IN THE FOLLOWING ORDER

   1   2
0THE FOLLOWING COLUMNS OF H ARE LINEARLY DEPENDENT.  IF MODE 1, THEY DID NOT ENTER THE REGRESSION.
 IF MODE 2, THEY ENTERED LAST.

   3   4
0NUMBER OF ZERO WEIGHTS =  0     DEG. OF FREEDOM =  1
0               REPORT ON            NUMBER OF    ESTIMATED NUMBER OF CORRECT
 B-VECTOR NO.   CONVERGENCE          ITERATIONS   DIGITS IN INITIAL SOLUTION

      1         CONVERGED                1.            6.9236898    
      2         CONVERGED                1.            6.9236898    
      3         CONVERGED                1.            6.9236898    
0SOLUTION FOR B-VECTOR NO.  1
0    J    COEFFICIENT(J)

     1   0.20000000    
     2  -0.66666678E-01
     3   0.26666665    
     4   0.20000002    
0    I    OBSERVED(I)         PREDICTED(I)          RESIDUAL(I)

     1    1.0000000           0.66666669           0.33333331    
     2    0.0000000          -0.33333334           0.33333334    
     3    0.0000000           0.33333331          -0.33333331    
0SUM OF SQUARED RESIDUALS    = 0.33333331    
 NORM OF RESIDUALS           = 0.57735026    
0SOLUTION FOR B-VECTOR NO.  2
0    J    COEFFICIENT(J)

     1    0.0000000    
     2   0.33333334    
     3  -0.33333334    
     4    0.0000000    
0    I    OBSERVED(I)         PREDICTED(I)          RESIDUAL(I)

     1    0.0000000          -0.33333334           0.33333334    
     2    1.0000000           0.66666669           0.33333331    
     3    0.0000000           0.33333334          -0.33333334    
0SUM OF SQUARED RESIDUALS    = 0.33333331    
 NORM OF RESIDUALS           = 0.57735026    
0SOLUTION FOR B-VECTOR NO.  3
0    J    COEFFICIENT(J)

     1   0.20000000    
     2   0.26666668    
     3  -0.66666670E-01
     4   0.19999999    
0    I    OBSERVED(I)         PREDICTED(I)          RESIDUAL(I)

     1    0.0000000           0.33333331          -0.33333331    
     2    0.0000000           0.33333334          -0.33333334    
     3    1.0000000           0.66666669           0.33333331    
0SUM OF SQUARED RESIDUALS    = 0.33333331    
 NORM OF RESIDUALS           = 0.57735026    
1*******************************************************************************************************************    PROBLEM   3
0(12) LAWSON-HANSON, SOLVING LEAST SQUARES PROBLEMS, P.252, SET 1, EX.16, TOL=.5.
0   M    N   M1    L     ITYPE     IWGHT      MODE       TOL
    8    6    4    1         2         1         2 0.50000000    
0FORMAT (7F6.0)                                                                         
0MATRIX A, MATRIX B AND VECTOR OF WEIGHTS

   155.00000      105.00000     -445.00000     -495.00000     -45.000000     -95.000000     -245.00000      1.0000000    
   355.00000      305.00000     -245.00000     -295.00000      155.00000      105.00000     -295.00000      1.0000000    
  -445.00000     -495.00000     -45.000000     -95.000000      355.00000      305.00000      155.00000      1.0000000    
  -245.00000     -295.00000      155.00000      105.00000     -445.00000     -495.00000      105.00000      1.0000000    
  -45.000000     -95.000000      355.00000      305.00000     -245.00000     -295.00000     -445.00000      1.0000000    
   155.00000      105.00000     -445.00000     -495.00000     -45.000000     -95.000000     -495.00000      1.0000000    
   355.00000      305.00000     -245.00000     -295.00000      155.00000      105.00000     -45.000000      1.0000000    
  -445.00000     -495.00000     -45.000000     -95.000000      355.00000      305.00000     -95.000000      1.0000000    
0COMPUTED RESULTS
0MODE =   2     IFAULT =   0
0N1 = COMPUTED RANK OF SYSTEM OF EQUATIONS =   4
0COLUMNS OF H = (SQRT(W))*A WERE SELECTED BY THE PIVOTING SCHEME IN THE FOLLOWING ORDER

   2   6   4   1
0THE FOLLOWING COLUMNS OF H ARE LINEARLY DEPENDENT.  IF MODE 1, THEY DID NOT ENTER THE REGRESSION.
 IF MODE 2, THEY ENTERED LAST.

