Sun Sep 14 16:51:47 2025

lapack_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test lapack().

dgbtrf_test():
  dgbtrf() factors a general band matrix.
  dgbtrs() solves a factored system.
  For a double precision real matrix (D)
  in general band storage mode (GB):

  Band matrix has kl =  1  ku =  1

  Solution x (all should be 1)
[1. 1. 1. 1. 1.]

dgecon_test():
  dgecon() computes the condition of a matrix that has been
  factored by dgetrf.

  The matrix A:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 0.]]

  Matrix 1-norm is  15.0

  Reciprocal condition number for 1-norm is 0.019354838709677417

dgeev_test():
  dgeev() computes the eigenvalues and eigenvectors
  of a matrix.

  The matrix A:
[[0.         2.         0.         0.         0.        ]
 [2.         0.         2.44948974 0.         0.        ]
 [0.         2.44948974 0.         2.44948974 0.        ]
 [0.         0.         2.44948974 0.         2.        ]
 [0.         0.         0.         2.         0.        ]]

  Eigenvalues:
[[ 4.00000000e+00  0.00000000e+00]
 [-4.00000000e+00  0.00000000e+00]
 [-2.00000000e+00  0.00000000e+00]
 [-1.08455718e-16  0.00000000e+00]
 [ 2.00000000e+00  0.00000000e+00]]

  Eigenvectors (real parts):
[[ 2.50000000e-01 -2.50000000e-01 -5.00000000e-01  6.12372436e-01
  -5.00000000e-01]
 [ 5.00000000e-01  5.00000000e-01  5.00000000e-01 -7.39078793e-18
  -5.00000000e-01]
 [ 6.12372436e-01 -6.12372436e-01 -2.65970010e-16 -5.00000000e-01
   0.00000000e+00]
 [ 5.00000000e-01  5.00000000e-01 -5.00000000e-01  1.94637744e-16
   5.00000000e-01]
 [ 2.50000000e-01 -2.50000000e-01  5.00000000e-01  6.12372436e-01
   5.00000000e-01]]

  Eigenvectors (imaginary parts):
[[ 2.50000000e-01 -2.50000000e-01 -5.00000000e-01  6.12372436e-01
  -5.00000000e-01]
 [ 5.00000000e-01  5.00000000e-01  5.00000000e-01  1.16614303e-16
  -5.00000000e-01]
 [ 6.12372436e-01 -6.12372436e-01 -4.53779085e-16 -5.00000000e-01
   3.59413791e-17]
 [ 5.00000000e-01  5.00000000e-01 -5.00000000e-01  1.55267443e-17
   5.00000000e-01]
 [ 2.50000000e-01 -2.50000000e-01  5.00000000e-01  6.12372436e-01
   5.00000000e-01]]

dgeqrf_test()
  dgeqrf() computes the QR factorization:
    A = Q * R
  dorgqr() computes the explicit form of the Q factor.
  For a double precision real matrix (D)
  in general storage mode (GE):

  The matrix A:
[[ 1.  2.  3.]
 [ 4.  5.  6.]
 [ 7.  8.  0.]
 [ 5. 13.  3.]]

  Q:
[[-0.10482848  0.07018624  0.42750483]
 [-0.41931393 -0.21055872  0.78375885]
 [-0.73379939 -0.49130368 -0.4400785 ]
 [-0.52414242  0.84223489 -0.09639815]]

  R:
[[ -9.53939201 -14.99047317  -4.40279631]
 [  0.           6.10620294   1.47391105]
 [  0.           0.           5.69587314]]

  Q * R:
[[1.00000000e+00 2.00000000e+00 3.00000000e+00]
 [4.00000000e+00 5.00000000e+00 6.00000000e+00]
 [7.00000000e+00 8.00000000e+00 1.43137723e-16]
 [5.00000000e+00 1.30000000e+01 3.00000000e+00]]

dgesvd_test():
  dgesvd() computes the singular value decomposition
  of a matrix.

  The matrix A:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 0.]]

  U:
[[-0.23035703 -0.39607121 -0.88885501]
 [-0.60728383 -0.65520761  0.44934322]
 [-0.76035649  0.64329665 -0.08959596]]
  S:
[13.20145862  5.43875711  0.37604705]
  vt:
[[-0.60462923 -0.72567626 -0.32835569]
 [ 0.27325634  0.19824248 -0.94129214]
 [ 0.74816741 -0.65885802  0.07843244]]

  U*S*VT:
[[1.00000000e+00 2.00000000e+00 3.00000000e+00]
 [4.00000000e+00 5.00000000e+00 6.00000000e+00]
 [7.00000000e+00 8.00000000e+00 9.68934426e-16]]

dgetrf_test():
  DGETRF factors a general matrix;
  DGETRS solves a linear system;
  For a double precision real matrix (D)
  in general storage mode (GE):

  The matrix A:
[[ 5. -1. -1. -1. -1.]
 [-1.  5. -1. -1. -1.]
 [-1. -1.  5. -1. -1.]
 [-1. -1. -1.  5. -1.]
 [-1. -1. -1. -1.  5.]]

