Sun Aug  9 11:13:44 2026

einsum_test():
  numpy version:      1.26.4
  python version:     3.10.12
  einsum() carries out Einstein summation.

  matrix_column_sum_test():
  A:
array([[11, 12, 13],
       [21, 22, 23],
       [31, 32, 33]])
  np.einsum ( 'ij -> j', A ):
array([63, 66, 69])

  matrix_diagonal_test():
  A:
array([[11, 12, 13],
       [21, 22, 23],
       [31, 32, 33]])
  np.einsum ( 'ii -> i', A ):
array([11, 22, 33])

  matrix_matrix_multiplication_test():
  A:
array([[11, 12, 13],
       [21, 22, 23]])
  B:
array([[1, 2],
       [3, 4],
       [5, 6]])
  np.einsum ( 'ij -> jk', A, B ):
array([[112, 148],
       [202, 268]])

  matrix_matrix_multiplication_hadamard_test():
  A:
array([[11, 12, 13],
       [21, 22, 23]])
  B:
array([[1, 2, 3],
       [4, 5, 6]])
  np.einsum ( 'ij,ij -> ij', A, B ):
array([[ 11,  24,  39],
       [ 84, 110, 138]])

  matrix_row_sum_test():
  A:
array([[11, 12, 13],
       [21, 22, 23],
       [31, 32, 33]])
  np.einsum ( 'ij -> i', A ):
array([36, 66, 96])

  matrix_trace_test():
  A:
array([[11, 12, 13],
       [21, 22, 23],
       [31, 32, 33]])
  np.einsum ( 'ii ->', A ):
66

  matrix_transpose_test():
  A:
array([[11, 12, 13],
       [21, 22, 23]])
  np.einsum ( 'ij -> ji', A ):
array([[11, 21],
       [12, 22],
       [13, 23]])

  matrix_vector_multiplication_test():
  A:
array([[11, 12, 13],
       [21, 22, 23]])
  v:
array([1, 2])
  np.einsum ( 'ij -> j', A, v ):
array([53, 56, 59])

  vector_inner_product_test():
  u:
array([1, 2, 3])
  v:
array([4, 5, 6])
  w:
32

  vector_norm_test():
  u:
array([1, 2, 3])
  s:
3.7416573867739413

  vector_outer_product_test():
  u:
array([1, 2, 3])
  v:
array([4, 5, 6])
  w:
90

einsum_test():
  Normal end of execution.
Sun Aug  9 11:13:44 2026