Fri Aug 12 23:59:25 2022

r8ge_test
  Python version: 3.6.9
  Test r8ge().

i4_log_10_test
  Python version: 3.6.9
  i4_log_10: whole part of log base 10,

  X, i4_log_10

     0             0
     1             0
     2             0
     3             0
     9             0
    10             1
    11             1
    99             1
   101             2
    -1             0
    -2             0
    -3             0
    -9             0

r8_sign_test
  Python version: 3.6.9
  r8_sign returns the sign of an R8.

     R8     r8_sign(R8)

   -1.2500        -1
   -0.2500        -1
    0.0000         1
    0.5000         1
    9.0000         1

r8ge_cg_test
  r8ge_cg applies CG to an R8GE matrix.

  Number of variables N = 10
  Norm of residual ||Ax-b|| = 3.66744e-16
  Norm of error ||x1-x2|| = 3.81861e-15

r8ge_co_test
  Python version: 3.6.9
  r8ge_co estimates the condition number of an R8GE matrix.

  Matrix order N = 4

  The L1 condition number is 10

  The r8ge_co estimate is 7

r8ge_det_test
  Python version: 3.6.9
  r8ge_det computes the determinant of an R8GE matrix.

  r8ge_det computes the determinant = 112
  Exact determinant =                 112

r8ge_dif2_test
  Python version: 3.6.9
  r8ge_dif2 returns the second difference matrix.

  DIF2 matrix:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           2  
          -1  
           0  
           0  

      1 :
          -1  
           2  
          -1  
           0  

      2 :
           0  
          -1  
           2  
          -1  

      3 :
           0  
           0  
          -1  
           2  

      4 :
           0  
           0  
           0  
          -1  


r8ge_dilu_test
  Python version: 3.6.9
  r8ge_dilu returns the DILU factors of an R8GE matrix.

  Matrix rows M =    9
  Matrix columns N = 9

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           4  
          -1  
           0  
          -1  
           0  

      1 :
          -1  
           4  
          -1  
           0  
          -1  

      2 :
           0  
          -1  
           4  
          -1  
           0  

      3 :
          -1  
           0  
          -1  
           4  
          -1  

      4 :
           0  
          -1  
           0  
          -1  
           4  

      5 :
           0  
           0  
          -1  
           0  
          -1  

      6 :
           0  
           0  
           0  
          -1  
           0  

      7 :
           0  
           0  
           0  
           0  
          -1  

      8 :
           0  
           0  
           0  
           0  
           0  


  Col: 
      5       
      6       
      7       
      8       

  Row
      0 :
           0  
           0  
           0  
           0  

      1 :
           0  
           0  
           0  
           0  

      2 :
          -1  
           0  
           0  
           0  

      3 :
           0  
          -1  
           0  
           0  

      4 :
          -1  
           0  
          -1  
           0  

      5 :
           4  
          -1  
           0  
          -1  

      6 :
          -1  
           4  
          -1  
           0  

      7 :
           0  
          -1  
           4  
          -1  

      8 :
          -1  
           0  
          -1  
           4  


  DILU factor:

     0:          0.25
     1:      0.266667
     2:      0.267857
     3:      0.287179
     4:      0.290179
     5:      0.290532
     6:      0.292202
     7:      0.292601
     8:      0.292666

r8ge_fa_test01
  Python version: 3.6.9
  r8ge_fa computes the LU factors of an R8GE matrix,
  r8ge_sl solves a factored R8GE system.

  Matrix order N = 10

  Solution:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10

  Solution:

     0:             1
     1:             1
     2:             1
     3:             1
     4:             1
     5:             1
     6:             1
     7:             1
     8:             1
     9:             1

  Solution of transposed system:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10

r8ge_fa_test02
  Python version: 3.6.9
  r8ge_fa computes the LU factors of an R8GE system,
  r8ge_sl solves a factored R8GE system.

  Matrix order N = 5

  The matrix:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.965717  
    0.953127  
    0.564809  
    0.411787  
    0.643371  

      1 :
    0.211463  
    0.741199  
    0.399248  
    0.852898  
    0.165694  

      2 :
   0.0485188  
    0.960416  
    0.849691  
    0.329799  
    0.362096  

      3 :
    0.571306  
    0.399714  
    0.884881  
    0.932222  
    0.956106  

      4 :
   0.0322117  
    0.636241  
    0.407786  
    0.167298  
    0.498778  


  The compressed LU factors:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.965717  
    0.953127  
    0.564809  
    0.411787  
    0.643371  

      1 :
    -0.21897  
     0.91253  
    0.821315  
     0.30911  
    0.329773  

      2 :
  -0.0502412  
   -0.583535  
    0.698484  
    0.744216  
    0.634815  

      3 :
   -0.591587  
    0.179878  
    0.291623  
    0.799383  
    0.017508  

      4 :
  -0.0333552  
   -0.662388  
    0.222027  
    -0.14267  
    0.397329  


  The pivot vector P:

     0       0
     1       2
     2       3
     3       3
     4       4

  Solution:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5

r8ge_fs_test
  Python version: 3.6.9
  r8ge_fs factors and solves a linear system involving
  an R8GE matrix.

