17 August 2022 11:44:21 PM

R83V_TEST
  C++ version
  Test the R83V library.

R83_CG_TEST
  R83_CG applies CG to an R83 matrix.

  Number of variables N = 10
  Norm of residual ||Ax-b|| = 8.47455e-16
  Norm of error ||x1-x2|| = 4.1616e-16

R83V_COPY_TEST
  R83V_COPY copies an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  B = copy of A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  B = copy of A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  R83V matrix A:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

  B = copy of A:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

R83V_CR_FA_TEST:
  R83V_CR_FA factors an R83V matrix using cyclic reduction;

  Matrix order N = 10
  The matrix is NOT symmetric.

  The matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               4             2                                          
     2               1             8             3                            
     3                             2            12             4              
     4                                           3            16             5
     5                                                         4            20
     6                                                                       5

  Col:       6             7             8             9            10       
  Row
  ---
     5               6                                                        
     6              24             7                                          
     7               6            28             8                            
     8                             7            32             9              
     9                                           8            36            10
    10                                                         9            40

  Solution:

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

R83V_CR_SL_TEST:
  R83V_CR_SL solves a linear system factored by R83V_CR_FA.

  Matrix order N = 10
  The matrix is NOT symmetric.

  The matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               4             2                                          
     2               1             8             3                            
     3                             2            12             4              
     4                                           3            16             5
     5                                                         4            20
     6                                                                       5

  Col:       6             7             8             9            10       
  Row
  ---
     5               6                                                        
     6              24             7                                          
     7               6            28             8                            
     8                             7            32             9              
     9                                           8            36            10
    10                                                         9            40

  Solution:

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

R83V_CR_SLS_TEST
  R83V_CR_SLS solves multiple linear systems A*x=b1:bn with R83V matrix
  using cyclic reduction, after factorization by R83V_CR_FA.

  Matrix order N = 5
  Number of linear systems = 2
  Demonstrate multiple system solution method.

  System matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               2            -1                                          
     2              -1             2            -1                            
     3                            -1             2            -1              
     4                                          -1             2            -1
     5                                                        -1             2

  RHS:

  Col:          1             2       
  Row
  ---
    1             0             1  
    2             0             0  
    3             0             0  
    4             0             0  
    5             6             1  

  Solutions:

  Col:          1             2       
  Row
  ---
    1             1             1  
    2             2             1  
    3             3             1  
    4             4             1  
    5             5             1  

R83V_DIF2_TEST
  R83V_DIF2 sets up an R83V second difference matrix.
  We check three cases, M<N, M=N, M>N.

  The R83V DIF2 matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               2            -1                                          
     2              -1             2            -1                            
     3                            -1             2            -1              

  The R83V DIF2 matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               2            -1                                          
     2              -1             2            -1                            
     3                            -1             2            -1              
     4                                          -1             2            -1
     5                                                        -1             2

  The R83V DIF2 matrix:

  Col:       1             2             3       
  Row
  ---
     1               2            -1              
     2              -1             2            -1
     3                            -1             2
     4                                          -1

R83V_FS_TEST
  R83V_FS factors and solves a linear system
  for an R83V matrix.

  Matrix order N = 10

  The right hand side:

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

  Solution:

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

R83V_GS_SL_TEST
  R83V_GS_SL solves a linear system using Gauss-Seidel
  iteration for an R83V matrix.

  Matrix order N = 10
  Iterations per call = 25

  The right hand side:

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

  Current estimated solution:

     1        0.634606
     2          1.3265
     3         2.09566
     4         2.95451
     5         3.90741
     6         4.95088
     7         6.07442
     8          7.2619
     9          8.4933
    10         9.74665

  Current estimated solution:

     1        0.953567
     2          1.9145
     3         2.88533
     4         3.86757
     5         4.86173
     6         5.86733
     7         6.88302
     8         7.90675
     9         8.93599
    10           9.968

  Current estimated solution:

     1        0.994126
     2         1.98918
     3         2.98549
     4         3.98325
     5         4.98251
     6         5.98322
     7          6.9852
     8          7.9882
     9          8.9919
    10         9.99595

R83V_INDICATOR_TEST
  R83V_INDICATOR sets up an R83V indicator matrix.
  We check three cases, M<N, M=N, M>N.

