
     X-F-W Data supply for smoothing from datafile  "XFWDAT" .

     Just below, input number of monotonic sections < 16


     (First monotonic section is required to be decreasing.)


     -----------------------------------------
     RETURN FROM L2WPMA WITH MODE =     1
     NUMBER OF DATA (F)           =    40
     NUMBER OF MONOTONIC SECTIONS =     4
     NUMBER OF LOCAL MINIMA IN F  =    13
     NUMBER OF LOCAL MAXIMA IN F  =    12
     -----------------------------------------


     -------------------------------------------------
     Best piecewise monotonic approximation to the data
     from file "XFWDAT" is now kept in file ..."WPMAPP".

     Indices of extrema of best approximation are now
     kept in file ............................"WIVAPP".

     Indices of spline representation of best apprxmtn
     are now kept in file ....................."WIAKN".

     Indices of active constraints of best apprxtn and 
     Lagrange multipliers are now kept in file "WACTLG".
     --------------------------------------------------


            INDICES OF EXTREMA AT OPTIMUM
            Increment      Data index
            (J)            (ITHETA)
                0                1
                1                6
                2               18
                3               35
                4               40


            INDICES OF ACTIVE CONSTRAINTS AT OPTIMUM
            Increment      Active constraint      Lagrange mult
            (I)            (IACT)                 (PAR(IACT))
                1                2                 -0.5490
                2                3                 -0.3858
                3                5                 -0.2187
                4                9                  0.6737
                5               10                  0.0652
                6               11                  0.0189
                7               16                  0.3702
                8               17                  0.2661
                9               20                 -0.0421
               10               22                 -0.4326
               11               23                 -0.8780
               12               24                 -0.6364
               13               26                 -0.0756
               14               28                 -0.3870
               15               29                 -0.0659
               16               31                 -0.1019
               17               33                 -0.0486


            INDICES OF KNOTS AT OPTIMUM
            Increment      Knot index
            (I)            (IAKN)
                1                1
                2                4
                3                6
                4                7
                5                8
                6               12
                7               13
                8               14
                9               15
               10               18
               11               19
               12               21
               13               25
               14               27
               15               30
               16               32
               17               34
               18               35
               19               36
               20               37
               21               38
               22               39
               23               40


       Data points  Measurements  Data weights  Best appxmtn  Lagrange mult
       (X)          (F)           (WF)          (Y)           (PAR)

    1   1.57079637  -0.49998477   1.00000000  -0.22548611
    2   1.81245732  -0.14387816   1.00000000  -0.22548611    -0.54899728
    3   2.05411839  -0.03259540   1.00000000  -0.22548611    -0.38578138
    4   2.29577947  -0.85495162   1.00000000  -0.74560165     0.00000000
    5   2.53744054  -0.63625175   1.00000000  -0.74560165    -0.21869993
    6   2.77910161  -1.37578082   1.00000000  -1.37578082     0.00000000
    7   3.02076268  -1.16831732   1.00000000  -1.16831732     0.00000000
    8   3.26242375  -0.49757642   1.00000000  -0.83444482     0.00000000
    9   3.50408483  -1.13873148   1.00000000  -0.83444482     0.67373657
   10   3.74574590  -0.85755271   1.00000000  -0.83444482     0.06516325
   11   3.98740697  -0.84391856   1.00000000  -0.83444482     0.01894748
   12   4.22906780  -0.56682825   1.00000000  -0.56682825     0.00000000
   13   4.47072887  -0.48874643   1.00000000  -0.48874643     0.00000000
   14   4.71238995   0.17338158   1.00000000   0.17338158     0.00000000
   15   4.95405102   0.70275611   1.00000000   0.51764011     0.00000000
   16   5.19571209   0.46558633   1.00000000   0.51764011     0.37023216
   17   5.43737316   0.38457781   1.00000000   0.51764011     0.26612461
   18   5.67903423   1.11544669   1.00000000   1.11544669     0.00000000
   19   5.92069530   0.98896503   1.00000000   1.01003671     0.00000000
   20   6.16235638   1.03110838   1.00000000   1.01003671    -0.04214334
   21   6.40401745   0.62352431   1.00000000   0.83980024     0.00000000
   22   6.64567852   0.61705577   1.00000000   0.83980024    -0.43255186
   23   6.88733959   0.96061152   1.00000000   0.83980024    -0.87804079
   24   7.12900066   1.15800953   1.00000000   0.83980024    -0.63641822
   25   7.37066174   0.11525160   1.00000000   0.15303981     0.00000000
   26   7.61232281   0.19082803   1.00000000   0.15303981    -0.07557642
   27   7.85398388  -0.48866478   1.00000000  -0.29518130     0.00000000
   28   8.09564495  -0.13463341   1.00000000  -0.29518130    -0.38696694
   29   8.33730602  -0.26224574   1.00000000  -0.29518130    -0.06587115
   30   8.57896709  -0.70288193   1.00000000  -0.65194333     0.00000000
   31   8.82062817  -0.60100472   1.00000000  -0.65194333    -0.10187721
   32   9.06228924  -1.08283901   1.00000000  -1.05851495     0.00000000
   33   9.30395031  -1.03419089   1.00000000  -1.05851495    -0.04864812
   34   9.54561138  -1.17510724   1.00000000  -1.17510724     0.00000000
   35   9.78727245  -1.36862314   1.00000000  -1.36862314     0.00000000
   36  10.02893353  -0.85123414   1.00000000  -0.85123414     0.00000000
   37  10.27059460  -0.82258469   1.00000000  -0.82258469     0.00000000
   38  10.51225567  -0.58174932   1.00000000  -0.58174932     0.00000000
   39  10.75391674  -0.14782690   1.00000000  -0.14782690     0.00000000
   40  10.99557495  -0.05223861   1.00000000  -0.05223861     0.00000000

  Value of objective function at the optimum=    0.6911643744E+00