  Matrix order N = 10

  Solution:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10

r8ge_fss_test
  Python version: 3.6.9
  r8ge_fss factors and solves multiple linear systems
  associated with an R8GE matrix.

  Matrix order N = 10

  Solution:

  Col: 
      0       
      1       
      2       

  Row
      0 :
           1  
           1  
           1  

      1 :
           1  
           2  
           2  

      2 :
           1  
           3  
           3  

      3 :
           1  
           4  
           1  

      4 :
           1  
           5  
           2  

      5 :
           1  
           6  
           3  

      6 :
           1  
           7  
           1  

      7 :
           1  
           8  
           2  

      8 :
           1  
           9  
           3  

      9 :
           1  
          10  
           1  


r8ge_hilbert_test
  Python version: 3.6.9
  r8ge_hilbert returns the Hilbert matrix.

  Hilbert matrix:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
         0.5  
    0.333333  
        0.25  

      1 :
         0.5  
    0.333333  
        0.25  
         0.2  

      2 :
    0.333333  
        0.25  
         0.2  
    0.166667  

      3 :
        0.25  
         0.2  
    0.166667  
    0.142857  

      4 :
         0.2  
    0.166667  
    0.142857  
       0.125  


r8ge_hilbert_inverse_test
  Python version: 3.6.9
  r8ge_hilbert_inverse computes the inverse of the
  Hilbert matrix, stored as an R8GE matrix.

  Matrix order N = 4

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
         0.5  
    0.333333  
        0.25  

      1 :
         0.5  
    0.333333  
        0.25  
         0.2  

      2 :
    0.333333  
        0.25  
         0.2  
    0.166667  

      3 :
        0.25  
         0.2  
    0.166667  
    0.142857  


  Inverse matrix B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
          16  
        -120  
         240  
        -140  

      1 :
        -120  
        1200  
       -2700  
        1680  

      2 :
         240  
       -2700  
        6480  
       -4200  

      3 :
        -140  
        1680  
       -4200  
        2800  


  Product A * B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           0  
           0  
           0  

      1 :
           0  
           1  
           0  
           0  

      2 :
           0  
           0  
           1  
-5.68434e-14  

      3 :
           0  
           0  
           0  
           1  


r8ge_house_axh_test
  Python version: 3.6.9
  r8ge_house_axh multiplies a matrix A times a
  compact Householder matrix.

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.343281  
     2.80878  
      3.5612  
     0.86138  
    -3.49801  

      1 :
    -3.39862  
     4.77576  
    -2.96749  
   -0.802756  
     1.85862  

      2 :
     3.01257  
    0.368083  
     2.81184  
    -3.96793  
     2.95409  

      3 :
     2.83373  
    -1.28526  
  -0.0906683  
     1.02983  
    -4.81051  

      4 :
     4.66951  
     1.30894  
     2.78924  
     4.04447  
   -0.118057  


  Compact vector V so column 3 of H*A is packed:

     0:             0
     1:             0
     2:      0.924599
     3:    -0.0123765
     4:       0.38074

  Householder matrix H:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           1  
           0  
           0  
           0  
           0  

      1 :
           0  
           1  
           0  
           0  
           0  

      2 :
           0  
           0  
   -0.709768  
   0.0228866  
   -0.704064  

      3 :
           0  
           0  
   0.0228866  
    0.999694  
  0.00942444  

      4 :
           0  
           0  
   -0.704064  
  0.00942444  
    0.710074  


  Indirect product A*H:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.343281  
     2.80878  
  -0.0450846  
    0.909653  
    -4.98304  

      1 :
    -3.39862  
     4.77576  
    0.779274  
   -0.852909  
      3.4015  

      2 :
     3.01257  
    0.368083  
    -4.16643  
    -3.87452  
   0.0805104  

      3 :
     2.83373  
    -1.28526  
     3.47483  
    0.982102  
    -3.34228  

      4 :
     4.66951  
     1.30894  
    -1.80403  
     4.10596  
    -2.00952  


  Direct product A*H:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.343281  
     2.80878  
  -0.0450846  
    0.909653  
    -4.98304  

      1 :
    -3.39862  
     4.77576  
    0.779274  
   -0.852909  
      3.4015  

      2 :
     3.01257  
    0.368083  
    -4.16643  
    -3.87452  
   0.0805104  

      3 :
     2.83373  
    -1.28526  
     3.47483  
    0.982102  
    -3.34228  

      4 :
     4.66951  
     1.30894  
    -1.80403  
     4.10596  
    -2.00952  


  H*A should pack column 3:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.343281  
     2.80878  
      3.5612  
     0.86138  
    -3.49801  

      1 :
    -3.39862  
     4.77576  
    -2.96749  
   -0.802756  
     1.85862  

      2 :
      -5.361  
    -1.21225  
    -3.96164  
 -0.00768837  
    -2.12369  

      3 :
     2.94581  
    -1.26411  
-3.46945e-18  
    0.976818  
    -4.74254  

      4 :
     1.22137  
     0.65818  
           0  
     5.67526  
    -2.20903  


r8ge_house_form_test
  Python version: 3.6.9
  r8ge_house_form forms a Householder
  matrix from its compact form.