  The R83V indicator matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  The R83V indicator matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  The R83V indicator matrix:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

R83V_JAC_SL_TEST
  R83V_JAC_SL solves a linear system using Jacobi iteration,
  for an R83V matrix.

  Matrix order N = 10
  Iterations per call = 25

  The right hand side:

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

  Current estimated solution:

     1        0.315171
     2        0.727797
     3         1.14042
     4         1.82758
     5         2.51474
     6         3.59047
     7          4.6662
     8          6.1282
     9          7.5902
    10          9.2951

  Current estimated solution:

     1        0.757545
     2         1.51509
     3         2.34936
     4         3.18363
     5         4.14729
     6         5.11094
     7         6.21581
     8         7.32068
     9         8.53366
    10         9.74665

  Current estimated solution:

     1        0.910021
     2         1.83432
     3         2.75863
     4         3.72124
     5         4.68386
     6         5.69666
     7         6.70946
     8         7.76839
     9         8.82731
    10         9.91366

R83V_MTV_TEST
  R83V_MTV computes b=A'*x, where A is an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  Product comparison:

     0:        1.26635         1.26635
     1:        4.05846         4.05846
     2:        1.76108         1.76108
     3:        0.32987         0.32987
     4:              0               0

  Product comparison:

     0:       0.852144        0.852144
     1:        3.63516         3.63516
     2:        4.21422         4.21422
     3:        4.59692         4.59692
     4:        1.82437         1.82437

  Product comparison:

     0:       0.998532        0.998532
     1:        3.95714         3.95714
     2:        3.73631         3.73631

R83V_MV_TEST
  R83V_MV computes b=A*x, where A is an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  Product comparison:

     0:       0.961747        0.961747
     1:        2.11454         2.11454
     2:        3.59838         3.59838

  Product comparison:

     0:        1.68324         1.68324
     1:       0.535837        0.535837
     2:        4.48352         4.48352
     3:        4.93489         4.93489
     4:        2.46593         2.46593

  Product comparison:

     0:        1.07685         1.07685
     1:         1.3789          1.3789
     2:        2.11099         2.11099
     3:        2.48853         2.48853
     4:              0               0

R83V_PRINT_TEST
  R83V_PRINT prints an R83V matrix.

  The R83V  matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

R83V_PRINT_SOME_TEST
  R83V_PRINT_SOME prints some of an R83V matrix.

  Rows 2-5, Cols 2-4:

  Col:       2             3             4       
  Row
  ---
     2              22            23              
     3              32            33            34
     4                            43            44
     5                                          54

R83V_RANDOM_TEST
  R83V_RANDOM sets up an R83V random matrix.
  We check three cases, M<N, M=N, M>N.

  The R83V random matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1        0.829509     0.0661187                                          
     2        0.218418      0.561695      0.257578                            
     3                      0.956318      0.415307      0.109957              

  The R83V random matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1        0.415307      0.633966                                          
     2        0.218418     0.0661187     0.0617272                            
     3                      0.956318      0.257578      0.449539              
     4                                    0.829509      0.109957      0.401306
     5                                                  0.561695      0.043829

  The R83V random matrix:

  Col:       1             2             3       
  Row
  ---
     1        0.561695      0.257578              
     2        0.218418      0.415307      0.109957
     3                      0.956318     0.0661187
     4                                    0.829509

R83V_RES_TEST
  R83V_RES computes b-A*x, where A is an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  Residual A*x-b:

     1               0
     2               0
     3               0

  Residual A*x-b:

     1               0
     2               0
     3               0
     4               0
     5               0

  Residual A*x-b:

     1               0
     2               0
     3               0
     4               0
     5               0

R83V_TO_R8GE_TEST
  R83V_TO_R8GE copies an R83V matrix to an R8GE matrix.
  We check three cases, M<N, M=N, M>N.

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  R8GE version of A:

  Col:          1             2             3             4             5       
  Row
  ---
    1            11            12             0             0             0  
    2            21            22            23             0             0  
    3             0            32            33            34             0  

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  R8GE version of A:

  Col:          1             2             3             4             5       
  Row
  ---
    1            11            12             0             0             0  
    2            21            22            23             0             0  
    3             0            32            33            34             0  
    4             0             0            43            44            45  
    5             0             0             0            54            55  

  R83V matrix A:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

  R8GE version of A:

  Col:          1             2             3       
  Row
  ---
    1            11            12             0  
    2            21            22            23  
    3             0            32            33  
    4             0             0            43  
    5             0             0             0  

R83V_TO_R8VEC_TEST
  R83V_TO_R8VEC copies an R83V matrix to an R8VEC.
  We check three cases, M<N, M=N, M>N.

