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bvls_prb_output.txt
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1 January 2011 10:43:29.908 AM
BVLS_PRB
Test driver for BVLS
Bounded Variables Least Squares.
If the algorithm succeeds the solution vector, X(),
and the dual vector, W(), should be related as follows:
X(i) not at a bound => W(i) = 0
X(i) at its lower bound => W(i) <= 0
X(i) at its upper bound => 0 <= W(i)
except that if an upper bound and lower bound are equal, then
the corresponding X(i) must take that value and W(i) may have
any value.
----------
Case 1
----------
M = 2, N = 2, UNBND = 0.10000E+07
Bounds:
1.00000 3.00000
2.00000 4.00000
Matrix A:
0.965915 0.367391
0.747928 0.480637
RHS B:
0.997560 0.566825
After BVLS: No. of components not at constraints = 0
Solution vector, X:
1.00000 3.00000
R = B - A*X Computed by the driver:
-1.07053 -1.62301
RNORM2 computed by the driver = 1.9443
RNORM computed by BVLS = 1.9443
W = (A**T)*R Computed by the driver:
-2.24794 -1.17338
Dual vector from BVLS, W() =
-2.24794 -1.17338
----------
Case 2
----------
M = 2, N = 4, UNBND = 0.10000E+07
Bounds:
0.00000 0.00000 0.00000 0.00000
10.0000 10.0000 10.0000 10.0000
Matrix A:
0.347081 0.217952 0.900524 0.445482
0.342244 0.133160 0.386766 0.661932
RHS B:
0.737543E-01 0.535518E-02
After BVLS: No. of components not at constraints = 1
Solution vector, X:
0.00000 0.00000 0.713028E-01 0.00000
R = B - A*X Computed by the driver:
0.954429E-02 -0.222223E-01
RNORM2 computed by the driver = 0.24185E-01
RNORM computed by BVLS = 0.24185E-01
W = (A**T)*R Computed by the driver:
-0.429281E-02 -0.878939E-03 0.251457E-07 -0.104579E-01
Dual vector from BVLS, W() =
-0.429282E-02 -0.878946E-03 0.00000 -0.104579E-01
----------
Case 3
----------
M = 4, N = 2, UNBND = 0.10000E+07
Bounds:
0.00000 -100.000
100.000 100.000
Matrix A:
0.855692 0.598400
0.401287 0.672981
0.206874 0.456882
0.968539 0.330015
RHS B:
0.161083E-01 0.650855 0.646409 0.322987
After BVLS: No. of components not at constraints = 1
Solution vector, X:
0.00000 0.752745
R = B - A*X Computed by the driver:
-0.434334 0.144272 0.302493 0.745701E-01
RNORM2 computed by the driver = 0.55365
RNORM computed by BVLS = 0.55365
W = (A**T)*R Computed by the driver:
-0.178959 0.238419E-06
Dual vector from BVLS, W() =
-0.178960 0.00000
----------
Case 4
----------
M = 5, N = 10, UNBND = 0.10000E+07
Bounds:
0.00000 -0.399400 -1.00000 -0.300000 21.0000
0.00000 -0.399400 1.00000 -0.200000 22.0000
-4.00000 45.0000 100.000 -0.340282E+39 -1.00000
-3.00000 46.0000 101.000 0.340282E+39 1.00000
Matrix A:
0.658229 0.256798 0.901923 0.147835 0.614369
0.150717 0.550865 0.657925 0.674529 0.820617
0.612315 0.659047 0.728858 0.769614 0.947095
0.978660 0.554005 0.402455 0.339323 0.731129
0.999142 0.977760 0.928628 0.115819 0.497604
0.374802 0.746310 0.946848 0.480381 0.885878
0.421506 0.953759 0.706176 0.597690 0.303810
0.552903 0.932747E-01 0.813810 0.137532 0.669657