  Compact vector form V:

     0:             0
     1:             0
     2:             1
     3:             2
     4:             3

  Householder matrix H:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           1  
           0  
           0  
           0  
           0  

      1 :
           0  
           1  
           0  
           0  
           0  

      2 :
           0  
           0  
    0.857143  
   -0.285714  
   -0.428571  

      3 :
           0  
           0  
   -0.285714  
    0.428571  
   -0.857143  

      4 :
           0  
           0  
   -0.428571  
   -0.857143  
   -0.285714  


r8ge_identity_test
  Python version: 3.6.9
  r8ge_identity returns the identity matrix.

  Identity matrix:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           0  
           0  
           0  

      1 :
           0  
           1  
           0  
           0  

      2 :
           0  
           0  
           1  
           0  

      3 :
           0  
           0  
           0  
           1  

      4 :
           0  
           0  
           0  
           0  


r8ge_ilu_test
  Python version: 3.6.9
  r8ge_ilu returns the ILU factors of an R8GE matrix.

  Matrix rows M =    9
  Matrix columns N = 9

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           4  
          -1  
           0  
          -1  
           0  

      1 :
          -1  
           4  
          -1  
           0  
          -1  

      2 :
           0  
          -1  
           4  
          -1  
           0  

      3 :
          -1  
           0  
          -1  
           4  
          -1  

      4 :
           0  
          -1  
           0  
          -1  
           4  

      5 :
           0  
           0  
          -1  
           0  
          -1  

      6 :
           0  
           0  
           0  
          -1  
           0  

      7 :
           0  
           0  
           0  
           0  
          -1  

      8 :
           0  
           0  
           0  
           0  
           0  


  Col: 
      5       
      6       
      7       
      8       

  Row
      0 :
           0  
           0  
           0  
           0  

      1 :
           0  
           0  
           0  
           0  

      2 :
          -1  
           0  
           0  
           0  

      3 :
           0  
          -1  
           0  
           0  

      4 :
          -1  
           0  
          -1  
           0  

      5 :
           4  
          -1  
           0  
          -1  

      6 :
          -1  
           4  
          -1  
           0  

      7 :
           0  
          -1  
           4  
          -1  

      8 :
          -1  
           0  
          -1  
           4  


  Factor L:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           1  
           0  
           0  
           0  
           0  

      1 :
       -0.25  
           1  
           0  
           0  
           0  

      2 :
           0  
   -0.266667  
           1  
           0  
           0  

      3 :
       -0.25  
           0  
   -0.267857  
           1  
           0  

      4 :
           0  
   -0.266667  
           0  
   -0.287179  
           1  

      5 :
           0  
           0  
   -0.267857  
           0  
   -0.290179  

      6 :
           0  
           0  
           0  
   -0.287179  
           0  

      7 :
           0  
           0  
           0  
           0  
   -0.290179  

      8 :
           0  
           0  
           0  
           0  
           0  


  Col: 
      5       
      6       
      7       
      8       

  Row
      0 :
           0  
           0  
           0  
           0  

      1 :
           0  
           0  
           0  
           0  

      2 :
           0  
           0  
           0  
           0  

      3 :
           0  
           0  
           0  
           0  

      4 :
           0  
           0  
           0  
           0  

      5 :
           1  
           0  
           0  
           0  

      6 :
   -0.290532  
           1  
           0  
           0  

      7 :
           0  
   -0.292202  
           1  
           0  

      8 :
   -0.290532  
           0  
   -0.292601  
           1  


  Factor U:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           4  
          -1  
           0  
          -1  
           0  

      1 :
           0  
        3.75  
          -1  
           0  
          -1  

      2 :
           0  
           0  
     3.73333  
          -1  
           0  

      3 :
           0  
           0  
           0  
     3.48214  
          -1  

      4 :
           0  
           0  
           0  
           0  
     3.44615  

      5 :
           0  
           0  
           0  
           0  
           0  

      6 :
           0  
           0  
           0  
           0  
           0  

      7 :
           0  
           0  
           0  
           0  
           0  

      8 :
           0  
           0  
           0  
           0  
           0  


  Col: 
      5       
      6       
      7       
      8       

  Row
      0 :
           0  
           0  
           0  
           0  

      1 :
           0  
           0  
           0  
           0  

      2 :
          -1  
           0  
           0  
           0  

      3 :
           0  
          -1  
           0  
           0  

      4 :
          -1  
           0  
          -1  
           0  

      5 :
     3.44196  
          -1  
           0  
          -1  

      6 :
           0  
     3.42229  
          -1  
           0  

      7 :
           0  
           0  
     3.41762  
          -1  

      8 :
           0  
           0  
           0  
     3.41687  


  Product L*U:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           4  
          -1  
           0  
          -1  
           0  

