
    sh                         S SK JrJrJrJr  S SKJrJr  S SKJ	r	  S SK
Jr  \	" S5      r\" S\\5      rS rS rS	 rS
 rg)    )luLofCholeskyqrsvd)Qask)Symbol)MatrixSymbolnXc                  &   [        [        5      u  pU R                  UR                  s=:X  a  [        R                  :X  d   e   e[        [        R
                  " U 5      5      (       d   e[        [        R                  " U5      5      (       d   eg N)r   r   shaper   r   lower_triangularupper_triangular)LUs     ڈ/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/sympy/matrices/expressions/tests/test_factorizations.pytest_LUr   	   sj    a5DA77agg((((((q!!!$%%%%q!!!$%%%%    c                  "    [        [        5        g r   )r   r    r   r   test_Choleskyr      s	    Nr   c                  &   [        [        5      u  pU R                  UR                  s=:X  a  [        R                  :X  d   e   e[        [        R
                  " U 5      5      (       d   e[        [        R                  " U5      5      (       d   eg r   )r   r   r   r   r   
orthogonalr   )Q_Rs     r   test_QRr      sh    qEEB88qww)!'')))))q||B    q!!!$%%%%r   c                     [        [        5      u  pnU R                  UR                  s=:X  a&  UR                  s=:X  a  [        R                  :X  d   e   e[        [        R
                  " U 5      5      (       d   e[        [        R
                  " U5      5      (       d   e[        [        R                  " U5      5      (       d   eg r   )r   r   r   r   r   r   diagonal)r   SVs      r   test_svdr#      s    !fGA!77agg33AGG33333q||Aq||Aqzz!}r   N))sympy.matrices.expressions.factorizationsr   r   r   r   sympy.assumptions.askr   r   sympy.core.symbolr	   "sympy.matrices.expressions.matexprr
   r   r   r   r   r   r#   r   r   r   <module>r(      s?    N N * $ ;
3Ka&&r   