   5   3
0NUMBER OF ZERO WEIGHTS =  0     DEG. OF FREEDOM =  4
0               REPORT ON            NUMBER OF    ESTIMATED NUMBER OF CORRECT
 B-VECTOR NO.   CONVERGENCE          ITERATIONS   DIGITS IN INITIAL SOLUTION

      1         CONVERGED                2.            6.5333591    
0SOLUTION FOR B-VECTOR NO.  1
0    J    COEFFICIENT(J)

     1  -0.66666669    
     2   0.16666667    
     3  -0.29166666    
     4   0.54166669    
     5  -0.41666666    
     6   0.41666666    
0    I    OBSERVED(I)         PREDICTED(I)          RESIDUAL(I)

     1   -245.00000           -245.00000            0.0000000    
     2   -295.00000           -295.00000            0.0000000    
     3    155.00000            155.00000            0.0000000    
     4    105.00000            105.00000            0.0000000    
     5   -445.00000            55.000000           -500.00000    
     6   -495.00000           -245.00000           -250.00000    
     7   -45.000000           -295.00000            250.00000    
     8   -95.000000            155.00000           -250.00000    
0SUM OF SQUARED RESIDUALS    =  437500.00    
 NORM OF RESIDUALS           =  661.43781    
1*******************************************************************************************************************    PROBLEM   4
0(14) LAWSON-HANSON, SOLVING LEAST SQUARES PROBLEMS, 1974, SET 1, EX.12. IFAULT=7
0   M    N   M1    L     ITYPE     IWGHT      MODE       TOL
    6    8    6    1         2         1         2  0.0000000    
0FORMAT (9F6.0)                                                                         
0MATRIX A, MATRIX B AND VECTOR OF WEIGHTS

  -245.00000     -295.00000      155.00000      105.00000     -445.00000     -495.00000     -45.000000     -95.000000    
   355.00000      1.0000000    
   355.00000      305.00000     -245.00000     -295.00000      155.00000      105.00000     -445.00000     -495.00000    
   305.00000      1.0000000    
  -45.000000     -95.000000      355.00000      305.00000     -245.00000     -295.00000      155.00000      105.00000    
  -245.00000      1.0000000    
  -445.00000     -495.00000     -45.000000     -95.000000      355.00000      305.00000     -245.00000     -295.00000    
  -295.00000      1.0000000    
   155.00000      105.00000     -445.00000     -495.00000     -45.000000     -95.000000      355.00000      305.00000    
   155.00000      1.0000000    
  -245.00000     -295.00000      155.00000      105.00000     -445.00000     -495.00000     -45.000000     -95.000000    
   105.00000      1.0000000    
0***  FOR B-VECTOR NO.  1 SOLUTION FAILED TO CONVERGE.
0***  ALL SOLUTIONS FAILED TO CONVERGE.
0COMPUTED RESULTS
0MODE =   2     IFAULT =   7
0N1 = COMPUTED RANK OF SYSTEM OF EQUATIONS =   6
0COLUMNS OF H = (SQRT(W))*A WERE SELECTED BY THE PIVOTING SCHEME IN THE FOLLOWING ORDER

   6   2   8   4   3   7
0THE FOLLOWING COLUMNS OF H ARE LINEARLY DEPENDENT.  IF MODE 1, THEY DID NOT ENTER THE REGRESSION.
 IF MODE 2, THEY ENTERED LAST.

   1   5
0NUMBER OF ZERO WEIGHTS =  0     DEG. OF FREEDOM =  0
0               REPORT ON            NUMBER OF    ESTIMATED NUMBER OF CORRECT
 B-VECTOR NO.   CONVERGENCE          ITERATIONS   DIGITS IN INITIAL SOLUTION

      1         FAILED TO CONVERGE       2.            1.6457564    