      1 :
          -1  
           4  
          -1  
        0.25  
          -1  

      2 :
           0  
          -1  
           4  
          -1  
    0.266667  

      3 :
          -1  
        0.25  
          -1  
           4  
          -1  

      4 :
           0  
          -1  
    0.266667  
          -1  
           4  

      5 :
           0  
           0  
          -1  
    0.267857  
          -1  

      6 :
           0  
           0  
           0  
          -1  
    0.287179  

      7 :
           0  
           0  
           0  
           0  
          -1  

      8 :
           0  
           0  
           0  
           0  
           0  


  Col: 
      5       
      6       
      7       
      8       

  Row
      0 :
           0  
           0  
           0  
           0  

      1 :
           0  
           0  
           0  
           0  

      2 :
          -1  
           0  
           0  
           0  

      3 :
    0.267857  
          -1  
           0  
           0  

      4 :
          -1  
    0.287179  
          -1  
           0  

      5 :
           4  
          -1  
    0.290179  
          -1  

      6 :
          -1  
           4  
          -1  
    0.290532  

      7 :
    0.290179  
          -1  
           4  
          -1  

      8 :
          -1  
    0.290532  
          -1  
           4  


r8ge_indicator_test
  Python version: 3.6.9
  r8ge_indicator returns the indicator matrix.

  Indicator matrix:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
          11  
          12  
          13  
          14  

      1 :
          21  
          22  
          23  
          24  

      2 :
          31  
          32  
          33  
          34  

      3 :
          41  
          42  
          43  
          44  

      4 :
          51  
          52  
          53  
          54  


r8ge_inverse_test
  Python version: 3.6.9
  r8ge_inverse computes the inverse of an R8GE matrix.

  Matrix order N = 4

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           5  
           3  
           3  
           3  

      1 :
           3  
           5  
           3  
           3  

      2 :
           3  
           3  
           5  
           3  

      3 :
           3  
           3  
           3  
           5  


  Inverse matrix B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    0.392857  
   -0.107143  
   -0.107143  
   -0.107143  

      1 :
   -0.107143  
    0.392857  
   -0.107143  
   -0.107143  

      2 :
   -0.107143  
   -0.107143  
    0.392857  
   -0.107143  

      3 :
   -0.107143  
   -0.107143  
   -0.107143  
    0.392857  


  Product matrix:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
-1.11022e-16  
           0  
           0  

      1 :
 3.33067e-16  
           1  
           0  
           0  

      2 :
 4.44089e-16  
-1.11022e-16  
           1  
 2.22045e-16  

      3 :
 4.44089e-16  
-1.11022e-16  
           0  
           1  


r8ge_ml_test
  Python version: 3.6.9
  r8ge_ml computes A*x or A'*X
  where A has been factored by r8ge_fa.

  Matrix order N = 10

  A*x and PLU*x

     0:        25.6697         25.6697
     1:        20.0519         20.0519
     2:        31.7259         31.7259
     3:        25.8187         25.8187
     4:        25.0653         25.0653
     5:        27.9361         27.9361
     6:         10.109          10.109
     7:        27.5894         27.5894
     8:        18.5708         18.5708
     9:        34.4201         34.4201

  A'*x and (PLU)'*x

     0:         31.817          31.817
     1:        28.2626         28.2626
     2:        24.7737         24.7737
     3:        32.7707         32.7707
     4:         25.305          25.305
     5:         27.833          27.833
     6:        19.2309         19.2309
     7:        24.3941         24.3941
     8:        20.1988         20.1988
     9:        32.3563         32.3563

r8ge_mm_test
  Python version: 3.6.9
  r8ge_mm computes a matrix-matrix product C = A * B;

  A:

  Col: 
      0       
      1       
      2       

  Row
      0 :
           1  
           0  
           0  

      1 :
           1  
           1  
           0  

      2 :
           1  
           2  
           1  

      3 :
           1  
           3  
           3  


  B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           1  
           1  
           1  

      1 :
           0  
           1  
           2  
           3  

      2 :
           0  
           0  
           1  
           3  


  C = A*B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           1  
           1  
           1  

      1 :
           1  
           2  
           3  
           4  

      2 :
           1  
           3  
           6  
          10  

      3 :
           1  
           4  
          10  
          19  


r8ge_mtm_test
  Python version: 3.6.9
  r8ge_mtm computes a matrix-matrix product C = A' * B;

  A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           0  
           0  
           0  

      1 :
           1  
           1  
           0  
           0  

      2 :
           1  
           2  
           1  
           0  


  B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           0  
           0  
           0  

      1 :
           1  
           1  
           0  
           0  

      2 :
           1  
           2  
           1  
           0  


  C = A'*B:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           3  
           3  
           1  
           0  

      1 :
           3  
           5  
           2  
           0  

      2 :
           1  
           2  
           1  
           0  

      3 :
           0  
           0  
           0  
           0  


r8ge_mtv_test
  Python version: 3.6.9
  r8ge_mtv computes a matrix product b=A'*x for an R8GE matrix.

