Tue Aug 22 07:52:06 2023

gram_schmidt_test():
  Python version: 3.8.10
  Test gram_schmidt().

cgs1_test():
  Test cgs1().
  A1:
[[1. 2.]
 [4. 5.]
 [7. 8.]]
  U:
[[ 1.          0.81818182]
 [ 4.          0.27272727]
 [ 7.         -0.27272727]]
  U' * U:
[[ 6.60000000e+01 -5.55111512e-15]
 [-5.55111512e-15  8.18181818e-01]]
  A2:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 9.]]
  U:
[[ 1.00000000e+00  8.18181818e-01  2.22044605e-16]
 [ 4.00000000e+00  2.72727273e-01  8.88178420e-16]
 [ 7.00000000e+00 -2.72727273e-01  1.77635684e-15]]
  U' * U:
[[ 6.60000000e+01 -5.55111512e-15  1.62092562e-14]
 [-5.55111512e-15  8.18181818e-01 -6.05576195e-17]
 [ 1.62092562e-14 -6.05576195e-17  3.99360833e-30]]
  A3:
[[ 1.  2.  3.  4.]
 [ 4.  5.  6.  7.]
 [ 7.  8.  9. 10.]]
  U:
[[ 1.00000000e+00  8.18181818e-01  2.22044605e-16  2.19303314e-16]
 [ 4.00000000e+00  2.72727273e-01  8.88178420e-16 -1.09651657e-17]
 [ 7.00000000e+00 -2.72727273e-01  1.77635684e-15 -2.19303314e-17]]
  U' * U:
[[ 6.60000000e+01 -5.55111512e-15  1.62092562e-14  2.19303314e-17]
 [-5.55111512e-15  8.18181818e-01 -6.05576195e-17  1.82420484e-16]
 [ 1.62092562e-14 -6.05576195e-17  3.99360833e-30 -2.18952885e-46]
 [ 2.19303314e-17  1.82420484e-16 -2.18952885e-46  4.86951176e-32]]

gram_schmidt_naive_test():
  Test gram_schmidt_naive().
  A1:
[[1. 2.]
 [4. 5.]
 [7. 8.]]
  U:
[[ 0.12309149  0.90453403]
 [ 0.49236596  0.30151134]
 [ 0.86164044 -0.30151134]]
  U' * U:
[[1.00000000e+00 1.45860311e-15]
 [1.45860311e-15 1.00000000e+00]]
  A2:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 9.]]
  U:
[[ 0.12309149  0.90453403  0.        ]
 [ 0.49236596  0.30151134  0.        ]
 [ 0.86164044 -0.30151134  0.        ]]
  U' * U:
[[1.00000000e+00 1.45860311e-15 0.00000000e+00]
 [1.45860311e-15 1.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00]]
  A3:
[[ 1.  2.  3.  4.]
 [ 4.  5.  6.  7.]
 [ 7.  8.  9. 10.]]
  U:
[[ 0.12309149  0.90453403  0.          0.        ]
 [ 0.49236596  0.30151134  0.         -0.06237829]
 [ 0.86164044 -0.30151134  0.         -0.99805258]]
  U' * U:
[[ 1.00000000e+00  1.45860311e-15  0.00000000e+00 -8.90675405e-01]
 [ 1.45860311e-15  1.00000000e+00  0.00000000e+00  2.82116414e-01]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]
 [-8.90675405e-01  2.82116414e-01  0.00000000e+00  1.00000000e+00]]

gram_schmidt_tolerance_test():
  Test gram_schmidt_tolerance().
  A1:
[[1. 2.]
 [4. 5.]
 [7. 8.]]
  U:
[[ 0.12309149  0.90453403]
 [ 0.49236596  0.30151134]
 [ 0.86164044 -0.30151134]]
  U' * U:
[[1.00000000e+00 1.45860311e-15]
 [1.45860311e-15 1.00000000e+00]]
  A2:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 9.]]
  U:
[[ 0.12309149  0.90453403]
 [ 0.49236596  0.30151134]
 [ 0.86164044 -0.30151134]]
  U' * U:
[[1.00000000e+00 1.45860311e-15]
 [1.45860311e-15 1.00000000e+00]]
  A3:
[[ 1.  2.  3.  4.]
 [ 4.  5.  6.  7.]
 [ 7.  8.  9. 10.]]
  U:
[[ 0.12309149  0.90453403]
 [ 0.49236596  0.30151134]
 [ 0.86164044 -0.30151134]]
  U' * U:
[[1.00000000e+00 1.45860311e-15]
 [1.45860311e-15 1.00000000e+00]]

mgs1_test():
  Test mgs1().
  A1:
[[1. 2.]
 [4. 5.]
 [7. 8.]]
  U:
  U' * U:
[[ 6.60000000e+01 -5.55111512e-15]
 [-5.55111512e-15  8.18181818e-01]]
  A2:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 9.]]
  U:
  U' * U:
[[ 6.60000000e+01 -5.55111512e-15  1.62092562e-14]
 [-5.55111512e-15  8.18181818e-01 -6.05576195e-17]
 [ 1.62092562e-14 -6.05576195e-17  3.99360833e-30]]
  A3:
[[ 1.  2.  3.  4.]
 [ 4.  5.  6.  7.]
 [ 7.  8.  9. 10.]]
  U:
  U' * U:
[[ 6.60000000e+01 -5.55111512e-15  1.62092562e-14  2.19303314e-17]
 [-5.55111512e-15  8.18181818e-01 -6.05576195e-17  1.82420484e-16]
 [ 1.62092562e-14 -6.05576195e-17  3.99360833e-30 -2.18952885e-46]
 [ 2.19303314e-17  1.82420484e-16 -2.18952885e-46  4.86951176e-32]]

gram_schmidt_test():
  Normal end of execution.
Tue Aug 22 07:52:06 2023