0.997919 0.734024 0.558594 0.587395 0.664940
0.990395 0.751762 0.617055E-01 0.519968 0.503677
RHS B:
0.100383 0.755453 0.605693 0.719048 0.897335
After BVLS: No. of components not at constraints = 1
Solution vector, X:
0.00000 -0.399400 -1.00000 -0.300000 21.0000
-3.00000 46.0000 100.000 -196.029 -1.00000
R = B - A*X Computed by the driver:
-44.5885 -11.1546 -74.4433 15.2718 56.4539
RNORM2 computed by the driver = 105.24
RNORM computed by BVLS = 105.24
W = (A**T)*R Computed by the driver:
-5.26195 -2.99752 -43.2420 -59.6880 -67.7949
8.57821 2.79044 -98.6641 0.419617E-04 -54.1510
Dual vector from BVLS, W() =
0.00000 0.00000 -43.2422 -59.6880 -67.7951
8.57813 2.79037 -98.6642 0.00000 -54.1511
----------
Case 5
----------
M = 10, N = 5, UNBND = 0.10000E+07
Bounds:
0.00000 -1.00000 0.00000 0.300000 0.480000E-01
1.00000 0.00000 1.00000 0.400000 0.490000E-01
Matrix A:
0.114244 0.208368 0.839778 0.665485 0.937705
0.318463 0.566998 0.678489 0.730737 0.456104
0.596820 0.243124E-01 0.581951 0.410604 0.808489
0.481529E-01 0.420291 0.733526 0.355722 0.908848
0.114206 0.397853 0.116043 0.735377 0.694877
0.215965 0.976585 0.840300 0.471318 0.219489
0.100573 0.692605 0.834996 0.462625 0.854955
0.733418E-01 0.494331E-02 0.746536 0.759692 0.744397
0.246862 0.129921 0.843201 0.702459 0.301113
0.443384 0.467772E-01 0.528839 0.257966 0.671969
RHS B:
0.261575 0.765595E-01 0.101250 0.549266 0.375585
0.151495E-01 0.792915 0.620878 0.773604 0.953581
After BVLS: No. of components not at constraints = 2
Solution vector, X:
0.00000 -0.352785 0.521598 0.300000 0.490000E-01
R = B - A*X Computed by the driver:
-0.348535 -0.318880 -0.356515 0.163682 0.200752
-0.230774 0.421044 -0.311532E-01 0.154134 0.583926
RNORM2 computed by the driver = 1.0068
RNORM computed by BVLS = 1.0068
W = (A**T)*R Computed by the driver:
-0.361610E-01 -0.139698E-06 -0.327826E-06 -0.842390E-01 0.252678
Dual vector from BVLS, W() =
-0.361609E-01 0.00000 0.00000 -0.842387E-01 0.252678
----------
Case 6
----------
M = 6, N = 4, UNBND = 999.00
Bounds:
-100.000 -0.340282E+39 -0.340282E+39 -0.340282E+39
100.000 0.340282E+39 0.340282E+39 0.340282E+39
Matrix A:
0.930943 0.356858 0.199921 0.845821
0.546529 0.665676 0.415428 0.709033
0.465513 0.618549 0.979303 0.528973
0.176914 0.468947 0.543212 0.663841
0.377994 0.316252 0.129518 0.900739
0.175221 0.268880 0.804742 0.941164
RHS B:
0.618714 0.967574 0.990239 0.338006 0.920767
0.339073
After BVLS: No. of components not at constraints = 4
Solution vector, X:
0.224131 1.24988 -0.189694 0.173490
R = B - A*X Computed by the driver:
-0.144789 -0.311455E-01 0.206784 -0.299901 0.309068
-0.468961E-01
RNORM2 computed by the driver = 0.50235
RNORM computed by BVLS = 0.50235
W = (A**T)*R Computed by the driver:
0.327826E-06 0.361353E-06 0.379980E-06 0.543892E-06
Dual vector from BVLS, W() =
0.00000 0.00000 0.00000 0.00000
BVLS_PRB:
Normal end of execution.
1 January 2011 10:43:29.926 AM