  The matrix A:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
          11  
          12  
          13  
          14  
          15  

      1 :
          21  
          22  
          23  
          24  
          25  

      2 :
          31  
          32  
          33  
          34  
          35  


  The vector x:

     0:             1
     1:             2
     2:             3

  The vector b=A'*x:

     0:           146
     1:           152
     2:           158
     3:           164
     4:           170

  The matrix A:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
          11  
          12  
          13  
          14  
          15  

      1 :
          21  
          22  
          23  
          24  
          25  

      2 :
          31  
          32  
          33  
          34  
          35  

      3 :
          41  
          42  
          43  
          44  
          45  

      4 :
          51  
          52  
          53  
          54  
          55  


  The vector x:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5

  The vector b=A'*x:

     0:           565
     1:           580
     2:           595
     3:           610
     4:           625

  The matrix A:

  Col: 
      0       
      1       
      2       

  Row
      0 :
          11  
          12  
          13  

      1 :
          21  
          22  
          23  

      2 :
          31  
          32  
          33  

      3 :
          41  
          42  
          43  

      4 :
          51  
          52  
          53  


  The vector x:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5

  The vector b=A'*x:

     0:           565
     1:           580
     2:           595

r8ge_mu_test
  Python version: 3.6.9
  r8ge_mu computes A*x or A'*X
  where A has been factored by r8ge_trf.

  Matrix rows M =    5
  Matrix columns N = 3

  A*x and PLU*x

     0:        3.09417         3.09417
     1:        3.82291         3.82291
     2:        4.40491         4.40491
     3:        4.38181         4.38181
     4:        3.97778         3.97778

  A'*x and (PLU)'*x

     0:         3.4187          3.4187
     1:        4.98489         4.98489
     2:        10.7645         10.7645

  Matrix is 3 by 5

  A*x and PLU*x

     0:        8.18563         8.18563
     1:        5.16106         5.16106
     2:        8.82864         8.82864

  A'*x and (PLU)'*x

     0:        5.23203         5.23203
     1:        4.44139         4.44139
     2:        2.51711         2.51711
     3:        2.86509         2.86509
     4:        1.66186         1.66186

r8ge_mv_test
  Python version: 3.6.9
  r8ge_mv computes a matrix product b=A*x for an R8GE matrix.

  The matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
          11  
          12  
          13  
          14  

      1 :
          21  
          22  
          23  
          24  

      2 :
          31  
          32  
          33  
          34  

      3 :
          41  
          42  
          43  
          44  

      4 :
          51  
          52  
          53  
          54  


  The vector X:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5

  The vector b=A*x:

     0:           130
     1:           230
     2:           330
     3:           430

r8ge_orth_random_test
  Python version: 3.6.9
  r8ge_orth_random computes a random orthogonal matrix.

  orth_random matrix:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
   -0.127775  
   -0.214159  
   -0.807809  
  -0.0865765  
   -0.527029  

      1 :
    0.295598  
   -0.484327  
    0.233789  
   -0.782587  
   -0.104643  

      2 :
   0.0542725  
   -0.813526  
  -0.0697447  
    0.456426  
    0.349344  

      3 :
    0.906513  
    0.114022  
  -0.0277633  
     0.30003  
   -0.272844  

      4 :
    0.267552  
    0.211514  
   -0.535866  
   -0.285867  
      0.7175  


r8ge_spd_random_test
  Python version: 3.6.9
  r8ge_spd_random computes the spd_random matrix.

  spd_random matrix:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
    0.841507  
   0.0124888  
   0.0371599  
   0.0918867  
   0.0559793  

      1 :
   0.0124888  
    0.654655  
   0.0912092  
   -0.172516  
   -0.120682  

      2 :
   0.0371599  
   0.0912092  
    0.831126  
  -0.0708292  
 -0.00601272  

      3 :
   0.0918867  
   -0.172516  
  -0.0708292  
    0.150357  
    -0.16669  

      4 :
   0.0559793  
   -0.120682  
 -0.00601272  
    -0.16669  
    0.753773  


r8ge_plu_test
  Python version: 3.6.9
  r8ge_plu returns the PLU factors of an R8GE matrix.

  Matrix rows M =    5
  Matrix columns N = 4

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    0.511546  
    0.597281  
    0.739694  
   0.0947821  

      1 :
     0.21844  
   0.0605904  
     0.74953  
    0.760736  

      2 :
     0.15801  
    0.207352  
   0.0432688  
    0.512537  

      3 :
    0.870322  
    0.545064  
   0.0689965  
    0.264023  

      4 :
    0.986369  
    0.861822  
    0.850338  
    0.766743  


  Factor P:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           0  
           0  
           0  
           0  
           1  

      1 :
           0  
           0  
           1  
           0  
           0  

      2 :
           0  
           0  
           0  
           1  
           0  

      3 :
           0  
           1  
           0  
           0  
           0  

      4 :
           1  
           0  
           0  
           0  
           0  


  Factor L:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
           1  
           0  
           0  
           0  
           0  

      1 :
    0.882349  
           1  
           0  
           0  
           0  

      2 :
    0.221458  
    0.604872  
           1  
           0  
           0  

      3 :
    0.160193  
   -0.321754  
   -0.320719  
           1  
           0  

      4 :
    0.518615  
   -0.698018  
   -0.181711  
    -0.83202  
           1  


  Factor U:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    0.986369  
    0.861822  
    0.850338  
    0.766743  

      1 :
           0  
   -0.215363  
   -0.681298  
   -0.412512  

      2 :
           0  
           0  
    0.973314  
    0.840451  

      3 :
           0  
           0  
           0  
    0.526531  

      4 :
           0  
           0  
           0  
           0  


  Product P*L*U:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    0.511546  
    0.597281  
    0.739694  
   0.0947821  

      1 :
     0.21844  
   0.0605904  
     0.74953  
    0.760736  

      2 :
     0.15801  
    0.207352  
   0.0432688  
    0.512537  

      3 :
    0.870322  
    0.545064  
   0.0689965  
    0.264023  

      4 :
    0.986369  
    0.861822  
    0.850338  
    0.766743  


r8ge_poly_test
  Python version: 3.6.9
  r8ge_poly computes the characteristic polynomial of an R8GE matrix.