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  Vector version of A:

     1              11
     2              21
     3              12
     4              22
     5              32
     6              23
     7              33
     8              34

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  Vector version of A:

     1              11
     2              21
     3              12
     4              22
     5              32
     6              23
     7              33
     8              43
     9              34
    10              44
    11              54
    12              45
    13              55

  R83V matrix A:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

  Vector version of A:

     1              11
     2              21
     3              12
     4              22
     5              32
     6              23
     7              33
     8              43

R83V_TRANSPOSE_TEST
  R83V_TRANSPOSE makes a transposed copy of an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  B = copy of A:

  Col:       1             2             3       
  Row
  ---
     1              11            21              
     2              12            22            32
     3                            23            33
     4                                          34

  R83V matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  B = copy of A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            21                                          
     2              12            22            32                            
     3                            23            33            43              
     4                                          34            44            54
     5                                                        45            55

  R83V matrix A:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

  B = copy of A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            21                                          
     2              12            22            32                            
     3                            23            33            43              

R83V_ZEROS_TEST
  R83V_ZEROS sets up an R83V zero matrix.
  We check three cases, M<N, M=N, M>N.

  The R83V zero matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               0             0                                          
     2               0             0             0                            
     3                             0             0             0              

  The R83V zero matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               0             0                                          
     2               0             0             0                            
     3                             0             0             0              
     4                                           0             0             0
     5                                                         0             0

  The R83V zero matrix:

  Col:       1             2             3       
  Row
  ---
     1               0             0              
     2               0             0             0
     3                             0             0
     4                                           0

R8GE_TO_R83V_TEST
  R8GE_TO_R83V copies an R8GE matrix to an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  R8GE matrix A:

  Col:          1             2             3             4             5       
  Row
  ---
    1            11            12            13            14            15  
    2            21            22            23            24            25  
    3            31            32            33            34            35  

  R83V copy of (some of ) matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              

  R8GE matrix A:

  Col:          1             2             3             4             5       
  Row
  ---
    1            11            12            13            14            15  
    2            21            22            23            24            25  
    3            31            32            33            34            35  
    4            41            42            43            44            45  
    5            51            52            53            54            55  

  R83V copy of (some of ) matrix A:

  Col:       1             2             3             4             5       
  Row
  ---
     1              11            12                                          
     2              21            22            23                            
     3                            32            33            34              
     4                                          43            44            45
     5                                                        54            55

  R8GE matrix A:

  Col:          1             2             3       
  Row
  ---
    1            11            12            13  
    2            21            22            23  
    3            31            32            33  
    4            41            42            43  
    5            51            52            53  

  R83V copy of (some of ) matrix A:

  Col:       1             2             3       
  Row
  ---
     1              11            12              
     2              21            22            23
     3                            32            33
     4                                          43

R8VEC_TO_R83V_TEST
  R8VEC_TO_R83V copies an R8VEC to an R83V matrix.
  We check three cases, M<N, M=N, M>N.

  R8VEC:

     1               1
     2               2
     3               3
     4               4
     5               5
     6               6
     7               7
     8               8

  R83V matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               1             3                                          
     2               2             4             6                            
     3                             5             7             8              

  R8VEC:

     1               1
     2               2
     3               3
     4               4
     5               5
     6               6
     7               7
     8               8
     9               9
    10              10
    11              11
    12              12
    13              13

  R83V matrix:

  Col:       1             2             3             4             5       
  Row
  ---
     1               1             3                                          
     2               2             4             6                            
     3                             5             7             9              
     4                                           8            10            12
     5                                                        11            13

  R8VEC:

     1               1
     2               2
     3               3
     4               4
     5               5
     6               6
     7               7
     8               8

  R83V matrix:

  Col:       1             2             3       
  Row
  ---
     1               1             3              
     2               2             4             6
     3                             5             7
     4                                           8

R83V_TEST
  Normal end of execution.

17 August 2022 11:44:21 PM