  The right hand side b:
[1. 1. 1. 1. 1.]

  The solution x (all entries should equal 1):
[1. 1. 1. 1. 1.]

dgetri_test():
  dgetri() computes the inverse of a matrix that has been
  factored by dgetrf.

  The matrix A:
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 0.]]

  Ainv:
[[-1.77777778  0.88888889 -0.11111111]
 [ 1.55555556 -0.77777778  0.22222222]
 [-0.11111111  0.22222222 -0.11111111]]

  A * Ainv:
[[ 1.00000000e+00  5.55111512e-17 -4.16333634e-17]
 [ 5.55111512e-17  1.00000000e+00 -8.32667268e-17]
 [ 1.77635684e-15 -8.88178420e-16  1.00000000e+00]]

dgtsv_test():
  dgtsv() factors and solves a linear system
  with a general tridiagonal matrix
  for a double precision real matrix (D)
  in general tridiagonal storage mode (GT).

  Solution x (should be 1, 2, 3, ... ):
[1. 2. 3. 4. 5.]

dpotrf_test():
  dpotrf() computes the Cholesky factorization R'*R
  for a double precision real matrix (D)
  in positive definite storage mode (PO).

  The matrix A:
[[ 2. -1.  0.  0.  0.]
 [-1.  2. -1.  0.  0.]
 [ 0. -1.  2. -1.  0.]
 [ 0.  0. -1.  2. -1.]
 [ 0.  0.  0. -1.  2.]]

  Cholesky factor R:

  R' * R:
[[ 2. -1.  0.  0.  0.]
 [-1.  2. -1.  0.  0.]
 [ 0. -1.  2. -1.  0.]
 [ 0.  0. -1.  2. -1.]
 [ 0.  0.  0. -1.  2.]]

dpotri_test():
  dpotri() computes the inverse
  for a double precision real matrix (D)
  in positive definite storage mode (PO).

  The matrix A:
[[ 2. -1.  0.  0.  0.]
 [-1.  2. -1.  0.  0.]
 [ 0. -1.  2. -1.  0.]
 [ 0.  0. -1.  2. -1.]
 [ 0.  0.  0. -1.  2.]]

  The Cholesky factor C:
[[ 1.41421356 -0.70710678  0.          0.          0.        ]
 [ 0.          1.22474487 -0.81649658  0.          0.        ]
 [ 0.          0.          1.15470054 -0.8660254   0.        ]
 [ 0.          0.          0.          1.11803399 -0.89442719]
 [ 0.          0.          0.          0.          1.09544512]]

  Inverse matrix Ainv:
[[0.83333333 0.66666667 0.5        0.33333333 0.16666667]
 [0.66666667 1.33333333 1.         0.66666667 0.33333333]
 [0.5        1.         1.5        1.         0.5       ]
 [0.33333333 0.66666667 1.         1.33333333 0.66666667]
 [0.16666667 0.33333333 0.5        0.66666667 0.83333333]]

  Product I = A * Ainv:
[[ 1.00000000e+00 -4.44089210e-16 -4.44089210e-16 -4.44089210e-16
  -1.66533454e-16]
 [ 3.33066907e-16  1.00000000e+00  4.44089210e-16  6.66133815e-16
   2.22044605e-16]
 [ 0.00000000e+00  0.00000000e+00  1.00000000e+00  0.00000000e+00
   0.00000000e+00]
 [-1.11022302e-16  5.55111512e-17 -4.44089210e-16  1.00000000e+00
  -2.22044605e-16]
 [ 0.00000000e+00 -1.11022302e-16  0.00000000e+00  0.00000000e+00
   1.00000000e+00]]

dsyev_test()
  dsyev() computes eigenvalues and eigenvectors
  For a double precision real matrix (D)
  in symmetric storage mode (SY).

  (symmetric half) of A:
[[0.         2.         0.         0.         0.        ]
 [0.         0.         2.44948974 0.         0.        ]
 [0.         0.         0.         2.44948974 0.        ]
 [0.         0.         0.         0.         2.        ]
 [0.         0.         0.         0.         0.        ]]

  Eigenvalues w:
[-4.00000000e+00 -2.00000000e+00  1.15640942e-16  2.00000000e+00
  4.00000000e+00]

  Eigenvector matrix V:
[[-2.50000000e-01  5.00000000e-01  6.12372436e-01 -5.00000000e-01
  -2.50000000e-01]
 [ 5.00000000e-01 -5.00000000e-01  3.04123327e-16 -5.00000000e-01
  -5.00000000e-01]
 [-6.12372436e-01 -2.89729077e-16 -5.00000000e-01 -2.10157702e-16
  -6.12372436e-01]
 [ 5.00000000e-01  5.00000000e-01 -3.60391453e-16  5.00000000e-01
  -5.00000000e-01]
 [-2.50000000e-01 -5.00000000e-01  6.12372436e-01  5.00000000e-01
  -2.50000000e-01]]

lapack_test():
  Normal end of execution.
Sun Sep 14 16:51:47 2025