  Matrix order N = 12

I, P(I), True P(I)

     0:              1               1
     1:            -23             -23
     2:            231             231
     3:          -1330           -1330
     4:           4845            4845
     5:         -11628          -11628
     6:          18564           18564
     7:         -19448          -19448
......  ..............  ..............
    12:              1               1

r8ge_print_test
  Python version: 3.6.9
  r8ge_print prints an R8GE matrix.

  Here is an R8GE:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
          11  
          12  
          13  
          14  
          15  

      1 :
          21  
          22  
          23  
          24  
          25  

      2 :
          31  
          32  
          33  
          34  
          35  

      3 :
          41  
          42  
          43  
          44  
          45  


  Col: 
      5       

  Row
      0 :
          16  

      1 :
          26  

      2 :
          36  

      3 :
          46  


r8ge_print_some_test
  Python version: 3.6.9
  r8ge_print_some prints some of an R8GE matrix.

  Rows 0:2, Cols 3:5:

  Col: 
      3       
      4       
      5       

  Row
      0 :
          14  
          15  
          16  

      1 :
          24  
          25  
          26  

      2 :
          34  
          35  
          36  


r8ge_random_test
  Python version: 3.6.9
  r8ge_random computes a random R8GE.

  0 <= X <= 1

  Random R8GE:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    0.649973  
    0.946487  
    0.173419  
    0.177892  

      1 :
    0.518456  
    0.769474  
    0.525587  
    0.649684  

      2 :
    0.592511  
    0.544677  
    0.973882  
    0.666595  

      3 :
   0.0320278  
     0.83084  
    0.169389  
    0.603694  

      4 :
    0.395468  
    0.339122  
    0.586397  
    0.424103  


r8ge_random_ab_test
  Python version: 3.6.9
  r8ge_random_ab computes a random R8GE.

  -1 <= X <= 5

  Random R8GE:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
   -0.372512  
     3.27986  
   -0.662025  
     4.88285  

      1 :
     2.54262  
   -0.784434  
     1.84283  
     4.64843  

      2 :
    0.355369  
     4.65893  
   -0.935691  
     1.75525  

      3 :
     2.98491  
   -0.738417  
      1.8244  
     2.21765  

      4 :
   -0.280533  
     2.33962  
    -0.75413  
     1.69599  


r8ge_res_test
  Python version: 3.6.9
  r8ge_res computes b-A*x, where A is an R8GE matrix.
  We check three cases, M<N, M=N, M>N.

  Residual A*x-b:

     0:   7.77156e-16
     1:  -8.88178e-16
     2:  -1.77636e-15

  Residual A*x-b:

     0:             0
     1:   2.22045e-16
     2:             0
     3:   4.44089e-16
     4:  -7.77156e-16

  Residual A*x-b:

     0:   2.22045e-16
     1:  -2.22045e-16
     2:   2.22045e-16
     3:             0
     4:             0

r8ge_sl_test
  Python version: 3.6.9
  r8ge_sl solves a linear system A*x=b that was factored
  by r8ge_fa.

  Matrix order N = 10

  Solution:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10

  Solution:

     0:             1
     1:             1
     2:             1
     3:             1
     4:             1
     5:             1
     6:             1
     7:             1
     8:             1
     9:             1

  Solution of transposed system:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10

r8ge_sl_it_test
  Python version: 3.6.9
  r8ge_sl_it applies one step of iterative
  refinement to a r8ge_sl solution.

  Matrix order N = 6

  i, x, b-A*x

     0:       0.166667     1.13687e-13
     1:       0.142857    -9.09495e-13
     2:          0.125     1.45519e-11
     3:       0.111111    -5.82077e-11
     4:            0.1               0
     5:      0.0909091    -1.45519e-11

Iterative refinement step 1

  I, DX:

       0    -1.24677e-11
       1    -1.03287e-11
       2    -8.79936e-12
       3    -7.66042e-12
       4    -6.78115e-12
       5    -6.08241e-12

  i, x, b-A*x

     0:       0.166667    -5.68434e-14
     1:       0.142857     1.81899e-12
     2:          0.125    -2.91038e-11
     3:       0.111111     2.91038e-11
     4:            0.1               0
     5:      0.0909091     7.27596e-12

Iterative refinement step 2

  I, DX:

       0    -3.60008e-13
       1     1.62139e-13
       2     3.75167e-13
       3     4.65078e-13
       4     4.99681e-13
       5     5.07613e-13

  i, x, b-A*x

     0:       0.166667     -1.7053e-13
     1:       0.142857     9.09495e-13
     2:          0.125    -1.45519e-11
     3:       0.111111     8.73115e-11
     4:            0.1    -2.91038e-11
     5:      0.0909091     3.63798e-11

Iterative refinement step 3

  I, DX:

       0      1.7504e-11
       1     1.43887e-11
       2     1.22018e-11
       3     1.05912e-11
       4     9.35679e-12
       5     8.38066e-12

  i, x, b-A*x

     0:       0.166667               0
     1:       0.142857               0
     2:          0.125    -2.18279e-11
     3:       0.111111               0
     4:            0.1               0
     5:      0.0909091    -1.45519e-11

Iterative refinement step 4

  I, DX:

       0    -9.70128e-12
       1    -7.53581e-12
       2    -6.18456e-12
       3    -5.25486e-12
       4    -4.57346e-12
       5    -4.05139e-12

  i, x, b-A*x

     0:       0.166667               0
     1:       0.142857     1.81899e-12
     2:          0.125     2.91038e-11
     3:       0.111111               0
     4:            0.1    -8.73115e-11
     5:      0.0909091               0

Iterative refinement step 5

  I, DX:

       0    -6.85153e-12
       1    -6.66963e-12
       2    -6.19756e-12
       3     -5.6995e-12
       4    -5.24042e-12
       5    -4.83331e-12

  i, x, b-A*x

     0:       0.166667               0
     1:       0.142857               0
     2:          0.125               0
     3:       0.111111               0
     4:            0.1     5.82077e-11
     5:      0.0909091     7.27596e-12

r8ge_to_r8po_test():
  r8ge_to_r8po() converts an R8GE matrix to R8PO format.

  Matrix order N = 5

  The random R8GE matrix:
[[0.75280664 0.84117284 0.85783235 0.5017785  0.38216845]
 [0.86429363 0.67194208 0.20395784 0.29767483 0.99533163]
 [0.14458216 0.50512679 0.98962745 0.41581275 0.27377342]
 [0.0364585  0.07301604 0.39129413 0.11813922 0.719169  ]
 [0.55529257 0.14423404 0.78626443 0.44092885 0.34258329]]

  The R8PO matrix:
[[0.75280664 0.84117284 0.85783235 0.5017785  0.38216845]
 [0.         0.67194208 0.20395784 0.29767483 0.99533163]
 [0.         0.         0.98962745 0.41581275 0.27377342]
 [0.         0.         0.         0.11813922 0.719169  ]
 [0.         0.         0.         0.         0.34258329]]

r8ge_to_r8pp_test():
  r8ge_to_r8pp() converts an R8GE matrix to R8PP format.

  Matrix order N =  5

  The positive definite symmetric R8GE matrix:
[[-1. -1. -1. -1. -1.]
 [-1.  1.  1.  1.  1.]
 [-1.  1.  3.  3.  3.]
 [-1.  1.  3.  5.  5.]
 [-1.  1.  3.  5.  7.]]

  The RPP matrix:
[-1. -1.  1. -1.  1.  3. -1.  1.  3.  5. -1.  1.  3.  5.  7.]

r8ge_to_r8vec_test
  Python version: 3.6.9
  r8ge_to_r8vec converts an R8GE matrix to an R8VEC vector.

  R8GE matrix:

  Col: 
      0       
      1       
      2       

  Row
      0 :
          11  
          12  
          13  

      1 :
          21  
          22  
          23  

      2 :
          31  
          32  
          33  

      3 :
          41  
          42  
          43  


  Corresponding R8VEC vector:

     0:            11
     1:            21
     2:            31
     3:            41
     4:            12
     5:            22
     6:            32
     7:            42
     8:            13
     9:            23
    10:            33
    11:            43

r8ge_transpose_test
  Python version: 3.6.9
  r8ge_transpose makes a transposed copy of an R8GE matrix.

  Indicator matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
          11  
          12  
          13  
          14  

      1 :
          21  
          22  
          23  
          24  

      2 :
          31  
          32  
          33  
          34  

      3 :
          41  
          42  
          43  
          44  

      4 :
          51  
          52  
          53  
          54  


  B = A':

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
          11  
          21  
          31  
          41  
          51  

      1 :
          12  
          22  
          32  
          42  
          52  

      2 :
          13  
          23  
          33  
          43  
          53  

      3 :
          14  
          24  
          34  
          44  
          54  


r8ge_transpose_print_test
  Python version: 3.6.9
  r8ge_transpose_print prints the transpose of an R8GE matrix.

  Here is an R8GE matrix, transposed:

  Row: 
      0       
      1       
      2       
      3       

  Col
      0 :
          11  
          21  
          31  
          41  

      1 :
          12  
          22  
          32  
          42  

      2 :
          13  
          23  
          33  
          43  


r8ge_transpose_print_some_test
  Python version: 3.6.9
  r8ge_transpose_print_some prints some of an R8GE matrix, transposed.

  R8GE matrix, rows 0:2, cols 3:5:

  Row: 
      0       
      1       
      2       

  Col
      3 :
          14  
          24  
          34  

      4 :
          15  
          25  
          35  

      5 :
          16  
          26  
          36  


r8ge_trf_test
  Python version: 3.6.9
  r8ge_trf computes the LU factors of an R8GE matrix,
  so that r8ge_trs can solve the factored system.

  Number of matrix rows M = 5
  Number of matrix columns N = 5

  Solution:

     0:             0
     1:             0
     2:             0
     3:             0
     4:             5

  Solution to transposed system:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5

r8ge_trs_test
  Python version: 3.6.9
  r8ge_trs solves a linear system
  that has been factored by r8ge_trf.

  Number of matrix rows M = 5
  Number of matrix columns N = 5

  Solution:

     0:             0
     1:             0
     2:             0
     3:             0
     4:             5

  Solution to transposed system:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5

r8ge_zeros_test
  Python version: 3.6.9
  r8ge_zeros zeros out space for a general matrix.

  Matrix order M, N = 5, 4

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           0  
           0  
           0  
           0  

      1 :
           0  
           0  
           0  
           0  

      2 :
           0  
           0  
           0  
           0  

      3 :
           0  
           0  
           0  
           0  

      4 :
           0  
           0  
           0  
           0  


r8vec_house_column_test
  Python version: 3.6.9
  r8vec_house_column returns the compact form of
  a Householder matrix that "packs" a column
  of a matrix.

  Matrix A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
     2.09836  
     1.63199  
    0.481879  
     1.55821  

      1 :
     3.93088  
    0.558191  
     1.88754  
    0.576407  

      2 :
    0.520219  
     1.99213  
      0.9968  
     2.88266  

      3 :
    0.785995  
     3.61776  
     3.93763  
     3.13554  


  Working on column K = 0

  Householder matrix H:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
   -0.460723  
   -0.863079  
   -0.114221  
   -0.172576  

      1 :
   -0.863079  
    0.490043  
  -0.0674884  
   -0.101968  

      2 :
   -0.114221  
  -0.0674884  
    0.991068  
  -0.0134946  

      3 :
   -0.172576  
   -0.101968  
  -0.0134946  
    0.979611  


  Product H*A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    -4.55449  
    -2.08554  
    -2.64451  
    -2.08577  

      1 :
 7.21645e-16  
    -1.63834  
   0.0402954  
    -1.57667  

      2 :
 1.56125e-16  
     1.70143  
    0.752333  
     2.59772  

      3 :
           0  
     3.17856  
     3.56826  
     2.70503  


  Working on column K = 1

  Householder matrix H:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           0  
           0  
           0  

      1 :
           0  
   -0.413713  
    0.429646  
    0.802649  

      2 :
           0  
    0.429646  
    0.869425  
   -0.243936  

      3 :
           0  
    0.802649  
   -0.243936  
    0.544288  


  Product H*A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    -4.55449  
    -2.08554  
    -2.64451  
    -2.08577  

      1 :
-2.31475e-16  
     3.96008  
     3.17063  
     3.93958  

      2 :
 4.45791e-16  
 1.11022e-16  
   -0.199017  
    0.921263  

      3 :
 5.41143e-16  
-2.22045e-16  
     1.79098  
   -0.426874  


  Working on column K = 2

  Householder matrix H:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
           1  
           0  
           0  
           0  

      1 :
           0  
           1  
           0  
           0  

      2 :
           0  
           0  
   -0.110442  
    0.993883  

      3 :
           0  
           0  
    0.993883  
    0.110442  


  Product H*A:

  Col: 
      0       
      1       
      2       
      3       

  Row
      0 :
    -4.55449  
    -2.08554  
    -2.64451  
    -2.08577  

      1 :
-2.31475e-16  
     3.96008  
     3.17063  
     3.93958  

      2 :
 4.88599e-16  
-2.32948e-16  
     1.80201  
   -0.526008  

      3 :
 5.02829e-16  
 8.58201e-17  
 1.11022e-16  
    0.868482  


r8vec_indicator1_test
  Python version: 3.6.9
  r8vec_indicator1 returns the 1-based indicator matrix.

  The 1-based indicator vector:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10

r8vec_to_r8ge_test
  Python version: 3.6.9
  r8vec_to_r8ge converts an R8VEC vector to an R8GE matrix.

  The R8VEC vector:

     0:             1
     1:             2
     2:             3
     3:             4
     4:             5
     5:             6
     6:             7
     7:             8
     8:             9
     9:            10
    10:            11
    11:            12

  Corresponding R8GE matrix:

  Col: 
      0       
      1       
      2       

  Row
      0 :
           1  
           5  
           9  

      1 :
           2  
           6  
          10  

      2 :
           3  
           7  
          11  

      3 :
           4  
           8  
          12  


r8vec2_print_some_test
  Python version: 3.6.9
  r8vec2_print_some prints some of a pair of R8VEC's.

  Square and square root:

     0:              1               1
     1:              4         1.41421
     2:              9         1.73205
     3:             16               2
     4:             25         2.23607
     5:             36         2.44949
     6:             49         2.64575
     7:             64         2.82843
......  ..............  ..............
    99:          10000              10

r8ge_test():
  Normal end of execution.
Fri Aug 12 23:59:25 2022